重学 PyTorch 第二天：Tensor 的基本操作

重学 PyTorch Tensor 的基本操作

基本算数操作

作为一个张量计算库，算数操作是最基本的修养。PyTorch 中有一百来个算数操作算子。

逐元素操作算子

PyTorch 中，Tensor 的逐元素操作可分为函数式操作和原位操作，在函数名中用 _ 后缀区分了二者，比如 tensor.abs() 是一个函数式操作，不改变 tensor 而将改变体现在返回值中，而 tensor.abs_() 是一个原位操作，既修改了原 tensor 又将这个修改后的值返回。

这里的操作都是逐元素进行的，元素之间没有关联。基本上每个 API 都有函数式和原位两个版本，也有作为 torch 模块的函数的过程化编程和作为 Tensor 的方法的面向对象式编程，其实面向过程和面向对象的唯一区别是第一个参数。每个算子一共有至少三种写法。

算子名	说明
abs	计算 input 中每个元素的绝对值.
absolute	Alias for torch.abs()
acos	inverse cosine 大家熟悉的 arccos input.
arccos	Alias for torch.acos().
acosh	inverse hyperbolic cosine of input.
arccosh	Alias for torch.acosh().
add	Adds other, scaled by alpha, to input.
addcdiv	Performs the element-wise division of tensor1 by tensor2, multiply the result by the scalar value and add it to input.
addcmul	Performs the element-wise multiplication of tensor1 by tensor2, multiply the result by the scalar value and add it to input.
angle	Computes the element-wise angle (in radians) of the given input tensor.
asin	Returns a new tensor with the arcsine of the elements of input.
arcsin	Alias for torch.asin().
asinh	Returns a new tensor with the inverse hyperbolic sine of the elements of input.
arcsinh	Alias for torch.asinh().
atan	Returns a new tensor with the arctangent of the elements of input.
arctan	Alias for torch.atan().
atanh	Returns a new tensor with the inverse hyperbolic tangent of the elements of input.
arctanh	Alias for torch.atanh().
atan2	Element-wise arctangent of \text{input}{i} / \text{other}{i}inputi/otheri with consideration of the quadrant.
arctan2	Alias for torch.atan2().
bitwise_not	Computes the bitwise NOT of the given input tensor.
bitwise_and	Computes the bitwise AND of input and other.
bitwise_or	Computes the bitwise OR of input and other.
bitwise_xor	Computes the bitwise XOR of input and other.
bitwise_left_shift	Computes the left arithmetic shift of input by other bits.
bitwise_right_shift	Computes the right arithmetic shift of input by other bits.
ceil	Returns a new tensor with the ceil of the elements of input, the smallest integer greater than or equal to each element.
clamp	Clamps all elements in input into the range [ min, max ].
clip	Alias for torch.clamp().
conj_physical	Computes the element-wise conjugate of the given input tensor.
copysign	Create a new floating-point tensor with the magnitude of input and the sign of other, elementwise.
cos	Returns a new tensor with the cosine of the elements of input.
cosh	Returns a new tensor with the hyperbolic cosine of the elements of input.
deg2rad	Returns a new tensor with each of the elements of input converted from angles in degrees to radians.
div	Divides each element of the input input by the corresponding element of other.
divide	Alias for torch.div().
digamma	Alias for torch.special.digamma().
erf	Alias for torch.special.erf().
erfc	Alias for torch.special.erfc().
erfinv	Alias for torch.special.erfinv().
exp	Returns a new tensor with the exponential of the elements of the input tensor input.
exp2	Alias for torch.special.exp2().
expm1	Alias for torch.special.expm1().
fake_quantize_per_channel_affine	Returns a new tensor with the data in input fake quantized per channel using scale, zero_point, quant_min and quant_max, across the channel specified by axis.
fake_quantize_per_tensor_affine	Returns a new tensor with the data in input fake quantized using scale, zero_point, quant_min and quant_max.
fix	Alias for torch.trunc()
float_power	Raises input to the power of exponent, elementwise, in double precision.
floor	Returns a new tensor with the floor of the elements of input, the largest integer less than or equal to each element.
floor_divide
fmod	Applies C++’s std::fmod entrywise.
frac	Computes the fractional portion of each element in input.
frexp	Decomposes input into mantissa and exponent tensors such that $\text{input}=\text{mantissa}\times 2^{\text{exponent}}$.
