2 * Jalview - A Sequence Alignment Editor and Viewer
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3 * Copyright (C) 2005 AM Waterhouse, J Procter, G Barton, M Clamp, S Searle
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5 * This program is free software; you can redistribute it and/or
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6 * modify it under the terms of the GNU General Public License
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7 * as published by the Free Software Foundation; either version 2
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8 * of the License, or (at your option) any later version.
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10 * This program is distributed in the hope that it will be useful,
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11 * but WITHOUT ANY WARRANTY; without even the implied warranty of
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12 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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13 * GNU General Public License for more details.
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15 * You should have received a copy of the GNU General Public License
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16 * along with this program; if not, write to the Free Software
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17 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA
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19 package jalview.math;
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21 import jalview.util.*;
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26 public class Matrix {
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30 public double[][] value;
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33 public double[] d; // Diagonal
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34 public double[] e; // off diagonal
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36 public Matrix(double[][] value, int rows, int cols) {
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42 public Matrix transpose() {
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43 double[][] out = new double[cols][rows];
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45 for (int i = 0; i < cols; i++) {
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46 for (int j = 0; j < rows; j++) {
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47 out[i][j] = value[j][i];
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51 return new Matrix(out, cols, rows);
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54 public void print(PrintStream ps) {
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55 for (int i = 0; i < rows; i++) {
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56 for (int j = 0; j < cols; j++) {
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57 Format.print(ps, "%8.2f", value[i][j]);
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64 public Matrix preMultiply(Matrix in) {
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65 double[][] tmp = new double[in.rows][this.cols];
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67 for (int i = 0; i < in.rows; i++) {
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68 for (int j = 0; j < this.cols; j++) {
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71 for (int k = 0; k < in.cols; k++) {
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72 tmp[i][j] += (in.value[i][k] * this.value[k][j]);
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77 return new Matrix(tmp, in.rows, this.cols);
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80 public double[] vectorPostMultiply(double[] in) {
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81 double[] out = new double[in.length];
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83 for (int i = 0; i < in.length; i++) {
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86 for (int k = 0; k < in.length; k++) {
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87 out[i] += (value[i][k] * in[k]);
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94 public Matrix postMultiply(Matrix in) {
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95 double[][] out = new double[this.rows][in.cols];
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97 for (int i = 0; i < this.rows; i++) {
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98 for (int j = 0; j < in.cols; j++) {
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101 for (int k = 0; k < rows; k++) {
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102 out[i][j] = out[i][j] + (value[i][k] * in.value[k][j]);
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107 return new Matrix(out, this.cols, in.rows);
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110 public Matrix copy() {
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111 double[][] newmat = new double[rows][cols];
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113 for (int i = 0; i < rows; i++) {
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114 for (int j = 0; j < cols; j++) {
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115 newmat[i][j] = value[i][j];
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119 return new Matrix(newmat, rows, cols);
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122 public void tred() {
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135 this.d = new double[rows];
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136 this.e = new double[rows];
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138 for (i = n; i >= 2; i--) {
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144 for (k = 1; k <= l; k++) {
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145 scale += Math.abs(value[i - 1][k - 1]);
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148 if (scale == 0.0) {
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149 e[i - 1] = value[i - 1][l - 1];
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151 for (k = 1; k <= l; k++) {
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152 value[i - 1][k - 1] /= scale;
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153 h += (value[i - 1][k - 1] * value[i - 1][k - 1]);
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156 f = value[i - 1][l - 1];
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159 g = -1.0 * Math.sqrt(h);
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164 e[i - 1] = scale * g;
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166 value[i - 1][l - 1] = f - g;
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169 for (j = 1; j <= l; j++) {
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170 value[j - 1][i - 1] = value[i - 1][j - 1] / h;
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173 for (k = 1; k <= j; k++) {
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174 g += (value[j - 1][k - 1] * value[i - 1][k - 1]);
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177 for (k = j + 1; k <= l; k++) {
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178 g += (value[k - 1][j - 1] * value[i - 1][k - 1]);
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182 f += (e[j - 1] * value[i - 1][j - 1]);
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187 for (j = 1; j <= l; j++) {
