Example #1
0
        /// <summary>
        /// Initializes a new instance of the <see cref="UserEvd"/> class. This object will compute the
        /// the eigenvalue decomposition when the constructor is called and cache it's decomposition.
        /// </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 EVD algorithm failed to converge with matrix <paramref name="matrix"/>.</exception>
        public static UserEvd Create(Matrix<Complex32> matrix)
        {
            if (matrix.RowCount != matrix.ColumnCount)
            {
                throw new ArgumentException(Resources.ArgumentMatrixSquare);
            }

            var order = matrix.RowCount;

            // Initialize matricies for eigenvalues and eigenvectors
            var eigenVectors = DenseMatrix.CreateIdentity(order);
            var blockDiagonal = matrix.CreateMatrix(order, order);
            var eigenValues = new LinearAlgebra.Complex.DenseVector(order);

            var isSymmetric = true;

            for (var i = 0; isSymmetric && i < order; i++)
            {
                for (var j = 0; isSymmetric && j < order; j++)
                {
                    isSymmetric &= matrix.At(i, j) == matrix.At(j, i).Conjugate();
                }
            }

            if (isSymmetric)
            {
                var matrixCopy = matrix.ToArray();
                var tau = new Complex32[order];
                var d = new float[order];
                var e = new float[order];

                SymmetricTridiagonalize(matrixCopy, d, e, tau, order);
                SymmetricDiagonalize(eigenVectors, d, e, order);
                SymmetricUntridiagonalize(eigenVectors, matrixCopy, tau, order);

                for (var i = 0; i < order; i++)
                {
                    eigenValues[i] = new Complex(d[i], e[i]);
                }
            }
            else
            {
                var matrixH = matrix.ToArray();
                NonsymmetricReduceToHessenberg(eigenVectors, matrixH, order);
                NonsymmetricReduceHessenberToRealSchur(eigenVectors, eigenValues, matrixH, order);
            }

            for (var i = 0; i < eigenValues.Count; i++)
            {
                blockDiagonal.At(i, i, (Complex32) eigenValues[i]);
            }

            return new UserEvd(eigenVectors, eigenValues, blockDiagonal, isSymmetric);
        }
        /// <summary>
        /// Initializes a new instance of the <see cref="UserEvd"/> class. This object will compute the
        /// the eigenvalue decomposition when the constructor is called and cache it's decomposition.
        /// </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 EVD algorithm failed to converge with matrix <paramref name="matrix"/>.</exception>
        public UserEvd(Matrix<Complex> matrix)
        {
            if (matrix == null)
            {
                throw new ArgumentNullException("matrix");
            }

            if (matrix.RowCount != matrix.ColumnCount)
            {
                throw new ArgumentException(Resources.ArgumentMatrixSquare);
            }

            var order = matrix.RowCount;

            // Initialize matricies for eigenvalues and eigenvectors
            MatrixEv = DenseMatrix.Identity(order);
            MatrixD = matrix.CreateMatrix(order, order);
            VectorEv = new DenseVector(order);
           
            IsSymmetric = true;

            for (var i = 0; IsSymmetric && i < order; i++)
            {
                for (var j = 0; IsSymmetric && j < order; j++)
                {
                    IsSymmetric &= matrix.At(i, j) == matrix.At(j, i).Conjugate();
                }
            }

            if (IsSymmetric)
            {
                var matrixCopy = matrix.ToArray();
                var tau = new Complex[order];
                var d = new double[order];
                var e = new double[order];

                SymmetricTridiagonalize(matrixCopy, d, e, tau, order);
                SymmetricDiagonalize(d, e, order);
                SymmetricUntridiagonalize(matrixCopy, tau, order);

                for (var i = 0; i < order; i++)
                {
                    VectorEv[i] = new Complex(d[i], e[i]);
                }
            }
            else
            {
                var matrixH = matrix.ToArray();
                NonsymmetricReduceToHessenberg(matrixH, order);
                NonsymmetricReduceHessenberToRealSchur(matrixH, order);
            }

            MatrixD.SetDiagonal(VectorEv);
        }
        /// <summary>
        /// Initializes a new instance of the <see cref="UserCholesky"/> 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 UserCholesky(Matrix matrix)
        {
            if (matrix == null)
            {
                throw new ArgumentNullException("matrix");
            }

            if (matrix.RowCount != matrix.ColumnCount)
            {
                throw new ArgumentException(Resources.ArgumentMatrixSquare);
            }

            // Create a new matrix for the Cholesky factor, then perform factorization (while overwriting).
            CholeskyFactor = matrix.Clone();
            for (var j = 0; j < CholeskyFactor.RowCount; j++)
            {
                var d = 0.0;
                for (var k = 0; k < j; k++)
                {
                    var s = 0.0;
                    for (var i = 0; i < k; i++)
                    {
                        s += CholeskyFactor.At(k, i) * CholeskyFactor.At(j, i);
                    }

                    s = (matrix.At(j, k) - s) / CholeskyFactor.At(k, k);
                    CholeskyFactor.At(j, k, s);
                    d += s * s;
                }

                d = matrix.At(j, j) - d;
                if (d <= 0.0)
                {
                    throw new ArgumentException(Resources.ArgumentMatrixPositiveDefinite);
                }

                CholeskyFactor.At(j, j, Math.Sqrt(d));
                for (var k = j + 1; k < CholeskyFactor.RowCount; k++)
                {
                    CholeskyFactor.At(j, k, 0.0);
                }
            }
        }
Example #4
0
        /// <summary>
        /// Initializes a new instance of the <see cref="UserEvd"/> class. This object will compute the
        /// the eigenvalue decomposition when the constructor is called and cache it's decomposition.
        /// </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 EVD algorithm failed to converge with matrix <paramref name="matrix"/>.</exception>
        public static UserEvd Create(Matrix<float> matrix)
        {
            if (matrix.RowCount != matrix.ColumnCount)
            {
                throw new ArgumentException(Resources.ArgumentMatrixSquare);
            }

            var order = matrix.RowCount;

            // Initialize matricies for eigenvalues and eigenvectors
            var eigenVectors = Matrix<float>.Build.SameAs(matrix, order, order);
            var blockDiagonal = Matrix<float>.Build.SameAs(matrix, order, order);
            var eigenValues = new LinearAlgebra.Complex.DenseVector(order);

            var isSymmetric = true;

            for (var i = 0; isSymmetric && i < order; i++)
            {
                for (var j = 0; isSymmetric && j < order; j++)
                {
                    isSymmetric &= matrix.At(i, j) == matrix.At(j, i);
                }
            }

            var d = new float[order];
            var e = new float[order];

            if (isSymmetric)
            {
                matrix.CopyTo(eigenVectors);
                d = eigenVectors.Row(order - 1).ToArray();

                SymmetricTridiagonalize(eigenVectors, d, e, order);
                SymmetricDiagonalize(eigenVectors, d, e, order);
            }
            else
            {
                var matrixH = matrix.ToArray();

