X-Git-Url: http://source.jalview.org/gitweb/?a=blobdiff_plain;ds=inline;f=src%2Fjalview%2Fmath%2FMatrix.java;h=b22bf4e1d27558fc09c6e59e64a45733f12d75cf;hb=2db5d47c785c67cdb7a82b609b3a7eb8af4e7e0c;hp=30c534b6bba92485945a3c469b6812ef9f49f237;hpb=588042b69abf8e60bcc950b24c283933c7dd422f;p=jalview.git
diff --git a/src/jalview/math/Matrix.java b/src/jalview/math/Matrix.java
index 30c534b..b22bf4e 100755
--- a/src/jalview/math/Matrix.java
+++ b/src/jalview/math/Matrix.java
@@ -1,638 +1,1025 @@
-/*
-* Jalview - A Sequence Alignment Editor and Viewer
-* Copyright (C) 2005 AM Waterhouse, J Procter, G Barton, M Clamp, S Searle
-*
-* This program is free software; you can redistribute it and/or
-* modify it under the terms of the GNU General Public License
-* as published by the Free Software Foundation; either version 2
-* of the License, or (at your option) any later version.
-*
-* This program is distributed in the hope that it will be useful,
-* but WITHOUT ANY WARRANTY; without even the implied warranty of
-* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-* GNU General Public License for more details.
-*
-* You should have received a copy of the GNU General Public License
-* along with this program; if not, write to the Free Software
-* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA
-*/
-package jalview.math;
-
-import jalview.util.*;
-
-import java.io.*;
-
-
-public class Matrix {
- /**
- * SMJSPUBLIC
- */
- public double[][] value;
- public int rows;
- public int cols;
- public double[] d; // Diagonal
- public double[] e; // off diagonal
-
- public Matrix(double[][] value, int rows, int cols) {
- this.rows = rows;
- this.cols = cols;
- this.value = value;
- }
-
- public Matrix transpose() {
- double[][] out = new double[cols][rows];
-
- for (int i = 0; i < cols; i++) {
- for (int j = 0; j < rows; j++) {
- out[i][j] = value[j][i];
- }
- }
-
- return new Matrix(out, cols, rows);
- }
-
- public void print(PrintStream ps) {
- for (int i = 0; i < rows; i++) {
- for (int j = 0; j < cols; j++) {
- Format.print(ps, "%8.2f", value[i][j]);
- }
-
- ps.println();
- }
- }
-
- public Matrix preMultiply(Matrix in) {
- double[][] tmp = new double[in.rows][this.cols];
-
- for (int i = 0; i < in.rows; i++) {
- for (int j = 0; j < this.cols; j++) {
- tmp[i][j] = 0.0;
-
- for (int k = 0; k < in.cols; k++) {
- tmp[i][j] += (in.value[i][k] * this.value[k][j]);
- }
- }
- }
-
- return new Matrix(tmp, in.rows, this.cols);
- }
-
- public double[] vectorPostMultiply(double[] in) {
- double[] out = new double[in.length];
-
- for (int i = 0; i < in.length; i++) {
- out[i] = 0.0;
-
- for (int k = 0; k < in.length; k++) {
- out[i] += (value[i][k] * in[k]);
- }
- }
-
- return out;
- }
-
- public Matrix postMultiply(Matrix in) {
- double[][] out = new double[this.rows][in.cols];
-
- for (int i = 0; i < this.rows; i++) {
- for (int j = 0; j < in.cols; j++) {
- out[i][j] = 0.0;
