np.bincount(x, weights=w)
array([ 0.3, 0.7, 1.1])
blackman(M)
Return the Blackman window.
The Blackman window is a taper formed by using the first three
terms of a summation of cosines. It was designed to have close to the
minimal leakage possible. It is close to optimal, only slightly worse
than a Kaiser window.
Parameters
----------
M : int
Number of points in the output window. If zero or less, an empty
array is returned.
Returns
-------
out : ndarray
The window, with the maximum value normalized to one (the value one
appears only if the number of samples is odd).
See Also
--------
bartlett, hamming, hanning, kaiser
Notes
-----
The Blackman window is defined as
.. math:: w(n) = 0.42 - 0.5 \cos(2\pi n/M) + 0.08 \cos(4\pi n/M)
Most references to the Blackman window come from the signal processing
literature, where it is used as one of many windowing functions for
smoothing values. It is also known as an apodization (which means
"removing the foot", i.e. smoothing discontinuities at the beginning
and end of the sampled signal) or tapering function. It is known as a
"near optimal" tapering function, almost as good (by some measures)
as the kaiser window.
References
----------
Blackman, R.B. and Tukey, J.W., (1958) The measurement of power spectra,
Dover Publications, New York.
Oppenheim, A.V., and R.W. Schafer. Discrete-Time Signal Processing.
Upper Saddle River, NJ: Prentice-Hall, 1999, pp. 468-471.
Examples
--------
np.blackman(12)
array([ -1.38777878e-17, 3.26064346e-02, 1.59903635e-01,
4.14397981e-01, 7.36045180e-01, 9.67046769e-01,
9.67046769e-01, 7.36045180e-01, 4.14397981e-01,
1.59903635e-01, 3.26064346e-02, -1.38777878e-17])
Plot the window and the frequency response:
from numpy.fft import fft, fftshift
window = np.blackman(51)
plt.plot(window)
[]
plt.title("Blackman window")
plt.ylabel("Amplitude")
plt.xlabel("Sample")
plt.show()
plt.figure()
A = fft(window, 2048) / 25.5
mag = np.abs(fftshift(A))
freq = np.linspace(-0.5, 0.5, len(A))
response = 20 * np.log10(mag)
response = np.clip(response, -100, 100)
plt.plot(freq, response)
[]
plt.title("Frequency response of Blackman window")
plt.ylabel("Magnitude [dB]")
plt.xlabel("Normalized frequency [cycles per sample]")
plt.axis('tight')
(-0.5, 0.5, -100.0, ...)
plt.show()
bmat(obj, ldict=None, gdict=None)
Build a matrix object from a string, nested sequence, or array.
Parameters
----------
obj : str or array_like
Input data. Names of variables in the current scope may be
referenced, even if `obj` is a string.
ldict : dict, optional
A dictionary that replaces local operands in current frame.
Ignored if `obj` is not a string or `gdict` is `None`.
gdict : dict, optional
A dictionary that replaces global operands in current frame.
Ignored if `obj` is not a string.
Returns
-------
out : matrix
Returns a matrix object, which is a specialized 2-D array.
See Also
--------
matrix
Examples
--------
A = np.mat('1 1; 1 1')
B = np.mat('2 2; 2 2')
C = np.mat('3 4; 5 6')
D = np.mat('7 8; 9 0')
All the following expressions construct the same block matrix:
np.bmat([[A, B], [C, D]])
matrix([[1, 1, 2, 2],
[1, 1, 2, 2],
[3, 4, 7, 8],
[5, 6, 9, 0]])
np.bmat(np.r_[np.c_[A, B], np.c_[C, D]])
matrix([[1, 1, 2, 2],
[1, 1, 2, 2],
[3, 4, 7, 8],
[5, 6, 9, 0]])
np.bmat('A,B; C,D')
matrix([[1, 1, 2, 2],
[1, 1, 2, 2],
[3, 4, 7, 8],
[5, 6, 9, 0]])
broadcast_arrays(*args, **kwargs)
Broadcast any number of arrays against each other.
Parameters
----------
`*args` : array_likes
The arrays to broadcast.
subok : bool, optional
If True, then sub-classes will be passed-through, otherwise
the returned arrays will be forced to be a base-class array (default).
Returns
-------
broadcasted : list of arrays
These arrays are views on the original arrays. They are typically
not contiguous. Furthermore, more than one element of a
broadcasted array may refer to a single memory location. If you
need to write to the arrays, make copies first.
Examples
--------
x = np.array([[1,2,3]])
y = np.array([[1],[2],[3]])
np.broadcast_arrays(x, y)
[array([[1, 2, 3],
[1, 2, 3],
[1, 2, 3]]), array([[1, 1, 1],
[2, 2, 2],
[3, 3, 3]])]
Here is a useful idiom for getting contiguous copies instead of
non-contiguous views.
[np.array(a) for a in np.broadcast_arrays(x, y)]
[array([[1, 2, 3],
[1, 2, 3],
[1, 2, 3]]), array([[1, 1, 1],
[2, 2, 2],
[3, 3, 3]])]
broadcast_to(array, shape, subok=False)
Broadcast an array to a new shape.
Parameters
----------
array : array_like
The array to broadcast.
shape : tuple
The shape of the desired array.
subok : bool, optional
If True, then sub-classes will be passed-through, otherwise
the returned array will be forced to be a base-class array (default).
Returns
-------
broadcast : array
A readonly view on the original array with the given shape. It is
typically not contiguous. Furthermore, more than one element of a
broadcasted array may refer to a single memory location.
Raises
------
ValueError
If the array is not compatible with the new shape according to NumPy's
broadcasting rules.
Notes
-----
.. versionadded:: 1.10.0
Examples
--------
x = np.array([1, 2, 3])
np.broadcast_to(x, (3, 3))
array([[1, 2, 3],
[1, 2, 3],
[1, 2, 3]])
busday_count(...)
busday_count(begindates, enddates, weekmask='1111100', holidays=[], busdaycal=None, out=None)
Counts the number of valid days between `begindates` and
`enddates`, not including the day of `enddates`.
If ``enddates`` specifies a date value that is earlier than the
corresponding ``begindates`` date value, the count will be negative.
.. versionadded:: 1.7.0
Parameters
----------
begindates : array_like of datetime64[D]
The array of the first dates for counting.
enddates : array_like of datetime64[D]
The array of the end dates for counting, which are excluded
from the count themselves.
weekmask : str or array_like of bool, optional
A seven-element array indicating which of Monday through Sunday are
valid days. May be specified as a length-seven list or array, like
[1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string
like "Mon Tue Wed Thu Fri", made up of 3-character abbreviations for
weekdays, optionally separated by white space. Valid abbreviations
are: Mon Tue Wed Thu Fri Sat Sun
holidays : array_like of datetime64[D], optional
An array of dates to consider as invalid dates. They may be
specified in any order, and NaT (not-a-time) dates are ignored.
This list is saved in a normalized form that is suited for
fast calculations of valid days.
busdaycal : busdaycalendar, optional
A `busdaycalendar` object which specifies the valid days. If this
parameter is provided, neither weekmask nor holidays may be
provided.
out : array of int, optional
If provided, this array is filled with the result.
Returns
-------
out : array of int
An array with a shape from broadcasting ``begindates`` and ``enddates``
together, containing the number of valid days between
the begin and end dates.
See Also
--------
busdaycalendar: An object that specifies a custom set of valid days.
is_busday : Returns a boolean array indicating valid days.
busday_offset : Applies an offset counted in valid days.
Examples
--------
# Number of weekdays in January 2011
np.busday_count('2011-01', '2011-02')
21
# Number of weekdays in 2011
np.busday_count('2011', '2012')
260
# Number of Saturdays in 2011
np.busday_count('2011', '2012', weekmask='Sat')
53
busday_offset(...)
busday_offset(dates, offsets, roll='raise', weekmask='1111100', holidays=None, busdaycal=None, out=None)
First adjusts the date to fall on a valid day according to
the ``roll`` rule, then applies offsets to the given dates
counted in valid days.
.. versionadded:: 1.7.0
Parameters
----------
dates : array_like of datetime64[D]
The array of dates to process.
offsets : array_like of int
The array of offsets, which is broadcast with ``dates``.
roll : {'raise', 'nat', 'forward', 'following', 'backward', 'preceding', 'modifiedfollowing', 'modifiedpreceding'}, optional
How to treat dates that do not fall on a valid day. The default
is 'raise'.
* 'raise' means to raise an exception for an invalid day.
* 'nat' means to return a NaT (not-a-time) for an invalid day.
* 'forward' and 'following' mean to take the first valid day
later in time.
* 'backward' and 'preceding' mean to take the first valid day
earlier in time.
* 'modifiedfollowing' means to take the first valid day
later in time unless it is across a Month boundary, in which
case to take the first valid day earlier in time.
* 'modifiedpreceding' means to take the first valid day
earlier in time unless it is across a Month boundary, in which
case to take the first valid day later in time.
weekmask : str or array_like of bool, optional
A seven-element array indicating which of Monday through Sunday are
valid days. May be specified as a length-seven list or array, like
[1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string
like "Mon Tue Wed Thu Fri", made up of 3-character abbreviations for
weekdays, optionally separated by white space. Valid abbreviations
are: Mon Tue Wed Thu Fri Sat Sun
holidays : array_like of datetime64[D], optional
An array of dates to consider as invalid dates. They may be
specified in any order, and NaT (not-a-time) dates are ignored.
This list is saved in a normalized form that is suited for
fast calculations of valid days.
busdaycal : busdaycalendar, optional
A `busdaycalendar` object which specifies the valid days. If this
parameter is provided, neither weekmask nor holidays may be
provided.
out : array of datetime64[D], optional
If provided, this array is filled with the result.
Returns
-------
out : array of datetime64[D]
An array with a shape from broadcasting ``dates`` and ``offsets``
together, containing the dates with offsets applied.
See Also
--------
busdaycalendar: An object that specifies a custom set of valid days.
is_busday : Returns a boolean array indicating valid days.
busday_count : Counts how many valid days are in a half-open date range.
Examples
--------
# First business day in October 2011 (not accounting for holidays)
np.busday_offset('2011-10', 0, roll='forward')
numpy.datetime64('2011-10-03','D')
# Last business day in February 2012 (not accounting for holidays)
np.busday_offset('2012-03', -1, roll='forward')
numpy.datetime64('2012-02-29','D')
# Third Wednesday in January 2011
np.busday_offset('2011-01', 2, roll='forward', weekmask='Wed')
numpy.datetime64('2011-01-19','D')
# 2012 Mother's Day in Canada and the U.S.
np.busday_offset('2012-05', 1, roll='forward', weekmask='Sun')
numpy.datetime64('2012-05-13','D')
# First business day on or after a date
np.busday_offset('2011-03-20', 0, roll='forward')
numpy.datetime64('2011-03-21','D')
np.busday_offset('2011-03-22', 0, roll='forward')
numpy.datetime64('2011-03-22','D')
# First business day after a date
np.busday_offset('2011-03-20', 1, roll='backward')
numpy.datetime64('2011-03-21','D')
np.busday_offset('2011-03-22', 1, roll='backward')
numpy.datetime64('2011-03-23','D')
byte_bounds(a)
Returns pointers to the end-points of an array.
Parameters
----------
a : ndarray
Input array. It must conform to the Python-side of the array
interface.
Returns
-------
(low, high) : tuple of 2 integers
The first integer is the first byte of the array, the second
integer is just past the last byte of the array. If `a` is not
contiguous it will not use every byte between the (`low`, `high`)
values.
Examples
--------
I = np.eye(2, dtype='f'); I.dtype
dtype('float32')
low, high = np.byte_bounds(I)
high - low == I.size*I.itemsize
True
I = np.eye(2, dtype='G'); I.dtype
dtype('complex192')
low, high = np.byte_bounds(I)
high - low == I.size*I.itemsize
True
can_cast(...)
can_cast(from, totype, casting = 'safe')
Returns True if cast between data types can occur according to the
casting rule. If from is a scalar or array scalar, also returns
True if the scalar value can be cast without overflow or truncation
to an integer.
Parameters
----------
from : dtype, dtype specifier, scalar, or array
Data type, scalar, or array to cast from.
totype : dtype or dtype specifier
Data type to cast to.
casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
Controls what kind of data casting may occur.
* 'no' means the data types should not be cast at all.
* 'equiv' means only byte-order changes are allowed.
* 'safe' means only casts which can preserve values are allowed.
* 'same_kind' means only safe casts or casts within a kind,
like float64 to float32, are allowed.
* 'unsafe' means any data conversions may be done.
Returns
-------
out : bool
True if cast can occur according to the casting rule.
Notes
-----
Starting in NumPy 1.9, can_cast function now returns False in 'safe'
casting mode for integer/float dtype and string dtype if the string dtype
length is not long enough to store the max integer/float value converted
to a string. Previously can_cast in 'safe' mode returned True for
integer/float dtype and a string dtype of any length.
See also
--------
dtype, result_type
Examples
--------
Basic examples
np.can_cast(np.int32, np.int64)
True
np.can_cast(np.float64, np.complex)
True
np.can_cast(np.complex, np.float)
False
np.can_cast('i8', 'f8')
True
np.can_cast('i8', 'f4')
False
np.can_cast('i4', 'S4')
False
Casting scalars
np.can_cast(100, 'i1')
True
np.can_cast(150, 'i1')
False
np.can_cast(150, 'u1')
True
np.can_cast(3.5e100, np.float32)
False
np.can_cast(1000.0, np.float32)
True
Array scalar checks the value, array does not
np.can_cast(np.array(1000.0), np.float32)
True
np.can_cast(np.array([1000.0]), np.float32)
False
Using the casting rules
np.can_cast('i8', 'i8', 'no')
True
np.can_cast('i8', 'no')
False
np.can_cast('i8', 'equiv')
True
np.can_cast('i8', 'equiv')
False
np.can_cast('i8', 'safe')
True
np.can_cast('i4', 'safe')
False
np.can_cast('i4', 'same_kind')
True
np.can_cast('u4', 'same_kind')
False
np.can_cast('u4', 'unsafe')
True
choose(a, choices, out=None, mode='raise')
Construct an array from an index array and a set of arrays to choose from.
First of all, if confused or uncertain, definitely look at the Examples -
in its full generality, this function is less simple than it might
seem from the following code description (below ndi =
`numpy.lib.index_tricks`):
``np.choose(a,c) == np.array([c[a[I]][I] for I in ndi.ndindex(a.shape)])``.
But this omits some subtleties. Here is a fully general summary:
Given an "index" array (`a`) of integers and a sequence of `n` arrays
(`choices`), `a` and each choice array are first broadcast, as necessary,
to arrays of a common shape; calling these *Ba* and *Bchoices[i], i =
0,...,n-1* we have that, necessarily, ``Ba.shape == Bchoices[i].shape``
for each `i`. Then, a new array with shape ``Ba.shape`` is created as
follows:
* if ``mode=raise`` (the default), then, first of all, each element of
`a` (and thus `Ba`) must be in the range `[0, n-1]`; now, suppose that
`i` (in that range) is the value at the `(j0, j1, ..., jm)` position
in `Ba` - then the value at the same position in the new array is the
value in `Bchoices[i]` at that same position;
* if ``mode=wrap``, values in `a` (and thus `Ba`) may be any (signed)
integer; modular arithmetic is used to map integers outside the range
`[0, n-1]` back into that range; and then the new array is constructed
as above;
* if ``mode=clip``, values in `a` (and thus `Ba`) may be any (signed)
integer; negative integers are mapped to 0; values greater than `n-1`
are mapped to `n-1`; and then the new array is constructed as above.
Parameters
----------
a : int array
This array must contain integers in `[0, n-1]`, where `n` is the number
of choices, unless ``mode=wrap`` or ``mode=clip``, in which cases any
integers are permissible.
choices : sequence of arrays
Choice arrays. `a` and all of the choices must be broadcastable to the
same shape. If `choices` is itself an array (not recommended), then
its outermost dimension (i.e., the one corresponding to
``choices.shape[0]``) is taken as defining the "sequence".
out : array, optional
If provided, the result will be inserted into this array. It should
be of the appropriate shape and dtype.
mode : {'raise' (default), 'wrap', 'clip'}, optional
Specifies how indices outside `[0, n-1]` will be treated:
* 'raise' : an exception is raised
* 'wrap' : value becomes value mod `n`
* 'clip' : values < 0 are mapped to 0, values > n-1 are mapped to n-1
Returns
-------
merged_array : array
The merged result.
Raises
------
ValueError: shape mismatch
If `a` and each choice array are not all broadcastable to the same
shape.
See Also
--------
ndarray.choose : equivalent method
Notes
-----
To reduce the chance of misinterpretation, even though the following
"abuse" is nominally supported, `choices` should neither be, nor be
thought of as, a single array, i.e., the outermost sequence-like container
should be either a list or a tuple.
Examples
--------
choices = [[0, 1, 2, 3], [10, 11, 12, 13],
[20, 21, 22, 23], [30, 31, 32, 33]]
np.choose([2, 3, 1, 0], choices
# the first element of the result will be the first element of the
# third (2+1) "array" in choices, namely, 20; the second element
# will be the second element of the fourth (3+1) choice array, i.e.,
# 31, etc.
)
array([20, 31, 12, 3])
np.choose([2, 4, 1, 0], choices, mode='clip') # 4 goes to 3 (4-1)
array([20, 31, 12, 3])
# because there are 4 choice arrays
np.choose([2, 4, 1, 0], choices, mode='wrap') # 4 goes to (4 mod 4)
array([20, 1, 12, 3])
# i.e., 0
A couple examples illustrating how choose broadcasts:
a = [[1, 0, 1], [0, 1, 0], [1, 0, 1]]
choices = [-10, 10]
np.choose(a, choices)
array([[ 10, -10, 10],
[-10, 10, -10],
[ 10, -10, 10]])
# With thanks to Anne Archibald
a = np.array([0, 1]).reshape((2,1,1))
c1 = np.array([1, 2, 3]).reshape((1,3,1))
c2 = np.array([-1, -2, -3, -4, -5]).reshape((1,1,5))
np.choose(a, (c1, c2)) # result is 2x3x5, res[0,:,:]=c1, res[1,:,:]=c2
array([[[ 1, 1, 1, 1, 1],
[ 2, 2, 2, 2, 2],
[ 3, 3, 3, 3, 3]],
[[-1, -2, -3, -4, -5],
[-1, -2, -3, -4, -5],
[-1, -2, -3, -4, -5]]])
clip(a, a_min, a_max, out=None)
Clip (limit) the values in an array.
Given an interval, values outside the interval are clipped to
the interval edges. For example, if an interval of ``[0, 1]``
is specified, values smaller than 0 become 0, and values larger
than 1 become 1.
Parameters
----------
a : array_like
Array containing elements to clip.
a_min : scalar or array_like
Minimum value.
a_max : scalar or array_like
Maximum value. If `a_min` or `a_max` are array_like, then they will
be broadcasted to the shape of `a`.
out : ndarray, optional
The results will be placed in this array. It may be the input
array for in-place clipping. `out` must be of the right shape
to hold the output. Its type is preserved.
Returns
-------
clipped_array : ndarray
An array with the elements of `a`, but where values
< `a_min` are replaced with `a_min`, and those > `a_max`
with `a_max`.
See Also
--------
numpy.doc.ufuncs : Section "Output arguments"
Examples
--------
a = np.arange(10)
np.clip(a, 1, 8)
array([1, 1, 2, 3, 4, 5, 6, 7, 8, 8])
a
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
np.clip(a, 3, 6, out=a)
array([3, 3, 3, 3, 4, 5, 6, 6, 6, 6])
a = np.arange(10)
a
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
np.clip(a, [3,4,1,1,1,4,4,4,4,4], 8)
array([3, 4, 2, 3, 4, 5, 6, 7, 8, 8])
column_stack(tup)
Stack 1-D arrays as columns into a 2-D array.
Take a sequence of 1-D arrays and stack them as columns
to make a single 2-D array. 2-D arrays are stacked as-is,
just like with `hstack`. 1-D arrays are turned into 2-D columns
first.
Parameters
----------
tup : sequence of 1-D or 2-D arrays.
Arrays to stack. All of them must have the same first dimension.
Returns
-------
stacked : 2-D array
The array formed by stacking the given arrays.
See Also
--------
hstack, vstack, concatenate
Examples
--------
a = np.array((1,2,3))
b = np.array((2,3,4))
np.column_stack((a,b))
array([[1, 2],
[2, 3],
[3, 4]])
common_type(*arrays)
Return a scalar type which is common to the input arrays.
The return type will always be an inexact (i.e. floating point) scalar
type, even if all the arrays are integer arrays. If one of the inputs is
an integer array, the minimum precision type that is returned is a
64-bit floating point dtype.
All input arrays can be safely cast to the returned dtype without loss
of information.
Parameters
----------
array1, array2, ... : ndarrays
Input arrays.
Returns
-------
out : data type code
Data type code.
See Also
--------
dtype, mintypecode
Examples
--------
np.common_type(np.arange(2, dtype=np.float32))
np.common_type(np.arange(2, dtype=np.float32), np.arange(2))
np.common_type(np.arange(4), np.array([45, 6.j]), np.array([45.0]))
compare_chararrays(...)
compress(condition, a, axis=None, out=None)
Return selected slices of an array along given axis.
When working along a given axis, a slice along that axis is returned in
`output` for each index where `condition` evaluates to True. When
working on a 1-D array, `compress` is equivalent to `extract`.
Parameters
----------
condition : 1-D array of bools
Array that selects which entries to return. If len(condition)
is less than the size of `a` along the given axis, then output is
truncated to the length of the condition array.
a : array_like
Array from which to extract a part.
axis : int, optional
Axis along which to take slices. If None (default), work on the
flattened array.
out : ndarray, optional
Output array. Its type is preserved and it must be of the right
shape to hold the output.
Returns
-------
compressed_array : ndarray
A copy of `a` without the slices along axis for which `condition`
is false.
See Also
--------
take, choose, diag, diagonal, select
ndarray.compress : Equivalent method in ndarray
np.extract: Equivalent method when working on 1-D arrays
numpy.doc.ufuncs : Section "Output arguments"
Examples
--------
a = np.array([[1, 2], [3, 4], [5, 6]])
a
array([[1, 2],
[3, 4],
[5, 6]])
np.compress([0, 1], a, axis=0)
array([[3, 4]])
np.compress([False, True, True], a, axis=0)
array([[3, 4],
[5, 6]])
np.compress([False, True], a, axis=1)
array([[2],
[4],
[6]])
Working on the flattened array does not return slices along an axis but
selects elements.
np.compress([False, True], a)
array([2])
concatenate(...)
concatenate((a1, a2, ...), axis=0)
Join a sequence of arrays along an existing axis.
Parameters
----------
a1, a2, ... : sequence of array_like
The arrays must have the same shape, except in the dimension
corresponding to `axis` (the first, by default).
axis : int, optional
The axis along which the arrays will be joined. Default is 0.
Returns
-------
res : ndarray
The concatenated array.
See Also
--------
ma.concatenate : Concatenate function that preserves input masks.
array_split : Split an array into multiple sub-arrays of equal or
near-equal size.
split : Split array into a list of multiple sub-arrays of equal size.
hsplit : Split array into multiple sub-arrays horizontally (column wise)
vsplit : Split array into multiple sub-arrays vertically (row wise)
dsplit : Split array into multiple sub-arrays along the 3rd axis (depth).
stack : Stack a sequence of arrays along a new axis.
hstack : Stack arrays in sequence horizontally (column wise)
vstack : Stack arrays in sequence vertically (row wise)
dstack : Stack arrays in sequence depth wise (along third dimension)
Notes
-----
When one or more of the arrays to be concatenated is a MaskedArray,
this function will return a MaskedArray object instead of an ndarray,
but the input masks are *not* preserved. In cases where a MaskedArray
is expected as input, use the ma.concatenate function from the masked
array module instead.
Examples
--------
a = np.array([[1, 2], [3, 4]])
b = np.array([[5, 6]])
np.concatenate((a, b), axis=0)
array([[1, 2],
[3, 4],
[5, 6]])
np.concatenate((a, b.T), axis=1)
array([[1, 2, 5],
[3, 4, 6]])
This function will not preserve masking of MaskedArray inputs.
a = np.ma.arange(3)
a[1] = np.ma.masked
b = np.arange(2, 5)
a
masked_array(data = [0 -- 2],
mask = [False True False],
fill_value = 999999)
b
array([2, 3, 4])
np.concatenate([a, b])
masked_array(data = [0 1 2 2 3 4],
mask = False,
fill_value = 999999)
np.ma.concatenate([a, b])
masked_array(data = [0 -- 2 2 3 4],
mask = [False True False False False False],
fill_value = 999999)
convolve(a, v, mode='full')
Returns the discrete, linear convolution of two one-dimensional sequences.
The convolution operator is often seen in signal processing, where it
models the effect of a linear time-invariant system on a signal [1]_. In
probability theory, the sum of two independent random variables is
distributed according to the convolution of their individual
distributions.
If `v` is longer than `a`, the arrays are swapped before computation.
Parameters
----------
a : (N,) array_like
First one-dimensional input array.
v : (M,) array_like
Second one-dimensional input array.
mode : {'full', 'valid', 'same'}, optional
'full':
By default, mode is 'full'. This returns the convolution
at each point of overlap, with an output shape of (N+M-1,). At
the end-points of the convolution, the signals do not overlap
completely, and boundary effects may be seen.
'same':
Mode `same` returns output of length ``max(M, N)``. Boundary
effects are still visible.
'valid':
Mode `valid` returns output of length
``max(M, N) - min(M, N) + 1``. The convolution product is only given
for points where the signals overlap completely. Values outside
the signal boundary have no effect.
Returns
-------
out : ndarray
Discrete, linear convolution of `a` and `v`.
See Also
--------
scipy.signal.fftconvolve : Convolve two arrays using the Fast Fourier
Transform.
scipy.linalg.toeplitz : Used to construct the convolution operator.
polymul : Polynomial multiplication. Same output as convolve, but also
accepts poly1d objects as input.
Notes
-----
The discrete convolution operation is defined as
.. math:: (a * v)[n] = \sum_{m = -\infty}^{\infty} a[m] v[n - m]
It can be shown that a convolution :math:`x(t) * y(t)` in time/space
is equivalent to the multiplication :math:`X(f) Y(f)` in the Fourier
domain, after appropriate padding (padding is necessary to prevent
circular convolution). Since multiplication is more efficient (faster)
than convolution, the function `scipy.signal.fftconvolve` exploits the
FFT to calculate the convolution of large data-sets.
References
----------
.. [1] Wikipedia, "Convolution", http://en.wikipedia.org/wiki/Convolution.
Examples
--------
Note how the convolution operator flips the second array
before "sliding" the two across one another:
np.convolve([1, 2, 3], [0, 1, 0.5])
array([ 0. , 1. , 2.5, 4. , 1.5])
Only return the middle values of the convolution.
Contains boundary effects, where zeros are taken
into account:
np.convolve([1,2,3],[0,1,0.5], 'same')
array([ 1. , 2.5, 4. ])
The two arrays are of the same length, so there
is only one position where they completely overlap:
np.convolve([1,2,3],[0,1,0.5], 'valid')
array([ 2.5])
copy(a, order='K')
Return an array copy of the given object.
Parameters
----------
a : array_like
Input data.
order : {'C', 'F', 'A', 'K'}, optional
Controls the memory layout of the copy. 'C' means C-order,
'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous,
'C' otherwise. 'K' means match the layout of `a` as closely
as possible. (Note that this function and :meth:ndarray.copy are very
similar, but have different default values for their order=
arguments.)
Returns
-------
arr : ndarray
Array interpretation of `a`.
Notes
-----
This is equivalent to
np.array(a, copy=True) #doctest: +SKIP
Examples
--------
Create an array x, with a reference y and a copy z:
x = np.array([1, 2, 3])
y = x
z = np.copy(x)
Note that, when we modify x, y changes, but not z:
x[0] = 10
x[0] == y[0]
True
x[0] == z[0]
False
copyto(...)
copyto(dst, src, casting='same_kind', where=None)
Copies values from one array to another, broadcasting as necessary.
Raises a TypeError if the `casting` rule is violated, and if
`where` is provided, it selects which elements to copy.
.. versionadded:: 1.7.0
Parameters
----------
dst : ndarray
The array into which values are copied.
src : array_like
The array from which values are copied.
casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
Controls what kind of data casting may occur when copying.
* 'no' means the data types should not be cast at all.
* 'equiv' means only byte-order changes are allowed.
* 'safe' means only casts which can preserve values are allowed.
* 'same_kind' means only safe casts or casts within a kind,
like float64 to float32, are allowed.
* 'unsafe' means any data conversions may be done.
where : array_like of bool, optional
A boolean array which is broadcasted to match the dimensions
of `dst`, and selects elements to copy from `src` to `dst`
wherever it contains the value True.
corrcoef(x, y=None, rowvar=1, bias=, ddof=)
Return Pearson product-moment correlation coefficients.
Please refer to the documentation for `cov` for more detail. The
relationship between the correlation coefficient matrix, `R`, and the
covariance matrix, `C`, is
.. math:: R_{ij} = \frac{ C_{ij} } { \sqrt{ C_{ii} * C_{jj} } }
The values of `R` are between -1 and 1, inclusive.
Parameters
----------
x : array_like
A 1-D or 2-D array containing multiple variables and observations.
Each row of `x` represents a variable, and each column a single
observation of all those variables. Also see `rowvar` below.
y : array_like, optional
An additional set of variables and observations. `y` has the same
shape as `x`.
rowvar : int, optional
If `rowvar` is non-zero (default), then each row represents a
variable, with observations in the columns. Otherwise, the relationship
is transposed: each column represents a variable, while the rows
contain observations.
bias : _NoValue, optional
Has no affect, do not use.
.. deprecated:: 1.10.0
ddof : _NoValue, optional
Has no affect, do not use.
.. deprecated:: 1.10.0
Returns
-------
R : ndarray
The correlation coefficient matrix of the variables.
See Also
--------
cov : Covariance matrix
Notes
-----
This function accepts but discards arguments `bias` and `ddof`. This is
for backwards compatibility with previous versions of this function. These
arguments had no effect on the return values of the function and can be
safely ignored in this and previous versions of numpy.
correlate(a, v, mode='valid')
Cross-correlation of two 1-dimensional sequences.
This function computes the correlation as generally defined in signal
processing texts::
c_{av}[k] = sum_n a[n+k] * conj(v[n])
with a and v sequences being zero-padded where necessary and conj being
the conjugate.
Parameters
----------
a, v : array_like
Input sequences.
mode : {'valid', 'same', 'full'}, optional
Refer to the `convolve` docstring. Note that the default
is `valid`, unlike `convolve`, which uses `full`.
old_behavior : bool
`old_behavior` was removed in NumPy 1.10. If you need the old
behavior, use `multiarray.correlate`.
Returns
-------
out : ndarray
Discrete cross-correlation of `a` and `v`.
See Also
--------
convolve : Discrete, linear convolution of two one-dimensional sequences.
multiarray.correlate : Old, no conjugate, version of correlate.
Notes
-----
The definition of correlation above is not unique and sometimes correlation
may be defined differently. Another common definition is::
c'_{av}[k] = sum_n a[n] conj(v[n+k])
which is related to ``c_{av}[k]`` by ``c'_{av}[k] = c_{av}[-k]``.
Examples
--------
np.correlate([1, 2, 3], [0, 1, 0.5])
array([ 3.5])
np.correlate([1, 2, 3], [0, 1, 0.5], "same")
array([ 2. , 3.5, 3. ])
np.correlate([1, 2, 3], [0, 1, 0.5], "full")
array([ 0.5, 2. , 3.5, 3. , 0. ])
Using complex sequences:
np.correlate([1+1j, 2, 3-1j], [0, 1, 0.5j], 'full')
array([ 0.5-0.5j, 1.0+0.j , 1.5-1.5j, 3.0-1.j , 0.0+0.j ])
Note that you get the time reversed, complex conjugated result
when the two input sequences change places, i.e.,
``c_{va}[k] = c^{*}_{av}[-k]``:
np.correlate([0, 1, 0.5j], [1+1j, 2, 3-1j], 'full')
array([ 0.0+0.j , 3.0+1.j , 1.5+1.5j, 1.0+0.j , 0.5+0.5j])
count_nonzero(...)
count_nonzero(a)
Counts the number of non-zero values in the array ``a``.
Parameters
----------
a : array_like
The array for which to count non-zeros.
Returns
-------
count : int or array of int
Number of non-zero values in the array.
See Also
--------
nonzero : Return the coordinates of all the non-zero values.
Examples
--------
np.count_nonzero(np.eye(4))
4
np.count_nonzero([[0,1,7,0,0],[3,0,0,2,19]])
5
cov(m, y=None, rowvar=1, bias=0, ddof=None, fweights=None, aweights=None)
Estimate a covariance matrix, given data and weights.
Covariance indicates the level to which two variables vary together.
If we examine N-dimensional samples, :math:`X = [x_1, x_2, ... x_N]^T`,
then the covariance matrix element :math:`C_{ij}` is the covariance of
:math:`x_i` and :math:`x_j`. The element :math:`C_{ii}` is the variance
of :math:`x_i`.
See the notes for an outline of the algorithm.
Parameters
----------
m : array_like
A 1-D or 2-D array containing multiple variables and observations.
Each row of `m` represents a variable, and each column a single
observation of all those variables. Also see `rowvar` below.
y : array_like, optional
An additional set of variables and observations. `y` has the same form
as that of `m`.
rowvar : int, optional
If `rowvar` is non-zero (default), then each row represents a
variable, with observations in the columns. Otherwise, the relationship
is transposed: each column represents a variable, while the rows
contain observations.
bias : int, optional
Default normalization is by ``(N - 1)``, where ``N`` corresponds to the
number of observations given (unbiased estimate). If `bias` is 1, then
normalization is by ``N``. These values can be overridden by using the
keyword ``ddof`` in numpy versions >= 1.5.
ddof : int, optional
If not ``None`` the default value implied by `bias` is overridden.
Note that ``ddof=1`` will return the unbiased estimate, even if both
`fweights` and `aweights` are specified, and ``ddof=0`` will return
the simple average. See the notes for the details. The default value
is ``None``.
.. versionadded:: 1.5
fweights : array_like, int, optional
1-D array of integer freguency weights; the number of times each
observation vector should be repeated.
.. versionadded:: 1.10
aweights : array_like, optional
1-D array of observation vector weights. These relative weights are
typically large for observations considered "important" and smaller for
observations considered less "important". If ``ddof=0`` the array of
weights can be used to assign probabilities to observation vectors.
.. versionadded:: 1.10
Returns
-------
out : ndarray
The covariance matrix of the variables.
See Also
--------
corrcoef : Normalized covariance matrix
Notes
-----
Assume that the observations are in the columns of the observation
array `m` and let ``f = fweights`` and ``a = aweights`` for brevity. The
steps to compute the weighted covariance are as follows::
w = f * a
v1 = np.sum(w)
v2 = np.sum(w * a)
m -= np.sum(m * w, axis=1, keepdims=True) / v1
cov = np.dot(m * w, m.T) * v1 / (v1**2 - ddof * v2)
Note that when ``a == 1``, the normalization factor
``v1 / (v1**2 - ddof * v2)`` goes over to ``1 / (np.sum(f) - ddof)``
as it should.
Examples
--------
Consider two variables, :math:`x_0` and :math:`x_1`, which
correlate perfectly, but in opposite directions:
x = np.array([[0, 2], [1, 1], [2, 0]]).T
x
array([[0, 1, 2],
[2, 1, 0]])
Note how :math:`x_0` increases while :math:`x_1` decreases. The covariance
matrix shows this clearly:
np.cov(x)
array([[ 1., -1.],
[-1., 1.]])
Note that element :math:`C_{0,1}`, which shows the correlation between
:math:`x_0` and :math:`x_1`, is negative.
Further, note how `x` and `y` are combined:
x = [-2.1, -1, 4.3]
y = [3, 1.1, 0.12]
X = np.vstack((x,y))
print np.cov(X)
[[ 11.71 -4.286 ]
[ -4.286 2.14413333]]
print np.cov(x, y)
[[ 11.71 -4.286 ]
[ -4.286 2.14413333]]
print np.cov(x)
11.71
cross(a, b, axisa=-1, axisb=-1, axisc=-1, axis=None)
Return the cross product of two (arrays of) vectors.
The cross product of `a` and `b` in :math:`R^3` is a vector perpendicular
to both `a` and `b`. If `a` and `b` are arrays of vectors, the vectors
are defined by the last axis of `a` and `b` by default, and these axes
can have dimensions 2 or 3. Where the dimension of either `a` or `b` is
2, the third component of the input vector is assumed to be zero and the
cross product calculated accordingly. In cases where both input vectors
have dimension 2, the z-component of the cross product is returned.
Parameters
----------
a : array_like
Components of the first vector(s).
b : array_like
Components of the second vector(s).
axisa : int, optional
Axis of `a` that defines the vector(s). By default, the last axis.
axisb : int, optional
Axis of `b` that defines the vector(s). By default, the last axis.
axisc : int, optional
Axis of `c` containing the cross product vector(s). Ignored if
both input vectors have dimension 2, as the return is scalar.
By default, the last axis.
axis : int, optional
If defined, the axis of `a`, `b` and `c` that defines the vector(s)
and cross product(s). Overrides `axisa`, `axisb` and `axisc`.
Returns
-------
c : ndarray
Vector cross product(s).
Raises
------
ValueError
When the dimension of the vector(s) in `a` and/or `b` does not
equal 2 or 3.
See Also
--------
inner : Inner product
outer : Outer product.
ix_ : Construct index arrays.
Notes
-----
.. versionadded:: 1.9.0
Supports full broadcasting of the inputs.
Examples
--------
Vector cross-product.
x = [1, 2, 3]
y = [4, 5, 6]
np.cross(x, y)
array([-3, 6, -3])
One vector with dimension 2.
x = [1, 2]
y = [4, 5, 6]
np.cross(x, y)
array([12, -6, -3])
Equivalently:
x = [1, 2, 0]
y = [4, 5, 6]
np.cross(x, y)
array([12, -6, -3])
Both vectors with dimension 2.
x = [1,2]
y = [4,5]
np.cross(x, y)
-3
Multiple vector cross-products. Note that the direction of the cross
product vector is defined by the `right-hand rule`.
x = np.array([[1,2,3], [4,5,6]])
y = np.array([[4,5,6], [1,2,3]])
np.cross(x, y)
array([[-3, 6, -3],
[ 3, -6, 3]])
The orientation of `c` can be changed using the `axisc` keyword.
np.cross(x, y, axisc=0)
array([[-3, 3],
[ 6, -6],
[-3, 3]])
Change the vector definition of `x` and `y` using `axisa` and `axisb`.
x = np.array([[1,2,3], [4,5,6], [7, 8, 9]])
y = np.array([[7, 8, 9], [4,5,6], [1,2,3]])
np.cross(x, y)
array([[ -6, 12, -6],
[ 0, 0, 0],
[ 6, -12, 6]])
np.cross(x, y, axisa=0, axisb=0)
array([[-24, 48, -24],
[-30, 60, -30],
[-36, 72, -36]])
cumprod(a, axis=None, dtype=None, out=None)
Return the cumulative product of elements along a given axis.
Parameters
----------
a : array_like
Input array.
axis : int, optional
Axis along which the cumulative product is computed. By default
the input is flattened.
dtype : dtype, optional
Type of the returned array, as well as of the accumulator in which
the elements are multiplied. If *dtype* is not specified, it
defaults to the dtype of `a`, unless `a` has an integer dtype with
a precision less than that of the default platform integer. In
that case, the default platform integer is used instead.
out : ndarray, optional
Alternative output array in which to place the result. It must
have the same shape and buffer length as the expected output
but the type of the resulting values will be cast if necessary.
Returns
-------
cumprod : ndarray
A new array holding the result is returned unless `out` is
specified, in which case a reference to out is returned.
See Also
--------
numpy.doc.ufuncs : Section "Output arguments"
Notes
-----
Arithmetic is modular when using integer types, and no error is
raised on overflow.
Examples
--------
a = np.array([1,2,3])
np.cumprod(a) # intermediate results 1, 1*2
# total product 1*2*3 = 6
array([1, 2, 6])
a = np.array([[1, 2, 3], [4, 5, 6]])
np.cumprod(a, dtype=float) # specify type of output
array([ 1., 2., 6., 24., 120., 720.])
The cumulative product for each column (i.e., over the rows) of `a`:
np.cumprod(a, axis=0)
array([[ 1, 2, 3],
[ 4, 10, 18]])
The cumulative product for each row (i.e. over the columns) of `a`:
np.cumprod(a,axis=1)
array([[ 1, 2, 6],
[ 4, 20, 120]])
cumproduct(a, axis=None, dtype=None, out=None)
Return the cumulative product over the given axis.
See Also
--------
cumprod : equivalent function; see for details.
cumsum(a, axis=None, dtype=None, out=None)
Return the cumulative sum of the elements along a given axis.
Parameters
----------
a : array_like
Input array.
axis : int, optional
Axis along which the cumulative sum is computed. The default
(None) is to compute the cumsum over the flattened array.
dtype : dtype, optional
Type of the returned array and of the accumulator in which the
elements are summed. If `dtype` is not specified, it defaults
to the dtype of `a`, unless `a` has an integer dtype with a
precision less than that of the default platform integer. In
that case, the default platform integer is used.
out : ndarray, optional
Alternative output array in which to place the result. It must
have the same shape and buffer length as the expected output
but the type will be cast if necessary. See `doc.ufuncs`
(Section "Output arguments") for more details.
Returns
-------
cumsum_along_axis : ndarray.
A new array holding the result is returned unless `out` is
specified, in which case a reference to `out` is returned. The
result has the same size as `a`, and the same shape as `a` if
`axis` is not None or `a` is a 1-d array.
See Also
--------
sum : Sum array elements.
trapz : Integration of array values using the composite trapezoidal rule.
diff : Calculate the n-th order discrete difference along given axis.
Notes
-----
Arithmetic is modular when using integer types, and no error is
raised on overflow.
Examples
--------
a = np.array([[1,2,3], [4,5,6]])
a
array([[1, 2, 3],
[4, 5, 6]])
np.cumsum(a)
array([ 1, 3, 6, 10, 15, 21])
np.cumsum(a, dtype=float) # specifies type of output value(s)
array([ 1., 3., 6., 10., 15., 21.])
np.cumsum(a,axis=0) # sum over rows for each of the 3 columns
array([[1, 2, 3],
[5, 7, 9]])
np.cumsum(a,axis=1) # sum over columns for each of the 2 rows
array([[ 1, 3, 6],
[ 4, 9, 15]])
datetime_as_string(...)
datetime_data(...)
delete(arr, obj, axis=None)
Return a new array with sub-arrays along an axis deleted. For a one
dimensional array, this returns those entries not returned by
`arr[obj]`.
Parameters
----------
arr : array_like
Input array.
obj : slice, int or array of ints
Indicate which sub-arrays to remove.
axis : int, optional
The axis along which to delete the subarray defined by `obj`.
If `axis` is None, `obj` is applied to the flattened array.
Returns
-------
out : ndarray
A copy of `arr` with the elements specified by `obj` removed. Note
that `delete` does not occur in-place. If `axis` is None, `out` is
a flattened array.
See Also
--------
insert : Insert elements into an array.
append : Append elements at the end of an array.
Notes
-----
Often it is preferable to use a boolean mask. For example:
mask = np.ones(len(arr), dtype=bool)
mask[[0,2,4]] = False
result = arr[mask,...]
Is equivalent to `np.delete(arr, [0,2,4], axis=0)`, but allows further
use of `mask`.
Examples
--------
arr = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]])
arr
array([[ 1, 2, 3, 4],
[ 5, 6, 7, 8],
[ 9, 10, 11, 12]])
np.delete(arr, 1, 0)
array([[ 1, 2, 3, 4],
[ 9, 10, 11, 12]])
np.delete(arr, np.s_[::2], 1)
array([[ 2, 4],
[ 6, 8],
[10, 12]])
np.delete(arr, [1,3,5], None)
array([ 1, 3, 5, 7, 8, 9, 10, 11, 12])
deprecate(*args, **kwargs)
Issues a DeprecationWarning, adds warning to `old_name`'s
docstring, rebinds ``old_name.__name__`` and returns the new
function object.