gradient	Estimates the gradient of a function $g:{\mathbb{R}}^n\to \mathbb{R}$ in one or more dimensions using the second-order accurate central differences method.
imag	Returns a new tensor containing imaginary values of the self tensor.
ldexp	Multiplies input by $2^{\text{other}}$.
lerp	Does a linear interpolation of two tensors start (given by input) and end based on a scalar or tensor weight and returns the resulting out tensor.
lgamma	Computes the natural logarithm of the absolute value of the gamma function on input.
log	Returns a new tensor with the natural logarithm of the elements of input.
log10	Returns a new tensor with the logarithm to the base 10 of the elements of input.
log1p	Returns a new tensor with the natural logarithm of (1 + input).
log2	Returns a new tensor with the logarithm to the base 2 of the elements of input.
logaddexp	Logarithm of the sum of exponentiations of the inputs.
logaddexp2	Logarithm of the sum of exponentiations of the inputs in base-2.
logical_and	Computes the element-wise logical AND of the given input tensors.
logical_not	Computes the element-wise logical NOT of the given input tensor.
logical_or	Computes the element-wise logical OR of the given input tensors.
logical_xor	Computes the element-wise logical XOR of the given input tensors.
logit	Alias for torch.special.logit().
hypot	Given the legs of a right triangle, return its hypotenuse.
i0	Alias for torch.special.i0().
igamma	Alias for torch.special.gammainc().
igammac	Alias for torch.special.gammaincc().
mul	Multiplies input by other.
multiply	Alias for torch.mul().
mvlgamma	Alias for torch.special.multigammaln().
nan_to_num	Replaces NaN, positive infinity, and negative infinity values in input with the values specified by nan, posinf, and neginf, respectively.
neg	Returns a new tensor with the negative of the elements of input.
negative	Alias for torch.neg()
nextafter	Return the next floating-point value after input towards other, elementwise.
polygamma	Alias for torch.special.polygamma().
positive	Returns input.
pow	Takes the power of each element in input with exponent and returns a tensor with the result.
quantized_batch_norm	Applies batch normalization on a 4D (NCHW) quantized tensor.
quantized_max_pool1d	Applies a 1D max pooling over an input quantized tensor composed of several input planes.
quantized_max_pool2d	Applies a 2D max pooling over an input quantized tensor composed of several input planes.
rad2deg	Returns a new tensor with each of the elements of input converted from angles in radians to degrees.
real	Returns a new tensor containing real values of the self tensor.
reciprocal	Returns a new tensor with the reciprocal of the elements of input
remainder	Computes Python’s modulus operation entrywise.
round	Rounds elements of input to the nearest integer.
rsqrt	Returns a new tensor with the reciprocal of the square-root of each of the elements of input.
sigmoid	Alias for torch.special.expit().
sign	Returns a new tensor with the signs of the elements of input.
sgn	This function is an extension of torch.sign() to complex tensors.
signbit	Tests if each element of input has its sign bit set (is less than zero) or not.
sin	Returns a new tensor with the sine of the elements of input.
sinc	Alias for torch.special.sinc().
sinh	Returns a new tensor with the hyperbolic sine of the elements of input.
sqrt	Returns a new tensor with the square-root of the elements of input.
square	Returns a new tensor with the square of the elements of input.
sub	Subtracts other, scaled by alpha, from input.
subtract	Alias for torch.sub().
tan	Returns a new tensor with the tangent of the elements of input.
tanh	Returns a new tensor with the hyperbolic tangent of the elements of input.
true_divide	Alias for torch.div() with rounding_mode=None.
trunc	Returns a new tensor with the truncated integer values of the elements of input.
xlogy	Alias for torch.special.xlogy().