-
- for (int k = 0; k < rows; k++) {
- out[i][j] = out[i][j] + (value[i][k] * in.value[k][j]);
- }
- }
- }
-
- return new Matrix(out, this.cols, in.rows);
- }
-
- public Matrix copy() {
- double[][] newmat = new double[rows][cols];
-
- for (int i = 0; i < rows; i++) {
- for (int j = 0; j < cols; j++) {
- newmat[i][j] = value[i][j];
- }
- }
-
- return new Matrix(newmat, rows, cols);
- }
-
- public void tred() {
- int n = rows;
- int l;
- int k;
- int j;
- int i;
-
- double scale;
- double hh;
- double h;
- double g;
- double f;
-
- this.d = new double[rows];
- this.e = new double[rows];
-
- for (i = n; i >= 2; i--) {
- l = i - 1;
- h = 0.0;
- scale = 0.0;
-
- if (l > 1) {
- for (k = 1; k <= l; k++) {
- scale += Math.abs(value[i - 1][k - 1]);
- }
-
- if (scale == 0.0) {
- e[i - 1] = value[i - 1][l - 1];
- } else {
- for (k = 1; k <= l; k++) {
- value[i - 1][k - 1] /= scale;
- h += (value[i - 1][k - 1] * value[i - 1][k - 1]);
- }
-
- f = value[i - 1][l - 1];
-
- if (f > 0) {
- g = -1.0 * Math.sqrt(h);
- } else {
- g = Math.sqrt(h);
- }
-
- e[i - 1] = scale * g;
- h -= (f * g);
- value[i - 1][l - 1] = f - g;
- f = 0.0;
-
- for (j = 1; j <= l; j++) {
- value[j - 1][i - 1] = value[i - 1][j - 1] / h;
- g = 0.0;
-
- for (k = 1; k <= j; k++) {
- g += (value[j - 1][k - 1] * value[i - 1][k - 1]);
- }
-
- for (k = j + 1; k <= l; k++) {
- g += (value[k - 1][j - 1] * value[i - 1][k - 1]);
- }
-
- e[j - 1] = g / h;
- f += (e[j - 1] * value[i - 1][j - 1]);
- }
-
- hh = f / (h + h);
-
- for (j = 1; j <= l; j++) {
- f = value[i - 1][j - 1];
- g = e[j - 1] - (hh * f);
- e[j - 1] = g;
-
- for (k = 1; k <= j; k++) {
- value[j - 1][k - 1] -= ((f * e[k - 1]) +
- (g * value[i - 1][k - 1]));
- }
- }
- }
- } else {
- e[i - 1] = value[i - 1][l - 1];
- }
-
- d[i - 1] = h;
- }
-
- d[0] = 0.0;
- e[0] = 0.0;
-
- for (i = 1; i <= n; i++) {
- l = i - 1;
-
- if (d[i - 1] != 0.0) {
- for (j = 1; j <= l; j++) {
- g = 0.0;
-
- for (k = 1; k <= l; k++) {
- g += (value[i - 1][k - 1] * value[k - 1][j - 1]);
- }
-
- for (k = 1; k <= l; k++) {
- value[k - 1][j - 1] -= (g * value[k - 1][i - 1]);
- }
- }
- }
-
- d[i - 1] = value[i - 1][i - 1];
- value[i - 1][i - 1] = 1.0;
-
- for (j = 1; j <= l; j++) {
- value[j - 1][i - 1] = 0.0;
- value[i - 1][j - 1] = 0.0;
- }
- }
- }
-
- public void tqli() {
- int n = rows;
-
- int m;
- int l;
- int iter;
- int i;
- int k;
- double s;
- double r;
- double p;
- ;
-
- double g;
- double f;
- double dd;
- double c;
- double b;
-
- for (i = 2; i <= n; i++) {
- e[i - 2] = e[i - 1];
- }
-
- e[n - 1] = 0.0;
-
- for (l = 1; l <= n; l++) {
- iter = 0;
-
- do {
- for (m = l; m <= (n - 1); m++) {
- dd = Math.abs(d[m - 1]) + Math.abs(d[m]);
-
- if ((Math.abs(e[m - 1]) + dd) == dd) {
- break;
- }
- }
-
- if (m != l) {
- iter++;
-
- if (iter == 30) {
- System.err.print("Too many iterations in tqli");
- System.exit(0); // JBPNote - should this really be here ???
