diff --git a/src/Numerics/LinearAlgebra/Double/Factorization/UserEvd.cs b/src/Numerics/LinearAlgebra/Double/Factorization/UserEvd.cs
new file mode 100644
index 00000000..cef5a57c
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+++ b/src/Numerics/LinearAlgebra/Double/Factorization/UserEvd.cs
@@ -0,0 +1,1256 @@
+//
+// Math.NET Numerics, part of the Math.NET Project
+// http://numerics.mathdotnet.com
+// http://github.com/mathnet/mathnet-numerics
+// http://mathnetnumerics.codeplex.com
+//
+// Copyright (c) 2009-2010 Math.NET
+//
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+//
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+//
+namespace MathNet.Numerics.LinearAlgebra.Double.Factorization
+{
+ using System;
+ using System.Numerics;
+ using Generic;
+ using Generic.Factorization;
+ using Properties;
+
+ ///
+ /// Eigenvalues and eigenvectors of a real matrix.
+ ///
+ ///
+ /// If A is symmetric, then A = V*D*V' where the eigenvalue matrix D is
+ /// diagonal and the eigenvector matrix V is orthogonal.
+ /// I.e. A = V*D*V' and V*VT=I.
+ /// If A is not symmetric, then the eigenvalue matrix D is block diagonal
+ /// with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues,
+ /// lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda]. The
+ /// columns of V represent the eigenvectors in the sense that A*V = V*D,
+ /// i.e. A.Multiply(V) equals V.Multiply(D). The matrix V may be badly
+ /// conditioned, or even singular, so the validity of the equation
+ /// A = V*D*Inverse(V) depends upon V.cond().
+ ///
+ public class UserEvd : Evd
+ {
+ ///
+ /// Initializes a new instance of the class. This object will compute the
+ /// the eigenvalue decomposition when the constructor is called and cache it's decomposition.
+ ///
+ /// The matrix to factor.
+ /// If is null.
+ /// If EVD algorithm failed to converge with matrix .
+ public UserEvd(Matrix 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 = matrix.CreateMatrix(order, order);
+ MatrixD = matrix.CreateMatrix(order, order);
+ VectorEv = new LinearAlgebra.Complex.DenseVector(order);
+
+ IsSymmetric = true;
+
+ for (var i = 0; i < order & IsSymmetric; i++)
+ {
+ for (var j = 0; j < order & IsSymmetric; j++)
+ {
+ IsSymmetric &= matrix[i, j] == matrix[j, i];
+ }
+ }
+
+ var d = new double[order];
+ var e = new double[order];
+
+ if (IsSymmetric)
+ {
+ matrix.CopyTo(MatrixEv);
+ d = MatrixEv.Row(order - 1).ToArray();
+
+ SymmetricTridiagonalize(d, e, order);
+ SymmetricDiagonalize(d, e, order);
+ }
+ else
+ {
+ var matrixH = matrix.ToArray();
+
+ NonsymmetricReduceToHessenberg(matrixH, order);
+ NonsymmetricReduceHessenberToRealSchur(matrixH, d, e, order);
+ }
+
+ for (var i = 0; i < order; i++)
+ {
+ MatrixD[i, i] = d[i];
+
+ if (e[i] > 0)
+ {
+ MatrixD[i, i + 1] = e[i];
+ }
+ else if (e[i] < 0)
+ {
+ MatrixD[i, i - 1] = e[i];
+ }
+ }
+
+ for (var i = 0; i < order; i++)
+ {
+ VectorEv[i] = new Complex(d[i], e[i]);
+ }
+ }
+
+ ///
+ /// Symmetric Householder reduction to tridiagonal form.
+ ///
+ /// Arrays for internal storage of real parts of eigenvalues
+ /// Arrays for internal storage of imaginary parts of eigenvalues
+ /// Order of initial matrix
+ /// 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.
+ private void SymmetricTridiagonalize(double[] d, double[] e, int order)
+ {
+ // Householder reduction to tridiagonal form.
+ for (var i = order - 1; i > 0; i--)
+ {
+ // Scale to avoid under/overflow.
+ var scale = 0.0;
+ var h = 0.0;
+
+ for (var k = 0; k < i; k++)
+ {
+ scale = scale + Math.Abs(d[k]);
+ }
+
+ if (scale == 0.0)
+ {
+ e[i] = d[i - 1];
+ for (var j = 0; j < i; j++)
+ {
+ d[j] = MatrixEv[i - 1, j];
+ MatrixEv[i, j] = 0.0;
+ MatrixEv[j, i] = 0.0;
+ }
+ }
+ 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 = 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] = 0.0;
+ }
+
+ // Apply similarity transformation to remaining columns.
+ for (var j = 0; j < i; j++)
+ {
+ f = d[j];
+ MatrixEv[j, i] = f;
+ g = e[j] + (MatrixEv[j, j] * f);
+
+ for (var k = j + 1; k <= i - 1; k++)
+ {
+ g += MatrixEv[k, j] * d[k];
+ e[k] += MatrixEv[k, j] * f;
+ }
+
+ e[j] = g;
+ }
+
+ f = 0.0;
+
+ 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++)
+ {
+ MatrixEv[k, j] -= (f * e[k]) + (g * d[k]);
+ }
+
+ d[j] = MatrixEv[i - 1, j];
+ MatrixEv[i, j] = 0.0;
+ }
+ }
+
+ d[i] = h;
+ }
+
+ // Accumulate transformations.