除了上述函数，PyTorch 还为我们重载了 Tensor 的很多运算符，这些运算符都符合 Python 的语义。PyTorch 的开发者为了 be Pythonic 还是费了相当大心思的，这也是 PyTorch 能很好融入 Python 生态的原因。

运算符	说明
+	add
-	sub
*	mul
/	div
//	truediv
@	matmul

规约算子

规约是函数式编程中的重要概念。

算子名	说明
argmax	Returns the indices of the maximum value of all elements in the input tensor.
argmin	Returns the indices of the minimum value(s) of the flattened tensor or along a dimension
amax	Returns the maximum value of each slice of the input tensor in the given dimension(s) dim.
amin	Returns the minimum value of each slice of the input tensor in the given dimension(s) dim.
aminmax	Computes the minimum and maximum values of the input tensor.
all	Tests if all elements in input evaluate to True.
any	Tests if any element in input evaluates to True.
max	Returns the maximum value of all elements in the input tensor.
min	Returns the minimum value of all elements in the input tensor.
dist	Returns the p-norm of (input - other)
logsumexp	Returns the log of summed exponentials of each row of the input tensor in the given dimension dim.
mean	Returns the mean value of all elements in the input tensor.
nanmean	Computes the mean of all non-NaN elements along the specified dimensions.
median	Returns the median of the values in input.
nanmedian	Returns the median of the values in input, ignoring NaN values.
mode	Returns a namedtuple (values, indices) where values is the mode value of each row of the input tensor in the given dimension dim, i.e. a value which appears most often in that row, and indices is the index location of each mode value found.
norm	Returns the matrix norm or vector norm of a given tensor.
nansum	Returns the sum of all elements, treating Not a Numbers (NaNs) as zero.
prod	Returns the product of all elements in the input tensor.
quantile	Computes the q-th quantiles of each row of the input tensor along the dimension dim.
nanquantile	This is a variant of torch.quantile() that “ignores” NaN values, computing the quantiles q as if NaN values in input did not exist.
std	If unbiased is True, Bessel’s correction will be used.
std_mean	If unbiased is True, Bessel’s correction will be used to calculate the standard deviation.
sum	Returns the sum of all elements in the input tensor.
unique	Returns the unique elements of the input tensor.
unique_consecutive	Eliminates all but the first element from every consecutive group of equivalent elements.
var	If unbiased is True, Bessel’s correction will be used.
var_mean	If unbiased is True, Bessel’s correction will be used to calculate the variance.
count_nonzero	Counts the number of non-zero values in the tensor input along the given dim.

比较算子

allclose	This function checks if all input and other satisfy the condition:
argsort	Returns the indices that sort a tensor along a given dimension in ascending order by value.
eq	Computes element-wise equality
equal	True if two tensors have the same size and elements, False otherwise.
ge	Computes \text{input} \geq \text{other}input≥other element-wise.
greater_equal	Alias for torch.ge().
gt	Computes \text{input} > \text{other}input>other element-wise.
greater	Alias for torch.gt().
isclose	Returns a new tensor with boolean elements representing if each element of input is “close” to the corresponding element of other.
isfinite	Returns a new tensor with boolean elements representing if each element is finite or not.
isin	Tests if each element of elements is in test_elements.
isinf	Tests if each element of input is infinite (positive or negative infinity) or not.
isposinf	Tests if each element of input is positive infinity or not.
isneginf	Tests if each element of input is negative infinity or not.
isnan	Returns a new tensor with boolean elements representing if each element of input is NaN or not.
isreal	Returns a new tensor with boolean elements representing if each element of input is real-valued or not.
kthvalue	Returns a namedtuple (values, indices) where values is the k th smallest element of each row of the input tensor in the given dimension dim.
le	Computes \text{input} \leq \text{other}input≤other element-wise.
less_equal	Alias for torch.le().
lt	Computes \text{input} < \text{other}input
less	Alias for torch.lt().
maximum	Computes the element-wise maximum of input and other.
minimum	Computes the element-wise minimum of input and other.
fmax	Computes the element-wise maximum of input and other.
fmin	Computes the element-wise minimum of input and other.
ne	Computes \text{input} \neq \text{other}input=other element-wise.
not_equal	Alias for torch.ne().
sort	Sorts the elements of the input tensor along a given dimension in ascending order by value.
topk	Returns the k largest elements of the given input tensor along a given dimension.
msort	Sorts the elements of the input tensor along its first dimension in ascending order by value.

