mathnet-numerics/src/Numerics/LinearAlgebra/Complex/Matrix.cs

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using System;
using MathNet.Numerics.LinearAlgebra.Complex.Factorization;
using MathNet.Numerics.LinearAlgebra.Factorization;
using MathNet.Numerics.LinearAlgebra.Storage;
using MathNet.Numerics.Properties;

namespace MathNet.Numerics.LinearAlgebra.Complex
{

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

    /// <summary>
    /// <c>Complex</c> version of the <see cref="Matrix{T}"/> class.
    /// </summary>
    [Serializable]
    public abstract class Matrix : Matrix<Complex>
    {        
        /// <summary>
        /// Initializes a new instance of the Matrix class.
        /// </summary>
        protected Matrix(MatrixStorage<Complex> storage)
            : base(storage)
        {
        }

        /// <summary>Calculates the L1 norm.</summary>
        /// <returns>The L1 norm of the matrix.</returns>
        public override double L1Norm()
        {
            var norm = 0d;
            for (var j = 0; j < ColumnCount; j++)
            {
                var s = 0d;
                for (var i = 0; i < RowCount; i++)
                {
                    s += At(i, j).Magnitude;
                }
                norm = Math.Max(norm, s);
            }
            return norm;
        }

        /// <summary>Calculates the infinity norm of this matrix.</summary>
        /// <returns>The infinity norm of this matrix.</returns>   
        public override double InfinityNorm()
        {
            var norm = 0d;
            for (var i = 0; i < RowCount; i++)
            {
                var s = 0d;
                for (var j = 0; j < ColumnCount; j++)
                {
                    s += At(i, j).Magnitude;
                }
                norm = Math.Max(norm, s);
            }
            return norm;
        }

        /// <summary>Calculates the Frobenius norm of this matrix.</summary>
        /// <returns>The Frobenius norm of this matrix.</returns>
        public override double FrobeniusNorm()
        {
            var transpose = ConjugateTranspose();
            var aat = this * transpose;
            var norm = 0d;
            for (var i = 0; i < RowCount; i++)
            {
                norm += aat.At(i, i).Magnitude;
            }
            return Math.Sqrt(norm);
        }

        /// <summary>
        /// Returns the conjugate transpose of this matrix.
        /// </summary>        
        /// <returns>The conjugate transpose of this matrix.</returns>
        public override Matrix<Complex> ConjugateTranspose()
        {
            var ret = CreateMatrix(ColumnCount, RowCount);
            for (var j = 0; j < ColumnCount; j++)
            {
                for (var i = 0; i < RowCount; i++)
                {
                    ret.At(j, i, At(i, j).Conjugate());
                }
            }

            return ret;
        }

        /// <summary>
        /// Add a scalar to each element of the matrix and stores the result in the result vector.
        /// </summary>
        /// <param name="scalar">The scalar to add.</param>
        /// <param name="result">The matrix to store the result of the addition.</param>
        protected override void DoAdd(Complex scalar, Matrix<Complex> result)
        {
            for (var i = 0; i < RowCount; i++)
            {
                for (var j = 0; j < ColumnCount; j++)
                {
                    result.At(i, j, At(i, j) + scalar);
                }
            }
        }

        /// <summary>
        /// Adds another matrix to this matrix.
        /// </summary>
        /// <param name="other">The matrix to add to this matrix.</param>
        /// <param name="result">The matrix to store the result of the addition.</param>
        /// <exception cref="ArgumentNullException">If the other matrix is <see langword="null"/>.</exception>
        /// <exception cref="ArgumentOutOfRangeException">If the two matrices don't have the same dimensions.</exception>
        protected override void DoAdd(Matrix<Complex> other, Matrix<Complex> result)
        {
            for (var i = 0; i < RowCount; i++)
            {
                for (var j = 0; j < ColumnCount; j++)
                {
                    result.At(i, j, At(i, j) + other.At(i, j));
                }
            }
        }

        /// <summary>
        /// Subtracts a scalar from each element of the vector and stores the result in the result vector.
        /// </summary>
        /// <param name="scalar">The scalar to subtract.</param>
        /// <param name="result">The matrix to store the result of the subtraction.</param>
        protected override void DoSubtract(Complex scalar, Matrix<Complex> result)
        {
            for (var i = 0; i < RowCount; i++)
            {
                for (var j = 0; j < ColumnCount; j++)
                {
                    result.At(i, j, At(i, j) - scalar);
                }
            }
        }

