# C# Symmetric Band Matrix Example

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```using System;

using CenterSpace.NMath.Core;

namespace CenterSpace.NMath.Examples.CSharp
{
/// <summary>
/// A .NET example in C# demonstrating the features of the banded symmetric matrix classes.
/// </summary>
class SymmetricBandMatrixExample
{

static void Main( string[] args )
{
// Set up the parameters that describe the shape of a Hermitian banded matrix.
int halfBandwidth = 1;
int order = 7;

// Set up a symmetric banded matrix B by creating a banded matrix, A,
// with random entries, and setting B equal to the product of the transpose
// of that matrix with itself.
var A = new DoubleBandMatrix( order, order, halfBandwidth, halfBandwidth );
var rng = new RandGenUniform( -1, 1 );
rng.Reset( 0x124 );
DoubleVector diag;

// Fill the non-zero entries of A, a diagonal at a time, with random numbers.
for ( int i = -A.LowerBandwidth; i <= A.UpperBandwidth; ++i )
{
diag = A.Diagonal( i );
for ( int j = 0; j < diag.Length; ++j )
{
diag[j] = rng.Next();
}
}
var B = new DoubleSymBandMatrix( MatrixFunctions.TransposeProduct( A, A ) );

Console.WriteLine();

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

// B =
// 0.249   -0.0333 0.0835  0       0       0       0
// -0.0333 0.121   -0.12   -0.0858 0       0       0
// 0.0835  -0.12   0.196   0.154   0.231   0       0
// 0       -0.0858 0.154   0.477   0.581   0.358   0
// 0       0       0.231   0.581   1.21    0.408   0.152
// 0       0       0       0.358   0.408   0.512   0.277
// 0       0       0       0       0.152   0.277   0.647

// Indexer accessor works just like it does for general matrices.
Console.WriteLine( "B[2,2] = {0}", B[2, 2] );
Console.WriteLine( "B[5,0] = {0}", B[5, 0] );

// You can set the values of elements in the bandwidth
// of a symmetric banded matrix using the indexer. Note that setting
// the element in row i and column j to a value implicitly sets the
// element in column j and row i to the same value.
double a = 99;
B[2, 1] = a;
Console.WriteLine( "B[2,1] = {0}", B[2, 1] ); // 99
Console.WriteLine( "B[1,2] = {0}", B[1, 2] ); // 99

// But setting an element outside the bandwidth of the
// matrix raises a NonModifiableElementException exception
try
{
B[6, 0] = a;
}
catch ( NonModifiableElementException e )
{
Console.WriteLine();
Console.WriteLine( "NonModifiableElementException: {0}", e.Message );
}

// Scalar multiplication and matrix addition/subtraction are supported.
DoubleSymBandMatrix C = a * B;
DoubleSymBandMatrix D = C + B;
Console.WriteLine();
Console.WriteLine( "D =" );
Console.WriteLine( D.ToTabDelimited( "G3" ) );

// Matrix/vector inner products too.
var x = new DoubleVector( B.Cols, rng );
DoubleVector y = MatrixFunctions.Product( B, x );
Console.WriteLine( "Bx = {0}", y.ToString( "G3" ) );

// You can transform the non-zero elements of a banded matrix object by using
// the Transform() method on its data vector.
// Change every element of C to its natural log.
C.DataVector.Transform( NMathFunctions.LogFunc );
Console.WriteLine();
Console.WriteLine( "ln(C) =" );
Console.WriteLine( C.ToTabDelimited( "G3" ) );

// You can also solve linear systems.
DoubleVector x2 = MatrixFunctions.Solve( B, y );

// x and x2 should be the same. Lets look at the l2 norm of
// their difference.
DoubleVector residual = x - x2;
double residualL2Norm = Math.Sqrt( NMathFunctions.Dot( residual, residual ) );
Console.WriteLine( "||x - x2|| = {0}", residualL2Norm );

// You can calculate the determinant too.
double det = MatrixFunctions.Determinant( B );
Console.WriteLine();
Console.WriteLine( "Determinant of B = {0}", det );

// If your symmetric banded matrix is positive definite, you can invoke
// the Solve function with a third - the isPositiveDefinite
// parameter - set to true.
// First make sure B is positive definite.
B = new DoubleSymBandMatrix( MatrixFunctions.TransposeProduct( A, A ) );
y = MatrixFunctions.Product( B, x );
x2 = MatrixFunctions.Solve( B, y, true ); // 3rd parameter isPositiveDefinite set to true.

// See how close Bx is to y by computing the l2 norm of their difference.
residual = x - x2;
residualL2Norm = Math.Sqrt( NMathFunctions.Dot( residual, residual ) );
Console.WriteLine();
Console.WriteLine( "PD ||x - x2|| = {0}", residualL2Norm );

// You can use the Resize() method to change the bandwidths.
D.Resize( D.Order, 2 );

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