- } else {
- // System.out.println("Iteration " + iter);
- }
-
- g = (d[l] - d[l - 1]) / (2.0 * e[l - 1]);
- r = Math.sqrt((g * g) + 1.0);
- g = d[m - 1] - d[l - 1] + (e[l - 1] / (g + sign(r, g)));
- c = 1.0;
- s = c;
- p = 0.0;
-
- for (i = m - 1; i >= l; i--) {
- f = s * e[i - 1];
- b = c * e[i - 1];
-
- if (Math.abs(f) >= Math.abs(g)) {
- c = g / f;
- r = Math.sqrt((c * c) + 1.0);
- e[i] = f * r;
- s = 1.0 / r;
- c *= s;
- } else {
- s = f / g;
- r = Math.sqrt((s * s) + 1.0);
- e[i] = g * r;
- c = 1.0 / r;
- s *= c;
- }
-
- g = d[i] - p;
- r = ((d[i - 1] - g) * s) + (2.0 * c * b);
- p = s * r;
- d[i] = g + p;
- g = (c * r) - b;
-
- for (k = 1; k <= n; k++) {
- f = value[k - 1][i];
- value[k - 1][i] = (s * value[k - 1][i - 1]) +
- (c * f);
- value[k - 1][i - 1] = (c * value[k - 1][i - 1]) -
- (s * f);
- }
- }
-
- d[l - 1] = d[l - 1] - p;
- e[l - 1] = g;
- e[m - 1] = 0.0;
- }
- } while (m != l);
- }
- }
-
- public void tred2() {
- int n = rows;
- int l;
- int k;
- int j;
- int i;
-
- double scale;
- double hh;
- double h;
- double g;
- double f;
-
- this.d = new double[rows];
- this.e = new double[rows];
-
- for (i = n - 1; i >= 1; i--) {
- l = i - 1;
- h = 0.0;
- scale = 0.0;
-
- if (l > 0) {
- for (k = 0; k < l; k++) {
- scale += Math.abs(value[i][k]);
- }
-
- if (scale == 0.0) {
- e[i] = value[i][l];
- } else {
- for (k = 0; k < l; k++) {
- value[i][k] /= scale;
- h += (value[i][k] * value[i][k]);
- }
-
- f = value[i][l];
-
- if (f > 0) {
- g = -1.0 * Math.sqrt(h);
- } else {
- g = Math.sqrt(h);
- }
-
- e[i] = scale * g;
- h -= (f * g);
- value[i][l] = f - g;
- f = 0.0;
-
- for (j = 0; j < l; j++) {
- value[j][i] = value[i][j] / h;
- g = 0.0;
-
- for (k = 0; k < j; k++) {
- g += (value[j][k] * value[i][k]);
- }
-
- for (k = j; k < l; k++) {
- g += (value[k][j] * value[i][k]);
- }
-
- e[j] = g / h;
- f += (e[j] * value[i][j]);
- }
-
- hh = f / (h + h);
-
- for (j = 0; j < l; j++) {
- f = value[i][j];
- g = e[j] - (hh * f);
- e[j] = g;
-
- for (k = 0; k < j; k++) {
- value[j][k] -= ((f * e[k]) + (g * value[i][k]));
- }
- }
- }
- } else {
- e[i] = value[i][l];
- }
-
- d[i] = h;
- }
-
- d[0] = 0.0;
- e[0] = 0.0;
-
- for (i = 0; i < n; i++) {
- l = i - 1;
-
- if (d[i] != 0.0) {
- for (j = 0; j < l; j++) {
- g = 0.0;
-
- for (k = 0; k < l; k++) {
- g += (value[i][k] * value[k][j]);
- }
-
- for (k = 0; k < l; k++) {
- value[k][j] -= (g * value[k][i]);
- }
- }
- }
-
- d[i] = value[i][i];
- value[i][i] = 1.0;
-
- for (j = 0; j < l; j++) {
- value[j][i] = 0.0;
- value[i][j] = 0.0;
- }
- }
- }
-
- public void tqli2() {
- int n = rows;
-
- int m;
- int l;
- int iter;
- int i;
- int k;
- double s;
- double r;
- double p;
- ;
-
- double g;
- double f;
- double dd;
- double c;
- double b;
-
- for (i = 2; i <= n; i++) {
- e[i - 2] = e[i - 1];
- }
-
- e[n - 1] = 0.0;
-
- for (l = 1; l <= n; l++) {
- iter = 0;
-
- do {
- for (m = l; m <= (n - 1); m++) {
- dd = Math.abs(d[m - 1]) + Math.abs(d[m]);
-
- if ((Math.abs(e[m - 1]) + dd) == dd) {
- break;
- }
- }
-
- if (m != l) {
- iter++;
-
- if (iter == 30) {
- System.err.print("Too many iterations in tqli");
- System.exit(0); // JBPNote - same as above - not a graceful exit!