                NonsymmetricReduceToHessenberg(eigenVectors, matrixH, order);
                NonsymmetricReduceHessenberToRealSchur(eigenVectors, matrixH, d, e, order);
            }

            for (var i = 0; i < order; i++)
            {
                blockDiagonal.At(i, i, d[i]);

                if (e[i] > 0)
                {
                    blockDiagonal.At(i, i + 1, e[i]);
                }
                else if (e[i] < 0)
                {
                    blockDiagonal.At(i, i - 1, e[i]);
                }
            }

            for (var i = 0; i < order; i++)
            {
                eigenValues[i] = new Complex(d[i], e[i]);
            }

            return new UserEvd(eigenVectors, eigenValues, blockDiagonal, isSymmetric);
        }
Example #5
0
        /// <summary>
        /// Nonsymmetric reduction from Hessenberg to real Schur form.
        /// </summary>
        /// <param name="eigenVectors">The eigen vectors to work on.</param>
        /// <param name="matrixH">Array for internal storage of nonsymmetric Hessenberg form.</param>
        /// <param name="d">Arrays for internal storage of real parts of eigenvalues</param>
        /// <param name="e">Arrays for internal storage of imaginary parts of eigenvalues</param>
        /// <param name="order">Order of initial matrix</param>
        /// <remarks>This is derived from the Algol procedure hqr2,
        /// by Martin and Wilkinson, Handbook for Auto. Comp.,
        /// Vol.ii-Linear Algebra, and the corresponding
        /// Fortran subroutine in EISPACK.</remarks>
        static void NonsymmetricReduceHessenberToRealSchur(Matrix<float> eigenVectors, float[,] matrixH, float[] d, float[] e, int order)
        {
            // Initialize
            var n = order - 1;
            var eps = (float) Precision.SinglePrecision;
            var exshift = 0.0f;
            float p = 0, q = 0, r = 0, s = 0, z = 0, w, x, y;

            // Store roots isolated by balanc and compute matrix norm
            var norm = 0.0f;
            for (var i = 0; i < order; i++)
            {
                for (var j = Math.Max(i - 1, 0); j < order; j++)
                {
                    norm = norm + Math.Abs(matrixH[i, j]);
                }
            }

            // Outer loop over eigenvalue index
            var iter = 0;
            while (n >= 0)
            {
                // Look for single small sub-diagonal element
                var l = n;
                while (l > 0)
                {
                    s = Math.Abs(matrixH[l - 1, l - 1]) + Math.Abs(matrixH[l, l]);

                    if (s == 0.0f)
                    {
                        s = norm;
                    }

                    if (Math.Abs(matrixH[l, l - 1]) < eps*s)
                    {
                        break;
                    }

                    l--;
                }

                // Check for convergence
                // One root found
                if (l == n)
                {
                    matrixH[n, n] = matrixH[n, n] + exshift;
                    d[n] = matrixH[n, n];
                    e[n] = 0.0f;
                    n--;
                    iter = 0;

                    // Two roots found
                }
                else if (l == n - 1)
                {
                    w = matrixH[n, n - 1]*matrixH[n - 1, n];
                    p = (matrixH[n - 1, n - 1] - matrixH[n, n])/2.0f;
                    q = (p*p) + w;
                    z = (float) Math.Sqrt(Math.Abs(q));
                    matrixH[n, n] = matrixH[n, n] + exshift;
                    matrixH[n - 1, n - 1] = matrixH[n - 1, n - 1] + exshift;
                    x = matrixH[n, n];

                    // Real pair
                    if (q >= 0)
                    {
                        if (p >= 0)
                        {
                            z = p + z;
                        }
                        else
                        {
                            z = p - z;
                        }

                        d[n - 1] = x + z;

                        d[n] = d[n - 1];
                        if (z != 0.0f)
                        {
                            d[n] = x - (w/z);
                        }

                        e[n - 1] = 0.0f;
                        e[n] = 0.0f;
                        x = matrixH[n, n - 1];
                        s = Math.Abs(x) + Math.Abs(z);
                        p = x/s;
                        q = z/s;
                        r = (float) Math.Sqrt((p*p) + (q*q));
                        p = p/r;
                        q = q/r;

                        // Row modification
                        for (var j = n - 1; j < order; j++)
                        {
                            z = matrixH[n - 1, j];
                            matrixH[n - 1, j] = (q*z) + (p*matrixH[n, j]);
                            matrixH[n, j] = (q*matrixH[n, j]) - (p*z);
                        }

                        // Column modification
                        for (var i = 0; i <= n; i++)
                        {
                            z = matrixH[i, n - 1];
                            matrixH[i, n - 1] = (q*z) + (p*matrixH[i, n]);
                            matrixH[i, n] = (q*matrixH[i, n]) - (p*z);
                        }

                        // Accumulate transformations
                        for (var i = 0; i < order; i++)
                        {
                            z = eigenVectors.At(i, n - 1);
                            eigenVectors.At(i, n - 1, (q*z) + (p*eigenVectors.At(i, n)));
                            eigenVectors.At(i, n, (q*eigenVectors.At(i, n)) - (p*z));
                        }

                        // Complex pair
                    }
                    else
                    {
                        d[n - 1] = x + p;
                        d[n] = x + p;
                        e[n - 1] = z;
                        e[n] = -z;
                    }

                    n = n - 2;
                    iter = 0;

                    // No convergence yet
                }
                else
                {
                    // Form shift
                    x = matrixH[n, n];
                    y = 0.0f;
                    w = 0.0f;
                    if (l < n)
                    {
                        y = matrixH[n - 1, n - 1];
                        w = matrixH[n, n - 1]*matrixH[n - 1, n];
                    }

                    // Wilkinson's original ad hoc shift
                    if (iter == 10)
                    {
                        exshift += x;
                        for (var i = 0; i <= n; i++)
                        {
                            matrixH[i, i] -= x;
                        }

                        s = Math.Abs(matrixH[n, n - 1]) + Math.Abs(matrixH[n - 1, n - 2]);
                        x = y = 0.75f*s;
                        w = (-0.4375f)*s*s;
                    }

                    // MATLAB's new ad hoc shift
                    if (iter == 30)
                    {
                        s = (y - x)/2.0f;
                        s = (s*s) + w;
                        if (s > 0)
                        {
                            s = (float) Math.Sqrt(s);
                            if (y < x)
                            {
                                s = -s;
                            }

                            s = x - (w/(((y - x)/2.0f) + s));
                            for (var i = 0; i <= n; i++)
                            {
                                matrixH[i, i] -= s;
                            }

                            exshift += s;
                            x = y = w = 0.964f;
                        }
                    }

                    iter = iter + 1; // (Could check iteration count here.)

                    // Look for two consecutive small sub-diagonal elements
                    var m = n - 2;
                    while (m >= l)
                    {
                        z = matrixH[m, m];
                        r = x - z;
                        s = y - z;
                        p = (((r*s) - w)/matrixH[m + 1, m]) + matrixH[m, m + 1];
                        q = matrixH[m + 1, m + 1] - z - r - s;
                        r = matrixH[m + 2, m + 1];
                        s = Math.Abs(p) + Math.Abs(q) + Math.Abs(r);
                        p = p/s;
                        q = q/s;
                        r = r/s;

                        if (m == l)
                        {
                            break;
                        }

                        if (Math.Abs(matrixH[m, m - 1])*(Math.Abs(q) + Math.Abs(r)) < eps*(Math.Abs(p)*(Math.Abs(matrixH[m - 1, m - 1]) + Math.Abs(z) + Math.Abs(matrixH[m + 1, m + 1]))))
                        {
                            break;
                        }

                        m--;
                    }

                    for (var i = m + 2; i <= n; i++)
                    {
                        matrixH[i, i - 2] = 0.0f;
                        if (i > m + 2)
                        {
                            matrixH[i, i - 3] = 0.0f;
                        }
                    }

                    // Double QR step involving rows l:n and columns m:n
                    for (var k = m; k <= n - 1; k++)
                    {
                        bool notlast = k != n - 1;

