Programming and Data Types

Vectorizing Loops

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

Note    Before taking the time to vectorize your code, read the section on Performance Acceleration. You may be able to speed up your program by just as much using the MATLAB JIT Accelerator instead of vectorizing.

A Simple Example

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 M-file scripts that contain the code shown, then using the tic and toc functions to time the M-files.

An Advanced Example

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)
  if nargin < 2
     error('Requires at least 2 inputs.')
  elseif nargin == 2
     N = M;
  end
  
  % 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 Creates 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,n_cols))
  

where n_cols 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:

1. 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), then nind(2,1), and so on. The result fills the first row of the output array.
2. 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.

Functions Used in Vectorizing

Some of the most commonly used functions for vectorizing are

all	diff	ipermute	permute	reshape	squeeze
any	find	logical	prod	shiftdim	sub2ind
cumsum	ind2sub	ndgrid	repmat	sort	sum

Techniques for Improving Performance

Preallocating Arrays