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 /// tridiagonal matrices. /// </summary> class TriDiagFactExample { static void Main( string[] args ) { // Construct a tridiagonal matrix with random entries. int rows = 5; int cols = 5; var rng = new RandGenUniform( -1, 1 ); rng.Reset( 0x124 ); var data1 = new FloatComplexVector( cols, rng ); var data2 = new FloatComplexVector( cols - 1, rng ); var data3 = new FloatComplexVector( cols - 1, rng ); var A = new FloatComplexTriDiagMatrix( rows, cols ); A.Diagonal()[Slice.All] = data1; A.Diagonal( 1 )[Slice.All] = data2; A.Diagonal( -1 )[Slice.All] = data3; Console.WriteLine(); Console.WriteLine( "A =" ); Console.WriteLine( A.ToTabDelimited( "F3" ) ); Console.WriteLine(); // A = // (-0.497,0.332) (0.560,0.306) (0.000,0.000) (0.000,0.000) (0.000,0.000) // (0.773,0.358) (-0.250,0.576) (0.220,-0.077) (0.000,0.000) (0.000,0.000) // (0.000,0.000) (-0.863,0.203) (0.196,0.182) (-0.168,-0.259) (0.000,0.000) // (0.000,0.000) (0.000,0.000) (-0.585,0.622) (-0.044,0.074) (-0.924,0.621) // (0.000,0.000) (0.000,0.000) (0.000,0.000) (-0.705,0.124) (-0.325,-0.280) // Construct a tridiagonal factorization class. var fact = new FloatComplexTriDiagFact( A ); // Check to see if A is singular. string isSingularString = fact.IsSingular ? "A is singular" : "A is NOT singular"; Console.WriteLine( isSingularString ); // Retrieve information about the matrix A. FloatComplex det = fact.Determinant(); // In order to get condition number, factor with estimateCondition = true fact.Factor( A, true ); float rcond = fact.ConditionNumber(); FloatComplexMatrix 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( "F3" ) ); // Use the factorization to solve some linear systems Ax = y. var y0 = new FloatComplexVector( fact.Cols, rng ); var y1 = new FloatComplexVector( fact.Cols, rng ); FloatComplexVector x0 = fact.Solve( y0 ); FloatComplexVector x1 = fact.Solve( y1 ); Console.WriteLine(); Console.WriteLine( "Solution to Ax = y0 is {0}", x0.ToString( "G5" ) ); Console.WriteLine(); Console.WriteLine( "y0 - Ax0 = {0}", ( y0 - MatrixFunctions.Product( A, 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( A, x1 ) ).ToString( "G5" ) ); // You can also solve for multiple right-hand sides. var Y = new FloatComplexMatrix( y1.Length, 2 ); Y.Col( 0 )[Slice.All] = y0; Y.Col( 1 )[Slice.All] = y1; FloatComplexMatrix 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( "G7" ) ); // Factor a different matrix. var z = new FloatComplex( 1.23F, -.76F ); FloatComplexTriDiagMatrix B = z * A; fact.Factor( B ); x0 = fact.Solve( y0 ); Console.WriteLine(); Console.WriteLine( "Solution to Bx = y0 is {0}", x0.ToString( "G5" ) ); Console.WriteLine(); Console.WriteLine( "Press Enter Key" ); Console.Read(); } } }← All NMath Code Examples