                        if (k != m)
                        {
                            p = matrixH[k, k - 1];
                            q = matrixH[k + 1, k - 1];
                            r = notlast ? matrixH[k + 2, k - 1] : 0.0f;
                            x = Math.Abs(p) + Math.Abs(q) + Math.Abs(r);
                            if (x != 0.0f)
                            {
                                p = p/x;
                                q = q/x;
                                r = r/x;
                            }
                        }

                        if (x == 0.0f)
                        {
                            break;
                        }

                        s = (float) Math.Sqrt((p*p) + (q*q) + (r*r));
                        if (p < 0)
                        {
                            s = -s;
                        }

                        if (s != 0.0f)
                        {
                            if (k != m)
                            {
                                matrixH[k, k - 1] = (-s)*x;
                            }
                            else if (l != m)
                            {
                                matrixH[k, k - 1] = -matrixH[k, k - 1];
                            }

                            p = p + s;
                            x = p/s;
                            y = q/s;
                            z = r/s;
                            q = q/p;
                            r = r/p;

                            // Row modification
                            for (var j = k; j < order; j++)
                            {
                                p = matrixH[k, j] + (q*matrixH[k + 1, j]);

                                if (notlast)
                                {
                                    p = p + (r*matrixH[k + 2, j]);
                                    matrixH[k + 2, j] = matrixH[k + 2, j] - (p*z);
                                }

                                matrixH[k, j] = matrixH[k, j] - (p*x);
                                matrixH[k + 1, j] = matrixH[k + 1, j] - (p*y);
                            }

                            // Column modification
                            for (var i = 0; i <= Math.Min(n, k + 3); i++)
                            {
                                p = (x*matrixH[i, k]) + (y*matrixH[i, k + 1]);

                                if (notlast)
                                {
                                    p = p + (z*matrixH[i, k + 2]);
                                    matrixH[i, k + 2] = matrixH[i, k + 2] - (p*r);
                                }

                                matrixH[i, k] = matrixH[i, k] - p;
                                matrixH[i, k + 1] = matrixH[i, k + 1] - (p*q);
                            }

                            // Accumulate transformations
                            for (var i = 0; i < order; i++)
                            {
                                p = (x*eigenVectors.At(i, k)) + (y*eigenVectors.At(i, k + 1));

                                if (notlast)
                                {
                                    p = p + (z*eigenVectors.At(i, k + 2));
                                    eigenVectors.At(i, k + 2, eigenVectors.At(i, k + 2) - (p*r));
                                }

                                eigenVectors.At(i, k, eigenVectors.At(i, k) - p);
                                eigenVectors.At(i, k + 1, eigenVectors.At(i, k + 1) - (p*q));
                            }
                        } // (s != 0)
                    } // k loop
                } // check convergence
            } // while (n >= low)

            // Backsubstitute to find vectors of upper triangular form
            if (norm == 0.0f)
            {
                return;
            }

            for (n = order - 1; n >= 0; n--)
            {
                float t;

                p = d[n];
                q = e[n];

                // Real vector
                if (q == 0.0f)
                {
                    var l = n;
                    matrixH[n, n] = 1.0f;
                    for (var i = n - 1; i >= 0; i--)
                    {
                        w = matrixH[i, i] - p;
                        r = 0.0f;
                        for (var j = l; j <= n; j++)
                        {
                            r = r + (matrixH[i, j]*matrixH[j, n]);
                        }

                        if (e[i] < 0.0f)
                        {
                            z = w;
                            s = r;
                        }
                        else
                        {
                            l = i;
                            if (e[i] == 0.0f)
                            {
                                if (w != 0.0f)
                                {
                                    matrixH[i, n] = (-r)/w;
                                }
                                else
                                {
                                    matrixH[i, n] = (-r)/(eps*norm);
                                }

                                // Solve real equations
                            }
                            else
                            {
                                x = matrixH[i, i + 1];
                                y = matrixH[i + 1, i];
                                q = ((d[i] - p)*(d[i] - p)) + (e[i]*e[i]);
                                t = ((x*s) - (z*r))/q;
                                matrixH[i, n] = t;
                                if (Math.Abs(x) > Math.Abs(z))
                                {
                                    matrixH[i + 1, n] = (-r - (w*t))/x;
                                }
                                else
                                {
                                    matrixH[i + 1, n] = (-s - (y*t))/z;
                                }
                            }

                            // Overflow control
                            t = Math.Abs(matrixH[i, n]);
                            if ((eps*t)*t > 1)
                            {
                                for (var j = i; j <= n; j++)
                                {
                                    matrixH[j, n] = matrixH[j, n]/t;
                                }
                            }
                        }
                    }

                    // Complex vector
                }
                else if (q < 0)
                {
                    var l = n - 1;

                    // Last vector component imaginary so matrix is triangular
                    if (Math.Abs(matrixH[n, n - 1]) > Math.Abs(matrixH[n - 1, n]))
                    {
                        matrixH[n - 1, n - 1] = q/matrixH[n, n - 1];
                        matrixH[n - 1, n] = (-(matrixH[n, n] - p))/matrixH[n, n - 1];
                    }
                    else
                    {
                        var res = Cdiv(0.0f, -matrixH[n - 1, n], matrixH[n - 1, n - 1] - p, q);
                        matrixH[n - 1, n - 1] = res.Real;
                        matrixH[n - 1, n] = res.Imaginary;
                    }

                    matrixH[n, n - 1] = 0.0f;
                    matrixH[n, n] = 1.0f;
                    for (var i = n - 2; i >= 0; i--)
                    {
                        float ra = 0.0f;
                        float sa = 0.0f;
                        for (var j = l; j <= n; j++)
                        {
                            ra = ra + (matrixH[i, j]*matrixH[j, n - 1]);
                            sa = sa + (matrixH[i, j]*matrixH[j, n]);
                        }

                        w = matrixH[i, i] - p;

                        if (e[i] < 0.0f)
                        {
                            z = w;
                            r = ra;
                            s = sa;
                        }
                        else
                        {
                            l = i;
                            if (e[i] == 0.0f)
                            {
                                var res = Cdiv(-ra, -sa, w, q);
                                matrixH[i, n - 1] = res.Real;
                                matrixH[i, n] = res.Imaginary;
                            }
                            else
                            {
                                // Solve complex equations
                                x = matrixH[i, i + 1];
                                y = matrixH[i + 1, i];

                                float vr = ((d[i] - p)*(d[i] - p)) + (e[i]*e[i]) - (q*q);
                                float vi = (d[i] - p)*2.0f*q;
                                if ((vr == 0.0f) && (vi == 0.0f))
                                {
                                    vr = eps*norm*(Math.Abs(w) + Math.Abs(q) + Math.Abs(x) + Math.Abs(y) + Math.Abs(z));
                                }

                                var res = Cdiv((x*r) - (z*ra) + (q*sa), (x*s) - (z*sa) - (q*ra), vr, vi);
                                matrixH[i, n - 1] = res.Real;
                                matrixH[i, n] = res.Imaginary;
                                if (Math.Abs(x) > (Math.Abs(z) + Math.Abs(q)))
                                {
                                    matrixH[i + 1, n - 1] = (-ra - (w*matrixH[i, n - 1]) + (q*matrixH[i, n]))/x;
                                    matrixH[i + 1, n] = (-sa - (w*matrixH[i, n]) - (q*matrixH[i, n - 1]))/x;
                                }
                                else
                                {
                                    res = Cdiv(-r - (y*matrixH[i, n - 1]), -s - (y*matrixH[i, n]), z, q);
                                    matrixH[i + 1, n - 1] = res.Real;
                                    matrixH[i + 1, n] = res.Imaginary;
                                }
                            }

