svds

Purpose

Computes the singular values of a x.

Format

s = svds(x)
Parameters:x (matrix or array) – NxP matrix or K-dimensional array where the last two dimensions are NxP, whose singular values are to be computed.
Returns:s (min(N,P)x1 vector or K-dimensional array) – singular values of x arranged in descending order, the last two dimensions are \(min(N,P)x1\).

Examples

// Create a 10x3 matrix
x = {  -0.60     3.50     0.47,
        8.40    16.50     0.27,
       11.40     6.50     0.17,
        7.40    -0.50    -2.43,
       -9.60   -10.50     0.57,
      -17.60    -5.50     0.67,
      -12.60   -14.50     0.87,
       18.40    12.50    -1.43,
      -11.60   -19.50     0.77,
        6.40    11.50     0.07 };

// Calculate the singular values
s = svds(x);

After the code above, s will be equal to:

49.58
14.96
 2.24

Remarks

  1. If x is an array, the result will be an array containing the singular values of each of the 2-dimensional arrays described by the two trailing dimensions of x. In other words, for a 10x4x5 array x, s will be a 10x4x1 array containing the singular values of each of the 10 4x5 arrays contained in x.

  2. If the singular values cannot be computed, either the program will be terminated with an error message, or the first element of the return, \(s[1]\), is set to a missing value. This behavior is controlled by the trap command. Below is an example with error trapping:

    // Turn on error trapping
    trap  1;
    
    // Calculate singular values
    s = svds(x);
    
    // Check for success or failure
    if ismiss(s);
    // Code to handle failure case
    endif;
    

    Note that in the trap 1 case, if the input to svds() is a multi-dimensional array and the singular values for a submatrix fail to compute, only the first value of that s submatrix will be set to a missing value. For a 3 dimensional array, you could change the if, else, elseif, endif check in the above example to:

    // Check for success or failure of each submatrix
    if ismiss(s[., 1, 1]);
    
  3. Call either svdcusv() or svdusv(), to also calculate the right and left singular vectors

See also

Functions svd(), svdcusv(), svdusv()