- * For a symmetric, positive definite matrix A, the Cholesky decomposition
- * is an lower triangular matrix L so that A = L*L'.
- *
- * If the matrix is not symmetric or positive definite, the constructor
- * returns a partial decomposition and sets an internal flag that may
- * be queried by the isSPD() method.
- */
-
-public class CholeskyDecomposition implements java.io.Serializable {
-
- /**
- * Array for internal storage of decomposition.
- *
- * @serial internal array storage.
- */
- private double[][] L;
-
- /**
- * Row and column dimension (square matrix).
- *
- * @serial matrix dimension.
- */
- private int n;
-
- /**
- * Symmetric and positive definite flag.
- *
- * @serial is symmetric and positive definite flag.
- */
- private boolean isspd;
-
- /**
- * Cholesky algorithm for symmetric and positive definite matrix.
- *
- * @param arg A square, symmetric matrix.
- * @return Structure to access L and isspd flag.
- */
-
- public CholeskyDecomposition(Matrix matrix) {
- // Initialize.
- double[][] A = matrix.getArray();
- n = matrix.getRowDimension();
- L = new double[n][n];
- isspd = (matrix.getColumnDimension() == n);
- // Main loop.
- for (int j = 0; j < n; j++) {
- double[] Lrowj = L[j];
- double d = 0.0;
- for (int k = 0; k < j; k++) {
- double[] Lrowk = L[k];
- double s = 0.0;
- for (int i = 0; i < k; i++) {
- s += Lrowk[i] * Lrowj[i];
- }
- Lrowj[k] = s = (A[j][k] - s) / L[k][k];
- d += s * s;
- isspd &= (A[k][j] == A[j][k]);
- }
- d = A[j][j] - d;
- isspd &= (d > 0.0);
- L[j][j] = Math.sqrt(Math.max(d, 0.0));
- for (int k = j + 1; k < n; k++) {
- L[j][k] = 0.0;
- }
- }
- }
-
-
-// \** Right Triangular Cholesky Decomposition.
-//
-// For a symmetric, positive definite matrix A, the Right Cholesky
-// decomposition is an upper triangular matrix R so that A = R'*R.
-// This constructor computes R with the Fortran inspired column oriented
-// algorithm used in LINPACK and MATLAB. In Java, we suspect a row oriented,
-// lower triangular decomposition is faster. We have temporarily included
-// this constructor here until timing experiments confirm this suspicion.
-// *\
-
-
- private transient double[][] R;
-
-
- public CholeskyDecomposition(Matrix Arg, int rightflag) {
- // Initialize.
- double[][] A = Arg.getArray();
- n = Arg.getColumnDimension();
- R = new double[n][n];
- isspd = (Arg.getColumnDimension() == n);
- // Main loop.
- for (int j = 0; j < n; j++) {
- double d = 0.0;
- for (int k = 0; k < j; k++) {
- double s = A[k][j];
- for (int i = 0; i < k; i++) {
- s -= R[i][k] * R[i][j];
- }
- R[k][j] = s /= R[k][k];
- d += s * s;
- isspd &= (A[k][j] == A[j][k]);
- }
- d = A[j][j] - d;
- isspd &= (d > 0.0);
- R[j][j] = Math.sqrt(Math.max(d, 0.0));
- for (int k = j + 1; k < n; k++) {
- R[k][j] = 0.0;
- }
- }
- }
-
-
- public Matrix getR() {
- return new Matrix(R, n, n);
- }
-
-
- /**
- * Is the matrix symmetric and positive definite?
- *
- * @return true if A is symmetric and positive definite.
- */
-
- public boolean isSPD() {
- return isspd;
- }
-
- /**
- * Return triangular factor.
- *
- * @return L
- */
-
- public Matrix getL() {
- return new Matrix(L, n, n);
- }
-
- /**
- * Solve A*X = B
- *
- * @param B A Matrix with as many rows as A and any number of columns.
- * @return X so that L*L'*X = B
- * @throws IllegalArgumentException Matrix row dimensions must agree.
- * @throws RuntimeException Matrix is not symmetric positive definite.
- */
-
- public Matrix solve(Matrix B) {
- if (B.getRowDimension() != n) {
- throw new IllegalArgumentException("Matrix row dimensions must agree.");
- }
- if (!isspd) {
- throw new RuntimeException("Matrix is not symmetric positive definite.");
- }
-
- // Copy right hand side.
- double[][] X = B.getArrayCopy();
- int nx = B.getColumnDimension();
-
- // Solve L*Y = B;
- for (int k = 0; k < n; k++) {
- for (int i = k + 1; i < n; i++) {
- for (int j = 0; j < nx; j++) {
- X[i][j] -= X[k][j] * L[i][k];
- }
- }
- for (int j = 0; j < nx; j++) {
- X[k][j] /= L[k][k];
- }
- }
-
- // Solve L'*X = Y;
- for (int k = n - 1; k >= 0; k--) {
- for (int j = 0; j < nx; j++) {
- X[k][j] /= L[k][k];
- }
- for (int i = 0; i < k; i++) {
- for (int j = 0; j < nx; j++) {
- X[i][j] -= X[k][j] * L[k][i];
- }
- }
- }
- return new Matrix(X, n, nx);
- }
-}
diff --git a/src/main/java/eva2/tools/math/Jama/EigenvalueDecomposition.java b/src/main/java/eva2/tools/math/Jama/EigenvalueDecomposition.java
deleted file mode 100644
index 50b03467..00000000
--- a/src/main/java/eva2/tools/math/Jama/EigenvalueDecomposition.java
+++ /dev/null
@@ -1,956 +0,0 @@
-package eva2.tools.math.Jama;
-
-import eva2.tools.math.Jama.util.Maths;
-
-
-/**
- * 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.times(D.times(V.transpose())) and
- * V.times(V.transpose()) equals the identiCty matrix.
- *
- * 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.times(V) equals V.times(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 EigenvalueDecomposition implements java.io.Serializable {
-
- /**
- * Row and column dimension (square matrix).
- *
- * @serial matrix dimension.
- */
- private int n;
-
- /**
- * Symmetry flag.
- *
- * @serial internal symmetry flag.
- */
- private boolean issymmetric;
-
- /**
- * Arrays for internal storage of eigenvalues.
- *
- * @serial internal storage of eigenvalues.
- */
- private double[] d, e;
-
- /**
- * Array for internal storage of eigenvectors.
- *
- * @serial internal storage of eigenvectors.
- */
- private double[][] V;
-
- /**
- * Array for internal storage of nonsymmetric Hessenberg form.
- *
- * @serial internal storage of nonsymmetric Hessenberg form.
- */
- private double[][] H;
-
- /**
- * Working storage for nonsymmetric algorithm.
- *
- * @serial working storage for nonsymmetric algorithm.
- */
- private double[] ort;
-
- // Symmetric Householder reduction to tridiagonal form.
-
- private void tred2() {
-
- // 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.
-
- System.arraycopy(V[n - 1], 0, d, 0, n);
-
- // Householder reduction to tridiagonal form.
-
- for (int i = n - 1; i > 0; i--) {
-
- // Scale to avoid under/overflow.
-
- double scale = 0.0;
- double h = 0.0;
- for (int k = 0; k < i; k++) {
- scale += Math.abs(d[k]);
- }
- if (scale == 0.0) {
- e[i] = d[i - 1];
- for (int j = 0; j < i; j++) {
- d[j] = V[i - 1][j];
- V[i][j] = 0.0;
- V[j][i] = 0.0;
- }
- } else {
-
- // Generate Householder vector.
-
- for (int k = 0; k < i; k++) {
- d[k] /= scale;
- h += d[k] * d[k];
- }
- double f = d[i - 1];
- double g = Math.sqrt(h);
- if (f > 0) {
- g = -g;
- }
- e[i] = scale * g;
- h -= f * g;
- d[i - 1] = f - g;
- for (int j = 0; j < i; j++) {
- e[j] = 0.0;
- }
-
- // Apply similarity transformation to remaining columns.
-
- for (int j = 0; j < i; j++) {
- f = d[j];
- V[j][i] = f;
- g = e[j] + V[j][j] * f;
- for (int k = j + 1; k <= i - 1; k++) {
- g += V[k][j] * d[k];
- e[k] += V[k][j] * f;
- }
- e[j] = g;
- }
- f = 0.0;
- for (int j = 0; j < i; j++) {
- e[j] /= h;
- f += e[j] * d[j];
- }
- double hh = f / (h + h);
- for (int j = 0; j < i; j++) {
- e[j] -= hh * d[j];
- }
- for (int j = 0; j < i; j++) {
- f = d[j];
- g = e[j];
- for (int k = j; k <= i - 1; k++) {
- V[k][j] -= (f * e[k] + g * d[k]);
- }
- d[j] = V[i - 1][j];
- V[i][j] = 0.0;
- }
- }
- d[i] = h;
- }
-
- // Accumulate transformations.