- } else {
- // System.out.println("Iteration " + iter);
- }
-
- g = (d[l] - d[l - 1]) / (2.0 * e[l - 1]);
- r = Math.sqrt((g * g) + 1.0);
- g = d[m - 1] - d[l - 1] + (e[l - 1] / (g + sign(r, g)));
- c = 1.0;
- s = c;
- p = 0.0;
-
- for (i = m - 1; i >= l; i--) {
- f = s * e[i - 1];
- b = c * e[i - 1];
-
- if (Math.abs(f) >= Math.abs(g)) {
- c = g / f;
- r = Math.sqrt((c * c) + 1.0);
- e[i] = f * r;
- s = 1.0 / r;
- c *= s;
- } else {
- s = f / g;
- r = Math.sqrt((s * s) + 1.0);
- e[i] = g * r;
- c = 1.0 / r;
- s *= c;
- }
-
- g = d[i] - p;
- r = ((d[i - 1] - g) * s) + (2.0 * c * b);
- p = s * r;
- d[i] = g + p;
- g = (c * r) - b;
-
- for (k = 1; k <= n; k++) {
- f = value[k - 1][i];
- value[k - 1][i] = (s * value[k - 1][i - 1]) +
- (c * f);
- value[k - 1][i - 1] = (c * value[k - 1][i - 1]) -
- (s * f);
- }
- }
-
- d[l - 1] = d[l - 1] - p;
- e[l - 1] = g;
- e[m - 1] = 0.0;
- }
- } while (m != l);
- }
- }
-
- public double sign(double a, double b) {
- if (b < 0) {
- return -Math.abs(a);
- } else {
- return Math.abs(a);
- }
- }
-
- public double[] getColumn(int n) {
- double[] out = new double[rows];
-
- for (int i = 0; i < rows; i++) {
- out[i] = value[i][n];
- }
-
- return out;
- }
-
- public void printD(PrintStream ps) {
- for (int j = 0; j < rows; j++) {
- Format.print(ps, "%15.4e", d[j]);
- }
- }
-
- public void printE(PrintStream ps) {
- for (int j = 0; j < rows; j++) {
- Format.print(ps, "%15.4e", e[j]);
- }
- }
-
- public static void main(String[] args) {
- int n = Integer.parseInt(args[0]);
- double[][] in = new double[n][n];
-
- for (int i = 0; i < n; i++) {
- for (int j = 0; j < n; j++) {
- in[i][j] = (double) Math.random();
- }
- }
-
- Matrix origmat = new Matrix(in, n, n);
-
- // System.out.println(" --- Original matrix ---- ");
- /// origmat.print(System.out);
- //System.out.println();
- //System.out.println(" --- transpose matrix ---- ");
- Matrix trans = origmat.transpose();
-
- //trans.print(System.out);
- //System.out.println();
- //System.out.println(" --- OrigT * Orig ---- ");
- Matrix symm = trans.postMultiply(origmat);
-
- //symm.print(System.out);
- //System.out.println();
- // Copy the symmetric matrix for later
- Matrix origsymm = symm.copy();
-
- // This produces the tridiagonal transformation matrix
- long tstart = System.currentTimeMillis();
- symm.tred();
-
- long tend = System.currentTimeMillis();
-
- //System.out.println("Time take for tred = " + (tend-tstart) + "ms");
- //System.out.println(" ---Tridiag transform matrix ---");
- //symm.print(System.out);
- //System.out.println();
- //System.out.println(" --- D vector ---");
- //symm.printD(System.out);
- //System.out.println();
- //System.out.println(" --- E vector ---");
- //symm.printE(System.out);
- //System.out.println();
- // Now produce the diagonalization matrix
- tstart = System.currentTimeMillis();
- symm.tqli();
- tend = System.currentTimeMillis();
-
- //System.out.println("Time take for tqli = " + (tend-tstart) + " ms");
- //System.out.println(" --- New diagonalization matrix ---");
- //symm.print(System.out);
- //System.out.println();
- //System.out.println(" --- D vector ---");
- //symm.printD(System.out);
- //System.out.println();
- //System.out.println(" --- E vector ---");
- //symm.printE(System.out);
- //System.out.println();
- //System.out.println(" --- First eigenvector --- ");
- //double[] eigenv = symm.getColumn(0);
- //for (int i=0; i < eigenv.length;i++) {
- // Format.print(System.out,"%15.4f",eigenv[i]);
- // }
- //System.out.println();
- //double[] neigenv = origsymm.vectorPostMultiply(eigenv);
- //for (int i=0; i < neigenv.length;i++) {
- // Format.print(System.out,"%15.4f",neigenv[i]/symm.d[0]);
- //}
- //System.out.println();
- }
-}
+/*
+ * Jalview - A Sequence Alignment Editor and Viewer ($$Version-Rel$$)
+ * Copyright (C) $$Year-Rel$$ The Jalview Authors
+ *
+ * This file is part of Jalview.