This function may also be used as a decorator.
Parameters
----------
func : function
The function to be deprecated.
old_name : str, optional
The name of the function to be deprecated. Default is None, in
which case the name of `func` is used.
new_name : str, optional
The new name for the function. Default is None, in which case the
deprecation message is that `old_name` is deprecated. If given, the
deprecation message is that `old_name` is deprecated and `new_name`
should be used instead.
message : str, optional
Additional explanation of the deprecation. Displayed in the
docstring after the warning.
Returns
-------
old_func : function
The deprecated function.
Examples
--------
Note that ``olduint`` returns a value after printing Deprecation
Warning:
olduint = np.deprecate(np.uint)
olduint(6)
/usr/lib/python2.5/site-packages/numpy/lib/utils.py:114:
DeprecationWarning: uint32 is deprecated
warnings.warn(str1, DeprecationWarning)
6
deprecate_with_doc lambda msg
diag(v, k=0)
Extract a diagonal or construct a diagonal array.
See the more detailed documentation for ``numpy.diagonal`` if you use this
function to extract a diagonal and wish to write to the resulting array;
whether it returns a copy or a view depends on what version of numpy you
are using.
Parameters
----------
v : array_like
If `v` is a 2-D array, return a copy of its `k`-th diagonal.
If `v` is a 1-D array, return a 2-D array with `v` on the `k`-th
diagonal.
k : int, optional
Diagonal in question. The default is 0. Use `k>0` for diagonals
above the main diagonal, and `k<0` for diagonals below the main
diagonal.
Returns
-------
out : ndarray
The extracted diagonal or constructed diagonal array.
See Also
--------
diagonal : Return specified diagonals.
diagflat : Create a 2-D array with the flattened input as a diagonal.
trace : Sum along diagonals.
triu : Upper triangle of an array.
tril : Lower triangle of an array.
Examples
--------
x = np.arange(9).reshape((3,3))
x
array([[0, 1, 2],
[3, 4, 5],
[6, 7, 8]])
np.diag(x)
array([0, 4, 8])
np.diag(x, k=1)
array([1, 5])
np.diag(x, k=-1)
array([3, 7])
np.diag(np.diag(x))
array([[0, 0, 0],
[0, 4, 0],
[0, 0, 8]])
diag_indices(n, ndim=2)
Return the indices to access the main diagonal of an array.
This returns a tuple of indices that can be used to access the main
diagonal of an array `a` with ``a.ndim >= 2`` dimensions and shape
(n, n, ..., n). For ``a.ndim = 2`` this is the usual diagonal, for
``a.ndim > 2`` this is the set of indices to access ``a[i, i, ..., i]``
for ``i = [0..n-1]``.
Parameters
----------
n : int
The size, along each dimension, of the arrays for which the returned
indices can be used.
ndim : int, optional
The number of dimensions.
See also
--------
diag_indices_from
Notes
-----
.. versionadded:: 1.4.0
Examples
--------
Create a set of indices to access the diagonal of a (4, 4) array:
di = np.diag_indices(4)
di
(array([0, 1, 2, 3]), array([0, 1, 2, 3]))
a = np.arange(16).reshape(4, 4)
a
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11],
[12, 13, 14, 15]])
a[di] = 100
a
array([[100, 1, 2, 3],
[ 4, 100, 6, 7],
[ 8, 9, 100, 11],
[ 12, 13, 14, 100]])
Now, we create indices to manipulate a 3-D array:
d3 = np.diag_indices(2, 3)
d3
(array([0, 1]), array([0, 1]), array([0, 1]))
And use it to set the diagonal of an array of zeros to 1:
a = np.zeros((2, 2, 2), dtype=np.int)
a[d3] = 1
a
array([[[1, 0],
[0, 0]],
[[0, 0],
[0, 1]]])
diag_indices_from(arr)
Return the indices to access the main diagonal of an n-dimensional array.
See `diag_indices` for full details.
Parameters
----------
arr : array, at least 2-D
See Also
--------
diag_indices
Notes
-----
.. versionadded:: 1.4.0
diagflat(v, k=0)
Create a two-dimensional array with the flattened input as a diagonal.
Parameters
----------
v : array_like
Input data, which is flattened and set as the `k`-th
diagonal of the output.
k : int, optional
Diagonal to set; 0, the default, corresponds to the "main" diagonal,
a positive (negative) `k` giving the number of the diagonal above
(below) the main.
Returns
-------
out : ndarray
The 2-D output array.
See Also
--------
diag : MATLAB work-alike for 1-D and 2-D arrays.
diagonal : Return specified diagonals.
trace : Sum along diagonals.
Examples
--------
np.diagflat([[1,2], [3,4]])
array([[1, 0, 0, 0],
[0, 2, 0, 0],
[0, 0, 3, 0],
[0, 0, 0, 4]])
np.diagflat([1,2], 1)
array([[0, 1, 0],
[0, 0, 2],
[0, 0, 0]])
diagonal(a, offset=0, axis1=0, axis2=1)
Return specified diagonals.
If `a` is 2-D, returns the diagonal of `a` with the given offset,
i.e., the collection of elements of the form ``a[i, i+offset]``. If
`a` has more than two dimensions, then the axes specified by `axis1`
and `axis2` are used to determine the 2-D sub-array whose diagonal is
returned. The shape of the resulting array can be determined by
removing `axis1` and `axis2` and appending an index to the right equal
to the size of the resulting diagonals.
In versions of NumPy prior to 1.7, this function always returned a new,
independent array containing a copy of the values in the diagonal.
In NumPy 1.7 and 1.8, it continues to return a copy of the diagonal,
but depending on this fact is deprecated. Writing to the resulting
array continues to work as it used to, but a FutureWarning is issued.
In NumPy 1.9 it returns a read-only view on the original array.
Attempting to write to the resulting array will produce an error.
In NumPy 1.10, it will return a read/write view and writing to the
returned array will alter your original array. The returned array
will have the same type as the input array.
If you don't write to the array returned by this function, then you can
just ignore all of the above.
If you depend on the current behavior, then we suggest copying the
returned array explicitly, i.e., use ``np.diagonal(a).copy()`` instead
of just ``np.diagonal(a)``. This will work with both past and future
versions of NumPy.
Parameters
----------
a : array_like
Array from which the diagonals are taken.
offset : int, optional
Offset of the diagonal from the main diagonal. Can be positive or
negative. Defaults to main diagonal (0).
axis1 : int, optional
Axis to be used as the first axis of the 2-D sub-arrays from which
the diagonals should be taken. Defaults to first axis (0).
axis2 : int, optional
Axis to be used as the second axis of the 2-D sub-arrays from
which the diagonals should be taken. Defaults to second axis (1).
Returns
-------
array_of_diagonals : ndarray
If `a` is 2-D and not a matrix, a 1-D array of the same type as `a`
containing the diagonal is returned. If `a` is a matrix, a 1-D
array containing the diagonal is returned in order to maintain
backward compatibility. If the dimension of `a` is greater than
two, then an array of diagonals is returned, "packed" from
left-most dimension to right-most (e.g., if `a` is 3-D, then the
diagonals are "packed" along rows).
Raises
------
ValueError
If the dimension of `a` is less than 2.
See Also
--------
diag : MATLAB work-a-like for 1-D and 2-D arrays.
diagflat : Create diagonal arrays.
trace : Sum along diagonals.
Examples
--------
a = np.arange(4).reshape(2,2)
a
array([[0, 1],
[2, 3]])
a.diagonal()
array([0, 3])
a.diagonal(1)
array([1])
A 3-D example:
a = np.arange(8).reshape(2,2,2); a
array([[[0, 1],
[2, 3]],
[[4, 5],
[6, 7]]])
a.diagonal(0, # Main diagonals of two arrays created by skipping
0, # across the outer(left)-most axis last and
1) # the "middle" (row) axis first.
array([[0, 6],
[1, 7]])
The sub-arrays whose main diagonals we just obtained; note that each
corresponds to fixing the right-most (column) axis, and that the
diagonals are "packed" in rows.
a[:,:,0] # main diagonal is [0 6]
array([[0, 2],
[4, 6]])
a[:,:,1] # main diagonal is [1 7]
array([[1, 3],
[5, 7]])
diff(a, n=1, axis=-1)
Calculate the n-th order discrete difference along given axis.
The first order difference is given by ``out[n] = a[n+1] - a[n]`` along
the given axis, higher order differences are calculated by using `diff`
recursively.
Parameters
----------
a : array_like
Input array
n : int, optional
The number of times values are differenced.
axis : int, optional
The axis along which the difference is taken, default is the last axis.
Returns
-------
diff : ndarray
The `n` order differences. The shape of the output is the same as `a`
except along `axis` where the dimension is smaller by `n`.
See Also
--------
gradient, ediff1d, cumsum
Examples
--------
x = np.array([1, 2, 4, 7, 0])
np.diff(x)
array([ 1, 2, 3, -7])
np.diff(x, n=2)
array([ 1, 1, -10])
x = np.array([[1, 3, 6, 10], [0, 5, 6, 8]])
np.diff(x)
array([[2, 3, 4],
[5, 1, 2]])
np.diff(x, axis=0)
array([[-1, 2, 0, -2]])
digitize(...)
digitize(x, bins, right=False)
Return the indices of the bins to which each value in input array belongs.
Each index ``i`` returned is such that ``bins[i-1] <= x < bins[i]`` if
`bins` is monotonically increasing, or ``bins[i-1] > x >= bins[i]`` if
`bins` is monotonically decreasing. If values in `x` are beyond the
bounds of `bins`, 0 or ``len(bins)`` is returned as appropriate. If right
is True, then the right bin is closed so that the index ``i`` is such
that ``bins[i-1] < x <= bins[i]`` or bins[i-1] >= x > bins[i]`` if `bins`
is monotonically increasing or decreasing, respectively.
Parameters
----------
x : array_like
Input array to be binned. Prior to Numpy 1.10.0, this array had to
be 1-dimensional, but can now have any shape.
bins : array_like
Array of bins. It has to be 1-dimensional and monotonic.
right : bool, optional
Indicating whether the intervals include the right or the left bin
edge. Default behavior is (right==False) indicating that the interval
does not include the right edge. The left bin end is open in this
case, i.e., bins[i-1] <= x < bins[i] is the default behavior for
monotonically increasing bins.
Returns
-------
out : ndarray of ints
Output array of indices, of same shape as `x`.
Raises
------
ValueError
If `bins` is not monotonic.
TypeError
If the type of the input is complex.
See Also
--------
bincount, histogram, unique
Notes
-----
If values in `x` are such that they fall outside the bin range,
attempting to index `bins` with the indices that `digitize` returns
will result in an IndexError.
.. versionadded:: 1.10.0
`np.digitize` is implemented in terms of `np.searchsorted`. This means
that a binary search is used to bin the values, which scales much better
for larger number of bins than the previous linear search. It also removes
the requirement for the input array to be 1-dimensional.
Examples
--------
x = np.array([0.2, 6.4, 3.0, 1.6])
bins = np.array([0.0, 1.0, 2.5, 4.0, 10.0])
inds = np.digitize(x, bins)
inds
array([1, 4, 3, 2])
for n in range(x.size):
print bins[inds[n]-1], "<=", x[n], "<", bins[inds[n]]
...
0.0 <= 0.2 < 1.0
4.0 <= 6.4 < 10.0
2.5 <= 3.0 < 4.0
1.0 <= 1.6 < 2.5
x = np.array([1.2, 10.0, 12.4, 15.5, 20.])
bins = np.array([0, 5, 10, 15, 20])
np.digitize(x,bins,right=True)
array([1, 2, 3, 4, 4])
np.digitize(x,bins,right=False)
array([1, 3, 3, 4, 5])
disp(mesg, device=None, linefeed=True)
Display a message on a device.
Parameters
----------
mesg : str
Message to display.
device : object
Device to write message. If None, defaults to ``sys.stdout`` which is
very similar to ``print``. `device` needs to have ``write()`` and
``flush()`` methods.
linefeed : bool, optional
Option whether to print a line feed or not. Defaults to True.
Raises
------
AttributeError
If `device` does not have a ``write()`` or ``flush()`` method.
Examples
--------
Besides ``sys.stdout``, a file-like object can also be used as it has
both required methods:
from StringIO import StringIO
buf = StringIO()
np.disp('"Display" in a file', device=buf)
buf.getvalue()
'"Display" in a file\n'
dot(...)
dot(a, b, out=None)
Dot product of two arrays.
For 2-D arrays it is equivalent to matrix multiplication, and for 1-D
arrays to inner product of vectors (without complex conjugation). For
N dimensions it is a sum product over the last axis of `a` and
the second-to-last of `b`::
dot(a, b)[i,j,k,m] = sum(a[i,j,:] * b[k,:,m])
Parameters
----------
a : array_like
First argument.
b : array_like
Second argument.
out : ndarray, optional
Output argument. This must have the exact kind that would be returned
if it was not used. In particular, it must have the right type, must be
C-contiguous, and its dtype must be the dtype that would be returned
for `dot(a,b)`. This is a performance feature. Therefore, if these
conditions are not met, an exception is raised, instead of attempting
to be flexible.
Returns
-------
output : ndarray
Returns the dot product of `a` and `b`. If `a` and `b` are both
scalars or both 1-D arrays then a scalar is returned; otherwise
an array is returned.
If `out` is given, then it is returned.
Raises
------
ValueError
If the last dimension of `a` is not the same size as
the second-to-last dimension of `b`.
See Also
--------
vdot : Complex-conjugating dot product.
tensordot : Sum products over arbitrary axes.
einsum : Einstein summation convention.
matmul : '@' operator as method with out parameter.
Examples
--------
np.dot(3, 4)
12
Neither argument is complex-conjugated:
np.dot([2j, 3j], [2j, 3j])
(-13+0j)
For 2-D arrays it is the matrix product:
a = [[1, 0], [0, 1]]
b = [[4, 1], [2, 2]]
np.dot(a, b)
array([[4, 1],
[2, 2]])
a = np.arange(3*4*5*6).reshape((3,4,5,6))
b = np.arange(3*4*5*6)[::-1].reshape((5,4,6,3))
np.dot(a, b)[2,3,2,1,2,2]
499128
sum(a[2,3,2,:] * b[1,2,:,2])
499128
dsplit(ary, indices_or_sections)
Split array into multiple sub-arrays along the 3rd axis (depth).
Please refer to the `split` documentation. `dsplit` is equivalent
to `split` with ``axis=2``, the array is always split along the third
axis provided the array dimension is greater than or equal to 3.
See Also
--------
split : Split an array into multiple sub-arrays of equal size.
Examples
--------
x = np.arange(16.0).reshape(2, 2, 4)
x
array([[[ 0., 1., 2., 3.],
[ 4., 5., 6., 7.]],
[[ 8., 9., 10., 11.],
[ 12., 13., 14., 15.]]])
np.dsplit(x, 2)
[array([[[ 0., 1.],
[ 4., 5.]],
[[ 8., 9.],
[ 12., 13.]]]),
array([[[ 2., 3.],
[ 6., 7.]],
[[ 10., 11.],
[ 14., 15.]]])]
np.dsplit(x, np.array([3, 6]))
[array([[[ 0., 1., 2.],
[ 4., 5., 6.]],
[[ 8., 9., 10.],
[ 12., 13., 14.]]]),
array([[[ 3.],
[ 7.]],
[[ 11.],
[ 15.]]]),
array([], dtype=float64)]
dstack(tup)
Stack arrays in sequence depth wise (along third axis).
Takes a sequence of arrays and stack them along the third axis
to make a single array. Rebuilds arrays divided by `dsplit`.
This is a simple way to stack 2D arrays (images) into a single
3D array for processing.
Parameters
----------
tup : sequence of arrays
Arrays to stack. All of them must have the same shape along all
but the third axis.
Returns
-------
stacked : ndarray
The array formed by stacking the given arrays.
See Also
--------
stack : Join a sequence of arrays along a new axis.
vstack : Stack along first axis.
hstack : Stack along second axis.
concatenate : Join a sequence of arrays along an existing axis.
dsplit : Split array along third axis.
Notes
-----
Equivalent to ``np.concatenate(tup, axis=2)``.
Examples
--------
a = np.array((1,2,3))
b = np.array((2,3,4))
np.dstack((a,b))
array([[[1, 2],
[2, 3],
[3, 4]]])
a = np.array([[1],[2],[3]])
b = np.array([[2],[3],[4]])
np.dstack((a,b))
array([[[1, 2]],
[[2, 3]],
[[3, 4]]])
ediff1d(ary, to_end=None, to_begin=None)
The differences between consecutive elements of an array.
Parameters
----------
ary : array_like
If necessary, will be flattened before the differences are taken.
to_end : array_like, optional
Number(s) to append at the end of the returned differences.
to_begin : array_like, optional
Number(s) to prepend at the beginning of the returned differences.
Returns
-------
ediff1d : ndarray
The differences. Loosely, this is ``ary.flat[1:] - ary.flat[:-1]``.
See Also
--------
diff, gradient
Notes
-----
When applied to masked arrays, this function drops the mask information
if the `to_begin` and/or `to_end` parameters are used.
Examples
--------
x = np.array([1, 2, 4, 7, 0])
np.ediff1d(x)
array([ 1, 2, 3, -7])
np.ediff1d(x, to_begin=-99, to_end=np.array([88, 99]))
array([-99, 1, 2, 3, -7, 88, 99])
The returned array is always 1D.
y = [[1, 2, 4], [1, 6, 24]]
np.ediff1d(y)
array([ 1, 2, -3, 5, 18])
einsum(...)
einsum(subscripts, *operands, out=None, dtype=None, order='K', casting='safe')
Evaluates the Einstein summation convention on the operands.
Using the Einstein summation convention, many common multi-dimensional
array operations can be represented in a simple fashion. This function
provides a way compute such summations. The best way to understand this
function is to try the examples below, which show how many common NumPy
functions can be implemented as calls to `einsum`.
Parameters
----------
subscripts : str
Specifies the subscripts for summation.
operands : list of array_like
These are the arrays for the operation.
out : ndarray, optional
If provided, the calculation is done into this array.
dtype : data-type, optional
If provided, forces the calculation to use the data type specified.
Note that you may have to also give a more liberal `casting`
parameter to allow the conversions.
order : {'C', 'F', 'A', 'K'}, optional
Controls the memory layout of the output. 'C' means it should
be C contiguous. 'F' means it should be Fortran contiguous,
'A' means it should be 'F' if the inputs are all 'F', 'C' otherwise.
'K' means it should be as close to the layout as the inputs as
is possible, including arbitrarily permuted axes.
Default is 'K'.
casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
Controls what kind of data casting may occur. Setting this to
'unsafe' is not recommended, as it can adversely affect accumulations.
* 'no' means the data types should not be cast at all.
* 'equiv' means only byte-order changes are allowed.
* 'safe' means only casts which can preserve values are allowed.
* 'same_kind' means only safe casts or casts within a kind,
like float64 to float32, are allowed.
* 'unsafe' means any data conversions may be done.
Returns
-------
output : ndarray
The calculation based on the Einstein summation convention.
See Also
--------
dot, inner, outer, tensordot
Notes
-----
.. versionadded:: 1.6.0
The subscripts string is a comma-separated list of subscript labels,
where each label refers to a dimension of the corresponding operand.
Repeated subscripts labels in one operand take the diagonal. For example,
``np.einsum('ii', a)`` is equivalent to ``np.trace(a)``.
Whenever a label is repeated, it is summed, so ``np.einsum('i,i', a, b)``
is equivalent to ``np.inner(a,b)``. If a label appears only once,
it is not summed, so ``np.einsum('i', a)`` produces a view of ``a``
with no changes.
The order of labels in the output is by default alphabetical. This
means that ``np.einsum('ij', a)`` doesn't affect a 2D array, while
``np.einsum('ji', a)`` takes its transpose.
The output can be controlled by specifying output subscript labels
as well. This specifies the label order, and allows summing to
be disallowed or forced when desired. The call ``np.einsum('i->', a)``
is like ``np.sum(a, axis=-1)``, and ``np.einsum('ii->i', a)``
is like ``np.diag(a)``. The difference is that `einsum` does not
allow broadcasting by default.
To enable and control broadcasting, use an ellipsis. Default
NumPy-style broadcasting is done by adding an ellipsis
to the left of each term, like ``np.einsum('...ii->...i', a)``.
To take the trace along the first and last axes,
you can do ``np.einsum('i...i', a)``, or to do a matrix-matrix
product with the left-most indices instead of rightmost, you can do
``np.einsum('ij...,jk...->ik...', a, b)``.
When there is only one operand, no axes are summed, and no output
parameter is provided, a view into the operand is returned instead
of a new array. Thus, taking the diagonal as ``np.einsum('ii->i', a)``
produces a view.
An alternative way to provide the subscripts and operands is as
``einsum(op0, sublist0, op1, sublist1, ..., [sublistout])``. The examples
below have corresponding `einsum` calls with the two parameter methods.
.. versionadded:: 1.10.0
Views returned from einsum are now writeable whenever the input array
is writeable. For example, ``np.einsum('ijk...->kji...', a)`` will now
have the same effect as ``np.swapaxes(a, 0, 2)`` and
``np.einsum('ii->i', a)`` will return a writeable view of the diagonal
of a 2D array.
Examples
--------
a = np.arange(25).reshape(5,5)
b = np.arange(5)
c = np.arange(6).reshape(2,3)
np.einsum('ii', a)
60
np.einsum(a, [0,0])
60
np.trace(a)
60
np.einsum('ii->i', a)
array([ 0, 6, 12, 18, 24])
np.einsum(a, [0,0], [0])
array([ 0, 6, 12, 18, 24])
np.diag(a)
array([ 0, 6, 12, 18, 24])
np.einsum('ij,j', a, b)
array([ 30, 80, 130, 180, 230])
np.einsum(a, [0,1], b, [1])
array([ 30, 80, 130, 180, 230])
np.dot(a, b)
array([ 30, 80, 130, 180, 230])
np.einsum('...j,j', a, b)
array([ 30, 80, 130, 180, 230])
np.einsum('ji', c)
array([[0, 3],
[1, 4],
[2, 5]])
np.einsum(c, [1,0])
array([[0, 3],
[1, 4],
[2, 5]])
c.T
array([[0, 3],
[1, 4],
[2, 5]])
np.einsum('..., ...', 3, c)
array([[ 0, 3, 6],
[ 9, 12, 15]])
np.einsum(3, [Ellipsis], c, [Ellipsis])
array([[ 0, 3, 6],
[ 9, 12, 15]])
np.multiply(3, c)
array([[ 0, 3, 6],
[ 9, 12, 15]])
np.einsum('i,i', b, b)
30
np.einsum(b, [0], b, [0])
30
np.inner(b,b)
30
np.einsum('i,j', np.arange(2)+1, b)
array([[0, 1, 2, 3, 4],
[0, 2, 4, 6, 8]])
np.einsum(np.arange(2)+1, [0], b, [1])
array([[0, 1, 2, 3, 4],
[0, 2, 4, 6, 8]])
np.outer(np.arange(2)+1, b)
array([[0, 1, 2, 3, 4],
[0, 2, 4, 6, 8]])
np.einsum('i...->...', a)
array([50, 55, 60, 65, 70])
np.einsum(a, [0,Ellipsis], [Ellipsis])
array([50, 55, 60, 65, 70])
np.sum(a, axis=0)
array([50, 55, 60, 65, 70])
a = np.arange(60.).reshape(3,4,5)
b = np.arange(24.).reshape(4,3,2)
np.einsum('ijk,jil->kl', a, b)
array([[ 4400., 4730.],
[ 4532., 4874.],
[ 4664., 5018.],
[ 4796., 5162.],
[ 4928., 5306.]])
np.einsum(a, [0,1,2], b, [1,0,3], [2,3])
array([[ 4400., 4730.],
[ 4532., 4874.],
[ 4664., 5018.],
[ 4796., 5162.],
[ 4928., 5306.]])
np.tensordot(a,b, axes=([1,0],[0,1]))
array([[ 4400., 4730.],
[ 4532., 4874.],
[ 4664., 5018.],
[ 4796., 5162.],
[ 4928., 5306.]])
a = np.arange(6).reshape((3,2))
b = np.arange(12).reshape((4,3))
np.einsum('ki,jk->ij', a, b)
array([[10, 28, 46, 64],
[13, 40, 67, 94]])
np.einsum('ki,...k->i...', a, b)
array([[10, 28, 46, 64],
[13, 40, 67, 94]])
np.einsum('k...,jk', a, b)
array([[10, 28, 46, 64],
[13, 40, 67, 94]])
# since version 1.10.0
a = np.zeros((3, 3))
np.einsum('ii->i', a)[:] = 1
a
array([[ 1., 0., 0.],
[ 0., 1., 0.],
[ 0., 0., 1.]])
empty(...)
empty(shape, dtype=float, order='C')
Return a new array of given shape and type, without initializing entries.
Parameters
----------
shape : int or tuple of int
Shape of the empty array
dtype : data-type, optional
Desired output data-type.
order : {'C', 'F'}, optional
Whether to store multi-dimensional data in row-major
(C-style) or column-major (Fortran-style) order in
memory.
Returns
-------
out : ndarray
Array of uninitialized (arbitrary) data with the given
shape, dtype, and order.
See Also
--------
empty_like, zeros, ones
Notes
-----
`empty`, unlike `zeros`, does not set the array values to zero,
and may therefore be marginally faster. On the other hand, it requires
the user to manually set all the values in the array, and should be
used with caution.
Examples
--------
np.empty([2, 2])
array([[ -9.74499359e+001, 6.69583040e-309],
[ 2.13182611e-314, 3.06959433e-309]]) #random
np.empty([2, 2], dtype=int)
array([[-1073741821, -1067949133],
[ 496041986, 19249760]]) #random
empty_like(...)
empty_like(a, dtype=None, order='K', subok=True)
Return a new array with the same shape and type as a given array.
Parameters
----------
a : array_like
The shape and data-type of `a` define these same attributes of the
returned array.
dtype : data-type, optional
Overrides the data type of the result.
.. versionadded:: 1.6.0
order : {'C', 'F', 'A', or 'K'}, optional
Overrides the memory layout of the result. 'C' means C-order,
'F' means F-order, 'A' means 'F' if ``a`` is Fortran contiguous,
'C' otherwise. 'K' means match the layout of ``a`` as closely
as possible.
.. versionadded:: 1.6.0
subok : bool, optional.
If True, then the newly created array will use the sub-class
type of 'a', otherwise it will be a base-class array. Defaults
to True.
Returns
-------
out : ndarray
Array of uninitialized (arbitrary) data with the same
shape and type as `a`.
See Also
--------
ones_like : Return an array of ones with shape and type of input.
zeros_like : Return an array of zeros with shape and type of input.
empty : Return a new uninitialized array.
ones : Return a new array setting values to one.
zeros : Return a new array setting values to zero.
Notes
-----
This function does *not* initialize the returned array; to do that use
`zeros_like` or `ones_like` instead. It may be marginally faster than
the functions that do set the array values.
Examples
--------
a = ([1,2,3], [4,5,6]) # a is array-like
np.empty_like(a)
array([[-1073741821, -1073741821, 3], #random
[ 0, 0, -1073741821]])
a = np.array([[1., 2., 3.],[4.,5.,6.]])
np.empty_like(a)
array([[ -2.00000715e+000, 1.48219694e-323, -2.00000572e+000],#random
[ 4.38791518e-305, -2.00000715e+000, 4.17269252e-309]])
expand_dims(a, axis)
Expand the shape of an array.
Insert a new axis, corresponding to a given position in the array shape.
Parameters
----------
a : array_like
Input array.
axis : int
Position (amongst axes) where new axis is to be inserted.
Returns
-------
res : ndarray
Output array. The number of dimensions is one greater than that of
the input array.
See Also
--------
doc.indexing, atleast_1d, atleast_2d, atleast_3d
Examples
--------
x = np.array([1,2])
x.shape
(2,)
The following is equivalent to ``x[np.newaxis,:]`` or ``x[np.newaxis]``:
y = np.expand_dims(x, axis=0)
y
array([[1, 2]])
y.shape
(1, 2)
y = np.expand_dims(x, axis=1) # Equivalent to x[:,newaxis]
y
array([[1],
[2]])
y.shape
(2, 1)
Note that some examples may use ``None`` instead of ``np.newaxis``. These
are the same objects:
np.newaxis is None
True
extract(condition, arr)
Return the elements of an array that satisfy some condition.
This is equivalent to ``np.compress(ravel(condition), ravel(arr))``. If
`condition` is boolean ``np.extract`` is equivalent to ``arr[condition]``.
Note that `place` does the exact opposite of `extract`.
Parameters
----------
condition : array_like
An array whose nonzero or True entries indicate the elements of `arr`
to extract.
arr : array_like
Input array of the same size as `condition`.
Returns
-------
extract : ndarray
Rank 1 array of values from `arr` where `condition` is True.
See Also
--------
take, put, copyto, compress, place
Examples
--------
arr = np.arange(12).reshape((3, 4))
arr
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
condition = np.mod(arr, 3)==0
condition
array([[ True, False, False, True],
[False, False, True, False],
[False, True, False, False]], dtype=bool)
np.extract(condition, arr)
array([0, 3, 6, 9])
If `condition` is boolean:
arr[condition]
array([0, 3, 6, 9])
eye(N, M=None, k=0, dtype=)
Return a 2-D array with ones on the diagonal and zeros elsewhere.
Parameters
----------
N : int
Number of rows in the output.
M : int, optional
Number of columns in the output. If None, defaults to `N`.
k : int, optional
Index of the diagonal: 0 (the default) refers to the main diagonal,
a positive value refers to an upper diagonal, and a negative value
to a lower diagonal.
dtype : data-type, optional
Data-type of the returned array.
Returns
-------
I : ndarray of shape (N,M)
An array where all elements are equal to zero, except for the `k`-th
diagonal, whose values are equal to one.
See Also
--------
identity : (almost) equivalent function
diag : diagonal 2-D array from a 1-D array specified by the user.
Examples
--------
np.eye(2, dtype=int)
array([[1, 0],
[0, 1]])
np.eye(3, k=1)
array([[ 0., 1., 0.],
[ 0., 0., 1.],
[ 0., 0., 0.]])
fastCopyAndTranspose = _fastCopyAndTranspose(...)
_fastCopyAndTranspose(a)
fill_diagonal(a, val, wrap=False)
Fill the main diagonal of the given array of any dimensionality.
For an array `a` with ``a.ndim > 2``, the diagonal is the list of
locations with indices ``a[i, i, ..., i]`` all identical. This function
modifies the input array in-place, it does not return a value.
Parameters
----------
a : array, at least 2-D.
Array whose diagonal is to be filled, it gets modified in-place.
val : scalar
Value to be written on the diagonal, its type must be compatible with
that of the array a.
wrap : bool
For tall matrices in NumPy version up to 1.6.2, the
diagonal "wrapped" after N columns. You can have this behavior
with this option. This affect only tall matrices.
See also
--------
diag_indices, diag_indices_from
Notes
-----
.. versionadded:: 1.4.0
This functionality can be obtained via `diag_indices`, but internally
this version uses a much faster implementation that never constructs the
indices and uses simple slicing.
Examples
--------
a = np.zeros((3, 3), int)
np.fill_diagonal(a, 5)
a
array([[5, 0, 0],
[0, 5, 0],
[0, 0, 5]])
The same function can operate on a 4-D array:
a = np.zeros((3, 3, 3, 3), int)
np.fill_diagonal(a, 4)
We only show a few blocks for clarity:
a[0, 0]
array([[4, 0, 0],
[0, 0, 0],
[0, 0, 0]])
a[1, 1]
array([[0, 0, 0],
[0, 4, 0],
[0, 0, 0]])
a[2, 2]
array([[0, 0, 0],
[0, 0, 0],
[0, 0, 4]])
The wrap option affects only tall matrices:
# tall matrices no wrap
a = np.zeros((5, 3),int)
fill_diagonal(a, 4)
a
array([[4, 0, 0],
[0, 4, 0],
[0, 0, 4],
[0, 0, 0],
[0, 0, 0]])
# tall matrices wrap
a = np.zeros((5, 3),int)
fill_diagonal(a, 4, wrap=True)
a
array([[4, 0, 0],
[0, 4, 0],
[0, 0, 4],
[0, 0, 0],
[4, 0, 0]])
# wide matrices
a = np.zeros((3, 5),int)
fill_diagonal(a, 4, wrap=True)
a
array([[4, 0, 0, 0, 0],
[0, 4, 0, 0, 0],
[0, 0, 4, 0, 0]])
find_common_type(array_types, scalar_types)
Determine common type following standard coercion rules.
Parameters
----------
array_types : sequence
A list of dtypes or dtype convertible objects representing arrays.
scalar_types : sequence
A list of dtypes or dtype convertible objects representing scalars.
Returns
-------
datatype : dtype
The common data type, which is the maximum of `array_types` ignoring
`scalar_types`, unless the maximum of `scalar_types` is of a
different kind (`dtype.kind`). If the kind is not understood, then
None is returned.
See Also
--------
dtype, common_type, can_cast, mintypecode
Examples
--------
np.find_common_type([], [np.int64, np.float32, np.complex])
dtype('complex128')
np.find_common_type([np.int64, np.float32], [])
dtype('float64')
The standard casting rules ensure that a scalar cannot up-cast an
array unless the scalar is of a fundamentally different kind of data
(i.e. under a different hierarchy in the data type hierarchy) then
the array:
np.find_common_type([np.float32], [np.int64, np.float64])
dtype('float32')
Complex is of a different type, so it up-casts the float in the
`array_types` argument:
np.find_common_type([np.float32], [np.complex])
dtype('complex128')
Type specifier strings are convertible to dtypes and can therefore
be used instead of dtypes:
np.find_common_type(['f4', 'f4', 'i4'], ['c8'])
dtype('complex128')
fix(x, y=None)
Round to nearest integer towards zero.
Round an array of floats element-wise to nearest integer towards zero.
The rounded values are returned as floats.
Parameters
----------
x : array_like
An array of floats to be rounded
y : ndarray, optional
Output array
Returns
-------
out : ndarray of floats
The array of rounded numbers
See Also
--------
trunc, floor, ceil
around : Round to given number of decimals
Examples
--------
np.fix(3.14)
3.0
np.fix(3)
3.0
np.fix([2.1, 2.9, -2.1, -2.9])
array([ 2., 2., -2., -2.])
flatnonzero(a)
Return indices that are non-zero in the flattened version of a.
This is equivalent to a.ravel().nonzero()[0].
Parameters
----------
a : ndarray
Input array.
Returns
-------
res : ndarray
Output array, containing the indices of the elements of `a.ravel()`
that are non-zero.
See Also
--------
nonzero : Return the indices of the non-zero elements of the input array.
ravel : Return a 1-D array containing the elements of the input array.
Examples
--------
x = np.arange(-2, 3)
x
array([-2, -1, 0, 1, 2])
np.flatnonzero(x)
array([0, 1, 3, 4])
Use the indices of the non-zero elements as an index array to extract
these elements:
x.ravel()[np.flatnonzero(x)]
array([-2, -1, 1, 2])
fliplr(m)
Flip array in the left/right direction.
Flip the entries in each row in the left/right direction.
Columns are preserved, but appear in a different order than before.
Parameters
----------
m : array_like
Input array, must be at least 2-D.
Returns
-------
f : ndarray
A view of `m` with the columns reversed. Since a view
is returned, this operation is :math:`\mathcal O(1)`.
See Also
--------
flipud : Flip array in the up/down direction.
rot90 : Rotate array counterclockwise.
Notes
-----
Equivalent to A[:,::-1]. Requires the array to be at least 2-D.
Examples
--------
A = np.diag([1.,2.,3.])
A
array([[ 1., 0., 0.],
[ 0., 2., 0.],
[ 0., 0., 3.]])
np.fliplr(A)
array([[ 0., 0., 1.],
[ 0., 2., 0.],
[ 3., 0., 0.]])
A = np.random.randn(2,3,5)
np.all(np.fliplr(A)==A[:,::-1,...])
True
flipud(m)
Flip array in the up/down direction.
Flip the entries in each column in the up/down direction.
Rows are preserved, but appear in a different order than before.
Parameters
----------
m : array_like
Input array.
Returns
-------
out : array_like
A view of `m` with the rows reversed. Since a view is
returned, this operation is :math:`\mathcal O(1)`.
See Also
--------
fliplr : Flip array in the left/right direction.
rot90 : Rotate array counterclockwise.
Notes
-----
Equivalent to ``A[::-1,...]``.
Does not require the array to be two-dimensional.
Examples
--------
A = np.diag([1.0, 2, 3])
A
array([[ 1., 0., 0.],
[ 0., 2., 0.],
[ 0., 0., 3.]])
np.flipud(A)
array([[ 0., 0., 3.],
[ 0., 2., 0.],
[ 1., 0., 0.]])
A = np.random.randn(2,3,5)
np.all(np.flipud(A)==A[::-1,...])
True
np.flipud([1,2])
array([2, 1])
frombuffer(...)
frombuffer(buffer, dtype=float, count=-1, offset=0)
Interpret a buffer as a 1-dimensional array.
Parameters
----------
buffer : buffer_like
An object that exposes the buffer interface.
dtype : data-type, optional
Data-type of the returned array; default: float.
count : int, optional
Number of items to read. ``-1`` means all data in the buffer.
offset : int, optional
Start reading the buffer from this offset; default: 0.
Notes
-----
If the buffer has data that is not in machine byte-order, this should
be specified as part of the data-type, e.g.::
dt = np.dtype(int)
dt = dt.newbyteorder('>')
np.frombuffer(buf, dtype=dt)
The data of the resulting array will not be byteswapped, but will be
interpreted correctly.
Examples
--------
s = 'hello world'
np.frombuffer(s, dtype='S1', count=5, offset=6)
array(['w', 'o', 'r', 'l', 'd'],
dtype='|S1')
fromfile(...)
fromfile(file, dtype=float, count=-1, sep='')
Construct an array from data in a text or binary file.
A highly efficient way of reading binary data with a known data-type,
as well as parsing simply formatted text files. Data written using the
`tofile` method can be read using this function.
Parameters
----------
file : file or str
Open file object or filename.
dtype : data-type
Data type of the returned array.
For binary files, it is used to determine the size and byte-order
of the items in the file.
count : int
Number of items to read. ``-1`` means all items (i.e., the complete
file).
sep : str
Separator between items if file is a text file.
Empty ("") separator means the file should be treated as binary.
Spaces (" ") in the separator match zero or more whitespace characters.
A separator consisting only of spaces must match at least one
whitespace.
See also
--------
load, save
ndarray.tofile
loadtxt : More flexible way of loading data from a text file.
Notes
-----
Do not rely on the combination of `tofile` and `fromfile` for
data storage, as the binary files generated are are not platform
independent. In particular, no byte-order or data-type information is
saved. Data can be stored in the platform independent ``.npy`` format
using `save` and `load` instead.
Examples
--------
Construct an ndarray:
dt = np.dtype([('time', [('min', int), ('sec', int)]),
('temp', float)])
x = np.zeros((1,), dtype=dt)
x['time']['min'] = 10; x['temp'] = 98.25
x
array([((10, 0), 98.25)],
dtype=[('time', [('min', ', comments='#', delimiter=None, skip_header=0, skip_footer=0, converters=None, missing_values=None, filling_values=None, usecols=None, names=None, excludelist=None, deletechars=None, replace_space='_', autostrip=False, case_sensitive=True, defaultfmt='f%i', unpack=None, usemask=False, loose=True, invalid_raise=True, max_rows=None)
Load data from a text file, with missing values handled as specified.
Each line past the first `skip_header` lines is split at the `delimiter`
character, and characters following the `comments` character are discarded.
Parameters
----------
fname : file or str
File, filename, or generator to read. If the filename extension is
`.gz` or `.bz2`, the file is first decompressed. Note that
generators must return byte strings in Python 3k.
dtype : dtype, optional
Data type of the resulting array.
If None, the dtypes will be determined by the contents of each
column, individually.
comments : str, optional
The character used to indicate the start of a comment.
All the characters occurring on a line after a comment are discarded
delimiter : str, int, or sequence, optional
The string used to separate values. By default, any consecutive
whitespaces act as delimiter. An integer or sequence of integers
can also be provided as width(s) of each field.
skiprows : int, optional
`skiprows` was removed in numpy 1.10. Please use `skip_header` instead.
skip_header : int, optional
The number of lines to skip at the beginning of the file.
skip_footer : int, optional
The number of lines to skip at the end of the file.
converters : variable, optional
The set of functions that convert the data of a column to a value.
The converters can also be used to provide a default value
for missing data: ``converters = {3: lambda s: float(s or 0)}``.
missing : variable, optional
`missing` was removed in numpy 1.10. Please use `missing_values`
instead.
missing_values : variable, optional
The set of strings corresponding to missing data.
filling_values : variable, optional
The set of values to be used as default when the data are missing.
usecols : sequence, optional
Which columns to read, with 0 being the first. For example,
``usecols = (1, 4, 5)`` will extract the 2nd, 5th and 6th columns.
names : {None, True, str, sequence}, optional
If `names` is True, the field names are read from the first valid line
after the first `skip_header` lines.
If `names` is a sequence or a single-string of comma-separated names,
the names will be used to define the field names in a structured dtype.
If `names` is None, the names of the dtype fields will be used, if any.
excludelist : sequence, optional
A list of names to exclude. This list is appended to the default list
['return','file','print']. Excluded names are appended an underscore:
for example, `file` would become `file_`.
deletechars : str, optional
A string combining invalid characters that must be deleted from the
names.
defaultfmt : str, optional
A format used to define default field names, such as "f%i" or "f_%02i".
autostrip : bool, optional
Whether to automatically strip white spaces from the variables.
replace_space : char, optional
Character(s) used in replacement of white spaces in the variables
names. By default, use a '_'.
case_sensitive : {True, False, 'upper', 'lower'}, optional
If True, field names are case sensitive.
If False or 'upper', field names are converted to upper case.
If 'lower', field names are converted to lower case.
unpack : bool, optional
If True, the returned array is transposed, so that arguments may be
unpacked using ``x, y, z = loadtxt(...)``
usemask : bool, optional
If True, return a masked array.
If False, return a regular array.
loose : bool, optional
If True, do not raise errors for invalid values.
invalid_raise : bool, optional
If True, an exception is raised if an inconsistency is detected in the
number of columns.
If False, a warning is emitted and the offending lines are skipped.
max_rows : int, optional
The maximum number of rows to read. Must not be used with skip_footer
at the same time. If given, the value must be at least 1. Default is
to read the entire file.
.. versionadded:: 1.10.0
Returns
-------
out : ndarray
Data read from the text file. If `usemask` is True, this is a
masked array.
See Also
--------
numpy.loadtxt : equivalent function when no data is missing.
Notes
-----
* When spaces are used as delimiters, or when no delimiter has been given
as input, there should not be any missing data between two fields.
* When the variables are named (either by a flexible dtype or with `names`,
there must not be any header in the file (else a ValueError
exception is raised).
* Individual values are not stripped of spaces by default.
When using a custom converter, make sure the function does remove spaces.
References
----------
.. [1] Numpy User Guide, section `I/O with Numpy
`_.
Examples
---------
from io import StringIO
import numpy as np
Comma delimited file with mixed dtype
s = StringIO("1,1.3,abcde")
data = np.genfromtxt(s, dtype=[('myint','i8'),('myfloat','f8'),
('mystring','S5')], delimiter=",")
data
array((1, 1.3, 'abcde'),
dtype=[('myint', '
getbufsize()
Return the size of the buffer used in ufuncs.
Returns
-------
getbufsize : int
Size of ufunc buffer in bytes.
geterr()
Get the current way of handling floating-point errors.
Returns
-------
res : dict
A dictionary with keys "divide", "over", "under", and "invalid",
whose values are from the strings "ignore", "print", "log", "warn",
"raise", and "call". The keys represent possible floating-point
exceptions, and the values define how these exceptions are handled.
See Also
--------
geterrcall, seterr, seterrcall
Notes
-----
For complete documentation of the types of floating-point exceptions and
treatment options, see `seterr`.
