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QuickStart Samples

Triangular Matrices QuickStart Sample (C#)

Illustrates how to work efficiently with upper or lower triangular or trapezoidal matrices in C#.

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using System;

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

    /// <summary>
    /// Illustrates the use of the TriangularMatrix class in the 
    /// Extreme.Mathematics.LinearAlgebra namespace of the Extreme Optimization
    /// Mathematics Library for .NET.
    /// </summary>
    class TriangularMatrices
    {
        /// <summary>
        /// The main entry point for the application.
        /// </summary>
        [STAThread]
        static void Main(string[] args)
        {
            // Triangular matrices are matrices whose elements
            // above or below the diagonal are all zero. The
            // former is called lower triangular, the latter
            // lower triangular. In addition, triangular matrices
            // can have all 1's on the diagonal.

            //
            // Constructing triangular matrices
            //

            // Constructing triangular matrices is similar to
            // constructing general matrices. See the
            // BasicMatrices QuickStart samples for a more
            // complete discussion.
            //
            // All constructors take a MatrixTriangle
            // value as their first parameter. This indicates
            // whether an upper or lower triangular matrix 
            // should be created. The following creates a
            // 5x5 lower triangular matrix:
            var t1 = Matrix.CreateLowerTriangular<double>(5, 5);
            // You can also specify whether the diagonal 
            // consists of all 1's using a unitDiagonal parameter:
            var t2 = Matrix.CreateLowerTriangular<double>(
                5, 5, MatrixDiagonal.UnitDiagonal);
            // Triangular matrices access and modify only the
            // elements that are non-zero. If the diagonal
            // mode is UnitDiagonal, the diagonal elements
            // are not used, since they are all equal to 1.
            double[] components = new double[]
                {
                    11, 12, 13, 14, 15,
                    21, 22, 23, 24, 25,
                    31, 32, 33, 34, 35,
                    41, 42, 43, 44, 45,
                    51, 52, 53, 54, 55
                };
            // The following creates a matrix using the
            // upper triangular part of the above.
            var t3 = Matrix.CreateUpperTriangular(5, 5, 
                components, MatrixElementOrder.RowMajor);
            Console.WriteLine("t3 = {0:F0}", t3);
            // Same as above, but unit diagonal:
            var t4 = Matrix.CreateUpperTriangular(5, 5, 
                components, MatrixDiagonal.UnitDiagonal, 
                MatrixElementOrder.RowMajor, true);
            Console.WriteLine("t4 = {0:F0}", t4);

            //
            // Extracting triangular matrices
            //

            // You may want to use part of a dense matrix
            // as a triangular matrix. The static 
            // ExtractUpperTriangle and ExtractLowerTriangle
            // methods perform this task.
            var m = Matrix.Create<double>(5, 5, components, MatrixElementOrder.ColumnMajor);
            Console.WriteLine("m = {0:F0}", m);
            // Both methods are overloaded. The simplest
            // returns a triangular matrix of the same dimension:
            var t5 = Matrix.ExtractLowerTriangle(m);
            Console.WriteLine("t5 = {0:F0}", t5);
            // You can also specify if the matrix is unit diagonal:
            var t6 = Matrix.ExtractUpperTriangle(
                    m, MatrixDiagonal.UnitDiagonal);
            Console.WriteLine("t6 = {0:F0}", t6);
            // Or the dimensions of the matrix if they don't 
            // match the original:
            var t7 = Matrix.ExtractUpperTriangle(
                m, 3, 3, MatrixDiagonal.UnitDiagonal);
            Console.WriteLine("t7 = {0:F0}", t7);
            Console.WriteLine();

            //
            // TriangularMatrix properties
            //

            // The IsLowerTriangular and IsUpperTriangular return
            // a boolean value:
            Console.WriteLine("t4 is lower triangular? - {0:F0}", 
                t4.IsLowerTriangular);
            Console.WriteLine("t4 is upper triangular? - {0:F0}", 
                t4.IsUpperTriangular);
            // The IsUnitDiagonal property indicates whether the
            // matrix has all 1's on its diagonal:
            Console.WriteLine("t3 is unit diagonal? - {0:F0}", 
                t3.IsUnitDiagonal);
            Console.WriteLine("t4 is unit diagonal? - {0:F0}", 
                t4.IsUnitDiagonal);
            Console.WriteLine();
            // You can get and set matrix elements:
            t3[1, 3] = 55;
            Console.WriteLine("t3[1, 3] = {0:F0}", t3[1, 3]);
            // But trying to set an element that is zero or
            // is on the diagonal for a unit diagonal matrix
            // causes an exception to be thrown:
            try
            {
                t3[3, 1] = 100;
            }
            catch(ComponentReadOnlyException e)
            {
                Console.WriteLine("Error accessing element: {0:F0}",
                    e.Message);
            }

            //
            // Rows and columns
            //

            // The GetRow and GetColumn methods are
            // available.
            var row = t3.GetRow(1);
            Console.WriteLine("row 2 of t3 = {0:F0}", row);
            var column = t4.GetColumn(1, 0, 2);
            Console.WriteLine("2nd column of t4 from row 1 to 3 = {0:F0}", column);

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