+ *
+ * Jalview is free software: you can redistribute it and/or
+ * modify it under the terms of the GNU General Public License
+ * as published by the Free Software Foundation, either version 3
+ * of the License, or (at your option) any later version.
+ *
+ * Jalview is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty
+ * of MERCHANTABILITY or FITNESS FOR A PARTICULAR
+ * PURPOSE. See the GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with Jalview. If not, see
+ * new Matrix(new double[][] {{2, 3, 4}, {5, 6, 7}) + * constructs + * (2 3 4) + * (5 6 7) + *+ * + * Note that ragged arrays (with not all rows, or columns, of the same + * length), are not supported by this class. They can be constructed, but + * results of operations on them are undefined and may throw exceptions. + * + * @param values + * the matrix values in row-major order + */ + public Matrix(double[][] values) + { + this.rows = values.length; + this.cols = this.rows == 0 ? 0 : values[0].length; + + /* + * make a copy of the values array, for immutability + */ + this.value = new double[rows][]; + int i = 0; + for (double[] row : values) + { + if (row != null) + { + value[i] = new double[row.length]; + System.arraycopy(row, 0, value[i], 0, row.length); + } + i++; + } + } + + @Override + public MatrixI transpose() + { + double[][] out = new double[cols][rows]; + + for (int i = 0; i < cols; i++) + { + for (int j = 0; j < rows; j++) + { + out[i][j] = value[j][i]; + } + } + + return new Matrix(out); + } + + /** + * DOCUMENT ME! + * + * @param ps + * DOCUMENT ME! + * @param format + */ + @Override + public void print(PrintStream ps, String format) + { + for (int i = 0; i < rows; i++) + { + for (int j = 0; j < cols; j++) + { + Format.print(ps, format, getValue(i, j)); + } + + ps.println(); + } + } + + @Override + public MatrixI preMultiply(MatrixI in) + { + if (in.width() != rows) + { + throw new IllegalArgumentException("Can't pre-multiply " + this.rows + + " rows by " + in.width() + " columns"); + } + double[][] tmp = new double[in.height()][this.cols]; + + for (int i = 0; i < in.height(); i++) + { + for (int j = 0; j < this.cols; j++) + { + /* + * result[i][j] is the vector product of + * in.row[i] and this.column[j] + */ + for (int k = 0; k < in.width(); k++) + { + tmp[i][j] += (in.getValue(i, k) * this.value[k][j]); + } + } + } + + return new Matrix(tmp); + } + + /** + * + * @param in + * + * @return + */ + public double[] vectorPostMultiply(double[] in) + { + double[] out = new double[in.length]; + + for (int i = 0; i < in.length; i++) + { + out[i] = 0.0; + + for (int k = 0; k < in.length; k++) + { + out[i] += (value[i][k] * in[k]); + } + } + + return out; + } + + @Override + public MatrixI postMultiply(MatrixI in) + { + if (in.height() != this.cols) + { + throw new IllegalArgumentException("Can't post-multiply " + this.cols + + " columns by " + in.height() + " rows"); + } + return in.preMultiply(this); + } + + @Override + public MatrixI copy() + { + double[][] newmat = new double[rows][cols]; + + for (int i = 0; i < rows; i++) + { + System.arraycopy(value[i], 0, newmat[i], 0, value[i].length); + } + + Matrix m = new Matrix(newmat); + if (this.d != null) + { + m.d = Arrays.copyOf(this.d, this.d.length); + } + if (this.e != null) + { + m.e = Arrays.copyOf(this.e, this.e.length); + } + + return m; + } + + /** + * DOCUMENT ME! + */ + @Override + public void tred() + { + int n = rows; + int k; + int j; + int i; + + double scale; + double hh; + double h; + double g; + double f; + + this.d = new double[rows]; + this.e = new double[rows]; + + for (i = n; i >= 2; i--) + { + final int l = i - 1; + h = 0.0; + scale = 0.0; + + if (l > 1) + { + for (k = 1; k <= l; k++) + { + double v = Math.abs(getValue(i - 1, k - 1)); + scale += v; + } + + if (scale == 0.0) + { + e[i - 1] = getValue(i - 1, l - 1); + } + else + { + for (k = 1; k <= l; k++) + { + double v = divideValue(i - 1, k - 1, scale); + h += v * v; + } + + f = getValue(i - 1, l - 1); + + if (f > 0) + { + g = -1.0 * Math.sqrt(h); + } + else + { + g = Math.sqrt(h); + } + + e[i - 1] = scale * g; + h -= (f * g); + setValue(i - 1, l - 1, f - g); + f = 0.0; + + for (j = 1; j <= l; j++) + { + double val = getValue(i - 1, j - 1) / h; + setValue(j - 1, i - 1, val); + g = 0.0; + + for (k = 1; k <= j; k++) + { + g += (getValue(j - 1, k - 1) * getValue(i - 1, k - 1)); + } + + for (k = j + 1; k <= l; k++) + { + g += (getValue(k - 1, j - 1) * getValue(i - 1, k - 1)); + } + + e[j - 1] = g / h; + f += (e[j - 1] * getValue(i - 1, j - 1)); + } + + hh = f / (h + h); + + for (j = 1; j <= l; j++) + { + f = getValue(i - 1, j - 1); + g = e[j - 1] - (hh * f); + e[j - 1] = g; + + for (k = 1; k <= j; k++) + { + double val = (f * e[k - 1]) + (g * getValue(i - 1, k - 1)); + addValue(j - 1, k - 1, -val); + } + } + } + } + else + { + e[i - 1] = getValue(i - 1, l - 1); + } + + d[i - 1] = h; + } + + d[0] = 0.0; + e[0] = 0.0; + + for (i = 1; i <= n; i++) + { + final int l = i - 1; + + if (d[i - 1] != 0.0) + { + for (j = 1; j <= l; j++) + { + g = 0.0; + + for (k = 1; k <= l; k++) + { + g += (getValue(i - 1, k - 1) * getValue(k - 1, j - 1)); + } + + for (k = 1; k <= l; k++) + { + addValue(k - 1, j - 1, -(g * getValue(k - 1, i - 1))); + } + } + } + + d[i - 1] = getValue(i - 1, i - 1); + setValue(i - 1, i - 1, 1.0); + + for (j = 1; j <= l; j++) + { + setValue(j - 1, i - 1, 0.0); + setValue(i - 1, j - 1, 0.0); + } + } + } + + /** + * Adds f to the value at [i, j] and returns the new value + * + * @param i + * @param j + * @param f + */ + protected double addValue(int i, int j, double f) + { + double v = value[i][j] + f; + value[i][j] = v; + return v; + } + + /** + * Divides the value at [i, j] by divisor and returns the new value. If d is + * zero, returns the unchanged value. + * + * @param i + * @param j + * @param divisor + * @return + */ + protected double divideValue(int i, int j, double divisor) + { + if (divisor == 0d) + { + return getValue(i, j); + } + double v = value[i][j]; + v = v / divisor; + value[i][j] = v; + return v; + } + + /** + * DOCUMENT ME! + */ + @Override + public void tqli() throws Exception + { + int n = rows; + + int m; + int l; + int iter; + int i; + int k; + double s; + double r; + double p; + + double g; + double f; + double dd; + double c; + double b; + + for (i = 2; i <= n; i++) + { + e[i - 2] = e[i - 1]; + } + + e[n - 1] = 0.0; + + for (l = 1; l <= n; l++) + { + iter = 0; + + do + { + for (m = l; m <= (n - 1); m++) + { + dd = Math.abs(d[m - 1]) + Math.abs(d[m]); + + if ((Math.abs(e[m - 1]) + dd) == dd) + { + break; + } + } + + if (m != l) + { + iter++; + + if (iter == MAX_ITER) + { + throw new Exception(MessageManager.formatMessage( + "exception.matrix_too_many_iteration", new String[] + { "tqli", Integer.valueOf(MAX_ITER).toString() })); + } + else + { + // System.out.println("Iteration " + iter); + } + + g = (d[l] - d[l - 1]) / (2.0 * e[l - 1]); + r = Math.sqrt((g * g) + 1.0); + g = d[m - 1] - d[l - 1] + (e[l - 1] / (g + sign(r, g))); + c = 1.0; + s = c; + p = 0.0; + + for (i = m - 1; i >= l; i--) + { + f = s * e[i - 1]; + b = c * e[i - 1]; + + if (Math.abs(f) >= Math.abs(g)) + { + c = g / f; + r = Math.sqrt((c * c) + 1.0); + e[i] = f * r; + s = 1.0 / r; + c *= s; + } + else + { + s = f / g; + r = Math.sqrt((s * s) + 1.0); + e[i] = g * r; + c = 1.0 / r; + s *= c; + } + + g = d[i] - p; + r = ((d[i - 1] - g) * s) + (2.0 * c * b); + p = s * r; + d[i] = g + p; + g = (c * r) - b; + + for (k = 1; k <= n; k++) + { + f = getValue(k - 1, i); + setValue(k - 1, i, (s * getValue(k - 1, i - 1)) + (c * f)); + setValue(k - 1, i - 1, + (c * getValue(k - 1, i - 1)) - (s * f)); + } + } + + d[l - 1] = d[l - 1] - p; + e[l - 1] = g; + e[m - 1] = 0.0; + } + } while (m != l); + } + } + + @Override + public double getValue(int i, int j) + { + return value[i][j]; + } + + @Override + public void setValue(int i, int j, double val) + { + value[i][j] = val; + } + + /** + * DOCUMENT ME! + */ + public void tred2() + { + int n = rows; + int l; + int k; + int j; + int i; + + double scale; + double hh; + double h; + double g; + double f; + + this.d = new double[rows]; + this.e = new double[rows]; + + for (i = n - 1; i >= 1; i--) + { + l = i - 1; + h = 0.0; + scale = 0.0; + + if (l > 0) + { + for (k = 0; k < l; k++) + { + scale += Math.abs(value[i][k]); + } + + if (scale == 0.0) + { + e[i] = value[i][l]; + } + else + { + for (k = 0; k < l; k++) + { + value[i][k] /= scale; + h += (value[i][k] * value[i][k]); + } + + f = value[i][l]; + + if (f > 0) + { + g = -1.0 * Math.sqrt(h); + } + else + { + g = Math.sqrt(h); + } + + e[i] = scale * g; + h -= (f * g); + value[i][l] = f - g; + f = 0.0; + + for (j = 0; j < l; j++) + { + value[j][i] = value[i][j] / h; + g = 0.0; + + for (k = 0; k < j; k++) + { + g += (value[j][k] * value[i][k]); + } + + for (k = j; k < l; k++) + { + g += (value[k][j] * value[i][k]); + } + + e[j] = g / h; + f += (e[j] * value[i][j]); + } + + hh = f / (h + h); + + for (j = 0; j < l; j++) + { + f = value[i][j]; + g = e[j] - (hh * f); + e[j] = g; + + for (k = 0; k < j; k++) + { + value[j][k] -= ((f * e[k]) + (g * value[i][k])); + } + } + } + } + else + { + e[i] = value[i][l]; + } + + d[i] = h; + } + + d[0] = 0.0; + e[0] = 0.0; + + for (i = 0; i < n; i++) + { + l = i - 1; + + if (d[i] != 0.0) + { + for (j = 0; j < l; j++) + { + g = 0.0; + + for (k = 0; k < l; k++) + { + g += (value[i][k] * value[k][j]); + } + + for (k = 0; k < l; k++) + { + value[k][j] -= (g * value[k][i]); + } + } + } + + d[i] = value[i][i]; + value[i][i] = 1.0; + + for (j = 0; j < l; j++) + { + value[j][i] = 0.0; + value[i][j] = 0.0; + } + } + } + + /** + * DOCUMENT ME! + */ + public void tqli2() throws Exception + { + int n = rows; + + int m; + int l; + int iter; + int i; + int k; + double s; + double r; + double p; + ; + + double g; + double f; + double dd; + double c; + double b; + + for (i = 2; i <= n; i++) + { + e[i - 2] = e[i - 1]; + } + + e[n - 1] = 0.0; + + for (l = 1; l <= n; l++) + { + iter = 0; + + do + { + for (m = l; m <= (n - 1); m++) + { + dd = Math.abs(d[m - 1]) + Math.abs(d[m]); + + if ((Math.abs(e[m - 1]) + dd) == dd) + { + break; + } + } + + if (m != l) + { + iter++; + + if (iter == MAX_ITER) + { + throw new Exception(MessageManager.formatMessage( + "exception.matrix_too_many_iteration", new String[] + { "tqli2", Integer.valueOf(MAX_ITER).toString() })); + } + else + { + // System.out.println("Iteration " + iter); + } + + g = (d[l] - d[l - 1]) / (2.0 * e[l - 1]); + r = Math.sqrt((g * g) + 1.0); + g = d[m - 1] - d[l - 1] + (e[l - 1] / (g + sign(r, g))); + c = 1.0; + s = c; + p = 0.0; + + for (i = m - 1; i >= l; i--) + { + f = s * e[i - 1]; + b = c * e[i - 1]; + + if (Math.abs(f) >= Math.abs(g)) + { + c = g / f; + r = Math.sqrt((c * c) + 1.0); + e[i] = f * r; + s = 1.0 / r; + c *= s; + } + else + { + s = f / g; + r = Math.sqrt((s * s) + 1.0); + e[i] = g * r; + c = 1.0 / r; + s *= c; + } + + g = d[i] - p; + r = ((d[i - 1] - g) * s) + (2.0 * c * b); + p = s * r; + d[i] = g + p; + g = (c * r) - b; + + for (k = 