Examples
--------
np.geterr()
{'over': 'warn', 'divide': 'warn', 'invalid': 'warn',
'under': 'ignore'}
np.arange(3.) / np.arange(3.)
array([ NaN, 1., 1.])
oldsettings = np.seterr(all='warn', over='raise')
np.geterr()
{'over': 'raise', 'divide': 'warn', 'invalid': 'warn', 'under': 'warn'}
np.arange(3.) / np.arange(3.)
__main__:1: RuntimeWarning: invalid value encountered in divide
array([ NaN, 1., 1.])
geterrcall()
Return the current callback function used on floating-point errors.
When the error handling for a floating-point error (one of "divide",
"over", "under", or "invalid") is set to 'call' or 'log', the function
that is called or the log instance that is written to is returned by
`geterrcall`. This function or log instance has been set with
`seterrcall`.
Returns
-------
errobj : callable, log instance or None
The current error handler. If no handler was set through `seterrcall`,
``None`` is returned.
See Also
--------
seterrcall, seterr, geterr
Notes
-----
For complete documentation of the types of floating-point exceptions and
treatment options, see `seterr`.
Examples
--------
np.geterrcall() # we did not yet set a handler, returns None
oldsettings = np.seterr(all='call')
def err_handler(type, flag):
print "Floating point error (%s), with flag %s" % (type, flag)
oldhandler = np.seterrcall(err_handler)
np.array([1, 2, 3]) / 0.0
Floating point error (divide by zero), with flag 1
array([ Inf, Inf, Inf])
cur_handler = np.geterrcall()
cur_handler is err_handler
True
geterrobj(...)
geterrobj()
Return the current object that defines floating-point error handling.
The error object contains all information that defines the error handling
behavior in Numpy. `geterrobj` is used internally by the other
functions that get and set error handling behavior (`geterr`, `seterr`,
`geterrcall`, `seterrcall`).
Returns
-------
errobj : list
The error object, a list containing three elements:
[internal numpy buffer size, error mask, error callback function].
The error mask is a single integer that holds the treatment information
on all four floating point errors. The information for each error type
is contained in three bits of the integer. If we print it in base 8, we
can see what treatment is set for "invalid", "under", "over", and
"divide" (in that order). The printed string can be interpreted with
* 0 : 'ignore'
* 1 : 'warn'
* 2 : 'raise'
* 3 : 'call'
* 4 : 'print'
* 5 : 'log'
See Also
--------
seterrobj, seterr, geterr, seterrcall, geterrcall
getbufsize, setbufsize
Notes
-----
For complete documentation of the types of floating-point exceptions and
treatment options, see `seterr`.
Examples
--------
np.geterrobj() # first get the defaults
[10000, 0, None]
def err_handler(type, flag):
print "Floating point error (%s), with flag %s" % (type, flag)
...
old_bufsize = np.setbufsize(20000)
old_err = np.seterr(divide='raise')
old_handler = np.seterrcall(err_handler)
np.geterrobj()
[20000, 2, ]
old_err = np.seterr(all='ignore')
np.base_repr(np.geterrobj()[1], 8)
'0'
old_err = np.seterr(divide='warn', over='log', under='call',
invalid='print')
np.base_repr(np.geterrobj()[1], 8)
'4351'
gradient(f, *varargs, **kwargs)
Return the gradient of an N-dimensional array.
The gradient is computed using second order accurate central differences
in the interior and either first differences or second order accurate
one-sides (forward or backwards) differences at the boundaries. The
returned gradient hence has the same shape as the input array.
Parameters
----------
f : array_like
An N-dimensional array containing samples of a scalar function.
varargs : list of scalar, optional
N scalars specifying the sample distances for each dimension,
i.e. `dx`, `dy`, `dz`, ... Default distance: 1.
edge_order : {1, 2}, optional
Gradient is calculated using N\ :sup:`th` order accurate differences
at the boundaries. Default: 1.
.. versionadded:: 1.9.1
Returns
-------
gradient : list of ndarray
Each element of `list` has the same shape as `f` giving the derivative
of `f` with respect to each dimension.
Examples
--------
x = np.array([1, 2, 4, 7, 11, 16], dtype=np.float)
np.gradient(x)
array([ 1. , 1.5, 2.5, 3.5, 4.5, 5. ])
np.gradient(x, 2)
array([ 0.5 , 0.75, 1.25, 1.75, 2.25, 2.5 ])
For two dimensional arrays, the return will be two arrays ordered by
axis. In this example the first array stands for the gradient in
rows and the second one in columns direction:
np.gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=np.float))
[array([[ 2., 2., -1.],
[ 2., 2., -1.]]), array([[ 1. , 2.5, 4. ],
[ 1. , 1. , 1. ]])]
x = np.array([0, 1, 2, 3, 4])
dx = np.gradient(x)
y = x**2
np.gradient(y, dx, edge_order=2)
array([-0., 2., 4., 6., 8.])
hamming(M)
Return the Hamming window.
The Hamming window is a taper formed by using a weighted cosine.
Parameters
----------
M : int
Number of points in the output window. If zero or less, an
empty array is returned.
Returns
-------
out : ndarray
The window, with the maximum value normalized to one (the value
one appears only if the number of samples is odd).
See Also
--------
bartlett, blackman, hanning, kaiser
Notes
-----
The Hamming window is defined as
.. math:: w(n) = 0.54 - 0.46cos\left(\frac{2\pi{n}}{M-1}\right)
\qquad 0 \leq n \leq M-1
The Hamming was named for R. W. Hamming, an associate of J. W. Tukey
and is described in Blackman and Tukey. It was recommended for
smoothing the truncated autocovariance function in the time domain.
Most references to the Hamming window come from the signal processing
literature, where it is used as one of many windowing functions for
smoothing values. It is also known as an apodization (which means
"removing the foot", i.e. smoothing discontinuities at the beginning
and end of the sampled signal) or tapering function.
References
----------
.. [1] Blackman, R.B. and Tukey, J.W., (1958) The measurement of power
spectra, Dover Publications, New York.
.. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics", The
University of Alberta Press, 1975, pp. 109-110.
.. [3] Wikipedia, "Window function",
http://en.wikipedia.org/wiki/Window_function
.. [4] W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling,
"Numerical Recipes", Cambridge University Press, 1986, page 425.
Examples
--------
np.hamming(12)
array([ 0.08 , 0.15302337, 0.34890909, 0.60546483, 0.84123594,
0.98136677, 0.98136677, 0.84123594, 0.60546483, 0.34890909,
0.15302337, 0.08 ])
Plot the window and the frequency response:
from numpy.fft import fft, fftshift
window = np.hamming(51)
plt.plot(window)
[]
plt.title("Hamming window")
plt.ylabel("Amplitude")
plt.xlabel("Sample")
plt.show()
plt.figure()
A = fft(window, 2048) / 25.5
mag = np.abs(fftshift(A))
freq = np.linspace(-0.5, 0.5, len(A))
response = 20 * np.log10(mag)
response = np.clip(response, -100, 100)
plt.plot(freq, response)
[]
plt.title("Frequency response of Hamming window")
plt.ylabel("Magnitude [dB]")
plt.xlabel("Normalized frequency [cycles per sample]")
plt.axis('tight')
(-0.5, 0.5, -100.0, ...)
plt.show()
hanning(M)
Return the Hanning window.
The Hanning window is a taper formed by using a weighted cosine.
Parameters
----------
M : int
Number of points in the output window. If zero or less, an
empty array is returned.
Returns
-------
out : ndarray, shape(M,)
The window, with the maximum value normalized to one (the value
one appears only if `M` is odd).
See Also
--------
bartlett, blackman, hamming, kaiser
Notes
-----
The Hanning window is defined as
.. math:: w(n) = 0.5 - 0.5cos\left(\frac{2\pi{n}}{M-1}\right)
\qquad 0 \leq n \leq M-1
The Hanning was named for Julius von Hann, an Austrian meteorologist.
It is also known as the Cosine Bell. Some authors prefer that it be
called a Hann window, to help avoid confusion with the very similar
Hamming window.
Most references to the Hanning window come from the signal processing
literature, where it is used as one of many windowing functions for
smoothing values. It is also known as an apodization (which means
"removing the foot", i.e. smoothing discontinuities at the beginning
and end of the sampled signal) or tapering function.
References
----------
.. [1] Blackman, R.B. and Tukey, J.W., (1958) The measurement of power
spectra, Dover Publications, New York.
.. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics",
The University of Alberta Press, 1975, pp. 106-108.
.. [3] Wikipedia, "Window function",
http://en.wikipedia.org/wiki/Window_function
.. [4] W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling,
"Numerical Recipes", Cambridge University Press, 1986, page 425.
Examples
--------
np.hanning(12)
array([ 0. , 0.07937323, 0.29229249, 0.57115742, 0.82743037,
0.97974649, 0.97974649, 0.82743037, 0.57115742, 0.29229249,
0.07937323, 0. ])
Plot the window and its frequency response:
from numpy.fft import fft, fftshift
window = np.hanning(51)
plt.plot(window)
[]
plt.title("Hann window")
plt.ylabel("Amplitude")
plt.xlabel("Sample")
plt.show()
plt.figure()
A = fft(window, 2048) / 25.5
mag = np.abs(fftshift(A))
freq = np.linspace(-0.5, 0.5, len(A))
response = 20 * np.log10(mag)
response = np.clip(response, -100, 100)
plt.plot(freq, response)
[]
plt.title("Frequency response of the Hann window")
plt.ylabel("Magnitude [dB]")
plt.xlabel("Normalized frequency [cycles per sample]")
plt.axis('tight')
(-0.5, 0.5, -100.0, ...)
plt.show()
histogram(a, bins=10, range=None, normed=False, weights=None, density=None)
Compute the histogram of a set of data.
Parameters
----------
a : array_like
Input data. The histogram is computed over the flattened array.
bins : int or sequence of scalars, optional
If `bins` is an int, it defines the number of equal-width
bins in the given range (10, by default). If `bins` is a sequence,
it defines the bin edges, including the rightmost edge, allowing
for non-uniform bin widths.
range : (float, float), optional
The lower and upper range of the bins. If not provided, range
is simply ``(a.min(), a.max())``. Values outside the range are
ignored.
normed : bool, optional
This keyword is deprecated in Numpy 1.6 due to confusing/buggy
behavior. It will be removed in Numpy 2.0. Use the density keyword
instead.
If False, the result will contain the number of samples
in each bin. If True, the result is the value of the
probability *density* function at the bin, normalized such that
the *integral* over the range is 1. Note that this latter behavior is
known to be buggy with unequal bin widths; use `density` instead.
weights : array_like, optional
An array of weights, of the same shape as `a`. Each value in `a`
only contributes its associated weight towards the bin count
(instead of 1). If `normed` is True, the weights are normalized,
so that the integral of the density over the range remains 1
density : bool, optional
If False, the result will contain the number of samples
in each bin. If True, the result is the value of the
probability *density* function at the bin, normalized such that
the *integral* over the range is 1. Note that the sum of the
histogram values will not be equal to 1 unless bins of unity
width are chosen; it is not a probability *mass* function.
Overrides the `normed` keyword if given.
Returns
-------
hist : array
The values of the histogram. See `normed` and `weights` for a
description of the possible semantics.
bin_edges : array of dtype float
Return the bin edges ``(length(hist)+1)``.
See Also
--------
histogramdd, bincount, searchsorted, digitize
Notes
-----
All but the last (righthand-most) bin is half-open. In other words, if
`bins` is::
[1, 2, 3, 4]
then the first bin is ``[1, 2)`` (including 1, but excluding 2) and the
second ``[2, 3)``. The last bin, however, is ``[3, 4]``, which *includes*
4.
Examples
--------
np.histogram([1, 2, 1], bins=[0, 1, 2, 3])
(array([0, 2, 1]), array([0, 1, 2, 3]))
np.histogram(np.arange(4), bins=np.arange(5), density=True)
(array([ 0.25, 0.25, 0.25, 0.25]), array([0, 1, 2, 3, 4]))
np.histogram([[1, 2, 1], [1, 0, 1]], bins=[0,1,2,3])
(array([1, 4, 1]), array([0, 1, 2, 3]))
a = np.arange(5)
hist, bin_edges = np.histogram(a, density=True)
hist
array([ 0.5, 0. , 0.5, 0. , 0. , 0.5, 0. , 0.5, 0. , 0.5])
hist.sum()
2.4999999999999996
np.sum(hist*np.diff(bin_edges))
1.0
histogram2d(x, y, bins=10, range=None, normed=False, weights=None)
Compute the bi-dimensional histogram of two data samples.
Parameters
----------
x : array_like, shape (N,)
An array containing the x coordinates of the points to be
histogrammed.
y : array_like, shape (N,)
An array containing the y coordinates of the points to be
histogrammed.
bins : int or array_like or [int, int] or [array, array], optional
The bin specification:
* If int, the number of bins for the two dimensions (nx=ny=bins).
* If array_like, the bin edges for the two dimensions
(x_edges=y_edges=bins).
* If [int, int], the number of bins in each dimension
(nx, ny = bins).
* If [array, array], the bin edges in each dimension
(x_edges, y_edges = bins).
* A combination [int, array] or [array, int], where int
is the number of bins and array is the bin edges.
range : array_like, shape(2,2), optional
The leftmost and rightmost edges of the bins along each dimension
(if not specified explicitly in the `bins` parameters):
``[[xmin, xmax], [ymin, ymax]]``. All values outside of this range
will be considered outliers and not tallied in the histogram.
normed : bool, optional
If False, returns the number of samples in each bin. If True,
returns the bin density ``bin_count / sample_count / bin_area``.
weights : array_like, shape(N,), optional
An array of values ``w_i`` weighing each sample ``(x_i, y_i)``.
Weights are normalized to 1 if `normed` is True. If `normed` is
False, the values of the returned histogram are equal to the sum of
the weights belonging to the samples falling into each bin.
Returns
-------
H : ndarray, shape(nx, ny)
The bi-dimensional histogram of samples `x` and `y`. Values in `x`
are histogrammed along the first dimension and values in `y` are
histogrammed along the second dimension.
xedges : ndarray, shape(nx,)
The bin edges along the first dimension.
yedges : ndarray, shape(ny,)
The bin edges along the second dimension.
See Also
--------
histogram : 1D histogram
histogramdd : Multidimensional histogram
Notes
-----
When `normed` is True, then the returned histogram is the sample
density, defined such that the sum over bins of the product
``bin_value * bin_area`` is 1.
Please note that the histogram does not follow the Cartesian convention
where `x` values are on the abscissa and `y` values on the ordinate
axis. Rather, `x` is histogrammed along the first dimension of the
array (vertical), and `y` along the second dimension of the array
(horizontal). This ensures compatibility with `histogramdd`.
Examples
--------
import matplotlib as mpl
import matplotlib.pyplot as plt
Construct a 2D-histogram with variable bin width. First define the bin
edges:
xedges = [0, 1, 1.5, 3, 5]
yedges = [0, 2, 3, 4, 6]
Next we create a histogram H with random bin content:
x = np.random.normal(3, 1, 100)
y = np.random.normal(1, 1, 100)
H, xedges, yedges = np.histogram2d(y, x, bins=(xedges, yedges))
Or we fill the histogram H with a determined bin content:
H = np.ones((4, 4)).cumsum().reshape(4, 4)
print H[::-1] # This shows the bin content in the order as plotted
[[ 13. 14. 15. 16.]
[ 9. 10. 11. 12.]
[ 5. 6. 7. 8.]
[ 1. 2. 3. 4.]]
Imshow can only do an equidistant representation of bins:
fig = plt.figure(figsize=(7, 3))
ax = fig.add_subplot(131)
ax.set_title('imshow: equidistant')
im = plt.imshow(H, interpolation='nearest', origin='low',
extent=[xedges[0], xedges[-1], yedges[0], yedges[-1]])
pcolormesh can display exact bin edges:
ax = fig.add_subplot(132)
ax.set_title('pcolormesh: exact bin edges')
X, Y = np.meshgrid(xedges, yedges)
ax.pcolormesh(X, Y, H)
ax.set_aspect('equal')
NonUniformImage displays exact bin edges with interpolation:
ax = fig.add_subplot(133)
ax.set_title('NonUniformImage: interpolated')
im = mpl.image.NonUniformImage(ax, interpolation='bilinear')
xcenters = xedges[:-1] + 0.5 * (xedges[1:] - xedges[:-1])
ycenters = yedges[:-1] + 0.5 * (yedges[1:] - yedges[:-1])
im.set_data(xcenters, ycenters, H)
ax.images.append(im)
ax.set_xlim(xedges[0], xedges[-1])
ax.set_ylim(yedges[0], yedges[-1])
ax.set_aspect('equal')
plt.show()
histogramdd(sample, bins=10, range=None, normed=False, weights=None)
Compute the multidimensional histogram of some data.
Parameters
----------
sample : array_like
The data to be histogrammed. It must be an (N,D) array or data
that can be converted to such. The rows of the resulting array
are the coordinates of points in a D dimensional polytope.
bins : sequence or int, optional
The bin specification:
* A sequence of arrays describing the bin edges along each dimension.
* The number of bins for each dimension (nx, ny, ... =bins)
* The number of bins for all dimensions (nx=ny=...=bins).
range : sequence, optional
A sequence of lower and upper bin edges to be used if the edges are
not given explicitly in `bins`. Defaults to the minimum and maximum
values along each dimension.
normed : bool, optional
If False, returns the number of samples in each bin. If True,
returns the bin density ``bin_count / sample_count / bin_volume``.
weights : (N,) array_like, optional
An array of values `w_i` weighing each sample `(x_i, y_i, z_i, ...)`.
Weights are normalized to 1 if normed is True. If normed is False,
the values of the returned histogram are equal to the sum of the
weights belonging to the samples falling into each bin.
Returns
-------
H : ndarray
The multidimensional histogram of sample x. See normed and weights
for the different possible semantics.
edges : list
A list of D arrays describing the bin edges for each dimension.
See Also
--------
histogram: 1-D histogram
histogram2d: 2-D histogram
Examples
--------
r = np.random.randn(100,3)
H, edges = np.histogramdd(r, bins = (5, 8, 4))
H.shape, edges[0].size, edges[1].size, edges[2].size
((5, 8, 4), 6, 9, 5)
hsplit(ary, indices_or_sections)
Split an array into multiple sub-arrays horizontally (column-wise).
Please refer to the `split` documentation. `hsplit` is equivalent
to `split` with ``axis=1``, the array is always split along the second
axis regardless of the array dimension.
See Also
--------
split : Split an array into multiple sub-arrays of equal size.
Examples
--------
x = np.arange(16.0).reshape(4, 4)
x
array([[ 0., 1., 2., 3.],
[ 4., 5., 6., 7.],
[ 8., 9., 10., 11.],
[ 12., 13., 14., 15.]])
np.hsplit(x, 2)
[array([[ 0., 1.],
[ 4., 5.],
[ 8., 9.],
[ 12., 13.]]),
array([[ 2., 3.],
[ 6., 7.],
[ 10., 11.],
[ 14., 15.]])]
np.hsplit(x, np.array([3, 6]))
[array([[ 0., 1., 2.],
[ 4., 5., 6.],
[ 8., 9., 10.],
[ 12., 13., 14.]]),
array([[ 3.],
[ 7.],
[ 11.],
[ 15.]]),
array([], dtype=float64)]
With a higher dimensional array the split is still along the second axis.
x = np.arange(8.0).reshape(2, 2, 2)
x
array([[[ 0., 1.],
[ 2., 3.]],
[[ 4., 5.],
[ 6., 7.]]])
np.hsplit(x, 2)
[array([[[ 0., 1.]],
[[ 4., 5.]]]),
array([[[ 2., 3.]],
[[ 6., 7.]]])]
hstack(tup)
Stack arrays in sequence horizontally (column wise).
Take a sequence of arrays and stack them horizontally to make
a single array. Rebuild arrays divided by `hsplit`.
Parameters
----------
tup : sequence of ndarrays
All arrays must have the same shape along all but the second axis.
Returns
-------
stacked : ndarray
The array formed by stacking the given arrays.
See Also
--------
stack : Join a sequence of arrays along a new axis.
vstack : Stack arrays in sequence vertically (row wise).
dstack : Stack arrays in sequence depth wise (along third axis).
concatenate : Join a sequence of arrays along an existing axis.
hsplit : Split array along second axis.
Notes
-----
Equivalent to ``np.concatenate(tup, axis=1)``
Examples
--------
a = np.array((1,2,3))
b = np.array((2,3,4))
np.hstack((a,b))
array([1, 2, 3, 2, 3, 4])
a = np.array([[1],[2],[3]])
b = np.array([[2],[3],[4]])
np.hstack((a,b))
array([[1, 2],
[2, 3],
[3, 4]])
i0(x)
Modified Bessel function of the first kind, order 0.
Usually denoted :math:`I_0`. This function does broadcast, but will *not*
"up-cast" int dtype arguments unless accompanied by at least one float or
complex dtype argument (see Raises below).
Parameters
----------
x : array_like, dtype float or complex
Argument of the Bessel function.
Returns
-------
out : ndarray, shape = x.shape, dtype = x.dtype
The modified Bessel function evaluated at each of the elements of `x`.
Raises
------
TypeError: array cannot be safely cast to required type
If argument consists exclusively of int dtypes.
See Also
--------
scipy.special.iv, scipy.special.ive
Notes
-----
We use the algorithm published by Clenshaw [1]_ and referenced by
Abramowitz and Stegun [2]_, for which the function domain is
partitioned into the two intervals [0,8] and (8,inf), and Chebyshev
polynomial expansions are employed in each interval. Relative error on
the domain [0,30] using IEEE arithmetic is documented [3]_ as having a
peak of 5.8e-16 with an rms of 1.4e-16 (n = 30000).
References
----------
.. [1] C. W. Clenshaw, "Chebyshev series for mathematical functions", in
*National Physical Laboratory Mathematical Tables*, vol. 5, London:
Her Majesty's Stationery Office, 1962.
.. [2] M. Abramowitz and I. A. Stegun, *Handbook of Mathematical
Functions*, 10th printing, New York: Dover, 1964, pp. 379.
http://www.math.sfu.ca/~cbm/aands/page_379.htm
.. [3] http://kobesearch.cpan.org/htdocs/Math-Cephes/Math/Cephes.html
Examples
--------
np.i0([0.])
array(1.0)
np.i0([0., 1. + 2j])
array([ 1.00000000+0.j , 0.18785373+0.64616944j])
identity(n, dtype=None)
Return the identity array.
The identity array is a square array with ones on
the main diagonal.
Parameters
----------
n : int
Number of rows (and columns) in `n` x `n` output.
dtype : data-type, optional
Data-type of the output. Defaults to ``float``.
Returns
-------
out : ndarray
`n` x `n` array with its main diagonal set to one,
and all other elements 0.
Examples
--------
np.identity(3)
array([[ 1., 0., 0.],
[ 0., 1., 0.],
[ 0., 0., 1.]])
imag(val)
Return the imaginary part of the elements of the array.
Parameters
----------
val : array_like
Input array.
Returns
-------
out : ndarray
Output array. If `val` is real, the type of `val` is used for the
output. If `val` has complex elements, the returned type is float.
See Also
--------
real, angle, real_if_close
Examples
--------
a = np.array([1+2j, 3+4j, 5+6j])
a.imag
array([ 2., 4., 6.])
a.imag = np.array([8, 10, 12])
a
array([ 1. +8.j, 3.+10.j, 5.+12.j])
in1d(ar1, ar2, assume_unique=False, invert=False)
Test whether each element of a 1-D array is also present in a second array.
Returns a boolean array the same length as `ar1` that is True
where an element of `ar1` is in `ar2` and False otherwise.
Parameters
----------
ar1 : (M,) array_like
Input array.
ar2 : array_like
The values against which to test each value of `ar1`.
assume_unique : bool, optional
If True, the input arrays are both assumed to be unique, which
can speed up the calculation. Default is False.
invert : bool, optional
If True, the values in the returned array are inverted (that is,
False where an element of `ar1` is in `ar2` and True otherwise).
Default is False. ``np.in1d(a, b, invert=True)`` is equivalent
to (but is faster than) ``np.invert(in1d(a, b))``.
.. versionadded:: 1.8.0
Returns
-------
in1d : (M,) ndarray, bool
The values `ar1[in1d]` are in `ar2`.
See Also
--------
numpy.lib.arraysetops : Module with a number of other functions for
performing set operations on arrays.
Notes
-----
`in1d` can be considered as an element-wise function version of the
python keyword `in`, for 1-D sequences. ``in1d(a, b)`` is roughly
equivalent to ``np.array([item in b for item in a])``.
However, this idea fails if `ar2` is a set, or similar (non-sequence)
container: As ``ar2`` is converted to an array, in those cases
``asarray(ar2)`` is an object array rather than the expected array of
contained values.
.. versionadded:: 1.4.0
Examples
--------
test = np.array([0, 1, 2, 5, 0])
states = [0, 2]
mask = np.in1d(test, states)
mask
array([ True, False, True, False, True], dtype=bool)
test[mask]
array([0, 2, 0])
mask = np.in1d(test, states, invert=True)
mask
array([False, True, False, True, False], dtype=bool)
test[mask]
array([1, 5])
indices(dimensions, dtype=)
Return an array representing the indices of a grid.
Compute an array where the subarrays contain index values 0,1,...
varying only along the corresponding axis.
Parameters
----------
dimensions : sequence of ints
The shape of the grid.
dtype : dtype, optional
Data type of the result.
Returns
-------
grid : ndarray
The array of grid indices,
``grid.shape = (len(dimensions),) + tuple(dimensions)``.
See Also
--------
mgrid, meshgrid
Notes
-----
The output shape is obtained by prepending the number of dimensions
in front of the tuple of dimensions, i.e. if `dimensions` is a tuple
``(r0, ..., rN-1)`` of length ``N``, the output shape is
``(N,r0,...,rN-1)``.
The subarrays ``grid[k]`` contains the N-D array of indices along the
``k-th`` axis. Explicitly::
grid[k,i0,i1,...,iN-1] = ik
Examples
--------
grid = np.indices((2, 3))
grid.shape
(2, 2, 3)
grid[0] # row indices
array([[0, 0, 0],
[1, 1, 1]])
grid[1] # column indices
array([[0, 1, 2],
[0, 1, 2]])
The indices can be used as an index into an array.
x = np.arange(20).reshape(5, 4)
row, col = np.indices((2, 3))
x[row, col]
array([[0, 1, 2],
[4, 5, 6]])
Note that it would be more straightforward in the above example to
extract the required elements directly with ``x[:2, :3]``.
info(object=None, maxwidth=76, output=', mode 'w'>, toplevel='numpy')
Get help information for a function, class, or module.
Parameters
----------
object : object or str, optional
Input object or name to get information about. If `object` is a
numpy object, its docstring is given. If it is a string, available
modules are searched for matching objects. If None, information
about `info` itself is returned.
maxwidth : int, optional
Printing width.
output : file like object, optional
File like object that the output is written to, default is
``stdout``. The object has to be opened in 'w' or 'a' mode.
toplevel : str, optional
Start search at this level.
See Also
--------
source, lookfor
Notes
-----
When used interactively with an object, ``np.info(obj)`` is equivalent
to ``help(obj)`` on the Python prompt or ``obj?`` on the IPython
prompt.
Examples
--------
np.info(np.polyval) # doctest: +SKIP
polyval(p, x)
Evaluate the polynomial p at x.
...
When using a string for `object` it is possible to get multiple results.
np.info('fft') # doctest: +SKIP
*** Found in numpy ***
Core FFT routines
...
*** Found in numpy.fft ***
fft(a, n=None, axis=-1)
...
*** Repeat reference found in numpy.fft.fftpack ***
*** Total of 3 references found. ***
inner(...)
inner(a, b)
Inner product of two arrays.
Ordinary inner product of vectors for 1-D arrays (without complex
conjugation), in higher dimensions a sum product over the last axes.
Parameters
----------
a, b : array_like
If `a` and `b` are nonscalar, their last dimensions of must match.
Returns
-------
out : ndarray
`out.shape = a.shape[:-1] + b.shape[:-1]`
Raises
------
ValueError
If the last dimension of `a` and `b` has different size.
See Also
--------
tensordot : Sum products over arbitrary axes.
dot : Generalised matrix product, using second last dimension of `b`.
einsum : Einstein summation convention.
Notes
-----
For vectors (1-D arrays) it computes the ordinary inner-product::
np.inner(a, b) = sum(a[:]*b[:])
More generally, if `ndim(a) = r > 0` and `ndim(b) = s > 0`::
np.inner(a, b) = np.tensordot(a, b, axes=(-1,-1))
or explicitly::
np.inner(a, b)[i0,...,ir-1,j0,...,js-1]
= sum(a[i0,...,ir-1,:]*b[j0,...,js-1,:])
In addition `a` or `b` may be scalars, in which case::
np.inner(a,b) = a*b
Examples
--------
Ordinary inner product for vectors:
a = np.array([1,2,3])
b = np.array([0,1,0])
np.inner(a, b)
2
A multidimensional example:
a = np.arange(24).reshape((2,3,4))
b = np.arange(4)
np.inner(a, b)
array([[ 14, 38, 62],
[ 86, 110, 134]])
An example where `b` is a scalar:
np.inner(np.eye(2), 7)
array([[ 7., 0.],
[ 0., 7.]])
insert(arr, obj, values, axis=None)
Insert values along the given axis before the given indices.
Parameters
----------
arr : array_like
Input array.
obj : int, slice or sequence of ints
Object that defines the index or indices before which `values` is
inserted.
.. versionadded:: 1.8.0
Support for multiple insertions when `obj` is a single scalar or a
sequence with one element (similar to calling insert multiple
times).
values : array_like
Values to insert into `arr`. If the type of `values` is different
from that of `arr`, `values` is converted to the type of `arr`.
`values` should be shaped so that ``arr[...,obj,...] = values``
is legal.
axis : int, optional
Axis along which to insert `values`. If `axis` is None then `arr`
is flattened first.
Returns
-------
out : ndarray
A copy of `arr` with `values` inserted. Note that `insert`
does not occur in-place: a new array is returned. If
`axis` is None, `out` is a flattened array.
See Also
--------
append : Append elements at the end of an array.
concatenate : Join a sequence of arrays along an existing axis.
delete : Delete elements from an array.
Notes
-----
Note that for higher dimensional inserts `obj=0` behaves very different
from `obj=[0]` just like `arr[:,0,:] = values` is different from
`arr[:,[0],:] = values`.
Examples
--------
a = np.array([[1, 1], [2, 2], [3, 3]])
a
array([[1, 1],
[2, 2],
[3, 3]])
np.insert(a, 1, 5)
array([1, 5, 1, 2, 2, 3, 3])
np.insert(a, 1, 5, axis=1)
array([[1, 5, 1],
[2, 5, 2],
[3, 5, 3]])
Difference between sequence and scalars:
np.insert(a, [1], [[1],[2],[3]], axis=1)
array([[1, 1, 1],
[2, 2, 2],
[3, 3, 3]])
np.array_equal(np.insert(a, 1, [1, 2, 3], axis=1),
np.insert(a, [1], [[1],[2],[3]], axis=1))
True
b = a.flatten()
b
array([1, 1, 2, 2, 3, 3])
np.insert(b, [2, 2], [5, 6])
array([1, 1, 5, 6, 2, 2, 3, 3])
np.insert(b, slice(2, 4), [5, 6])
array([1, 1, 5, 2, 6, 2, 3, 3])
np.insert(b, [2, 2], [7.13, False]) # type casting
array([1, 1, 7, 0, 2, 2, 3, 3])
x = np.arange(8).reshape(2, 4)
idx = (1, 3)
np.insert(x, idx, 999, axis=1)
array([[ 0, 999, 1, 2, 999, 3],
[ 4, 999, 5, 6, 999, 7]])
int_asbuffer(...)
interp(x, xp, fp, left=None, right=None, period=None)
One-dimensional linear interpolation.
Returns the one-dimensional piecewise linear interpolant to a function
with given values at discrete data-points.
Parameters
----------
x : array_like
The x-coordinates of the interpolated values.
xp : 1-D sequence of floats
The x-coordinates of the data points, must be increasing if argument
`period` is not specified. Otherwise, `xp` is internally sorted after
normalizing the periodic boundaries with ``xp = xp % period``.
fp : 1-D sequence of floats
The y-coordinates of the data points, same length as `xp`.
left : float, optional
Value to return for `x < xp[0]`, default is `fp[0]`.
right : float, optional
Value to return for `x > xp[-1]`, default is `fp[-1]`.
period : None or float, optional
A period for the x-coordinates. This parameter allows the proper
interpolation of angular x-coordinates. Parameters `left` and `right`
are ignored if `period` is specified.
.. versionadded:: 1.10.0
Returns
-------
y : float or ndarray
The interpolated values, same shape as `x`.
Raises
------
ValueError
If `xp` and `fp` have different length
If `xp` or `fp` are not 1-D sequences
If `period == 0`
Notes
-----
Does not check that the x-coordinate sequence `xp` is increasing.
If `xp` is not increasing, the results are nonsense.
A simple check for increasing is::
np.all(np.diff(xp) > 0)
Examples
--------
xp = [1, 2, 3]
fp = [3, 2, 0]
np.interp(2.5, xp, fp)
1.0
np.interp([0, 1, 1.5, 2.72, 3.14], xp, fp)
array([ 3. , 3. , 2.5 , 0.56, 0. ])
UNDEF = -99.0
np.interp(3.14, xp, fp, right=UNDEF)
-99.0
Plot an interpolant to the sine function:
x = np.linspace(0, 2*np.pi, 10)
y = np.sin(x)
xvals = np.linspace(0, 2*np.pi, 50)
yinterp = np.interp(xvals, x, y)
import matplotlib.pyplot as plt
plt.plot(x, y, 'o')
[]
plt.plot(xvals, yinterp, '-x')
[]
plt.show()
Interpolation with periodic x-coordinates:
x = [-180, -170, -185, 185, -10, -5, 0, 365]
xp = [190, -190, 350, -350]
fp = [5, 10, 3, 4]
np.interp(x, xp, fp, period=360)
array([7.5, 5., 8.75, 6.25, 3., 3.25, 3.5, 3.75])
intersect1d(ar1, ar2, assume_unique=False)
Find the intersection of two arrays.
Return the sorted, unique values that are in both of the input arrays.
Parameters
----------
ar1, ar2 : array_like
Input arrays.
assume_unique : bool
If True, the input arrays are both assumed to be unique, which
can speed up the calculation. Default is False.
Returns
-------
intersect1d : ndarray
Sorted 1D array of common and unique elements.
See Also
--------
numpy.lib.arraysetops : Module with a number of other functions for
performing set operations on arrays.
Examples
--------
np.intersect1d([1, 3, 4, 3], [3, 1, 2, 1])
array([1, 3])
To intersect more than two arrays, use functools.reduce:
from functools import reduce
reduce(np.intersect1d, ([1, 3, 4, 3], [3, 1, 2, 1], [6, 3, 4, 2]))
array([3])
ipmt(rate, per, nper, pv, fv=0.0, when='end')
Compute the interest portion of a payment.
Parameters
----------
rate : scalar or array_like of shape(M, )
Rate of interest as decimal (not per cent) per period
per : scalar or array_like of shape(M, )
Interest paid against the loan changes during the life or the loan.
The `per` is the payment period to calculate the interest amount.
nper : scalar or array_like of shape(M, )
Number of compounding periods
pv : scalar or array_like of shape(M, )
Present value
fv : scalar or array_like of shape(M, ), optional
Future value
when : {{'begin', 1}, {'end', 0}}, {string, int}, optional
When payments are due ('begin' (1) or 'end' (0)).
Defaults to {'end', 0}.
Returns
-------
out : ndarray
Interest portion of payment. If all input is scalar, returns a scalar
float. If any input is array_like, returns interest payment for each
input element. If multiple inputs are array_like, they all must have
the same shape.
See Also
--------
ppmt, pmt, pv
Notes
-----
The total payment is made up of payment against principal plus interest.
``pmt = ppmt + ipmt``
Examples
--------
What is the amortization schedule for a 1 year loan of $2500 at
8.24% interest per year compounded monthly?
principal = 2500.00
The 'per' variable represents the periods of the loan. Remember that
financial equations start the period count at 1!
per = np.arange(1*12) + 1
ipmt = np.ipmt(0.0824/12, per, 1*12, principal)
ppmt = np.ppmt(0.0824/12, per, 1*12, principal)
Each element of the sum of the 'ipmt' and 'ppmt' arrays should equal
'pmt'.
pmt = np.pmt(0.0824/12, 1*12, principal)
np.allclose(ipmt + ppmt, pmt)
True
fmt = '{0:2d} {1:8.2f} {2:8.2f} {3:8.2f}'
for payment in per:
index = payment - 1
principal = principal + ppmt[index]
print fmt.format(payment, ppmt[index], ipmt[index], principal)
1 -200.58 -17.17 2299.42
2 -201.96 -15.79 2097.46
3 -203.35 -14.40 1894.11
4 -204.74 -13.01 1689.37
5 -206.15 -11.60 1483.22
6 -207.56 -10.18 1275.66
7 -208.99 -8.76 1066.67
8 -210.42 -7.32 856.25
9 -211.87 -5.88 644.38
10 -213.32 -4.42 431.05
11 -214.79 -2.96 216.26
12 -216.26 -1.49 -0.00
interestpd = np.sum(ipmt)
np.round(interestpd, 2)
-112.98
irr(values)
Return the Internal Rate of Return (IRR).
This is the "average" periodically compounded rate of return
that gives a net present value of 0.0; for a more complete explanation,
see Notes below.
Parameters
----------
values : array_like, shape(N,)
Input cash flows per time period. By convention, net "deposits"
are negative and net "withdrawals" are positive. Thus, for
example, at least the first element of `values`, which represents
the initial investment, will typically be negative.
Returns
-------
out : float
Internal Rate of Return for periodic input values.
Notes
-----
The IRR is perhaps best understood through an example (illustrated
using np.irr in the Examples section below). Suppose one invests 100
units and then makes the following withdrawals at regular (fixed)
intervals: 39, 59, 55, 20. Assuming the ending value is 0, one's 100
unit investment yields 173 units; however, due to the combination of
compounding and the periodic withdrawals, the "average" rate of return
is neither simply 0.73/4 nor (1.73)^0.25-1. Rather, it is the solution
(for :math:`r`) of the equation:
.. math:: -100 + \frac{39}{1+r} + \frac{59}{(1+r)^2}
+ \frac{55}{(1+r)^3} + \frac{20}{(1+r)^4} = 0
In general, for `values` :math:`= [v_0, v_1, ... v_M]`,
irr is the solution of the equation: [G]_
.. math:: \sum_{t=0}^M{\frac{v_t}{(1+irr)^{t}}} = 0
References
----------
.. [G] L. J. Gitman, "Principles of Managerial Finance, Brief," 3rd ed.,
Addison-Wesley, 2003, pg. 348.
Examples
--------
round(irr([-100, 39, 59, 55, 20]), 5)
0.28095
round(irr([-100, 0, 0, 74]), 5)
-0.0955
round(irr([-100, 100, 0, -7]), 5)
-0.0833
round(irr([-100, 100, 0, 7]), 5)
0.06206
round(irr([-5, 10.5, 1, -8, 1]), 5)
0.0886
(Compare with the Example given for numpy.lib.financial.npv)
is_busday(...)
is_busday(dates, weekmask='1111100', holidays=None, busdaycal=None, out=None)
Calculates which of the given dates are valid days, and which are not.
.. versionadded:: 1.7.0
Parameters
----------
dates : array_like of datetime64[D]
The array of dates to process.
weekmask : str or array_like of bool, optional
A seven-element array indicating which of Monday through Sunday are
valid days. May be specified as a length-seven list or array, like
[1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string
like "Mon Tue Wed Thu Fri", made up of 3-character abbreviations for
weekdays, optionally separated by white space. Valid abbreviations
are: Mon Tue Wed Thu Fri Sat Sun
holidays : array_like of datetime64[D], optional
An array of dates to consider as invalid dates. They may be
specified in any order, and NaT (not-a-time) dates are ignored.
This list is saved in a normalized form that is suited for
fast calculations of valid days.
busdaycal : busdaycalendar, optional
A `busdaycalendar` object which specifies the valid days. If this
parameter is provided, neither weekmask nor holidays may be
provided.
out : array of bool, optional
If provided, this array is filled with the result.
Returns
-------
out : array of bool
An array with the same shape as ``dates``, containing True for
each valid day, and False for each invalid day.
See Also
--------
busdaycalendar: An object that specifies a custom set of valid days.
busday_offset : Applies an offset counted in valid days.
busday_count : Counts how many valid days are in a half-open date range.
Examples
--------
# The weekdays are Friday, Saturday, and Monday
np.is_busday(['2011-07-01', '2011-07-02', '2011-07-18'],
holidays=['2011-07-01', '2011-07-04', '2011-07-17'])
array([False, False, True], dtype='bool')
isclose(a, b, rtol=1e-05, atol=1e-08, equal_nan=False)
Returns a boolean array where two arrays are element-wise equal within a
tolerance.
The tolerance values are positive, typically very small numbers. The
relative difference (`rtol` * abs(`b`)) and the absolute difference
`atol` are added together to compare against the absolute difference
between `a` and `b`.
Parameters
----------
a, b : array_like
Input arrays to compare.
rtol : float
The relative tolerance parameter (see Notes).
atol : float
The absolute tolerance parameter (see Notes).
equal_nan : bool
Whether to compare NaN's as equal. If True, NaN's in `a` will be
considered equal to NaN's in `b` in the output array.
Returns
-------
y : array_like
Returns a boolean array of where `a` and `b` are equal within the
given tolerance. If both `a` and `b` are scalars, returns a single
boolean value.
See Also
--------
allclose
Notes
-----
.. versionadded:: 1.7.0
For finite values, isclose uses the following equation to test whether
two floating point values are equivalent.
absolute(`a` - `b`) <= (`atol` + `rtol` * absolute(`b`))
The above equation is not symmetric in `a` and `b`, so that
`isclose(a, b)` might be different from `isclose(b, a)` in
some rare cases.
Examples
--------
np.isclose([1e10,1e-7], [1.00001e10,1e-8])
array([True, False])
np.isclose([1e10,1e-8], [1.00001e10,1e-9])
array([True, True])
np.isclose([1e10,1e-8], [1.0001e10,1e-9])
array([False, True])
np.isclose([1.0, np.nan], [1.0, np.nan])
array([True, False])
np.isclose([1.0, np.nan], [1.0, np.nan], equal_nan=True)
array([True, True])
iscomplex(x)
Returns a bool array, where True if input element is complex.
What is tested is whether the input has a non-zero imaginary part, not if
the input type is complex.
Parameters
----------
x : array_like
Input array.
Returns
-------
out : ndarray of bools
Output array.
See Also
--------
isreal
iscomplexobj : Return True if x is a complex type or an array of complex
numbers.
Examples
--------
np.iscomplex([1+1j, 1+0j, 4.5, 3, 2, 2j])
array([ True, False, False, False, False, True], dtype=bool)
iscomplexobj(x)
Check for a complex type or an array of complex numbers.
The type of the input is checked, not the value. Even if the input
has an imaginary part equal to zero, `iscomplexobj` evaluates to True.
Parameters
----------
x : any
The input can be of any type and shape.
Returns
-------
iscomplexobj : bool
The return value, True if `x` is of a complex type or has at least
one complex element.
See Also
--------
isrealobj, iscomplex
Examples
--------
np.iscomplexobj(1)
False
np.iscomplexobj(1+0j)
True
np.iscomplexobj([3, 1+0j, True])
True
isfortran(a)
Returns True if the array is Fortran contiguous but *not* C contiguous.
This function is obsolete and, because of changes due to relaxed stride
checking, its return value for the same array may differ for versions
of Numpy >= 1.10 and previous versions. If you only want to check if an
array is Fortran contiguous use ``a.flags.f_contiguous`` instead.
Parameters
----------
a : ndarray
Input array.