        /// <summary>
        /// Subtracts another matrix from this matrix.
        /// </summary>
        /// <param name="other">The matrix to subtract to this matrix.</param>
        /// <param name="result">The matrix to store the result of subtraction.</param>
        /// <exception cref="ArgumentNullException">If the other matrix is <see langword="null"/>.</exception>
        /// <exception cref="ArgumentOutOfRangeException">If the two matrices don't have the same dimensions.</exception>
        protected override void DoSubtract(Matrix<Complex> other, Matrix<Complex> result)
        {
            for (var i = 0; i < RowCount; i++)
            {
                for (var j = 0; j < ColumnCount; j++)
                {
                    result.At(i, j, At(i, j) - other.At(i, j));
                }
            }
        }

        /// <summary>
        /// Multiplies each element of the matrix by a scalar and places results into the result matrix.
        /// </summary>
        /// <param name="scalar">The scalar to multiply the matrix with.</param>
        /// <param name="result">The matrix to store the result of the multiplication.</param>
        protected override void DoMultiply(Complex scalar, Matrix<Complex> result)
        {
            for (var i = 0; i < RowCount; i++)
            {
                for (var j = 0; j < ColumnCount; j++)
                {
                    result.At(i, j, At(i, j) * scalar);
                }
            }
        }

        /// <summary>
        /// Multiplies this matrix with a vector and places the results into the result vector.
        /// </summary>
        /// <param name="rightSide">The vector to multiply with.</param>
        /// <param name="result">The result of the multiplication.</param>
        protected override void DoMultiply(Vector<Complex> rightSide, Vector<Complex> result)
         {
            for (var i = 0; i < RowCount; i++)
            {
                var s = Complex.Zero;
                for (var j = 0; j != ColumnCount; j++)
                {
                    s += At(i, j) * rightSide[j];
                }

                result[i] = s;
            }
         }

        /// <summary>
        /// Multiplies this matrix with another matrix and places the results into the result matrix.
        /// </summary>
        /// <param name="other">The matrix to multiply with.</param>
        /// <param name="result">The result of the multiplication.</param>
        protected override void DoMultiply(Matrix<Complex> other, Matrix<Complex> result)
        {
            for (var j = 0; j < RowCount; j++)
            {
                for (var i = 0; i != other.ColumnCount; i++)
                {
                    var s = Complex.Zero;
                    for (var l = 0; l < ColumnCount; l++)
                    {
                        s += At(j, l) * other.At(l, i);
                    }

                    result.At(j, i, s);
                }
            }
        }

        /// <summary>
        /// Divides each element of the matrix by a scalar and places results into the result matrix.
        /// </summary>
        /// <param name="divisor">The scalar to divide the matrix with.</param>
        /// <param name="result">The matrix to store the result of the division.</param>
        protected override void DoDivide(Complex divisor, Matrix<Complex> result)
        {
            DoMultiply(1.0 / divisor, result);
        }

        /// <summary>
        /// Divides a scalar by each element of the matrix and stores the result in the result matrix.
        /// </summary>
        /// <param name="dividend">The scalar to add.</param>
        /// <param name="result">The matrix to store the result of the division.</param>
        protected override void DoDivideByThis(Complex dividend, Matrix<Complex> result)
        {
            for (var i = 0; i < RowCount; i++)
            {
                for (var j = 0; j < ColumnCount; j++)
                {
                    result.At(i, j, dividend / At(i, j));
                }
            }
        }

        /// <summary>
        /// Multiplies this matrix with transpose of another matrix and places the results into the result matrix.
        /// </summary>
        /// <param name="other">The matrix to multiply with.</param>
        /// <param name="result">The result of the multiplication.</param>
        protected override void DoTransposeAndMultiply(Matrix<Complex> other, Matrix<Complex> result)
        {
            for (var j = 0; j < other.RowCount; j++)
            {
                for (var i = 0; i < RowCount; i++)
                {
                    var s = Complex.Zero;
                    for (var l = 0; l < ColumnCount; l++)
                    {
                        s += At(i, l) * other.At(j, l);
                    }

                    result.At(i, j, s);
                }
            }
        }

        /// <summary>
        /// Multiplies the transpose of this matrix with another matrix and places the results into the result matrix.
        /// </summary>
        /// <param name="other">The matrix to multiply with.</param>
        /// <param name="result">The result of the multiplication.</param>
        protected override void DoTransposeThisAndMultiply(Matrix<Complex> other, Matrix<Complex> result)
        {
            for (var j = 0; j < other.ColumnCount; j++)
            {
                for (var i = 0; i < ColumnCount; i++)
                {
                    var s = Complex.Zero;
                    for (var l = 0; l < RowCount; l++)
                    {
                        s += At(l, i) * other.At(l, j);
                    }

