Example: Singular Value Decomposition of a Matrix

using System;
using Imsl.Math;

public class SVDEx1
{
    public static void  Main(String[] args)
    {
        double[,] a = {
            {1, 2, 1, 4},
            {3, 2, 1, 3},
            {4, 3, 1, 4}, 
            {2, 1, 3, 1}, 
            {1, 5, 2, 2},
            {1, 2, 2, 3}
        };
        
        // Compute the SVD factorization of A
        SVD svd = new SVD(a);
        
        // Print U, S and V.
        new PrintMatrix("U").SetPageWidth(80).Print(svd.GetU());
        new PrintMatrix("S").SetPageWidth(80).Print(svd.GetS());
        new PrintMatrix("V").SetPageWidth(80).Print(svd.GetV());
        
        // Find the rank of A.
        int rank = svd.Rank;
        Console.Out.WriteLine("rank = " + rank);
    }
}

Output

                                U
           0                    1                    2            
0  -0.380475586320569   0.119670992640587    0.439082824383239    
1  -0.403753713172442   0.345110837105607   -0.0565761852901658   
2  -0.545120486248343   0.429264893493195    0.0513926928086694   
3  -0.264784294004146  -0.0683195253271513  -0.883860867430429    
4  -0.446310112301556  -0.816827623278282    0.141899675060401    
5  -0.354628656614145  -0.102147399162125   -0.00431844397986985  

           3                    4                    5           
0  -0.565399585908374   0.0243115161463761  -0.57258686109915    
1   0.214775576522681   0.80890058872827     0.11929741721493    
2   0.432144162809737  -0.572327648171096    0.0403309248707933  
3  -0.215253698182974  -0.0625209225900579  -0.30621669907105    
4   0.321269584269887   0.0621337820958098  -0.0799352679998222  
5  -0.545800221853259  -0.0987946265624981   0.745739576113111   

          S
           0          
0  11.4850179115597   
1   3.2697512144125   
2   2.65335616200783  
3   2.08872967244092  

                               V
           0                   1                   2           
0  -0.444294128842354   0.555531257799947  -0.435378966673942  
1  -0.558067238190387  -0.654298740112323   0.277456900458814  
2  -0.32438610320628   -0.351360645592513  -0.732099533429598  
3  -0.621238553843379   0.37393031038343    0.444401954223745  

           3           
0   0.55175438744187   
1   0.428336065179864  
2  -0.485128463324533  
3  -0.526066236587424  

rank = 4