+ for (var i = 0; i < order - 1; i++)
+ {
+ MatrixEv[order - 1, i] = MatrixEv[i, i];
+ MatrixEv[i, i] = 1.0;
+ var h = d[i + 1];
+ if (h != 0.0)
+ {
+ for (var k = 0; k <= i; k++)
+ {
+ d[k] = MatrixEv[k, i + 1] / h;
+ }
+
+ for (var j = 0; j <= i; j++)
+ {
+ var g = 0.0;
+ for (var k = 0; k <= i; k++)
+ {
+ g += MatrixEv[k, i + 1] * MatrixEv[k, j];
+ }
+
+ for (var k = 0; k <= i; k++)
+ {
+ MatrixEv[k, j] -= g * d[k];
+ }
+ }
+ }
+
+ for (var k = 0; k <= i; k++)
+ {
+ MatrixEv[k, i + 1] = 0.0;
+ }
+ }
+
+ for (var j = 0; j < order; j++)
+ {
+ d[j] = MatrixEv[order - 1, j];
+ MatrixEv[order - 1, j] = 0.0;
+ }
+
+ MatrixEv[order - 1, order - 1] = 1.0;
+ e[0] = 0.0;
+ }
+
+ ///
+ /// Symmetric tridiagonal QL algorithm.
+ ///
+ /// Arrays for internal storage of real parts of eigenvalues
+ /// Arrays for internal storage of imaginary parts of eigenvalues
+ /// Order of initial matrix
+ /// 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.
+ private void SymmetricDiagonalize(double[] d, double[] e, int order)
+ {
+ const int Maxiter = 1000;
+
+ for (var i = 1; i < order; i++)
+ {
+ e[i - 1] = e[i];
+ }
+
+ e[order - 1] = 0.0;
+
+ var f = 0.0;
+ var tst1 = 0.0;
+ var eps = Precision.DoubleMachinePrecision;
+ 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) / (2.0 * e[l]);
+ var r = SpecialFunctions.Hypotenuse(p, 1.0);
+ 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 = 1.0;
+ var c2 = c;
+ var c3 = c;
+ var el1 = e[l + 1];
+ var s = 0.0;
+ var s2 = 0.0;
+ 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 = MatrixEv[k, i + 1];
+ MatrixEv[k, i + 1] = (s * MatrixEv[k, i]) + (c * h);
+ MatrixEv[k, i] = (c * MatrixEv[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 ArgumentException(Resources.ConvergenceFailed);
+ }
+ }
+ while (Math.Abs(e[l]) > eps * tst1);
+ }
+
+ d[l] = d[l] + f;
+ e[l] = 0.0;
+ }
+
+ // 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 = MatrixEv[j, i];
+ MatrixEv[j, i] = MatrixEv[j, k];
+ MatrixEv[j, k] = p;
+ }
+ }
+ }
+ }
+
+ ///
+ /// Nonsymmetric reduction to Hessenberg form.
+ ///
+ /// Array for internal storage of nonsymmetric Hessenberg form.
+ /// Order of initial matrix
+ /// 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.
+ private void NonsymmetricReduceToHessenberg(double[,] matrixH, int order)
+ {
+ const int Low = 0;
+ var high = order - 1;
+
+ var ort = new double[order];
+
+ for (var m = Low + 1; m <= high - 1; m++)
+ {
+ // Scale column.
+ var scale = 0.0;
+ for (var i = m; i <= high; i++)
+ {
+ scale = scale + Math.Abs(matrixH[i, m - 1]);
+ }
+
+ if (scale != 0.0)
+ {
+ // Compute Householder transformation.
+ var h = 0.0;
+ for (var i = high; i >= m; i--)
+ {
+ ort[i] = matrixH[i, m - 1] / scale;
+ h += ort[i] * ort[i];
+ }
+
+ var g = 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 = 0.0;
+ for (var i = high; i >= m; i--)
+ {
+ f += ort[i] * matrixH[i, j];
+ }
+
+ f = f / h;
+ for (var i = m; i <= high; i++)
+ {
+ matrixH[i, j] -= f * ort[i];
+ }
+ }
+
+ for (var i = 0; i <= high; i++)
+ {
+ var f = 0.0;
+ for (var j = high; j >= m; j--)
+ {
+ f += ort[j] * matrixH[i, j];
+ }
+
+ f = f / h;
+ for (var j = m; j <= high; 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++)
+ {
+ MatrixEv[i, j] = i == j ? 1.0 : 0.0;
+ }
+ }
+
+ for (var m = high - 1; m >= Low + 1; m--)
+ {
+ if (matrixH[m, m - 1] != 0.0)
+ {
+ for (var i = m + 1; i <= high; i++)
+ {
+ ort[i] = matrixH[i, m - 1];
+ }
+
+ for (var j = m; j <= high; j++)
+ {
+ var g = 0.0;
+ for (var i = m; i <= high; i++)
+ {
+ g += ort[i] * MatrixEv[i, j];
+ }
+
+ // Double division avoids possible underflow
+ g = (g / ort[m]) / matrixH[m, m - 1];
+ for (var i = m; i <= high; i++)
+ {
+ MatrixEv[i, j] += g * ort[i];
+ }
+ }
+ }
+ }
+ }
+
+ ///
+ /// Nonsymmetric reduction from Hessenberg to real Schur form.
+ ///
+ /// Array for internal storage of nonsymmetric Hessenberg form.
+ /// Arrays for internal storage of real parts of eigenvalues
+ /// Arrays for internal storage of imaginary parts of eigenvalues
+ /// Order of initial matrix
+ /// 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.
