Bug in Singular Value Decomposition

["Brian Shier" <abcshier@hotmail.com>]

There appear to be two bugs in the JAMA SVD code.

1. I noted an error with the following 2x3 test matrix.

                   [ 1       2        3
                     4       5        6 ]

  I believe that the change noted in the following code snippet is needed 
when n > m.

  // If required, generate V.

  if (wantv)
    {
    for (k = n-1; k >= 0; k--)
      {
      if ((k < nrt) & (e[k] != 0.0))
        {
//      for (j = k+1; j < nu; j++)        // Error in JAMA
        for (j = k+1; j < n; j++)         // Correction


2. The need to initialize the elements of U to zero in the constructor is 
suspicious. It suggests that some element is being accessed prematurely 
elsewhere in the code. I suspect an error in the following snippet, but have 
yet to locate it exactly.

  // If required, generate U.

  if (wantu)
    {
    for (j = nct; j < nu; j++)       // Error in JAMA version
      {
      for (i = 0; i < m; i++)
        U[i][j] = 0.0;

      U[j][j] = 1.0;
      }

Please investigate.

-- Brian Shier

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