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188 f = value[i - 1][j - 1];
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189 g = e[j - 1] - (hh * f);
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192 for (k = 1; k <= j; k++) {
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193 value[j - 1][k - 1] -= ((f * e[k - 1]) +
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194 (g * value[i - 1][k - 1]));
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199 e[i - 1] = value[i - 1][l - 1];
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208 for (i = 1; i <= n; i++) {
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211 if (d[i - 1] != 0.0) {
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212 for (j = 1; j <= l; j++) {
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215 for (k = 1; k <= l; k++) {
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216 g += (value[i - 1][k - 1] * value[k - 1][j - 1]);
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219 for (k = 1; k <= l; k++) {
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220 value[k - 1][j - 1] -= (g * value[k - 1][i - 1]);
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225 d[i - 1] = value[i - 1][i - 1];
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226 value[i - 1][i - 1] = 1.0;
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228 for (j = 1; j <= l; j++) {
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229 value[j - 1][i - 1] = 0.0;
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230 value[i - 1][j - 1] = 0.0;
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235 public void tqli() {
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254 for (i = 2; i <= n; i++) {
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255 e[i - 2] = e[i - 1];
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260 for (l = 1; l <= n; l++) {
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264 for (m = l; m <= (n - 1); m++) {
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265 dd = Math.abs(d[m - 1]) + Math.abs(d[m]);
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267 if ((Math.abs(e[m - 1]) + dd) == dd) {
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276 System.err.print("Too many iterations in tqli");
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277 System.exit(0); // JBPNote - should this really be here ???
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279 // System.out.println("Iteration " + iter);
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282 g = (d[l] - d[l - 1]) / (2.0 * e[l - 1]);
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283 r = Math.sqrt((g * g) + 1.0);
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284 g = d[m - 1] - d[l - 1] + (e[l - 1] / (g + sign(r, g)));
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289 for (i = m - 1; i >= l; i--) {
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293 if (Math.abs(f) >= Math.abs(g)) {
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295 r = Math.sqrt((c * c) + 1.0);
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301 r = Math.sqrt((s * s) + 1.0);
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308 r = ((d[i - 1] - g) * s) + (2.0 * c * b);
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313 for (k = 1; k <= n; k++) {
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314 f = value[k - 1][i];
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315 value[k - 1][i] = (s * value[k - 1][i - 1]) +
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317 value[k - 1][i - 1] = (c * value[k - 1][i - 1]) -
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322 d[l - 1] = d[l - 1] - p;
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330 public void tred2() {
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343 this.d = new double[rows];
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344 this.e = new double[rows];
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346 for (i = n - 1; i >= 1; i--) {
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352 for (k = 0; k < l; k++) {
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353 scale += Math.abs(value[i][k]);
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356 if (scale == 0.0) {
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357 e[i] = value[i][l];
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359 for (k = 0; k < l; k++) {
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360 value[i][k] /= scale;
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361 h += (value[i][k] * value[i][k]);
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367 g = -1.0 * Math.sqrt(h);
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374 value[i][l] = f - g;
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377 for (j = 0; j < l; j++) {
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378 value[j][i] = value[i][j] / h;
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381 for (k = 0; k < j; k++) {
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382 g += (value[j][k] * value[i][k]);
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385 for (k = j; k < l; k++) {
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386 g += (value[k][j] * value[i][k]);
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390 f += (e[j] * value[i][j]);
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395 for (j = 0; j < l; j++) {
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397 g = e[j] - (hh * f);
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400 for (k = 0; k < j; k++) {
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401 value[j][k] -= ((f * e[k]) + (g * value[i][k]));
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406 e[i] = value[i][l];
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415 for (i = 0; i < n; i++) {
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419 for (j = 0; j < l; j++) {
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422 for (k = 0; k < l; k++) {
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423 g += (value[i][k] * value[k][j]);
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426 for (k = 0; k < l; k++) {
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427 value[k][j] -= (g * value[k][i]);
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432 d[i] = value[i][i];
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435 for (j = 0; j < l; j++) {
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442 public void tqli2() {
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461 for (i = 2; i <= n; i++) {
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462 e[i - 2] = e[i - 1];
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467 for (l = 1; l <= n; l++) {
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471 for (m = l; m <= (n - 1); m++) {
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472 dd = Math.abs(d[m - 1]) + Math.abs(d[m]);
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474 if ((Math.abs(e[m - 1]) + dd) == dd) {
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483 System.err.print("Too many iterations in tqli");
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484 System.exit(0); // JBPNote - same as above - not a graceful exit!