+ private void NonsymmetricReduceHessenberToRealSchur(double[,] matrixH, double[] d, double[] e, int order)
+ {
+ // Initialize
+ var n = order - 1;
+ const int Low = 0;
+ var high = order - 1;
+ var eps = Precision.DoubleMachinePrecision;
+ var exshift = 0.0;
+ double p = 0, q = 0, r = 0, s = 0, z = 0, w, x, y;
+
+ // Store roots isolated by balanc and compute matrix norm
+ var norm = 0.0;
+ for (var i = 0; i < order; i++)
+ {
+ if (i < Low | i > high)
+ {
+ d[i] = matrixH[i, i];
+ e[i] = 0.0;
+ }
+
+ 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 >= Low)
+ {
+ // Look for single small sub-diagonal element
+ var l = n;
+ while (l > Low)
+ {
+ s = Math.Abs(matrixH[l - 1, l - 1]) + Math.Abs(matrixH[l, l]);
+
+ if (s == 0.0)
+ {
+ 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] = 0.0;
+ 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]) / 2.0;
+ q = (p * p) + w;
+ z = 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 != 0.0)
+ {
+ d[n] = x - (w / z);
+ }
+
+ e[n - 1] = 0.0;
+ e[n] = 0.0;
+ x = matrixH[n, n - 1];
+ s = Math.Abs(x) + Math.Abs(z);
+ p = x / s;
+ q = z / s;
+ r = 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 = Low; i <= high; i++)
+ {
+ z = MatrixEv[i, n - 1];
+ MatrixEv[i, n - 1] = (q * z) + (p * MatrixEv[i, n]);
+ MatrixEv[i, n] = (q * MatrixEv[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 = 0.0;
+ w = 0.0;
+ 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 = Low; i <= n; i++)
+ {
+ matrixH[i, i] -= x;
+ }
+
+ s = Math.Abs(matrixH[n, n - 1]) + Math.Abs(matrixH[n - 1, n - 2]);
+ x = y = 0.75 * s;
+ w = (-0.4375) * s * s;
+ }
+
+ // MATLAB's new ad hoc shift
+ if (iter == 30)
+ {
+ s = (y - x) / 2.0;
+ s = (s * s) + w;
+ if (s > 0)
+ {
+ s = Math.Sqrt(s);
+ if (y < x)
+ {
+ s = -s;
+ }
+
+ s = x - (w / (((y - x) / 2.0) + s));
+ for (var i = Low; i <= n; i++)
+ {
+ matrixH[i, i] -= s;
+ }
+
+ exshift += s;
+ x = y = w = 0.964;
+ }
+ }
+
+ 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] = 0.0;
+ if (i > m + 2)
+ {
+ matrixH[i, i - 3] = 0.0;
+ }
+ }
+
+ // 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] : 0.0;
+ x = Math.Abs(p) + Math.Abs(q) + Math.Abs(r);
+ if (x != 0.0)
+ {
+ p = p / x;
+ q = q / x;
+ r = r / x;
+ }
+ }
+
+ if (x == 0.0)
+ {
+ break;
+ }
+
+ s = Math.Sqrt((p * p) + (q * q) + (r * r));
+ if (p < 0)
+ {
+ s = -s;
+ }
+
+ if (s != 0.0)
+ {
+ 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 = Low; i <= high; i++)
+ {
+ p = (x * MatrixEv[i, k]) + (y * MatrixEv[i, k + 1]);
+
+ if (notlast)
+ {
+ p = p + (z * MatrixEv[i, k + 2]);
+ MatrixEv[i, k + 2] = MatrixEv[i, k + 2] - (p * r);
+ }
+
+ MatrixEv[i, k] = MatrixEv[i, k] - p;
+ MatrixEv[i, k + 1] = MatrixEv[i, k + 1] - (p * q);
+ }
+ } // (s != 0)
+ } // k loop
+ } // check convergence
+ } // while (n >= low)
+
+ // Backsubstitute to find vectors of upper triangular form
+ if (norm == 0.0)
+ {
+ return;
+ }
+
+ for (n = order - 1; n >= 0; n--)
+ {
+ double t;
+
+ p = d[n];
+ q = e[n];
+
+ // Real vector
+ if (q == 0.0)
+ {
+ var l = n;
+ matrixH[n, n] = 1.0;
+ for (var i = n - 1; i >= 0; i--)
+ {
+ w = matrixH[i, i] - p;
+ r = 0.0;
+ for (var j = l; j <= n; j++)
+ {
+ r = r + (matrixH[i, j] * matrixH[j, n]);
+ }
+
+ if (e[i] < 0.0)
+ {
+ z = w;
+ s = r;
+ }
+ else
+ {
+ l = i;
+ if (e[i] == 0.0)
+ {
+ if (w != 0.0)
+ {
+ 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(0.0, -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] = 0.0;
+ matrixH[n, n] = 1.0;
+ for (var i = n - 2; i >= 0; i--)
+ {
+ double ra = 0.0;
+ double sa = 0.0;
+ 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] < 0.0)
+ {
+ z = w;
+ r = ra;
+ s = sa;
+ }
+ else
+ {
+ l = i;
+ if (e[i] == 0.0)
+ {
+ 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];
+
+ double vr = ((d[i] - p) * (d[i] - p)) + (e[i] * e[i]) - (q * q);
+ double vi = (d[i] - p) * 2.0 * q;
+ if ((vr == 0.0) && (vi == 0.0))
+ {
+ 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;
+ }
+ }
+ }
+ }
+ }
+ }
+
+ // Vectors of isolated roots
+ for (var i = 0; i < order; i++)
+ {
+ if (i < Low | i > high)
+ {
+ for (var j = i; j < order; j++)
+ {
+ MatrixEv[i, j] = matrixH[i, j];
+ }
+ }
+ }
+
+ // Back transformation to get eigenvectors of original matrix
+ for (var j = order - 1; j >= Low; j--)
+ {
+ for (var i = Low; i <= high; i++)
+ {
+ z = 0.0;
+ for (var k = Low; k <= Math.Min(j, high); k++)
+ {
+ z = z + (MatrixEv[i, k] * matrixH[k, j]);
+ }
+
+ MatrixEv[i, j] = z;
+ }
+ }
+ }
+
+ ///
+ /// Complex scalar division X/Y.
