Maximal number of iterations (540) exceeded
--------------------------------------------

                 Key: MATH-327
                 URL: https://issues.apache.org/jira/browse/MATH-327
             Project: Commons Math
          Issue Type: Bug
         Environment: Windows 7 (32-bit)  JDK 1.6_16
            Reporter: Mansoor Ahmed Khan
            Priority: Critical



I have a matrix of size 49x19 and when I apply SVD on this matrix it raises the 
following exception. The problem which I am facing is that SVD works for some 
matrix and doesn't work for others. I have no clue what is the possible reason.

Exception::
org.apache.commons.math.linear.InvalidMatrixException: 
org.apache.commons.math.MaxIterationsExceededException: Maximal number of 
iterations (540) exceeded


RealMatrix m = [[1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 
1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 
0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096, 1.00000000, 
1.00000000, 0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000, 
1.00000000, 1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000, 
1.00000000, 0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096, 
1.00000000, 1.00000000, 0.96428573],[1.00000000, 1.00000000, 1.00000000, 
1.00000000, 1.00000000, 1.00000000, 0.99107143, 1.00000000, 1.00000000, 
1.00000000, 1.00000000, 0.94450431, 1.00000000, 1.00000000, 0.99107143, 
0.95238096, 1.00000000, 1.00000000, 0.96428573],[1.00000000, 1.00000000, 
1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.99107143, 1.00000000, 
1.00000000, 1.00000000, 1.00000000, 0.94450431, 1.00000000, 1.00000000, 
0.99107143, 0.95238096, 1.00000000, 1.00000000, 0.96428573],[1.00000000, 
1.00000000, 0.94999999, 0.95833331, 1.00000000, 1.00000000, 0.99107143, 
0.94583333, 1.00000000, 0.95000000, 0.98333333, 0.92106681, 0.97368419, 
1.00000000, 0.95357142, 0.95238096, 1.00000000, 0.93333334, 
0.96428573],[1.00000000, 1.00000000, 0.94999999, 0.95833331, 1.00000000, 
1.00000000, 0.99107143, 0.94583333, 1.00000000, 0.95000000, 0.98333333, 
0.92106681, 0.97368419, 1.00000000, 0.95357142, 0.95238096, 1.00000000, 
0.93333334, 0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000, 
1.00000000, 1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000, 
1.00000000, 0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096, 
1.00000000, 1.00000000, 0.96428573],[1.00000000, 1.00000000, 1.00000000, 
1.00000000, 1.00000000, 1.00000000, 0.99107143, 1.00000000, 1.00000000, 
1.00000000, 1.00000000, 0.94450431, 1.00000000, 1.00000000, 0.99107143, 
0.95238096, 1.00000000, 1.00000000, 0.96428573],[1.00000000, 1.00000000, 
1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.99107143, 1.00000000, 
1.00000000, 1.00000000, 1.00000000, 0.94450431, 1.00000000, 1.00000000, 
0.99107143, 0.95238096, 1.00000000, 1.00000000, 0.96428573],[1.00000000, 
1.00000000, 0.94999999, 0.95833331, 1.00000000, 1.00000000, 0.99107143, 
0.94583333, 1.00000000, 0.95000000, 0.98333333, 0.92106681, 0.97368419, 
1.00000000, 0.95357142, 0.95238096, 1.00000000, 0.93333334, 
0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 
1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 
0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096, 1.00000000, 
1.00000000, 0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000, 
1.00000000, 1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000, 
1.00000000, 0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096, 
1.00000000, 1.00000000, 0.96428573],[1.00000000, 1.00000000, 0.94999999, 
0.95833331, 1.00000000, 1.00000000, 0.99107143, 0.94583333, 1.00000000, 
0.95000000, 0.98333333, 0.92106681, 0.97368419, 1.00000000, 0.95357142, 
0.95238096, 1.00000000, 0.93333334, 0.96428573],[1.00000000, 1.00000000, 
1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.99107143, 1.00000000, 
1.00000000, 1.00000000, 1.00000000, 0.94450431, 1.00000000, 1.00000000, 
0.99107143, 0.95238096, 1.00000000, 1.00000000, 0.96428573],[1.00000000, 
1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.99107143, 
1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.94450431, 1.00000000, 
1.00000000, 0.99107143, 0.95238096, 1.00000000, 1.00000000, 
0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 
1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 
0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096, 1.00000000, 
1.00000000, 0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000, 
1.00000000, 1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000, 
1.00000000, 0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096, 
1.00000000, 1.00000000, 0.96428573],[1.00000000, 1.00000000, 1.00000000, 
1.00000000, 1.00000000, 1.00000000, 0.99107143, 1.00000000, 1.00000000, 
1.00000000, 1.00000000, 0.94450431, 1.00000000, 1.00000000, 0.99107143, 
0.95238096, 1.00000000, 1.00000000, 0.96428573],[1.00000000, 1.00000000, 
0.94999999, 0.95833331, 1.00000000, 1.00000000, 0.99107143, 0.94583333, 
1.00000000, 0.95000000, 0.98333333, 0.92106681, 0.97368419, 1.00000000, 
0.95357142, 0.95238096, 1.00000000, 0.93333334, 0.96428573],[1.00000000, 
1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.99107143, 
1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.94450431, 1.00000000, 
1.00000000, 0.99107143, 0.95238096, 1.00000000, 1.00000000, 
0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 
1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 
0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096, 1.00000000, 
1.00000000, 0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000, 
1.00000000, 1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000, 
1.00000000, 0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096, 
1.00000000, 1.00000000, 0.96428573],[1.00000000, 1.00000000, 1.00000000, 
1.00000000, 1.00000000, 1.00000000, 0.99107143, 1.00000000, 1.00000000, 
1.00000000, 1.00000000, 0.94450431, 1.00000000, 1.00000000, 0.99107143, 
0.95238096, 1.00000000, 1.00000000, 0.96428573],[1.00000000, 1.00000000, 
1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.99107143, 1.00000000, 