-
- for (int i = 0; i < n - 1; i++) {
- V[n - 1][i] = V[i][i];
- V[i][i] = 1.0;
- double h = d[i + 1];
- if (h != 0.0) {
- for (int k = 0; k <= i; k++) {
- d[k] = V[k][i + 1] / h;
- }
- for (int j = 0; j <= i; j++) {
- double g = 0.0;
- for (int k = 0; k <= i; k++) {
- g += V[k][i + 1] * V[k][j];
- }
- for (int k = 0; k <= i; k++) {
- V[k][j] -= g * d[k];
- }
- }
- }
- for (int k = 0; k <= i; k++) {
- V[k][i + 1] = 0.0;
- }
- }
- for (int j = 0; j < n; j++) {
- d[j] = V[n - 1][j];
- V[n - 1][j] = 0.0;
- }
- V[n - 1][n - 1] = 1.0;
- e[0] = 0.0;
- }
-
- // Symmetric tridiagonal QL algorithm.
-
- private void tql2() {
-
- // 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.
-
- System.arraycopy(e, 1, e, 0, n - 1);
- e[n - 1] = 0.0;
-
- double f = 0.0;
- double tst1 = 0.0;
- double eps = Math.pow(2.0, -52.0);
- for (int l = 0; l < n; l++) {
-
- // Find small subdiagonal element
-
- tst1 = Math.max(tst1, Math.abs(d[l]) + Math.abs(e[l]));
- int m = l;
- while (m < n) {
- if (Math.abs(e[m]) <= eps * tst1) {
- break;
- }
- m++;
- }
-
- // If m == l, d[l] is an eigenvalue,
- // otherwise, iterate.
-
- if (m > l) {
- int iter = 0;
- do {
- iter += 1; // (Could check iteration count here.)
-
- // Compute implicit shift
-
- double g = d[l];
- double p = (d[l + 1] - g) / (2.0 * e[l]);
- double r = Maths.hypot(p, 1.0);
- if (p < 0) {
- r = -r;
- }
- d[l] = e[l] / (p + r);
- d[l + 1] = e[l] * (p + r);
- double dl1 = d[l + 1];
- double h = g - d[l];
- for (int i = l + 2; i < n; i++) {
- d[i] -= h;
- }
- f += h;
-
- // Implicit QL transformation.
-
- p = d[m];
- double c = 1.0;
- double c2 = c;
- double c3 = c;
- double el1 = e[l + 1];
- double s = 0.0;
- double s2 = 0.0;
- for (int i = m - 1; i >= l; i--) {
- c3 = c2;
- c2 = c;
- s2 = s;
- g = c * e[i];
- h = c * p;
- r = Maths.hypot(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 (int k = 0; k < n; k++) {
- h = V[k][i + 1];
- V[k][i + 1] = s * V[k][i] + c * h;
- V[k][i] = c * V[k][i] - s * h;
- }
- }
- p = -s * s2 * c3 * el1 * e[l] / dl1;
- e[l] = s * p;
- d[l] = c * p;
-
- // Check for convergence.
-
- } while (Math.abs(e[l]) > eps * tst1);
- }
- d[l] += f;
- e[l] = 0.0;
- }
-
- // Sort eigenvalues and corresponding vectors.
-
- for (int i = 0; i < n - 1; i++) {
- int k = i;
- double p = d[i];
- for (int j = i + 1; j < n; j++) {
- if (d[j] < p) {
- k = j;
- p = d[j];
- }
- }
- if (k != i) {
- d[k] = d[i];
- d[i] = p;
- for (int j = 0; j < n; j++) {
- p = V[j][i];
- V[j][i] = V[j][k];
- V[j][k] = p;
- }
- }
- }
- }
-
- // Nonsymmetric reduction to Hessenberg form.
-
- private void orthes() {
-
- // 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.
-
- int low = 0;
- int high = n - 1;
-
- for (int m = low + 1; m <= high - 1; m++) {
-
- // Scale column.
-
- double scale = 0.0;
- for (int i = m; i <= high; i++) {
- scale += Math.abs(H[i][m - 1]);
- }
- if (scale != 0.0) {
-
- // Compute Householder transformation.
-
- double h = 0.0;
- for (int i = high; i >= m; i--) {
- ort[i] = H[i][m - 1] / scale;
- h += ort[i] * ort[i];
- }
- double g = Math.sqrt(h);
- if (ort[m] > 0) {
- g = -g;
- }
- h -= ort[m] * g;
- ort[m] -= g;
-
- // Apply Householder similarity transformation
- // H = (I-u*u'/h)*H*(I-u*u')/h)
-
- for (int j = m; j < n; j++) {
- double f = 0.0;
- for (int i = high; i >= m; i--) {
- f += ort[i] * H[i][j];
- }
- f /= h;
- for (int i = m; i <= high; i++) {
- H[i][j] -= f * ort[i];
- }
- }
-
- for (int i = 0; i <= high; i++) {
- double f = 0.0;
- for (int j = high; j >= m; j--) {
- f += ort[j] * H[i][j];
- }
- f /= h;
- for (int j = m; j <= high; j++) {
- H[i][j] -= f * ort[j];
- }
- }
- ort[m] = scale * ort[m];
- H[m][m - 1] = scale * g;
- }
- }
-
- // Accumulate transformations (Algol's ortran).
-
- for (int i = 0; i < n; i++) {
- for (int j = 0; j < n; j++) {
- V[i][j] = (i == j ? 1.0 : 0.0);
- }
- }
-
- for (int m = high - 1; m >= low + 1; m--) {
- if (H[m][m - 1] != 0.0) {
- for (int i = m + 1; i <= high; i++) {
- ort[i] = H[i][m - 1];
- }
- for (int j = m; j <= high; j++) {
- double g = 0.0;
- for (int i = m; i <= high; i++) {
- g += ort[i] * V[i][j];
- }
- // Double division avoids possible underflow
- g = (g / ort[m]) / H[m][m - 1];
- for (int i = m; i <= high; i++) {
- V[i][j] += g * ort[i];
- }
- }
- }
- }
- }
-
-
- // Complex scalar division.
-
- private transient double cdivr, cdivi;
-
- private void cdiv(double xr, double xi, double yr, double yi) {
- double r, d;
- if (Math.abs(yr) > Math.abs(yi)) {
- r = yi / yr;
- d = yr + r * yi;
- cdivr = (xr + r * xi) / d;
- cdivi = (xi - r * xr) / d;
- } else {
- r = yr / yi;
- d = yi + r * yr;
- cdivr = (r * xr + xi) / d;
- cdivi = (r * xi - xr) / d;
- }
- }
-
-
- // Nonsymmetric reduction from Hessenberg to real Schur form.
-
- private void hqr2() {
-
- // 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.
-
- // Initialize
-
- int nn = this.n;
- int n = nn - 1;
- int low = 0;
- int high = nn - 1;
- double eps = Math.pow(2.0, -52.0);
- double exshift = 0.0;
- double p = 0, q = 0, r = 0, s = 0, z = 0, t, w, x, y;
-
- // Store roots isolated by balanc and compute matrix norm
-
- double norm = 0.0;
- for (int i = 0; i < nn; i++) {
- if (i < low | i > high) {
- d[i] = H[i][i];
- e[i] = 0.0;
- }
- for (int j = Math.max(i - 1, 0); j < nn; j++) {
- norm += Math.abs(H[i][j]);
- }
- }
-
- // Outer loop over eigenvalue index
-
- int iter = 0;
- while (n >= low) {
-
- // Look for single small sub-diagonal element
-
- int l = n;
- while (l > low) {
- s = Math.abs(H[l - 1][l - 1]) + Math.abs(H[l][l]);
- if (s == 0.0) {
- s = norm;
- }
- if (Math.abs(H[l][l - 1]) < eps * s) {
- break;
- }
- l--;
- }
-
- // Check for convergence
- // One root found
-
- if (l == n) {
- H[n][n] += exshift;
- d[n] = H[n][n];
- e[n] = 0.0;
- n--;
- iter = 0;
-
- // Two roots found
-
- } else if (l == n - 1) {
- w = H[n][n - 1] * H[n - 1][n];
- p = (H[n - 1][n - 1] - H[n][n]) / 2.0;
- q = p * p + w;
- z = Math.sqrt(Math.abs(q));
- H[n][n] += exshift;
- H[n - 1][n - 1] += exshift;
- x = H[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 = H[n][n - 1];
- s = Math.abs(x) + Math.abs(z);
- p = x / s;
- q = z / s;
- r = Math.sqrt(p * p + q * q);
- p /= r;
- q /= r;
-
- // Row modification
-
- for (int j = n - 1; j < nn; j++) {
- z = H[n - 1][j];
- H[n - 1][j] = q * z + p * H[n][j];
- H[n][j] = q * H[n][j] - p * z;
- }
-
- // Column modification
-
- for (int i = 0; i <= n; i++) {
- z = H[i][n - 1];
- H[i][n - 1] = q * z + p * H[i][n];
- H[i][n] = q * H[i][n] - p * z;
- }
-
- // Accumulate transformations
-
- for (int i = low; i <= high; i++) {
- z = V[i][n - 1];
- V[i][n - 1] = q * z + p * V[i][n];
- V[i][n] = q * V[i][n] - p * z;
- }
-
- // Complex pair
-
- } else {
- d[n - 1] = x + p;
- d[n] = x + p;
- e[n - 1] = z;
- e[n] = -z;
- }
- n -= 2;
- iter = 0;
-
- // No convergence yet
-
- } else {
-
- // Form shift
-
- x = H[n][n];
- y = 0.0;
- w = 0.0;
- if (l < n) {
- y = H[n - 1][n - 1];
- w = H[n][n - 1] * H[n - 1][n];
- }
-
- // Wilkinson's original ad hoc shift
-
- if (iter == 10) {
- exshift += x;
- for (int i = low; i <= n; i++) {
- H[i][i] -= x;
- }
- s = Math.abs(H[n][n - 1]) + Math.abs(H[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 (int i = low; i <= n; i++) {
- H[i][i] -= s;
- }
- exshift += s;
- x = y = w = 0.964;
- }
- }
-
- iter += 1; // (Could check iteration count here.)