谱算子 Spectral Ops

stft	Short-time Fourier transform (STFT).
istft	Inverse short time Fourier Transform.
bartlett_window	Bartlett window function.
blackman_window	Blackman window function.
hamming_window	Hamming window function.
hann_window	Hann window function.
kaiser_window	Computes the Kaiser window with window length window_length and shape parameter beta.

杂类数学算子

atleast_1d	Returns a 1-dimensional view of each input tensor with zero dimensions.
atleast_2d	Returns a 2-dimensional view of each input tensor with zero dimensions.
atleast_3d	Returns a 3-dimensional view of each input tensor with zero dimensions.
bincount	Count the frequency of each value in an array of non-negative ints.
block_diag	Create a block diagonal matrix from provided tensors.
broadcast_tensors	Broadcasts the given tensors according to Broadcasting semantics.
broadcast_to	Broadcasts input to the shape shape.
broadcast_shapes	Similar to broadcast_tensors() but for shapes.
bucketize	Returns the indices of the buckets to which each value in the input belongs, where the boundaries of the buckets are set by boundaries.
cartesian_prod	Do cartesian product of the given sequence of tensors.
cdist	Computes batched the p-norm distance between each pair of the two collections of row vectors.
clone	Returns a copy of input.
combinations	Compute combinations of length rr of the given tensor.
corrcoef	Estimates the Pearson product-moment correlation coefficient matrix of the variables given by the input matrix, where rows are the variables and columns are the observations.
cov	Estimates the covariance matrix of the variables given by the input matrix, where rows are the variables and columns are the observations.
cross	Returns the cross product of vectors in dimension dim of input and other.
cummax	Returns a namedtuple (values, indices) where values is the cumulative maximum of elements of input in the dimension dim.
cummin	Returns a namedtuple (values, indices) where values is the cumulative minimum of elements of input in the dimension dim.
cumprod	Returns the cumulative product of elements of input in the dimension dim.
cumsum	Returns the cumulative sum of elements of input in the dimension dim.
diag	If input is a vector (1-D tensor), then returns a 2-D square tensor
diag_embed	Creates a tensor whose diagonals of certain 2D planes (specified by dim1 and dim2) are filled by input.
diagflat	If input is a vector (1-D tensor), then returns a 2-D square tensor
diagonal	Returns a partial view of input with the its diagonal elements with respect to dim1 and dim2 appended as a dimension at the end of the shape.
diff	Computes the n-th forward difference along the given dimension.
einsum	Sums the product of the elements of the input operands along dimensions specified using a notation based on the Einstein summation convention.
flatten	Flattens input by reshaping it into a one-dimensional tensor.
flip	Reverse the order of a n-D tensor along given axis in dims.
fliplr	Flip tensor in the left/right direction, returning a new tensor.
flipud	Flip tensor in the up/down direction, returning a new tensor.
kron	Computes the Kronecker product, denoted by \otimes⊗, of input and other.
rot90	Rotate a n-D tensor by 90 degrees in the plane specified by dims axis.
gcd	Computes the element-wise greatest common divisor (GCD) of input and other.
histc	Computes the histogram of a tensor.
histogram	Computes a histogram of the values in a tensor.
histogramdd	Computes a multi-dimensional histogram of the values in a tensor.
meshgrid	Creates grids of coordinates specified by the 1D inputs in attr:tensors.
lcm	Computes the element-wise least common multiple (LCM) of input and other.
logcumsumexp	Returns the logarithm of the cumulative summation of the exponentiation of elements of input in the dimension dim.
ravel	Return a contiguous flattened tensor.
renorm	Returns a tensor where each sub-tensor of input along dimension dim is normalized such that the p-norm of the sub-tensor is lower than the value maxnorm
repeat_interleave	Repeat elements of a tensor.
roll	Roll the tensor input along the given dimension(s).
searchsorted	Find the indices from the innermost dimension of sorted_sequence such that, if the corresponding values in values were inserted before the indices, when sorted, the order of the corresponding innermost dimension within sorted_sequence would be preserved.
tensordot	Returns a contraction of a and b over multiple dimensions.
trace	Returns the sum of the elements of the diagonal of the input 2-D matrix.
tril	Returns the lower triangular part of the matrix (2-D tensor) or batch of matrices input, the other elements of the result tensor out are set to 0.
tril_indices	Returns the indices of the lower triangular part of a row-by- col matrix in a 2-by-N Tensor, where the first row contains row coordinates of all indices and the second row contains column coordinates.
triu	Returns the upper triangular part of a matrix (2-D tensor) or batch of matrices input, the other elements of the result tensor out are set to 0.
triu_indices	Returns the indices of the upper triangular part of a row by col matrix in a 2-by-N Tensor, where the first row contains row coordinates of all indices and the second row contains column coordinates.
vander	Generates a Vandermonde matrix.
view_as_real	Returns a view of input as a real tensor.
view_as_complex	Returns a view of input as a complex tensor.
resolve_conj	Returns a new tensor with materialized conjugation if input’s conjugate bit is set to True, else returns input.
resolve_neg	Returns a new tensor with materialized negation if input’s negative bit is set to True, else returns input.

