matlab中怎么将for向量化,matlab中的循环向量化 | 学步园

来自matlab 2011b的帮助文件，有时间会翻译一下。

Vectorizing Loops

The MATLAB software uses a matrix language, which means it is designed for vector and matrix operations. You can often speed up your code by using vectorizing algorithms that take advantage of this design. Vectorization means converting for and while loops

to equivalent vector or matrix operations.

Simple Example of Vectorizing

Here is one way to compute the sine of 1001 values ranging from 0 to 10:

i = 0;

for t = 0:.01:10

i = i + 1;

y(i) = sin(t);

end

A vectorized version of the same code is

t = 0:.01:10;

y = sin(t);

The second example executes much faster than the first and is the way MATLAB is meant to be used. Test this on your system by creating scripts that contain the code shown, and then using the tic and toc functions to measure the performance.

Advanced Example of Vectorizing

repmat is an example of a function that takes advantage of vectorization. It accepts three input arguments: an array A, a row dimension M, and a column dimension N.

repmat creates an output array that contains the elements of array A, replicated and "tiled" in an M-by-N arrangement:

A = [1 2 3; 4 5 6];

B = repmat(A,2,3);

B =

1    2    3    1    2    3    1    2    3

4    5    6    4    5    6    4    5    6

1    2    3    1    2    3    1    2    3

4    5    6    4    5    6    4    5    6

repmat uses vectorization to create the indices that place elements in the output array:

function B = repmat(A, M, N)

% Step 1 Get row and column sizes

[m,n] = size(A);

% Step 2 Generate vectors of indices from 1 to row/column size

mind = (1:m)';

nind = (1:n)';

% Step 3 Create index matrices from vectors above

mind = mind(:,ones(1, M));

nind = nind(:,ones(1, N));

% Step 4 Create output array

B = A(mind,nind);

Step 1, above, obtains the row and column sizes of the input array.

Step 2 creates two column vectors. mind contains the integers from 1 through the row size of A. The nind variable contains the integers from 1 through the column size of A.

Step 3 uses a MATLAB vectorization trick to replicate a single column of data through any number of columns. The code is

B  = A(:,ones(1,nCols))

where nCols is the desired number of columns in the resulting matrix.

Step 4 uses array indexing to create the output array. Each element of the row index array, mind, is paired with each element of the column index array, nind, using the following procedure:

The first element of mind, the row index, is paired with each element of nind. MATLAB moves through the nind matrix in a columnwise fashion, so mind(1,1) goes with nind(1,1), and then nind(2,1), and so on. The result fills the first row of the output array.

Moving columnwise through mind, each element is paired with the elements of nind as above. Each complete pass through the nind matrix fills one row of the output array.

Caution   While repmat can take advantage of vectorization, it can do so at the expense of memory usage. When this is the case, you might find the bsxfun function be more appropriate in this respect.

Functions Used in Vectorizing

Some of the most commonly used functions for vectorizing are as follows

Function：Description

all：Test to determine if all elements are nonzero

any：Test for any nonzeros

cumsum：Find cumulative sum

diff：Find differences and approximate derivatives

find：Find indices and values of nonzero elements

ind2sub：Convert from linear index to subscripts

ipermute：Inverse permute dimensions of a multidimensional array

logical：Convert numeric values to logical

meshgrid：Generate X and Y arrays for 3-D plots

ndgrid：Generate arrays for multidimensional functions and interpolation

permute：Rearrange dimensions of a multidimensional array

prod：Find product of array elements

repmat：Replicate and tile an array

reshape：Change the shape of an array

shiftdim：Shift array dimensions

sort：Sort array elements in ascending or descending order

squeeze：Remove singleton dimensions from an array

sub2ind：Convert from subscripts to linear index

sum：Find the sum of array elements