-
- // Look for two consecutive small sub-diagonal elements
-
- int m = n - 2;
- while (m >= l) {
- z = H[m][m];
- r = x - z;
- s = y - z;
- p = (r * s - w) / H[m + 1][m] + H[m][m + 1];
- q = H[m + 1][m + 1] - z - r - s;
- r = H[m + 2][m + 1];
- s = Math.abs(p) + Math.abs(q) + Math.abs(r);
- p /= s;
- q /= s;
- r /= s;
- if (m == l) {
- break;
- }
- if (Math.abs(H[m][m - 1]) * (Math.abs(q) + Math.abs(r)) <
- eps * (Math.abs(p) * (Math.abs(H[m - 1][m - 1]) + Math.abs(z) +
- Math.abs(H[m + 1][m + 1])))) {
- break;
- }
- m--;
- }
-
- for (int i = m + 2; i <= n; i++) {
- H[i][i - 2] = 0.0;
- if (i > m + 2) {
- H[i][i - 3] = 0.0;
- }
- }
-
- // Double QR step involving rows l:n and columns m:n
-
- for (int k = m; k <= n - 1; k++) {
- boolean notlast = (k != n - 1);
- if (k != m) {
- p = H[k][k - 1];
- q = H[k + 1][k - 1];
- r = (notlast ? H[k + 2][k - 1] : 0.0);
- x = Math.abs(p) + Math.abs(q) + Math.abs(r);
- if (x != 0.0) {
- p /= x;
- q /= x;
- r /= x;
- }
- }
- if (x == 0.0) {
- break;
- }
- s = Math.sqrt(p * p + q * q + r * r);
- if (p < 0) {
- s = -s;
- }
- if (s != 0) {
- if (k != m) {
- H[k][k - 1] = -s * x;
- } else if (l != m) {
- H[k][k - 1] = -H[k][k - 1];
- }
- p += s;
- x = p / s;
- y = q / s;
- z = r / s;
- q /= p;
- r /= p;
-
- // Row modification
-
- for (int j = k; j < nn; j++) {
- p = H[k][j] + q * H[k + 1][j];
- if (notlast) {
- p += r * H[k + 2][j];
- H[k + 2][j] -= p * z;
- }
- H[k][j] -= p * x;
- H[k + 1][j] -= p * y;
- }
-
- // Column modification
-
- for (int i = 0; i <= Math.min(n, k + 3); i++) {
- p = x * H[i][k] + y * H[i][k + 1];
- if (notlast) {
- p += z * H[i][k + 2];
- H[i][k + 2] -= p * r;
- }
- H[i][k] -= p;
- H[i][k + 1] -= p * q;
- }
-
- // Accumulate transformations
-
- for (int i = low; i <= high; i++) {
- p = x * V[i][k] + y * V[i][k + 1];
- if (notlast) {
- p += z * V[i][k + 2];
- V[i][k + 2] -= p * r;
- }
- V[i][k] -= p;
- V[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 = nn - 1; n >= 0; n--) {
- p = d[n];
- q = e[n];
-
- // Real vector
-
- if (q == 0) {
- int l = n;
- H[n][n] = 1.0;
- for (int i = n - 1; i >= 0; i--) {
- w = H[i][i] - p;
- r = 0.0;
- for (int j = l; j <= n; j++) {
- r += H[i][j] * H[j][n];
- }
- if (e[i] < 0.0) {
- z = w;
- s = r;
- } else {
- l = i;
- if (e[i] == 0.0) {
- if (w != 0.0) {
- H[i][n] = -r / w;
- } else {
- H[i][n] = -r / (eps * norm);
- }
-
- // Solve real equations
-
- } else {
- x = H[i][i + 1];
- y = H[i + 1][i];
- q = (d[i] - p) * (d[i] - p) + e[i] * e[i];
- t = (x * s - z * r) / q;
- H[i][n] = t;
- if (Math.abs(x) > Math.abs(z)) {
- H[i + 1][n] = (-r - w * t) / x;
- } else {
- H[i + 1][n] = (-s - y * t) / z;
- }
- }
-
- // Overflow control
-
- t = Math.abs(H[i][n]);
- if ((eps * t) * t > 1) {
- for (int j = i; j <= n; j++) {
- H[j][n] /= t;
- }
- }
- }
- }
-
- // Complex vector
-
- } else if (q < 0) {
- int l = n - 1;
-
- // Last vector component imaginary so matrix is triangular
-
- if (Math.abs(H[n][n - 1]) > Math.abs(H[n - 1][n])) {
- H[n - 1][n - 1] = q / H[n][n - 1];
- H[n - 1][n] = -(H[n][n] - p) / H[n][n - 1];
- } else {
- cdiv(0.0, -H[n - 1][n], H[n - 1][n - 1] - p, q);
- H[n - 1][n - 1] = cdivr;
- H[n - 1][n] = cdivi;
- }
- H[n][n - 1] = 0.0;
- H[n][n] = 1.0;
- for (int i = n - 2; i >= 0; i--) {
- double ra, sa, vr, vi;
- ra = 0.0;
- sa = 0.0;
- for (int j = l; j <= n; j++) {
- ra += H[i][j] * H[j][n - 1];
- sa += H[i][j] * H[j][n];
- }
- w = H[i][i] - p;
-
- if (e[i] < 0.0) {
- z = w;
- r = ra;
- s = sa;
- } else {
- l = i;
- if (e[i] == 0) {
- cdiv(-ra, -sa, w, q);
- H[i][n - 1] = cdivr;
- H[i][n] = cdivi;
- } else {
-
- // Solve complex equations
-
- x = H[i][i + 1];
- y = H[i + 1][i];
- vr = (d[i] - p) * (d[i] - p) + e[i] * e[i] - q * q;
- 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));
- }
- cdiv(x * r - z * ra + q * sa, x * s - z * sa - q * ra, vr, vi);
- H[i][n - 1] = cdivr;
- H[i][n] = cdivi;
- if (Math.abs(x) > (Math.abs(z) + Math.abs(q))) {
- H[i + 1][n - 1] = (-ra - w * H[i][n - 1] + q * H[i][n]) / x;
- H[i + 1][n] = (-sa - w * H[i][n] - q * H[i][n - 1]) / x;
- } else {
- cdiv(-r - y * H[i][n - 1], -s - y * H[i][n], z, q);
- H[i + 1][n - 1] = cdivr;
- H[i + 1][n] = cdivi;
- }
- }
-
- // Overflow control
-
- t = Math.max(Math.abs(H[i][n - 1]), Math.abs(H[i][n]));
- if ((eps * t) * t > 1) {
- for (int j = i; j <= n; j++) {
- H[j][n - 1] /= t;
- H[j][n] /= t;
- }
- }
- }
- }
- }
- }
-
- // Vectors of isolated roots
-
- for (int i = 0; i < nn; i++) {
- if (i < low | i > high) {
- System.arraycopy(H[i], i, V[i], i, nn - i);
- }
- }
-
- // Back transformation to get eigenvectors of original matrix
-
- for (int j = nn - 1; j >= low; j--) {
- for (int i = low; i <= high; i++) {
- z = 0.0;
- for (int k = low; k <= Math.min(j, high); k++) {
- z += V[i][k] * H[k][j];
- }
- V[i][j] = z;
- }
- }
- }
-
- /**
- * Check for symmetry, then construct the eigenvalue decomposition
- *
- * @param arg A Square matrix
- * @return Structure to access D and V.