+ ///
+ /// Real part of X
+ /// Imaginary part of X
+ /// Real part of Y
+ /// Imaginary part of Y
+ /// Division result as a number.
+ private static Complex Cdiv(double xreal, double ximag, double yreal, double yimag)
+ {
+ if (Math.Abs(yimag) < Math.Abs(yreal))
+ {
+ return new Complex((xreal + (ximag * (yimag / yreal))) / (yreal + (yimag * (yimag / yreal))), (ximag - (xreal * (yimag / yreal))) / (yreal + (yimag * (yimag / yreal))));
+ }
+
+ return new Complex((ximag + (xreal * (yreal / yimag))) / (yimag + (yreal * (yreal / yimag))), (-xreal + (ximag * (yreal / yimag))) / (yimag + (yreal * (yreal / yimag))));
+ }
+
+ ///
+ /// Solves a system of linear equations, AX = B, with A SVD factorized.
+ ///
+ /// The right hand side , B.
+ /// The left hand side , X.
+ public override void Solve(Matrix input, Matrix 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 (VectorEv.Count != input.RowCount)
+ {
+ throw new ArgumentException(Resources.ArgumentMatrixSameRowDimension);
+ }
+
+ // The solution X row dimension is equal to the column dimension of A
+ if (VectorEv.Count != result.RowCount)
+ {
+ throw new ArgumentException(Resources.ArgumentMatrixSameColumnDimension);
+ }
+
+ if (IsSymmetric)
+ {
+ var order = VectorEv.Count;
+ var tmp = new double[order];
+
+ for (var k = 0; k < order; k++)
+ {
+ for (var j = 0; j < order; j++)
+ {
+ double value = 0;
+ if (j < order)
+ {
+ for (var i = 0; i < order; i++)
+ {
+ value += MatrixEv.At(i, j) * input.At(i, k);
+ }
+
+ value /= VectorEv[j].Real;
+ }
+
+ tmp[j] = value;
+ }
+
+ for (var j = 0; j < order; j++)
+ {
+ double value = 0;
+ for (var i = 0; i < order; i++)
+ {
+ value += MatrixEv.At(j, i) * tmp[i];
+ }
+
+ result[j, k] = value;
+ }
+ }
+ }
+ else
+ {
+ throw new NotImplementedException();
+ }
+ }
+
+ ///
+ /// Solves a system of linear equations, Ax = b, with A EVD factorized.
+ ///
+ /// The right hand side vector, b.
+ /// The left hand side , x.
+ public override void Solve(Vector input, Vector result)
+ {
+ if (input == null)
+ {
+ throw new ArgumentNullException("input");
+ }
+
+ if (result == null)
+ {
+ throw new ArgumentNullException("result");
+ }
+
+ // Ax=b where A is an m x m matrix
+ // Check that b is a column vector with m entries
+ if (VectorEv.Count != input.Count)
+ {
+ throw new ArgumentException(Resources.ArgumentVectorsSameLength);
+ }
+
+ // Check that x is a column vector with n entries
+ if (VectorEv.Count != result.Count)
+ {
+ throw new ArgumentException(Resources.ArgumentMatrixDimensions);
+ }
+
+ if (IsSymmetric)
+ {
+ // Symmetric case -> x = V * inv(λ) * VT * b;
+ var order = VectorEv.Count;
+ var tmp = new double[order];
+ double value;
+
+ for (var j = 0; j < order; j++)
+ {
+ value = 0;
+ if (j < order)
+ {
+ for (var i = 0; i < order; i++)
+ {
+ value += MatrixEv.At(i, j) * input[i];
+ }
+
+ value /= VectorEv[j].Real;
+ }
+
+ tmp[j] = value;
+ }
+
+ for (var j = 0; j < order; j++)
+ {
+ value = 0;
+ for (int i = 0; i < order; i++)
+ {
+ value += MatrixEv.At(j, i) * tmp[i];
+ }
+
+ result[j] = value;
+ }
+ }
+ else
+ {
+ throw new NotImplementedException();
+ }
+ }
+
+ ///
+ /// Multiply two values T*T
+ ///
+ /// Left operand value
+ /// Right operand value
+ /// Result of multiplication
+ protected sealed override double MultiplyT(double val1, double val2)
+ {
+ return val1 * val2;
+ }
+ }
+}
\ No newline at end of file
diff --git a/src/Numerics/LinearAlgebra/Generic/Factorization/Evd.cs b/src/Numerics/LinearAlgebra/Generic/Factorization/Evd.cs
new file mode 100644
index 00000000..5ab4176b
--- /dev/null
+++ b/src/Numerics/LinearAlgebra/Generic/Factorization/Evd.cs
@@ -0,0 +1,294 @@
+//
+// Math.NET Numerics, part of the Math.NET Project
+// http://numerics.mathdotnet.com
+// http://github.com/mathnet/mathnet-numerics
+// http://mathnetnumerics.codeplex.com
+//
+// Copyright (c) 2009-2010 Math.NET
+//
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+//
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+//
+
+namespace MathNet.Numerics.LinearAlgebra.Generic.Factorization
+{
+ using System;
+ using System.Linq;
+ using System.Numerics;
+ using Generic;
+ using Numerics;
+
+ ///
+ /// Eigenvalues and eigenvectors of a real matrix.