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486 // System.out.println("Iteration " + iter);
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489 g = (d[l] - d[l - 1]) / (2.0 * e[l - 1]);
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490 r = Math.sqrt((g * g) + 1.0);
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491 g = d[m - 1] - d[l - 1] + (e[l - 1] / (g + sign(r, g)));
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496 for (i = m - 1; i >= l; i--) {
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500 if (Math.abs(f) >= Math.abs(g)) {
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502 r = Math.sqrt((c * c) + 1.0);
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508 r = Math.sqrt((s * s) + 1.0);
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515 r = ((d[i - 1] - g) * s) + (2.0 * c * b);
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520 for (k = 1; k <= n; k++) {
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521 f = value[k - 1][i];
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522 value[k - 1][i] = (s * value[k - 1][i - 1]) +
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524 value[k - 1][i - 1] = (c * value[k - 1][i - 1]) -
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529 d[l - 1] = d[l - 1] - p;
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537 public double sign(double a, double b) {
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539 return -Math.abs(a);
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541 return Math.abs(a);
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545 public double[] getColumn(int n) {
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546 double[] out = new double[rows];
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548 for (int i = 0; i < rows; i++) {
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549 out[i] = value[i][n];
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555 public void printD(PrintStream ps) {
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556 for (int j = 0; j < rows; j++) {
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557 Format.print(ps, "%15.4e", d[j]);
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561 public void printE(PrintStream ps) {
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562 for (int j = 0; j < rows; j++) {
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563 Format.print(ps, "%15.4e", e[j]);
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567 public static void main(String[] args) {
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568 int n = Integer.parseInt(args[0]);
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569 double[][] in = new double[n][n];
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571 for (int i = 0; i < n; i++) {
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572 for (int j = 0; j < n; j++) {
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573 in[i][j] = (double) Math.random();
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577 Matrix origmat = new Matrix(in, n, n);
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579 // System.out.println(" --- Original matrix ---- ");
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580 /// origmat.print(System.out);
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581 //System.out.println();
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582 //System.out.println(" --- transpose matrix ---- ");
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583 Matrix trans = origmat.transpose();
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585 //trans.print(System.out);
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586 //System.out.println();
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587 //System.out.println(" --- OrigT * Orig ---- ");
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588 Matrix symm = trans.postMultiply(origmat);
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590 //symm.print(System.out);
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591 //System.out.println();
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592 // Copy the symmetric matrix for later
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593 Matrix origsymm = symm.copy();
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595 // This produces the tridiagonal transformation matrix
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596 long tstart = System.currentTimeMillis();
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599 long tend = System.currentTimeMillis();
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601 //System.out.println("Time take for tred = " + (tend-tstart) + "ms");
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602 //System.out.println(" ---Tridiag transform matrix ---");
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603 //symm.print(System.out);
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604 //System.out.println();
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605 //System.out.println(" --- D vector ---");
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606 //symm.printD(System.out);
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607 //System.out.println();
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608 //System.out.println(" --- E vector ---");
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609 //symm.printE(System.out);
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610 //System.out.println();
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611 // Now produce the diagonalization matrix
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612 tstart = System.currentTimeMillis();
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614 tend = System.currentTimeMillis();
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616 //System.out.println("Time take for tqli = " + (tend-tstart) + " ms");
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617 //System.out.println(" --- New diagonalization matrix ---");
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618 //symm.print(System.out);
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619 //System.out.println();
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620 //System.out.println(" --- D vector ---");
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621 //symm.printD(System.out);
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622 //System.out.println();
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623 //System.out.println(" --- E vector ---");
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624 //symm.printE(System.out);
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625 //System.out.println();
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626 //System.out.println(" --- First eigenvector --- ");
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627 //double[] eigenv = symm.getColumn(0);
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628 //for (int i=0; i < eigenv.length;i++) {
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629 // Format.print(System.out,"%15.4f",eigenv[i]);
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631 //System.out.println();
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632 //double[] neigenv = origsymm.vectorPostMultiply(eigenv);
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633 //for (int i=0; i < neigenv.length;i++) {
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634 // Format.print(System.out,"%15.4f",neigenv[i]/symm.d[0]);
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636 //System.out.println();
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