mathnet-numerics/src/Numerics/LinearAlgebra/Complex/Factorization/DenseCholesky.cs

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using MathNet.Numerics.Properties;
using System;

namespace MathNet.Numerics.LinearAlgebra.Complex.Factorization
{

#if NOSYSNUMERICS
    using Numerics;
#else
    using System.Numerics;
#endif

    /// <summary>
    /// <para>A class which encapsulates the functionality of a Cholesky factorization for dense matrices.</para>
    /// <para>For a symmetric, positive definite matrix A, the Cholesky factorization
    /// is an lower triangular matrix L so that A = L*L'.</para>
    /// </summary>
    /// <remarks>
    /// The computation of the Cholesky factorization is done at construction time. If the matrix is not symmetric
    /// or positive definite, the constructor will throw an exception.
    /// </remarks>
    internal sealed class DenseCholesky : Cholesky
    {
        /// <summary>
        /// Initializes a new instance of the <see cref="DenseCholesky"/> class. This object will compute the
        /// Cholesky factorization when the constructor is called and cache it's factorization.
        /// </summary>
        /// <param name="matrix">The matrix to factor.</param>
        /// <exception cref="ArgumentNullException">If <paramref name="matrix"/> is <c>null</c>.</exception>
        /// <exception cref="ArgumentException">If <paramref name="matrix"/> is not a square matrix.</exception>
        /// <exception cref="ArgumentException">If <paramref name="matrix"/> is not positive definite.</exception>
        public static DenseCholesky Create(DenseMatrix matrix)
        {
            if (matrix.RowCount != matrix.ColumnCount)
            {
                throw new ArgumentException(Resources.ArgumentMatrixSquare);
            }

            // Create a new matrix for the Cholesky factor, then perform factorization (while overwriting).
            var factor = (DenseMatrix) matrix.Clone();
            Control.LinearAlgebraProvider.CholeskyFactor(factor.Values, factor.RowCount);
            return new DenseCholesky(factor);
        }

        DenseCholesky(Matrix<Complex> factor)
            : base(factor)
        {
        }

        /// <summary>
        /// Solves a system of linear equations, <b>AX = B</b>, with A Cholesky factorized.
        /// </summary>
        /// <param name="input">The right hand side <see cref="Matrix{T}"/>, <b>B</b>.</param>
        /// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>X</b>.</param>
        public override void Solve(Matrix<Complex> input, Matrix<Complex> result)
        {
            if (result.RowCount != input.RowCount)
            {
                throw new ArgumentException(Resources.ArgumentMatrixSameRowDimension);
            }

            if (result.ColumnCount != input.ColumnCount)
            {
                throw new ArgumentException(Resources.ArgumentMatrixSameColumnDimension);
            }

            if (input.RowCount != Factor.RowCount)
            {
                throw Matrix.DimensionsDontMatch<ArgumentException>(input, Factor);
            }

            var dinput = input as DenseMatrix;
            if (dinput == null)
            {
                throw new NotSupportedException("Can only do Cholesky factorization for dense matrices at the moment.");
            }

            var dresult = result as DenseMatrix;
            if (dresult == null)
            {
                throw new NotSupportedException("Can only do Cholesky factorization for dense matrices at the moment.");
            }

            // Copy the contents of input to result.
            Array.Copy(dinput.Values, 0, dresult.Values, 0, dinput.Values.Length);

            // Cholesky solve by overwriting result.
            var dfactor = (DenseMatrix) Factor;
            Control.LinearAlgebraProvider.CholeskySolveFactored(dfactor.Values, dfactor.RowCount, dresult.Values, dresult.ColumnCount);
        }

        /// <summary>
        /// Solves a system of linear equations, <b>Ax = b</b>, with A Cholesky factorized.
        /// </summary>
        /// <param name="input">The right hand side vector, <b>b</b>.</param>
        /// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>x</b>.</param>
        public override void Solve(Vector<Complex> input, Vector<Complex> result)
        {
            if (input.Count != result.Count)
            {
                throw new ArgumentException(Resources.ArgumentVectorsSameLength);
            }

            if (input.Count != Factor.RowCount)
            {
                throw Matrix.DimensionsDontMatch<ArgumentException>(input, Factor);
            }

            var dinput = input as DenseVector;
            if (dinput == null)
            {
                throw new NotSupportedException("Can only do Cholesky factorization for dense vectors at the moment.");
            }

            var dresult = result as DenseVector;
            if (dresult == null)
            {
                throw new NotSupportedException("Can only do Cholesky factorization for dense vectors at the moment.");
            }

            // Copy the contents of input to result.
            Array.Copy(dinput.Values, 0, dresult.Values, 0, dinput.Values.Length);

            // Cholesky solve by overwriting result.
            var dfactor = (DenseMatrix) Factor;
            Control.LinearAlgebraProvider.CholeskySolveFactored(dfactor.Values, dfactor.RowCount, dresult.Values, 1);
        }

        /// <summary>
        /// Calculates the Cholesky factorization of the input matrix.
        /// </summary>
        /// <param name="matrix">The matrix to be factorized<see cref="Matrix{T}"/>.</param>
        /// <exception cref="ArgumentNullException">If <paramref name="matrix"/> is <c>null</c>.</exception>
        /// <exception cref="ArgumentException">If <paramref name="matrix"/> is not a square matrix.</exception>
        /// <exception cref="ArgumentException">If <paramref name="matrix"/> is not positive definite.</exception>
        /// <exception cref="ArgumentOutOfRangeException">If <paramref name="matrix"/> does not have the same dimensions as the existing factor.</exception>
        public override void Factorize(Matrix<Complex> matrix)
        {
            if (matrix.RowCount != matrix.ColumnCount)
            {
                throw new ArgumentException(Resources.ArgumentMatrixSquare);
            }

            if (matrix.RowCount != Factor.RowCount || matrix.ColumnCount != Factor.ColumnCount)
            {
                throw Matrix.DimensionsDontMatch<ArgumentException>(matrix, Factor);
            }

            var dmatrix = matrix as DenseMatrix;
            if (dmatrix == null)
            {
                throw new NotSupportedException("Can only do Cholesky factorization for dense matrices at the moment.");
            }

            var dfactor = (DenseMatrix)Factor;

            // Overwrite the existing Factor matrix with the input.
            Array.Copy(dmatrix.Values, 0, dfactor.Values, 0, dmatrix.Values.Length);

            // Perform factorization (while overwriting).
            Control.LinearAlgebraProvider.CholeskyFactor(dfactor.Values, dfactor.RowCount);
        }
    }
}