- */
-
- public EigenvalueDecomposition(Matrix matrix) {
- double[][] A = matrix.getArray();
- n = matrix.getColumnDimension();
- V = new double[n][n];
- d = new double[n];
- e = new double[n];
-
- issymmetric = true;
- for (int j = 0; (j < n) & issymmetric; j++) {
- for (int i = 0; (i < n) & issymmetric; i++) {
- issymmetric = (A[i][j] == A[j][i]);
- }
- }
-
- if (issymmetric) {
- for (int i = 0; i < n; i++) {
- System.arraycopy(A[i], 0, V[i], 0, n);
- }
-
- // Tridiagonalize.
- tred2();
-
- // Diagonalize.
- tql2();
-
- } else {
- H = new double[n][n];
- ort = new double[n];
-
- for (int j = 0; j < n; j++) {
- for (int i = 0; i < n; i++) {
- H[i][j] = A[i][j];
- }
- }
-
- // Reduce to Hessenberg form.
- orthes();
-
- // Reduce Hessenberg to real Schur form.
- hqr2();
- }
- }
-
- /**
- * Return the eigenvector matrix
- *
- * @return V
- */
-
- public Matrix getV() {
- return new Matrix(V, n, n);
- }
-
- /**
- * Return the real parts of the eigenvalues
- *
- * @return real(diag(D))
- */
-
- public double[] getRealEigenvalues() {
- return d;
- }
-
- /**
- * Return the imaginary parts of the eigenvalues
- *
- * @return imag(diag(D))
- */
-
- public double[] getImagEigenvalues() {
- return e;
- }
-
- /**
- * Return the block diagonal eigenvalue matrix
- *
- * @return D
- */
-
- public Matrix getD() {
- Matrix X = new Matrix(n, n);
- double[][] D = X.getArray();
- for (int i = 0; i < n; i++) {
- for (int j = 0; j < n; j++) {
- D[i][j] = 0.0;
- }
- D[i][i] = d[i];
- if (e[i] > 0) {
- D[i][i + 1] = e[i];
- } else if (e[i] < 0) {
- D[i][i - 1] = e[i];
- }
- }
- return X;
- }
-}
diff --git a/src/main/java/eva2/tools/math/Jama/LUDecomposition.java b/src/main/java/eva2/tools/math/Jama/LUDecomposition.java
deleted file mode 100644
index 10c82e97..00000000
--- a/src/main/java/eva2/tools/math/Jama/LUDecomposition.java
+++ /dev/null
@@ -1,261 +0,0 @@
-package eva2.tools.math.Jama;
-
-
-/**
- * LU Decomposition.
- *
- * For an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n
- * unit lower triangular matrix L, an n-by-n upper triangular matrix U,
- * and a permutation vector piv of length m so that A(piv,:) = L*U.
- * If m < n, then L is m-by-m and U is m-by-n.
- *
- * The LU decompostion with pivoting always exists, even if the matrix is
- * singular, so the constructor will never fail. The primary use of the
- * LU decomposition is in the solution of square systems of simultaneous
- * linear equations. This will fail if isNonsingular() returns false.
- */
-
-public class LUDecomposition implements java.io.Serializable {
-
- /**
- * Array for internal storage of decomposition.
- *
- * @serial internal array storage.
- */
- private double[][] LU;
-
- /**
- * Row and column dimensions, and pivot sign.
- *
- * @serial column dimension.
- * @serial row dimension.
- * @serial pivot sign.
- */
- private int m, n, pivsign;
-
- /**
- * Internal storage of pivot vector.
- *
- * @serial pivot vector.
- */
- private int[] piv;
-
- /**
- * LU Decomposition
- *
- * @param A Rectangular matrix
- * @return Structure to access L, U and piv.
- */
-
- public LUDecomposition(Matrix A) {
- LU = A.getArrayCopy();
- m = A.getRowDimension();
- n = A.getColumnDimension();
- piv = new int[m];
- for (int i = 0; i < m; i++) {
- piv[i] = i;
- }
- pivsign = 1;
- double[] LUrowi;
- double[] LUcolj = new double[m];
-
- // Outer loop.
-
- for (int j = 0; j < n; j++) {
-
- // Make a copy of the j-th column to localize references.
-
- for (int i = 0; i < m; i++) {
- LUcolj[i] = LU[i][j];
- }
-
- // Apply previous transformations.
-
- for (int i = 0; i < m; i++) {
- LUrowi = LU[i];
-
- // Most of the time is spent in the following dot product.
-
- int kmax = Math.min(i, j);
- double s = 0.0;
- for (int k = 0; k < kmax; k++) {
- s += LUrowi[k] * LUcolj[k];
- }
-
- LUrowi[j] = LUcolj[i] -= s;
- }
-
- // Find pivot and exchange if necessary.
-
- int p = j;
- for (int i = j + 1; i < m; i++) {
- if (Math.abs(LUcolj[i]) > Math.abs(LUcolj[p])) {
- p = i;
- }
- }
- if (p != j) {
- for (int k = 0; k < n; k++) {
- double t = LU[p][k];
- LU[p][k] = LU[j][k];
- LU[j][k] = t;
- }
- int k = piv[p];
- piv[p] = piv[j];
- piv[j] = k;
- pivsign = -pivsign;
- }
-
- // Compute multipliers.
-
- if (j < m & LU[j][j] != 0.0) {
- for (int i = j + 1; i < m; i++) {
- LU[i][j] /= LU[j][j];
- }
- }
- }
- }
-
- /**
- * Is the matrix nonsingular?
- *
- * @return true if U, and hence A, is nonsingular.
- */
-
- public boolean isNonsingular() {
- for (int j = 0; j < n; j++) {
- if (LU[j][j] == 0) {
- return false;
- }
-
- }
- return true;
- }
-
- /**
- * Return lower triangular factor
- *
- * @return L
- */
-
- public Matrix getL() {
- Matrix X = new Matrix(m, n);
- double[][] L = X.getArray();
- for (int i = 0; i < m; i++) {
- for (int j = 0; j < n; j++) {
- if (i > j) {
- L[i][j] = LU[i][j];
- } else if (i == j) {
- L[i][j] = 1.0;
- } else {
- L[i][j] = 0.0;
- }
- }
- }
- return X;
- }
-
- /**
- * Return upper triangular factor
- *
- * @return U
- */
-
- public Matrix getU() {
- Matrix X = new Matrix(n, n);
- double[][] U = X.getArray();
- for (int i = 0; i < n; i++) {
- for (int j = 0; j < n; j++) {
- if (i <= j) {
- U[i][j] = LU[i][j];
- } else {
- U[i][j] = 0.0;
- }
- }
- }
- return X;
- }
-
- /**
- * Return pivot permutation vector
- *
- * @return piv
- */
- public int[] getPivot() {
- int[] p = new int[m];
- System.arraycopy(piv, 0, p, 0, m);
- return p;
- }
-
- /**
- * Return pivot permutation vector as a one-dimensional double array
- *
- * @return (double) piv
- */
- public double[] getDoublePivot() {
- double[] vals = new double[m];
- for (int i = 0; i < m; i++) {
- vals[i] = (double) piv[i];
- }
- return vals;
- }
-
- /**
- * Determinant
- *
- * @return det(A)
- * @throws IllegalArgumentException Matrix must be square
- */
- public double det() {
- if (m != n) {
- throw new IllegalArgumentException("Matrix must be square.");
- }
- double d = (double) pivsign;
- for (int j = 0; j < n; j++) {
- d *= LU[j][j];
- }
- return d;
- }
-
- /**
- * Solve A*X = B
- *
- * @param B A Matrix with as many rows as A and any number of columns.
- * @return X so that L*U*X = B(piv,:)
- * @throws IllegalArgumentException Matrix row dimensions must agree.
- * @throws RuntimeException Matrix is singular.
