public Solve ( double value ) : ].double[ | ||
value | double | Right-hand-side matrix with as many rows as |
return | ].double[ |
public void QrDecompositionConstructorTest() { double[,] value = { { 2, -1, 0 }, { -1, 2, -1 }, { 0, -1, 2 } }; QrDecomposition target = new QrDecomposition(value); // Decomposition Identity var Q = target.OrthogonalFactor; var QQt = Q.Multiply(Q.Transpose()); Assert.IsTrue(Matrix.IsEqual(QQt, Matrix.Identity(3), 0.0000001)); // Linear system solving double[,] B = Matrix.ColumnVector(new double[] { 1, 2, 3 }); double[,] expected = Matrix.ColumnVector(new double[] { 2.5, 4.0, 3.5 }); double[,] actual = target.Solve(B); Assert.IsTrue(Matrix.IsEqual(expected, actual, 0.0000000000001)); }
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); value[i, j] = double.NaN; var target = new QrDecomposition(value); var solution = target.Solve(I); var inverse = target.Inverse(); Assert.IsTrue(Matrix.IsEqual(solution, inverse)); } } }
public void SolveTest2() { // Example from Lecture notes for MATHS 370: Advanced Numerical Methods // http://www.math.auckland.ac.nz/~sharp/370/qr-solving.pdf double[,] value = { { 1, 0, 0 }, { 1, 7, 49 }, { 1, 14, 196 }, { 1, 21, 441 }, { 1, 28, 784 }, { 1, 35, 1225 }, }; // Matrices { double[,] b = { { 4 }, { 1 }, { 0 }, { 0 }, { 2 }, { 5 }, }; double[,] expected = { { 3.9286 }, { -0.5031 }, { 0.0153 }, }; QrDecomposition target = new QrDecomposition(value); double[,] actual = target.Solve(b); Assert.IsTrue(Matrix.IsEqual(expected, actual, 1e-4)); } // Vectors { double[] b = { 4, 1, 0, 0, 2, 5 }; double[] expected = { 3.9286, -0.5031, 0.0153 }; QrDecomposition target = new QrDecomposition(value); double[] actual = target.Solve(b); Assert.IsTrue(Matrix.IsEqual(expected, actual, 1e-4)); } }
public void SolveTest() { double[,] value = { { 2, -1, 0 }, { -1, 2, -1 }, { 0, -1, 2 } }; double[] b = { 1, 2, 3 }; double[] expected = { 2.5000, 4.0000, 3.5000 }; QrDecomposition target = new QrDecomposition(value); double[] actual = target.Solve(b); Assert.IsTrue(Matrix.IsEqual(expected, actual, 0.0000000000001)); }
public void SolveTest3() { double[][] value = { new double[] { 41.9, 29.1, 1 }, new double[] { 43.4, 29.3, 1 }, new double[] { 43.9, 29.5, 0 }, new double[] { 44.5, 29.7, 0 }, new double[] { 47.3, 29.9, 0 }, new double[] { 47.5, 30.3, 0 }, new double[] { 47.9, 30.5, 0 }, new double[] { 50.2, 30.7, 0 }, new double[] { 52.8, 30.8, 0 }, new double[] { 53.2, 30.9, 0 }, new double[] { 56.7, 31.5, 0 }, new double[] { 57.0, 31.7, 0 }, new double[] { 63.5, 31.9, 0 }, new double[] { 65.3, 32.0, 0 }, new double[] { 71.1, 32.1, 0 }, new double[] { 77.0, 32.5, 0 }, new double[] { 77.8, 32.9, 0 } }; double[][] b = { new double[] { 251.3 }, new double[] { 251.3 }, new double[] { 248.3 }, new double[] { 267.5 }, new double[] { 273.0 }, new double[] { 276.5 }, new double[] { 270.3 }, new double[] { 274.9 }, new double[] { 285.0 }, new double[] { 290.0 }, new double[] { 297.0 }, new double[] { 302.5 }, new double[] { 304.5 }, new double[] { 309.3 }, new double[] { 321.7 }, new double[] { 330.7 }, new double[] { 349.0 } }; double[][] expected = { new double[] { 1.7315235669547167 }, new double[] { 6.25142110500275 }, new double[] { -5.0909763966987178 }, }; var target = new JaggedQrDecomposition(value); double[][] actual = target.Solve(b); Assert.IsTrue(Matrix.IsEqual(expected, actual, atol: 1e-4)); var reconstruct = value.Dot(expected); Assert.IsTrue(Matrix.IsEqual(reconstruct, b, rtol: 1e-1)); double[] b2 = b.GetColumn(0); double[] expected2 = expected.GetColumn(0); var target2 = new JaggedQrDecomposition(value); double[] actual2 = target2.Solve(b2); Assert.IsTrue(Matrix.IsEqual(expected2, actual2, atol: 1e-4)); var targetMat = new QrDecomposition(value.ToMatrix()); double[,] actualMat = targetMat.Solve(b.ToMatrix()); Assert.IsTrue(Matrix.IsEqual(expected, actualMat, atol: 1e-4)); var reconstructMat = value.ToMatrix().Dot(expected); Assert.IsTrue(Matrix.IsEqual(reconstruct, b, rtol: 1e-1)); var targetMat2 = new QrDecomposition(value.ToMatrix()); double[] actualMat2 = targetMat2.Solve(b2); Assert.IsTrue(Matrix.IsEqual(expected2, actualMat2, atol: 1e-4)); }