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QuickStart Samples

Band Matrices QuickStart Sample (C#)

Illustrates how to work with the BandMatrix class in C#.

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using System;

namespace Extreme.Numerics.QuickStart.CSharp
{
    using Extreme.Mathematics;
    // The BandMatrix class resides in the Extreme.Mathematics.LinearAlgebra
    // namespace.
    using Extreme.Mathematics.LinearAlgebra;

    /// <summary>
    /// Illustrates the use of the BandMatrix class in the 
    /// Extreme.Mathematics.LinearAlgebra namespace of the Extreme Optimization
    /// Numerical Libraries for .NET.
    /// </summary>
    class BandMatrices
    {
        /// <summary>
        /// The main entry point for the application.
        /// </summary>
        [STAThread]
        static void Main(string[] args)
        {
            // Band matrices are matrices whose elements
            // are nonzero only in a diagonal band around
            // the main diagonal.
            //
            // General band matrices, upper and lower band
            // matrices, and symmetric band matrices are all
            // represented by a single class: BandMatrix.

            //
            // Constructing band matrices
            //

            // Constructing band matrices is similar to
            // constructing general matrices. It is done by
            // calling a factory method on the Matrix class.
            // See theBasicMatrices QuickStart samples 
            // for a more complete discussion.

            // The following creates a 7x5 band matrix with
            // upper bandwidth 1 and lower bandwidth 2:
            var b1 = Matrix.CreateBanded<double>(7, 5, 2, 1);

            // Once the upper and lower bandwidth are set, 
            // it cannot be changed. Elements that are outside
            // the band cannot be set.

            // A second factory method lets you create upper
            // or lower band matrices. The following constructs
            // an 11x11 upper band matrix with unit diagonal
            // and three non-zero upper diagonals.
            var b2 = Matrix.CreateUpperBanded<double>(11, 11, 3, MatrixDiagonal.UnitDiagonal);

            // To create a symmetric band matrix, you only need
            // the size and the bandwith. The following creates
            // a 6x6 symmetric tri-diagonal matrix:
            var b3 = Matrix.CreateSymmetricBanded<double>(7, 1);

            // We can assign values to the components by using
            // the GetDiagonal method.
            b3.GetDiagonal(0).SetValue(2);
            b3.GetDiagonal(1).SetValue(-1);

            // Extracting band matrices

            // Another way to construct a band matrix is by
            // extracting them from an existing matrix.
            var m = Matrix.Create(3, 4, new double[]
                {
                    1, 2, 3, 
                    2, 3, 4,
                    3, 4, 5,
                    4, 5, 7
                }, MatrixElementOrder.ColumnMajor);
            // To get the lower band part of m with bandwidth 2:
            var b4 = BandMatrix<double>.Extract(m, 2, 0);

            //
            // BandMatrix properties
            //

            // A number of properties are available to determine 
            // whether a BandMatrix has a special structure:
            Console.WriteLine("b2 is upper? {0}", b2.IsUpperTriangular);
            Console.WriteLine("b2 is lower? {0}", b2.IsUpperTriangular);
            Console.WriteLine("b2 is unit diagonal? {0}", b2.IsUnitDiagonal);
            Console.WriteLine("b2 is symmetrical? {0}", b2.IsSymmetrical);

            //
            // BandMatrix methods
            //

            // You can get and set matrix elements:
            b3[2, 3] = 55;
            Console.WriteLine("b3[2, 3] = {0:F0}", b3[2, 3]);
            // And the change will automatically be reflected
            // in the symmetric element:
            Console.WriteLine("b3[3, 2] = {0:F0}", b3[3, 2]);

            //
            // Row and column views
            //

            // The GetRow and GetColumn methods are
            // available.
            var row = b2.GetRow(1);
            Console.WriteLine("row 1 of b2 = {0:F0}", row);
            var column = b2.GetColumn(2, 3, 4);
            Console.WriteLine("column 3 of b2 from row 4 to ");
            Console.WriteLine("  row 5 = {0:F0}", column);

            //
            // Band matrix decompositions
            //

            // Specialized classes exist to represent the
            // LU decomposition of a general band matrix
            // and the Cholesky decomposition of a 
            // symmetric band matrix.

            // Because of pivoting, the upper band matrix of
            // the LU decomposition has larger bandwidth.
            // You need to allocate extra space to be able to
            // overwrite a matrix with its LU decomposition.

            // The following creates a 7x5 band matrix with
            // upper bandwidth 1 and lower bandwidth 2.
            var b5 = Matrix.CreateBanded<double>(7, 7, 2, 1, true);
            b5.GetDiagonal(0).SetValue(2.0);
            b5.GetDiagonal(-2).SetValue(-1.0);
            b5.GetDiagonal(1).SetValue(-1.0);

            // Other than that, the API is the same as
            // other decomposition classes.
            var blu = b5.GetLUDecomposition(true);
            var solution = blu.Solve(Vector.CreateConstant(b5.ColumnCount, 1.0));
            Console.WriteLine("  solution of b5*x = ones: {0:F4}", solution);

            Console.Write("Press Enter key to exit...");
            Console.ReadLine();
        }
    }
}