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Posted 19 Sep 2012
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Yet Another Math Parser (YAMP)

, 30 Sep 2012
Constructing a fast math parser using Reflection to do numerics like Matlab.
YAMP
YAMPCompare
LLMathParser
MathFormula
MathParser
MathParserNet
Exceptions
MathParserTK
YAMPCompare.pidb
YAMPConsole
YAMPConsole.pidb
Exceptions
Expressions
Functions
ArgumentFunctions
LinearAlgebra
LogicFunctions
Spectroscopy
StandardFunctions
Trigonometric
Interfaces
Numerics
Decompositions
Integration
Interpolations
ODE
Optimization
Others
Solvers
Operators
AssigmentOperators
BinaryOperators
DotOperators
LogicOperators
UnaryOperators
Values
YAMP.csproj.user
YAMP.pidb
YAMP.csproj.user
YAMP.pidb
using System;
using YAMP;

namespace YAMP.Numerics
{
    /// <summary>
    /// Cholesky Decomposition.
    /// For a symmetric, positive definite matrix A, the Cholesky decomposition
    /// is an lower triangular matrix L so that A = L*L'.
    /// If the matrix is not symmetric or positive definite, the constructor
    /// returns a partial decomposition and sets an internal flag that may
    /// be queried by the isSPD() method.
    /// </summary>
    public class CholeskyDecomposition : DirectSolver
    {
        #region Members

        /// <summary>
        /// Array for internal storage of decomposition.
        /// </summary>
        double[][] L;

        /// <summary>
        /// Row and column dimension (square matrix).
        /// </summary>
        int n;

        /// <summary>
        /// Symmetric and positive definite flag.
        /// </summary>
        bool isspd;

        #endregion //  Class variables

        #region Constructor

        /// <summary>
        /// Cholesky algorithm for symmetric and positive definite matrix.
        /// </summary>
        /// <param name="Arg">Square, symmetric matrix.</param>
        /// <returns>Structure to access L and isspd flag.</returns>
        public CholeskyDecomposition(MatrixValue Arg)
        {
            // Initialize.
            double[][] A = Arg.GetRealArray();
            n = Arg.DimensionY;
            L = new double[n][];

            for (int i = 0; i < n; i++)
                L[i] = new double[n];

            isspd = (Arg.DimensionX == n);

            // Main loop.
            for (int j = 0; j < n; j++)
            {
                double[] Lrowj = L[j];
                double d = 0.0;

                for (int k = 0; k < j; k++)
                {
                    double[] Lrowk = L[k];
                    double s = 0.0;

                    for (int i = 0; i < k; i++)
                        s += Lrowk[i] * Lrowj[i];
                    
                    Lrowj[k] = s = (A[j][k] - s) / L[k][k];
                    d = d + s * s;
                    isspd = isspd & (A[k][j] == A[j][k]);
                }

                d = A[j][j] - d;
                isspd = isspd & (d > 0.0);
                L[j][j] = Math.Sqrt(Math.Max(d, 0.0));

                for (int k = j + 1; k < n; k++)
                    L[j][k] = 0.0;
            }
        }

        #endregion //  Constructor

        #region Properties
        /// <summary>
        /// Is the matrix symmetric and positive definite?
        /// </summary>
        /// <returns>true if A is symmetric and positive definite.</returns>
        public bool SPD
        {
            get
            {
                return isspd;
            }
        }
        #endregion   // Public Properties

        #region Public Methods

        /// <summary>
        /// Return triangular factor.
        /// </summary>
        /// <returns>L</returns>

        public virtual MatrixValue GetL()
        {
            return new MatrixValue(L, n, n);
        }

        /// <summary>Solve A*X = B</summary>
        /// <param name="B">  A Matrix with as many rows as A and any number of columns.
        /// </param>
        /// <returns>     X so that L*L'*X = B
        /// </returns>
        /// <exception cref="System.ArgumentException">  Matrix row dimensions must agree.
        /// </exception>
        /// <exception cref="System.SystemException"> Matrix is not symmetric positive definite.
        /// </exception>

        public override MatrixValue Solve(MatrixValue B)
        {
            if (B.DimensionY != n)
                throw new DimensionException(n, B.DimensionY);

            if (!isspd)
                throw new MatrixFormatException("symmetric positive definite");

            // Copy right hand side.
            double[][] X = B.GetRealArray();
            int nx = B.DimensionX;

            // Solve L*Y = B;
            for (int k = 0; k < n; k++)
            {
                for (int i = k + 1; i < n; i++)
                {
                    for (int j = 0; j < nx; j++)
                        X[i][j] -= X[k][j] * L[i][k];
                }

                for (int j = 0; j < nx; j++)
                    X[k][j] /= L[k][k];
            }

            // Solve L'*X = Y;
            for (int k = n - 1; k >= 0; k--)
            {
                for (int j = 0; j < nx; j++)
                    X[k][j] /= L[k][k];

                for (int i = 0; i < k; i++)
                {
                    for (int j = 0; j < nx; j++)
                        X[i][j] -= X[k][j] * L[k][i];
                }
            }

            return new MatrixValue(X, n, nx);
        }

        #endregion //  Public Methods
    }
}

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About the Author

Florian Rappl
Architect
Germany Germany
Florian lives in Munich, Germany. He started his programming career with Perl. After programming C/C++ for some years he discovered his favorite programming language C#. He did work at Siemens as a programmer until he decided to study Physics.

During his studies he worked as an IT consultant for various companies. After graduating with a PhD in theoretical particle Physics he is working as a senior technical consultant in the field of home automation and IoT.

Florian has been giving lectures in C#, HTML5 with CSS3 and JavaScript, software design, and other topics. He is regularly giving talks at user groups, conferences, and companies. He is actively contributing to open-source projects. Florian is the maintainer of AngleSharp, a completely managed browser engine.

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