# C# Sym Fact Example

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```using System;

using CenterSpace.NMath.Core;
using CenterSpace.NMath.Matrix;

namespace CenterSpace.NMath.Matrix.Examples.CSharp
{
/// <summary>
/// A .NET example in C# demonstrating the features of the factorization classes for
/// symmetric matrices.
/// </summary>
class SymFactExample
{

static void Main( string[] args )
{
// Construct a symmetric matrix as the product of the transpose of a
// matrix with itself.
int rows = 5;
int cols = 5;
var rng = new RandGenUniform( -1, 1 );
rng.Reset( 0x124 );
var A = new DoubleMatrix( rows, cols, rng );
DoubleMatrix ATA = NMathFunctions.TransposeProduct( A, A );
var S = new DoubleSymmetricMatrix( ATA );

Console.WriteLine();

Console.WriteLine( "S =" );
Console.WriteLine( S.ToTabDelimited( "G3" ) );

// S =
// 0.791   -0.366  -0.31   0.183   0.863
// -0.366  0.224   0.177   -0.312  -0.214
// -0.31   0.177   0.49    -0.411  -0.48
// 0.183   -0.312  -0.411  2.03    -0.0979
// 0.863   -0.214  -0.48   -0.0979 2.01

// Construct a symmetric factorization class.
var fact = new DoubleSymFact( S );

// Check to see if S is singular.
string isSingularString = fact.IsSingular ? "S is singular" : "S is NOT singular";
Console.WriteLine( isSingularString );

// Retrieve information about the matrix S.
double det = fact.Determinant();

// In order to get condition number, factor with estimateCondition = true
fact.Factor( S, true );
double rcond = fact.ConditionNumber();

DoubleSymmetricMatrix SInv = fact.Inverse();

Console.WriteLine();
Console.WriteLine( "Determinant of S = {0}", det );

Console.WriteLine();
Console.WriteLine( "Reciprocal condition number = {0}", rcond );

Console.WriteLine();
Console.WriteLine( "S inverse =" );
Console.WriteLine( SInv.ToTabDelimited( "G3" ) );

// Use the factorization to solve some linear systems Ax = y.
var y0 = new DoubleVector( fact.Cols, rng );
var y1 = new DoubleVector( fact.Cols, rng );
DoubleVector x0 = fact.Solve( y0 );
DoubleVector x1 = fact.Solve( y1 );

Console.WriteLine( "Solution to Ax = y0 is {0}", x0.ToString( "G5" ) );

Console.WriteLine();
Console.WriteLine( "y0 - Ax0 = {0}", ( y0 - MatrixFunctions.Product( S, x0 ) ).ToString( "G5" ) );

Console.WriteLine();
Console.WriteLine( "Solution to Ax = y1 is {0}", x1.ToString( "G5" ) );

Console.WriteLine();
Console.WriteLine( "y1 - Ax1 = {0}", ( y1 - MatrixFunctions.Product( S, x1 ) ).ToString( "G5" ) );

// You can also solve for multiple right-hand sides.
var Y = new DoubleMatrix( y1.Length, 2 );
Y.Col( 0 )[Slice.All] = y0;
Y.Col( 1 )[Slice.All] = y1;
DoubleMatrix X = fact.Solve( Y );

// The first column of X should be x0; the second column should be x1.
Console.WriteLine();
Console.WriteLine( "X =" );
Console.WriteLine( X.ToTabDelimited( "G3" ) );

// Factor a different matrix.
DoubleSymmetricMatrix B = 1.2 * S;
fact.Factor( B );
x0 = fact.Solve( y0 );

Console.WriteLine( "Solution to Bx = y0 is {0}", x0.ToString( "G5" ) );

Console.WriteLine();
Console.WriteLine( "Press Enter Key" );