                            // Overflow control
                            t = Math.Max(Math.Abs(matrixH[i, n - 1]), Math.Abs(matrixH[i, n]));
                            if ((eps*t)*t > 1)
                            {
                                for (var j = i; j <= n; j++)
                                {
                                    matrixH[j, n - 1] = matrixH[j, n - 1]/t;
                                    matrixH[j, n] = matrixH[j, n]/t;
                                }
                            }
                        }
                    }
                }
            }

            // Back transformation to get eigenvectors of original matrix
            for (var j = order - 1; j >= 0; j--)
            {
                for (var i = 0; i < order; i++)
                {
                    z = 0.0f;
                    for (var k = 0; k <= j; k++)
                    {
                        z = z + (eigenVectors.At(i, k)*matrixH[k, j]);
                    }

                    eigenVectors.At(i, j, z);
                }
            }
        }
Example #6
0
        /// <summary>
        /// Symmetric Householder reduction to tridiagonal form.
        /// </summary>
        /// <param name="eigenVectors">The eigen vectors to work on.</param>
        /// <param name="d">Arrays for internal storage of real parts of eigenvalues</param>
        /// <param name="e">Arrays for internal storage of imaginary parts of eigenvalues</param>
        /// <param name="order">Order of initial matrix</param>
        /// <remarks>This is derived from the Algol procedures tred2 by 
        /// Bowdler, Martin, Reinsch, and Wilkinson, Handbook for 
        /// Auto. Comp., Vol.ii-Linear Algebra, and the corresponding 
        /// Fortran subroutine in EISPACK.</remarks>
        static void SymmetricTridiagonalize(Matrix<float> eigenVectors, float[] d, float[] e, int order)
        {
            // Householder reduction to tridiagonal form.
            for (var i = order - 1; i > 0; i--)
            {
                // Scale to avoid under/overflow.
                var scale = 0.0f;
                var h = 0.0f;

                for (var k = 0; k < i; k++)
                {
                    scale = scale + Math.Abs(d[k]);
                }

                if (scale == 0.0f)
                {
                    e[i] = d[i - 1];
                    for (var j = 0; j < i; j++)
                    {
                        d[j] = eigenVectors.At(i - 1, j);
                        eigenVectors.At(i, j, 0.0f);
                        eigenVectors.At(j, i, 0.0f);
                    }
                }
                else
                {
                    // Generate Householder vector.
                    for (var k = 0; k < i; k++)
                    {
                        d[k] /= scale;
                        h += d[k]*d[k];
                    }

                    var f = d[i - 1];
                    var g = (float) Math.Sqrt(h);
                    if (f > 0)
                    {
                        g = -g;
                    }

                    e[i] = scale*g;
                    h = h - (f*g);
                    d[i - 1] = f - g;

                    for (var j = 0; j < i; j++)
                    {
                        e[j] = 0.0f;
                    }

                    // Apply similarity transformation to remaining columns.
                    for (var j = 0; j < i; j++)
                    {
                        f = d[j];
                        eigenVectors.At(j, i, f);
                        g = e[j] + (eigenVectors.At(j, j)*f);

                        for (var k = j + 1; k <= i - 1; k++)
                        {
                            g += eigenVectors.At(k, j)*d[k];
                            e[k] += eigenVectors.At(k, j)*f;
                        }

                        e[j] = g;
                    }

                    f = 0.0f;

                    for (var j = 0; j < i; j++)
                    {
                        e[j] /= h;
                        f += e[j]*d[j];
                    }

                    var hh = f/(h + h);

                    for (var j = 0; j < i; j++)
                    {
                        e[j] -= hh*d[j];
                    }

                    for (var j = 0; j < i; j++)
                    {
                        f = d[j];
                        g = e[j];

                        for (var k = j; k <= i - 1; k++)
                        {
                            eigenVectors.At(k, j, eigenVectors.At(k, j) - (f*e[k]) - (g*d[k]));
                        }

                        d[j] = eigenVectors.At(i - 1, j);
                        eigenVectors.At(i, j, 0.0f);
                    }
                }

                d[i] = h;
            }

            // Accumulate transformations.
            for (var i = 0; i < order - 1; i++)
            {
                eigenVectors.At(order - 1, i, eigenVectors.At(i, i));
                eigenVectors.At(i, i, 1.0f);
                var h = d[i + 1];
                if (h != 0.0f)
                {
                    for (var k = 0; k <= i; k++)
                    {
                        d[k] = eigenVectors.At(k, i + 1)/h;
                    }

                    for (var j = 0; j <= i; j++)
                    {
                        var g = 0.0f;
                        for (var k = 0; k <= i; k++)
                        {
                            g += eigenVectors.At(k, i + 1)*eigenVectors.At(k, j);
                        }

                        for (var k = 0; k <= i; k++)
                        {
                            eigenVectors.At(k, j, eigenVectors.At(k, j) - g*d[k]);
                        }
                    }
                }

                for (var k = 0; k <= i; k++)
                {
                    eigenVectors.At(k, i + 1, 0.0f);
                }
            }

            for (var j = 0; j < order; j++)
            {
                d[j] = eigenVectors.At(order - 1, j);
                eigenVectors.At(order - 1, j, 0.0f);
            }

            eigenVectors.At(order - 1, order - 1, 1.0f);
            e[0] = 0.0f;
        }
        /// <summary>
        /// Calculate Cholesky step
        /// </summary>
        /// <param name="data">Factor matrix</param>
        /// <param name="rowDim">Number of rows</param>
        /// <param name="firstCol">Column start</param>
        /// <param name="colLimit">Total columns</param>
        /// <param name="multipliers">Multipliers calculated previously</param>
        /// <param name="availableCores">Number of available processors</param>
        private static void DoCholeskyStep(Matrix<Complex32> data, int rowDim, int firstCol, int colLimit, Complex32[] multipliers, int availableCores)
        {
            var tmpColCount = colLimit - firstCol;

            if ((availableCores > 1) && (tmpColCount > 200))
            {
                var tmpSplit = firstCol + (tmpColCount / 3);
                var tmpCores = availableCores / 2;

                CommonParallel.Invoke(
                    () => DoCholeskyStep(data, rowDim, firstCol, tmpSplit, multipliers, tmpCores),
                    () => DoCholeskyStep(data, rowDim, tmpSplit, colLimit, multipliers, tmpCores));
            }
            else
            {
                for (var j = firstCol; j < colLimit; j++)
                {
                    var tmpVal = multipliers[j];
                    for (var i = j; i < rowDim; i++)
                    {
                        data.At(i, j, data.At(i, j) - (multipliers[i] * tmpVal.Conjugate()));
                    }
                }
            }
        }
        /// <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)
        {
            var diagonalOther = other as DiagonalMatrix;
            var diagonalResult = result as DiagonalMatrix;
            if (diagonalOther != null && diagonalResult != null)
            {
                var thisDataCopy = new Complex[diagonalResult._data.Length];
                var otherDataCopy = new Complex[diagonalResult._data.Length];
                Array.Copy(_data, thisDataCopy, (diagonalResult._data.Length > _data.Length) ? _data.Length : diagonalResult._data.Length);
                Array.Copy(diagonalOther._data, otherDataCopy, (diagonalResult._data.Length > diagonalOther._data.Length) ? diagonalOther._data.Length : diagonalResult._data.Length);
                Control.LinearAlgebraProvider.PointWiseMultiplyArrays(thisDataCopy, otherDataCopy, diagonalResult._data);
                return;
            }