- */
- public Matrix solve(Matrix B) {
- if (B.getRowDimension() != m) {
- throw new IllegalArgumentException("Matrix row dimensions must agree.");
- }
- if (!this.isNonsingular()) {
- throw new RuntimeException("Matrix is singular.");
- }
-
- // Copy right hand side with pivoting
- int nx = B.getColumnDimension();
- Matrix Xmat = B.getMatrix(piv, 0, nx - 1);
- double[][] X = Xmat.getArray();
-
- // Solve L*Y = B(piv,:)
- for (int k = 0; k < n; k++) {
- for (int i = k + 1; i < n; i++) {
- for (int j = 0; j < nx; j++) {
- X[i][j] -= X[k][j] * LU[i][k];
- }
- }
- }
- // Solve U*X = Y;
- for (int k = n - 1; k >= 0; k--) {
- for (int j = 0; j < nx; j++) {
- X[k][j] /= LU[k][k];
- }
- for (int i = 0; i < k; i++) {
- for (int j = 0; j < nx; j++) {
- X[i][j] -= X[k][j] * LU[i][k];
- }
- }
- }
- return Xmat;
- }
-}
diff --git a/src/main/java/eva2/tools/math/Jama/Matrix.java b/src/main/java/eva2/tools/math/Jama/Matrix.java
deleted file mode 100644
index d6179b67..00000000
--- a/src/main/java/eva2/tools/math/Jama/Matrix.java
+++ /dev/null
@@ -1,1487 +0,0 @@
-package eva2.tools.math.Jama;
-
-
-import eva2.gui.BeanInspector;
-import eva2.tools.Pair;
-import eva2.tools.math.Jama.util.Maths;
-import eva2.tools.math.Mathematics;
-
-import java.io.BufferedReader;
-import java.io.PrintWriter;
-import java.io.Serializable;
-import java.io.StreamTokenizer;
-import java.text.DecimalFormat;
-import java.text.DecimalFormatSymbols;
-import java.text.NumberFormat;
-import java.util.Arrays;
-import java.util.Locale;
-import java.util.Vector;
-
-/**
- * Jama = Java Matrix class.
- *
- * The Java Matrix Class provides the fundamental operations of numerical
- * linear algebra. Various constructors create Matrices from two dimensional
- * arrays of double precision floating point numbers. Various "gets" and
- * "sets" provide access to submatrices and matrix elements. Several methods
- * implement basic matrix arithmetic, including matrix addition and
- * multiplication, matrix norms, and element-by-element array operations.
- * Methods for reading and printing matrices are also included. All the
- * operations in this version of the Matrix Class involve real matrices.
- * Complex matrices may be handled in a future version.
- *
- * Five fundamental matrix decompositions, which consist of pairs or triples
- * of matrices, permutation vectors, and the like, produce results in five
- * decomposition classes. These decompositions are accessed by the Matrix
- * class to compute solutions of simultaneous linear equations, determinants,
- * inverses and other matrix functions. The five decompositions are:
- *
- *
Cholesky Decomposition of symmetric, positive definite matrices.
- *
LU Decomposition of rectangular matrices.
- *
QR Decomposition of rectangular matrices.
- *
Singular Value Decomposition of rectangular matrices.
- *
Eigenvalue Decomposition of both symmetric and nonsymmetric square matrices.
- *
- *
- *
Example of use:
- *
- *
Solve a linear system A x = b and compute the residual norm, ||b - A x||.
- *
- * double[][] vals = {{1.,2.,3},{4.,5.,6.},{7.,8.,10.}};
- * Matrix A = new Matrix(vals);
- * Matrix b = Matrix.random(3,1);
- * Matrix x = A.solve(b);
- * Matrix r = A.times(x).minus(b);
- * double rnorm = r.normInf();
- *
- *
- *
- * @author The MathWorks, Inc. and the National Institute of Standards and Technology.
- * @version 5 August 1998
- */
-
-public class Matrix implements Cloneable, Serializable {
-
- /**
- * Generated serial version identifier.
- */
- private static final long serialVersionUID = 3672826349694248499L;
-
- /**
- * Array for internal storage of elements.
- *
- * @serial internal array storage.
- */
- private double[][] A;
-
- /**
- * Row and column dimensions.
- *
- * @serial row dimension.
- * @serial column dimension.
- */
- private int m, n;
-
- /**
- * Construct an m-by-n matrix of zeros.
- *
- * @param m Number of rows.
- * @param n Number of colums.
- */
-
- public Matrix(int m, int n) {
- this.m = m;
- this.n = n;
- A = new double[m][n];
- }
-
- /**
- * Construct an m-by-n constant matrix.
- *
- * @param m Number of rows.
- * @param n Number of colums.
- * @param s Fill the matrix with this scalar value.
- */
-
- public Matrix(int m, int n, double s) {
- this.m = m;
- this.n = n;
- A = new double[m][n];
- for (int i = 0; i < m; i++) {
- for (int j = 0; j < n; j++) {
- A[i][j] = s;
- }
- }
- }
-
- /**
- * Construct a matrix from a 2-D array.
- *
- * @param A Two-dimensional array of doubles.
- * @throws IllegalArgumentException All rows must have the same length
- * @see #constructWithCopy
- */
-
- public Matrix(double[][] A) {
- this(A, true);
- }
-
- /**
- * @param A
- * @param checkDims
- */
- public Matrix(double[][] A, boolean checkDims) {
- m = A.length;
- n = m == 0 ? 0 : A[0].length;
- if (checkDims) {
- for (int i = 0; i < m; i++) {
- if (A[i].length != n) {
- throw new IllegalArgumentException("All rows must have the same length.");
- }
- }
- }
- this.A = A;
- }
-
- /**
- * Construct a matrix quickly without checking arguments.
- *
- * @param A Two-dimensional array of doubles.
- * @param m Number of rows.
- * @param n Number of colums.
- */
-
- public Matrix(double[][] A, int m, int n) {
- this.A = A;
- this.m = m;
- this.n = n;
- }
-
- /**
- * Construct a matrix from a one-dimensional packed array
- *
- * @param vals One-dimensional array of doubles, packed by columns (ala Fortran).
- * @param m Number of rows.
- * @throws IllegalArgumentException Array length must be a multiple of m.
- */
-
- public Matrix(double vals[], int m) {
- this.m = m;
- n = (m != 0 ? vals.length / m : 0);
- if (m * n != vals.length) {
- throw new IllegalArgumentException("Array length must be a multiple of m.");
- }
- A = new double[m][n];
- for (int i = 0; i < m; i++) {
- for (int j = 0; j < n; j++) {
- A[i][j] = vals[i + j * m];
- }
- }
- }
-
- /**
- *
- */
- public static Matrix repMat(Matrix A, int m, int n) {
- int An = A.getColumnDimension();
- int Am = A.getRowDimension();
- Matrix Ret = new Matrix(m * Am, n * An);
- int nn = 0;
- int mm = 0;
- for (int im = 0; im < m * Am; im++) {
- if (mm == Am) {
- mm = 0;
- }
- for (int in = 0; in < n * An; in++) {
- if (nn == An) {
- nn = 0;
- }
- Ret.set(im, in, A.get(mm, nn));
- nn++;
- }
- mm++;
- }
- return Ret;
- }
-
- /**
- * Construct a matrix from a copy of a 2-D array.
- *
- * @param A Two-dimensional array of doubles.
- * @throws IllegalArgumentException All rows must have the same length
- */
-
- public static Matrix constructWithCopy(double[][] A) {
- int m = A.length;
- int n = A[0].length;
- Matrix X = new Matrix(m, n);
- double[][] C = X.getArray();
- for (int i = 0; i < m; i++) {
- if (A[i].length != n) {
- throw new IllegalArgumentException
- ("All rows must have the same length.");
- }
- System.arraycopy(A[i], 0, C[i], 0, n);
- }
- return X;
- }
-
- /**
- * Make a deep copy of a matrix
- */
-
- public Matrix copy() {
- Matrix X = new Matrix(m, n);
- double[][] C = X.getArray();
- for (int i = 0; i < m; i++) {
- System.arraycopy(A[i], 0, C[i], 0, n);
- }
- return X;
- }
-
- /**
- * Clone the Matrix object.
- */
-
- @Override
- public Object clone() {
- return this.copy();
- }
-
- /**
- * Access the internal two-dimensional array.
- *
- * @return Pointer to the two-dimensional array of matrix elements.
- */
-
- public double[][] getArray() {
- return A;
- }
-
- /**
- * Produce a matrix with the diagonal entries of the instance. All others are set to zero.
- *
- * @return a diagonal matrix
- */
- public Matrix getDiagonalMatrix() {
- double[][] D = new double[m][n];
- for (int i = 0; i < Math.min(m, n); i++) {
- D[i][i] = A[i][i];
- }
- return new Matrix(D);
- }
-
- /**
- * Return the diagonal array for a matrix.
- *
- * @return
- */
- public double[] diag() {
- double[] d = new double[Math.min(getColumnDimension(), getRowDimension())];
- for (int i = 0; i < d.length; i++) {
- d[i] = get(i, i);
- }
- return d;
- }
-
- /**
- * Copy the internal two-dimensional array.
- *
- * @return Two-dimensional array copy of matrix elements.