+ ///
+ ///
+ /// If A is symmetric, then A = V*D*V' where the eigenvalue matrix D is
+ /// diagonal and the eigenvector matrix V is orthogonal.
+ /// I.e. A = V*D*V' and V*VT=I.
+ /// If A is not symmetric, then the eigenvalue matrix D is block diagonal
+ /// with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues,
+ /// lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda]. The
+ /// columns of V represent the eigenvectors in the sense that A*V = V*D,
+ /// i.e. A.Multiply(V) equals V.Multiply(D). The matrix V may be badly
+ /// conditioned, or even singular, so the validity of the equation
+ /// A = V*D*Inverse(V) depends upon V.cond().
+ ///
+ /// Supported data types are double, single, , and .
+ public abstract class Evd : ISolver
+ where T : struct, IEquatable, IFormattable
+ {
+ ///
+ /// Gets or sets a value indicating whether matrix is symmetric or not
+ ///
+ public bool IsSymmetric
+ {
+ get;
+ protected set;
+ }
+
+ ///
+ /// Gets or sets the eigen values (λ) of matrix in ascending value.
+ ///
+ protected Vector VectorEv
+ {
+ get;
+ set;
+ }
+
+ ///
+ /// Gets or sets eigenvectors.
+ ///
+ protected Matrix MatrixEv
+ {
+ get;
+ set;
+ }
+
+ ///
+ /// Gets or sets the block diagonal eigenvalue matrix.
+ ///
+ protected Matrix MatrixD
+ {
+ get;
+ set;
+ }
+
+ ///
+ /// Internal method which routes the call to perform the singular value decomposition to the appropriate class.
+ ///
+ /// The matrix to factor.
+ /// An EVD object.
+ internal static Evd Create(Matrix matrix)
+ {
+ if (typeof(T) == typeof(double))
+ {
+ return new LinearAlgebra.Double.Factorization.UserEvd(matrix as Matrix) as Evd;
+ }
+
+ // if (typeof(T) == typeof(float))
+ // {
+ // return new LinearAlgebra.Single.Factorization.UserEvd(matrix as Matrix, computeVectors) as Evd;
+ // }
+
+ // if (typeof(T) == typeof(Complex))
+ // {
+ // return new LinearAlgebra.Complex.Factorization.UserEvd(matrix as Matrix, computeVectors) as Evd;
+ // }
+
+ // if (typeof(T) == typeof(Complex32))
+ // {
+ // return new LinearAlgebra.Complex32.Factorization.UserEvd(matrix as Matrix, computeVectors) as Evd;
+ // }
+ throw new NotImplementedException();
+ }
+
+ ///
+ /// Gets the absolute value of determinant of the square matrix for which the EVD was computed.
+ ///
+ public virtual double Determinant
+ {
+ get
+ {
+ var det = Complex.One;
+ for (var i = 0; i < VectorEv.Count; i++)
+ {
+ det *= VectorEv[i];
+ if (VectorEv[i].AlmostEqual(Complex.Zero))
+ {
+ return 0;
+ }
+ }
+
+ return det.Magnitude;
+ }
+ }
+
+ ///
+ /// Gets the effective numerical matrix rank.
+ ///
+ /// The number of non-negligible singular values.
+ public virtual int Rank
+ {
+ get
+ {
+ return VectorEv.Count(t => !t.AlmostEqual(Complex.Zero));
+ }
+ }
+
+ ///
+ /// Gets a value indicating whether the matrix is full rank or not.
+ ///
+ /// true if the matrix is full rank; otherwise false.
+ public virtual bool IsFullRank
+ {
+ get
+ {
+ for (var i = 0; i < VectorEv.Count; i++)
+ {
+ if (VectorEv[i].AlmostEqual(Complex.Zero))
+ {
+ return false;
+ }
+ }
+
+ return true;
+ }
+ }
+
+ /// Returns the eigen values as a .
+ /// The eigen values.
+ public Vector EValues()
+ {
+ return VectorEv.Clone();
+ }
+
+ /// Returns the right eigen vectors as a .
+ /// The eigen vectors.
+ public Matrix EVectors()
+ {
+ return MatrixEv.Clone();
+ }
+
+ /// Returns the block diagonal eigenvalue matrix .
+ /// The block diagonal eigenvalue matrix .
+ public Matrix D()
+ {
+ return MatrixD.Clone();
+ }
+
+ ///
+ /// Solves a system of linear equations, AX = B, with A SVD factorized.
+ ///
+ /// The right hand side , B.
+ /// The left hand side , X.
+ public virtual Matrix Solve(Matrix input)
+ {
+ // Check for proper arguments.
+ if (input == null)
+ {
+ throw new ArgumentNullException("input");
+ }
+
+ var result = MatrixEv.CreateMatrix(MatrixEv.ColumnCount, input.ColumnCount);
+ Solve(input, result);
+ return result;
+ }
+
+ ///
+ /// Solves a system of linear equations, AX = B, with A SVD factorized.
+ ///
+ /// The right hand side , B.
+ /// The left hand side , X.
+ public abstract void Solve(Matrix input, Matrix result);
+
+ ///
+ /// Solves a system of linear equations, Ax = b, with A SVD factorized.