            var denseOther = other.Storage as DenseColumnMajorMatrixStorage<Complex>;
            if (denseOther != null)
            {
                var dense = denseOther.Data;
                var diagonal = _data;
                var d = Math.Min(denseOther.RowCount, ColumnCount);
                if (d < ColumnCount)
                {
                    result.ClearSubMatrix(denseOther.RowCount, ColumnCount - denseOther.RowCount, 0, denseOther.ColumnCount);
                }
                int index = 0;
                for (int i = 0; i < denseOther.ColumnCount; i++)
                {
                    for (int j = 0; j < d; j++)
                    {
                        result.At(j, i, dense[index]*diagonal[j]);
                        index++;
                    }
                    index += (denseOther.RowCount - d);
                }
                return;
            }

            base.DoTransposeThisAndMultiply(other, result);
        }
        /// <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)
        {
            var diagResult = result as DiagonalMatrix;
            if (diagResult != null)
            {
                Control.LinearAlgebraProvider.ScaleArray(-1, _data, diagResult._data);
                return;
            }

            result.Clear();
            for (var i = 0; i < _data.Length; i++)
            {
                result.At(i, i, -_data[i]);
            }
        }
Example #10
0
        /// <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<float> other, Matrix<float> result)
        {
            var sparseOther = other as SparseMatrix;
            var sparseResult = result as SparseMatrix;
            if (sparseOther == null || sparseResult == null)
            {
                base.DoAdd(other, result);
                return;
            }

            if (ReferenceEquals(this, other))
            {
                if (!ReferenceEquals(this, result))
                {
                    CopyTo(result);
                }

                Control.LinearAlgebraProvider.ScaleArray(2.0f, _storage.Values, _storage.Values);
                return;
            }

            SparseMatrix left;

            if (ReferenceEquals(sparseOther, sparseResult))
            {
                left = this;
            }
            else if (ReferenceEquals(this, sparseResult))
            {
                left = sparseOther;
            }
            else
            {
                CopyTo(sparseResult);
                left = sparseOther;
            }

            var leftStorage = left._storage;
            for (var i = 0; i < leftStorage.RowCount; i++)
            {
                var endIndex = leftStorage.RowPointers[i + 1];
                for (var j = leftStorage.RowPointers[i]; j < endIndex; j++)
                {
                    var columnIndex = leftStorage.ColumnIndices[j];
                    var resVal = leftStorage.Values[j] + result.At(i, columnIndex);
                    result.At(i, columnIndex, resVal);
                }
            }
        }
Example #11
0
        /// <summary>
        /// Puts the upper triangle of this matrix into the result matrix.
        /// </summary>
        /// <param name="result">Where to store the lower triangle.</param>
        private void UpperTriangleImpl(Matrix<float> result)
        {
            var rowPointers = _storage.RowPointers;
            var columnIndices = _storage.ColumnIndices;
            var values = _storage.Values;

            for (var row = 0; row < result.RowCount; row++)
            {
                var endIndex = rowPointers[row + 1];
                for (var j = rowPointers[row]; j < endIndex; j++)
                {
                    if (row <= columnIndices[j])
                    {
                        result.At(row, columnIndices[j], values[j]);
                    }
                }
            }
        }
Example #12
0
        /// <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<float> other, Matrix<float> result)
        {
            var otherSparse = other as SparseMatrix;
            var resultSparse = result as SparseMatrix;

            if (otherSparse == null || resultSparse == null)
            {
                base.DoTransposeAndMultiply(other, result);
                return;
            }

            resultSparse.Clear();

            var rowPointers = _storage.RowPointers;
            var values = _storage.Values;

            var otherStorage = otherSparse._storage;

            for (var j = 0; j < RowCount; j++)
            {
                var startIndexOther = otherStorage.RowPointers[j];
                var endIndexOther = otherStorage.RowPointers[j + 1];

                if (startIndexOther == endIndexOther)
                {
                    continue;
                }

                for (var i = 0; i < RowCount; i++)
                {
                    // Multiply row of matrix A on row of matrix B

                    var startIndexThis = rowPointers[i];
                    var endIndexThis = rowPointers[i + 1];

                    if (startIndexThis == endIndexThis)
                    {
                        continue;
                    }

                    var sum = 0f;
                    for (var index = startIndexOther; index < endIndexOther; index++)
                    {
                        var ind = _storage.FindItem(i, otherStorage.ColumnIndices[index]);
                        if (ind >= 0)
                        {
                            sum += otherStorage.Values[index]*values[ind];
                        }
                    }

                    resultSparse._storage.At(i, j, sum + result.At(i, j));
                }
            }
        }
Example #13
0
        /// <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<float> other, Matrix<float> result)
        {
            var sparseOther = other as SparseMatrix;
            var sparseResult = result as SparseMatrix;
            if (sparseOther == null || sparseResult == null)
            {
                base.DoSubtract(other, result);
                return;
            }

            if (ReferenceEquals(this, other))
            {
                result.Clear();
                return;
            }

            var otherStorage = sparseOther._storage;

            if (ReferenceEquals(this, sparseResult))
            {
                for (var i = 0; i < otherStorage.RowCount; i++)
                {
                    var endIndex = otherStorage.RowPointers[i + 1];
                    for (var j = otherStorage.RowPointers[i]; j < endIndex; j++)
                    {
                        var columnIndex = otherStorage.ColumnIndices[j];
                        var resVal = sparseResult.At(i, columnIndex) - otherStorage.Values[j];
                        result.At(i, columnIndex, resVal);
                    }
                }
            }
            else
            {
                if (!ReferenceEquals(sparseOther, sparseResult))
                {
                    sparseOther.CopyTo(sparseResult);
                }

                sparseResult.Negate(sparseResult);

                var rowPointers = _storage.RowPointers;
                var columnIndices = _storage.ColumnIndices;
                var values = _storage.Values;

                for (var i = 0; i < RowCount; i++)
                {
                    var endIndex = rowPointers[i + 1];
                    for (var j = rowPointers[i]; j < endIndex; j++)
                    {
                        var columnIndex = columnIndices[j];
                        var resVal = sparseResult.At(i, columnIndex) + values[j];
                        result.At(i, columnIndex, resVal);
                    }
                }
            }
        }
Example #14
0
        /// <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<float> other, Matrix<float> result)
        {
            result.Clear();

            var rowPointers = _storage.RowPointers;
            var columnIndices = _storage.ColumnIndices;
            var values = _storage.Values;

            for (var i = 0; i < RowCount; i++)
            {
                var endIndex = rowPointers[i + 1];
                for (var j = rowPointers[i]; j < endIndex; j++)
                {
                    var resVal = values[j]*other.At(i, columnIndices[j]);
                    if (resVal != 0f)
                    {
                        result.At(i, columnIndices[j], resVal);
                    }
                }
            }
        }
Example #15
0
        /// <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<float> divisor, Matrix<float> result)
        {
            result.Clear();

            var rowPointers = _storage.RowPointers;
            var columnIndices = _storage.ColumnIndices;
            var values = _storage.Values;

            for (var i = 0; i < RowCount; i++)
            {
                var endIndex = rowPointers[i + 1];
                for (var j = rowPointers[i]; j < endIndex; j++)
                {
                    if (values[j] != 0f)
                    {
                        result.At(i, columnIndices[j], values[j]/divisor.At(i, columnIndices[j]));
                    }
                }
            }
        }
Example #16
0
        /// <summary>
        /// Initializes a new instance of the <see cref="SparseMatrix"/> class, copying
        /// the values from the given matrix.
        /// </summary>
        /// <param name="matrix">The matrix to copy.</param>
        public SparseMatrix(Matrix<Complex> matrix)
            : this(matrix.RowCount, matrix.ColumnCount)
        {
            var sparseMatrix = matrix as SparseMatrix;

            var rows = matrix.RowCount;
            var columns = matrix.ColumnCount;

            if (sparseMatrix == null)
            {
                for (var i = 0; i < rows; i++)
                {
                    for (var j = 0; j < columns; j++)
                    {
                        SetValueAt(i, j, matrix.At(i, j));
                    }
                }
            }
            else
            {
                NonZerosCount = sparseMatrix.NonZerosCount;
                _rowIndex = new int[rows];
                _columnIndices = new int[NonZerosCount];
                _nonZeroValues = new Complex[NonZerosCount];

