private void decompose(Matrix a) { int n = a.rowSize(); L.assign(a); // column-wise submatrix cholesky with simple pivoting for (int k = 0; k < n; k++) { double akk = L.get(k, k); // set upper part of column to 0. L.viewColumn(k).viewPart(0, k).assign(0); double epsilon = 1.0e-10 * L.viewColumn(k).aggregate(Functions.MAX, Functions.ABS); if (akk <= epsilon) { // degenerate column case. Set diagonal to 1, all others to zero L.viewColumn(k).viewPart(k, n - k).assign(0); isPositiveDefinite = false; // no need to subtract from remaining sub-matrix } else { // normalize column by diagonal element akk = Math.sqrt(Math.max(0, akk)); L.set(k, k, akk); L.viewColumn(k).viewPart(k + 1, n - k - 1).assign(Functions.div(akk)); // now subtract scaled version of column for (int j = k + 1; j < n; j++) { Vector columnJ = L.viewColumn(j).viewPart(j, n - j); Vector columnK = L.viewColumn(k).viewPart(j, n - j); columnJ.assign(columnK, Functions.minusMult(L.get(j, k))); } } } }
double epsilon = 1.0e-10 * Math.max(uberMax, L.viewColumn(k).aggregate(Functions.MAX, Functions.ABS)); } else if (akk <= epsilon) { L.viewColumn(k).assign(0); isPositiveDefinite = false; L.viewColumn(k).viewPart(k, n - k).assign(Functions.div(akk)); L.viewColumn(k).viewPart(0, k).assign(0); Vector columnJ = L.viewColumn(j).viewPart(k, n - k); Vector columnK = L.viewColumn(k).viewPart(k, n - k); columnJ.assign(columnK, Functions.minusMult(columnK.get(j - k)));
@Test public void testSwap() { Matrix m = new DenseMatrix(10, 10); for (int i = 0; i < 10; i++) { for (int j = 0; j < 10; j++) { m.set(i, j, 10 * i + j); } } PivotedMatrix pm = new PivotedMatrix(m); pm.swap(3, 5); assertEquals(0, pm.viewDiagonal().minus( new DenseVector(new double[]{0, 11, 22, 55, 44, 33, 66, 77, 88, 99})).norm(1), 1.0e-10); pm.swap(2, 7); assertEquals(0, pm.viewDiagonal().minus( new DenseVector(new double[]{0, 11, 77, 55, 44, 33, 66, 22, 88, 99})).norm(1), 1.0e-10); pm.swap(5, 8); assertEquals(0, pm.viewColumn(4).minus( new DenseVector(new double[]{4.0,14.0,74.0,54.0,44.0,84.0,64.0,24.0,34.0,94.0})).norm(1), 1.0e-10); assertEquals(0, pm.viewDiagonal().minus( new DenseVector(new double[]{0, 11, 77, 55, 44, 88, 66, 22, 33, 99})).norm(1), 1.0e-10); } }
private void decompose(Matrix a) { int n = a.rowSize(); L.assign(a); // column-wise submatrix cholesky with simple pivoting for (int k = 0; k < n; k++) { double akk = L.get(k, k); // set upper part of column to 0. L.viewColumn(k).viewPart(0, k).assign(0); double epsilon = 1.0e-10 * L.viewColumn(k).aggregate(Functions.MAX, Functions.ABS); if (akk <= epsilon) { // degenerate column case. Set diagonal to 1, all others to zero L.viewColumn(k).viewPart(k, n - k).assign(0); isPositiveDefinite = false; // no need to subtract from remaining sub-matrix } else { // normalize column by diagonal element akk = Math.sqrt(Math.max(0, akk)); L.set(k, k, akk); L.viewColumn(k).viewPart(k + 1, n - k - 1).assign(Functions.div(akk)); // now subtract scaled version of column for (int j = k + 1; j < n; j++) { Vector columnJ = L.viewColumn(j).viewPart(j, n - j); Vector columnK = L.viewColumn(k).viewPart(j, n - j); columnJ.assign(columnK, Functions.minusMult(L.get(j, k))); } } } }
private void decompose(Matrix a) { int n = a.rowSize(); L.assign(a); // column-wise submatrix cholesky with simple pivoting for (int k = 0; k < n; k++) { double akk = L.get(k, k); // set upper part of column to 0. L.viewColumn(k).viewPart(0, k).assign(0); double epsilon = 1.0e-10 * L.viewColumn(k).aggregate(Functions.MAX, Functions.ABS); if (akk <= epsilon) { // degenerate column case. Set diagonal to 1, all others to zero L.viewColumn(k).viewPart(k, n - k).assign(0); isPositiveDefinite = false; // no need to subtract from remaining sub-matrix } else { // normalize column by diagonal element akk = Math.sqrt(Math.max(0, akk)); L.set(k, k, akk); L.viewColumn(k).viewPart(k + 1, n - k - 1).assign(Functions.div(akk)); // now subtract scaled version of column for (int j = k + 1; j < n; j++) { Vector columnJ = L.viewColumn(j).viewPart(j, n - j); Vector columnK = L.viewColumn(k).viewPart(j, n - j); columnJ.assign(columnK, Functions.minusMult(L.get(j, k))); } } } }
double epsilon = 1.0e-10 * Math.max(uberMax, L.viewColumn(k).aggregate(Functions.MAX, Functions.ABS)); } else if (akk <= epsilon) { L.viewColumn(k).assign(0); isPositiveDefinite = false; L.viewColumn(k).viewPart(k, n - k).assign(Functions.div(akk)); L.viewColumn(k).viewPart(0, k).assign(0); Vector columnJ = L.viewColumn(j).viewPart(k, n - k); Vector columnK = L.viewColumn(k).viewPart(k, n - k); columnJ.assign(columnK, Functions.minusMult(columnK.get(j - k)));
double epsilon = 1.0e-10 * Math.max(uberMax, L.viewColumn(k).aggregate(Functions.MAX, Functions.ABS)); } else if (akk <= epsilon) { L.viewColumn(k).assign(0); isPositiveDefinite = false; L.viewColumn(k).viewPart(k, n - k).assign(Functions.div(akk)); L.viewColumn(k).viewPart(0, k).assign(0); Vector columnJ = L.viewColumn(j).viewPart(k, n - k); Vector columnK = L.viewColumn(k).viewPart(k, n - k); columnJ.assign(columnK, Functions.minusMult(columnK.get(j - k)));
@Test public void testSwap() { Matrix m = new DenseMatrix(10, 10); for (int i = 0; i < 10; i++) { for (int j = 0; j < 10; j++) { m.set(i, j, 10 * i + j); } } PivotedMatrix pm = new PivotedMatrix(m); pm.swap(3, 5); assertEquals(0, pm.viewDiagonal().minus( new DenseVector(new double[]{0, 11, 22, 55, 44, 33, 66, 77, 88, 99})).norm(1), 1.0e-10); pm.swap(2, 7); assertEquals(0, pm.viewDiagonal().minus( new DenseVector(new double[]{0, 11, 77, 55, 44, 33, 66, 22, 88, 99})).norm(1), 1.0e-10); pm.swap(5, 8); assertEquals(0, pm.viewColumn(4).minus( new DenseVector(new double[]{4.0,14.0,74.0,54.0,44.0,84.0,64.0,24.0,34.0,94.0})).norm(1), 1.0e-10); assertEquals(0, pm.viewDiagonal().minus( new DenseVector(new double[]{0, 11, 77, 55, 44, 88, 66, 22, 33, 99})).norm(1), 1.0e-10); } }