+ ///
+ /// The right hand side vector, b.
+ /// The left hand side , x.
+ public virtual Vector Solve(Vector input)
+ {
+ // Check for proper arguments.
+ if (input == null)
+ {
+ throw new ArgumentNullException("input");
+ }
+
+ var x = MatrixEv.CreateVector(MatrixEv.ColumnCount);
+ Solve(input, x);
+ return x;
+ }
+
+ ///
+ /// Solves a system of linear equations, Ax = b, with A SVD factorized.
+ ///
+ /// The right hand side vector, b.
+ /// The left hand side , x.
+ public abstract void Solve(Vector input, Vector result);
+
+ #region Simple arithmetic of type T
+ ///
+ /// Multiply two values T*T
+ ///
+ /// Left operand value
+ /// Right operand value
+ /// Result of multiplication
+ protected abstract T MultiplyT(T val1, T val2);
+
+ ///
+ /// Gets value of type T equal to one
+ ///
+ /// One value
+ private static T OneValueT
+ {
+ get
+ {
+ if (typeof(T) == typeof(Complex))
+ {
+ object one = Complex.One;
+ return (T)one;
+ }
+
+ if (typeof(T) == typeof(Complex32))
+ {
+ object one = Complex32.One;
+ return (T)one;
+ }
+
+ if (typeof(T) == typeof(double))
+ {
+ object one = 1.0d;
+ return (T)one;
+ }
+
+ if (typeof(T) == typeof(float))
+ {
+ object one = 1.0f;
+ return (T)one;
+ }
+
+ throw new NotSupportedException();
+ }
+ }
+
+ #endregion
+ }
+}
diff --git a/src/Numerics/LinearAlgebra/Generic/Factorization/ExtensionMethods.cs b/src/Numerics/LinearAlgebra/Generic/Factorization/ExtensionMethods.cs
index 9b908390..0f89e881 100644
--- a/src/Numerics/LinearAlgebra/Generic/Factorization/ExtensionMethods.cs
+++ b/src/Numerics/LinearAlgebra/Generic/Factorization/ExtensionMethods.cs
@@ -109,11 +109,22 @@ namespace MathNet.Numerics.LinearAlgebra.Generic.Factorization
///
/// The matrix to factor.
/// Compute the singular U and VT vectors or not.
- /// The QR decomposition object.
+ /// The SVD decomposition object.
/// Supported data types are double, single, , and .
public static Svd Svd(this Matrix matrix, bool computeVectors) where T : struct, IEquatable, IFormattable
{
return Factorization.Svd.Create(matrix, computeVectors);
}
+
+ ///
+ /// Computes the EVD decomposition for a matrix.
+ ///
+ /// The matrix to factor.
+ /// The EVD decomposition object.
+ /// Supported data types are double, single, , and .
+ public static Evd Evd(this Matrix matrix) where T : struct, IEquatable, IFormattable
+ {
+ return Factorization.Evd.Create(matrix);
+ }
}
}
diff --git a/src/Numerics/Numerics.csproj b/src/Numerics/Numerics.csproj
index 12487fa1..5cba634b 100644
--- a/src/Numerics/Numerics.csproj
+++ b/src/Numerics/Numerics.csproj
@@ -168,6 +168,8 @@
+
+
diff --git a/src/Silverlight/Silverlight.csproj b/src/Silverlight/Silverlight.csproj
index d79f43aa..cb19f88e 100644
--- a/src/Silverlight/Silverlight.csproj
+++ b/src/Silverlight/Silverlight.csproj
@@ -428,6 +428,9 @@
LinearAlgebra\Double\Factorization\UserCholesky.cs
+
+ LinearAlgebra\Double\Factorization\UserEvd.cs
+
LinearAlgebra\Double\Factorization\UserLU.cs
@@ -500,6 +503,9 @@
LinearAlgebra\Double\SparseVector.cs
+
+ LinearAlgebra\Generic\Factorization\Evd.cs
+
LinearAlgebra\Single\DenseMatrix.cs
diff --git a/src/UnitTests/LinearAlgebraTests/Double/Factorization/UserEvdTests.cs b/src/UnitTests/LinearAlgebraTests/Double/Factorization/UserEvdTests.cs
new file mode 100644
index 00000000..43f13acf
--- /dev/null
+++ b/src/UnitTests/LinearAlgebraTests/Double/Factorization/UserEvdTests.cs
@@ -0,0 +1,357 @@
+//
+// Math.NET Numerics, part of the Math.NET Project
+// http://numerics.mathdotnet.com
+// http://github.com/mathnet/mathnet-numerics
+// http://mathnetnumerics.codeplex.com
+//
+// Copyright (c) 2009-2010 Math.NET
+//
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+//
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+//
+
+namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Double.Factorization
+{
+ using System.Numerics;
+ using LinearAlgebra.Generic.Factorization;
+ using MbUnit.Framework;
+ using LinearAlgebra.Double.Factorization;
+
+ public class UserEvdTests