                Array.Copy(sparseMatrix._nonZeroValues, _nonZeroValues, NonZerosCount);
                Array.Copy(sparseMatrix._columnIndices, _columnIndices, NonZerosCount);
                Array.Copy(sparseMatrix._rowIndex, _rowIndex, rows);
            }
        }
        /// <summary>
        /// Puts the upper triangle of this matrix into the result matrix.
        /// </summary>
        /// <param name="result">Where to store the lower triangle.</param>
        /// <exception cref="ArgumentException">If the result matrix's dimensions are not the same as this matrix.</exception>
        public override void UpperTriangle(Matrix<Complex> result)
        {
            if (result.RowCount != RowCount || result.ColumnCount != ColumnCount)
            {
                throw DimensionsDontMatch<ArgumentException>(this, result, "result");
            }

            result.Clear();
            for (var i = 0; i < _data.Length; i++)
            {
                result.At(i, i, _data[i]);
            }
        }
Example #18
0
        /// <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)
        {
            var sparseOther = other as SparseMatrix;
            var sparseResult = result as SparseMatrix;
            if (sparseOther == null || sparseResult == null)
            {
                base.DoAdd(other, result);
                return;
            }

            if (ReferenceEquals(this, other))
            {
                if (!ReferenceEquals(this, result))
                {
                    CopyTo(result);
                }

                Control.LinearAlgebraProvider.ScaleArray(2.0, _nonZeroValues, _nonZeroValues);
                return;
            }

            SparseMatrix left;

            if (ReferenceEquals(sparseOther, sparseResult))
            {
                left = this;
            }
            else if (ReferenceEquals(this, sparseResult))
            {
                left = sparseOther;
            }
            else
            {
                CopyTo(sparseResult);
                left = sparseOther;
            }

            for (var i = 0; i < left.RowCount; i++)
            {
                // Get the begin / end index for the current row
                var startIndex = left._rowIndex[i];
                var endIndex = i < left._rowIndex.Length - 1 ? left._rowIndex[i + 1] : left.NonZerosCount;

                for (var j = startIndex; j < endIndex; j++)
                {
                    var columnIndex = left._columnIndices[j];
                    var resVal = left._nonZeroValues[j] + result.At(i, columnIndex);
                    result.At(i, columnIndex, resVal);
                }
            }
        }
        /// <summary>
        /// Subtracts another matrix from this matrix.
        /// </summary>
        /// <param name="other">The matrix to subtract.</param>
        /// <param name="result">The matrix to store the result of the subtraction.</param>
        /// <exception cref="ArgumentOutOfRangeException">If the two matrices don't have the same dimensions.</exception>
        protected override void DoSubtract(Matrix<Complex> other, Matrix<Complex> result)
        {
            // diagonal - diagonal = diagonal
            var diagOther = other as DiagonalMatrix;
            var diagResult = result as DiagonalMatrix;
            if (diagOther != null && diagResult != null)
            {
                Control.LinearAlgebraProvider.SubtractArrays(_data, diagOther._data, diagResult._data);
                return;
            }

            other.Negate(result);
            for (int i = 0; i < _data.Length; i++)
            {
                result.At(i, i, result.At(i, i) + _data[i]);
            }
        }
Example #20
0
        /// <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)
        {
            if (scalar == 1.0)
            {
                CopyTo(result);
                return;
            }

            if (scalar == 0.0 || NonZerosCount == 0)
            {
                result.Clear();
                return;
            }

            var sparseResult = result as SparseMatrix;
            if (sparseResult == null)
            {
                result.Clear();

                for (var row = 0; row < RowCount; row++)
                {
                    var start = _rowIndex[row];
                    var end = _rowIndex[row + 1];

                    if (start == end)
                    {
                        continue;
                    }

                    for (var index = start; index < end; index++)
                    {
                        var column = _columnIndices[index];
                        result.At(row, column, _nonZeroValues[index] * scalar);
                    }
                }
            }
            else
            {
                if (!ReferenceEquals(this, result))
                {
                    CopyTo(sparseResult);
                }

                CommonParallel.For(0, NonZerosCount, index => sparseResult._nonZeroValues[index] *= scalar);
            }
        }
Example #21
0
        /// <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<Complex32> input, Matrix<Complex32> result)
        {
            if (input == null)
            {
                throw new ArgumentNullException("input");
            }

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

            // Check for proper dimensions.
            if (result.RowCount != input.RowCount)
            {
                throw new ArgumentException(Resources.ArgumentMatrixSameRowDimension);
            }

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

            if (input.RowCount != CholeskyFactor.RowCount)
            {
                throw new ArgumentException(Resources.ArgumentMatrixDimensions);
            }

            input.CopyTo(result);
            var order = CholeskyFactor.RowCount;

            for (var c = 0; c < result.ColumnCount; c++)
            {
                // Solve L*Y = B;
                Complex32 sum;
                for (var i = 0; i < order; i++)
                {
                    sum = result.At(i, c);
                    for (var k = i - 1; k >= 0; k--)
                    {
                        sum -= CholeskyFactor.At(i, k) * result.At(k, c);
                    }

                    result.At(i, c, sum / CholeskyFactor.At(i, i));
                }

                // Solve L'*X = Y;
                for (var i = order - 1; i >= 0; i--)
                {
                    sum = result.At(i, c);
                    for (var k = i + 1; k < order; k++)
                    {
                        sum -= CholeskyFactor.At(k, i).Conjugate() * result.At(k, c);
                    }

                    result.At(i, c, sum / CholeskyFactor.At(i, i));
                }
            }
        }
Example #22
0
        /// <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)
        {
            var columnVector = new DenseVector(other.RowCount);
            for (var row = 0; row < RowCount; row++)
            {
                // Get the begin / end index for the current row
                var startIndex = _rowIndex[row];
                var endIndex = row < _rowIndex.Length - 1 ? _rowIndex[row + 1] : NonZerosCount;
                if (startIndex == endIndex)
                {
                    continue;
                }

                for (var column = 0; column < other.ColumnCount; column++)
                {
                    // Multiply row of matrix A on column of matrix B
                    other.Column(column, columnVector);

                    var sum = Complex.Zero;
                    for (var index = startIndex; index < endIndex; index++)
                    {
                        sum += _nonZeroValues[index] * columnVector[_columnIndices[index]];
                    }

                    result.At(row, column, sum);
                }
            }
        }
        /// <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 (MatrixQ.RowCount != input.RowCount)
            {
                throw new ArgumentException(Resources.ArgumentMatrixSameRowDimension);
            }

