mathnet-numerics/src/Numerics/LinearAlgebra/Complex32/Factorization/DenseQR.cs

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using MathNet.Numerics.LinearAlgebra.Generic.Factorization;

namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization
{
    using System;
    using Generic;
    using Numerics;
    using Properties;

    /// <summary>
    /// <para>A class which encapsulates the functionality of the QR decomposition.</para>
    /// <para>Any real square matrix A may be decomposed as A = QR where Q is an orthogonal matrix 
    /// (its columns are orthogonal unit vectors meaning QTQ = I) and R is an upper triangular matrix 
    /// (also called right triangular matrix).</para>
    /// </summary>
    /// <remarks>
    /// The computation of the QR decomposition is done at construction time by Householder transformation.
    /// </remarks>
    public class DenseQR : QR
    {
        /// <summary>
        ///  Gets or sets Tau vector. Contains additional information on Q - used for native solver.
        /// </summary>
        public Complex32[] Tau
        {
            get;
            set;
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="DenseQR"/> class. This object will compute the
        /// QR factorization when the constructor is called and cache it's factorization.
        /// </summary>
        /// <param name="matrix">The matrix to factor.</param>
        /// <param name="method">The QR factorization method to use.</param>
        /// <exception cref="ArgumentNullException">If <paramref name="matrix"/> is <c>null</c>.</exception>
        /// <exception cref="ArgumentException">If <paramref name="matrix"/> row count is less then column count</exception>
        public DenseQR(DenseMatrix matrix, QRMethod method = QRMethod.Full)
        {
            if (matrix == null)
            {
                throw new ArgumentNullException("matrix");
            }

            if (matrix.RowCount < matrix.ColumnCount)
            {
                throw Matrix.DimensionsDontMatch<ArgumentException>(matrix);
            }

            QrMethod = method;
            Tau = new Complex32[Math.Min(matrix.RowCount, matrix.ColumnCount)];

            if (method == QRMethod.Full)
            {
                MatrixR = matrix.Clone();
                MatrixQ = new DenseMatrix(matrix.RowCount);
                Control.LinearAlgebraProvider.QRFactor(((DenseMatrix)MatrixR).Values, matrix.RowCount, matrix.ColumnCount,
                                                       ((DenseMatrix)MatrixQ).Values, Tau);
            }
            else
            {
                MatrixQ = matrix.Clone();
                MatrixR = new DenseMatrix(matrix.ColumnCount);
                Control.LinearAlgebraProvider.ThinQRFactor(((DenseMatrix)MatrixQ).Values, matrix.RowCount, matrix.ColumnCount,
                                                       ((DenseMatrix)MatrixR).Values, Tau);
            }
        }

        /// <summary>
        /// Solves a system of linear equations, <b>AX = B</b>, with A QR 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<Complex32> input, Matrix<Complex32> result)
        {
            // Check for proper arguments.
            if (input == null)
            {
                throw new ArgumentNullException("input");
            }

            if (result == null)
            {
                throw new ArgumentNullException("result");
            }

            // The solution X should have the same number of columns as B
            if (input.ColumnCount != result.ColumnCount)
            {
                throw new ArgumentException(Resources.ArgumentMatrixSameColumnDimension);
            }

            // The dimension compatibility conditions for X = A\B require the two matrices A and B to have the same number of rows
            if (MatrixR.RowCount != input.RowCount)
            {
                throw new ArgumentException(Resources.ArgumentMatrixSameRowDimension);
            }

            // The solution X row dimension is equal to the column dimension of A
            if (MatrixR.ColumnCount != result.RowCount)
            {
                throw new ArgumentException(Resources.ArgumentMatrixSameColumnDimension);
            }

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

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

            Control.LinearAlgebraProvider.QRSolveFactored(((DenseMatrix)MatrixQ).Values, ((DenseMatrix)MatrixR).Values, MatrixR.RowCount, MatrixR.ColumnCount, Tau, dinput.Values, input.ColumnCount, dresult.Values, QrMethod);
        }

        /// <summary>
        /// Solves a system of linear equations, <b>Ax = b</b>, with A QR 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<Complex32> input, Vector<Complex32> result)
        {
            if (input == null)
            {
                throw new ArgumentNullException("input");
            }

            if (result == null)
            {
                throw new ArgumentNullException("result");
            }

            // Ax=b where A is an m x n matrix
            // Check that b is a column vector with m entries
            if (MatrixR.RowCount != input.Count)
            {
                throw new ArgumentException(Resources.ArgumentVectorsSameLength);
            }

            // Check that x is a column vector with n entries
            if (MatrixR.ColumnCount != result.Count)
            {
                throw Matrix.DimensionsDontMatch<ArgumentException>(MatrixR, result);
            }

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

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

            Control.LinearAlgebraProvider.QRSolveFactored(((DenseMatrix)MatrixQ).Values, ((DenseMatrix)MatrixR).Values, MatrixR.RowCount, MatrixR.ColumnCount, Tau, dinput.Values, 1, dresult.Values, QrMethod);
        }
    }
}