+ {
+
+ [Test]
+ [ExpectedArgumentNullException]
+ public void ConstructorNull()
+ {
+ new UserEvd(null);
+ }
+
+ [Test]
+ [Row(1)]
+ [Row(10)]
+ [Row(100)]
+ public void CanFactorizeIdentity(int order)
+ {
+ var I = UserDefinedMatrix.Identity(order);
+ var factorEvd = I.Evd();
+
+ Assert.AreEqual(I.RowCount, factorEvd.EVectors().RowCount);
+ Assert.AreEqual(I.RowCount, factorEvd.EVectors().ColumnCount);
+
+ Assert.AreEqual(I.ColumnCount, factorEvd.D().RowCount);
+ Assert.AreEqual(I.ColumnCount, factorEvd.D().ColumnCount);
+
+ for (var i = 0; i < factorEvd.EValues().Count; i++)
+ {
+ Assert.AreEqual(Complex.One, factorEvd.EValues()[i]);
+ }
+ }
+
+ [Test]
+ [Row(1)]
+ [Row(2)]
+ [Row(5)]
+ [Row(10)]
+ [Row(50)]
+ [Row(100)]
+ [MultipleAsserts]
+ public void CanFactorizeRandomMatrix(int order)
+ {
+ var matrixA = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
+ var factorEvd = matrixA.Evd();
+
+ Assert.AreEqual(order, factorEvd.EVectors().RowCount);
+ Assert.AreEqual(order, factorEvd.EVectors().ColumnCount);
+
+ Assert.AreEqual(order, factorEvd.D().RowCount);
+ Assert.AreEqual(order, factorEvd.D().ColumnCount);
+
+ // Make sure the A*V = λ*V
+ var matrixAv = matrixA * factorEvd.EVectors();
+ var matrixLv = factorEvd.EVectors() * factorEvd.D();
+
+ for (var i = 0; i < matrixAv.RowCount; i++)
+ {
+ for (var j = 0; j < matrixAv.ColumnCount; j++)
+ {
+ Assert.AreApproximatelyEqual(matrixAv[i, j], matrixLv[i, j], 1.0e-11);
+ }
+ }
+ }
+
+ [Test]
+ [Row(1)]
+ [Row(2)]
+ [Row(5)]
+ [Row(10)]
+ [Row(50)]
+ [Row(100)]
+ [MultipleAsserts]
+ public void CanFactorizeRandomSymmetricMatrix(int order)
+ {
+ var matrixA = MatrixLoader.GenerateRandomPositiveDefiniteUserDefinedMatrix(order);
+ var factorEvd = matrixA.Evd();
+
+ Assert.AreEqual(order, factorEvd.EVectors().RowCount);
+ Assert.AreEqual(order, factorEvd.EVectors().ColumnCount);
+
+ Assert.AreEqual(order, factorEvd.D().RowCount);
+ Assert.AreEqual(order, factorEvd.D().ColumnCount);
+
+ // Make sure the A = V*λ*VT
+ var matrix = factorEvd.EVectors() * factorEvd.D() * factorEvd.EVectors().Transpose();
+
+ for (var i = 0; i < matrix.RowCount; i++)
+ {
+ for (var j = 0; j < matrix.ColumnCount; j++)
+ {
+ Assert.AreApproximatelyEqual(matrix[i, j], matrixA[i, j], 1.0e-11);
+ }
+ }
+ }
+
+ [Test]
+ [Row(10)]
+ [Row(50)]
+ [Row(100)]
+ [MultipleAsserts]
+ public void CheckRankSquare(int order)
+ {
+ var matrixA = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
+ var factorEvd = matrixA.Evd();
+
+ Assert.AreEqual(factorEvd.Rank, order);
+ }
+
+
+ [Test]
+ [Row(10)]
+ [Row(50)]
+ [Row(100)]
+ [MultipleAsserts]
+ public void CheckRankOfSquareSingular(int order)
+ {
+ var matrixA = new UserDefinedMatrix(order, order);
+ matrixA[0, 0] = 1;
+ matrixA[order - 1, order - 1] = 1;
+ for (var i = 1; i < order - 1; i++)
+ {
+ matrixA[i, i - 1] = 1;
+ matrixA[i, i + 1] = 1;
+ matrixA[i - 1, i] = 1;
+ matrixA[i + 1, i] = 1;
+ }
+ var factorEvd = matrixA.Evd();
+
+ Assert.AreEqual(factorEvd.Determinant, 0);
+ Assert.AreEqual(factorEvd.Rank, order - 1);
+ }
+
+ [Test]
+ [Row(1)]
+ [Row(10)]
+ [Row(100)]
+ public void IdentityDeterminantIsOne(int order)
+ {
+ var I = UserDefinedMatrix.Identity(order);
+ var factorEvd = I.Evd();
+ Assert.AreEqual(1.0, factorEvd.Determinant);
+ }
+
+ [Test]
+ [Row(1)]
+ [Row(2)]
+ [Row(5)]
+ [Row(10)]
+ [Row(50)]
+ [Row(100)]
+ [MultipleAsserts]
+ public void CanSolveForRandomVectorAndSymmetricMatrix(int order)
+ {
+ var matrixA = MatrixLoader.GenerateRandomPositiveDefiniteUserDefinedMatrix(order);
+ var matrixACopy = matrixA.Clone();
+ var factorSvd = matrixA.Svd(true);
+
+ var vectorb = MatrixLoader.GenerateRandomUserDefinedVector(order);
+ var resultx = factorSvd.Solve(vectorb);
+
+ Assert.AreEqual(matrixA.ColumnCount, resultx.Count);
+
+ var bReconstruct = matrixA * resultx;
+
+ // Check the reconstruction.
+ for (var i = 0; i < vectorb.Count; i++)
+ {
+ Assert.AreApproximatelyEqual(vectorb[i], bReconstruct[i], 1.0e-11);
+ }
+
+ // Make sure A didn't change.