Examples
--------
np.array allows to specify whether the array is written in C-contiguous
order (last index varies the fastest), or FORTRAN-contiguous order in
memory (first index varies the fastest).
a = np.array([[1, 2, 3], [4, 5, 6]], order='C')
a
array([[1, 2, 3],
[4, 5, 6]])
np.isfortran(a)
False
b = np.array([[1, 2, 3], [4, 5, 6]], order='FORTRAN')
b
array([[1, 2, 3],
[4, 5, 6]])
np.isfortran(b)
True
The transpose of a C-ordered array is a FORTRAN-ordered array.
a = np.array([[1, 2, 3], [4, 5, 6]], order='C')
a
array([[1, 2, 3],
[4, 5, 6]])
np.isfortran(a)
False
b = a.T
b
array([[1, 4],
[2, 5],
[3, 6]])
np.isfortran(b)
True
C-ordered arrays evaluate as False even if they are also FORTRAN-ordered.
np.isfortran(np.array([1, 2], order='FORTRAN'))
False
isneginf(x, y=None)
Test element-wise for negative infinity, return result as bool array.
Parameters
----------
x : array_like
The input array.
y : array_like, optional
A boolean array with the same shape and type as `x` to store the
result.
Returns
-------
y : ndarray
A boolean array with the same dimensions as the input.
If second argument is not supplied then a numpy boolean array is
returned with values True where the corresponding element of the
input is negative infinity and values False where the element of
the input is not negative infinity.
If a second argument is supplied the result is stored there. If the
type of that array is a numeric type the result is represented as
zeros and ones, if the type is boolean then as False and True. The
return value `y` is then a reference to that array.
See Also
--------
isinf, isposinf, isnan, isfinite
Notes
-----
Numpy uses the IEEE Standard for Binary Floating-Point for Arithmetic
(IEEE 754).
Errors result if the second argument is also supplied when x is a scalar
input, or if first and second arguments have different shapes.
Examples
--------
np.isneginf(np.NINF)
array(True, dtype=bool)
np.isneginf(np.inf)
array(False, dtype=bool)
np.isneginf(np.PINF)
array(False, dtype=bool)
np.isneginf([-np.inf, 0., np.inf])
array([ True, False, False], dtype=bool)
x = np.array([-np.inf, 0., np.inf])
y = np.array([2, 2, 2])
np.isneginf(x, y)
array([1, 0, 0])
y
array([1, 0, 0])
isposinf(x, y=None)
Test element-wise for positive infinity, return result as bool array.
Parameters
----------
x : array_like
The input array.
y : array_like, optional
A boolean array with the same shape as `x` to store the result.
Returns
-------
y : ndarray
A boolean array with the same dimensions as the input.
If second argument is not supplied then a boolean array is returned
with values True where the corresponding element of the input is
positive infinity and values False where the element of the input is
not positive infinity.
If a second argument is supplied the result is stored there. If the
type of that array is a numeric type the result is represented as zeros
and ones, if the type is boolean then as False and True.
The return value `y` is then a reference to that array.
See Also
--------
isinf, isneginf, isfinite, isnan
Notes
-----
Numpy uses the IEEE Standard for Binary Floating-Point for Arithmetic
(IEEE 754).
Errors result if the second argument is also supplied when `x` is a
scalar input, or if first and second arguments have different shapes.
Examples
--------
np.isposinf(np.PINF)
array(True, dtype=bool)
np.isposinf(np.inf)
array(True, dtype=bool)
np.isposinf(np.NINF)
array(False, dtype=bool)
np.isposinf([-np.inf, 0., np.inf])
array([False, False, True], dtype=bool)
x = np.array([-np.inf, 0., np.inf])
y = np.array([2, 2, 2])
np.isposinf(x, y)
array([0, 0, 1])
y
array([0, 0, 1])
isreal(x)
Returns a bool array, where True if input element is real.
If element has complex type with zero complex part, the return value
for that element is True.
Parameters
----------
x : array_like
Input array.
Returns
-------
out : ndarray, bool
Boolean array of same shape as `x`.
See Also
--------
iscomplex
isrealobj : Return True if x is not a complex type.
Examples
--------
np.isreal([1+1j, 1+0j, 4.5, 3, 2, 2j])
array([False, True, True, True, True, False], dtype=bool)
isrealobj(x)
Return True if x is a not complex type or an array of complex numbers.
The type of the input is checked, not the value. So even if the input
has an imaginary part equal to zero, `isrealobj` evaluates to False
if the data type is complex.
Parameters
----------
x : any
The input can be of any type and shape.
Returns
-------
y : bool
The return value, False if `x` is of a complex type.
See Also
--------
iscomplexobj, isreal
Examples
--------
np.isrealobj(1)
True
np.isrealobj(1+0j)
False
np.isrealobj([3, 1+0j, True])
False
isscalar(num)
Returns True if the type of `num` is a scalar type.
Parameters
----------
num : any
Input argument, can be of any type and shape.
Returns
-------
val : bool
True if `num` is a scalar type, False if it is not.
Examples
--------
np.isscalar(3.1)
True
np.isscalar([3.1])
False
np.isscalar(False)
True
issctype(rep)
Determines whether the given object represents a scalar data-type.
Parameters
----------
rep : any
If `rep` is an instance of a scalar dtype, True is returned. If not,
False is returned.
Returns
-------
out : bool
Boolean result of check whether `rep` is a scalar dtype.
See Also
--------
issubsctype, issubdtype, obj2sctype, sctype2char
Examples
--------
np.issctype(np.int32)
True
np.issctype(list)
False
np.issctype(1.1)
False
Strings are also a scalar type:
np.issctype(np.dtype('str'))
True
issubclass_(arg1, arg2)
Determine if a class is a subclass of a second class.
`issubclass_` is equivalent to the Python built-in ``issubclass``,
except that it returns False instead of raising a TypeError if one
of the arguments is not a class.
Parameters
----------
arg1 : class
Input class. True is returned if `arg1` is a subclass of `arg2`.
arg2 : class or tuple of classes.
Input class. If a tuple of classes, True is returned if `arg1` is a
subclass of any of the tuple elements.
Returns
-------
out : bool
Whether `arg1` is a subclass of `arg2` or not.
See Also
--------
issubsctype, issubdtype, issctype
Examples
--------
np.issubclass_(np.int32, np.int)
True
np.issubclass_(np.int32, np.float)
False
issubdtype(arg1, arg2)
Returns True if first argument is a typecode lower/equal in type hierarchy.
Parameters
----------
arg1, arg2 : dtype_like
dtype or string representing a typecode.
Returns
-------
out : bool
See Also
--------
issubsctype, issubclass_
numpy.core.numerictypes : Overview of numpy type hierarchy.
Examples
--------
np.issubdtype('S1', str)
True
np.issubdtype(np.float64, np.float32)
False
issubsctype(arg1, arg2)
Determine if the first argument is a subclass of the second argument.
Parameters
----------
arg1, arg2 : dtype or dtype specifier
Data-types.
Returns
-------
out : bool
The result.
See Also
--------
issctype, issubdtype,obj2sctype
Examples
--------
np.issubsctype('S8', str)
True
np.issubsctype(np.array([1]), np.int)
True
np.issubsctype(np.array([1]), np.float)
False
iterable(y)
Check whether or not an object can be iterated over.
Parameters
----------
y : object
Input object.
Returns
-------
b : {0, 1}
Return 1 if the object has an iterator method or is a sequence,
and 0 otherwise.
Examples
--------
np.iterable([1, 2, 3])
1
np.iterable(2)
0
ix_(*args)
Construct an open mesh from multiple sequences.
This function takes N 1-D sequences and returns N outputs with N
dimensions each, such that the shape is 1 in all but one dimension
and the dimension with the non-unit shape value cycles through all
N dimensions.
Using `ix_` one can quickly construct index arrays that will index
the cross product. ``a[np.ix_([1,3],[2,5])]`` returns the array
``[[a[1,2] a[1,5]], [a[3,2] a[3,5]]]``.
Parameters
----------
args : 1-D sequences
Returns
-------
out : tuple of ndarrays
N arrays with N dimensions each, with N the number of input
sequences. Together these arrays form an open mesh.
See Also
--------
ogrid, mgrid, meshgrid
Examples
--------
a = np.arange(10).reshape(2, 5)
a
array([[0, 1, 2, 3, 4],
[5, 6, 7, 8, 9]])
ixgrid = np.ix_([0,1], [2,4])
ixgrid
(array([[0],
[1]]), array([[2, 4]]))
ixgrid[0].shape, ixgrid[1].shape
((2, 1), (1, 2))
a[ixgrid]
array([[2, 4],
[7, 9]])
kaiser(M, beta)
Return the Kaiser window.
The Kaiser window is a taper formed by using a Bessel function.
Parameters
----------
M : int
Number of points in the output window. If zero or less, an
empty array is returned.
beta : float
Shape parameter for window.
Returns
-------
out : array
The window, with the maximum value normalized to one (the value
one appears only if the number of samples is odd).
See Also
--------
bartlett, blackman, hamming, hanning
Notes
-----
The Kaiser window is defined as
.. math:: w(n) = I_0\left( \beta \sqrt{1-\frac{4n^2}{(M-1)^2}}
\right)/I_0(\beta)
with
.. math:: \quad -\frac{M-1}{2} \leq n \leq \frac{M-1}{2},
where :math:`I_0` is the modified zeroth-order Bessel function.
The Kaiser was named for Jim Kaiser, who discovered a simple
approximation to the DPSS window based on Bessel functions. The Kaiser
window is a very good approximation to the Digital Prolate Spheroidal
Sequence, or Slepian window, which is the transform which maximizes the
energy in the main lobe of the window relative to total energy.
The Kaiser can approximate many other windows by varying the beta
parameter.
==== =======================
beta Window shape
==== =======================
0 Rectangular
5 Similar to a Hamming
6 Similar to a Hanning
8.6 Similar to a Blackman
==== =======================
A beta value of 14 is probably a good starting point. Note that as beta
gets large, the window narrows, and so the number of samples needs to be
large enough to sample the increasingly narrow spike, otherwise NaNs will
get returned.
Most references to the Kaiser window come from the signal processing
literature, where it is used as one of many windowing functions for
smoothing values. It is also known as an apodization (which means
"removing the foot", i.e. smoothing discontinuities at the beginning
and end of the sampled signal) or tapering function.
References
----------
.. [1] J. F. Kaiser, "Digital Filters" - Ch 7 in "Systems analysis by
digital computer", Editors: F.F. Kuo and J.F. Kaiser, p 218-285.
John Wiley and Sons, New York, (1966).
.. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics", The
University of Alberta Press, 1975, pp. 177-178.
.. [3] Wikipedia, "Window function",
http://en.wikipedia.org/wiki/Window_function
Examples
--------
np.kaiser(12, 14)
array([ 7.72686684e-06, 3.46009194e-03, 4.65200189e-02,
2.29737120e-01, 5.99885316e-01, 9.45674898e-01,
9.45674898e-01, 5.99885316e-01, 2.29737120e-01,
4.65200189e-02, 3.46009194e-03, 7.72686684e-06])
Plot the window and the frequency response:
from numpy.fft import fft, fftshift
window = np.kaiser(51, 14)
plt.plot(window)
[]
plt.title("Kaiser window")
plt.ylabel("Amplitude")
plt.xlabel("Sample")
plt.show()
plt.figure()
A = fft(window, 2048) / 25.5
mag = np.abs(fftshift(A))
freq = np.linspace(-0.5, 0.5, len(A))
response = 20 * np.log10(mag)
response = np.clip(response, -100, 100)
plt.plot(freq, response)
[]
plt.title("Frequency response of Kaiser window")
plt.ylabel("Magnitude [dB]")
plt.xlabel("Normalized frequency [cycles per sample]")
plt.axis('tight')
(-0.5, 0.5, -100.0, ...)
plt.show()
kron(a, b)
Kronecker product of two arrays.
Computes the Kronecker product, a composite array made of blocks of the
second array scaled by the first.
Parameters
----------
a, b : array_like
Returns
-------
out : ndarray
See Also
--------
outer : The outer product
Notes
-----
The function assumes that the number of dimensions of `a` and `b`
are the same, if necessary prepending the smallest with ones.
If `a.shape = (r0,r1,..,rN)` and `b.shape = (s0,s1,...,sN)`,
the Kronecker product has shape `(r0*s0, r1*s1, ..., rN*SN)`.
The elements are products of elements from `a` and `b`, organized
explicitly by::
kron(a,b)[k0,k1,...,kN] = a[i0,i1,...,iN] * b[j0,j1,...,jN]
where::
kt = it * st + jt, t = 0,...,N
In the common 2-D case (N=1), the block structure can be visualized::
[[ a[0,0]*b, a[0,1]*b, ... , a[0,-1]*b ],
[ ... ... ],
[ a[-1,0]*b, a[-1,1]*b, ... , a[-1,-1]*b ]]
Examples
--------
np.kron([1,10,100], [5,6,7])
array([ 5, 6, 7, 50, 60, 70, 500, 600, 700])
np.kron([5,6,7], [1,10,100])
array([ 5, 50, 500, 6, 60, 600, 7, 70, 700])
np.kron(np.eye(2), np.ones((2,2)))
array([[ 1., 1., 0., 0.],
[ 1., 1., 0., 0.],
[ 0., 0., 1., 1.],
[ 0., 0., 1., 1.]])
a = np.arange(100).reshape((2,5,2,5))
b = np.arange(24).reshape((2,3,4))
c = np.kron(a,b)
c.shape
(2, 10, 6, 20)
I = (1,3,0,2)
J = (0,2,1)
J1 = (0,) + J # extend to ndim=4
S1 = (1,) + b.shape
K = tuple(np.array(I) * np.array(S1) + np.array(J1))
c[K] == a[I]*b[J]
True
lexsort(...)
lexsort(keys, axis=-1)
Perform an indirect sort using a sequence of keys.
Given multiple sorting keys, which can be interpreted as columns in a
spreadsheet, lexsort returns an array of integer indices that describes
the sort order by multiple columns. The last key in the sequence is used
for the primary sort order, the second-to-last key for the secondary sort
order, and so on. The keys argument must be a sequence of objects that
can be converted to arrays of the same shape. If a 2D array is provided
for the keys argument, it's rows are interpreted as the sorting keys and
sorting is according to the last row, second last row etc.
Parameters
----------
keys : (k, N) array or tuple containing k (N,)-shaped sequences
The `k` different "columns" to be sorted. The last column (or row if
`keys` is a 2D array) is the primary sort key.
axis : int, optional
Axis to be indirectly sorted. By default, sort over the last axis.
Returns
-------
indices : (N,) ndarray of ints
Array of indices that sort the keys along the specified axis.
See Also
--------
argsort : Indirect sort.
ndarray.sort : In-place sort.
sort : Return a sorted copy of an array.
Examples
--------
Sort names: first by surname, then by name.
surnames = ('Hertz', 'Galilei', 'Hertz')
first_names = ('Heinrich', 'Galileo', 'Gustav')
ind = np.lexsort((first_names, surnames))
ind
array([1, 2, 0])
[surnames[i] + ", " + first_names[i] for i in ind]
['Galilei, Galileo', 'Hertz, Gustav', 'Hertz, Heinrich']
Sort two columns of numbers:
a = [1,5,1,4,3,4,4] # First column
b = [9,4,0,4,0,2,1] # Second column
ind = np.lexsort((b,a)) # Sort by a, then by b
print ind
[2 0 4 6 5 3 1]
[(a[i],b[i]) for i in ind]
[(1, 0), (1, 9), (3, 0), (4, 1), (4, 2), (4, 4), (5, 4)]
Note that sorting is first according to the elements of ``a``.
Secondary sorting is according to the elements of ``b``.
A normal ``argsort`` would have yielded:
[(a[i],b[i]) for i in np.argsort(a)]
[(1, 9), (1, 0), (3, 0), (4, 4), (4, 2), (4, 1), (5, 4)]
Structured arrays are sorted lexically by ``argsort``:
x = np.array([(1,9), (5,4), (1,0), (4,4), (3,0), (4,2), (4,1)],
dtype=np.dtype([('x', int), ('y', int)]))
np.argsort(x) # or np.argsort(x, order=('x', 'y'))
array([2, 0, 4, 6, 5, 3, 1])
linspace(start, stop, num=50, endpoint=True, retstep=False, dtype=None)
Return evenly spaced numbers over a specified interval.
Returns `num` evenly spaced samples, calculated over the
interval [`start`, `stop`].
The endpoint of the interval can optionally be excluded.
Parameters
----------
start : scalar
The starting value of the sequence.
stop : scalar
The end value of the sequence, unless `endpoint` is set to False.
In that case, the sequence consists of all but the last of ``num + 1``
evenly spaced samples, so that `stop` is excluded. Note that the step
size changes when `endpoint` is False.
num : int, optional
Number of samples to generate. Default is 50. Must be non-negative.
endpoint : bool, optional
If True, `stop` is the last sample. Otherwise, it is not included.
Default is True.
retstep : bool, optional
If True, return (`samples`, `step`), where `step` is the spacing
between samples.
dtype : dtype, optional
The type of the output array. If `dtype` is not given, infer the data
type from the other input arguments.
.. versionadded:: 1.9.0
Returns
-------
samples : ndarray
There are `num` equally spaced samples in the closed interval
``[start, stop]`` or the half-open interval ``[start, stop)``
(depending on whether `endpoint` is True or False).
step : float
Only returned if `retstep` is True
Size of spacing between samples.
See Also
--------
arange : Similar to `linspace`, but uses a step size (instead of the
number of samples).
logspace : Samples uniformly distributed in log space.
Examples
--------
np.linspace(2.0, 3.0, num=5)
array([ 2. , 2.25, 2.5 , 2.75, 3. ])
np.linspace(2.0, 3.0, num=5, endpoint=False)
array([ 2. , 2.2, 2.4, 2.6, 2.8])
np.linspace(2.0, 3.0, num=5, retstep=True)
(array([ 2. , 2.25, 2.5 , 2.75, 3. ]), 0.25)
Graphical illustration:
import matplotlib.pyplot as plt
N = 8
y = np.zeros(N)
x1 = np.linspace(0, 10, N, endpoint=True)
x2 = np.linspace(0, 10, N, endpoint=False)
plt.plot(x1, y, 'o')
[]
plt.plot(x2, y + 0.5, 'o')
[]
plt.ylim([-0.5, 1])
(-0.5, 1)
plt.show()
load(file, mmap_mode=None, allow_pickle=True, fix_imports=True, encoding='ASCII')
Load arrays or pickled objects from ``.npy``, ``.npz`` or pickled files.
Parameters
----------
file : file-like object or string
The file to read. File-like objects must support the
``seek()`` and ``read()`` methods. Pickled files require that the
file-like object support the ``readline()`` method as well.
mmap_mode : {None, 'r+', 'r', 'w+', 'c'}, optional
If not None, then memory-map the file, using the given mode (see
`numpy.memmap` for a detailed description of the modes). A
memory-mapped array is kept on disk. However, it can be accessed
and sliced like any ndarray. Memory mapping is especially useful
for accessing small fragments of large files without reading the
entire file into memory.
allow_pickle : bool, optional
Allow loading pickled object arrays stored in npy files. Reasons for
disallowing pickles include security, as loading pickled data can
execute arbitrary code. If pickles are disallowed, loading object
arrays will fail.
Default: True
fix_imports : bool, optional
Only useful when loading Python 2 generated pickled files on Python 3,
which includes npy/npz files containing object arrays. If `fix_imports`
is True, pickle will try to map the old Python 2 names to the new names
used in Python 3.
encoding : str, optional
What encoding to use when reading Python 2 strings. Only useful when
loading Python 2 generated pickled files on Python 3, which includes
npy/npz files containing object arrays. Values other than 'latin1',
'ASCII', and 'bytes' are not allowed, as they can corrupt numerical
data. Default: 'ASCII'
Returns
-------
result : array, tuple, dict, etc.
Data stored in the file. For ``.npz`` files, the returned instance
of NpzFile class must be closed to avoid leaking file descriptors.
Raises
------
IOError
If the input file does not exist or cannot be read.
ValueError
The file contains an object array, but allow_pickle=False given.
See Also
--------
save, savez, savez_compressed, loadtxt
memmap : Create a memory-map to an array stored in a file on disk.
Notes
-----
- If the file contains pickle data, then whatever object is stored
in the pickle is returned.
- If the file is a ``.npy`` file, then a single array is returned.
- If the file is a ``.npz`` file, then a dictionary-like object is
returned, containing ``{filename: array}`` key-value pairs, one for
each file in the archive.
- If the file is a ``.npz`` file, the returned value supports the
context manager protocol in a similar fashion to the open function::
with load('foo.npz') as data:
a = data['a']
The underlying file descriptor is closed when exiting the 'with'
block.
Examples
--------
Store data to disk, and load it again:
np.save('/tmp/123', np.array([[1, 2, 3], [4, 5, 6]]))
np.load('/tmp/123.npy')
array([[1, 2, 3],
[4, 5, 6]])
Store compressed data to disk, and load it again:
a=np.array([[1, 2, 3], [4, 5, 6]])
b=np.array([1, 2])
np.savez('/tmp/123.npz', a=a, b=b)
data = np.load('/tmp/123.npz')
data['a']
array([[1, 2, 3],
[4, 5, 6]])
data['b']
array([1, 2])
data.close()
Mem-map the stored array, and then access the second row
directly from disk:
X = np.load('/tmp/123.npy', mmap_mode='r')
X[1, :]
memmap([4, 5, 6])
loads(...)
loads(string) -- Load a pickle from the given string
loadtxt(fname, dtype=, comments='#', delimiter=None, converters=None, skiprows=0, usecols=None, unpack=False, ndmin=0)
Load data from a text file.
Each row in the text file must have the same number of values.
Parameters
----------
fname : file or str
File, filename, or generator to read. If the filename extension is
``.gz`` or ``.bz2``, the file is first decompressed. Note that
generators should return byte strings for Python 3k.
dtype : data-type, optional
Data-type of the resulting array; default: float. If this is a
structured data-type, the resulting array will be 1-dimensional, and
each row will be interpreted as an element of the array. In this
case, the number of columns used must match the number of fields in
the data-type.
comments : str or sequence, optional
The characters or list of characters used to indicate the start of a
comment;
default: '#'.
delimiter : str, optional
The string used to separate values. By default, this is any
whitespace.
converters : dict, optional
A dictionary mapping column number to a function that will convert
that column to a float. E.g., if column 0 is a date string:
``converters = {0: datestr2num}``. Converters can also be used to
provide a default value for missing data (but see also `genfromtxt`):
``converters = {3: lambda s: float(s.strip() or 0)}``. Default: None.
skiprows : int, optional
Skip the first `skiprows` lines; default: 0.
usecols : sequence, optional
Which columns to read, with 0 being the first. For example,
``usecols = (1,4,5)`` will extract the 2nd, 5th and 6th columns.
The default, None, results in all columns being read.
unpack : bool, optional
If True, the returned array is transposed, so that arguments may be
unpacked using ``x, y, z = loadtxt(...)``. When used with a structured
data-type, arrays are returned for each field. Default is False.
ndmin : int, optional
The returned array will have at least `ndmin` dimensions.
Otherwise mono-dimensional axes will be squeezed.
Legal values: 0 (default), 1 or 2.
.. versionadded:: 1.6.0
Returns
-------
out : ndarray
Data read from the text file.
See Also
--------
load, fromstring, fromregex
genfromtxt : Load data with missing values handled as specified.
scipy.io.loadmat : reads MATLAB data files
Notes
-----
This function aims to be a fast reader for simply formatted files. The
`genfromtxt` function provides more sophisticated handling of, e.g.,
lines with missing values.
.. versionadded:: 1.10.0
The strings produced by the Python float.hex method can be used as
input for floats.
Examples
--------
from io import StringIO # StringIO behaves like a file object
c = StringIO("0 1\n2 3")
np.loadtxt(c)
array([[ 0., 1.],
[ 2., 3.]])
d = StringIO("M 21 72\nF 35 58")
np.loadtxt(d, dtype={'names': ('gender', 'age', 'weight'),
'formats': ('S1', 'i4', 'f4')})
array([('M', 21, 72.0), ('F', 35, 58.0)],
dtype=[('gender', '|S1'), ('age', ']
plt.plot(x2, y + 0.5, 'o')
[]
plt.ylim([-0.5, 1])
(-0.5, 1)
plt.show()
lookfor(what, module=None, import_modules=True, regenerate=False, output=None)
Do a keyword search on docstrings.
A list of of objects that matched the search is displayed,
sorted by relevance. All given keywords need to be found in the
docstring for it to be returned as a result, but the order does
not matter.
Parameters
----------
what : str
String containing words to look for.
module : str or list, optional
Name of module(s) whose docstrings to go through.
import_modules : bool, optional
Whether to import sub-modules in packages. Default is True.
regenerate : bool, optional
Whether to re-generate the docstring cache. Default is False.
output : file-like, optional
File-like object to write the output to. If omitted, use a pager.
See Also
--------
source, info
Notes
-----
Relevance is determined only roughly, by checking if the keywords occur
in the function name, at the start of a docstring, etc.
Examples
--------
np.lookfor('binary representation')
Search results for 'binary representation'
------------------------------------------
numpy.binary_repr
Return the binary representation of the input number as a string.
numpy.core.setup_common.long_double_representation
Given a binary dump as given by GNU od -b, look for long double
numpy.base_repr
Return a string representation of a number in the given base system.
...
mafromtxt(fname, **kwargs)
Load ASCII data stored in a text file and return a masked array.
Parameters
----------
fname, kwargs : For a description of input parameters, see `genfromtxt`.
See Also
--------
numpy.genfromtxt : generic function to load ASCII data.
mask_indices(n, mask_func, k=0)
Return the indices to access (n, n) arrays, given a masking function.
Assume `mask_func` is a function that, for a square array a of size
``(n, n)`` with a possible offset argument `k`, when called as
``mask_func(a, k)`` returns a new array with zeros in certain locations
(functions like `triu` or `tril` do precisely this). Then this function
returns the indices where the non-zero values would be located.
Parameters
----------
n : int
The returned indices will be valid to access arrays of shape (n, n).
mask_func : callable
A function whose call signature is similar to that of `triu`, `tril`.
That is, ``mask_func(x, k)`` returns a boolean array, shaped like `x`.
`k` is an optional argument to the function.
k : scalar
An optional argument which is passed through to `mask_func`. Functions
like `triu`, `tril` take a second argument that is interpreted as an
offset.
Returns
-------
indices : tuple of arrays.
The `n` arrays of indices corresponding to the locations where
``mask_func(np.ones((n, n)), k)`` is True.
See Also
--------
triu, tril, triu_indices, tril_indices
Notes
-----
.. versionadded:: 1.4.0
Examples
--------
These are the indices that would allow you to access the upper triangular
part of any 3x3 array:
iu = np.mask_indices(3, np.triu)
For example, if `a` is a 3x3 array:
a = np.arange(9).reshape(3, 3)
a
array([[0, 1, 2],
[3, 4, 5],
[6, 7, 8]])
a[iu]
array([0, 1, 2, 4, 5, 8])
An offset can be passed also to the masking function. This gets us the
indices starting on the first diagonal right of the main one:
iu1 = np.mask_indices(3, np.triu, 1)
with which we now extract only three elements:
a[iu1]
array([1, 2, 5])
mat = asmatrix(data, dtype=None)
Interpret the input as a matrix.
Unlike `matrix`, `asmatrix` does not make a copy if the input is already
a matrix or an ndarray. Equivalent to ``matrix(data, copy=False)``.
Parameters
----------
data : array_like
Input data.
dtype : data-type
Data-type of the output matrix.
Returns
-------
mat : matrix
`data` interpreted as a matrix.
Examples
--------
x = np.array([[1, 2], [3, 4]])
m = np.asmatrix(x)
x[0,0] = 5
m
matrix([[5, 2],
[3, 4]])
matmul(...)
matmul(a, b, out=None)
Matrix product of two arrays.
The behavior depends on the arguments in the following way.
- If both arguments are 2-D they are multiplied like conventional
matrices.
- If either argument is N-D, N > 2, it is treated as a stack of
matrices residing in the last two indexes and broadcast accordingly.
- If the first argument is 1-D, it is promoted to a matrix by
prepending a 1 to its dimensions. After matrix multiplication
the prepended 1 is removed.
- If the second argument is 1-D, it is promoted to a matrix by
appending a 1 to its dimensions. After matrix multiplication
the appended 1 is removed.
Multiplication by a scalar is not allowed, use ``*`` instead. Note that
multiplying a stack of matrices with a vector will result in a stack of
vectors, but matmul will not recognize it as such.
``matmul`` differs from ``dot`` in two important ways.
- Multiplication by scalars is not allowed.
- Stacks of matrices are broadcast together as if the matrices
were elements.
.. warning::
This function is preliminary and included in Numpy 1.10 for testing
and documentation. Its semantics will not change, but the number and
order of the optional arguments will.
.. versionadded:: 1.10.0
Parameters
----------
a : array_like
First argument.
b : array_like
Second argument.
out : ndarray, optional
Output argument. This must have the exact kind that would be returned
if it was not used. In particular, it must have the right type, must be
C-contiguous, and its dtype must be the dtype that would be returned
for `dot(a,b)`. This is a performance feature. Therefore, if these
conditions are not met, an exception is raised, instead of attempting
to be flexible.
Returns
-------
output : ndarray
Returns the dot product of `a` and `b`. If `a` and `b` are both
1-D arrays then a scalar is returned; otherwise an array is
returned. If `out` is given, then it is returned.
Raises
------
ValueError
If the last dimension of `a` is not the same size as
the second-to-last dimension of `b`.
If scalar value is passed.
See Also
--------
vdot : Complex-conjugating dot product.
tensordot : Sum products over arbitrary axes.
einsum : Einstein summation convention.
dot : alternative matrix product with different broadcasting rules.
Notes
-----
The matmul function implements the semantics of the `@` operator introduced
in Python 3.5 following PEP465.
Examples
--------
For 2-D arrays it is the matrix product:
a = [[1, 0], [0, 1]]
b = [[4, 1], [2, 2]]
np.matmul(a, b)
array([[4, 1],
[2, 2]])
For 2-D mixed with 1-D, the result is the usual.
a = [[1, 0], [0, 1]]
b = [1, 2]
np.matmul(a, b)
array([1, 2])
np.matmul(b, a)
array([1, 2])
Broadcasting is conventional for stacks of arrays
a = np.arange(2*2*4).reshape((2,2,4))
b = np.arange(2*2*4).reshape((2,4,2))
np.matmul(a,b).shape
(2, 2, 2)
np.matmul(a,b)[0,1,1]
98
sum(a[0,1,:] * b[0,:,1])
98
Vector, vector returns the scalar inner product, but neither argument
is complex-conjugated:
np.matmul([2j, 3j], [2j, 3j])
(-13+0j)
Scalar multiplication raises an error.
np.matmul([1,2], 3)
Traceback (most recent call last):
...
ValueError: Scalar operands are not allowed, use '*' instead
maximum_sctype(t)
Return the scalar type of highest precision of the same kind as the input.
Parameters
----------
t : dtype or dtype specifier
The input data type. This can be a `dtype` object or an object that
is convertible to a `dtype`.
Returns
-------
out : dtype
The highest precision data type of the same kind (`dtype.kind`) as `t`.
See Also
--------
obj2sctype, mintypecode, sctype2char
dtype
Examples
--------
np.maximum_sctype(np.int)
np.maximum_sctype(np.uint8)
np.maximum_sctype(np.complex)
np.maximum_sctype(str)
np.maximum_sctype('i2')
np.maximum_sctype('f4')
may_share_memory(...)
Determine if two arrays can share memory
The memory-bounds of a and b are computed. If they overlap then
this function returns True. Otherwise, it returns False.
A return of True does not necessarily mean that the two arrays
share any element. It just means that they *might*.
Parameters
----------
a, b : ndarray
Returns
-------
out : bool
Examples
--------
np.may_share_memory(np.array([1,2]), np.array([5,8,9]))
False
mean(a, axis=None, dtype=None, out=None, keepdims=False)
Compute the arithmetic mean along the specified axis.
Returns the average of the array elements. The average is taken over
the flattened array by default, otherwise over the specified axis.
`float64` intermediate and return values are used for integer inputs.
Parameters
----------
a : array_like
Array containing numbers whose mean is desired. If `a` is not an
array, a conversion is attempted.
axis : None or int or tuple of ints, optional
Axis or axes along which the means are computed. The default is to
compute the mean of the flattened array.
.. versionadded: 1.7.0
If this is a tuple of ints, a mean is performed over multiple axes,
instead of a single axis or all the axes as before.
dtype : data-type, optional
Type to use in computing the mean. For integer inputs, the default
is `float64`; for floating point inputs, it is the same as the
input dtype.
out : ndarray, optional
Alternate output array in which to place the result. The default
is ``None``; if provided, it must have the same shape as the
expected output, but the type will be cast if necessary.
See `doc.ufuncs` for details.
keepdims : bool, optional
If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option,
the result will broadcast correctly against the original `arr`.
Returns
-------
m : ndarray, see dtype parameter above
If `out=None`, returns a new array containing the mean values,
otherwise a reference to the output array is returned.
See Also
--------
average : Weighted average
std, var, nanmean, nanstd, nanvar
Notes
-----
The arithmetic mean is the sum of the elements along the axis divided
by the number of elements.
Note that for floating-point input, the mean is computed using the
same precision the input has. Depending on the input data, this can
cause the results to be inaccurate, especially for `float32` (see
example below). Specifying a higher-precision accumulator using the
`dtype` keyword can alleviate this issue.
Examples
--------
a = np.array([[1, 2], [3, 4]])
np.mean(a)
2.5
np.mean(a, axis=0)
array([ 2., 3.])
np.mean(a, axis=1)
array([ 1.5, 3.5])
In single precision, `mean` can be inaccurate:
a = np.zeros((2, 512*512), dtype=np.float32)
a[0, :] = 1.0
a[1, :] = 0.1
np.mean(a)
0.546875
Computing the mean in float64 is more accurate:
np.mean(a, dtype=np.float64)
0.55000000074505806
median(a, axis=None, out=None, overwrite_input=False, keepdims=False)
Compute the median along the specified axis.
Returns the median of the array elements.
Parameters
----------
a : array_like
Input array or object that can be converted to an array.
axis : int or sequence of int, optional
Axis along which the medians are computed. The default (axis=None)
is to compute the median along a flattened version of the array.
A sequence of axes is supported since version 1.9.0.
out : ndarray, optional
Alternative output array in which to place the result. It must have
the same shape and buffer length as the expected output, but the
type (of the output) will be cast if necessary.
overwrite_input : bool, optional
If True, then allow use of memory of input array (a) for
calculations. The input array will be modified by the call to
median. This will save memory when you do not need to preserve the
contents of the input array. Treat the input as undefined, but it
will probably be fully or partially sorted. Default is False. Note
that, if `overwrite_input` is True and the input is not already an
ndarray, an error will be raised.
keepdims : bool, optional
If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option,
the result will broadcast correctly against the original `arr`.
.. versionadded:: 1.9.0
Returns
-------
median : ndarray
A new array holding the result (unless `out` is specified, in which
case that array is returned instead). If the input contains
integers, or floats of smaller precision than 64, then the output
data-type is float64. Otherwise, the output data-type is the same
as that of the input.
See Also
--------
mean, percentile
Notes
-----
Given a vector V of length N, the median of V is the middle value of
a sorted copy of V, ``V_sorted`` - i.e., ``V_sorted[(N-1)/2]``, when N is
odd. When N is even, it is the average of the two middle values of
``V_sorted``.
Examples
--------
a = np.array([[10, 7, 4], [3, 2, 1]])
a
array([[10, 7, 4],
[ 3, 2, 1]])
np.median(a)
3.5
np.median(a, axis=0)
array([ 6.5, 4.5, 2.5])
np.median(a, axis=1)
array([ 7., 2.])
m = np.median(a, axis=0)
out = np.zeros_like(m)
np.median(a, axis=0, out=m)
array([ 6.5, 4.5, 2.5])
m
array([ 6.5, 4.5, 2.5])
b = a.copy()
np.median(b, axis=1, overwrite_input=True)
array([ 7., 2.])
assert not np.all(a==b)
b = a.copy()
np.median(b, axis=None, overwrite_input=True)
3.5
assert not np.all(a==b)
meshgrid(*xi, **kwargs)
Return coordinate matrices from coordinate vectors.
Make N-D coordinate arrays for vectorized evaluations of
N-D scalar/vector fields over N-D grids, given
one-dimensional coordinate arrays x1, x2,..., xn.
.. versionchanged:: 1.9
1-D and 0-D cases are allowed.
Parameters
----------
x1, x2,..., xn : array_like
1-D arrays representing the coordinates of a grid.
indexing : {'xy', 'ij'}, optional
Cartesian ('xy', default) or matrix ('ij') indexing of output.
See Notes for more details.
.. versionadded:: 1.7.0
sparse : bool, optional
If True a sparse grid is returned in order to conserve memory.
Default is False.
.. versionadded:: 1.7.0
copy : bool, optional
If False, a view into the original arrays are returned in order to
conserve memory. Default is True. Please note that
``sparse=False, copy=False`` will likely return non-contiguous
arrays. Furthermore, more than one element of a broadcast array
may refer to a single memory location. If you need to write to the
arrays, make copies first.
.. versionadded:: 1.7.0
Returns
-------
X1, X2,..., XN : ndarray
For vectors `x1`, `x2`,..., 'xn' with lengths ``Ni=len(xi)`` ,
return ``(N1, N2, N3,...Nn)`` shaped arrays if indexing='ij'
or ``(N2, N1, N3,...Nn)`` shaped arrays if indexing='xy'
with the elements of `xi` repeated to fill the matrix along
the first dimension for `x1`, the second for `x2` and so on.
Notes
-----
This function supports both indexing conventions through the indexing
keyword argument. Giving the string 'ij' returns a meshgrid with
matrix indexing, while 'xy' returns a meshgrid with Cartesian indexing.
In the 2-D case with inputs of length M and N, the outputs are of shape
(N, M) for 'xy' indexing and (M, N) for 'ij' indexing. In the 3-D case
with inputs of length M, N and P, outputs are of shape (N, M, P) for
'xy' indexing and (M, N, P) for 'ij' indexing. The difference is
illustrated by the following code snippet::
xv, yv = meshgrid(x, y, sparse=False, indexing='ij')
for i in range(nx):
for j in range(ny):
# treat xv[i,j], yv[i,j]
xv, yv = meshgrid(x, y, sparse=False, indexing='xy')
for i in range(nx):
for j in range(ny):
# treat xv[j,i], yv[j,i]
In the 1-D and 0-D case, the indexing and sparse keywords have no effect.
See Also
--------
index_tricks.mgrid : Construct a multi-dimensional "meshgrid"
using indexing notation.
index_tricks.ogrid : Construct an open multi-dimensional "meshgrid"
using indexing notation.
Examples
--------
nx, ny = (3, 2)
x = np.linspace(0, 1, nx)
y = np.linspace(0, 1, ny)
xv, yv = meshgrid(x, y)
xv
array([[ 0. , 0.5, 1. ],
[ 0. , 0.5, 1. ]])
yv
array([[ 0., 0., 0.],
[ 1., 1., 1.]])
xv, yv = meshgrid(x, y, sparse=True) # make sparse output arrays
xv
array([[ 0. , 0.5, 1. ]])
yv
array([[ 0.],
[ 1.]])
`meshgrid` is very useful to evaluate functions on a grid.
x = np.arange(-5, 5, 0.1)
y = np.arange(-5, 5, 0.1)
xx, yy = meshgrid(x, y, sparse=True)
z = np.sin(xx**2 + yy**2) / (xx**2 + yy**2)
h = plt.contourf(x,y,z)
min_scalar_type(...)
min_scalar_type(a)
For scalar ``a``, returns the data type with the smallest size
and smallest scalar kind which can hold its value. For non-scalar
array ``a``, returns the vector's dtype unmodified.
Floating point values are not demoted to integers,
and complex values are not demoted to floats.
Parameters
----------
a : scalar or array_like
The value whose minimal data type is to be found.
Returns
-------
out : dtype
The minimal data type.
Notes
-----
.. versionadded:: 1.6.0
See Also
--------
result_type, promote_types, dtype, can_cast
Examples
--------
np.min_scalar_type(10)
dtype('uint8')
np.min_scalar_type(-260)
dtype('int16')
np.min_scalar_type(3.1)
dtype('float16')
np.min_scalar_type(1e50)
dtype('float64')
np.min_scalar_type(np.arange(4,dtype='f8'))
dtype('float64')
mintypecode(typechars, typeset='GDFgdf', default='d')
Return the character for the minimum-size type to which given types can
be safely cast.
The returned type character must represent the smallest size dtype such
that an array of the returned type can handle the data from an array of
all types in `typechars` (or if `typechars` is an array, then its
dtype.char).
Parameters
----------
typechars : list of str or array_like
If a list of strings, each string should represent a dtype.
If array_like, the character representation of the array dtype is used.
typeset : str or list of str, optional
The set of characters that the returned character is chosen from.
The default set is 'GDFgdf'.
default : str, optional
The default character, this is returned if none of the characters in
`typechars` matches a character in `typeset`.
Returns
-------
typechar : str
The character representing the minimum-size type that was found.
See Also
--------
dtype, sctype2char, maximum_sctype
Examples
--------
np.mintypecode(['d', 'f', 'S'])
'd'
x = np.array([1.1, 2-3.j])
np.mintypecode(x)
'D'
np.mintypecode('abceh', default='G')
'G'
mirr(values, finance_rate, reinvest_rate)
Modified internal rate of return.
Parameters
----------
values : array_like
Cash flows (must contain at least one positive and one negative
value) or nan is returned. The first value is considered a sunk
cost at time zero.
finance_rate : scalar
Interest rate paid on the cash flows
reinvest_rate : scalar
Interest rate received on the cash flows upon reinvestment
Returns
-------
out : float
Modified internal rate of return
msort(a)
Return a copy of an array sorted along the first axis.
Parameters
----------
a : array_like
Array to be sorted.
Returns
-------
sorted_array : ndarray
Array of the same type and shape as `a`.
See Also
--------
sort
Notes
-----
``np.msort(a)`` is equivalent to ``np.sort(a, axis=0)``.
nan_to_num(x)
Replace nan with zero and inf with finite numbers.
Returns an array or scalar replacing Not a Number (NaN) with zero,
(positive) infinity with a very large number and negative infinity
with a very small (or negative) number.
Parameters
----------
x : array_like
Input data.
Returns
-------
out : ndarray
New Array with the same shape as `x` and dtype of the element in
`x` with the greatest precision. If `x` is inexact, then NaN is
replaced by zero, and infinity (-infinity) is replaced by the
largest (smallest or most negative) floating point value that fits
in the output dtype. If `x` is not inexact, then a copy of `x` is
returned.
See Also
--------
isinf : Shows which elements are negative or negative infinity.
isneginf : Shows which elements are negative infinity.
isposinf : Shows which elements are positive infinity.
isnan : Shows which elements are Not a Number (NaN).
isfinite : Shows which elements are finite (not NaN, not infinity)
Notes
-----
Numpy uses the IEEE Standard for Binary Floating-Point for Arithmetic
(IEEE 754). This means that Not a Number is not equivalent to infinity.
Examples
--------
np.set_printoptions(precision=8)
x = np.array([np.inf, -np.inf, np.nan, -128, 128])
np.nan_to_num(x)
array([ 1.79769313e+308, -1.79769313e+308, 0.00000000e+000,
-1.28000000e+002, 1.28000000e+002])
nanargmax(a, axis=None)
Return the indices of the maximum values in the specified axis ignoring
NaNs. For all-NaN slices ``ValueError`` is raised. Warning: the
results cannot be trusted if a slice contains only NaNs and -Infs.
Parameters
----------
a : array_like
Input data.
axis : int, optional
Axis along which to operate. By default flattened input is used.
Returns
-------
index_array : ndarray
An array of indices or a single index value.
See Also
--------
argmax, nanargmin
Examples
--------
a = np.array([[np.nan, 4], [2, 3]])
np.argmax(a)
0
np.nanargmax(a)
1
np.nanargmax(a, axis=0)
array([1, 0])
np.nanargmax(a, axis=1)
array([1, 1])
nanargmin(a, axis=None)
Return the indices of the minimum values in the specified axis ignoring
NaNs. For all-NaN slices ``ValueError`` is raised. Warning: the results
cannot be trusted if a slice contains only NaNs and Infs.
Parameters
----------
a : array_like
Input data.
axis : int, optional
Axis along which to operate. By default flattened input is used.
Returns
-------
index_array : ndarray
An array of indices or a single index value.