- */
- public double[][] getArrayCopy() {
- double[][] C = new double[m][n];
- for (int i = 0; i < m; i++) {
- System.arraycopy(A[i], 0, C[i], 0, n);
- }
- return C;
- }
-
- /**
- * Make a one-dimensional column packed copy of the internal array.
- *
- * @return Matrix elements packed in a one-dimensional array by columns.
- */
- public double[] getColumnPackedCopy() {
- double[] vals = new double[m * n];
- for (int i = 0; i < m; i++) {
- for (int j = 0; j < n; j++) {
- vals[i + j * m] = A[i][j];
- }
- }
- return vals;
- }
-
- /**
- * Copy a column from the matrix.
- *
- * @return Matrix elements packed in a one-dimensional array by columns.
- */
- public double[] getColumn(int k) {
- double[] vals = new double[m];
- for (int i = 0; i < m; i++) {
- vals[i] = A[i][k];
- }
- return vals;
- }
-
- public double[] getRowShallow(int i) {
- return A[i];
- }
-
- /**
- * Make a one-dimensional row packed copy of the internal array.
- *
- * @return Matrix elements packed in a one-dimensional array by rows.
- */
- public double[] getRowPackedCopy() {
- double[] vals = new double[m * n];
- for (int i = 0; i < m; i++) {
- System.arraycopy(A[i], 0, vals, i * n, n);
- }
- return vals;
- }
-
- /**
- * Get row dimension.
- *
- * @return m, the number of rows.
- */
- public int getRowDimension() {
- return m;
- }
-
- /**
- * Get column dimension.
- *
- * @return n, the number of columns.
- */
- public int getColumnDimension() {
- return n;
- }
-
- /**
- * Get a single element.
- *
- * @param i Row index.
- * @param j Column index.
- * @return A(i, j)
- * @throws ArrayIndexOutOfBoundsException
- */
- public double get(int i, int j) {
- return A[i][j];
- }
-
- /**
- * Get a submatrix.
- *
- * @param i0 Initial row index
- * @param i1 Final row index
- * @param j0 Initial column index
- * @param j1 Final column index
- * @return A(i0:i1, j0:j1)
- * @throws ArrayIndexOutOfBoundsException Submatrix indices
- */
- public Matrix getMatrix(int i0, int i1, int j0, int j1) {
- Matrix X = new Matrix(i1 - i0 + 1, j1 - j0 + 1);
- double[][] B = X.getArray();
- try {
- for (int i = i0; i <= i1; i++) {
- System.arraycopy(A[i], j0, B[i - i0], 0, j1 + 1 - j0);
- }
- } catch (ArrayIndexOutOfBoundsException e) {
- throw new ArrayIndexOutOfBoundsException("Submatrix indices");
- }
- return X;
- }
-
- /**
- * Get a submatrix.
- *
- * @param r Array of row indices.
- * @param c Array of column indices.
- * @return A(r(:), c(:))
- * @throws ArrayIndexOutOfBoundsException Submatrix indices
- */
- public Matrix getMatrix(int[] r, int[] c) {
- Matrix X = new Matrix(r.length, c.length);
- double[][] B = X.getArray();
- try {
- for (int i = 0; i < r.length; i++) {
- for (int j = 0; j < c.length; j++) {
- B[i][j] = A[r[i]][c[j]];
- }
- }
- } catch (ArrayIndexOutOfBoundsException e) {
- throw new ArrayIndexOutOfBoundsException("Submatrix indices");
- }
- return X;
- }
-
- /**
- * Get a submatrix.
- *
- * @param i0 Initial row index
- * @param i1 Final row index
- * @param c Array of column indices.
- * @return A(i0:i1, c(:))
- * @throws ArrayIndexOutOfBoundsException Submatrix indices
- */
-
- public Matrix getMatrix(int i0, int i1, int[] c) {
- Matrix X = new Matrix(i1 - i0 + 1, c.length);
- double[][] B = X.getArray();
- try {
- for (int i = i0; i <= i1; i++) {
- for (int j = 0; j < c.length; j++) {
- B[i - i0][j] = A[i][c[j]];
- }
- }
- } catch (ArrayIndexOutOfBoundsException e) {
- throw new ArrayIndexOutOfBoundsException("Submatrix indices");
- }
- return X;
- }
-
- /**
- * Get a submatrix.
- *
- * @param r Array of row indices.
- * @param j0 Initial column index
- * @param j1 Final column index
- * @return A(r(:), j0:j1)
- * @throws ArrayIndexOutOfBoundsException Submatrix indices
- */
-
- public Matrix getMatrix(int[] r, int j0, int j1) {
- Matrix X = new Matrix(r.length, j1 - j0 + 1);
- double[][] B = X.getArray();
- try {
- for (int i = 0; i < r.length; i++) {
- System.arraycopy(A[r[i]], j0, B[i], 0, j1 + 1 - j0);
- }
- } catch (ArrayIndexOutOfBoundsException e) {
- throw new ArrayIndexOutOfBoundsException("Submatrix indices");
- }
- return X;
- }
-
- /**
- * Set a single element.
- *
- * @param i Row index.
- * @param j Column index.
- * @param s A(i,j).
- * @throws ArrayIndexOutOfBoundsException
- */
-
- public void set(int i, int j, double s) {
- A[i][j] = s;
- }
-
- /**
- * Set all matrix values to the given value. Overwrites the Matrix completely.
- *
- * @param v
- */
- public void fill(double v) {
- for (int i = 0; i < A.length; i++) {
- Arrays.fill(A[i], v);
- }
- }
-
- /**
- * Set a submatrix.
- *
- * @param i0 Initial row index
- * @param i1 Final row index
- * @param j0 Initial column index
- * @param j1 Final column index
- * @param X A(i0:i1,j0:j1)
- * @throws ArrayIndexOutOfBoundsException Submatrix indices
- */
-
- public void setMatrix(int i0, int i1, int j0, int j1, Matrix X) {
- try {
- for (int i = i0; i <= i1; i++) {
- for (int j = j0; j <= j1; j++) {
- A[i][j] = X.get(i - i0, j - j0);
- }
- }
- } catch (ArrayIndexOutOfBoundsException e) {
- throw new ArrayIndexOutOfBoundsException("Submatrix indices");
- }
- }
-
- /**
- * Set a submatrix.
- *
- * @param r Array of row indices.
- * @param c Array of column indices.
- * @param X A(r(:),c(:))
- * @throws ArrayIndexOutOfBoundsException Submatrix indices
- */
-
- public void setMatrix(int[] r, int[] c, Matrix X) {
- try {
- for (int i = 0; i < r.length; i++) {
- for (int j = 0; j < c.length; j++) {
- A[r[i]][c[j]] = X.get(i, j);
- }
- }
- } catch (ArrayIndexOutOfBoundsException e) {
- throw new ArrayIndexOutOfBoundsException("Submatrix indices");
- }
- }
-
- /**
- * Set a submatrix.
- *
- * @param r Array of row indices.
- * @param j0 Initial column index
- * @param j1 Final column index
- * @param X A(r(:),j0:j1)
- * @throws ArrayIndexOutOfBoundsException Submatrix indices
- */
-
- public void setMatrix(int[] r, int j0, int j1, Matrix X) {
- try {
- for (int i = 0; i < r.length; i++) {
- for (int j = j0; j <= j1; j++) {
- A[r[i]][j] = X.get(i, j - j0);
- }
- }
- } catch (ArrayIndexOutOfBoundsException e) {
- throw new ArrayIndexOutOfBoundsException("Submatrix indices");
- }
- }
-
- /**
- * Set a submatrix.
- *
- * @param i0 Initial row index
- * @param i1 Final row index
- * @param c Array of column indices.
- * @param X A(i0:i1,c(:))
- * @throws ArrayIndexOutOfBoundsException Submatrix indices
- */
-
- public void setMatrix(int i0, int i1, int[] c, Matrix X) {
- try {
- for (int i = i0; i <= i1; i++) {
- for (int j = 0; j < c.length; j++) {
- A[i][c[j]] = X.get(i - i0, j);
- }
- }
- } catch (ArrayIndexOutOfBoundsException e) {
- throw new ArrayIndexOutOfBoundsException("Submatrix indices");
- }
- }
-
- /**
- * Matrix transpose.
- *
- * @return A'
- */
-
- public Matrix transpose() {
- Matrix X = new Matrix(n, m);
- double[][] C = X.getArray();
- for (int i = 0; i < m; i++) {
- for (int j = 0; j < n; j++) {
- C[j][i] = A[i][j];
- }
- }
- return X;
- }
-
- /**
- * One norm
- *
- * @return maximum column sum.
- */
-
- public double norm1() {
- double f = 0;
- for (int j = 0; j < n; j++) {
- double s = 0;
- for (int i = 0; i < m; i++) {
- s += Math.abs(A[i][j]);
- }
- f = Math.max(f, s);
- }
- return f;
- }
-
- /**
- * Two norm
- *
- * @return maximum singular value.