+ for (var i = 0; i < matrixA.RowCount; i++)
+ {
+ for (var j = 0; j < matrixA.ColumnCount; j++)
+ {
+ Assert.AreEqual(matrixACopy[i, j], matrixA[i, j]);
+ }
+ }
+ }
+
+ [Test]
+ [Row(1)]
+ [Row(2)]
+ [Row(5)]
+ [Row(10)]
+ [Row(50)]
+ [Row(100)]
+ [MultipleAsserts]
+ public void CanSolveForRandomMatrixAndSymmetricMatrix(int order)
+ {
+ var matrixA = MatrixLoader.GenerateRandomPositiveDefiniteUserDefinedMatrix(order);
+ var matrixACopy = matrixA.Clone();
+ var factorSvd = matrixA.Svd(true);
+
+ var matrixB = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
+ var matrixX = factorSvd.Solve(matrixB);
+
+ // The solution X row dimension is equal to the column dimension of A
+ Assert.AreEqual(matrixA.ColumnCount, matrixX.RowCount);
+ // The solution X has the same number of columns as B
+ Assert.AreEqual(matrixB.ColumnCount, matrixX.ColumnCount);
+
+ var matrixBReconstruct = matrixA * matrixX;
+
+ // Check the reconstruction.
+ for (var i = 0; i < matrixB.RowCount; i++)
+ {
+ for (var j = 0; j < matrixB.ColumnCount; j++)
+ {
+ Assert.AreApproximatelyEqual(matrixB[i, j], matrixBReconstruct[i, j], 1.0e-11);
+ }
+ }
+
+ // Make sure A didn't change.
+ for (var i = 0; i < matrixA.RowCount; i++)
+ {
+ for (var j = 0; j < matrixA.ColumnCount; j++)
+ {
+ Assert.AreEqual(matrixACopy[i, j], matrixA[i, j]);
+ }
+ }
+ }
+
+ [Test]
+ [Row(1)]
+ [Row(2)]
+ [Row(5)]
+ [Row(10)]
+ [Row(50)]
+ [Row(100)]
+ [MultipleAsserts]
+ public void CanSolveForRandomVectorAndSymmetricMatrixWhenResultVectorGiven(int order)
+ {
+ var matrixA = MatrixLoader.GenerateRandomPositiveDefiniteUserDefinedMatrix(order);
+ var matrixACopy = matrixA.Clone();
+ var factorSvd = matrixA.Svd(true);
+ var vectorb = MatrixLoader.GenerateRandomUserDefinedVector(order);
+ var vectorbCopy = vectorb.Clone();
+ var resultx = new UserDefinedVector(order);
+ factorSvd.Solve(vectorb, resultx);
+
+ var bReconstruct = matrixA * resultx;
+
+ // Check the reconstruction.
+ for (var i = 0; i < vectorb.Count; i++)
+ {
+ Assert.AreApproximatelyEqual(vectorb[i], bReconstruct[i], 1.0e-11);
+ }
+
+ // Make sure A didn't change.
+ for (var i = 0; i < matrixA.RowCount; i++)
+ {
+ for (var j = 0; j < matrixA.ColumnCount; j++)
+ {
+ Assert.AreEqual(matrixACopy[i, j], matrixA[i, j]);
+ }
+ }
+
+ // Make sure b didn't change.
+ for (var i = 0; i < vectorb.Count; i++)
+ {
+ Assert.AreEqual(vectorbCopy[i], vectorb[i]);
+ }
+ }
+
+ [Test]
+ [Row(1)]
+ [Row(2)]
+ [Row(5)]
+ [Row(10)]
+ [Row(50)]
+ [Row(100)]
+ [MultipleAsserts]
+ public void CanSolveForRandomMatrixAndSymmetricMatrixWhenResultMatrixGiven(int order)
+ {
+ var matrixA = MatrixLoader.GenerateRandomPositiveDefiniteUserDefinedMatrix(order);
+ var matrixACopy = matrixA.Clone();
+ var factorSvd = matrixA.Svd(true);
+
+ var matrixB = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
+ var matrixBCopy = matrixB.Clone();
+
+ var matrixX = new UserDefinedMatrix(order, order);
+ factorSvd.Solve(matrixB, matrixX);
+
+ // The solution X row dimension is equal to the column dimension of A
+ Assert.AreEqual(matrixA.ColumnCount, matrixX.RowCount);
+ // The solution X has the same number of columns as B
+ Assert.AreEqual(matrixB.ColumnCount, matrixX.ColumnCount);
+
+ var matrixBReconstruct = matrixA * matrixX;
+
+ // Check the reconstruction.
+ for (var i = 0; i < matrixB.RowCount; i++)
+ {
+ for (var j = 0; j < matrixB.ColumnCount; j++)
+ {
+ Assert.AreApproximatelyEqual(matrixB[i, j], matrixBReconstruct[i, j], 1.0e-11);
+ }
+ }
+
+ // Make sure A didn't change.
+ for (var i = 0; i < matrixA.RowCount; i++)
+ {
+ for (var j = 0; j < matrixA.ColumnCount; j++)
+ {
+ Assert.AreEqual(matrixACopy[i, j], matrixA[i, j]);
+ }
+ }
+
+ // Make sure B didn't change.
+ for (var i = 0; i < matrixB.RowCount; i++)
+ {
+ for (var j = 0; j < matrixB.ColumnCount; j++)
+ {
+ Assert.AreEqual(matrixBCopy[i, j], matrixB[i, j]);
+ }
+ }
+ }
+ }
+}
diff --git a/src/UnitTests/UnitTests.csproj b/src/UnitTests/UnitTests.csproj
index e33c0a39..1136ba89 100644
--- a/src/UnitTests/UnitTests.csproj
+++ b/src/UnitTests/UnitTests.csproj
@@ -169,6 +169,7 @@
+