Programming

Techniques for Improving Performance

This section covers the following suggestions on how you can improve the performance of your MATLAB programs:

• Vectorizing Loops
• Preallocating Arrays
• Coding Loops in a MEX-File
• Assigning to Variables
• Operating on Real Data
• Using Appropriate Logical Operators
• Overloading Built-In Functions
• Functions Are Generally Faster Than Scripts
• Load and Save Are Faster Than File I/O Functions
• Avoid Large Background Processes

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.

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

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:

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), and 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 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
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

Analyzing Your Program's Performance

Preallocating Arrays

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