- */
-
- public double norm2() {
- return (new SingularValueDecomposition(this).norm2());
- }
-
- /**
- * Infinity norm
- *
- * @return maximum row sum.
- */
-
- public double normInf() {
- double f = 0;
- for (int i = 0; i < m; i++) {
- double s = 0;
- for (int j = 0; j < n; j++) {
- s += Math.abs(A[i][j]);
- }
- f = Math.max(f, s);
- }
- return f;
- }
-
- /**
- * Frobenius norm
- *
- * @return sqrt of sum of squares of all elements.
- */
-
- public double normF() {
- double f = 0;
- for (int i = 0; i < m; i++) {
- for (int j = 0; j < n; j++) {
- f = Maths.hypot(f, A[i][j]);
- }
- }
- return f;
- }
-
- /**
- * Unary minus
- *
- * @return -A
- */
-
- public Matrix uminus() {
- Matrix X = new Matrix(m, n);
- double[][] C = X.getArray();
- for (int i = 0; i < m; i++) {
- for (int j = 0; j < n; j++) {
- C[i][j] = -A[i][j];
- }
- }
- return X;
- }
-
- /**
- * C = A + B
- *
- * @param B another matrix
- * @return A + B
- */
-
- public Matrix plus(Matrix B) {
- checkMatrixDimensions(B);
- Matrix X = new Matrix(m, n);
- double[][] C = X.getArray();
- for (int i = 0; i < m; i++) {
- for (int j = 0; j < n; j++) {
- C[i][j] = A[i][j] + B.A[i][j];
- }
- }
- return X;
- }
-
- /**
- *
- */
- public void power(double p) {
- for (int i = 0; i < m; i++) {
- for (int j = 0; j < n; j++) {
- A[i][j] = Math.pow(A[i][j], p);
- }
- }
- }
-
- /**
- * In-place multiplication of every entry by a scalar.
- */
- public Matrix multi(double multi) {
- for (int i = 0; i < m; i++) {
- for (int j = 0; j < n; j++) {
- A[i][j] = multi * A[i][j];
- }
- }
- return this;
- }
-
- /**
- * A = A + B
- *
- * @param B another matrix
- * @return A + B
- */
-
- public Matrix plusEquals(Matrix B) {
- checkMatrixDimensions(B);
- for (int i = 0; i < m; i++) {
- for (int j = 0; j < n; j++) {
- A[i][j] += B.A[i][j];
- }
- }
- return this;
- }
-
- /**
- * A = A + B
- *
- * @param B another matrix
- * @return A + B
- */
-
- public Matrix plusEqualsArrayAsMatrix(double[][] B) {
- if ((B.length != m) || (B[0].length != n)) {
- throw new IllegalArgumentException("Matrix dimensions must agree.");
- }
- for (int i = 0; i < m; i++) {
- for (int j = 0; j < n; j++) {
- A[i][j] += B[i][j];
- }
- }
- return this;
- }
-
- /**
- * C = A - B
- *
- * @param B another matrix
- * @return A - B
- */
-
- public Matrix minus(Matrix B) {
- checkMatrixDimensions(B);
- Matrix X = new Matrix(m, n);
- double[][] C = X.getArray();
- for (int i = 0; i < m; i++) {
- for (int j = 0; j < n; j++) {
- C[i][j] = A[i][j] - B.A[i][j];
- }
- }
- return X;
- }
-
- /**
- * A = A - B
- *
- * @param B another matrix
- * @return A - B
- */
-
- public Matrix minusEquals(Matrix B) {
- checkMatrixDimensions(B);
- for (int i = 0; i < m; i++) {
- for (int j = 0; j < n; j++) {
- A[i][j] -= B.A[i][j];
- }
- }
- return this;
- }
-
- /**
- * Element-by-element multiplication, C = A.*B
- *
- * @param B another matrix
- * @return A.*B
- */
- public Matrix arrayTimes(Matrix B) {
- checkMatrixDimensions(B);
- Matrix X = new Matrix(m, n);
- double[][] C = X.getArray();
- for (int i = 0; i < m; i++) {
- for (int j = 0; j < n; j++) {
- C[i][j] = A[i][j] * B.A[i][j];
- }
- }
- return X;
- }
-
- /**
- * Element-by-element multiplication in place, A = A.*B
- *
- * @param B another matrix
- * @return A.*B
- */
- public Matrix arrayTimesEquals(Matrix B) {
- checkMatrixDimensions(B);
- for (int i = 0; i < m; i++) {
- for (int j = 0; j < n; j++) {
- A[i][j] *= B.A[i][j];
- }
- }
- return this;
- }
-
- /**
- * Element-by-element right division, C = A./B
- *
- * @param B another matrix
- * @return A./B
- */
- public Matrix arrayRightDivide(Matrix B) {
- checkMatrixDimensions(B);
- Matrix X = new Matrix(m, n);
- double[][] C = X.getArray();
- for (int i = 0; i < m; i++) {
- for (int j = 0; j < n; j++) {
- C[i][j] = A[i][j] / B.A[i][j];
- }
- }
- return X;
- }
-
- /**
- * Element-by-element right division in place, A = A./B
- *
- * @param B another matrix
- * @return A./B
- */
- public Matrix arrayRightDivideEquals(Matrix B) {
- checkMatrixDimensions(B);
- for (int i = 0; i < m; i++) {
- for (int j = 0; j < n; j++) {
- A[i][j] /= B.A[i][j];
- }
- }
- return this;
- }
-
- /**
- * Element-by-element left division, C = A.\B
- *
- * @param B another matrix
- * @return A.\B
- */
- public Matrix arrayLeftDivide(Matrix B) {
- checkMatrixDimensions(B);
- Matrix X = new Matrix(m, n);
- double[][] C = X.getArray();
- for (int i = 0; i < m; i++) {
- for (int j = 0; j < n; j++) {
- C[i][j] = B.A[i][j] / A[i][j];
- }
- }
- return X;
- }
-
- /**
- * Element-by-element left division in place, A = A.\B
- *
- * @param B another matrix
- * @return A.\B
- */
- public Matrix arrayLeftDivideEquals(Matrix B) {
- checkMatrixDimensions(B);
- for (int i = 0; i < m; i++) {
- for (int j = 0; j < n; j++) {
- A[i][j] = B.A[i][j] / A[i][j];
- }
- }
- return this;
- }
-
- /**
- * Multiply a matrix by a scalar, C = s*A
- *
- * @param s scalar
- * @return s*A
- */
- public Matrix times(double s) {
- Matrix X = new Matrix(m, n);
- double[][] C = X.getArray();
- for (int i = 0; i < m; i++) {
- for (int j = 0; j < n; j++) {
- C[i][j] = s * A[i][j];
- }
- }
- return X;
- }
-
- /**
- * Multiply a matrix in place by a scalar, A = s*A. Returns A.
- *
- * @param s scalar
- * @return s*A
- */
- public Matrix timesInplace(double s) {
- for (int i = 0; i < m; i++) {
- for (int j = 0; j < n; j++) {
- A[i][j] = s * A[i][j];
- }
- }
- return this;
- }
-
- /**
- * Multiply a matrix by a vector, returning A*v.
- *
- * @param v vector
- * @return result vector
- */
- public double[] times(double[] v) {
- // m: no rows
- double[] result = new double[m];
- times(v, result);
- return result;
- }
-
- /**
- * Multiply a matrix by a vector in place, result=A*v.
- *
- * @param v vector
- * @param result
- * @return result vector
- */
- public void times(double[] v, double[] result) {
- // m: no rows
- for (int i = 0; i < m; i++) {
- result[i] = 0;
- for (int j = 0; j < n; j++) {
- result[i] += get(i, j) * v[j];
- }
- }
- }
-
- @Override
- public String toString() {
- StringBuilder sb = new StringBuilder();
- for (int i = 0; i < m; i++) {
- sb.append(BeanInspector.toString(A[i]));
- sb.append("\n");
- }
- return sb.toString();
- }
-
- /**
- * Multiply a matrix by a scalar in place, A = s*A
- *
- * @param s scalar
- * @return replace A by s*A
- */
- public Matrix timesEquals(double s) {
- for (int i = 0; i < m; i++) {
- for (int j = 0; j < n; j++) {
- A[i][j] = s * A[i][j];
- }
- }
- return this;
- }
-
- /**
- * Linear algebraic matrix multiplication, A * B
- *
- * @param B another matrix
- * @return Matrix product, A * B
- * @throws IllegalArgumentException Matrix inner dimensions must agree.