线性代数算子 BLAS

addbmm	Performs a batch matrix-matrix product of matrices stored in batch1 and batch2, with a reduced add step (all matrix multiplications get accumulated along the first dimension).
addmm	Performs a matrix multiplication of the matrices mat1 and mat2.
addmv	Performs a matrix-vector product of the matrix mat and the vector vec.
addr	Performs the outer-product of vectors vec1 and vec2 and adds it to the matrix input.
baddbmm	Performs a batch matrix-matrix product of matrices in batch1 and batch2.
bmm	Performs a batch matrix-matrix product of matrices stored in input and mat2.
chain_matmul	Returns the matrix product of the NN 2-D tensors.
cholesky	Computes the Cholesky decomposition of a symmetric positive-definite matrix AA or for batches of symmetric positive-definite matrices.
cholesky_inverse	Computes the inverse of a symmetric positive-definite matrix AA using its Cholesky factor uu: returns matrix inv.
cholesky_solve	Solves a linear system of equations with a positive semidefinite matrix to be inverted given its Cholesky factor matrix uu.
dot	Computes the dot product of two 1D tensors.
eig	Computes the eigenvalues and eigenvectors of a real square matrix.
geqrf	This is a low-level function for calling LAPACK’s geqrf directly.
ger	Alias of torch.outer().
inner	Computes the dot product for 1D tensors.
inverse	Alias for torch.linalg.inv()
det	Alias for torch.linalg.det()
logdet	Calculates log determinant of a square matrix or batches of square matrices.
slogdet	Alias for torch.linalg.slogdet()
lstsq	Computes the solution to the least squares and least norm problems for a full rank matrix AA of size (m \times n)(m×n) and a matrix BB of size (m \times k)(m×k).
lu	Computes the LU factorization of a matrix or batches of matrices A.
lu_solve	Returns the LU solve of the linear system Ax = bA**x=b using the partially pivoted LU factorization of A from torch.lu().
lu_unpack	Unpacks the data and pivots from a LU factorization of a tensor into tensors L and U and a permutation tensor P such that LU_data, LU_pivots = (P @ L @ U).lu().
matmul	Matrix product of two tensors.
matrix_power	Alias for torch.linalg.matrix_power()
matrix_rank	Returns the numerical rank of a 2-D tensor.
matrix_exp	Alias for torch.linalg.matrix_exp().
mm	Performs a matrix multiplication of the matrices input and mat2.
mv	Performs a matrix-vector product of the matrix input and the vector vec.
orgqr	Alias for torch.linalg.householder_product().
ormqr	Computes the matrix-matrix multiplication of a product of Householder matrices with a general matrix.
outer	Outer product of input and vec2.
pinverse	Alias for torch.linalg.pinv()
qr	Computes the QR decomposition of a matrix or a batch of matrices input, and returns a namedtuple (Q, R) of tensors such that \text{input} = Q Rinput=QR with QQ being an orthogonal matrix or batch of orthogonal matrices and RR being an upper triangular matrix or batch of upper triangular matrices.