See Also
--------
argmin, nanargmax
Examples
--------
a = np.array([[np.nan, 4], [2, 3]])
np.argmin(a)
0
np.nanargmin(a)
2
np.nanargmin(a, axis=0)
array([1, 1])
np.nanargmin(a, axis=1)
array([1, 0])
nanmax(a, axis=None, out=None, keepdims=False)
Return the maximum of an array or maximum along an axis, ignoring any
NaNs. When all-NaN slices are encountered a ``RuntimeWarning`` is
raised and NaN is returned for that slice.
Parameters
----------
a : array_like
Array containing numbers whose maximum is desired. If `a` is not an
array, a conversion is attempted.
axis : int, optional
Axis along which the maximum is computed. The default is to compute
the maximum of the flattened array.
out : ndarray, optional
Alternate output array in which to place the result. The default
is ``None``; if provided, it must have the same shape as the
expected output, but the type will be cast if necessary. See
`doc.ufuncs` for details.
.. versionadded:: 1.8.0
keepdims : bool, optional
If this is set to True, the axes which are reduced are left in the
result as dimensions with size one. With this option, the result
will broadcast correctly against the original `a`.
.. versionadded:: 1.8.0
Returns
-------
nanmax : ndarray
An array with the same shape as `a`, with the specified axis removed.
If `a` is a 0-d array, or if axis is None, an ndarray scalar is
returned. The same dtype as `a` is returned.
See Also
--------
nanmin :
The minimum value of an array along a given axis, ignoring any NaNs.
amax :
The maximum value of an array along a given axis, propagating any NaNs.
fmax :
Element-wise maximum of two arrays, ignoring any NaNs.
maximum :
Element-wise maximum of two arrays, propagating any NaNs.
isnan :
Shows which elements are Not a Number (NaN).
isfinite:
Shows which elements are neither NaN nor infinity.
amin, fmin, minimum
Notes
-----
Numpy uses the IEEE Standard for Binary Floating-Point for Arithmetic
(IEEE 754). This means that Not a Number is not equivalent to infinity.
Positive infinity is treated as a very large number and negative
infinity is treated as a very small (i.e. negative) number.
If the input has a integer type the function is equivalent to np.max.
Examples
--------
a = np.array([[1, 2], [3, np.nan]])
np.nanmax(a)
3.0
np.nanmax(a, axis=0)
array([ 3., 2.])
np.nanmax(a, axis=1)
array([ 2., 3.])
When positive infinity and negative infinity are present:
np.nanmax([1, 2, np.nan, np.NINF])
2.0
np.nanmax([1, 2, np.nan, np.inf])
inf
nanmean(a, axis=None, dtype=None, out=None, keepdims=False)
Compute the arithmetic mean along the specified axis, ignoring NaNs.
Returns the average of the array elements. The average is taken over
the flattened array by default, otherwise over the specified axis.
`float64` intermediate and return values are used for integer inputs.
For all-NaN slices, NaN is returned and a `RuntimeWarning` is raised.
.. versionadded:: 1.8.0
Parameters
----------
a : array_like
Array containing numbers whose mean is desired. If `a` is not an
array, a conversion is attempted.
axis : int, optional
Axis along which the means are computed. The default is to compute
the mean of the flattened array.
dtype : data-type, optional
Type to use in computing the mean. For integer inputs, the default
is `float64`; for inexact inputs, it is the same as the input
dtype.
out : ndarray, optional
Alternate output array in which to place the result. The default
is ``None``; if provided, it must have the same shape as the
expected output, but the type will be cast if necessary. See
`doc.ufuncs` for details.
keepdims : bool, optional
If this is set to True, the axes which are reduced are left in the
result as dimensions with size one. With this option, the result
will broadcast correctly against the original `arr`.
Returns
-------
m : ndarray, see dtype parameter above
If `out=None`, returns a new array containing the mean values,
otherwise a reference to the output array is returned. Nan is
returned for slices that contain only NaNs.
See Also
--------
average : Weighted average
mean : Arithmetic mean taken while not ignoring NaNs
var, nanvar
Notes
-----
The arithmetic mean is the sum of the non-NaN elements along the axis
divided by the number of non-NaN elements.
Note that for floating-point input, the mean is computed using the same
precision the input has. Depending on the input data, this can cause
the results to be inaccurate, especially for `float32`. Specifying a
higher-precision accumulator using the `dtype` keyword can alleviate
this issue.
Examples
--------
a = np.array([[1, np.nan], [3, 4]])
np.nanmean(a)
2.6666666666666665
np.nanmean(a, axis=0)
array([ 2., 4.])
np.nanmean(a, axis=1)
array([ 1., 3.5])
nanmedian(a, axis=None, out=None, overwrite_input=False, keepdims=False)
Compute the median along the specified axis, while ignoring NaNs.
Returns the median of the array elements.
.. versionadded:: 1.9.0
Parameters
----------
a : array_like
Input array or object that can be converted to an array.
axis : int, optional
Axis along which the medians are computed. The default (axis=None)
is to compute the median along a flattened version of the array.
A sequence of axes is supported since version 1.9.0.
out : ndarray, optional
Alternative output array in which to place the result. It must have
the same shape and buffer length as the expected output, but the
type (of the output) will be cast if necessary.
overwrite_input : bool, optional
If True, then allow use of memory of input array (a) for
calculations. The input array will be modified by the call to
median. This will save memory when you do not need to preserve
the contents of the input array. Treat the input as undefined,
but it will probably be fully or partially sorted. Default is
False. Note that, if `overwrite_input` is True and the input
is not already an ndarray, an error will be raised.
keepdims : bool, optional
If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option,
the result will broadcast correctly against the original `arr`.
Returns
-------
median : ndarray
A new array holding the result. If the input contains integers, or
floats of smaller precision than 64, then the output data-type is
float64. Otherwise, the output data-type is the same as that of the
input.
See Also
--------
mean, median, percentile
Notes
-----
Given a vector V of length N, the median of V is the middle value of
a sorted copy of V, ``V_sorted`` - i.e., ``V_sorted[(N-1)/2]``, when N is
odd. When N is even, it is the average of the two middle values of
``V_sorted``.
Examples
--------
a = np.array([[10.0, 7, 4], [3, 2, 1]])
a[0, 1] = np.nan
a
array([[ 10., nan, 4.],
[ 3., 2., 1.]])
np.median(a)
nan
np.nanmedian(a)
3.0
np.nanmedian(a, axis=0)
array([ 6.5, 2., 2.5])
np.median(a, axis=1)
array([ 7., 2.])
b = a.copy()
np.nanmedian(b, axis=1, overwrite_input=True)
array([ 7., 2.])
assert not np.all(a==b)
b = a.copy()
np.nanmedian(b, axis=None, overwrite_input=True)
3.0
assert not np.all(a==b)
nanmin(a, axis=None, out=None, keepdims=False)
Return minimum of an array or minimum along an axis, ignoring any NaNs.
When all-NaN slices are encountered a ``RuntimeWarning`` is raised and
Nan is returned for that slice.
Parameters
----------
a : array_like
Array containing numbers whose minimum is desired. If `a` is not an
array, a conversion is attempted.
axis : int, optional
Axis along which the minimum is computed. The default is to compute
the minimum of the flattened array.
out : ndarray, optional
Alternate output array in which to place the result. The default
is ``None``; if provided, it must have the same shape as the
expected output, but the type will be cast if necessary. See
`doc.ufuncs` for details.
.. versionadded:: 1.8.0
keepdims : bool, optional
If this is set to True, the axes which are reduced are left in the
result as dimensions with size one. With this option, the result
will broadcast correctly against the original `a`.
.. versionadded:: 1.8.0
Returns
-------
nanmin : ndarray
An array with the same shape as `a`, with the specified axis
removed. If `a` is a 0-d array, or if axis is None, an ndarray
scalar is returned. The same dtype as `a` is returned.
See Also
--------
nanmax :
The maximum value of an array along a given axis, ignoring any NaNs.
amin :
The minimum value of an array along a given axis, propagating any NaNs.
fmin :
Element-wise minimum of two arrays, ignoring any NaNs.
minimum :
Element-wise minimum of two arrays, propagating any NaNs.
isnan :
Shows which elements are Not a Number (NaN).
isfinite:
Shows which elements are neither NaN nor infinity.
amax, fmax, maximum
Notes
-----
Numpy uses the IEEE Standard for Binary Floating-Point for Arithmetic
(IEEE 754). This means that Not a Number is not equivalent to infinity.
Positive infinity is treated as a very large number and negative
infinity is treated as a very small (i.e. negative) number.
If the input has a integer type the function is equivalent to np.min.
Examples
--------
a = np.array([[1, 2], [3, np.nan]])
np.nanmin(a)
1.0
np.nanmin(a, axis=0)
array([ 1., 2.])
np.nanmin(a, axis=1)
array([ 1., 3.])
When positive infinity and negative infinity are present:
np.nanmin([1, 2, np.nan, np.inf])
1.0
np.nanmin([1, 2, np.nan, np.NINF])
-inf
nanpercentile(a, q, axis=None, out=None, overwrite_input=False, interpolation='linear', keepdims=False)
Compute the qth percentile of the data along the specified axis, while
ignoring nan values.
Returns the qth percentile of the array elements.
.. versionadded:: 1.9.0
Parameters
----------
a : array_like
Input array or object that can be converted to an array.
q : float in range of [0,100] (or sequence of floats)
Percentile to compute which must be between 0 and 100 inclusive.
axis : int or sequence of int, optional
Axis along which the percentiles are computed. The default (None)
is to compute the percentiles along a flattened version of the array.
A sequence of axes is supported since version 1.9.0.
out : ndarray, optional
Alternative output array in which to place the result. It must
have the same shape and buffer length as the expected output,
but the type (of the output) will be cast if necessary.
overwrite_input : bool, optional
If True, then allow use of memory of input array `a` for
calculations. The input array will be modified by the call to
percentile. This will save memory when you do not need to preserve
the contents of the input array. In this case you should not make
any assumptions about the content of the passed in array `a` after
this function completes -- treat it as undefined. Default is False.
Note that, if the `a` input is not already an array this parameter
will have no effect, `a` will be converted to an array internally
regardless of the value of this parameter.
interpolation : {'linear', 'lower', 'higher', 'midpoint', 'nearest'}
This optional parameter specifies the interpolation method to use,
when the desired quantile lies between two data points `i` and `j`:
* linear: `i + (j - i) * fraction`, where `fraction` is the
fractional part of the index surrounded by `i` and `j`.
* lower: `i`.
* higher: `j`.
* nearest: `i` or `j` whichever is nearest.
* midpoint: (`i` + `j`) / 2.
keepdims : bool, optional
If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option,
the result will broadcast correctly against the original `arr`.
Returns
-------
nanpercentile : scalar or ndarray
If a single percentile `q` is given and axis=None a scalar is
returned. If multiple percentiles `q` are given an array holding
the result is returned. The results are listed in the first axis.
(If `out` is specified, in which case that array is returned
instead). If the input contains integers, or floats of smaller
precision than 64, then the output data-type is float64. Otherwise,
the output data-type is the same as that of the input.
See Also
--------
nanmean, nanmedian, percentile, median, mean
Notes
-----
Given a vector V of length N, the q-th percentile of V is the q-th ranked
value in a sorted copy of V. The values and distances of the two
nearest neighbors as well as the `interpolation` parameter will
determine the percentile if the normalized ranking does not match q
exactly. This function is the same as the median if ``q=50``, the same
as the minimum if ``q=0``and the same as the maximum if ``q=100``.
Examples
--------
a = np.array([[10., 7., 4.], [3., 2., 1.]])
a[0][1] = np.nan
a
array([[ 10., nan, 4.],
[ 3., 2., 1.]])
np.percentile(a, 50)
nan
np.nanpercentile(a, 50)
3.5
np.nanpercentile(a, 50, axis=0)
array([[ 6.5, 4.5, 2.5]])
np.nanpercentile(a, 50, axis=1)
array([[ 7.],
[ 2.]])
m = np.nanpercentile(a, 50, axis=0)
out = np.zeros_like(m)
np.nanpercentile(a, 50, axis=0, out=m)
array([[ 6.5, 4.5, 2.5]])
m
array([[ 6.5, 4.5, 2.5]])
b = a.copy()
np.nanpercentile(b, 50, axis=1, overwrite_input=True)
array([[ 7.],
[ 2.]])
assert not np.all(a==b)
b = a.copy()
np.nanpercentile(b, 50, axis=None, overwrite_input=True)
array([ 3.5])
nanprod(a, axis=None, dtype=None, out=None, keepdims=0)
Return the product of array elements over a given axis treating Not a
Numbers (NaNs) as zero.
One is returned for slices that are all-NaN or empty.
.. versionadded:: 1.10.0
Parameters
----------
a : array_like
Array containing numbers whose sum is desired. If `a` is not an
array, a conversion is attempted.
axis : int, optional
Axis along which the product is computed. The default is to compute
the product of the flattened array.
dtype : data-type, optional
The type of the returned array and of the accumulator in which the
elements are summed. By default, the dtype of `a` is used. An
exception is when `a` has an integer type with less precision than
the platform (u)intp. In that case, the default will be either
(u)int32 or (u)int64 depending on whether the platform is 32 or 64
bits. For inexact inputs, dtype must be inexact.
out : ndarray, optional
Alternate output array in which to place the result. The default
is ``None``. If provided, it must have the same shape as the
expected output, but the type will be cast if necessary. See
`doc.ufuncs` for details. The casting of NaN to integer can yield
unexpected results.
keepdims : bool, optional
If True, the axes which are reduced are left in the result as
dimensions with size one. With this option, the result will
broadcast correctly against the original `arr`.
Returns
-------
y : ndarray or numpy scalar
See Also
--------
numpy.prod : Product across array propagating NaNs.
isnan : Show which elements are NaN.
Notes
-----
Numpy integer arithmetic is modular. If the size of a product exceeds
the size of an integer accumulator, its value will wrap around and the
result will be incorrect. Specifying ``dtype=double`` can alleviate
that problem.
Examples
--------
np.nanprod(1)
1
np.nanprod([1])
1
np.nanprod([1, np.nan])
1.0
a = np.array([[1, 2], [3, np.nan]])
np.nanprod(a)
6.0
np.nanprod(a, axis=0)
array([ 3., 2.])
nanstd(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False)
Compute the standard deviation along the specified axis, while
ignoring NaNs.
Returns the standard deviation, a measure of the spread of a
distribution, of the non-NaN array elements. The standard deviation is
computed for the flattened array by default, otherwise over the
specified axis.
For all-NaN slices or slices with zero degrees of freedom, NaN is
returned and a `RuntimeWarning` is raised.
.. versionadded:: 1.8.0
Parameters
----------
a : array_like
Calculate the standard deviation of the non-NaN values.
axis : int, optional
Axis along which the standard deviation is computed. The default is
to compute the standard deviation of the flattened array.
dtype : dtype, optional
Type to use in computing the standard deviation. For arrays of
integer type the default is float64, for arrays of float types it
is the same as the array type.
out : ndarray, optional
Alternative output array in which to place the result. It must have
the same shape as the expected output but the type (of the
calculated values) will be cast if necessary.
ddof : int, optional
Means Delta Degrees of Freedom. The divisor used in calculations
is ``N - ddof``, where ``N`` represents the number of non-NaN
elements. By default `ddof` is zero.
keepdims : bool, optional
If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option,
the result will broadcast correctly against the original `arr`.
Returns
-------
standard_deviation : ndarray, see dtype parameter above.
If `out` is None, return a new array containing the standard
deviation, otherwise return a reference to the output array. If
ddof is >= the number of non-NaN elements in a slice or the slice
contains only NaNs, then the result for that slice is NaN.
See Also
--------
var, mean, std
nanvar, nanmean
numpy.doc.ufuncs : Section "Output arguments"
Notes
-----
The standard deviation is the square root of the average of the squared
deviations from the mean: ``std = sqrt(mean(abs(x - x.mean())**2))``.
The average squared deviation is normally calculated as
``x.sum() / N``, where ``N = len(x)``. If, however, `ddof` is
specified, the divisor ``N - ddof`` is used instead. In standard
statistical practice, ``ddof=1`` provides an unbiased estimator of the
variance of the infinite population. ``ddof=0`` provides a maximum
likelihood estimate of the variance for normally distributed variables.
The standard deviation computed in this function is the square root of
the estimated variance, so even with ``ddof=1``, it will not be an
unbiased estimate of the standard deviation per se.
Note that, for complex numbers, `std` takes the absolute value before
squaring, so that the result is always real and nonnegative.
For floating-point input, the *std* is computed using the same
precision the input has. Depending on the input data, this can cause
the results to be inaccurate, especially for float32 (see example
below). Specifying a higher-accuracy accumulator using the `dtype`
keyword can alleviate this issue.
Examples
--------
a = np.array([[1, np.nan], [3, 4]])
np.nanstd(a)
1.247219128924647
np.nanstd(a, axis=0)
array([ 1., 0.])
np.nanstd(a, axis=1)
array([ 0., 0.5])
nansum(a, axis=None, dtype=None, out=None, keepdims=0)
Return the sum of array elements over a given axis treating Not a
Numbers (NaNs) as zero.
In Numpy versions <= 1.8 Nan is returned for slices that are all-NaN or
empty. In later versions zero is returned.
Parameters
----------
a : array_like
Array containing numbers whose sum is desired. If `a` is not an
array, a conversion is attempted.
axis : int, optional
Axis along which the sum is computed. The default is to compute the
sum of the flattened array.
dtype : data-type, optional
The type of the returned array and of the accumulator in which the
elements are summed. By default, the dtype of `a` is used. An
exception is when `a` has an integer type with less precision than
the platform (u)intp. In that case, the default will be either
(u)int32 or (u)int64 depending on whether the platform is 32 or 64
bits. For inexact inputs, dtype must be inexact.
.. versionadded:: 1.8.0
out : ndarray, optional
Alternate output array in which to place the result. The default
is ``None``. If provided, it must have the same shape as the
expected output, but the type will be cast if necessary. See
`doc.ufuncs` for details. The casting of NaN to integer can yield
unexpected results.
.. versionadded:: 1.8.0
keepdims : bool, optional
If True, the axes which are reduced are left in the result as
dimensions with size one. With this option, the result will
broadcast correctly against the original `arr`.
.. versionadded:: 1.8.0
Returns
-------
y : ndarray or numpy scalar
See Also
--------
numpy.sum : Sum across array propagating NaNs.
isnan : Show which elements are NaN.
isfinite: Show which elements are not NaN or +/-inf.
Notes
-----
If both positive and negative infinity are present, the sum will be Not
A Number (NaN).
Numpy integer arithmetic is modular. If the size of a sum exceeds the
size of an integer accumulator, its value will wrap around and the
result will be incorrect. Specifying ``dtype=double`` can alleviate
that problem.
Examples
--------
np.nansum(1)
1
np.nansum([1])
1
np.nansum([1, np.nan])
1.0
a = np.array([[1, 1], [1, np.nan]])
np.nansum(a)
3.0
np.nansum(a, axis=0)
array([ 2., 1.])
np.nansum([1, np.nan, np.inf])
inf
np.nansum([1, np.nan, np.NINF])
-inf
np.nansum([1, np.nan, np.inf, -np.inf]) # both +/- infinity present
nan
nanvar(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False)
Compute the variance along the specified axis, while ignoring NaNs.
Returns the variance of the array elements, a measure of the spread of
a distribution. The variance is computed for the flattened array by
default, otherwise over the specified axis.
For all-NaN slices or slices with zero degrees of freedom, NaN is
returned and a `RuntimeWarning` is raised.
.. versionadded:: 1.8.0
Parameters
----------
a : array_like
Array containing numbers whose variance is desired. If `a` is not an
array, a conversion is attempted.
axis : int, optional
Axis along which the variance is computed. The default is to compute
the variance of the flattened array.
dtype : data-type, optional
Type to use in computing the variance. For arrays of integer type
the default is `float32`; for arrays of float types it is the same as
the array type.
out : ndarray, optional
Alternate output array in which to place the result. It must have
the same shape as the expected output, but the type is cast if
necessary.
ddof : int, optional
"Delta Degrees of Freedom": the divisor used in the calculation is
``N - ddof``, where ``N`` represents the number of non-NaN
elements. By default `ddof` is zero.
keepdims : bool, optional
If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option,
the result will broadcast correctly against the original `arr`.
Returns
-------
variance : ndarray, see dtype parameter above
If `out` is None, return a new array containing the variance,
otherwise return a reference to the output array. If ddof is >= the
number of non-NaN elements in a slice or the slice contains only
NaNs, then the result for that slice is NaN.
See Also
--------
std : Standard deviation
mean : Average
var : Variance while not ignoring NaNs
nanstd, nanmean
numpy.doc.ufuncs : Section "Output arguments"
Notes
-----
The variance is the average of the squared deviations from the mean,
i.e., ``var = mean(abs(x - x.mean())**2)``.
The mean is normally calculated as ``x.sum() / N``, where ``N = len(x)``.
If, however, `ddof` is specified, the divisor ``N - ddof`` is used
instead. In standard statistical practice, ``ddof=1`` provides an
unbiased estimator of the variance of a hypothetical infinite
population. ``ddof=0`` provides a maximum likelihood estimate of the
variance for normally distributed variables.
Note that for complex numbers, the absolute value is taken before
squaring, so that the result is always real and nonnegative.
For floating-point input, the variance is computed using the same
precision the input has. Depending on the input data, this can cause
the results to be inaccurate, especially for `float32` (see example
below). Specifying a higher-accuracy accumulator using the ``dtype``
keyword can alleviate this issue.
Examples
--------
a = np.array([[1, np.nan], [3, 4]])
np.var(a)
1.5555555555555554
np.nanvar(a, axis=0)
array([ 1., 0.])
np.nanvar(a, axis=1)
array([ 0., 0.25])
ndfromtxt(fname, **kwargs)
Load ASCII data stored in a file and return it as a single array.
Parameters
----------
fname, kwargs : For a description of input parameters, see `genfromtxt`.
See Also
--------
numpy.genfromtxt : generic function.
ndim(a)
Return the number of dimensions of an array.
Parameters
----------
a : array_like
Input array. If it is not already an ndarray, a conversion is
attempted.
Returns
-------
number_of_dimensions : int
The number of dimensions in `a`. Scalars are zero-dimensional.
See Also
--------
ndarray.ndim : equivalent method
shape : dimensions of array
ndarray.shape : dimensions of array
Examples
--------
np.ndim([[1,2,3],[4,5,6]])
2
np.ndim(np.array([[1,2,3],[4,5,6]]))
2
np.ndim(1)
0
nested_iters(...)
newbuffer(...)
newbuffer(size)
Return a new uninitialized buffer object.
Parameters
----------
size : int
Size in bytes of returned buffer object.
Returns
-------
newbuffer : buffer object
Returned, uninitialized buffer object of `size` bytes.
nonzero(a)
Return the indices of the elements that are non-zero.
Returns a tuple of arrays, one for each dimension of `a`,
containing the indices of the non-zero elements in that
dimension. The values in `a` are always tested and returned in
row-major, C-style order. The corresponding non-zero
values can be obtained with::
a[nonzero(a)]
To group the indices by element, rather than dimension, use::
transpose(nonzero(a))
The result of this is always a 2-D array, with a row for
each non-zero element.
Parameters
----------
a : array_like
Input array.
Returns
-------
tuple_of_arrays : tuple
Indices of elements that are non-zero.
See Also
--------
flatnonzero :
Return indices that are non-zero in the flattened version of the input
array.
ndarray.nonzero :
Equivalent ndarray method.
count_nonzero :
Counts the number of non-zero elements in the input array.
Examples
--------
x = np.eye(3)
x
array([[ 1., 0., 0.],
[ 0., 1., 0.],
[ 0., 0., 1.]])
np.nonzero(x)
(array([0, 1, 2]), array([0, 1, 2]))
x[np.nonzero(x)]
array([ 1., 1., 1.])
np.transpose(np.nonzero(x))
array([[0, 0],
[1, 1],
[2, 2]])
A common use for ``nonzero`` is to find the indices of an array, where
a condition is True. Given an array `a`, the condition `a` > 3 is a
boolean array and since False is interpreted as 0, np.nonzero(a > 3)
yields the indices of the `a` where the condition is true.
a = np.array([[1,2,3],[4,5,6],[7,8,9]])
a > 3
array([[False, False, False],
[ True, True, True],
[ True, True, True]], dtype=bool)
np.nonzero(a > 3)
(array([1, 1, 1, 2, 2, 2]), array([0, 1, 2, 0, 1, 2]))
The ``nonzero`` method of the boolean array can also be called.
(a > 3).nonzero()
(array([1, 1, 1, 2, 2, 2]), array([0, 1, 2, 0, 1, 2]))
nper(rate, pmt, pv, fv=0, when='end')
Compute the number of periodic payments.
Parameters
----------
rate : array_like
Rate of interest (per period)
pmt : array_like
Payment
pv : array_like
Present value
fv : array_like, optional
Future value
when : {{'begin', 1}, {'end', 0}}, {string, int}, optional
When payments are due ('begin' (1) or 'end' (0))
Notes
-----
The number of periods ``nper`` is computed by solving the equation::
fv + pv*(1+rate)**nper + pmt*(1+rate*when)/rate*((1+rate)**nper-1) = 0
but if ``rate = 0`` then::
fv + pv + pmt*nper = 0
Examples
--------
If you only had $150/month to pay towards the loan, how long would it take
to pay-off a loan of $8,000 at 7% annual interest?
print round(np.nper(0.07/12, -150, 8000), 5)
64.07335
So, over 64 months would be required to pay off the loan.
The same analysis could be done with several different interest rates
and/or payments and/or total amounts to produce an entire table.
np.nper(*(np.ogrid[0.07/12: 0.08/12: 0.01/12,
-150 : -99 : 50 ,
8000 : 9001 : 1000]))
array([[[ 64.07334877, 74.06368256],
[ 108.07548412, 127.99022654]],
[[ 66.12443902, 76.87897353],
[ 114.70165583, 137.90124779]]])
npv(rate, values)
Returns the NPV (Net Present Value) of a cash flow series.
Parameters
----------
rate : scalar
The discount rate.
values : array_like, shape(M, )
The values of the time series of cash flows. The (fixed) time
interval between cash flow "events" must be the same as that for
which `rate` is given (i.e., if `rate` is per year, then precisely
a year is understood to elapse between each cash flow event). By
convention, investments or "deposits" are negative, income or
"withdrawals" are positive; `values` must begin with the initial
investment, thus `values[0]` will typically be negative.
Returns
-------
out : float
The NPV of the input cash flow series `values` at the discount
`rate`.
Notes
-----
Returns the result of: [G]_
.. math :: \sum_{t=0}^{M-1}{\frac{values_t}{(1+rate)^{t}}}
References
----------
.. [G] L. J. Gitman, "Principles of Managerial Finance, Brief," 3rd ed.,
Addison-Wesley, 2003, pg. 346.
Examples
--------
np.npv(0.281,[-100, 39, 59, 55, 20])
-0.0084785916384548798
(Compare with the Example given for numpy.lib.financial.irr)
obj2sctype(rep, default=None)
Return the scalar dtype or NumPy equivalent of Python type of an object.
Parameters
----------
rep : any
The object of which the type is returned.
default : any, optional
If given, this is returned for objects whose types can not be
determined. If not given, None is returned for those objects.
Returns
-------
dtype : dtype or Python type
The data type of `rep`.
See Also
--------
sctype2char, issctype, issubsctype, issubdtype, maximum_sctype
Examples
--------
np.obj2sctype(np.int32)
np.obj2sctype(np.array([1., 2.]))
np.obj2sctype(np.array([1.j]))
np.obj2sctype(dict)
np.obj2sctype('string')
np.obj2sctype(1, default=list)
ones(shape, dtype=None, order='C')
Return a new array of given shape and type, filled with ones.
Parameters
----------
shape : int or sequence of ints
Shape of the new array, e.g., ``(2, 3)`` or ``2``.
dtype : data-type, optional
The desired data-type for the array, e.g., `numpy.int8`. Default is
`numpy.float64`.
order : {'C', 'F'}, optional
Whether to store multidimensional data in C- or Fortran-contiguous
(row- or column-wise) order in memory.
Returns
-------
out : ndarray
Array of ones with the given shape, dtype, and order.
See Also
--------
zeros, ones_like
Examples
--------
np.ones(5)
array([ 1., 1., 1., 1., 1.])
np.ones((5,), dtype=np.int)
array([1, 1, 1, 1, 1])
np.ones((2, 1))
array([[ 1.],
[ 1.]])
s = (2,2)
np.ones(s)
array([[ 1., 1.],
[ 1., 1.]])
ones_like(a, dtype=None, order='K', subok=True)
Return an array of ones with the same shape and type as a given array.
Parameters
----------
a : array_like
The shape and data-type of `a` define these same attributes of
the returned array.
dtype : data-type, optional
Overrides the data type of the result.
.. versionadded:: 1.6.0
order : {'C', 'F', 'A', or 'K'}, optional
Overrides the memory layout of the result. 'C' means C-order,
'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous,
'C' otherwise. 'K' means match the layout of `a` as closely
as possible.
.. versionadded:: 1.6.0
subok : bool, optional.
If True, then the newly created array will use the sub-class
type of 'a', otherwise it will be a base-class array. Defaults
to True.
Returns
-------
out : ndarray
Array of ones with the same shape and type as `a`.
See Also
--------
zeros_like : Return an array of zeros with shape and type of input.
empty_like : Return an empty array with shape and type of input.
zeros : Return a new array setting values to zero.
ones : Return a new array setting values to one.
empty : Return a new uninitialized array.
Examples
--------
x = np.arange(6)
x = x.reshape((2, 3))
x
array([[0, 1, 2],
[3, 4, 5]])
np.ones_like(x)
array([[1, 1, 1],
[1, 1, 1]])
y = np.arange(3, dtype=np.float)
y
array([ 0., 1., 2.])
np.ones_like(y)
array([ 1., 1., 1.])
outer(a, b, out=None)
Compute the outer product of two vectors.
Given two vectors, ``a = [a0, a1, ..., aM]`` and
``b = [b0, b1, ..., bN]``,
the outer product [1]_ is::
[[a0*b0 a0*b1 ... a0*bN ]
[a1*b0 .
[ ... .
[aM*b0 aM*bN ]]
Parameters
----------
a : (M,) array_like
First input vector. Input is flattened if
not already 1-dimensional.
b : (N,) array_like
Second input vector. Input is flattened if
not already 1-dimensional.
out : (M, N) ndarray, optional
A location where the result is stored
.. versionadded:: 1.9.0
Returns
-------
out : (M, N) ndarray
``out[i, j] = a[i] * b[j]``
See also
--------
inner, einsum
References
----------
.. [1] : G. H. Golub and C. F. van Loan, *Matrix Computations*, 3rd
ed., Baltimore, MD, Johns Hopkins University Press, 1996,
pg. 8.
Examples
--------
Make a (*very* coarse) grid for computing a Mandelbrot set:
rl = np.outer(np.ones((5,)), np.linspace(-2, 2, 5))
rl
array([[-2., -1., 0., 1., 2.],
[-2., -1., 0., 1., 2.],
[-2., -1., 0., 1., 2.],
[-2., -1., 0., 1., 2.],
[-2., -1., 0., 1., 2.]])
im = np.outer(1j*np.linspace(2, -2, 5), np.ones((5,)))
im
array([[ 0.+2.j, 0.+2.j, 0.+2.j, 0.+2.j, 0.+2.j],
[ 0.+1.j, 0.+1.j, 0.+1.j, 0.+1.j, 0.+1.j],
[ 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],
[ 0.-1.j, 0.-1.j, 0.-1.j, 0.-1.j, 0.-1.j],
[ 0.-2.j, 0.-2.j, 0.-2.j, 0.-2.j, 0.-2.j]])
grid = rl + im
grid
array([[-2.+2.j, -1.+2.j, 0.+2.j, 1.+2.j, 2.+2.j],
[-2.+1.j, -1.+1.j, 0.+1.j, 1.+1.j, 2.+1.j],
[-2.+0.j, -1.+0.j, 0.+0.j, 1.+0.j, 2.+0.j],
[-2.-1.j, -1.-1.j, 0.-1.j, 1.-1.j, 2.-1.j],
[-2.-2.j, -1.-2.j, 0.-2.j, 1.-2.j, 2.-2.j]])
An example using a "vector" of letters:
x = np.array(['a', 'b', 'c'], dtype=object)
np.outer(x, [1, 2, 3])
array([[a, aa, aaa],
[b, bb, bbb],
[c, cc, ccc]], dtype=object)
packbits(...)
packbits(myarray, axis=None)
Packs the elements of a binary-valued array into bits in a uint8 array.
The result is padded to full bytes by inserting zero bits at the end.
Parameters
----------
myarray : array_like
An integer type array whose elements should be packed to bits.
axis : int, optional
The dimension over which bit-packing is done.
``None`` implies packing the flattened array.
Returns
-------
packed : ndarray
Array of type uint8 whose elements represent bits corresponding to the
logical (0 or nonzero) value of the input elements. The shape of
`packed` has the same number of dimensions as the input (unless `axis`
is None, in which case the output is 1-D).
See Also
--------
unpackbits: Unpacks elements of a uint8 array into a binary-valued output
array.
Examples
--------
a = np.array([[[1,0,1],
[0,1,0]],
[[1,1,0],
[0,0,1]]])
b = np.packbits(a, axis=-1)
b
array([[[160],[64]],[[192],[32]]], dtype=uint8)
Note that in binary 160 = 1010 0000, 64 = 0100 0000, 192 = 1100 0000,
and 32 = 0010 0000.
pad(array, pad_width, mode=None, **kwargs)
Pads an array.
Parameters
----------
array : array_like of rank N
Input array
pad_width : {sequence, array_like, int}
Number of values padded to the edges of each axis.
((before_1, after_1), ... (before_N, after_N)) unique pad widths
for each axis.
((before, after),) yields same before and after pad for each axis.
(pad,) or int is a shortcut for before = after = pad width for all
axes.
mode : str or function
One of the following string values or a user supplied function.
'constant'
Pads with a constant value.
'edge'
Pads with the edge values of array.
'linear_ramp'
Pads with the linear ramp between end_value and the
array edge value.
'maximum'
Pads with the maximum value of all or part of the
vector along each axis.
'mean'
Pads with the mean value of all or part of the
vector along each axis.
'median'
Pads with the median value of all or part of the
vector along each axis.
'minimum'
Pads with the minimum value of all or part of the
vector along each axis.
'reflect'
Pads with the reflection of the vector mirrored on
the first and last values of the vector along each
axis.
'symmetric'
Pads with the reflection of the vector mirrored
along the edge of the array.
'wrap'
Pads with the wrap of the vector along the axis.
The first values are used to pad the end and the
end values are used to pad the beginning.
Padding function, see Notes.
stat_length : sequence or int, optional
Used in 'maximum', 'mean', 'median', and 'minimum'. Number of
values at edge of each axis used to calculate the statistic value.
((before_1, after_1), ... (before_N, after_N)) unique statistic
lengths for each axis.
((before, after),) yields same before and after statistic lengths
for each axis.
(stat_length,) or int is a shortcut for before = after = statistic
length for all axes.
Default is ``None``, to use the entire axis.
constant_values : sequence or int, optional
Used in 'constant'. The values to set the padded values for each
axis.
((before_1, after_1), ... (before_N, after_N)) unique pad constants
for each axis.
((before, after),) yields same before and after constants for each
axis.
(constant,) or int is a shortcut for before = after = constant for
all axes.
Default is 0.
end_values : sequence or int, optional
Used in 'linear_ramp'. The values used for the ending value of the
linear_ramp and that will form the edge of the padded array.
((before_1, after_1), ... (before_N, after_N)) unique end values
for each axis.
((before, after),) yields same before and after end values for each
axis.
(constant,) or int is a shortcut for before = after = end value for
all axes.
Default is 0.
reflect_type : {'even', 'odd'}, optional
Used in 'reflect', and 'symmetric'. The 'even' style is the
default with an unaltered reflection around the edge value. For
the 'odd' style, the extented part of the array is created by
subtracting the reflected values from two times the edge value.
Returns
-------
pad : ndarray
Padded array of rank equal to `array` with shape increased
according to `pad_width`.
Notes
-----
.. versionadded:: 1.7.0
For an array with rank greater than 1, some of the padding of later
axes is calculated from padding of previous axes. This is easiest to
think about with a rank 2 array where the corners of the padded array
are calculated by using padded values from the first axis.
The padding function, if used, should return a rank 1 array equal in
length to the vector argument with padded values replaced. It has the
following signature::
padding_func(vector, iaxis_pad_width, iaxis, **kwargs)
where
vector : ndarray
A rank 1 array already padded with zeros. Padded values are
vector[:pad_tuple[0]] and vector[-pad_tuple[1]:].
iaxis_pad_width : tuple
A 2-tuple of ints, iaxis_pad_width[0] represents the number of
values padded at the beginning of vector where
iaxis_pad_width[1] represents the number of values padded at
the end of vector.
iaxis : int
The axis currently being calculated.
kwargs : misc
Any keyword arguments the function requires.
Examples
--------
a = [1, 2, 3, 4, 5]
np.lib.pad(a, (2,3), 'constant', constant_values=(4, 6))
array([4, 4, 1, 2, 3, 4, 5, 6, 6, 6])
np.lib.pad(a, (2, 3), 'edge')
array([1, 1, 1, 2, 3, 4, 5, 5, 5, 5])
np.lib.pad(a, (2, 3), 'linear_ramp', end_values=(5, -4))
array([ 5, 3, 1, 2, 3, 4, 5, 2, -1, -4])
np.lib.pad(a, (2,), 'maximum')
array([5, 5, 1, 2, 3, 4, 5, 5, 5])
np.lib.pad(a, (2,), 'mean')
array([3, 3, 1, 2, 3, 4, 5, 3, 3])
np.lib.pad(a, (2,), 'median')
array([3, 3, 1, 2, 3, 4, 5, 3, 3])
a = [[1, 2], [3, 4]]
np.lib.pad(a, ((3, 2), (2, 3)), 'minimum')
array([[1, 1, 1, 2, 1, 1, 1],
[1, 1, 1, 2, 1, 1, 1],
[1, 1, 1, 2, 1, 1, 1],
[1, 1, 1, 2, 1, 1, 1],
[3, 3, 3, 4, 3, 3, 3],
[1, 1, 1, 2, 1, 1, 1],
[1, 1, 1, 2, 1, 1, 1]])
a = [1, 2, 3, 4, 5]
np.lib.pad(a, (2, 3), 'reflect')
array([3, 2, 1, 2, 3, 4, 5, 4, 3, 2])
np.lib.pad(a, (2, 3), 'reflect', reflect_type='odd')
array([-1, 0, 1, 2, 3, 4, 5, 6, 7, 8])
np.lib.pad(a, (2, 3), 'symmetric')
array([2, 1, 1, 2, 3, 4, 5, 5, 4, 3])
np.lib.pad(a, (2, 3), 'symmetric', reflect_type='odd')
array([0, 1, 1, 2, 3, 4, 5, 5, 6, 7])
np.lib.pad(a, (2, 3), 'wrap')
array([4, 5, 1, 2, 3, 4, 5, 1, 2, 3])
def padwithtens(vector, pad_width, iaxis, kwargs):
vector[:pad_width[0]] = 10
vector[-pad_width[1]:] = 10
return vector
a = np.arange(6)
a = a.reshape((2, 3))
np.lib.pad(a, 2, padwithtens)
array([[10, 10, 10, 10, 10, 10, 10],
[10, 10, 10, 10, 10, 10, 10],
[10, 10, 0, 1, 2, 10, 10],
[10, 10, 3, 4, 5, 10, 10],
[10, 10, 10, 10, 10, 10, 10],
[10, 10, 10, 10, 10, 10, 10]])
partition(a, kth, axis=-1, kind='introselect', order=None)
Return a partitioned copy of an array.
Creates a copy of the array with its elements rearranged in such a way that
the value of the element in kth position is in the position it would be in
a sorted array. All elements smaller than the kth element are moved before
this element and all equal or greater are moved behind it. The ordering of
the elements in the two partitions is undefined.
.. versionadded:: 1.8.0
Parameters
----------
a : array_like
Array to be sorted.
kth : int or sequence of ints
Element index to partition by. The kth value of the element will be in
its final sorted position and all smaller elements will be moved before
it and all equal or greater elements behind it.
The order all elements in the partitions is undefined.
If provided with a sequence of kth it will partition all elements
indexed by kth of them into their sorted position at once.
axis : int or None, optional
Axis along which to sort. If None, the array is flattened before
sorting. The default is -1, which sorts along the last axis.
kind : {'introselect'}, optional
Selection algorithm. Default is 'introselect'.
order : str or list of str, optional
When `a` is an array with fields defined, this argument specifies
which fields to compare first, second, etc. A single field can
be specified as a string. Not all fields need be specified, but
unspecified fields will still be used, in the order in which they
come up in the dtype, to break ties.
Returns
-------
partitioned_array : ndarray
Array of the same type and shape as `a`.
See Also
--------
ndarray.partition : Method to sort an array in-place.
argpartition : Indirect partition.
sort : Full sorting
Notes
-----
The various selection algorithms are characterized by their average speed,
worst case performance, work space size, and whether they are stable. A
stable sort keeps items with the same key in the same relative order. The
available algorithms have the following properties:
================= ======= ============= ============ =======
kind speed worst case work space stable
================= ======= ============= ============ =======
'introselect' 1 O(n) 0 no
================= ======= ============= ============ =======
All the partition algorithms make temporary copies of the data when
partitioning along any but the last axis. Consequently, partitioning
along the last axis is faster and uses less space than partitioning
along any other axis.
The sort order for complex numbers is lexicographic. If both the real
and imaginary parts are non-nan then the order is determined by the
real parts except when they are equal, in which case the order is
determined by the imaginary parts.
Examples
--------
a = np.array([3, 4, 2, 1])
np.partition(a, 3)
array([2, 1, 3, 4])
np.partition(a, (1, 3))
array([1, 2, 3, 4])
percentile(a, q, axis=None, out=None, overwrite_input=False, interpolation='linear', keepdims=False)
Compute the qth percentile of the data along the specified axis.
Returns the qth percentile of the array elements.
Parameters
----------
a : array_like
Input array or object that can be converted to an array.
q : float in range of [0,100] (or sequence of floats)
Percentile to compute which must be between 0 and 100 inclusive.
axis : int or sequence of int, optional
Axis along which the percentiles are computed. The default (None)
is to compute the percentiles along a flattened version of the array.
A sequence of axes is supported since version 1.9.0.
out : ndarray, optional
Alternative output array in which to place the result. It must
have the same shape and buffer length as the expected output,
but the type (of the output) will be cast if necessary.
overwrite_input : bool, optional
If True, then allow use of memory of input array `a` for
calculations. The input array will be modified by the call to
percentile. This will save memory when you do not need to preserve
the contents of the input array. In this case you should not make
any assumptions about the content of the passed in array `a` after
this function completes -- treat it as undefined. Default is False.
Note that, if the `a` input is not already an array this parameter
will have no effect, `a` will be converted to an array internally
regardless of the value of this parameter.
interpolation : {'linear', 'lower', 'higher', 'midpoint', 'nearest'}
This optional parameter specifies the interpolation method to use,
when the desired quantile lies between two data points `i` and `j`:
* linear: `i + (j - i) * fraction`, where `fraction` is the
fractional part of the index surrounded by `i` and `j`.
* lower: `i`.
* higher: `j`.
* nearest: `i` or `j` whichever is nearest.
* midpoint: (`i` + `j`) / 2.
.. versionadded:: 1.9.0
keepdims : bool, optional
If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option,
the result will broadcast correctly against the original array `a`.
.. versionadded:: 1.9.0
Returns
-------
percentile : scalar or ndarray
If a single percentile `q` is given and axis=None a scalar is
returned. If multiple percentiles `q` are given an array holding
the result is returned. The results are listed in the first axis.
(If `out` is specified, in which case that array is returned
instead). If the input contains integers, or floats of smaller
precision than 64, then the output data-type is float64. Otherwise,
the output data-type is the same as that of the input.
See Also
--------
mean, median
Notes
-----
Given a vector V of length N, the q-th percentile of V is the q-th ranked
value in a sorted copy of V. The values and distances of the two
nearest neighbors as well as the `interpolation` parameter will
determine the percentile if the normalized ranking does not match q
exactly. This function is the same as the median if ``q=50``, the same
as the minimum if ``q=0`` and the same as the maximum if ``q=100``.