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

            var inputCopy = input.Clone();
            
            // Compute Y = transpose(Q)*B
            var column = new Complex32[MatrixQ.RowCount];
            for (var j = 0; j < input.ColumnCount; j++)
            {
                for (var k = 0; k < MatrixQ.RowCount; k++)
                {
                    column[k] = inputCopy.At(k, j);
                }

                for (var i = 0; i < MatrixQ.ColumnCount; i++)
                {
                    var s = Complex32.Zero;
                    for (var k = 0; k < MatrixQ.RowCount; k++)
                    {
                        s += MatrixQ.At(k, i).Conjugate() * column[k];
                    }

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

            // Solve R*X = Y;
            for (var k = MatrixQ.ColumnCount - 1; k >= 0; k--)
            {
                for (var j = 0; j < input.ColumnCount; j++)
                {
                    inputCopy.At(k, j, inputCopy.At(k, j) / MatrixR.At(k, k));
                }

                for (var i = 0; i < k; i++)
                {
                    for (var j = 0; j < input.ColumnCount; j++)
                    {
                        inputCopy.At(i, j, inputCopy.At(i, j) - (inputCopy.At(k, j) * MatrixR.At(i, k)));
                    }
                }
            }

            for (var i = 0; i < MatrixR.ColumnCount; i++)
            {
                for (var j = 0; j < input.ColumnCount; j++)
                {
                    result.At(i, j, inputCopy.At(i, j));
                }
            }
        }
Example #24
0
        /// <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)
        {
            result.Clear();

            for (var i = 0; i < other.RowCount; i++)
            {
                // Get the begin / end index for the current row
                var startIndex = _rowIndex[i];
                var endIndex = i < _rowIndex.Length - 1 ? _rowIndex[i + 1] : NonZerosCount;

                for (var j = startIndex; j < endIndex; j++)
                {
                    var resVal = _nonZeroValues[j] * other.At(i, _columnIndices[j]);
                    if (resVal != 0.0)
                    {
                        result.At(i, _columnIndices[j], resVal);
                    }
                }
            }
        }
Example #25
0
        /// <summary>
        /// Solves a system of linear equations, <b>AX = B</b>, with A SVD 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<float> input, Matrix<float> 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 (EigenValues.Count != input.RowCount)
            {
                throw new ArgumentException(Resources.ArgumentMatrixSameRowDimension);
            }

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

            if (IsSymmetric)
            {
                var order = EigenValues.Count;
                var tmp = new float[order];

                for (var k = 0; k < order; k++)
                {
                    for (var j = 0; j < order; j++)
                    {
                        float value = 0;
                        if (j < order)
                        {
                            for (var i = 0; i < order; i++)
                            {
                                value += EigenVectors.At(i, j)*input.At(i, k);
                            }

                            value /= (float) EigenValues[j].Real;
                        }

                        tmp[j] = value;
                    }

                    for (var j = 0; j < order; j++)
                    {
                        float value = 0;
                        for (var i = 0; i < order; i++)
                        {
                            value += EigenVectors.At(j, i)*tmp[i];
                        }

                        result.At(j, k, value);
                    }
                }
            }
            else
            {
                throw new ArgumentException(Resources.ArgumentMatrixSymmetric);
            }
        }
Example #26
0
        /// <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)
        {
            var sparseOther = other as SparseMatrix;
            var sparseResult = result as SparseMatrix;
            if (sparseOther == null || sparseResult == null)
            {
                base.DoSubtract(other, result);
                return;
            }

            if (ReferenceEquals(this, other))
            {
                result.Clear();
                return;
            }

            if (ReferenceEquals(this, sparseResult))
            {
                for (var i = 0; i < sparseOther.RowCount; i++)
                {
                    // Get the begin / end index for the current row
                    var startIndex = sparseOther._rowIndex[i];
                    var endIndex = i < sparseOther._rowIndex.Length - 1 ? sparseOther._rowIndex[i + 1] : sparseOther.NonZerosCount;

                    for (var j = startIndex; j < endIndex; j++)
                    {
                        var columnIndex = sparseOther._columnIndices[j];
                        var resVal = sparseResult.At(i, columnIndex) - sparseOther._nonZeroValues[j];
                        result.At(i, columnIndex, resVal);
                    }
                }
            }
            else
            {
                if (!ReferenceEquals(sparseOther, sparseResult))
                {
                    sparseOther.CopyTo(sparseResult);
                }

                sparseResult.Negate(sparseResult);

                for (var i = 0; i < RowCount; i++)
                {
                    // Get the begin / end index for the current row
                    var startIndex = _rowIndex[i];
                    var endIndex = i < _rowIndex.Length - 1 ? _rowIndex[i + 1] : NonZerosCount;

                    for (var j = startIndex; j < endIndex; j++)
                    {
                        var columnIndex = _columnIndices[j];
                        var resVal = sparseResult.At(i, columnIndex) + _nonZeroValues[j];
                        result.At(i, columnIndex, resVal);
                    }
                }
            }
        }
Example #27
0
        /// <summary>
        /// Nonsymmetric reduction to Hessenberg form.
        /// </summary>
        /// <param name="eigenVectors">The eigen vectors to work on.</param>
        /// <param name="matrixH">Array for internal storage of nonsymmetric Hessenberg form.</param>
        /// <param name="order">Order of initial matrix</param>
        /// <remarks>This is derived from the Algol procedures orthes and ortran,
        /// by Martin and Wilkinson, Handbook for Auto. Comp.,
        /// Vol.ii-Linear Algebra, and the corresponding
        /// Fortran subroutines in EISPACK.</remarks>
        static void NonsymmetricReduceToHessenberg(Matrix<float> eigenVectors, float[,] matrixH, int order)
        {
            var ort = new float[order];

            for (var m = 1; m < order - 1; m++)
            {
                // Scale column.
                var scale = 0.0f;
                for (var i = m; i < order; i++)
                {
                    scale = scale + Math.Abs(matrixH[i, m - 1]);
                }

                if (scale != 0.0f)
                {
                    // Compute Householder transformation.
                    var h = 0.0f;
                    for (var i = order - 1; i >= m; i--)
                    {
                        ort[i] = matrixH[i, m - 1]/scale;
                        h += ort[i]*ort[i];
                    }

                    var g = (float) Math.Sqrt(h);
                    if (ort[m] > 0)
                    {
                        g = -g;
                    }

                    h = h - (ort[m]*g);
                    ort[m] = ort[m] - g;

                    // Apply Householder similarity transformation
                    // H = (I-u*u'/h)*H*(I-u*u')/h)
                    for (var j = m; j < order; j++)
                    {
                        var f = 0.0f;
                        for (var i = order - 1; i >= m; i--)
                        {
                            f += ort[i]*matrixH[i, j];
                        }

                        f = f/h;
                        for (var i = m; i < order; i++)
                        {
                            matrixH[i, j] -= f*ort[i];
                        }
                    }

                    for (var i = 0; i < order; i++)
                    {
                        var f = 0.0f;
                        for (var j = order - 1; j >= m; j--)
                        {
                            f += ort[j]*matrixH[i, j];
                        }

                        f = f/h;
                        for (var j = m; j < order; j++)
                        {
                            matrixH[i, j] -= f*ort[j];
                        }
                    }

                    ort[m] = scale*ort[m];
                    matrixH[m, m - 1] = scale*g;
                }
            }