svd	Computes the singular value decomposition of either a matrix or batch of matrices input.
svd_lowrank	Return the singular value decomposition (U, S, V) of a matrix, batches of matrices, or a sparse matrix AA such that A \approx U diag(S) V^TA≈Udia**g(S)V**T.
pca_lowrank	Performs linear Principal Component Analysis (PCA) on a low-rank matrix, batches of such matrices, or sparse matrix.
symeig	This function returns eigenvalues and eigenvectors of a real symmetric or complex Hermitian matrix input or a batch thereof, represented by a namedtuple (eigenvalues, eigenvectors).
lobpcg	Find the k largest (or smallest) eigenvalues and the corresponding eigenvectors of a symmetric positive definite generalized eigenvalue problem using matrix-free LOBPCG methods.
trapz	Alias for torch.trapezoid().
trapezoid	Computes the trapezoidal rule along dim.
cumulative_trapezoid	Cumulatively computes the trapezoidal rule along dim.
triangular_solve	Solves a system of equations with a square upper or lower triangular invertible matrix AA and multiple right-hand sides bb.
vdot	Computes the dot product of two 1D tensors.

下标操作

随机操作

序列化与反序列化

杂项

compiled_with_cxx11_abi	Returns whether PyTorch was built with _GLIBCXX_USE_CXX11_ABI=1
result_type	Returns the torch.dtype that would result from performing an arithmetic operation on the provided input tensors.
can_cast	Determines if a type conversion is allowed under PyTorch casting rules described in the type promotion documentation.
promote_types	Returns the torch.dtype with the smallest size and scalar kind that is not smaller nor of lower kind than either type1 or type2.
use_deterministic_algorithms	Sets whether PyTorch operations must use “deterministic” algorithms.
are_deterministic_algorithms_enabled	Returns True if the global deterministic flag is turned on.
is_deterministic_algorithms_warn_only_enabled	Returns True if the global deterministic flag is set to warn only.
set_deterministic_debug_mode	Sets the debug mode for deterministic operations.
get_deterministic_debug_mode	Returns the current value of the debug mode for deterministic operations.
set_float32_matmul_precision	Sets the internal precision of float32 matrix multiplications.
get_float32_matmul_precision	Returns the current value of float32 matrix multiplication precision.
set_warn_always	When this flag is False (default) then some PyTorch warnings may only appear once per process.
is_warn_always_enabled	Returns True if the global warn_always flag is turned on.
_assert	A wrapper around Python’s assert which is symbolically traceable.

说明

PyTorch 的算子大多为异步惰性求值，尤其是 GPU 版本。

算子只定义了入口，真正的实现依赖于不同的后端，常用的有 cpu、cuda、mkldnn、npu 等等。

知道这些的意义是，不用管这些，爱怎么编程就怎么编就可以了，PyTorch 引擎会帮你搞定一切的。