Examples
--------
a = np.array([[10, 7, 4], [3, 2, 1]])
a
array([[10, 7, 4],
[ 3, 2, 1]])
np.percentile(a, 50)
array([ 3.5])
np.percentile(a, 50, axis=0)
array([[ 6.5, 4.5, 2.5]])
np.percentile(a, 50, axis=1)
array([[ 7.],
[ 2.]])
m = np.percentile(a, 50, axis=0)
out = np.zeros_like(m)
np.percentile(a, 50, axis=0, out=m)
array([[ 6.5, 4.5, 2.5]])
m
array([[ 6.5, 4.5, 2.5]])
b = a.copy()
np.percentile(b, 50, axis=1, overwrite_input=True)
array([[ 7.],
[ 2.]])
assert not np.all(a==b)
b = a.copy()
np.percentile(b, 50, axis=None, overwrite_input=True)
array([ 3.5])
piecewise(x, condlist, funclist, *args, **kw)
Evaluate a piecewise-defined function.
Given a set of conditions and corresponding functions, evaluate each
function on the input data wherever its condition is true.
Parameters
----------
x : ndarray
The input domain.
condlist : list of bool arrays
Each boolean array corresponds to a function in `funclist`. Wherever
`condlist[i]` is True, `funclist[i](x)` is used as the output value.
Each boolean array in `condlist` selects a piece of `x`,
and should therefore be of the same shape as `x`.
The length of `condlist` must correspond to that of `funclist`.
If one extra function is given, i.e. if
``len(funclist) - len(condlist) == 1``, then that extra function
is the default value, used wherever all conditions are false.
funclist : list of callables, f(x,*args,**kw), or scalars
Each function is evaluated over `x` wherever its corresponding
condition is True. It should take an array as input and give an array
or a scalar value as output. If, instead of a callable,
a scalar is provided then a constant function (``lambda x: scalar``) is
assumed.
args : tuple, optional
Any further arguments given to `piecewise` are passed to the functions
upon execution, i.e., if called ``piecewise(..., ..., 1, 'a')``, then
each function is called as ``f(x, 1, 'a')``.
kw : dict, optional
Keyword arguments used in calling `piecewise` are passed to the
functions upon execution, i.e., if called
``piecewise(..., ..., lambda=1)``, then each function is called as
``f(x, lambda=1)``.
Returns
-------
out : ndarray
The output is the same shape and type as x and is found by
calling the functions in `funclist` on the appropriate portions of `x`,
as defined by the boolean arrays in `condlist`. Portions not covered
by any condition have a default value of 0.
See Also
--------
choose, select, where
Notes
-----
This is similar to choose or select, except that functions are
evaluated on elements of `x` that satisfy the corresponding condition from
`condlist`.
The result is::
|--
|funclist[0](x[condlist[0]])
out = |funclist[1](x[condlist[1]])
|...
|funclist[n2](x[condlist[n2]])
|--
Examples
--------
Define the sigma function, which is -1 for ``x < 0`` and +1 for ``x >= 0``.
x = np.linspace(-2.5, 2.5, 6)
np.piecewise(x, [x < 0, x >= 0], [-1, 1])
array([-1., -1., -1., 1., 1., 1.])
Define the absolute value, which is ``-x`` for ``x <0`` and ``x`` for
``x >= 0``.
np.piecewise(x, [x < 0, x >= 0], [lambda x: -x, lambda x: x])
array([ 2.5, 1.5, 0.5, 0.5, 1.5, 2.5])
pkgload(*packages, **options)
Load one or more packages into parent package top-level namespace.
This function is intended to shorten the need to import many
subpackages, say of scipy, constantly with statements such as
import scipy.linalg, scipy.fftpack, scipy.etc...
Instead, you can say:
import scipy
scipy.pkgload('linalg','fftpack',...)
or
scipy.pkgload()
to load all of them in one call.
If a name which doesn't exist in scipy's namespace is
given, a warning is shown.
Parameters
----------
*packages : arg-tuple
the names (one or more strings) of all the modules one
wishes to load into the top-level namespace.
verbose= : integer
verbosity level [default: -1].
verbose=-1 will suspend also warnings.
force= : bool
when True, force reloading loaded packages [default: False].
postpone= : bool
when True, don't load packages [default: False]
place(arr, mask, vals)
Change elements of an array based on conditional and input values.
Similar to ``np.copyto(arr, vals, where=mask)``, the difference is that
`place` uses the first N elements of `vals`, where N is the number of
True values in `mask`, while `copyto` uses the elements where `mask`
is True.
Note that `extract` does the exact opposite of `place`.
Parameters
----------
arr : array_like
Array to put data into.
mask : array_like
Boolean mask array. Must have the same size as `a`.
vals : 1-D sequence
Values to put into `a`. Only the first N elements are used, where
N is the number of True values in `mask`. If `vals` is smaller
than N it will be repeated.
See Also
--------
copyto, put, take, extract
Examples
--------
arr = np.arange(6).reshape(2, 3)
np.place(arr, arr>2, [44, 55])
arr
array([[ 0, 1, 2],
[44, 55, 44]])
pmt(rate, nper, pv, fv=0, when='end')
Compute the payment against loan principal plus interest.
Given:
* a present value, `pv` (e.g., an amount borrowed)
* a future value, `fv` (e.g., 0)
* an interest `rate` compounded once per period, of which
there are
* `nper` total
* and (optional) specification of whether payment is made
at the beginning (`when` = {'begin', 1}) or the end
(`when` = {'end', 0}) of each period
Return:
the (fixed) periodic payment.
Parameters
----------
rate : array_like
Rate of interest (per period)
nper : array_like
Number of compounding periods
pv : array_like
Present value
fv : array_like, optional
Future value (default = 0)
when : {{'begin', 1}, {'end', 0}}, {string, int}
When payments are due ('begin' (1) or 'end' (0))
Returns
-------
out : ndarray
Payment against loan plus interest. If all input is scalar, returns a
scalar float. If any input is array_like, returns payment for each
input element. If multiple inputs are array_like, they all must have
the same shape.
Notes
-----
The payment is computed by solving the equation::
fv +
pv*(1 + rate)**nper +
pmt*(1 + rate*when)/rate*((1 + rate)**nper - 1) == 0
or, when ``rate == 0``::
fv + pv + pmt * nper == 0
for ``pmt``.
Note that computing a monthly mortgage payment is only
one use for this function. For example, pmt returns the
periodic deposit one must make to achieve a specified
future balance given an initial deposit, a fixed,
periodically compounded interest rate, and the total
number of periods.
References
----------
.. [WRW] Wheeler, D. A., E. Rathke, and R. Weir (Eds.) (2009, May).
Open Document Format for Office Applications (OpenDocument)v1.2,
Part 2: Recalculated Formula (OpenFormula) Format - Annotated Version,
Pre-Draft 12. Organization for the Advancement of Structured Information
Standards (OASIS). Billerica, MA, USA. [ODT Document].
Available:
http://www.oasis-open.org/committees/documents.php
?wg_abbrev=office-formulaOpenDocument-formula-20090508.odt
Examples
--------
What is the monthly payment needed to pay off a $200,000 loan in 15
years at an annual interest rate of 7.5%?
np.pmt(0.075/12, 12*15, 200000)
-1854.0247200054619
In order to pay-off (i.e., have a future-value of 0) the $200,000 obtained
today, a monthly payment of $1,854.02 would be required. Note that this
example illustrates usage of `fv` having a default value of 0.
poly(seq_of_zeros)
Find the coefficients of a polynomial with the given sequence of roots.
Returns the coefficients of the polynomial whose leading coefficient
is one for the given sequence of zeros (multiple roots must be included
in the sequence as many times as their multiplicity; see Examples).
A square matrix (or array, which will be treated as a matrix) can also
be given, in which case the coefficients of the characteristic polynomial
of the matrix are returned.
Parameters
----------
seq_of_zeros : array_like, shape (N,) or (N, N)
A sequence of polynomial roots, or a square array or matrix object.
Returns
-------
c : ndarray
1D array of polynomial coefficients from highest to lowest degree:
``c[0] * x**(N) + c[1] * x**(N-1) + ... + c[N-1] * x + c[N]``
where c[0] always equals 1.
Raises
------
ValueError
If input is the wrong shape (the input must be a 1-D or square
2-D array).
See Also
--------
polyval : Evaluate a polynomial at a point.
roots : Return the roots of a polynomial.
polyfit : Least squares polynomial fit.
poly1d : A one-dimensional polynomial class.
Notes
-----
Specifying the roots of a polynomial still leaves one degree of
freedom, typically represented by an undetermined leading
coefficient. [1]_ In the case of this function, that coefficient -
the first one in the returned array - is always taken as one. (If
for some reason you have one other point, the only automatic way
presently to leverage that information is to use ``polyfit``.)
The characteristic polynomial, :math:`p_a(t)`, of an `n`-by-`n`
matrix **A** is given by
:math:`p_a(t) = \mathrm{det}(t\, \mathbf{I} - \mathbf{A})`,
where **I** is the `n`-by-`n` identity matrix. [2]_
References
----------
.. [1] M. Sullivan and M. Sullivan, III, "Algebra and Trignometry,
Enhanced With Graphing Utilities," Prentice-Hall, pg. 318, 1996.
.. [2] G. Strang, "Linear Algebra and Its Applications, 2nd Edition,"
Academic Press, pg. 182, 1980.
Examples
--------
Given a sequence of a polynomial's zeros:
np.poly((0, 0, 0)) # Multiple root example
array([1, 0, 0, 0])
The line above represents z**3 + 0*z**2 + 0*z + 0.
np.poly((-1./2, 0, 1./2))
array([ 1. , 0. , -0.25, 0. ])
The line above represents z**3 - z/4
np.poly((np.random.random(1.)[0], 0, np.random.random(1.)[0]))
array([ 1. , -0.77086955, 0.08618131, 0. ]) #random
Given a square array object:
P = np.array([[0, 1./3], [-1./2, 0]])
np.poly(P)
array([ 1. , 0. , 0.16666667])
Or a square matrix object:
np.poly(np.matrix(P))
array([ 1. , 0. , 0.16666667])
Note how in all cases the leading coefficient is always 1.
polyadd(a1, a2)
Find the sum of two polynomials.
Returns the polynomial resulting from the sum of two input polynomials.
Each input must be either a poly1d object or a 1D sequence of polynomial
coefficients, from highest to lowest degree.
Parameters
----------
a1, a2 : array_like or poly1d object
Input polynomials.
Returns
-------
out : ndarray or poly1d object
The sum of the inputs. If either input is a poly1d object, then the
output is also a poly1d object. Otherwise, it is a 1D array of
polynomial coefficients from highest to lowest degree.
See Also
--------
poly1d : A one-dimensional polynomial class.
poly, polyadd, polyder, polydiv, polyfit, polyint, polysub, polyval
Examples
--------
np.polyadd([1, 2], [9, 5, 4])
array([9, 6, 6])
Using poly1d objects:
p1 = np.poly1d([1, 2])
p2 = np.poly1d([9, 5, 4])
print p1
1 x + 2
print p2
2
9 x + 5 x + 4
print np.polyadd(p1, p2)
2
9 x + 6 x + 6
polyder(p, m=1)
Return the derivative of the specified order of a polynomial.
Parameters
----------
p : poly1d or sequence
Polynomial to differentiate.
A sequence is interpreted as polynomial coefficients, see `poly1d`.
m : int, optional
Order of differentiation (default: 1)
Returns
-------
der : poly1d
A new polynomial representing the derivative.
See Also
--------
polyint : Anti-derivative of a polynomial.
poly1d : Class for one-dimensional polynomials.
Examples
--------
The derivative of the polynomial :math:`x^3 + x^2 + x^1 + 1` is:
p = np.poly1d([1,1,1,1])
p2 = np.polyder(p)
p2
poly1d([3, 2, 1])
which evaluates to:
p2(2.)
17.0
We can verify this, approximating the derivative with
``(f(x + h) - f(x))/h``:
(p(2. + 0.001) - p(2.)) / 0.001
17.007000999997857
The fourth-order derivative of a 3rd-order polynomial is zero:
np.polyder(p, 2)
poly1d([6, 2])
np.polyder(p, 3)
poly1d([6])
np.polyder(p, 4)
poly1d([ 0.])
polydiv(u, v)
Returns the quotient and remainder of polynomial division.
The input arrays are the coefficients (including any coefficients
equal to zero) of the "numerator" (dividend) and "denominator"
(divisor) polynomials, respectively.
Parameters
----------
u : array_like or poly1d
Dividend polynomial's coefficients.
v : array_like or poly1d
Divisor polynomial's coefficients.
Returns
-------
q : ndarray
Coefficients, including those equal to zero, of the quotient.
r : ndarray
Coefficients, including those equal to zero, of the remainder.
See Also
--------
poly, polyadd, polyder, polydiv, polyfit, polyint, polymul, polysub,
polyval
Notes
-----
Both `u` and `v` must be 0-d or 1-d (ndim = 0 or 1), but `u.ndim` need
not equal `v.ndim`. In other words, all four possible combinations -
``u.ndim = v.ndim = 0``, ``u.ndim = v.ndim = 1``,
``u.ndim = 1, v.ndim = 0``, and ``u.ndim = 0, v.ndim = 1`` - work.
Examples
--------
.. math:: \frac{3x^2 + 5x + 2}{2x + 1} = 1.5x + 1.75, remainder 0.25
x = np.array([3.0, 5.0, 2.0])
y = np.array([2.0, 1.0])
np.polydiv(x, y)
(array([ 1.5 , 1.75]), array([ 0.25]))
polyfit(x, y, deg, rcond=None, full=False, w=None, cov=False)
Least squares polynomial fit.
Fit a polynomial ``p(x) = p[0] * x**deg + ... + p[deg]`` of degree `deg`
to points `(x, y)`. Returns a vector of coefficients `p` that minimises
the squared error.
Parameters
----------
x : array_like, shape (M,)
x-coordinates of the M sample points ``(x[i], y[i])``.
y : array_like, shape (M,) or (M, K)
y-coordinates of the sample points. Several data sets of sample
points sharing the same x-coordinates can be fitted at once by
passing in a 2D-array that contains one dataset per column.
deg : int
Degree of the fitting polynomial
rcond : float, optional
Relative condition number of the fit. Singular values smaller than
this relative to the largest singular value will be ignored. The
default value is len(x)*eps, where eps is the relative precision of
the float type, about 2e-16 in most cases.
full : bool, optional
Switch determining nature of return value. When it is False (the
default) just the coefficients are returned, when True diagnostic
information from the singular value decomposition is also returned.
w : array_like, shape (M,), optional
weights to apply to the y-coordinates of the sample points.
cov : bool, optional
Return the estimate and the covariance matrix of the estimate
If full is True, then cov is not returned.
Returns
-------
p : ndarray, shape (M,) or (M, K)
Polynomial coefficients, highest power first. If `y` was 2-D, the
coefficients for `k`-th data set are in ``p[:,k]``.
residuals, rank, singular_values, rcond :
Present only if `full` = True. Residuals of the least-squares fit,
the effective rank of the scaled Vandermonde coefficient matrix,
its singular values, and the specified value of `rcond`. For more
details, see `linalg.lstsq`.
V : ndarray, shape (M,M) or (M,M,K)
Present only if `full` = False and `cov`=True. The covariance
matrix of the polynomial coefficient estimates. The diagonal of
this matrix are the variance estimates for each coefficient. If y
is a 2-D array, then the covariance matrix for the `k`-th data set
are in ``V[:,:,k]``
Warns
-----
RankWarning
The rank of the coefficient matrix in the least-squares fit is
deficient. The warning is only raised if `full` = False.
The warnings can be turned off by
import warnings
warnings.simplefilter('ignore', np.RankWarning)
See Also
--------
polyval : Computes polynomial values.
linalg.lstsq : Computes a least-squares fit.
scipy.interpolate.UnivariateSpline : Computes spline fits.
Notes
-----
The solution minimizes the squared error
.. math ::
E = \sum_{j=0}^k |p(x_j) - y_j|^2
in the equations::
x[0]**n * p[0] + ... + x[0] * p[n-1] + p[n] = y[0]
x[1]**n * p[0] + ... + x[1] * p[n-1] + p[n] = y[1]
...
x[k]**n * p[0] + ... + x[k] * p[n-1] + p[n] = y[k]
The coefficient matrix of the coefficients `p` is a Vandermonde matrix.
`polyfit` issues a `RankWarning` when the least-squares fit is badly
conditioned. This implies that the best fit is not well-defined due
to numerical error. The results may be improved by lowering the polynomial
degree or by replacing `x` by `x` - `x`.mean(). The `rcond` parameter
can also be set to a value smaller than its default, but the resulting
fit may be spurious: including contributions from the small singular
values can add numerical noise to the result.
Note that fitting polynomial coefficients is inherently badly conditioned
when the degree of the polynomial is large or the interval of sample points
is badly centered. The quality of the fit should always be checked in these
cases. When polynomial fits are not satisfactory, splines may be a good
alternative.
References
----------
.. [1] Wikipedia, "Curve fitting",
http://en.wikipedia.org/wiki/Curve_fitting
.. [2] Wikipedia, "Polynomial interpolation",
http://en.wikipedia.org/wiki/Polynomial_interpolation
Examples
--------
x = np.array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0])
y = np.array([0.0, 0.8, 0.9, 0.1, -0.8, -1.0])
z = np.polyfit(x, y, 3)
z
array([ 0.08703704, -0.81349206, 1.69312169, -0.03968254])
It is convenient to use `poly1d` objects for dealing with polynomials:
p = np.poly1d(z)
p(0.5)
0.6143849206349179
p(3.5)
-0.34732142857143039
p(10)
22.579365079365115
High-order polynomials may oscillate wildly:
p30 = np.poly1d(np.polyfit(x, y, 30))
/... RankWarning: Polyfit may be poorly conditioned...
p30(4)
-0.80000000000000204
p30(5)
-0.99999999999999445
p30(4.5)
-0.10547061179440398
Illustration:
import matplotlib.pyplot as plt
xp = np.linspace(-2, 6, 100)
_ = plt.plot(x, y, '.', xp, p(xp), '-', xp, p30(xp), '--')
plt.ylim(-2,2)
(-2, 2)
plt.show()
polyint(p, m=1, k=None)
Return an antiderivative (indefinite integral) of a polynomial.
The returned order `m` antiderivative `P` of polynomial `p` satisfies
:math:`\frac{d^m}{dx^m}P(x) = p(x)` and is defined up to `m - 1`
integration constants `k`. The constants determine the low-order
polynomial part
.. math:: \frac{k_{m-1}}{0!} x^0 + \ldots + \frac{k_0}{(m-1)!}x^{m-1}
of `P` so that :math:`P^{(j)}(0) = k_{m-j-1}`.
Parameters
----------
p : array_like or poly1d
Polynomial to differentiate.
A sequence is interpreted as polynomial coefficients, see `poly1d`.
m : int, optional
Order of the antiderivative. (Default: 1)
k : list of `m` scalars or scalar, optional
Integration constants. They are given in the order of integration:
those corresponding to highest-order terms come first.
If ``None`` (default), all constants are assumed to be zero.
If `m = 1`, a single scalar can be given instead of a list.
See Also
--------
polyder : derivative of a polynomial
poly1d.integ : equivalent method
Examples
--------
The defining property of the antiderivative:
p = np.poly1d([1,1,1])
P = np.polyint(p)
P
poly1d([ 0.33333333, 0.5 , 1. , 0. ])
np.polyder(P) == p
True
The integration constants default to zero, but can be specified:
P = np.polyint(p, 3)
P(0)
0.0
np.polyder(P)(0)
0.0
np.polyder(P, 2)(0)
0.0
P = np.polyint(p, 3, k=[6,5,3])
P
poly1d([ 0.01666667, 0.04166667, 0.16666667, 3. , 5. , 3. ])
Note that 3 = 6 / 2!, and that the constants are given in the order of
integrations. Constant of the highest-order polynomial term comes first:
np.polyder(P, 2)(0)
6.0
np.polyder(P, 1)(0)
5.0
P(0)
3.0
polymul(a1, a2)
Find the product of two polynomials.
Finds the polynomial resulting from the multiplication of the two input
polynomials. Each input must be either a poly1d object or a 1D sequence
of polynomial coefficients, from highest to lowest degree.
Parameters
----------
a1, a2 : array_like or poly1d object
Input polynomials.
Returns
-------
out : ndarray or poly1d object
The polynomial resulting from the multiplication of the inputs. If
either inputs is a poly1d object, then the output is also a poly1d
object. Otherwise, it is a 1D array of polynomial coefficients from
highest to lowest degree.
See Also
--------
poly1d : A one-dimensional polynomial class.
poly, polyadd, polyder, polydiv, polyfit, polyint, polysub,
polyval
convolve : Array convolution. Same output as polymul, but has parameter
for overlap mode.
Examples
--------
np.polymul([1, 2, 3], [9, 5, 1])
array([ 9, 23, 38, 17, 3])
Using poly1d objects:
p1 = np.poly1d([1, 2, 3])
p2 = np.poly1d([9, 5, 1])
print p1
2
1 x + 2 x + 3
print p2
2
9 x + 5 x + 1
print np.polymul(p1, p2)
4 3 2
9 x + 23 x + 38 x + 17 x + 3
polysub(a1, a2)
Difference (subtraction) of two polynomials.
Given two polynomials `a1` and `a2`, returns ``a1 - a2``.
`a1` and `a2` can be either array_like sequences of the polynomials'
coefficients (including coefficients equal to zero), or `poly1d` objects.
Parameters
----------
a1, a2 : array_like or poly1d
Minuend and subtrahend polynomials, respectively.
Returns
-------
out : ndarray or poly1d
Array or `poly1d` object of the difference polynomial's coefficients.
See Also
--------
polyval, polydiv, polymul, polyadd
Examples
--------
.. math:: (2 x^2 + 10 x - 2) - (3 x^2 + 10 x -4) = (-x^2 + 2)
np.polysub([2, 10, -2], [3, 10, -4])
array([-1, 0, 2])
polyval(p, x)
Evaluate a polynomial at specific values.
If `p` is of length N, this function returns the value:
``p[0]*x**(N-1) + p[1]*x**(N-2) + ... + p[N-2]*x + p[N-1]``
If `x` is a sequence, then `p(x)` is returned for each element of `x`.
If `x` is another polynomial then the composite polynomial `p(x(t))`
is returned.
Parameters
----------
p : array_like or poly1d object
1D array of polynomial coefficients (including coefficients equal
to zero) from highest degree to the constant term, or an
instance of poly1d.
x : array_like or poly1d object
A number, a 1D array of numbers, or an instance of poly1d, "at"
which to evaluate `p`.
Returns
-------
values : ndarray or poly1d
If `x` is a poly1d instance, the result is the composition of the two
polynomials, i.e., `x` is "substituted" in `p` and the simplified
result is returned. In addition, the type of `x` - array_like or
poly1d - governs the type of the output: `x` array_like => `values`
array_like, `x` a poly1d object => `values` is also.
See Also
--------
poly1d: A polynomial class.
Notes
-----
Horner's scheme [1]_ is used to evaluate the polynomial. Even so,
for polynomials of high degree the values may be inaccurate due to
rounding errors. Use carefully.
References
----------
.. [1] I. N. Bronshtein, K. A. Semendyayev, and K. A. Hirsch (Eng.
trans. Ed.), *Handbook of Mathematics*, New York, Van Nostrand
Reinhold Co., 1985, pg. 720.
Examples
--------
np.polyval([3,0,1], 5) # 3 * 5**2 + 0 * 5**1 + 1
76
np.polyval([3,0,1], np.poly1d(5))
poly1d([ 76.])
np.polyval(np.poly1d([3,0,1]), 5)
76
np.polyval(np.poly1d([3,0,1]), np.poly1d(5))
poly1d([ 76.])
ppmt(rate, per, nper, pv, fv=0.0, when='end')
Compute the payment against loan principal.
Parameters
----------
rate : array_like
Rate of interest (per period)
per : array_like, int
Amount paid against the loan changes. The `per` is the period of
interest.
nper : array_like
Number of compounding periods
pv : array_like
Present value
fv : array_like, optional
Future value
when : {{'begin', 1}, {'end', 0}}, {string, int}
When payments are due ('begin' (1) or 'end' (0))
See Also
--------
pmt, pv, ipmt
prod(a, axis=None, dtype=None, out=None, keepdims=False)
Return the product of array elements over a given axis.
Parameters
----------
a : array_like
Input data.
axis : None or int or tuple of ints, optional
Axis or axes along which a product is performed.
The default (`axis` = `None`) is perform a product over all
the dimensions of the input array. `axis` may be negative, in
which case it counts from the last to the first axis.
.. versionadded:: 1.7.0
If this is a tuple of ints, a product is performed on multiple
axes, instead of a single axis or all the axes as before.
dtype : data-type, optional
The data-type of the returned array, as well as of the accumulator
in which the elements are multiplied. By default, if `a` is of
integer type, `dtype` is the default platform integer. (Note: if
the type of `a` is unsigned, then so is `dtype`.) Otherwise,
the dtype is the same as that of `a`.
out : ndarray, optional
Alternative output array in which to place the result. It must have
the same shape as the expected output, but the type of the
output values will be cast if necessary.
keepdims : bool, optional
If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option,
the result will broadcast correctly against the original `arr`.
Returns
-------
product_along_axis : ndarray, see `dtype` parameter above.
An array shaped as `a` but with the specified axis removed.
Returns a reference to `out` if specified.
See Also
--------
ndarray.prod : equivalent method
numpy.doc.ufuncs : Section "Output arguments"
Notes
-----
Arithmetic is modular when using integer types, and no error is
raised on overflow. That means that, on a 32-bit platform:
x = np.array([536870910, 536870910, 536870910, 536870910])
np.prod(x) #random
16
The product of an empty array is the neutral element 1:
np.prod([])
1.0
Examples
--------
By default, calculate the product of all elements:
np.prod([1.,2.])
2.0
Even when the input array is two-dimensional:
np.prod([[1.,2.],[3.,4.]])
24.0
But we can also specify the axis over which to multiply:
np.prod([[1.,2.],[3.,4.]], axis=1)
array([ 2., 12.])
If the type of `x` is unsigned, then the output type is
the unsigned platform integer:
x = np.array([1, 2, 3], dtype=np.uint8)
np.prod(x).dtype == np.uint
True
If `x` is of a signed integer type, then the output type
is the default platform integer:
x = np.array([1, 2, 3], dtype=np.int8)
np.prod(x).dtype == np.int
True
product(a, axis=None, dtype=None, out=None, keepdims=False)
Return the product of array elements over a given axis.
See Also
--------
prod : equivalent function; see for details.
promote_types(...)
promote_types(type1, type2)
Returns the data type with the smallest size and smallest scalar
kind to which both ``type1`` and ``type2`` may be safely cast.
The returned data type is always in native byte order.
This function is symmetric and associative.
Parameters
----------
type1 : dtype or dtype specifier
First data type.
type2 : dtype or dtype specifier
Second data type.
Returns
-------
out : dtype
The promoted data type.
Notes
-----
.. versionadded:: 1.6.0
Starting in NumPy 1.9, promote_types function now returns a valid string
length when given an integer or float dtype as one argument and a string
dtype as another argument. Previously it always returned the input string
dtype, even if it wasn't long enough to store the max integer/float value
converted to a string.
See Also
--------
result_type, dtype, can_cast
Examples
--------
np.promote_types('f4', 'f8')
dtype('float64')
np.promote_types('i8', 'f4')
dtype('float64')
np.promote_types('>i8', '2, x**2)
x
array([[ 0, 1, 2],
[ 9, 16, 25]])
If `values` is smaller than `a` it is repeated:
x = np.arange(5)
np.putmask(x, x>1, [-33, -44])
x
array([ 0, 1, -33, -44, -33])
pv(rate, nper, pmt, fv=0.0, when='end')
Compute the present value.
Given:
* a future value, `fv`
* an interest `rate` compounded once per period, of which
there are
* `nper` total
* a (fixed) payment, `pmt`, paid either
* at the beginning (`when` = {'begin', 1}) or the end
(`when` = {'end', 0}) of each period
Return:
the value now
Parameters
----------
rate : array_like
Rate of interest (per period)
nper : array_like
Number of compounding periods
pmt : array_like
Payment
fv : array_like, optional
Future value
when : {{'begin', 1}, {'end', 0}}, {string, int}, optional
When payments are due ('begin' (1) or 'end' (0))
Returns
-------
out : ndarray, float
Present value of a series of payments or investments.
Notes
-----
The present value is computed by solving the equation::
fv +
pv*(1 + rate)**nper +
pmt*(1 + rate*when)/rate*((1 + rate)**nper - 1) = 0
or, when ``rate = 0``::
fv + pv + pmt * nper = 0
for `pv`, which is then returned.
References
----------
.. [WRW] Wheeler, D. A., E. Rathke, and R. Weir (Eds.) (2009, May).
Open Document Format for Office Applications (OpenDocument)v1.2,
Part 2: Recalculated Formula (OpenFormula) Format - Annotated Version,
Pre-Draft 12. Organization for the Advancement of Structured Information
Standards (OASIS). Billerica, MA, USA. [ODT Document].
Available:
http://www.oasis-open.org/committees/documents.php?wg_abbrev=office-formula
OpenDocument-formula-20090508.odt
Examples
--------
What is the present value (e.g., the initial investment)
of an investment that needs to total $15692.93
after 10 years of saving $100 every month? Assume the
interest rate is 5% (annually) compounded monthly.
np.pv(0.05/12, 10*12, -100, 15692.93)
-100.00067131625819
By convention, the negative sign represents cash flow out
(i.e., money not available today). Thus, to end up with
$15,692.93 in 10 years saving $100 a month at 5% annual
interest, one's initial deposit should also be $100.
If any input is array_like, ``pv`` returns an array of equal shape.
Let's compare different interest rates in the example above:
a = np.array((0.05, 0.04, 0.03))/12
np.pv(a, 10*12, -100, 15692.93)
array([ -100.00067132, -649.26771385, -1273.78633713])
So, to end up with the same $15692.93 under the same $100 per month
"savings plan," for annual interest rates of 4% and 3%, one would
need initial investments of $649.27 and $1273.79, respectively.
rank(a)
Return the number of dimensions of an array.
If `a` is not already an array, a conversion is attempted.
Scalars are zero dimensional.
.. note::
This function is deprecated in NumPy 1.9 to avoid confusion with
`numpy.linalg.matrix_rank`. The ``ndim`` attribute or function
should be used instead.
Parameters
----------
a : array_like
Array whose number of dimensions is desired. If `a` is not an array,
a conversion is attempted.
Returns
-------
number_of_dimensions : int
The number of dimensions in the array.
See Also
--------
ndim : equivalent function
ndarray.ndim : equivalent property
shape : dimensions of array
ndarray.shape : dimensions of array
Notes
-----
In the old Numeric package, `rank` was the term used for the number of
dimensions, but in Numpy `ndim` is used instead.
Examples
--------
np.rank([1,2,3])
1
np.rank(np.array([[1,2,3],[4,5,6]]))
2
np.rank(1)
0
rate(nper, pmt, pv, fv, when='end', guess=0.1, tol=1e-06, maxiter=100)
Compute the rate of interest per period.
Parameters
----------
nper : array_like
Number of compounding periods
pmt : array_like
Payment
pv : array_like
Present value
fv : array_like
Future value
when : {{'begin', 1}, {'end', 0}}, {string, int}, optional
When payments are due ('begin' (1) or 'end' (0))
guess : float, optional
Starting guess for solving the rate of interest
tol : float, optional
Required tolerance for the solution
maxiter : int, optional
Maximum iterations in finding the solution
Notes
-----
The rate of interest is computed by iteratively solving the
(non-linear) equation::
fv + pv*(1+rate)**nper + pmt*(1+rate*when)/rate * ((1+rate)**nper - 1) = 0
for ``rate``.
References
----------
Wheeler, D. A., E. Rathke, and R. Weir (Eds.) (2009, May). Open Document
Format for Office Applications (OpenDocument)v1.2, Part 2: Recalculated
Formula (OpenFormula) Format - Annotated Version, Pre-Draft 12.
Organization for the Advancement of Structured Information Standards
(OASIS). Billerica, MA, USA. [ODT Document]. Available:
http://www.oasis-open.org/committees/documents.php?wg_abbrev=office-formula
OpenDocument-formula-20090508.odt
ravel(a, order='C')
Return a contiguous flattened array.
A 1-D array, containing the elements of the input, is returned. A copy is
made only if needed.
As of NumPy 1.10, the returned array will have the same type as the input
array. (for example, a masked array will be returned for a masked array
input)
Parameters
----------
a : array_like
Input array. The elements in `a` are read in the order specified by
`order`, and packed as a 1-D array.
order : {'C','F', 'A', 'K'}, optional
The elements of `a` are read using this index order. 'C' means
to index the elements in row-major, C-style order,
with the last axis index changing fastest, back to the first
axis index changing slowest. 'F' means to index the elements
in column-major, Fortran-style order, with the
first index changing fastest, and the last index changing
slowest. Note that the 'C' and 'F' options take no account of
the memory layout of the underlying array, and only refer to
the order of axis indexing. 'A' means to read the elements in
Fortran-like index order if `a` is Fortran *contiguous* in
memory, C-like order otherwise. 'K' means to read the
elements in the order they occur in memory, except for
reversing the data when strides are negative. By default, 'C'
index order is used.
Returns
-------
y : array_like
If `a` is a matrix, y is a 1-D ndarray, otherwise y is an array of
the same subtype as `a`. The shape of the returned array is
``(a.size,)``. Matrices are special cased for backward
compatibility.
See Also
--------
ndarray.flat : 1-D iterator over an array.
ndarray.flatten : 1-D array copy of the elements of an array
in row-major order.
ndarray.reshape : Change the shape of an array without changing its data.
Notes
-----
In row-major, C-style order, in two dimensions, the row index
varies the slowest, and the column index the quickest. This can
be generalized to multiple dimensions, where row-major order
implies that the index along the first axis varies slowest, and
the index along the last quickest. The opposite holds for
column-major, Fortran-style index ordering.
When a view is desired in as many cases as possible, ``arr.reshape(-1)``
may be preferable.
Examples
--------
It is equivalent to ``reshape(-1, order=order)``.
x = np.array([[1, 2, 3], [4, 5, 6]])
print np.ravel(x)
[1 2 3 4 5 6]
print x.reshape(-1)
[1 2 3 4 5 6]
print np.ravel(x, order='F')
[1 4 2 5 3 6]
When ``order`` is 'A', it will preserve the array's 'C' or 'F' ordering:
print np.ravel(x.T)
[1 4 2 5 3 6]
print np.ravel(x.T, order='A')
[1 2 3 4 5 6]
When ``order`` is 'K', it will preserve orderings that are neither 'C'
nor 'F', but won't reverse axes:
a = np.arange(3)[::-1]; a
array([2, 1, 0])
a.ravel(order='C')
array([2, 1, 0])
a.ravel(order='K')
array([2, 1, 0])
a = np.arange(12).reshape(2,3,2).swapaxes(1,2); a
array([[[ 0, 2, 4],
[ 1, 3, 5]],
[[ 6, 8, 10],
[ 7, 9, 11]]])
a.ravel(order='C')
array([ 0, 2, 4, 1, 3, 5, 6, 8, 10, 7, 9, 11])
a.ravel(order='K')
array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11])
ravel_multi_index(...)
ravel_multi_index(multi_index, dims, mode='raise', order='C')
Converts a tuple of index arrays into an array of flat
indices, applying boundary modes to the multi-index.
Parameters
----------
multi_index : tuple of array_like
A tuple of integer arrays, one array for each dimension.
dims : tuple of ints
The shape of array into which the indices from ``multi_index`` apply.
mode : {'raise', 'wrap', 'clip'}, optional
Specifies how out-of-bounds indices are handled. Can specify
either one mode or a tuple of modes, one mode per index.
* 'raise' -- raise an error (default)
* 'wrap' -- wrap around
* 'clip' -- clip to the range
In 'clip' mode, a negative index which would normally
wrap will clip to 0 instead.
order : {'C', 'F'}, optional
Determines whether the multi-index should be viewed as
indexing in row-major (C-style) or column-major
(Fortran-style) order.
Returns
-------
raveled_indices : ndarray
An array of indices into the flattened version of an array
of dimensions ``dims``.
See Also
--------
unravel_index
Notes
-----
.. versionadded:: 1.6.0
Examples
--------
arr = np.array([[3,6,6],[4,5,1]])
np.ravel_multi_index(arr, (7,6))
array([22, 41, 37])
np.ravel_multi_index(arr, (7,6), order='F')
array([31, 41, 13])
np.ravel_multi_index(arr, (4,6), mode='clip')
array([22, 23, 19])
np.ravel_multi_index(arr, (4,4), mode=('clip','wrap'))
array([12, 13, 13])
np.ravel_multi_index((3,1,4,1), (6,7,8,9))
1621
real(val)
Return the real part of the elements of the array.
Parameters
----------
val : array_like
Input array.
Returns
-------
out : ndarray
Output array. If `val` is real, the type of `val` is used for the
output. If `val` has complex elements, the returned type is float.
See Also
--------
real_if_close, imag, angle
Examples
--------
a = np.array([1+2j, 3+4j, 5+6j])
a.real
array([ 1., 3., 5.])
a.real = 9
a
array([ 9.+2.j, 9.+4.j, 9.+6.j])
a.real = np.array([9, 8, 7])
a
array([ 9.+2.j, 8.+4.j, 7.+6.j])
real_if_close(a, tol=100)
If complex input returns a real array if complex parts are close to zero.
"Close to zero" is defined as `tol` * (machine epsilon of the type for
`a`).
Parameters
----------
a : array_like
Input array.
tol : float
Tolerance in machine epsilons for the complex part of the elements
in the array.
Returns
-------
out : ndarray
If `a` is real, the type of `a` is used for the output. If `a`
has complex elements, the returned type is float.
See Also
--------
real, imag, angle
Notes
-----
Machine epsilon varies from machine to machine and between data types
but Python floats on most platforms have a machine epsilon equal to
2.2204460492503131e-16. You can use 'np.finfo(np.float).eps' to print
out the machine epsilon for floats.
Examples
--------
np.finfo(np.float).eps
2.2204460492503131e-16
np.real_if_close([2.1 + 4e-14j], tol=1000)
array([ 2.1])
np.real_if_close([2.1 + 4e-13j], tol=1000)
array([ 2.1 +4.00000000e-13j])
recfromcsv(fname, **kwargs)
Load ASCII data stored in a comma-separated file.
The returned array is a record array (if ``usemask=False``, see
`recarray`) or a masked record array (if ``usemask=True``,
see `ma.mrecords.MaskedRecords`).
Parameters
----------
fname, kwargs : For a description of input parameters, see `genfromtxt`.
See Also
--------
numpy.genfromtxt : generic function to load ASCII data.
Notes
-----
By default, `dtype` is None, which means that the data-type of the output
array will be determined from the data.
recfromtxt(fname, **kwargs)
Load ASCII data from a file and return it in a record array.
If ``usemask=False`` a standard `recarray` is returned,
if ``usemask=True`` a MaskedRecords array is returned.
Parameters
----------
fname, kwargs : For a description of input parameters, see `genfromtxt`.
See Also
--------
numpy.genfromtxt : generic function
Notes
-----
By default, `dtype` is None, which means that the data-type of the output
array will be determined from the data.
repeat(a, repeats, axis=None)
Repeat elements of an array.
Parameters
----------
a : array_like
Input array.
repeats : int or array of ints
The number of repetitions for each element. `repeats` is broadcasted
to fit the shape of the given axis.
axis : int, optional
The axis along which to repeat values. By default, use the
flattened input array, and return a flat output array.
Returns
-------
repeated_array : ndarray
Output array which has the same shape as `a`, except along
the given axis.
See Also
--------
tile : Tile an array.
Examples
--------
x = np.array([[1,2],[3,4]])
np.repeat(x, 2)
array([1, 1, 2, 2, 3, 3, 4, 4])
np.repeat(x, 3, axis=1)
array([[1, 1, 1, 2, 2, 2],
[3, 3, 3, 4, 4, 4]])
np.repeat(x, [1, 2], axis=0)
array([[1, 2],
[3, 4],
[3, 4]])
require(a, dtype=None, requirements=None)
Return an ndarray of the provided type that satisfies requirements.
This function is useful to be sure that an array with the correct flags
is returned for passing to compiled code (perhaps through ctypes).
Parameters
----------
a : array_like
The object to be converted to a type-and-requirement-satisfying array.
dtype : data-type
The required data-type. If None preserve the current dtype. If your
application requires the data to be in native byteorder, include
a byteorder specification as a part of the dtype specification.
requirements : str or list of str
The requirements list can be any of the following
* 'F_CONTIGUOUS' ('F') - ensure a Fortran-contiguous array
* 'C_CONTIGUOUS' ('C') - ensure a C-contiguous array
* 'ALIGNED' ('A') - ensure a data-type aligned array
* 'WRITEABLE' ('W') - ensure a writable array
* 'OWNDATA' ('O') - ensure an array that owns its own data
* 'ENSUREARRAY', ('E') - ensure a base array, instead of a subclass
See Also
--------
asarray : Convert input to an ndarray.
asanyarray : Convert to an ndarray, but pass through ndarray subclasses.
ascontiguousarray : Convert input to a contiguous array.
asfortranarray : Convert input to an ndarray with column-major
memory order.
ndarray.flags : Information about the memory layout of the array.
Notes
-----
The returned array will be guaranteed to have the listed requirements
by making a copy if needed.
Examples
--------
x = np.arange(6).reshape(2,3)
x.flags
C_CONTIGUOUS : True
F_CONTIGUOUS : False
OWNDATA : False
WRITEABLE : True
ALIGNED : True
UPDATEIFCOPY : False
y = np.require(x, dtype=np.float32, requirements=['A', 'O', 'W', 'F'])
y.flags
C_CONTIGUOUS : False
F_CONTIGUOUS : True
OWNDATA : True
WRITEABLE : True
ALIGNED : True
UPDATEIFCOPY : False
reshape(a, newshape, order='C')
Gives a new shape to an array without changing its data.
Parameters
----------
a : array_like
Array to be reshaped.
newshape : int or tuple of ints
The new shape should be compatible with the original shape. If
an integer, then the result will be a 1-D array of that length.
One shape dimension can be -1. In this case, the value is inferred
from the length of the array and remaining dimensions.
order : {'C', 'F', 'A'}, optional
Read the elements of `a` using this index order, and place the elements
into the reshaped array using this index order. 'C' means to
read / write the elements using C-like index order, with the last axis
index changing fastest, back to the first axis index changing slowest.
'F' means to read / write the elements using Fortran-like index order,
with the first index changing fastest, and the last index changing
slowest.
Note that the 'C' and 'F' options take no account of the memory layout
of the underlying array, and only refer to the order of indexing. 'A'
means to read / write the elements in Fortran-like index order if `a`
is Fortran *contiguous* in memory, C-like order otherwise.
Returns
-------
reshaped_array : ndarray
This will be a new view object if possible; otherwise, it will
be a copy. Note there is no guarantee of the *memory layout* (C- or
Fortran- contiguous) of the returned array.
See Also
--------
ndarray.reshape : Equivalent method.
Notes
-----
It is not always possible to change the shape of an array without
copying the data. If you want an error to be raise if the data is copied,
you should assign the new shape to the shape attribute of the array::
a = np.zeros((10, 2))
# A transpose make the array non-contiguous
b = a.T
# Taking a view makes it possible to modify the shape without modifying
# the initial object.
c = b.view()
c.shape = (20)
AttributeError: incompatible shape for a non-contiguous array
The `order` keyword gives the index ordering both for *fetching* the values
from `a`, and then *placing* the values into the output array.