            // Accumulate transformations (Algol's ortran).
            for (var i = 0; i < order; i++)
            {
                for (var j = 0; j < order; j++)
                {
                    eigenVectors.At(i, j, i == j ? 1.0f : 0.0f);
                }
            }

            for (var m = order - 2; m >= 1; m--)
            {
                if (matrixH[m, m - 1] != 0.0f)
                {
                    for (var i = m + 1; i < order; i++)
                    {
                        ort[i] = matrixH[i, m - 1];
                    }

                    for (var j = m; j < order; j++)
                    {
                        var g = 0.0f;
                        for (var i = m; i < order; i++)
                        {
                            g += ort[i]*eigenVectors.At(i, j);
                        }

                        // Double division avoids possible underflow
                        g = (g/ort[m])/matrixH[m, m - 1];
                        for (var i = m; i < order; i++)
                        {
                            eigenVectors.At(i, j, eigenVectors.At(i, j) + g*ort[i]);
                        }
                    }
                }
            }
        }
Example #28
0
        /// <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)
        {
            var otherSparse = other as SparseMatrix;
            var resultSparse = result as SparseMatrix;

            if (otherSparse == null || resultSparse == null)
            {
                base.DoTransposeAndMultiply(other, result);
                return;
            }

            resultSparse.Clear();
            for (var j = 0; j < RowCount; j++)
            {
                // Get the begin / end index for the row
                var startIndexOther = otherSparse._rowIndex[j];
                var endIndexOther = j < otherSparse._rowIndex.Length - 1 ? otherSparse._rowIndex[j + 1] : otherSparse.NonZerosCount;
                if (startIndexOther == endIndexOther)
                {
                    continue;
                }

                for (var i = 0; i < RowCount; i++)
                {
                    // Multiply row of matrix A on row of matrix B
                    // Get the begin / end index for the row
                    var startIndexThis = _rowIndex[i];
                    var endIndexThis = i < _rowIndex.Length - 1 ? _rowIndex[i + 1] : NonZerosCount;
                    if (startIndexThis == endIndexThis)
                    {
                        continue;
                    }

                    var sum = Complex.Zero;
                    for (var index = startIndexOther; index < endIndexOther; index++)
                    {
                        var ind = FindItem(i, otherSparse._columnIndices[index]);
                        if (ind >= 0)
                        {
                            sum += otherSparse._nonZeroValues[index] * _nonZeroValues[ind];
                        }
                    }

                    resultSparse.SetValueAt(i, j, sum + result.At(i, j));
                }
            }
        }
Example #29
0
        /// <summary>
        /// Symmetric tridiagonal QL algorithm.
        /// </summary>
        /// <param name="eigenVectors">The eigen vectors to work on.</param>
        /// <param name="d">Arrays for internal storage of real parts of eigenvalues</param>
        /// <param name="e">Arrays for internal storage of imaginary parts of eigenvalues</param>
        /// <param name="order">Order of initial matrix</param>
        /// <remarks>This is derived from the Algol procedures tql2, by
        /// Bowdler, Martin, Reinsch, and Wilkinson, Handbook for
        /// Auto. Comp., Vol.ii-Linear Algebra, and the corresponding
        /// Fortran subroutine in EISPACK.</remarks>
        /// <exception cref="NonConvergenceException"></exception>
        static void SymmetricDiagonalize(Matrix<float> eigenVectors, float[] d, float[] e, int order)
        {
            const int maxiter = 1000;

            for (var i = 1; i < order; i++)
            {
                e[i - 1] = e[i];
            }

            e[order - 1] = 0.0f;

            var f = 0.0f;
            var tst1 = 0.0f;
            var eps = Precision.DoublePrecision;
            for (var l = 0; l < order; l++)
            {
                // Find small subdiagonal element
                tst1 = Math.Max(tst1, Math.Abs(d[l]) + Math.Abs(e[l]));
                var m = l;
                while (m < order)
                {
                    if (Math.Abs(e[m]) <= eps*tst1)
                    {
                        break;
                    }

                    m++;
                }

                // If m == l, d[l] is an eigenvalue,
                // otherwise, iterate.
                if (m > l)
                {
                    var iter = 0;
                    do
                    {
                        iter = iter + 1; // (Could check iteration count here.)

                        // Compute implicit shift
                        var g = d[l];
                        var p = (d[l + 1] - g)/(2.0f*e[l]);
                        var r = SpecialFunctions.Hypotenuse(p, 1.0f);
                        if (p < 0)
                        {
                            r = -r;
                        }

                        d[l] = e[l]/(p + r);
                        d[l + 1] = e[l]*(p + r);

                        var dl1 = d[l + 1];
                        var h = g - d[l];
                        for (var i = l + 2; i < order; i++)
                        {
                            d[i] -= h;
                        }

                        f = f + h;

                        // Implicit QL transformation.
                        p = d[m];
                        var c = 1.0f;
                        var c2 = c;
                        var c3 = c;
                        var el1 = e[l + 1];
                        var s = 0.0f;
                        var s2 = 0.0f;
                        for (var i = m - 1; i >= l; i--)
                        {
                            c3 = c2;
                            c2 = c;
                            s2 = s;
                            g = c*e[i];
                            h = c*p;
                            r = SpecialFunctions.Hypotenuse(p, e[i]);
                            e[i + 1] = s*r;
                            s = e[i]/r;
                            c = p/r;
                            p = (c*d[i]) - (s*g);
                            d[i + 1] = h + (s*((c*g) + (s*d[i])));

                            // Accumulate transformation.
                            for (var k = 0; k < order; k++)
                            {
                                h = eigenVectors.At(k, i + 1);
                                eigenVectors.At(k, i + 1, (s*eigenVectors.At(k, i)) + (c*h));
                                eigenVectors.At(k, i, (c*eigenVectors.At(k, i)) - (s*h));
                            }
                        }

                        p = (-s)*s2*c3*el1*e[l]/dl1;
                        e[l] = s*p;
                        d[l] = c*p;

                        // Check for convergence. If too many iterations have been performed,
                        // throw exception that Convergence Failed
                        if (iter >= maxiter)
                        {
                            throw new NonConvergenceException();
                        }
                    } while (Math.Abs(e[l]) > eps*tst1);
                }

                d[l] = d[l] + f;
                e[l] = 0.0f;
            }

            // Sort eigenvalues and corresponding vectors.
            for (var i = 0; i < order - 1; i++)
            {
                var k = i;
                var p = d[i];
                for (var j = i + 1; j < order; j++)
                {
                    if (d[j] < p)
                    {
                        k = j;
                        p = d[j];
                    }
                }

                if (k != i)
                {
                    d[k] = d[i];
                    d[i] = p;
                    for (var j = 0; j < order; j++)
                    {
                        p = eigenVectors.At(j, i);
                        eigenVectors.At(j, i, eigenVectors.At(j, k));
                        eigenVectors.At(j, k, p);
                    }
                }
            }
        }
Example #30
0
 /// <summary>
 /// Puts the upper triangle of this matrix into the result matrix.
 /// </summary>
 /// <param name="result">Where to store the lower triangle.</param>
 private void UpperTriangleImpl(Matrix<Complex> result)
 {
     for (var row = 0; row < result.RowCount; row++)
     {
         var startIndex = _rowIndex[row];
         var endIndex = row < _rowIndex.Length - 1 ? _rowIndex[row + 1] : NonZerosCount;
         for (var j = startIndex; j < endIndex; j++)
         {
             if (row <= _columnIndices[j])
             {
                 result.At(row, _columnIndices[j], _nonZeroValues[j]);
             }
         }
     }
 }