# C# Band Fact 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 factorization classes for
/// banded matrices.
/// </summary>
class BandFactExample
{

static void Main( string[] args )
{
// Construct a banded matrix with random entries from a data vector
// of the appropriate length,
int upperBandwidth = 2;
int lowerBandwidth = 1;
int rows = 7;
int cols = 7;
var rng = new RandGenUniform( -1, 1 );
rng.Reset( 0x124 );
var data = new FloatVector( ( lowerBandwidth + upperBandwidth + 1 ) * cols, rng );
var A = new FloatBandMatrix( data, rows, cols, lowerBandwidth, upperBandwidth );

Console.WriteLine();

Console.WriteLine( "A = " );

Console.WriteLine( A.ToTabDelimited( "G3" ) );

// A =
// -0.25   0.182   -0.325  0       0       0       0
// 0.576   -0.0443 -0.28   0.22    0       0       0
// 0       0.0738  0.56    -0.077  -0.924  0       0
// 0       0       0.306   -0.168  0.621   -0.863  0
// 0       0       0       -0.259  0.773   0.203   -0.705
// 0       0       0       0       0.358   -0.585  0.124
// 0       0       0       0       0       0.622   0.87

// Construct a band factorization class.
var fact = new FloatBandFact( A );

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

// Retrieve information about the matrix A:
float det = fact.Determinant();

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

FloatMatrix AInv = fact.Inverse();

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

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

Console.WriteLine();
Console.WriteLine( "A inverse =" );
Console.WriteLine( AInv.ToTabDelimited( "G5" ) );

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

Console.WriteLine();
Console.WriteLine( "Solution to Ax = y0 is {0}", x0.ToString( "G3" ) );

Console.WriteLine();
Console.WriteLine( "y0 - Ax0 = {0}", ( y0 - MatrixFunctions.Product( A, x0 ) ).ToString( "G3" ) );

Console.WriteLine();
Console.WriteLine( "Solution to Ax = y1 is {0}", x1.ToString( "G3" ) );

Console.WriteLine();
Console.WriteLine( "y1 - Ax1 = {0}", ( y1 - MatrixFunctions.Product( A, x1 ) ).ToString( "G3" ) );

// You can also solve for multiple right hand sides.
var Y = new FloatMatrix( y1.Length, 2 );
Y.Col( 0 )[Slice.All] = y0;
Y.Col( 1 )[Slice.All] = y1;
FloatMatrix 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( "G5" ) );

// Factor a different matrix.
FloatBandMatrix B = 1.2F * A;
fact.Factor( B );
x0 = fact.Solve( y0 );

Console.WriteLine();
Console.WriteLine( "Solution to Bx = y0 is {0}", x0.ToString( "G3" ) );

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