1; k <= n; k++) + { + f = value[k - 1][i]; + value[k - 1][i] = (s * value[k - 1][i - 1]) + (c * f); + value[k - 1][i - 1] = (c * value[k - 1][i - 1]) - (s * f); + } + } + + d[l - 1] = d[l - 1] - p; + e[l - 1] = g; + e[m - 1] = 0.0; + } + } while (m != l); + } + } + + /** + * Answers the first argument with the sign of the second argument + * + * @param a + * @param b + * + * @return + */ + static double sign(double a, double b) + { + if (b < 0) + { + return -Math.abs(a); + } + else + { + return Math.abs(a); + } + } + + /** + * Returns an array containing the values in the specified column + * + * @param col + * + * @return + */ + public double[] getColumn(int col) + { + double[] out = new double[rows]; + + for (int i = 0; i < rows; i++) + { + out[i] = value[i][col]; + } + + return out; + } + + /** + * DOCUMENT ME! + * + * @param ps + * DOCUMENT ME! + * @param format + */ + @Override + public void printD(PrintStream ps, String format) + { + for (int j = 0; j < rows; j++) + { + Format.print(ps, format, d[j]); + } + } + + /** + * DOCUMENT ME! + * + * @param ps + * DOCUMENT ME! + * @param format + * TODO + */ + @Override + public void printE(PrintStream ps, String format) + { + for (int j = 0; j < rows; j++) + { + Format.print(ps, format, e[j]); + } + } + + @Override + public double[] getD() + { + return d; + } + + @Override + public double[] getE() + { + return e; + } + + @Override + public int height() + { + return rows; + } + + @Override + public int width() + { + return cols; + } + + @Override + public double[] getRow(int i) + { + double[] row = new double[cols]; + System.arraycopy(value[i], 0, row, 0, cols); + return row; + } + + /** + * Returns a length 2 array of {minValue, maxValue} of all values in the + * matrix. Returns null if the matrix is null or empty. + * + * @return + */ + double[] findMinMax() + { + if (value == null) + { + return null; + } + double min = Double.MAX_VALUE; + double max = -Double.MAX_VALUE; + boolean empty = true; + for (double[] row : value) + { + if (row != null) + { + for (double x : row) + { + empty = false; + if (x > max) + { + max = x; + } + if (x < min) + { + min = x; + } + } + } + } + return empty ? null : new double[] { min, max }; + } + + /** + * {@inheritDoc} + */ + @Override + public void reverseRange(boolean maxToZero) + { + if (value == null) + { + return; + } + double[] minMax = findMinMax(); + if (minMax == null) + { + return; // empty matrix + } + double subtractFrom = maxToZero ? minMax[1] : minMax[0] + minMax[1]; + + for (double[] row : value) + { + if (row != null) + { + int j = 0; + for (double x : row) + { + row[j] = subtractFrom - x; + j++; + } + } + } + } + + /** + * Multiplies every entry in the matrix by the given value. + * + * @param + */ + @Override + public void multiply(double by) + { + for (double[] row : value) + { + if (row != null) + { + for (int i = 0; i < row.length; i++) + { + row[i] *= by; + } + } + } + } + + @Override + public void setD(double[] v) + { + d = v; + } + + @Override + public void setE(double[] v) + { + e = v; + } + + public double getTotal() + { + double d = 0d; + for (int i = 0; i < this.height(); i++) + { + for (int j = 0; j < this.width(); j++) + { + d += value[i][j]; + } + } + return d; + } + + /** + * {@inheritDoc} + */ + @Override + public boolean equals(MatrixI m2, double delta) + { + if (m2 == null || this.height() != m2.height() + || this.width() != m2.width()) + { + return false; + } + for (int i = 0; i < this.height(); i++) + { + for (int j = 0; j < this.width(); j++) + { + double diff = this.getValue(i, j) - m2.getValue(i, j); + if (Math.abs(diff) > delta) + { + return false; + } + } + } + return true; + } +}