For example, let's say you have an array:
a = np.arange(6).reshape((3, 2))
a
array([[0, 1],
[2, 3],
[4, 5]])
You can think of reshaping as first raveling the array (using the given
index order), then inserting the elements from the raveled array into the
new array using the same kind of index ordering as was used for the
raveling.
np.reshape(a, (2, 3)) # C-like index ordering
array([[0, 1, 2],
[3, 4, 5]])
np.reshape(np.ravel(a), (2, 3)) # equivalent to C ravel then C reshape
array([[0, 1, 2],
[3, 4, 5]])
np.reshape(a, (2, 3), order='F') # Fortran-like index ordering
array([[0, 4, 3],
[2, 1, 5]])
np.reshape(np.ravel(a, order='F'), (2, 3), order='F')
array([[0, 4, 3],
[2, 1, 5]])
Examples
--------
a = np.array([[1,2,3], [4,5,6]])
np.reshape(a, 6)
array([1, 2, 3, 4, 5, 6])
np.reshape(a, 6, order='F')
array([1, 4, 2, 5, 3, 6])
np.reshape(a, (3,-1)) # the unspecified value is inferred to be 2
array([[1, 2],
[3, 4],
[5, 6]])
resize(a, new_shape)
Return a new array with the specified shape.
If the new array is larger than the original array, then the new
array is filled with repeated copies of `a`. Note that this behavior
is different from a.resize(new_shape) which fills with zeros instead
of repeated copies of `a`.
Parameters
----------
a : array_like
Array to be resized.
new_shape : int or tuple of int
Shape of resized array.
Returns
-------
reshaped_array : ndarray
The new array is formed from the data in the old array, repeated
if necessary to fill out the required number of elements. The
data are repeated in the order that they are stored in memory.
See Also
--------
ndarray.resize : resize an array in-place.
Examples
--------
a=np.array([[0,1],[2,3]])
np.resize(a,(2,3))
array([[0, 1, 2],
[3, 0, 1]])
np.resize(a,(1,4))
array([[0, 1, 2, 3]])
np.resize(a,(2,4))
array([[0, 1, 2, 3],
[0, 1, 2, 3]])
restoredot()
Restore `dot`, `vdot`, and `innerproduct` to the default non-BLAS
implementations.
Typically, the user will only need to call this when troubleshooting
and installation problem, reproducing the conditions of a build without
an accelerated BLAS, or when being very careful about benchmarking
linear algebra operations.
.. note:: Deprecated in Numpy 1.10
The cblas functions have been integrated into the multarray
module and restoredot now longer does anything. It will be
removed in Numpy 1.11.0.
See Also
--------
alterdot : `restoredot` undoes the effects of `alterdot`.
result_type(...)
result_type(*arrays_and_dtypes)
Returns the type that results from applying the NumPy
type promotion rules to the arguments.
Type promotion in NumPy works similarly to the rules in languages
like C++, with some slight differences. When both scalars and
arrays are used, the array's type takes precedence and the actual value
of the scalar is taken into account.
For example, calculating 3*a, where a is an array of 32-bit floats,
intuitively should result in a 32-bit float output. If the 3 is a
32-bit integer, the NumPy rules indicate it can't convert losslessly
into a 32-bit float, so a 64-bit float should be the result type.
By examining the value of the constant, '3', we see that it fits in
an 8-bit integer, which can be cast losslessly into the 32-bit float.
Parameters
----------
arrays_and_dtypes : list of arrays and dtypes
The operands of some operation whose result type is needed.
Returns
-------
out : dtype
The result type.
See also
--------
dtype, promote_types, min_scalar_type, can_cast
Notes
-----
.. versionadded:: 1.6.0
The specific algorithm used is as follows.
Categories are determined by first checking which of boolean,
integer (int/uint), or floating point (float/complex) the maximum
kind of all the arrays and the scalars are.
If there are only scalars or the maximum category of the scalars
is higher than the maximum category of the arrays,
the data types are combined with :func:`promote_types`
to produce the return value.
Otherwise, `min_scalar_type` is called on each array, and
the resulting data types are all combined with :func:`promote_types`
to produce the return value.
The set of int values is not a subset of the uint values for types
with the same number of bits, something not reflected in
:func:`min_scalar_type`, but handled as a special case in `result_type`.
Examples
--------
np.result_type(3, np.arange(7, dtype='i1'))
dtype('int8')
np.result_type('i4', 'c8')
dtype('complex128')
np.result_type(3.0, -2)
dtype('float64')
roll(a, shift, axis=None)
Roll array elements along a given axis.
Elements that roll beyond the last position are re-introduced at
the first.
Parameters
----------
a : array_like
Input array.
shift : int
The number of places by which elements are shifted.
axis : int, optional
The axis along which elements are shifted. By default, the array
is flattened before shifting, after which the original
shape is restored.
Returns
-------
res : ndarray
Output array, with the same shape as `a`.
See Also
--------
rollaxis : Roll the specified axis backwards, until it lies in a
given position.
Examples
--------
x = np.arange(10)
np.roll(x, 2)
array([8, 9, 0, 1, 2, 3, 4, 5, 6, 7])
x2 = np.reshape(x, (2,5))
x2
array([[0, 1, 2, 3, 4],
[5, 6, 7, 8, 9]])
np.roll(x2, 1)
array([[9, 0, 1, 2, 3],
[4, 5, 6, 7, 8]])
np.roll(x2, 1, axis=0)
array([[5, 6, 7, 8, 9],
[0, 1, 2, 3, 4]])
np.roll(x2, 1, axis=1)
array([[4, 0, 1, 2, 3],
[9, 5, 6, 7, 8]])
rollaxis(a, axis, start=0)
Roll the specified axis backwards, until it lies in a given position.
Parameters
----------
a : ndarray
Input array.
axis : int
The axis to roll backwards. The positions of the other axes do not
change relative to one another.
start : int, optional
The axis is rolled until it lies before this position. The default,
0, results in a "complete" roll.
Returns
-------
res : ndarray
For Numpy >= 1.10 a view of `a` is always returned. For earlier
Numpy versions a view of `a` is returned only if the order of the
axes is changed, otherwise the input array is returned.
See Also
--------
roll : Roll the elements of an array by a number of positions along a
given axis.
Examples
--------
a = np.ones((3,4,5,6))
np.rollaxis(a, 3, 1).shape
(3, 6, 4, 5)
np.rollaxis(a, 2).shape
(5, 3, 4, 6)
np.rollaxis(a, 1, 4).shape
(3, 5, 6, 4)
roots(p)
Return the roots of a polynomial with coefficients given in p.
The values in the rank-1 array `p` are coefficients of a polynomial.
If the length of `p` is n+1 then the polynomial is described by::
p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n]
Parameters
----------
p : array_like
Rank-1 array of polynomial coefficients.
Returns
-------
out : ndarray
An array containing the complex roots of the polynomial.
Raises
------
ValueError
When `p` cannot be converted to a rank-1 array.
See also
--------
poly : Find the coefficients of a polynomial with a given sequence
of roots.
polyval : Evaluate a polynomial at a point.
polyfit : Least squares polynomial fit.
poly1d : A one-dimensional polynomial class.
Notes
-----
The algorithm relies on computing the eigenvalues of the
companion matrix [1]_.
References
----------
.. [1] R. A. Horn & C. R. Johnson, *Matrix Analysis*. Cambridge, UK:
Cambridge University Press, 1999, pp. 146-7.
Examples
--------
coeff = [3.2, 2, 1]
np.roots(coeff)
array([-0.3125+0.46351241j, -0.3125-0.46351241j])
rot90(m, k=1)
Rotate an array by 90 degrees in the counter-clockwise direction.
The first two dimensions are rotated; therefore, the array must be at
least 2-D.
Parameters
----------
m : array_like
Array of two or more dimensions.
k : integer
Number of times the array is rotated by 90 degrees.
Returns
-------
y : ndarray
Rotated array.
See Also
--------
fliplr : Flip an array horizontally.
flipud : Flip an array vertically.
Examples
--------
m = np.array([[1,2],[3,4]], int)
m
array([[1, 2],
[3, 4]])
np.rot90(m)
array([[2, 4],
[1, 3]])
np.rot90(m, 2)
array([[4, 3],
[2, 1]])
round_(a, decimals=0, out=None)
Round an array to the given number of decimals.
Refer to `around` for full documentation.
See Also
--------
around : equivalent function
row_stack = vstack(tup)
Stack arrays in sequence vertically (row wise).
Take a sequence of arrays and stack them vertically to make a single
array. Rebuild arrays divided by `vsplit`.
Parameters
----------
tup : sequence of ndarrays
Tuple containing arrays to be stacked. The arrays must have the same
shape along all but the first axis.
Returns
-------
stacked : ndarray
The array formed by stacking the given arrays.
See Also
--------
stack : Join a sequence of arrays along a new axis.
hstack : Stack arrays in sequence horizontally (column wise).
dstack : Stack arrays in sequence depth wise (along third dimension).
concatenate : Join a sequence of arrays along an existing axis.
vsplit : Split array into a list of multiple sub-arrays vertically.
Notes
-----
Equivalent to ``np.concatenate(tup, axis=0)`` if `tup` contains arrays that
are at least 2-dimensional.
Examples
--------
a = np.array([1, 2, 3])
b = np.array([2, 3, 4])
np.vstack((a,b))
array([[1, 2, 3],
[2, 3, 4]])
a = np.array([[1], [2], [3]])
b = np.array([[2], [3], [4]])
np.vstack((a,b))
array([[1],
[2],
[3],
[2],
[3],
[4]])
safe_eval(source)
Protected string evaluation.
Evaluate a string containing a Python literal expression without
allowing the execution of arbitrary non-literal code.
Parameters
----------
source : str
The string to evaluate.
Returns
-------
obj : object
The result of evaluating `source`.
Raises
------
SyntaxError
If the code has invalid Python syntax, or if it contains
non-literal code.
Examples
--------
np.safe_eval('1')
1
np.safe_eval('[1, 2, 3]')
[1, 2, 3]
np.safe_eval('{"foo": ("bar", 10.0)}')
{'foo': ('bar', 10.0)}
np.safe_eval('import os')
Traceback (most recent call last):
...
SyntaxError: invalid syntax
np.safe_eval('open("/home/user/.ssh/id_dsa").read()')
Traceback (most recent call last):
...
SyntaxError: Unsupported source construct: compiler.ast.CallFunc
save(file, arr, allow_pickle=True, fix_imports=True)
Save an array to a binary file in NumPy ``.npy`` format.
Parameters
----------
file : file or str
File or filename to which the data is saved. If file is a file-object,
then the filename is unchanged. If file is a string, a ``.npy``
extension will be appended to the file name if it does not already
have one.
allow_pickle : bool, optional
Allow saving object arrays using Python pickles. Reasons for disallowing
pickles include security (loading pickled data can execute arbitrary
code) and portability (pickled objects may not be loadable on different
Python installations, for example if the stored objects require libraries
that are not available, and not all pickled data is compatible between
Python 2 and Python 3).
Default: True
fix_imports : bool, optional
Only useful in forcing objects in object arrays on Python 3 to be
pickled in a Python 2 compatible way. If `fix_imports` is True, pickle
will try to map the new Python 3 names to the old module names used in
Python 2, so that the pickle data stream is readable with Python 2.
arr : array_like
Array data to be saved.
See Also
--------
savez : Save several arrays into a ``.npz`` archive
savetxt, load
Notes
-----
For a description of the ``.npy`` format, see the module docstring
of `numpy.lib.format` or the Numpy Enhancement Proposal
http://docs.scipy.org/doc/numpy/neps/npy-format.html
Examples
--------
from tempfile import TemporaryFile
outfile = TemporaryFile()
x = np.arange(10)
np.save(outfile, x)
outfile.seek(0) # Only needed here to simulate closing & reopening file
np.load(outfile)
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
savetxt(fname, X, fmt='%.18e', delimiter=' ', newline='\n', header='', footer='', comments='# ')
Save an array to a text file.
Parameters
----------
fname : filename or file handle
If the filename ends in ``.gz``, the file is automatically saved in
compressed gzip format. `loadtxt` understands gzipped files
transparently.
X : array_like
Data to be saved to a text file.
fmt : str or sequence of strs, optional
A single format (%10.5f), a sequence of formats, or a
multi-format string, e.g. 'Iteration %d -- %10.5f', in which
case `delimiter` is ignored. For complex `X`, the legal options
for `fmt` are:
a) a single specifier, `fmt='%.4e'`, resulting in numbers formatted
like `' (%s+%sj)' % (fmt, fmt)`
b) a full string specifying every real and imaginary part, e.g.
`' %.4e %+.4j %.4e %+.4j %.4e %+.4j'` for 3 columns
c) a list of specifiers, one per column - in this case, the real
and imaginary part must have separate specifiers,
e.g. `['%.3e + %.3ej', '(%.15e%+.15ej)']` for 2 columns
delimiter : str, optional
String or character separating columns.
newline : str, optional
String or character separating lines.
.. versionadded:: 1.5.0
header : str, optional
String that will be written at the beginning of the file.
.. versionadded:: 1.7.0
footer : str, optional
String that will be written at the end of the file.
.. versionadded:: 1.7.0
comments : str, optional
String that will be prepended to the ``header`` and ``footer`` strings,
to mark them as comments. Default: '# ', as expected by e.g.
``numpy.loadtxt``.
.. versionadded:: 1.7.0
See Also
--------
save : Save an array to a binary file in NumPy ``.npy`` format
savez : Save several arrays into an uncompressed ``.npz`` archive
savez_compressed : Save several arrays into a compressed ``.npz`` archive
Notes
-----
Further explanation of the `fmt` parameter
(``%[flag]width[.precision]specifier``):
flags:
``-`` : left justify
``+`` : Forces to precede result with + or -.
``0`` : Left pad the number with zeros instead of space (see width).
width:
Minimum number of characters to be printed. The value is not truncated
if it has more characters.
precision:
- For integer specifiers (eg. ``d,i,o,x``), the minimum number of
digits.
- For ``e, E`` and ``f`` specifiers, the number of digits to print
after the decimal point.
- For ``g`` and ``G``, the maximum number of significant digits.
- For ``s``, the maximum number of characters.
specifiers:
``c`` : character
``d`` or ``i`` : signed decimal integer
``e`` or ``E`` : scientific notation with ``e`` or ``E``.
``f`` : decimal floating point
``g,G`` : use the shorter of ``e,E`` or ``f``
``o`` : signed octal
``s`` : string of characters
``u`` : unsigned decimal integer
``x,X`` : unsigned hexadecimal integer
This explanation of ``fmt`` is not complete, for an exhaustive
specification see [1]_.
References
----------
.. [1] `Format Specification Mini-Language
`_, Python Documentation.
Examples
--------
x = y = z = np.arange(0.0,5.0,1.0)
np.savetxt('test.out', x, delimiter=',') # X is an array
np.savetxt('test.out', (x,y,z)) # x,y,z equal sized 1D arrays
np.savetxt('test.out', x, fmt='%1.4e') # use exponential notation
savez(file, *args, **kwds)
Save several arrays into a single file in uncompressed ``.npz`` format.
If arguments are passed in with no keywords, the corresponding variable
names, in the ``.npz`` file, are 'arr_0', 'arr_1', etc. If keyword
arguments are given, the corresponding variable names, in the ``.npz``
file will match the keyword names.
Parameters
----------
file : str or file
Either the file name (string) or an open file (file-like object)
where the data will be saved. If file is a string, the ``.npz``
extension will be appended to the file name if it is not already there.
args : Arguments, optional
Arrays to save to the file. Since it is not possible for Python to
know the names of the arrays outside `savez`, the arrays will be saved
with names "arr_0", "arr_1", and so on. These arguments can be any
expression.
kwds : Keyword arguments, optional
Arrays to save to the file. Arrays will be saved in the file with the
keyword names.
Returns
-------
None
See Also
--------
save : Save a single array to a binary file in NumPy format.
savetxt : Save an array to a file as plain text.
savez_compressed : Save several arrays into a compressed ``.npz`` archive
Notes
-----
The ``.npz`` file format is a zipped archive of files named after the
variables they contain. The archive is not compressed and each file
in the archive contains one variable in ``.npy`` format. For a
description of the ``.npy`` format, see `numpy.lib.format` or the
Numpy Enhancement Proposal
http://docs.scipy.org/doc/numpy/neps/npy-format.html
When opening the saved ``.npz`` file with `load` a `NpzFile` object is
returned. This is a dictionary-like object which can be queried for
its list of arrays (with the ``.files`` attribute), and for the arrays
themselves.
Examples
--------
from tempfile import TemporaryFile
outfile = TemporaryFile()
x = np.arange(10)
y = np.sin(x)
Using `savez` with \*args, the arrays are saved with default names.
np.savez(outfile, x, y)
outfile.seek(0) # Only needed here to simulate closing & reopening file
npzfile = np.load(outfile)
npzfile.files
['arr_1', 'arr_0']
npzfile['arr_0']
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
Using `savez` with \**kwds, the arrays are saved with the keyword names.
outfile = TemporaryFile()
np.savez(outfile, x=x, y=y)
outfile.seek(0)
npzfile = np.load(outfile)
npzfile.files
['y', 'x']
npzfile['x']
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
savez_compressed(file, *args, **kwds)
Save several arrays into a single file in compressed ``.npz`` format.
If keyword arguments are given, then filenames are taken from the keywords.
If arguments are passed in with no keywords, then stored file names are
arr_0, arr_1, etc.
Parameters
----------
file : str
File name of ``.npz`` file.
args : Arguments
Function arguments.
kwds : Keyword arguments
Keywords.
See Also
--------
numpy.savez : Save several arrays into an uncompressed ``.npz`` file format
numpy.load : Load the files created by savez_compressed.
sctype2char(sctype)
Return the string representation of a scalar dtype.
Parameters
----------
sctype : scalar dtype or object
If a scalar dtype, the corresponding string character is
returned. If an object, `sctype2char` tries to infer its scalar type
and then return the corresponding string character.
Returns
-------
typechar : str
The string character corresponding to the scalar type.
Raises
------
ValueError
If `sctype` is an object for which the type can not be inferred.
See Also
--------
obj2sctype, issctype, issubsctype, mintypecode
Examples
--------
for sctype in [np.int32, np.float, np.complex, np.string_, np.ndarray]:
print np.sctype2char(sctype)
l
d
D
S
O
x = np.array([1., 2-1.j])
np.sctype2char(x)
'D'
np.sctype2char(list)
'O'
searchsorted(a, v, side='left', sorter=None)
Find indices where elements should be inserted to maintain order.
Find the indices into a sorted array `a` such that, if the
corresponding elements in `v` were inserted before the indices, the
order of `a` would be preserved.
Parameters
----------
a : 1-D array_like
Input array. If `sorter` is None, then it must be sorted in
ascending order, otherwise `sorter` must be an array of indices
that sort it.
v : array_like
Values to insert into `a`.
side : {'left', 'right'}, optional
If 'left', the index of the first suitable location found is given.
If 'right', return the last such index. If there is no suitable
index, return either 0 or N (where N is the length of `a`).
sorter : 1-D array_like, optional
Optional array of integer indices that sort array a into ascending
order. They are typically the result of argsort.
.. versionadded:: 1.7.0
Returns
-------
indices : array of ints
Array of insertion points with the same shape as `v`.
See Also
--------
sort : Return a sorted copy of an array.
histogram : Produce histogram from 1-D data.
Notes
-----
Binary search is used to find the required insertion points.
As of Numpy 1.4.0 `searchsorted` works with real/complex arrays containing
`nan` values. The enhanced sort order is documented in `sort`.
Examples
--------
np.searchsorted([1,2,3,4,5], 3)
2
np.searchsorted([1,2,3,4,5], 3, side='right')
3
np.searchsorted([1,2,3,4,5], [-10, 10, 2, 3])
array([0, 5, 1, 2])
select(condlist, choicelist, default=0)
Return an array drawn from elements in choicelist, depending on conditions.
Parameters
----------
condlist : list of bool ndarrays
The list of conditions which determine from which array in `choicelist`
the output elements are taken. When multiple conditions are satisfied,
the first one encountered in `condlist` is used.
choicelist : list of ndarrays
The list of arrays from which the output elements are taken. It has
to be of the same length as `condlist`.
default : scalar, optional
The element inserted in `output` when all conditions evaluate to False.
Returns
-------
output : ndarray
The output at position m is the m-th element of the array in
`choicelist` where the m-th element of the corresponding array in
`condlist` is True.
See Also
--------
where : Return elements from one of two arrays depending on condition.
take, choose, compress, diag, diagonal
Examples
--------
x = np.arange(10)
condlist = [x<3, x>5]
choicelist = [x, x**2]
np.select(condlist, choicelist)
array([ 0, 1, 2, 0, 0, 0, 36, 49, 64, 81])
set_numeric_ops(...)
set_numeric_ops(op1=func1, op2=func2, ...)
Set numerical operators for array objects.
Parameters
----------
op1, op2, ... : callable
Each ``op = func`` pair describes an operator to be replaced.
For example, ``add = lambda x, y: np.add(x, y) % 5`` would replace
addition by modulus 5 addition.
Returns
-------
saved_ops : list of callables
A list of all operators, stored before making replacements.
Notes
-----
.. WARNING::
Use with care! Incorrect usage may lead to memory errors.
A function replacing an operator cannot make use of that operator.
For example, when replacing add, you may not use ``+``. Instead,
directly call ufuncs.
Examples
--------
def add_mod5(x, y):
return np.add(x, y) % 5
...
old_funcs = np.set_numeric_ops(add=add_mod5)
x = np.arange(12).reshape((3, 4))
x + x
array([[0, 2, 4, 1],
[3, 0, 2, 4],
[1, 3, 0, 2]])
ignore = np.set_numeric_ops(**old_funcs) # restore operators
set_printoptions(precision=None, threshold=None, edgeitems=None, linewidth=None, suppress=None, nanstr=None, infstr=None, formatter=None)
Set printing options.
These options determine the way floating point numbers, arrays and
other NumPy objects are displayed.
Parameters
----------
precision : int, optional
Number of digits of precision for floating point output (default 8).
threshold : int, optional
Total number of array elements which trigger summarization
rather than full repr (default 1000).
edgeitems : int, optional
Number of array items in summary at beginning and end of
each dimension (default 3).
linewidth : int, optional
The number of characters per line for the purpose of inserting
line breaks (default 75).
suppress : bool, optional
Whether or not suppress printing of small floating point values
using scientific notation (default False).
nanstr : str, optional
String representation of floating point not-a-number (default nan).
infstr : str, optional
String representation of floating point infinity (default inf).
formatter : dict of callables, optional
If not None, the keys should indicate the type(s) that the respective
formatting function applies to. Callables should return a string.
Types that are not specified (by their corresponding keys) are handled
by the default formatters. Individual types for which a formatter
can be set are::
- 'bool'
- 'int'
- 'timedelta' : a `numpy.timedelta64`
- 'datetime' : a `numpy.datetime64`
- 'float'
- 'longfloat' : 128-bit floats
- 'complexfloat'
- 'longcomplexfloat' : composed of two 128-bit floats
- 'numpy_str' : types `numpy.string_` and `numpy.unicode_`
- 'str' : all other strings
Other keys that can be used to set a group of types at once are::
- 'all' : sets all types
- 'int_kind' : sets 'int'
- 'float_kind' : sets 'float' and 'longfloat'
- 'complex_kind' : sets 'complexfloat' and 'longcomplexfloat'
- 'str_kind' : sets 'str' and 'numpystr'
See Also
--------
get_printoptions, set_string_function, array2string
Notes
-----
`formatter` is always reset with a call to `set_printoptions`.
Examples
--------
Floating point precision can be set:
np.set_printoptions(precision=4)
print np.array([1.123456789])
[ 1.1235]
Long arrays can be summarised:
np.set_printoptions(threshold=5)
print np.arange(10)
[0 1 2 ..., 7 8 9]
Small results can be suppressed:
eps = np.finfo(float).eps
x = np.arange(4.)
x**2 - (x + eps)**2
array([ -4.9304e-32, -4.4409e-16, 0.0000e+00, 0.0000e+00])
np.set_printoptions(suppress=True)
x**2 - (x + eps)**2
array([-0., -0., 0., 0.])
A custom formatter can be used to display array elements as desired:
np.set_printoptions(formatter={'all':lambda x: 'int: '+str(-x)})
x = np.arange(3)
x
array([int: 0, int: -1, int: -2])
np.set_printoptions() # formatter gets reset
x
array([0, 1, 2])
To put back the default options, you can use:
np.set_printoptions(edgeitems=3,infstr='inf',
linewidth=75, nanstr='nan', precision=8,
suppress=False, threshold=1000, formatter=None)
set_string_function(f, repr=True)
Set a Python function to be used when pretty printing arrays.
Parameters
----------
f : function or None
Function to be used to pretty print arrays. The function should expect
a single array argument and return a string of the representation of
the array. If None, the function is reset to the default NumPy function
to print arrays.
repr : bool, optional
If True (default), the function for pretty printing (``__repr__``)
is set, if False the function that returns the default string
representation (``__str__``) is set.
See Also
--------
set_printoptions, get_printoptions
Examples
--------
def pprint(arr):
return 'HA! - What are you going to do now?'
...
np.set_string_function(pprint)
a = np.arange(10)
a
HA! - What are you going to do now?
print a
[0 1 2 3 4 5 6 7 8 9]
We can reset the function to the default:
np.set_string_function(None)
a
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
`repr` affects either pretty printing or normal string representation.
Note that ``__repr__`` is still affected by setting ``__str__``
because the width of each array element in the returned string becomes
equal to the length of the result of ``__str__()``.
x = np.arange(4)
np.set_string_function(lambda x:'random', repr=False)
x.__str__()
'random'
x.__repr__()
'array([ 0, 1, 2, 3])'
setbufsize(size)
Set the size of the buffer used in ufuncs.
Parameters
----------
size : int
Size of buffer.
setdiff1d(ar1, ar2, assume_unique=False)
Find the set difference of two arrays.
Return the sorted, unique values in `ar1` that are not in `ar2`.
Parameters
----------
ar1 : array_like
Input array.
ar2 : array_like
Input comparison array.
assume_unique : bool
If True, the input arrays are both assumed to be unique, which
can speed up the calculation. Default is False.
Returns
-------
setdiff1d : ndarray
Sorted 1D array of values in `ar1` that are not in `ar2`.
See Also
--------
numpy.lib.arraysetops : Module with a number of other functions for
performing set operations on arrays.
Examples
--------
a = np.array([1, 2, 3, 2, 4, 1])
b = np.array([3, 4, 5, 6])
np.setdiff1d(a, b)
array([1, 2])
seterr(all=None, divide=None, over=None, under=None, invalid=None)
Set how floating-point errors are handled.
Note that operations on integer scalar types (such as `int16`) are
handled like floating point, and are affected by these settings.
Parameters
----------
all : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional
Set treatment for all types of floating-point errors at once:
- ignore: Take no action when the exception occurs.
- warn: Print a `RuntimeWarning` (via the Python `warnings` module).
- raise: Raise a `FloatingPointError`.
- call: Call a function specified using the `seterrcall` function.
- print: Print a warning directly to ``stdout``.
- log: Record error in a Log object specified by `seterrcall`.
The default is not to change the current behavior.
divide : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional
Treatment for division by zero.
over : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional
Treatment for floating-point overflow.
under : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional
Treatment for floating-point underflow.
invalid : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional
Treatment for invalid floating-point operation.
Returns
-------
old_settings : dict
Dictionary containing the old settings.
See also
--------
seterrcall : Set a callback function for the 'call' mode.
geterr, geterrcall, errstate
Notes
-----
The floating-point exceptions are defined in the IEEE 754 standard [1]:
- Division by zero: infinite result obtained from finite numbers.
- Overflow: result too large to be expressed.
- Underflow: result so close to zero that some precision
was lost.
- Invalid operation: result is not an expressible number, typically
indicates that a NaN was produced.
.. [1] http://en.wikipedia.org/wiki/IEEE_754
Examples
--------
old_settings = np.seterr(all='ignore') #seterr to known value
np.seterr(over='raise')
{'over': 'ignore', 'divide': 'ignore', 'invalid': 'ignore',
'under': 'ignore'}
np.seterr(**old_settings) # reset to default
{'over': 'raise', 'divide': 'ignore', 'invalid': 'ignore', 'under': 'ignore'}
np.int16(32000) * np.int16(3)
30464
old_settings = np.seterr(all='warn', over='raise')
np.int16(32000) * np.int16(3)
Traceback (most recent call last):
File "", line 1, in
FloatingPointError: overflow encountered in short_scalars
old_settings = np.seterr(all='print')
np.geterr()
{'over': 'print', 'divide': 'print', 'invalid': 'print', 'under': 'print'}
np.int16(32000) * np.int16(3)
Warning: overflow encountered in short_scalars
30464
seterrcall(func)
Set the floating-point error callback function or log object.
There are two ways to capture floating-point error messages. The first
is to set the error-handler to 'call', using `seterr`. Then, set
the function to call using this function.
The second is to set the error-handler to 'log', using `seterr`.
Floating-point errors then trigger a call to the 'write' method of
the provided object.
Parameters
----------
func : callable f(err, flag) or object with write method
Function to call upon floating-point errors ('call'-mode) or
object whose 'write' method is used to log such message ('log'-mode).
The call function takes two arguments. The first is a string describing the
type of error (such as "divide by zero", "overflow", "underflow", or "invalid value"),
and the second is the status flag. The flag is a byte, whose four
least-significant bits indicate the type of error, one of "divide", "over",
"under", "invalid"::
[0 0 0 0 divide over under invalid]
In other words, ``flags = divide + 2*over + 4*under + 8*invalid``.
If an object is provided, its write method should take one argument,
a string.
Returns
-------
h : callable, log instance or None
The old error handler.
See Also
--------
seterr, geterr, geterrcall
Examples
--------
Callback upon error:
def err_handler(type, flag):
print "Floating point error (%s), with flag %s" % (type, flag)
...
saved_handler = np.seterrcall(err_handler)
save_err = np.seterr(all='call')
np.array([1, 2, 3]) / 0.0
Floating point error (divide by zero), with flag 1
array([ Inf, Inf, Inf])
np.seterrcall(saved_handler)
np.seterr(**save_err)
{'over': 'call', 'divide': 'call', 'invalid': 'call', 'under': 'call'}
Log error message:
class Log(object):
def write(self, msg):
print "LOG: %s" % msg
...
log = Log()
saved_handler = np.seterrcall(log)
save_err = np.seterr(all='log')
np.array([1, 2, 3]) / 0.0
LOG: Warning: divide by zero encountered in divide
array([ Inf, Inf, Inf])
np.seterrcall(saved_handler)
<__main__.Log object at 0x...>
np.seterr(**save_err)
{'over': 'log', 'divide': 'log', 'invalid': 'log', 'under': 'log'}
seterrobj(...)
seterrobj(errobj)
Set the object that defines floating-point error handling.
The error object contains all information that defines the error handling
behavior in Numpy. `seterrobj` is used internally by the other
functions that set error handling behavior (`seterr`, `seterrcall`).
Parameters
----------
errobj : list
The error object, a list containing three elements:
[internal numpy buffer size, error mask, error callback function].
The error mask is a single integer that holds the treatment information
on all four floating point errors. The information for each error type
is contained in three bits of the integer. If we print it in base 8, we
can see what treatment is set for "invalid", "under", "over", and
"divide" (in that order). The printed string can be interpreted with
* 0 : 'ignore'
* 1 : 'warn'
* 2 : 'raise'
* 3 : 'call'
* 4 : 'print'
* 5 : 'log'
See Also
--------
geterrobj, seterr, geterr, seterrcall, geterrcall
getbufsize, setbufsize
Notes
-----
For complete documentation of the types of floating-point exceptions and
treatment options, see `seterr`.
Examples
--------
old_errobj = np.geterrobj() # first get the defaults
old_errobj
[10000, 0, None]
def err_handler(type, flag):
print "Floating point error (%s), with flag %s" % (type, flag)
...
new_errobj = [20000, 12, err_handler]
np.seterrobj(new_errobj)
np.base_repr(12, 8) # int for divide=4 ('print') and over=1 ('warn')
'14'
np.geterr()
{'over': 'warn', 'divide': 'print', 'invalid': 'ignore', 'under': 'ignore'}
np.geterrcall() is err_handler
True
setxor1d(ar1, ar2, assume_unique=False)
Find the set exclusive-or of two arrays.
Return the sorted, unique values that are in only one (not both) of the
input arrays.
Parameters
----------
ar1, ar2 : array_like
Input arrays.
assume_unique : bool
If True, the input arrays are both assumed to be unique, which
can speed up the calculation. Default is False.
Returns
-------
setxor1d : ndarray
Sorted 1D array of unique values that are in only one of the input
arrays.
Examples
--------
a = np.array([1, 2, 3, 2, 4])
b = np.array([2, 3, 5, 7, 5])
np.setxor1d(a,b)
array([1, 4, 5, 7])
shape(a)
Return the shape of an array.
Parameters
----------
a : array_like
Input array.
Returns
-------
shape : tuple of ints
The elements of the shape tuple give the lengths of the
corresponding array dimensions.
See Also
--------
alen
ndarray.shape : Equivalent array method.
Examples
--------
np.shape(np.eye(3))
(3, 3)
np.shape([[1, 2]])
(1, 2)
np.shape([0])
(1,)
np.shape(0)
()
a = np.array([(1, 2), (3, 4)], dtype=[('x', 'i4'), ('y', 'i4')])
np.shape(a)
(2,)
a.shape
(2,)
show_config = show()
sinc(x)
Return the sinc function.
The sinc function is :math:`\sin(\pi x)/(\pi x)`.
Parameters
----------
x : ndarray
Array (possibly multi-dimensional) of values for which to to
calculate ``sinc(x)``.
Returns
-------
out : ndarray
``sinc(x)``, which has the same shape as the input.
Notes
-----
``sinc(0)`` is the limit value 1.
The name sinc is short for "sine cardinal" or "sinus cardinalis".
The sinc function is used in various signal processing applications,
including in anti-aliasing, in the construction of a Lanczos resampling
filter, and in interpolation.
For bandlimited interpolation of discrete-time signals, the ideal
interpolation kernel is proportional to the sinc function.
References
----------
.. [1] Weisstein, Eric W. "Sinc Function." From MathWorld--A Wolfram Web
Resource. http://mathworld.wolfram.com/SincFunction.html
.. [2] Wikipedia, "Sinc function",
http://en.wikipedia.org/wiki/Sinc_function
Examples
--------
x = np.linspace(-4, 4, 41)
np.sinc(x)
array([ -3.89804309e-17, -4.92362781e-02, -8.40918587e-02,
-8.90384387e-02, -5.84680802e-02, 3.89804309e-17,
6.68206631e-02, 1.16434881e-01, 1.26137788e-01,
8.50444803e-02, -3.89804309e-17, -1.03943254e-01,
-1.89206682e-01, -2.16236208e-01, -1.55914881e-01,
3.89804309e-17, 2.33872321e-01, 5.04551152e-01,
7.56826729e-01, 9.35489284e-01, 1.00000000e+00,
9.35489284e-01, 7.56826729e-01, 5.04551152e-01,
2.33872321e-01, 3.89804309e-17, -1.55914881e-01,
-2.16236208e-01, -1.89206682e-01, -1.03943254e-01,
-3.89804309e-17, 8.50444803e-02, 1.26137788e-01,
1.16434881e-01, 6.68206631e-02, 3.89804309e-17,
-5.84680802e-02, -8.90384387e-02, -8.40918587e-02,
-4.92362781e-02, -3.89804309e-17])
plt.plot(x, np.sinc(x))
[]
plt.title("Sinc Function")
plt.ylabel("Amplitude")
plt.xlabel("X")
plt.show()
It works in 2-D as well:
x = np.linspace(-4, 4, 401)
xx = np.outer(x, x)
plt.imshow(np.sinc(xx))
size(a, axis=None)
Return the number of elements along a given axis.
Parameters
----------
a : array_like
Input data.
axis : int, optional
Axis along which the elements are counted. By default, give
the total number of elements.
Returns
-------
element_count : int
Number of elements along the specified axis.
See Also
--------
shape : dimensions of array
ndarray.shape : dimensions of array
ndarray.size : number of elements in array
Examples
--------
a = np.array([[1,2,3],[4,5,6]])
np.size(a)
6
np.size(a,1)
3
np.size(a,0)
2
sometrue(a, axis=None, out=None, keepdims=False)
Check whether some values are true.
Refer to `any` for full documentation.
See Also
--------
any : equivalent function
sort(a, axis=-1, kind='quicksort', order=None)
Return a sorted copy of an array.
Parameters
----------
a : array_like
Array to be sorted.
axis : int or None, optional
Axis along which to sort. If None, the array is flattened before
sorting. The default is -1, which sorts along the last axis.
kind : {'quicksort', 'mergesort', 'heapsort'}, optional
Sorting algorithm. Default is 'quicksort'.
order : str or list of str, optional
When `a` is an array with fields defined, this argument specifies
which fields to compare first, second, etc. A single field can
be specified as a string, and not all fields need be specified,
but unspecified fields will still be used, in the order in which
they come up in the dtype, to break ties.
Returns
-------
sorted_array : ndarray
Array of the same type and shape as `a`.
See Also
--------
ndarray.sort : Method to sort an array in-place.
argsort : Indirect sort.
lexsort : Indirect stable sort on multiple keys.
searchsorted : Find elements in a sorted array.
partition : Partial sort.
Notes
-----
The various sorting algorithms are characterized by their average speed,
worst case performance, work space size, and whether they are stable. A
stable sort keeps items with the same key in the same relative
order. The three available algorithms have the following
properties:
=========== ======= ============= ============ =======
kind speed worst case work space stable
=========== ======= ============= ============ =======
'quicksort' 1 O(n^2) 0 no
'mergesort' 2 O(n*log(n)) ~n/2 yes
'heapsort' 3 O(n*log(n)) 0 no
=========== ======= ============= ============ =======
All the sort algorithms make temporary copies of the data when
sorting along any but the last axis. Consequently, sorting along
the last axis is faster and uses less space than sorting along
any other axis.
The sort order for complex numbers is lexicographic. If both the real
and imaginary parts are non-nan then the order is determined by the
real parts except when they are equal, in which case the order is
determined by the imaginary parts.
Previous to numpy 1.4.0 sorting real and complex arrays containing nan
values led to undefined behaviour. In numpy versions >= 1.4.0 nan
values are sorted to the end. The extended sort order is:
* Real: [R, nan]
* Complex: [R + Rj, R + nanj, nan + Rj, nan + nanj]
where R is a non-nan real value. Complex values with the same nan
placements are sorted according to the non-nan part if it exists.
Non-nan values are sorted as before.
Examples
--------
a = np.array([[1,4],[3,1]])
np.sort(a) # sort along the last axis
array([[1, 4],
[1, 3]])
np.sort(a, axis=None) # sort the flattened array
array([1, 1, 3, 4])
np.sort(a, axis=0) # sort along the first axis
array([[1, 1],
[3, 4]])
Use the `order` keyword to specify a field to use when sorting a
structured array:
dtype = [('name', 'S10'), ('height', float), ('age', int)]
values = [('Arthur', 1.8, 41), ('Lancelot', 1.9, 38),
('Galahad', 1.7, 38)]
a = np.array(values, dtype=dtype) # create a structured array
np.sort(a, order='height') # doctest: +SKIP
array([('Galahad', 1.7, 38), ('Arthur', 1.8, 41),
('Lancelot', 1.8999999999999999, 38)],
dtype=[('name', '|S10'), ('height', '', mode 'w'>)
Print or write to a file the source code for a Numpy object.
The source code is only returned for objects written in Python. Many
functions and classes are defined in C and will therefore not return
useful information.
Parameters
----------
object : numpy object
Input object. This can be any object (function, class, module,
...).
output : file object, optional
If `output` not supplied then source code is printed to screen
(sys.stdout). File object must be created with either write 'w' or
append 'a' modes.
See Also
--------
lookfor, info
Examples
--------
np.source(np.interp) #doctest: +SKIP
In file: /usr/lib/python2.6/dist-packages/numpy/lib/function_base.py
def interp(x, xp, fp, left=None, right=None):
""".... (full docstring printed)"""
if isinstance(x, (float, int, number)):
return compiled_interp([x], xp, fp, left, right).item()
else:
return compiled_interp(x, xp, fp, left, right)
The source code is only returned for objects written in Python.
np.source(np.array) #doctest: +SKIP
Not available for this object.
split(ary, indices_or_sections, axis=0)
Split an array into multiple sub-arrays.
Parameters
----------
ary : ndarray
Array to be divided into sub-arrays.
indices_or_sections : int or 1-D array
If `indices_or_sections` is an integer, N, the array will be divided
into N equal arrays along `axis`. If such a split is not possible,
an error is raised.
If `indices_or_sections` is a 1-D array of sorted integers, the entries
indicate where along `axis` the array is split. For example,
``[2, 3]`` would, for ``axis=0``, result in
- ary[:2]
- ary[2:3]
- ary[3:]
If an index exceeds the dimension of the array along `axis`,
an empty sub-array is returned correspondingly.
axis : int, optional
The axis along which to split, default is 0.
Returns
-------
sub-arrays : list of ndarrays
A list of sub-arrays.
Raises
------
ValueError
If `indices_or_sections` is given as an integer, but
a split does not result in equal division.
See Also
--------
array_split : Split an array into multiple sub-arrays of equal or
near-equal size. Does not raise an exception if
an equal division cannot be made.
hsplit : Split array into multiple sub-arrays horizontally (column-wise).
vsplit : Split array into multiple sub-arrays vertically (row wise).
dsplit : Split array into multiple sub-arrays along the 3rd axis (depth).
concatenate : Join a sequence of arrays along an existing axis.
stack : Join a sequence of arrays along a new axis.
hstack : Stack arrays in sequence horizontally (column wise).
vstack : Stack arrays in sequence vertically (row wise).
dstack : Stack arrays in sequence depth wise (along third dimension).
Examples
--------
x = np.arange(9.0)
np.split(x, 3)
[array([ 0., 1., 2.]), array([ 3., 4., 5.]), array([ 6., 7., 8.])]
x = np.arange(8.0)
np.split(x, [3, 5, 6, 10])
[array([ 0., 1., 2.]),
array([ 3., 4.]),
array([ 5.]),
array([ 6., 7.]),
array([], dtype=float64)]
squeeze(a, axis=None)
Remove single-dimensional entries from the shape of an array.
Parameters
----------
a : array_like
Input data.
axis : None or int or tuple of ints, optional
.. versionadded:: 1.7.0
Selects a subset of the single-dimensional entries in the
shape. If an axis is selected with shape entry greater than
one, an error is raised.
Returns
-------
squeezed : ndarray
The input array, but with all or a subset of the
dimensions of length 1 removed. This is always `a` itself
or a view into `a`.
Examples
--------
x = np.array([[[0], [1], [2]]])
x.shape
(1, 3, 1)
np.squeeze(x).shape
(3,)
np.squeeze(x, axis=(2,)).shape
(1, 3)
stack(arrays, axis=0)
Join a sequence of arrays along a new axis.
The `axis` parameter specifies the index of the new axis in the dimensions
of the result. For example, if ``axis=0`` it will be the first dimension
and if ``axis=-1`` it will be the last dimension.
.. versionadded:: 1.10.0
Parameters
----------
arrays : sequence of array_like
Each array must have the same shape.
axis : int, optional
The axis in the result array along which the input arrays are stacked.
Returns
-------
stacked : ndarray
The stacked array has one more dimension than the input arrays.
See Also
--------
concatenate : Join a sequence of arrays along an existing axis.
split : Split array into a list of multiple sub-arrays of equal size.
Examples
--------
arrays = [np.random.randn(3, 4) for _ in range(10)]
np.stack(arrays, axis=0).shape
(10, 3, 4)
np.stack(arrays, axis=1).shape
(3, 10, 4)
np.stack(arrays, axis=2).shape
(3, 4, 10)
a = np.array([1, 2, 3])
b = np.array([2, 3, 4])
np.stack((a, b))
array([[1, 2, 3],
[2, 3, 4]])
np.stack((a, b), axis=-1)
array([[1, 2],
[2, 3],
[3, 4]])
std(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False)
Compute the standard deviation along the specified axis.
Returns the standard deviation, a measure of the spread of a distribution,
of the array elements. The standard deviation is computed for the
flattened array by default, otherwise over the specified axis.
Parameters
----------
a : array_like
Calculate the standard deviation of these values.
axis : None or int or tuple of ints, optional
Axis or axes along which the standard deviation is computed. The
default is to compute the standard deviation of the flattened array.