1.00000000, 1.00000000, 1.00000000, 0.94450431, 1.00000000, 1.00000000, 
0.99107143, 0.95238096, 1.00000000, 1.00000000, 0.96428573],[1.00000000, 
1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.99107143, 
1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.94450431, 1.00000000, 
1.00000000, 0.99107143, 0.95238096, 1.00000000, 1.00000000, 
0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 
1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 
0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096, 1.00000000, 
1.00000000, 0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000, 
1.00000000, 1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000, 
1.00000000, 0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096, 
1.00000000, 1.00000000, 0.96428573],[1.00000000, 1.00000000, 0.94999999, 
0.95833331, 1.00000000, 1.00000000, 0.99107143, 0.94583333, 1.00000000, 
0.95000000, 0.98333333, 0.92106681, 0.97368419, 1.00000000, 0.95357142, 
0.95238096, 1.00000000, 0.93333334, 0.96428573],[1.00000000, 1.00000000, 
1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.99107143, 1.00000000, 
1.00000000, 1.00000000, 1.00000000, 0.94450431, 1.00000000, 1.00000000, 
0.99107143, 0.95238096, 1.00000000, 1.00000000, 0.96428573],[1.00000000, 
1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.99107143, 
1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.94450431, 1.00000000, 
1.00000000, 0.99107143, 0.95238096, 1.00000000, 1.00000000, 
0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 
1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 
0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096, 1.00000000, 
1.00000000, 0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000, 
1.00000000, 1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000, 
1.00000000, 0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096, 
1.00000000, 1.00000000, 0.96428573],[1.00000000, 1.00000000, 0.94999999, 
0.95833331, 1.00000000, 1.00000000, 0.99107143, 0.94583333, 1.00000000, 
0.95000000, 0.98333333, 0.92106681, 0.97368419, 1.00000000, 0.95357142, 
0.95238096, 1.00000000, 0.93333334, 0.96428573],[1.00000000, 1.00000000, 
1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.99107143, 1.00000000, 
1.00000000, 1.00000000, 1.00000000, 0.94450431, 1.00000000, 1.00000000, 
0.99107143, 0.95238096, 1.00000000, 1.00000000, 0.96428573],[1.00000000, 
1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.99107143, 
1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.94450431, 1.00000000, 
1.00000000, 0.99107143, 0.95238096, 1.00000000, 1.00000000, 
0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 
1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 
0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096, 1.00000000, 
1.00000000, 0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000, 
1.00000000, 1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000, 
1.00000000, 0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096, 
1.00000000, 1.00000000, 0.96428573],[1.00000000, 1.00000000, 1.00000000, 
1.00000000, 1.00000000, 1.00000000, 0.99107143, 1.00000000, 1.00000000, 
1.00000000, 1.00000000, 0.94450431, 1.00000000, 1.00000000, 0.99107143, 
0.95238096, 1.00000000, 1.00000000, 0.96428573],[1.00000000, 1.00000000, 
1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.99107143, 1.00000000, 
1.00000000, 1.00000000, 1.00000000, 0.94450431, 1.00000000, 1.00000000, 
0.99107143, 0.95238096, 1.00000000, 1.00000000, 0.96428573],[1.00000000, 
1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.99107143, 
1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.94450431, 1.00000000, 
1.00000000, 0.99107143, 0.95238096, 1.00000000, 1.00000000, 
0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 
1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 
0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096, 1.00000000, 
1.00000000, 0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000, 
1.00000000, 1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000, 
1.00000000, 0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096, 
1.00000000, 1.00000000, 0.96428573],[1.00000000, 1.00000000, 1.00000000, 
1.00000000, 1.00000000, 1.00000000, 0.99107143, 1.00000000, 1.00000000, 
1.00000000, 1.00000000, 0.94450431, 1.00000000, 1.00000000, 0.99107143, 
0.95238096, 1.00000000, 1.00000000, 0.96428573],[1.00000000, 1.00000000, 
1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.99107143, 1.00000000, 
1.00000000, 1.00000000, 1.00000000, 0.94450431, 1.00000000, 1.00000000, 
0.99107143, 0.95238096, 1.00000000, 1.00000000, 0.96428573],[1.00000000, 
1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.99107143, 
1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.94450431, 1.00000000, 
1.00000000, 0.99107143, 0.95238096, 1.00000000, 1.00000000, 
0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 
1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 
0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096, 1.00000000, 
1.00000000, 0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000, 
1.00000000, 1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000, 
1.00000000, 0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096, 
1.00000000, 1.00000000, 0.96428573],[1.00000000, 1.00000000, 0.94999999, 
0.95833331, 1.00000000, 1.00000000, 0.99107143, 0.94583333, 1.00000000, 
0.95000000, 0.98333333, 0.92106681, 0.97368419, 1.00000000, 0.95357142, 
0.95238096, 1.00000000, 0.93333334, 0.96428573],[1.00000000, 1.00000000, 
0.94999999, 0.95833331, 1.00000000, 1.00000000, 0.99107143, 0.94583333, 
1.00000000, 0.95000000, 0.98333333, 0.92106681, 0.97368419, 1.00000000, 
0.95357142, 0.95238096, 1.00000000, 0.93333334, 0.96428573]]

RealMatrix rcp = MatrixUtils.createRealMatrix(CP);      
SingularValueDecomposition svd = new SingularValueDecompositionImpl(rcp);       
        

RealMatrix U = svd.getU();
RealMatrix S = svd.getS();
RealMatrix Vt = svd.getVT();
double[] singularValues = svd.getSingularValues();

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