- */
- public Matrix times(Matrix B) {
- if (B.m != n) {
- throw new IllegalArgumentException("Matrix inner dimensions must agree.");
- }
- Matrix X = new Matrix(m, B.n);
- double[][] C = X.getArray();
- double[] Bcolj = new double[n];
- for (int j = 0; j < B.n; j++) {
- for (int k = 0; k < n; k++) {
- Bcolj[k] = B.A[k][j];
- }
- for (int i = 0; i < m; i++) {
- double[] Arowi = A[i];
- double s = 0;
- for (int k = 0; k < n; k++) {
- s += Arowi[k] * Bcolj[k];
- }
- C[i][j] = s;
- }
- }
- return X;
- }
-
- /**
- * A.*B
- */
- public Matrix timesC(Matrix B) {
- if (B.n != n || B.m != m) {
- throw new IllegalArgumentException("Matrix dimensions must agree.");
- }
- Matrix X = new Matrix(m, n);
- double[][] C = X.getArray();
- for (int j = 0; j < n; j++) {
- for (int i = 0; i < m; i++) {
- C[i][j] = B.get(i, j) * this.A[i][j];
- }
- }
- return X;
- }
-
-
- /**
- * LU Decomposition
- *
- * @return LUDecomposition
- * @see LUDecomposition
- */
- public LUDecomposition lu() {
- return new LUDecomposition(this);
- }
-
- /**
- * QR Decomposition
- *
- * @return QRDecomposition
- * @see QRDecomposition
- */
- public QRDecomposition qr() {
- return new QRDecomposition(this);
- }
-
- /**
- * Cholesky Decomposition
- *
- * @return CholeskyDecomposition
- * @see CholeskyDecomposition
- */
- public CholeskyDecomposition chol() {
- return new CholeskyDecomposition(this);
- }
-
- /**
- * Singular Value Decomposition
- *
- * @return SingularValueDecomposition
- * @see SingularValueDecomposition
- */
- public SingularValueDecomposition svd() {
- return new SingularValueDecomposition(this);
- }
-
- /**
- * Eigenvalue Decomposition
- *
- * @return EigenvalueDecomposition
- * @see EigenvalueDecomposition
- */
- public EigenvalueDecomposition eig() {
- return new EigenvalueDecomposition(this);
- }
-
- /**
- * Solve A*X = B
- *
- * @param B right hand side
- * @return solution if A is square, least squares solution otherwise
- */
- public Matrix solve(Matrix B) {
- //System.out.print("m="+m+"n"+n);
- return (m == n ? (new LUDecomposition(this)).solve(B) :
- (new QRDecomposition(this)).solve(B));
- }
-
- /**
- * Solve X*A = B, which is also A'*X' = B'
- *
- * @param B right hand side
- * @return solution if A is square, least squares solution otherwise.
- */
- public Matrix solveTranspose(Matrix B) {
- return transpose().solve(B.transpose());
- }
-
- /**
- * Matrix inverse or pseudoinverse
- *
- * @return inverse(A) if A is square, pseudoinverse otherwise.
- */
- public Matrix inverse() {
- return solve(identity(m, m));
- }
-
- /**
- * Matrix determinant
- *
- * @return determinant
- */
- public double det() {
- return new LUDecomposition(this).det();
- }
-
- /**
- * Matrix rank
- *
- * @return effective numerical rank, obtained from SVD.
- */
- public int rank() {
- return new SingularValueDecomposition(this).rank();
- }
-
- /**
- * Matrix condition (2 norm)
- *
- * @return ratio of largest to smallest singular value.
- */
- public double cond() {
- return new SingularValueDecomposition(this).cond();
- }
-
- /**
- * Matrix trace.
- *
- * @return sum of the diagonal elements.
- */
- public double trace() {
- double t = 0;
- for (int i = 0; i < Math.min(m, n); i++) {
- t += A[i][i];
- }
- return t;
- }
-
- /**
- * Generate matrix with random elements
- *
- * @param m Number of rows.
- * @param n Number of colums.
- * @return An m-by-n matrix with uniformly distributed random elements.
- */
- public static Matrix random(int m, int n) {
- Matrix A = new Matrix(m, n);
- double[][] X = A.getArray();
- for (int i = 0; i < m; i++) {
- for (int j = 0; j < n; j++) {
- X[i][j] = Math.random();
- }
- }
- return A;
- }
-
- /**
- * Generate identity matrix
- *
- * @param m Number of rows.
- * @param n Number of colums.
- * @return An m-by-n matrix with ones on the diagonal and zeros elsewhere.
- */
- public static Matrix identity(int m, int n) {
- Matrix A = new Matrix(m, n);
- double[][] X = A.getArray();
- for (int i = 0; i < m; i++) {
- for (int j = 0; j < n; j++) {
- X[i][j] = (i == j ? 1.0 : 0.0);
- }
- }
- return A;
- }
-
- /**
- * Return the minimum and maximum value on the diagonal
- * as a pair.
- *
- * @return
- */
- public Pair getMinMaxDiag() {
- if (m < 1 || n < 1) {
- return null;
- }
-
- double v = get(0, 0);
- Pair ret = new Pair<>(v, v);
- for (int i = 1; i < Math.min(m, n); i++) {
- v = get(i, i);
- ret.head = Math.min(ret.head, v);
- ret.tail = Math.max(ret.tail, v);
- }
- return ret;
- }
-
-
- /**
- * Print the matrix to stdout. Line the elements up in columns
- * with a Fortran-like 'Fw.d' style format.
- *
- * @param w Column width.
- * @param d Number of digits after the decimal.
- */
- public void print(int w, int d) {
- print(new PrintWriter(System.out, true), w, d);
- }
-
- /**
- * Print the matrix to the output stream. Line the elements up in
- * columns with a Fortran-like 'Fw.d' style format.
- *
- * @param output Output stream.
- * @param w Column width.
- * @param d Number of digits after the decimal.
- */
- public void print(PrintWriter output, int w, int d) {
- DecimalFormat format = new DecimalFormat();
- format.setDecimalFormatSymbols(new DecimalFormatSymbols(Locale.US));
- format.setMinimumIntegerDigits(1);
- format.setMaximumFractionDigits(d);
- format.setMinimumFractionDigits(d);
- format.setGroupingUsed(false);
- print(output, format, w + 2);
- }
-
- /**
- * Print the matrix to stdout. Line the elements up in columns.
- * Use the format object, and right justify within columns of width
- * characters.
- * Note that is the matrix is to be read back in, you probably will want
- * to use a NumberFormat that is set to US Locale.
- *
- * @param format A Formatting object for individual elements.
- * @param width Field width for each column.
- * @see java.text.DecimalFormat#setDecimalFormatSymbols
- */
- public void print(NumberFormat format, int width) {
- print(new PrintWriter(System.out, true), format, width);
- }
-
- // DecimalFormat is a little disappointing coming from Fortran or C's printf.
- // Since it doesn't pad on the left, the elements will come out different
- // widths. Consequently, we'll pass the desired column width in as an
- // argument and do the extra padding ourselves.
-
- /**
- * Print the matrix to the output stream. Line the elements up in columns.
- * Use the format object, and right justify within columns of width
- * characters.
- * Note that is the matrix is to be read back in, you probably will want
- * to use a NumberFormat that is set to US Locale.
- *
- * @param output the output stream.
- * @param format A formatting object to format the matrix elements
- * @param width Column width.
- * @see java.text.DecimalFormat#setDecimalFormatSymbols
- */
-
- public void print(PrintWriter output, NumberFormat format, int width) {
- output.println(); // start on new line.
- for (int i = 0; i < m; i++) {
- for (int j = 0; j < n; j++) {
- String s = format.format(A[i][j]); // format the number
- int padding = Math.max(1, width - s.length()); // At _least_ 1 space
- for (int k = 0; k < padding; k++) {
- output.print(' ');
- }
- output.print(s);
- }
- output.println();
- }
- output.println(); // end with blank line.
- }
-
- /**
- * Read a matrix from a stream. The format is the same the print method,
- * so printed matrices can be read back in (provided they were printed using
- * US Locale). Elements are separated by
- * whitespace, all the elements for each row appear on a single line,
- * the last row is followed by a blank line.
- *
- * @param input the input stream.
- */
- public static Matrix read(BufferedReader input) throws java.io.IOException {
- StreamTokenizer tokenizer = new StreamTokenizer(input);
-
- // Although StreamTokenizer will parse numbers, it doesn't recognize
- // scientific notation (E or D); however, Double.valueOf does.
- // The strategy here is to disable StreamTokenizer's number parsing.
- // We'll only get whitespace delimited words, EOL's and EOF's.
- // These words should all be numbers, for Double.valueOf to parse.
-
- tokenizer.resetSyntax();
- tokenizer.wordChars(0, 255);
- tokenizer.whitespaceChars(0, ' ');
- tokenizer.eolIsSignificant(true);
- Vector