.. versionadded: 1.7.0
If this is a tuple of ints, a standard deviation is performed over
multiple axes, instead of a single axis or all the axes as before.
dtype : dtype, optional
Type to use in computing the standard deviation. For arrays of
integer type the default is float64, for arrays of float types it is
the same as the array type.
out : ndarray, optional
Alternative output array in which to place the result. It must have
the same shape as the expected output but the type (of the calculated
values) will be cast if necessary.
ddof : int, optional
Means Delta Degrees of Freedom. The divisor used in calculations
is ``N - ddof``, where ``N`` represents the number of elements.
By default `ddof` is zero.
keepdims : bool, optional
If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option,
the result will broadcast correctly against the original `arr`.
Returns
-------
standard_deviation : ndarray, see dtype parameter above.
If `out` is None, return a new array containing the standard deviation,
otherwise return a reference to the output array.
See Also
--------
var, mean, nanmean, nanstd, nanvar
numpy.doc.ufuncs : Section "Output arguments"
Notes
-----
The standard deviation is the square root of the average of the squared
deviations from the mean, i.e., ``std = sqrt(mean(abs(x - x.mean())**2))``.
The average squared deviation is normally calculated as
``x.sum() / N``, where ``N = len(x)``. If, however, `ddof` is specified,
the divisor ``N - ddof`` is used instead. In standard statistical
practice, ``ddof=1`` provides an unbiased estimator of the variance
of the infinite population. ``ddof=0`` provides a maximum likelihood
estimate of the variance for normally distributed variables. The
standard deviation computed in this function is the square root of
the estimated variance, so even with ``ddof=1``, it will not be an
unbiased estimate of the standard deviation per se.
Note that, for complex numbers, `std` takes the absolute
value before squaring, so that the result is always real and nonnegative.
For floating-point input, the *std* is computed using the same
precision the input has. Depending on the input data, this can cause
the results to be inaccurate, especially for float32 (see example below).
Specifying a higher-accuracy accumulator using the `dtype` keyword can
alleviate this issue.
Examples
--------
a = np.array([[1, 2], [3, 4]])
np.std(a)
1.1180339887498949
np.std(a, axis=0)
array([ 1., 1.])
np.std(a, axis=1)
array([ 0.5, 0.5])
In single precision, std() can be inaccurate:
a = np.zeros((2, 512*512), dtype=np.float32)
a[0, :] = 1.0
a[1, :] = 0.1
np.std(a)
0.45000005
Computing the standard deviation in float64 is more accurate:
np.std(a, dtype=np.float64)
0.44999999925494177
sum(a, axis=None, dtype=None, out=None, keepdims=False)
Sum of array elements over a given axis.
Parameters
----------
a : array_like
Elements to sum.
axis : None or int or tuple of ints, optional
Axis or axes along which a sum is performed.
The default (`axis` = `None`) is perform a sum over all
the dimensions of the input array. `axis` may be negative, in
which case it counts from the last to the first axis.
.. versionadded:: 1.7.0
If this is a tuple of ints, a sum is performed on multiple
axes, instead of a single axis or all the axes as before.
dtype : dtype, optional
The type of the returned array and of the accumulator in which
the elements are summed. By default, the dtype of `a` is used.
An exception is when `a` has an integer type with less precision
than the default platform integer. In that case, the default
platform integer is used instead.
out : ndarray, optional
Array into which the output is placed. By default, a new array is
created. If `out` is given, it must be of the appropriate shape
(the shape of `a` with `axis` removed, i.e.,
``numpy.delete(a.shape, axis)``). Its type is preserved. See
`doc.ufuncs` (Section "Output arguments") for more details.
keepdims : bool, optional
If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option,
the result will broadcast correctly against the original `arr`.
Returns
-------
sum_along_axis : ndarray
An array with the same shape as `a`, with the specified
axis removed. If `a` is a 0-d array, or if `axis` is None, a scalar
is returned. If an output array is specified, a reference to
`out` is returned.
See Also
--------
ndarray.sum : Equivalent method.
cumsum : Cumulative sum of array elements.
trapz : Integration of array values using the composite trapezoidal rule.
mean, average
Notes
-----
Arithmetic is modular when using integer types, and no error is
raised on overflow.
The sum of an empty array is the neutral element 0:
np.sum([])
0.0
Examples
--------
np.sum([0.5, 1.5])
2.0
np.sum([0.5, 0.7, 0.2, 1.5], dtype=np.int32)
1
np.sum([[0, 1], [0, 5]])
6
np.sum([[0, 1], [0, 5]], axis=0)
array([0, 6])
np.sum([[0, 1], [0, 5]], axis=1)
array([1, 5])
If the accumulator is too small, overflow occurs:
np.ones(128, dtype=np.int8).sum(dtype=np.int8)
-128
swapaxes(a, axis1, axis2)
Interchange two axes of an array.
Parameters
----------
a : array_like
Input array.
axis1 : int
First axis.
axis2 : int
Second axis.
Returns
-------
a_swapped : ndarray
For Numpy >= 1.10, if `a` is an ndarray, then a view of `a` is
returned; otherwise a new array is created. For earlier Numpy
versions a view of `a` is returned only if the order of the
axes is changed, otherwise the input array is returned.
Examples
--------
x = np.array([[1,2,3]])
np.swapaxes(x,0,1)
array([[1],
[2],
[3]])
x = np.array([[[0,1],[2,3]],[[4,5],[6,7]]])
x
array([[[0, 1],
[2, 3]],
[[4, 5],
[6, 7]]])
np.swapaxes(x,0,2)
array([[[0, 4],
[2, 6]],
[[1, 5],
[3, 7]]])
take(a, indices, axis=None, out=None, mode='raise')
Take elements from an array along an axis.
This function does the same thing as "fancy" indexing (indexing arrays
using arrays); however, it can be easier to use if you need elements
along a given axis.
Parameters
----------
a : array_like
The source array.
indices : array_like
The indices of the values to extract.
.. versionadded:: 1.8.0
Also allow scalars for indices.
axis : int, optional
The axis over which to select values. By default, the flattened
input array is used.
out : ndarray, optional
If provided, the result will be placed in this array. It should
be of the appropriate shape and dtype.
mode : {'raise', 'wrap', 'clip'}, optional
Specifies how out-of-bounds indices will behave.
* 'raise' -- raise an error (default)
* 'wrap' -- wrap around
* 'clip' -- clip to the range
'clip' mode means that all indices that are too large are replaced
by the index that addresses the last element along that axis. Note
that this disables indexing with negative numbers.
Returns
-------
subarray : ndarray
The returned array has the same type as `a`.
See Also
--------
compress : Take elements using a boolean mask
ndarray.take : equivalent method
Examples
--------
a = [4, 3, 5, 7, 6, 8]
indices = [0, 1, 4]
np.take(a, indices)
array([4, 3, 6])
In this example if `a` is an ndarray, "fancy" indexing can be used.
a = np.array(a)
a[indices]
array([4, 3, 6])
If `indices` is not one dimensional, the output also has these dimensions.
np.take(a, [[0, 1], [2, 3]])
array([[4, 3],
[5, 7]])
tensordot(a, b, axes=2)
Compute tensor dot product along specified axes for arrays >= 1-D.
Given two tensors (arrays of dimension greater than or equal to one),
`a` and `b`, and an array_like object containing two array_like
objects, ``(a_axes, b_axes)``, sum the products of `a`'s and `b`'s
elements (components) over the axes specified by ``a_axes`` and
``b_axes``. The third argument can be a single non-negative
integer_like scalar, ``N``; if it is such, then the last ``N``
dimensions of `a` and the first ``N`` dimensions of `b` are summed
over.
Parameters
----------
a, b : array_like, len(shape) >= 1
Tensors to "dot".
axes : int or (2,) array_like
* integer_like
If an int N, sum over the last N axes of `a` and the first N axes
of `b` in order. The sizes of the corresponding axes must match.
* (2,) array_like
Or, a list of axes to be summed over, first sequence applying to `a`,
second to `b`. Both elements array_like must be of the same length.
See Also
--------
dot, einsum
Notes
-----
Three common use cases are:
``axes = 0`` : tensor product $a\otimes b$
``axes = 1`` : tensor dot product $a\cdot b$
``axes = 2`` : (default) tensor double contraction $a:b$
When `axes` is integer_like, the sequence for evaluation will be: first
the -Nth axis in `a` and 0th axis in `b`, and the -1th axis in `a` and
Nth axis in `b` last.
When there is more than one axis to sum over - and they are not the last
(first) axes of `a` (`b`) - the argument `axes` should consist of
two sequences of the same length, with the first axis to sum over given
first in both sequences, the second axis second, and so forth.
Examples
--------
A "traditional" example:
a = np.arange(60.).reshape(3,4,5)
b = np.arange(24.).reshape(4,3,2)
c = np.tensordot(a,b, axes=([1,0],[0,1]))
c.shape
(5, 2)
c
array([[ 4400., 4730.],
[ 4532., 4874.],
[ 4664., 5018.],
[ 4796., 5162.],
[ 4928., 5306.]])
# A slower but equivalent way of computing the same...
d = np.zeros((5,2))
for i in range(5):
for j in range(2):
for k in range(3):
for n in range(4):
d[i,j] += a[k,n,i] * b[n,k,j]
c == d
array([[ True, True],
[ True, True],
[ True, True],
[ True, True],
[ True, True]], dtype=bool)
An extended example taking advantage of the overloading of + and \*:
a = np.array(range(1, 9))
a.shape = (2, 2, 2)
A = np.array(('a', 'b', 'c', 'd'), dtype=object)
A.shape = (2, 2)
a; A
array([[[1, 2],
[3, 4]],
[[5, 6],
[7, 8]]])
array([[a, b],
[c, d]], dtype=object)
np.tensordot(a, A) # third argument default is 2 for double-contraction
array([abbcccdddd, aaaaabbbbbbcccccccdddddddd], dtype=object)
np.tensordot(a, A, 1)
array([[[acc, bdd],
[aaacccc, bbbdddd]],
[[aaaaacccccc, bbbbbdddddd],
[aaaaaaacccccccc, bbbbbbbdddddddd]]], dtype=object)
np.tensordot(a, A, 0) # tensor product (result too long to incl.)
array([[[[[a, b],
[c, d]],
...
np.tensordot(a, A, (0, 1))
array([[[abbbbb, cddddd],
[aabbbbbb, ccdddddd]],
[[aaabbbbbbb, cccddddddd],
[aaaabbbbbbbb, ccccdddddddd]]], dtype=object)
np.tensordot(a, A, (2, 1))
array([[[abb, cdd],
[aaabbbb, cccdddd]],
[[aaaaabbbbbb, cccccdddddd],
[aaaaaaabbbbbbbb, cccccccdddddddd]]], dtype=object)
np.tensordot(a, A, ((0, 1), (0, 1)))
array([abbbcccccddddddd, aabbbbccccccdddddddd], dtype=object)
np.tensordot(a, A, ((2, 1), (1, 0)))
array([acccbbdddd, aaaaacccccccbbbbbbdddddddd], dtype=object)
tile(A, reps)
Construct an array by repeating A the number of times given by reps.
If `reps` has length ``d``, the result will have dimension of
``max(d, A.ndim)``.
If ``A.ndim < d``, `A` is promoted to be d-dimensional by prepending new
axes. So a shape (3,) array is promoted to (1, 3) for 2-D replication,
or shape (1, 1, 3) for 3-D replication. If this is not the desired
behavior, promote `A` to d-dimensions manually before calling this
function.
If ``A.ndim > d``, `reps` is promoted to `A`.ndim by pre-pending 1's to it.
Thus for an `A` of shape (2, 3, 4, 5), a `reps` of (2, 2) is treated as
(1, 1, 2, 2).
Parameters
----------
A : array_like
The input array.
reps : array_like
The number of repetitions of `A` along each axis.
Returns
-------
c : ndarray
The tiled output array.
See Also
--------
repeat : Repeat elements of an array.
Examples
--------
a = np.array([0, 1, 2])
np.tile(a, 2)
array([0, 1, 2, 0, 1, 2])
np.tile(a, (2, 2))
array([[0, 1, 2, 0, 1, 2],
[0, 1, 2, 0, 1, 2]])
np.tile(a, (2, 1, 2))
array([[[0, 1, 2, 0, 1, 2]],
[[0, 1, 2, 0, 1, 2]]])
b = np.array([[1, 2], [3, 4]])
np.tile(b, 2)
array([[1, 2, 1, 2],
[3, 4, 3, 4]])
np.tile(b, (2, 1))
array([[1, 2],
[3, 4],
[1, 2],
[3, 4]])
trace(a, offset=0, axis1=0, axis2=1, dtype=None, out=None)
Return the sum along diagonals of the array.
If `a` is 2-D, the sum along its diagonal with the given offset
is returned, i.e., the sum of elements ``a[i,i+offset]`` for all i.
If `a` has more than two dimensions, then the axes specified by axis1 and
axis2 are used to determine the 2-D sub-arrays whose traces are returned.
The shape of the resulting array is the same as that of `a` with `axis1`
and `axis2` removed.
Parameters
----------
a : array_like
Input array, from which the diagonals are taken.
offset : int, optional
Offset of the diagonal from the main diagonal. Can be both positive
and negative. Defaults to 0.
axis1, axis2 : int, optional
Axes to be used as the first and second axis of the 2-D sub-arrays
from which the diagonals should be taken. Defaults are the first two
axes of `a`.
dtype : dtype, optional
Determines the data-type of the returned array and of the accumulator
where the elements are summed. If dtype has the value None and `a` is
of integer type of precision less than the default integer
precision, then the default integer precision is used. Otherwise,
the precision is the same as that of `a`.
out : ndarray, optional
Array into which the output is placed. Its type is preserved and
it must be of the right shape to hold the output.
Returns
-------
sum_along_diagonals : ndarray
If `a` is 2-D, the sum along the diagonal is returned. If `a` has
larger dimensions, then an array of sums along diagonals is returned.
See Also
--------
diag, diagonal, diagflat
Examples
--------
np.trace(np.eye(3))
3.0
a = np.arange(8).reshape((2,2,2))
np.trace(a)
array([6, 8])
a = np.arange(24).reshape((2,2,2,3))
np.trace(a).shape
(2, 3)
transpose(a, axes=None)
Permute the dimensions of an array.
Parameters
----------
a : array_like
Input array.
axes : list of ints, optional
By default, reverse the dimensions, otherwise permute the axes
according to the values given.
Returns
-------
p : ndarray
`a` with its axes permuted. A view is returned whenever
possible.
See Also
--------
rollaxis
argsort
Notes
-----
Use `transpose(a, argsort(axes))` to invert the transposition of tensors
when using the `axes` keyword argument.
Transposing a 1-D array returns an unchanged view of the original array.
Examples
--------
x = np.arange(4).reshape((2,2))
x
array([[0, 1],
[2, 3]])
np.transpose(x)
array([[0, 2],
[1, 3]])
x = np.ones((1, 2, 3))
np.transpose(x, (1, 0, 2)).shape
(2, 1, 3)
trapz(y, x=None, dx=1.0, axis=-1)
Integrate along the given axis using the composite trapezoidal rule.
Integrate `y` (`x`) along given axis.
Parameters
----------
y : array_like
Input array to integrate.
x : array_like, optional
If `x` is None, then spacing between all `y` elements is `dx`.
dx : scalar, optional
If `x` is None, spacing given by `dx` is assumed. Default is 1.
axis : int, optional
Specify the axis.
Returns
-------
trapz : float
Definite integral as approximated by trapezoidal rule.
See Also
--------
sum, cumsum
Notes
-----
Image [2]_ illustrates trapezoidal rule -- y-axis locations of points
will be taken from `y` array, by default x-axis distances between
points will be 1.0, alternatively they can be provided with `x` array
or with `dx` scalar. Return value will be equal to combined area under
the red lines.
References
----------
.. [1] Wikipedia page: http://en.wikipedia.org/wiki/Trapezoidal_rule
.. [2] Illustration image:
http://en.wikipedia.org/wiki/File:Composite_trapezoidal_rule_illustration.png
Examples
--------
np.trapz([1,2,3])
4.0
np.trapz([1,2,3], x=[4,6,8])
8.0
np.trapz([1,2,3], dx=2)
8.0
a = np.arange(6).reshape(2, 3)
a
array([[0, 1, 2],
[3, 4, 5]])
np.trapz(a, axis=0)
array([ 1.5, 2.5, 3.5])
np.trapz(a, axis=1)
array([ 2., 8.])
tri(N, M=None, k=0, dtype=)
An array with ones at and below the given diagonal and zeros elsewhere.
Parameters
----------
N : int
Number of rows in the array.
M : int, optional
Number of columns in the array.
By default, `M` is taken equal to `N`.
k : int, optional
The sub-diagonal at and below which the array is filled.
`k` = 0 is the main diagonal, while `k` < 0 is below it,
and `k` > 0 is above. The default is 0.
dtype : dtype, optional
Data type of the returned array. The default is float.
Returns
-------
tri : ndarray of shape (N, M)
Array with its lower triangle filled with ones and zero elsewhere;
in other words ``T[i,j] == 1`` for ``i <= j + k``, 0 otherwise.
Examples
--------
np.tri(3, 5, 2, dtype=int)
array([[1, 1, 1, 0, 0],
[1, 1, 1, 1, 0],
[1, 1, 1, 1, 1]])
np.tri(3, 5, -1)
array([[ 0., 0., 0., 0., 0.],
[ 1., 0., 0., 0., 0.],
[ 1., 1., 0., 0., 0.]])
tril(m, k=0)
Lower triangle of an array.
Return a copy of an array with elements above the `k`-th diagonal zeroed.
Parameters
----------
m : array_like, shape (M, N)
Input array.
k : int, optional
Diagonal above which to zero elements. `k = 0` (the default) is the
main diagonal, `k < 0` is below it and `k > 0` is above.
Returns
-------
tril : ndarray, shape (M, N)
Lower triangle of `m`, of same shape and data-type as `m`.
See Also
--------
triu : same thing, only for the upper triangle
Examples
--------
np.tril([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1)
array([[ 0, 0, 0],
[ 4, 0, 0],
[ 7, 8, 0],
[10, 11, 12]])
tril_indices(n, k=0, m=None)
Return the indices for the lower-triangle of an (n, m) array.
Parameters
----------
n : int
The row dimension of the arrays for which the returned
indices will be valid.
k : int, optional
Diagonal offset (see `tril` for details).
m : int, optional
.. versionadded:: 1.9.0
The column dimension of the arrays for which the returned
arrays will be valid.
By default `m` is taken equal to `n`.
Returns
-------
inds : tuple of arrays
The indices for the triangle. The returned tuple contains two arrays,
each with the indices along one dimension of the array.
See also
--------
triu_indices : similar function, for upper-triangular.
mask_indices : generic function accepting an arbitrary mask function.
tril, triu
Notes
-----
.. versionadded:: 1.4.0
Examples
--------
Compute two different sets of indices to access 4x4 arrays, one for the
lower triangular part starting at the main diagonal, and one starting two
diagonals further right:
il1 = np.tril_indices(4)
il2 = np.tril_indices(4, 2)
Here is how they can be used with a sample array:
a = np.arange(16).reshape(4, 4)
a
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11],
[12, 13, 14, 15]])
Both for indexing:
a[il1]
array([ 0, 4, 5, 8, 9, 10, 12, 13, 14, 15])
And for assigning values:
a[il1] = -1
a
array([[-1, 1, 2, 3],
[-1, -1, 6, 7],
[-1, -1, -1, 11],
[-1, -1, -1, -1]])
These cover almost the whole array (two diagonals right of the main one):
a[il2] = -10
a
array([[-10, -10, -10, 3],
[-10, -10, -10, -10],
[-10, -10, -10, -10],
[-10, -10, -10, -10]])
tril_indices_from(arr, k=0)
Return the indices for the lower-triangle of arr.
See `tril_indices` for full details.
Parameters
----------
arr : array_like
The indices will be valid for square arrays whose dimensions are
the same as arr.
k : int, optional
Diagonal offset (see `tril` for details).
See Also
--------
tril_indices, tril
Notes
-----
.. versionadded:: 1.4.0
trim_zeros(filt, trim='fb')
Trim the leading and/or trailing zeros from a 1-D array or sequence.
Parameters
----------
filt : 1-D array or sequence
Input array.
trim : str, optional
A string with 'f' representing trim from front and 'b' to trim from
back. Default is 'fb', trim zeros from both front and back of the
array.
Returns
-------
trimmed : 1-D array or sequence
The result of trimming the input. The input data type is preserved.
Examples
--------
a = np.array((0, 0, 0, 1, 2, 3, 0, 2, 1, 0))
np.trim_zeros(a)
array([1, 2, 3, 0, 2, 1])
np.trim_zeros(a, 'b')
array([0, 0, 0, 1, 2, 3, 0, 2, 1])
The input data type is preserved, list/tuple in means list/tuple out.
np.trim_zeros([0, 1, 2, 0])
[1, 2]
triu(m, k=0)
Upper triangle of an array.
Return a copy of a matrix with the elements below the `k`-th diagonal
zeroed.
Please refer to the documentation for `tril` for further details.
See Also
--------
tril : lower triangle of an array
Examples
--------
np.triu([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1)
array([[ 1, 2, 3],
[ 4, 5, 6],
[ 0, 8, 9],
[ 0, 0, 12]])
triu_indices(n, k=0, m=None)
Return the indices for the upper-triangle of an (n, m) array.
Parameters
----------
n : int
The size of the arrays for which the returned indices will
be valid.
k : int, optional
Diagonal offset (see `triu` for details).
m : int, optional
.. versionadded:: 1.9.0
The column dimension of the arrays for which the returned
arrays will be valid.
By default `m` is taken equal to `n`.
Returns
-------
inds : tuple, shape(2) of ndarrays, shape(`n`)
The indices for the triangle. The returned tuple contains two arrays,
each with the indices along one dimension of the array. Can be used
to slice a ndarray of shape(`n`, `n`).
See also
--------
tril_indices : similar function, for lower-triangular.
mask_indices : generic function accepting an arbitrary mask function.
triu, tril
Notes
-----
.. versionadded:: 1.4.0
Examples
--------
Compute two different sets of indices to access 4x4 arrays, one for the
upper triangular part starting at the main diagonal, and one starting two
diagonals further right:
iu1 = np.triu_indices(4)
iu2 = np.triu_indices(4, 2)
Here is how they can be used with a sample array:
a = np.arange(16).reshape(4, 4)
a
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11],
[12, 13, 14, 15]])
Both for indexing:
a[iu1]
array([ 0, 1, 2, 3, 5, 6, 7, 10, 11, 15])
And for assigning values:
a[iu1] = -1
a
array([[-1, -1, -1, -1],
[ 4, -1, -1, -1],
[ 8, 9, -1, -1],
[12, 13, 14, -1]])
These cover only a small part of the whole array (two diagonals right
of the main one):
a[iu2] = -10
a
array([[ -1, -1, -10, -10],
[ 4, -1, -1, -10],
[ 8, 9, -1, -1],
[ 12, 13, 14, -1]])
triu_indices_from(arr, k=0)
Return the indices for the upper-triangle of arr.
See `triu_indices` for full details.
Parameters
----------
arr : ndarray, shape(N, N)
The indices will be valid for square arrays.
k : int, optional
Diagonal offset (see `triu` for details).
Returns
-------
triu_indices_from : tuple, shape(2) of ndarray, shape(N)
Indices for the upper-triangle of `arr`.
See Also
--------
triu_indices, triu
Notes
-----
.. versionadded:: 1.4.0
typename(char)
Return a description for the given data type code.
Parameters
----------
char : str
Data type code.
Returns
-------
out : str
Description of the input data type code.
See Also
--------
dtype, typecodes
Examples
--------
typechars = ['S1', '?', 'B', 'D', 'G', 'F', 'I', 'H', 'L', 'O', 'Q',
'S', 'U', 'V', 'b', 'd', 'g', 'f', 'i', 'h', 'l', 'q']
for typechar in typechars:
print typechar, ' : ', np.typename(typechar)
...
S1 : character
? : bool
B : unsigned char
D : complex double precision
G : complex long double precision
F : complex single precision
I : unsigned integer
H : unsigned short
L : unsigned long integer
O : object
Q : unsigned long long integer
S : string
U : unicode
V : void
b : signed char
d : double precision
g : long precision
f : single precision
i : integer
h : short
l : long integer
q : long long integer
union1d(ar1, ar2)
Find the union of two arrays.
Return the unique, sorted array of values that are in either of the two
input arrays.
Parameters
----------
ar1, ar2 : array_like
Input arrays. They are flattened if they are not already 1D.
Returns
-------
union1d : ndarray
Unique, sorted union of the input arrays.
See Also
--------
numpy.lib.arraysetops : Module with a number of other functions for
performing set operations on arrays.
Examples
--------
np.union1d([-1, 0, 1], [-2, 0, 2])
array([-2, -1, 0, 1, 2])
To find the union of more than two arrays, use functools.reduce:
from functools import reduce
reduce(np.union1d, ([1, 3, 4, 3], [3, 1, 2, 1], [6, 3, 4, 2]))
array([1, 2, 3, 4, 6])
unique(ar, return_index=False, return_inverse=False, return_counts=False)
Find the unique elements of an array.
Returns the sorted unique elements of an array. There are three optional
outputs in addition to the unique elements: the indices of the input array
that give the unique values, the indices of the unique array that
reconstruct the input array, and the number of times each unique value
comes up in the input array.
Parameters
----------
ar : array_like
Input array. This will be flattened if it is not already 1-D.
return_index : bool, optional
If True, also return the indices of `ar` that result in the unique
array.
return_inverse : bool, optional
If True, also return the indices of the unique array that can be used
to reconstruct `ar`.
return_counts : bool, optional
If True, also return the number of times each unique value comes up
in `ar`.
.. versionadded:: 1.9.0
Returns
-------
unique : ndarray
The sorted unique values.
unique_indices : ndarray, optional
The indices of the first occurrences of the unique values in the
(flattened) original array. Only provided if `return_index` is True.
unique_inverse : ndarray, optional
The indices to reconstruct the (flattened) original array from the
unique array. Only provided if `return_inverse` is True.
unique_counts : ndarray, optional
The number of times each of the unique values comes up in the
original array. Only provided if `return_counts` is True.
.. versionadded:: 1.9.0
See Also
--------
numpy.lib.arraysetops : Module with a number of other functions for
performing set operations on arrays.
Examples
--------
np.unique([1, 1, 2, 2, 3, 3])
array([1, 2, 3])
a = np.array([[1, 1], [2, 3]])
np.unique(a)
array([1, 2, 3])
Return the indices of the original array that give the unique values:
a = np.array(['a', 'b', 'b', 'c', 'a'])
u, indices = np.unique(a, return_index=True)
u
array(['a', 'b', 'c'],
dtype='|S1')
indices
array([0, 1, 3])
a[indices]
array(['a', 'b', 'c'],
dtype='|S1')
Reconstruct the input array from the unique values:
a = np.array([1, 2, 6, 4, 2, 3, 2])
u, indices = np.unique(a, return_inverse=True)
u
array([1, 2, 3, 4, 6])
indices
array([0, 1, 4, 3, 1, 2, 1])
u[indices]
array([1, 2, 6, 4, 2, 3, 2])
unpackbits(...)
unpackbits(myarray, axis=None)
Unpacks elements of a uint8 array into a binary-valued output array.
Each element of `myarray` represents a bit-field that should be unpacked
into a binary-valued output array. The shape of the output array is either
1-D (if `axis` is None) or the same shape as the input array with unpacking
done along the axis specified.
Parameters
----------
myarray : ndarray, uint8 type
Input array.
axis : int, optional
Unpacks along this axis.
Returns
-------
unpacked : ndarray, uint8 type
The elements are binary-valued (0 or 1).
See Also
--------
packbits : Packs the elements of a binary-valued array into bits in a uint8
array.
Examples
--------
a = np.array([[2], [7], [23]], dtype=np.uint8)
a
array([[ 2],
[ 7],
[23]], dtype=uint8)
b = np.unpackbits(a, axis=1)
b
array([[0, 0, 0, 0, 0, 0, 1, 0],
[0, 0, 0, 0, 0, 1, 1, 1],
[0, 0, 0, 1, 0, 1, 1, 1]], dtype=uint8)
unravel_index(...)
unravel_index(indices, dims, order='C')
Converts a flat index or array of flat indices into a tuple
of coordinate arrays.
Parameters
----------
indices : array_like
An integer array whose elements are indices into the flattened
version of an array of dimensions ``dims``. Before version 1.6.0,
this function accepted just one index value.
dims : tuple of ints
The shape of the array to use for unraveling ``indices``.
order : {'C', 'F'}, optional
Determines whether the indices should be viewed as indexing in
row-major (C-style) or column-major (Fortran-style) order.
.. versionadded:: 1.6.0
Returns
-------
unraveled_coords : tuple of ndarray
Each array in the tuple has the same shape as the ``indices``
array.
See Also
--------
ravel_multi_index
Examples
--------
np.unravel_index([22, 41, 37], (7,6))
(array([3, 6, 6]), array([4, 5, 1]))
np.unravel_index([31, 41, 13], (7,6), order='F')
(array([3, 6, 6]), array([4, 5, 1]))
np.unravel_index(1621, (6,7,8,9))
(3, 1, 4, 1)
unwrap(p, discont=3.141592653589793, axis=-1)
Unwrap by changing deltas between values to 2*pi complement.
Unwrap radian phase `p` by changing absolute jumps greater than
`discont` to their 2*pi complement along the given axis.
Parameters
----------
p : array_like
Input array.
discont : float, optional
Maximum discontinuity between values, default is ``pi``.
axis : int, optional
Axis along which unwrap will operate, default is the last axis.
Returns
-------
out : ndarray
Output array.
See Also
--------
rad2deg, deg2rad
Notes
-----
If the discontinuity in `p` is smaller than ``pi``, but larger than
`discont`, no unwrapping is done because taking the 2*pi complement
would only make the discontinuity larger.
Examples
--------
phase = np.linspace(0, np.pi, num=5)
phase[3:] += np.pi
phase
array([ 0. , 0.78539816, 1.57079633, 5.49778714, 6.28318531])
np.unwrap(phase)
array([ 0. , 0.78539816, 1.57079633, -0.78539816, 0. ])
vander(x, N=None, increasing=False)
Generate a Vandermonde matrix.
The columns of the output matrix are powers of the input vector. The
order of the powers is determined by the `increasing` boolean argument.
Specifically, when `increasing` is False, the `i`-th output column is
the input vector raised element-wise to the power of ``N - i - 1``. Such
a matrix with a geometric progression in each row is named for Alexandre-
Theophile Vandermonde.
Parameters
----------
x : array_like
1-D input array.
N : int, optional
Number of columns in the output. If `N` is not specified, a square
array is returned (``N = len(x)``).
increasing : bool, optional
Order of the powers of the columns. If True, the powers increase
from left to right, if False (the default) they are reversed.
.. versionadded:: 1.9.0
Returns
-------
out : ndarray
Vandermonde matrix. If `increasing` is False, the first column is
``x^(N-1)``, the second ``x^(N-2)`` and so forth. If `increasing` is
True, the columns are ``x^0, x^1, ..., x^(N-1)``.
See Also
--------
polynomial.polynomial.polyvander
Examples
--------
x = np.array([1, 2, 3, 5])
N = 3
np.vander(x, N)
array([[ 1, 1, 1],
[ 4, 2, 1],
[ 9, 3, 1],
[25, 5, 1]])
np.column_stack([x**(N-1-i) for i in range(N)])
array([[ 1, 1, 1],
[ 4, 2, 1],
[ 9, 3, 1],
[25, 5, 1]])
x = np.array([1, 2, 3, 5])
np.vander(x)
array([[ 1, 1, 1, 1],
[ 8, 4, 2, 1],
[ 27, 9, 3, 1],
[125, 25, 5, 1]])
np.vander(x, increasing=True)
array([[ 1, 1, 1, 1],
[ 1, 2, 4, 8],
[ 1, 3, 9, 27],
[ 1, 5, 25, 125]])
The determinant of a square Vandermonde matrix is the product
of the differences between the values of the input vector:
np.linalg.det(np.vander(x))
48.000000000000043
(5-3)*(5-2)*(5-1)*(3-2)*(3-1)*(2-1)
48
var(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False)
Compute the variance along the specified axis.
Returns the variance of the array elements, a measure of the spread of a
distribution. The variance is computed for the flattened array by
default, otherwise over the specified axis.
Parameters
----------
a : array_like
Array containing numbers whose variance is desired. If `a` is not an
array, a conversion is attempted.
axis : None or int or tuple of ints, optional
Axis or axes along which the variance is computed. The default is to
compute the variance of the flattened array.
.. versionadded: 1.7.0
If this is a tuple of ints, a variance is performed over multiple axes,
instead of a single axis or all the axes as before.
dtype : data-type, optional
Type to use in computing the variance. For arrays of integer type
the default is `float32`; for arrays of float types it is the same as
the array type.
out : ndarray, optional
Alternate output array in which to place the result. It must have
the same shape as the expected output, but the type is cast if
necessary.
ddof : int, optional
"Delta Degrees of Freedom": the divisor used in the calculation is
``N - ddof``, where ``N`` represents the number of elements. By
default `ddof` is zero.
keepdims : bool, optional
If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option,
the result will broadcast correctly against the original `arr`.
Returns
-------
variance : ndarray, see dtype parameter above
If ``out=None``, returns a new array containing the variance;
otherwise, a reference to the output array is returned.
See Also
--------
std , mean, nanmean, nanstd, nanvar
numpy.doc.ufuncs : Section "Output arguments"
Notes
-----
The variance is the average of the squared deviations from the mean,
i.e., ``var = mean(abs(x - x.mean())**2)``.
The mean is normally calculated as ``x.sum() / N``, where ``N = len(x)``.
If, however, `ddof` is specified, the divisor ``N - ddof`` is used
instead. In standard statistical practice, ``ddof=1`` provides an
unbiased estimator of the variance of a hypothetical infinite population.
``ddof=0`` provides a maximum likelihood estimate of the variance for
normally distributed variables.
Note that for complex numbers, the absolute value is taken before
squaring, so that the result is always real and nonnegative.
For floating-point input, the variance is computed using the same
precision the input has. Depending on the input data, this can cause
the results to be inaccurate, especially for `float32` (see example
below). Specifying a higher-accuracy accumulator using the ``dtype``
keyword can alleviate this issue.
Examples
--------
a = np.array([[1, 2], [3, 4]])
np.var(a)
1.25
np.var(a, axis=0)
array([ 1., 1.])
np.var(a, axis=1)
array([ 0.25, 0.25])
In single precision, var() can be inaccurate:
a = np.zeros((2, 512*512), dtype=np.float32)
a[0, :] = 1.0
a[1, :] = 0.1
np.var(a)
0.20250003
Computing the variance in float64 is more accurate:
np.var(a, dtype=np.float64)
0.20249999932944759
((1-0.55)**2 + (0.1-0.55)**2)/2
0.2025
vdot(...)
vdot(a, b)
Return the dot product of two vectors.
The vdot(`a`, `b`) function handles complex numbers differently than
dot(`a`, `b`). If the first argument is complex the complex conjugate
of the first argument is used for the calculation of the dot product.
Note that `vdot` handles multidimensional arrays differently than `dot`:
it does *not* perform a matrix product, but flattens input arguments
to 1-D vectors first. Consequently, it should only be used for vectors.
Parameters
----------
a : array_like
If `a` is complex the complex conjugate is taken before calculation
of the dot product.
b : array_like
Second argument to the dot product.
Returns
-------
output : ndarray
Dot product of `a` and `b`. Can be an int, float, or
complex depending on the types of `a` and `b`.
See Also
--------
dot : Return the dot product without using the complex conjugate of the
first argument.
Examples
--------
a = np.array([1+2j,3+4j])
b = np.array([5+6j,7+8j])
np.vdot(a, b)
(70-8j)
np.vdot(b, a)
(70+8j)
Note that higher-dimensional arrays are flattened!
a = np.array([[1, 4], [5, 6]])
b = np.array([[4, 1], [2, 2]])
np.vdot(a, b)
30
np.vdot(b, a)
30
1*4 + 4*1 + 5*2 + 6*2
30
vsplit(ary, indices_or_sections)
Split an array into multiple sub-arrays vertically (row-wise).
Please refer to the ``split`` documentation. ``vsplit`` is equivalent
to ``split`` with `axis=0` (default), the array is always split along the
first axis regardless of the array dimension.
See Also
--------
split : Split an array into multiple sub-arrays of equal size.
Examples
--------
x = np.arange(16.0).reshape(4, 4)
x
array([[ 0., 1., 2., 3.],
[ 4., 5., 6., 7.],
[ 8., 9., 10., 11.],
[ 12., 13., 14., 15.]])
np.vsplit(x, 2)
[array([[ 0., 1., 2., 3.],
[ 4., 5., 6., 7.]]),
array([[ 8., 9., 10., 11.],
[ 12., 13., 14., 15.]])]
np.vsplit(x, np.array([3, 6]))
[array([[ 0., 1., 2., 3.],
[ 4., 5., 6., 7.],
[ 8., 9., 10., 11.]]),
array([[ 12., 13., 14., 15.]]),
array([], dtype=float64)]
With a higher dimensional array the split is still along the first axis.
x = np.arange(8.0).reshape(2, 2, 2)
x
array([[[ 0., 1.],
[ 2., 3.]],
[[ 4., 5.],
[ 6., 7.]]])
np.vsplit(x, 2)
[array([[[ 0., 1.],
[ 2., 3.]]]),
array([[[ 4., 5.],
[ 6., 7.]]])]
vstack(tup)
Stack arrays in sequence vertically (row wise).
Take a sequence of arrays and stack them vertically to make a single
array. Rebuild arrays divided by `vsplit`.
Parameters
----------
tup : sequence of ndarrays
Tuple containing arrays to be stacked. The arrays must have the same
shape along all but the first axis.
Returns
-------
stacked : ndarray
The array formed by stacking the given arrays.
See Also
--------
stack : Join a sequence of arrays along a new axis.
hstack : Stack arrays in sequence horizontally (column wise).
dstack : Stack arrays in sequence depth wise (along third dimension).
concatenate : Join a sequence of arrays along an existing axis.
vsplit : Split array into a list of multiple sub-arrays vertically.
Notes
-----
Equivalent to ``np.concatenate(tup, axis=0)`` if `tup` contains arrays that
are at least 2-dimensional.
Examples
--------
a = np.array([1, 2, 3])
b = np.array([2, 3, 4])
np.vstack((a,b))
array([[1, 2, 3],
[2, 3, 4]])
a = np.array([[1], [2], [3]])
b = np.array([[2], [3], [4]])
np.vstack((a,b))
array([[1],
[2],
[3],
[2],
[3],
[4]])
where(...)
where(condition, [x, y])
Return elements, either from `x` or `y`, depending on `condition`.
If only `condition` is given, return ``condition.nonzero()``.
Parameters
----------
condition : array_like, bool
When True, yield `x`, otherwise yield `y`.
x, y : array_like, optional
Values from which to choose. `x` and `y` need to have the same
shape as `condition`.
Returns
-------
out : ndarray or tuple of ndarrays
If both `x` and `y` are specified, the output array contains
elements of `x` where `condition` is True, and elements from
`y` elsewhere.
If only `condition` is given, return the tuple
``condition.nonzero()``, the indices where `condition` is True.
See Also
--------
nonzero, choose
Notes
-----
If `x` and `y` are given and input arrays are 1-D, `where` is
equivalent to::
[xv if c else yv for (c,xv,yv) in zip(condition,x,y)]
Examples
--------
np.where([[True, False], [True, True]],
[[1, 2], [3, 4]],
[[9, 8], [7, 6]])
array([[1, 8],
[3, 4]])
np.where([[0, 1], [1, 0]])
(array([0, 1]), array([1, 0]))
x = np.arange(9.).reshape(3, 3)
np.where( x > 5 )
(array([2, 2, 2]), array([0, 1, 2]))
x[np.where( x > 3.0 )] # Note: result is 1D.
array([ 4., 5., 6., 7., 8.])
np.where(x < 5, x, -1) # Note: broadcasting.
array([[ 0., 1., 2.],
[ 3., 4., -1.],
[-1., -1., -1.]])
Find the indices of elements of `x` that are in `goodvalues`.
goodvalues = [3, 4, 7]
ix = np.in1d(x.ravel(), goodvalues).reshape(x.shape)
ix
array([[False, False, False],
[ True, True, False],
[False, True, False]], dtype=bool)
np.where(ix)
(array([1, 1, 2]), array([0, 1, 1]))
who(vardict=None)
Print the Numpy arrays in the given dictionary.
If there is no dictionary passed in or `vardict` is None then returns
Numpy arrays in the globals() dictionary (all Numpy arrays in the
namespace).
Parameters
----------
vardict : dict, optional
A dictionary possibly containing ndarrays. Default is globals().
Returns
-------
out : None
Returns 'None'.
Notes
-----
Prints out the name, shape, bytes and type of all of the ndarrays
present in `vardict`.
Examples
--------
a = np.arange(10)
b = np.ones(20)
np.who()
Name Shape Bytes Type
===========================================================
a 10 40 int32
b 20 160 float64
Upper bound on total bytes = 200
d = {'x': np.arange(2.0), 'y': np.arange(3.0), 'txt': 'Some str',
'idx':5}
np.who(d)
Name Shape Bytes Type
===========================================================
y 3 24 float64
x 2 16 float64
Upper bound on total bytes = 40
zeros(...)
zeros(shape, dtype=float, order='C')
Return a new array of given shape and type, filled with zeros.
Parameters
----------
shape : int or sequence of ints
Shape of the new array, e.g., ``(2, 3)`` or ``2``.
dtype : data-type, optional
The desired data-type for the array, e.g., `numpy.int8`. Default is
`numpy.float64`.
order : {'C', 'F'}, optional
Whether to store multidimensional data in C- or Fortran-contiguous
(row- or column-wise) order in memory.
Returns
-------
out : ndarray
Array of zeros with the given shape, dtype, and order.
See Also
--------
zeros_like : Return an array of zeros with shape and type of input.
ones_like : Return an array of ones with shape and type of input.
empty_like : Return an empty array with shape and type of input.
ones : Return a new array setting values to one.
empty : Return a new uninitialized array.
Examples
--------
np.zeros(5)
array([ 0., 0., 0., 0., 0.])
np.zeros((5,), dtype=np.int)
array([0, 0, 0, 0, 0])
np.zeros((2, 1))
array([[ 0.],
[ 0.]])
s = (2,2)
np.zeros(s)
array([[ 0., 0.],
[ 0., 0.]])
np.zeros((2,), dtype=[('x', 'i4'), ('y', 'i4')]) # custom dtype
array([(0, 0), (0, 0)],
dtype=[('x', ', , ,
add =
arccos =
arccosh =
arcsin =
arcsinh =
arctan =
arctan2 =
arctanh =
bitwise_and =
bitwise_not =
bitwise_or =
bitwise_xor =
c_ =
cast = {: at ...128'>:
ceil =
conj =
conjugate =
copysign =
cos =
cosh =
deg2rad =
degrees =
divide =
e = 2.718281828459045
equal =
euler_gamma = 0.5772156649015329
exp =
exp2 =
expm1 =
fabs =
floor =
floor_divide =
fmax =
fmin =
fmod =
frexp =
greater =
greater_equal =
hypot =
index_exp =
inf = inf
infty = inf
invert =
isfinite =
isinf =
isnan =
ldexp =
left_shift =
less =
less_equal =
little_endian = True
log =
log10 =
log1p =
log2 =
logaddexp =
logaddexp2 =
logical_and =
logical_not =
logical_or =
logical_xor =
maximum =
mgrid =
minimum =
mod =
modf =
multiply =
nan = nan
nbytes = {: 0,
newaxis = None
nextafter =
not_equal =
ogrid =
pi = 3.141592653589793
power =
r_ =
rad2deg =
radians =
reciprocal =
remainder =
right_shift =
rint =
s_ =
sctypeDict = {0: , 1: , 2: , '...
sctypes = {'complex': [,
signbit =
sin =
sinh =
spacing =
sqrt =
square =
subtract =
tan =
tanh =
true_divide =
trunc =
typeDict = {0: , 1: , 2: , 'Co...
typecodes = {'All': '?bhilqpBHILQPefdgFDGSUVOMm', 'AllFloat': 'efdgFDG...
VERSION
1.10.4
