public Solve ( double value ) : ].double[ | ||
value | double | Right hand side matrix with as many rows as |
리턴 | ].double[ |
public void InverseTestNaN() { int n = 5; var I = Matrix.Identity(n); for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { double[,] value = Matrix.Magic(n); // Make symmetric value = Matrix.Multiply(value, value.Transpose()); value[i, j] = double.NaN; value[j, i] = double.NaN; Assert.IsTrue(value.IsSymmetric()); bool thrown = false; var target = new CholeskyDecomposition(value); try { target.Solve(I); } catch (Exception) { thrown = true; } Assert.IsTrue(thrown); } } }
/// <summary> /// Gets the probability density function (pdf) for /// this distribution evaluated at point <c>x</c>. /// </summary> /// /// <param name="x">A single point in the distribution range. /// For a matrix distribution, such as the Wishart's, this /// should be a positive-definite matrix or a matrix written /// in flat vector form. /// </param> /// /// <returns> /// The probability of <c>x</c> occurring /// in the current distribution. /// </returns> /// /// <remarks> /// The Probability Density Function (PDF) describes the /// probability that a given value <c>x</c> will occur. /// </remarks> /// public double LogProbabilityDensityFunction(double[,] x) { var chol = new CholeskyDecomposition(x); double det = chol.Determinant; double[,] Vx = chol.Solve(inverseScaleMatrix); double z = -0.5 * Vx.Trace(); return Math.Log(constant) + power * Math.Log(det) + z; }
/// <summary> /// Gets the probability density function (pdf) for /// this distribution evaluated at point <c>x</c>. /// </summary> /// /// <param name="x">A single point in the distribution range. /// For a matrix distribution, such as the Wishart's, this /// should be a positive-definite matrix or a matrix written /// in flat vector form. /// </param> /// /// <returns> /// The probability of <c>x</c> occurring /// in the current distribution. /// </returns> /// /// <remarks> /// The Probability Density Function (PDF) describes the /// probability that a given value <c>x</c> will occur. /// </remarks> /// public double ProbabilityDensityFunction(double[,] x) { var chol = new CholeskyDecomposition(x); double det = chol.Determinant; double[,] Vx = chol.Solve(inverseScaleMatrix); double z = -0.5 * Vx.Trace(); double a = Math.Pow(det, power); double b = Math.Exp(z); return constant * a * b; }
public void SolveTest4() { double[,] value = // not positive-definite { { 6, -1, 2, 6 }, { -1, 3, -3, -2 }, { 2, -3, 2, 0 }, { 6, -2, 0, 0 }, }; CholeskyDecomposition chol = new CholeskyDecomposition(value, true); double[,] L = chol.LeftTriangularFactor; double[] B = new double[] { 1, 2, 3, 4 }; double[] expected = { 5, 13, 16, -8 }; double[] actual = chol.Solve(B); Assert.IsTrue(Matrix.IsEqual(expected, actual, 0.0000000000001)); }
public void SolveTest2() { double[,] value = // not positive-definite { { 6, -1, 2, 6 }, { -1, 3, -3, -2 }, { 2, -3, 2, 0 }, { 6, -2, 0, 0 }, }; CholeskyDecomposition chol = new CholeskyDecomposition(value, true); double[,] L = chol.LeftTriangularFactor; double[,] B = Matrix.Identity(4); double[,] expected = { { 0.4000, 1.2000, 1.4000, -0.5000 }, { 1.2000, 3.6000, 4.2000, -2.0000 }, { 1.4000, 4.2000, 5.4000, -2.5000 }, { -0.5000, -2.0000, -2.5000, 1.0000 }, }; double[,] actual = chol.Solve(B); Assert.IsTrue(Matrix.IsEqual(expected, actual, 0.0000000000001)); }
public void SolveTest3() { double[,] value = // positive-definite { { 2, -1, 0 }, { -1, 2, -1 }, { 0, -1, 2 } }; CholeskyDecomposition chol = new CholeskyDecomposition(value); double[,] L = chol.LeftTriangularFactor; double[] B = new double[] { 1, 2, 3 }; double[] expected = new double[] { 2.5, 4.0, 3.5 }; double[] actual = chol.Solve(B); Assert.IsTrue(Matrix.IsEqual(expected, actual, 0.0000000000001)); actual = chol.Solve(B, true); Assert.AreEqual(actual, B); Assert.IsTrue(Matrix.IsEqual(expected, B, 0.0000000000001)); }
public void InverseTest1() { double[,] value = // positive-definite { { 2, -1, 0 }, { -1, 2, -1 }, { 0, -1, 2 } }; var chol = new CholeskyDecomposition(value, robust: false); Assert.IsTrue(chol.IsPositiveDefinite); var L = chol.LeftTriangularFactor; float[][] expected = { new float[] { 0.750f, 0.500f, 0.250f }, new float[] { 0.500f, 1.000f, 0.500f }, new float[] { 0.250f, 0.500f, 0.750f }, }; double[,] actual = chol.Inverse(); Assert.IsTrue(actual.IsEqual(expected, 1e-6)); double[,] inv = chol.Solve(Matrix.Identity(3)); Assert.IsTrue(inv.IsEqual(expected, 1e-6)); }
public void SolveTest() { double[,] value = // positive-definite { { 2, -1, 0 }, { -1, 2, -1 }, { 0, -1, 2 } }; CholeskyDecomposition chol = new CholeskyDecomposition(value); double[,] L = chol.LeftTriangularFactor; double[,] B = Matrix.ColumnVector(new double[] { 1, 2, 3 }); double[,] expected = Matrix.ColumnVector(new double[] { 2.5, 4.0, 3.5 }); double[,] actual = chol.Solve(B); Assert.IsTrue(Matrix.IsEqual(expected, actual, 1e-10)); Assert.AreNotEqual(actual, B); actual = chol.Solve(B, true); Assert.AreEqual(actual, B); Assert.IsTrue(Matrix.IsEqual(expected, B, 1e-10)); Assert.IsTrue(Matrix.IsEqual(chol.Reverse(), value, 1e-6)); }
/// <summary> /// Gets the probability density function (pdf) for /// this distribution evaluated at point <c>x</c>. /// </summary> /// /// <param name="x">A single point in the distribution range.</param> /// /// <returns> /// The probability of <c>x</c> occurring /// in the current distribution. /// </returns> /// /// <remarks> /// The Probability Density Function (PDF) describes the /// probability that a given value <c>x</c> will occur. /// </remarks> /// public override double ProbabilityDensityFunction(double[] x) { // http://www.buch-kromann.dk/tine/nonpar/Nonparametric_Density_Estimation_multidim.pdf // http://sfb649.wiwi.hu-berlin.de/fedc_homepage/xplore/ebooks/html/spm/spmhtmlnode18.html double sum = 0; CholeskyDecomposition chol = new CholeskyDecomposition(smoothing); double[] delta = new double[Dimension]; for (int i = 0; i < samples.Length; i++) { for (int j = 0; j < x.Length; j++) delta[j] = (x[j] - samples[i][j]); sum += kernel.Function(chol.Solve(delta)); } return sum / (samples.Length * determinant); }