                    result.At(i, j, s);
                }
            }
        }

        /// <summary>
        /// Multiplies the transpose of this matrix with a vector and places the results into the result vector.
        /// </summary>
        /// <param name="rightSide">The vector to multiply with.</param>
        /// <param name="result">The result of the multiplication.</param>
        protected override void DoTransposeThisAndMultiply(Vector<Complex> rightSide, Vector<Complex> result)
        {
            for (var i = 0; i < ColumnCount; i++)
            {
                var s = Complex.Zero;
                for (var j = 0; j != RowCount; j++)
                {
                    s += At(j, i) * rightSide[j];
                }

                result[i] = s;
            }
        }

        /// <summary>
        /// Negate each element of this matrix and place the results into the result matrix.
        /// </summary>
        /// <param name="result">The result of the negation.</param>
        protected override void DoNegate(Matrix<Complex> result)
        {
            for (var i = 0; i < RowCount; i++)
            {
                for (var j = 0; j != ColumnCount; j++)
                {
                    result.At(i, j, -At(i, j));
                }
            }
        }

        /// <summary>
        /// Complex conjugates each element of this matrix and place the results into the result matrix.
        /// </summary>
        /// <param name="result">The result of the conjugation.</param>
        protected override void DoConjugate(Matrix<Complex> result)
        {
            for (var i = 0; i < RowCount; i++)
            {
                for (var j = 0; j != ColumnCount; j++)
                {
                    result.At(i, j, At(i, j).Conjugate());
                }
            }
        }

        /// <summary>
        /// Pointwise multiplies this matrix with another matrix and stores the result into the result matrix.
        /// </summary>
        /// <param name="other">The matrix to pointwise multiply with this one.</param>
        /// <param name="result">The matrix to store the result of the pointwise multiplication.</param>
        protected override void DoPointwiseMultiply(Matrix<Complex> other, Matrix<Complex> result)
        {
            for (var j = 0; j < ColumnCount; j++)
            {
                for (var i = 0; i < RowCount; i++)
                {
                    result.At(i, j, At(i, j) * other.At(i, j));
                }
            }
        }

        /// <summary>
        /// Pointwise divide this matrix by another matrix and stores the result into the result matrix.
        /// </summary>
        /// <param name="divisor">The matrix to pointwise divide this one by.</param>
        /// <param name="result">The matrix to store the result of the pointwise division.</param>
        protected override void DoPointwiseDivide(Matrix<Complex> divisor, Matrix<Complex> result)
        {
            for (var j = 0; j < ColumnCount; j++)
            {
                for (var i = 0; i < RowCount; i++)
                {
                    result.At(i, j, At(i, j) / divisor.At(i, j));
                }
            }
        }

        /// <summary>
        /// Pointwise modulus this matrix with another matrix and stores the result into the result matrix.
        /// </summary>
        /// <param name="divisor">The pointwise denominator matrix to use</param>
        /// <param name="result">The result of the modulus.</param>
        protected override void DoPointwiseModulus(Matrix<Complex> divisor, Matrix<Complex> result)
        {
            throw new NotSupportedException();
        }

        /// <summary>
        /// Computes the modulus for each element of the matrix.
        /// </summary>
        /// <param name="divisor">The scalar denominator to use.</param>
        /// <param name="result">Matrix to store the results in.</param>
        protected override void DoModulus(Complex divisor, Matrix<Complex> result)
        {
            throw new NotSupportedException();
        }

        /// <summary>
        /// Computes the modulus for each element of the matrix.
        /// </summary>
        /// <param name="dividend">The scalar numerator to use.</param>
        /// <param name="result">Matrix to store the results in.</param>
        protected override void DoModulusByThis(Complex dividend, Matrix<Complex> result)
        {
            throw new NotSupportedException();
        }

        /// <summary>
        /// Computes the trace of this matrix.
        /// </summary>
        /// <returns>The trace of this matrix</returns>
        /// <exception cref="ArgumentException">If the matrix is not square</exception>
        public override Complex Trace()
        {
            if (RowCount != ColumnCount)
            {
                throw new ArgumentException(Resources.ArgumentMatrixSquare);
            }

            var sum = Complex.Zero;
            for (var i = 0; i < RowCount; i++)
            {
                sum += At(i, i);
            }

            return sum;
        }

        public override Cholesky<Complex> Cholesky()
        {
            return UserCholesky.Create(this);
        }

        public override LU<Complex> LU()
        {
            return UserLU.Create(this);
        }

        public override QR<Complex> QR(QRMethod method = QRMethod.Thin)
        {
            return UserQR.Create(this, method);
        }

        public override GramSchmidt<Complex> GramSchmidt()
        {
            return UserGramSchmidt.Create(this);
        }

        public override Svd<Complex> Svd(bool computeVectors = true)
        {
            return UserSvd.Create(this, computeVectors);
        }

        public override Evd<Complex> Evd()
        {
            return UserEvd.Create(this);
        }
    }
}