public void CholeskyDecompositionComputeTest() { for (Int32 matrixIndex = 0; matrixIndex < this.matrices.Length; matrixIndex++) { CholeskyDecomposition decomposition = new CholeskyDecomposition(this.matrices[matrixIndex]); decomposition.Compute(); decomposition.L.ShouldBe(this.expectedL[matrixIndex], 0.001); decomposition.LT.ShouldBe(this.expectedLT[matrixIndex], 0.001); } }
public void CholeskyDecompositionComputeTest() { for (Int32 i = 0; i < _matrix.Length; i++) { CholeskyDecomposition decomposition = new CholeskyDecomposition(_matrix[i]); decomposition.Compute(); for (Int32 j = 0; j < _matrix[i].NumberOfRows; j++) { for (Int32 k = 0; k < _matrix[i].NumberOfColumns; k++) { Assert.AreEqual(_lExpected[i][j, k], decomposition.L[j, k], 0.01); Assert.AreEqual(_ltExpected[i][j, k], decomposition.LT[j, k], 0.01); } } } }
public static void test_Matrices() { int N = 200; //int N = 2500; DenseMatrix M1 = new DenseMatrix(N, N); SymmetricSparseMatrix M2 = new SymmetricSparseMatrix(); for (int i = 0; i < N; ++i) { for (int j = i; j < N; ++j) { if (i == j) { M1.Set(i, i, N); M2.Set(i, i, N); } else if (j % 2 != 0) { double d = 1.0 / Math.Sqrt(i + j); M1.Set(i, j, d); M1.Set(j, i, d); M2.Set(i, j, d); } } } double[] X = new double[N], b1 = new double[N], b2 = new double[N]; for (int i = 0; i < N; ++i) { X[i] = (double)i / (double)N; } M1.Multiply(X, b1); M2.Multiply(X, b2); for (int i = 0; i < N; ++i) { Debug.Assert(MathUtil.EpsilonEqual(b1[i], b2[i])); } Debug.Assert(M1.IsSymmetric()); Debug.Assert(M1.IsPositiveDefinite()); // test parallel cholesky decomposition LocalProfiler p = new LocalProfiler(); p.Start("chol"); CholeskyDecomposition decompM = new CholeskyDecomposition(M1); decompM.ComputeParallel(); p.Stop("chol"); //System.Console.WriteLine(p.AllTimes()); DenseMatrix LLT_M1 = decompM.L.Multiply(decompM.L.Transpose()); if (LLT_M1.EpsilonEquals(M1) == false) { System.Console.WriteLine("FAIL choleskyM1 did not reproduce input"); } // test cholesky-decomp backsubstitution Random r = new Random(31337); double[] RealX = TestUtil.RandomScalars(N, r, new Interval1d(-10, 10)); double[] B = new double[N], SolvedX = new double[N], TmpY = new double[N]; M1.Multiply(RealX, B); decompM.Solve(B, SolvedX, TmpY); if (BufferUtil.DistanceSquared(RealX, SolvedX) > MathUtil.ZeroTolerance) { System.Console.WriteLine("FAIL choleskyM1 backsubstution did not reproduce input vector"); } // test case from: https://people.cs.kuleuven.be/~karl.meerbergen/didactiek/h03g1a/ilu.pdf //DenseMatrix tmp = new DenseMatrix(6, 6); //tmp.Set(new double[] { // 3,0,-1,-1,0,-1, // 0,2,0,-1,0,0, // -1,0,3,0,-1,0, // -1,-1,0,2,0,-1, // 0,0,-1,0,3,-1, // -1,0,0,-1,-1,4}); //CholeskyDecomposition decompDense = new CholeskyDecomposition(tmp); //decompDense.Compute(); //PackedSparseMatrix M1_sparse = PackedSparseMatrix.FromDense(tmp, true); //M1_sparse.Sort(); //SparseCholeskyDecomposition decompM1_sparse = new SparseCholeskyDecomposition(M1_sparse); //decompM1_sparse.ComputeIncomplete(); // cholesky decomposition known-result test DenseMatrix MSym3x3 = new DenseMatrix(3, 3); MSym3x3.Set(new double[] { 25, 15, -5, 15, 18, 0, -5, 0, 11 }); DenseMatrix MSym3x3_Chol = new DenseMatrix(3, 3); MSym3x3_Chol.Set(new double[] { 5, 0, 0, 3, 3, 0, -1, 1, 3 }); CholeskyDecomposition decomp3x3 = new CholeskyDecomposition(MSym3x3); decomp3x3.Compute(); if (decomp3x3.L.EpsilonEquals(MSym3x3_Chol) == false) { System.Console.WriteLine("FAIL cholesky3x3 incorrect result"); } if (decomp3x3.L.Multiply(decomp3x3.L.Transpose()).EpsilonEquals(MSym3x3) == false) { System.Console.WriteLine("FAIL cholesky3x3 did not reproduce input"); } // cholesky decomposition known-result test DenseMatrix MSym4x4 = new DenseMatrix(4, 4); MSym4x4.Set(new double[] { 18, 22, 54, 42, 22, 70, 86, 62, 54, 86, 174, 134, 42, 62, 134, 106 }); DenseMatrix MSym4x4_Chol = new DenseMatrix(4, 4); MSym4x4_Chol.Set(new double[] { 4.24264, 0, 0, 0, 5.18545, 6.56591, 0, 0, 12.72792, 3.04604, 1.64974, 0, 9.89949, 1.62455, 1.84971, 1.39262 }); CholeskyDecomposition decomp4x4 = new CholeskyDecomposition(MSym4x4); decomp4x4.Compute(); if (decomp4x4.L.EpsilonEquals(MSym4x4_Chol, 0.0001) == false) { System.Console.WriteLine("FAIL cholesky4x4 incorrect result"); } if (decomp4x4.L.Multiply(decomp4x4.L.Transpose()).EpsilonEquals(MSym4x4) == false) { System.Console.WriteLine("FAIL cholesky4x4 did not reproduce input"); } }