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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20 package jalview.math;
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22 import jalview.util.*;
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26 public class Matrix {
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31 public double[][] value;
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34 public double[] d; // Diagonal
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35 public double[] e; // off diagonal
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37 public Matrix(double[][] value, int rows, int cols) {
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43 public Matrix transpose() {
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44 double[][] out = new double[cols][rows];
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46 for (int i = 0; i < cols; i++) {
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47 for (int j = 0; j < rows ; j++) {
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48 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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56 for (int i = 0; i < rows; i++) {
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57 for (int j = 0; j < cols; j++) {
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58 Format.print(ps,"%8.2f",value[i][j]);
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65 public Matrix preMultiply(Matrix in) {
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66 double[][] tmp = new double[in.rows][this.cols];
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68 for (int i = 0; i < in.rows; i++) {
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69 for (int j = 0; j < this.cols; j++ ) {
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72 for (int k = 0; k < in.cols; k++) {
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73 tmp[i][j] += in.value[i][k]*this.value[k][j];
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79 return new Matrix(tmp,in.rows,this.cols);
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82 public double[] vectorPostMultiply(double[] in) {
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83 double[] out = new double[in.length];
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84 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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92 public Matrix postMultiply(Matrix in) {
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94 double[][] out = new double[this.rows][in.cols];
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95 for (int i = 0; i < this.rows; i++) {
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96 for (int j = 0; j < in.cols; j++ ) {
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100 for (int k = 0; k < rows; k++) {
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101 out[i][j] = out[i][j] + value[i][k]*in.value[k][j];
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106 return new Matrix(out,this.cols,in.rows);
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109 public Matrix copy() {
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110 double[][] newmat = new double[rows][cols];
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112 for (int i = 0; i < rows; i++) {
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113 for (int j = 0; j < cols; j++) {
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114 newmat[i][j] = value[i][j];
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117 return new Matrix(newmat,rows,cols);
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120 public void tred() {
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133 this.d = new double[rows];
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134 this.e = new double[rows];
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136 for (i=n; i >= 2;i--) {
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142 for (k=1;k<=l;k++) {
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143 scale += Math.abs(value[i-1][k-1]);
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145 if (scale == 0.0) {
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146 e[i-1] = value[i-1][l-1];
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148 for (k=1; k <= l; k++) {
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149 value[i-1][k-1] /= scale;
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150 h += value[i-1][k-1]*value[i-1][k-1];
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152 f = value[i-1][l-1];
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154 g = -1.0*Math.sqrt(h);
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160 value[i-1][l-1] = f-g;
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162 for (j=1; j <= l; j++) {
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163 value[j-1][i-1] = value[i-1][j-1]/h;
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165 for (k= 1; k <= j; k++) {
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166 g += value[j-1][k-1]*value[i-1][k-1];
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168 for (k=j+1; k<=l;k++) {
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169 g+= value[k-1][j-1]*value[i-1][k-1];
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172 f+=e[j-1]*value[i-1][j-1];
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175 for (j=1;j<=l;j++) {
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179 for (k=1;k<=j;k++) {
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180 value[j-1][k-1] -= (f*e[k-1]+g*value[i-1][k-1]);
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185 e[i-1] = value[i-1][l-1];
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191 for (i=1;i<=n;i++) {
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193 if (d[i-1] != 0.0) {
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194 for (j=1;j<=l;j++) {
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196 for (k=1;k<=l;k++) {
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197 g+= value[i-1][k-1]*value[k-1][j-1];
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199 for (k=1;k<=l;k++) {
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200 value[k-1][j-1] -= g*value[k-1][i-1];
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204 d[i-1] = value[i-1][i-1];
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205 value[i-1][i-1] = 1.0;
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206 for (j=1;j<=l;j++) {
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207 value[j-1][i-1] = 0.0;
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208 value[i-1][j-1] = 0.0;
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213 public void tqli() {
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231 for (i=2;i<=n;i++) {
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235 for (l=1;l<=n;l++) {
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238 for (m=l;m<=(n-1);m++) {
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239 dd=Math.abs(d[m-1]) + Math.abs(d[m]);
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240 if (Math.abs(e[m-1]) + dd == dd)
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246 System.err.print("Too many iterations in tqli");
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247 System.exit(0); // JBPNote - should this really be here ???
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249 // System.out.println("Iteration " + iter);
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251 g=(d[l]-d[l-1])/(2.0*e[l-1]);
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252 r = Math.sqrt((g*g) + 1.0);
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253 g=d[m-1]-d[l-1]+e[l-1]/(g + sign(r,g));
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257 for (i=m-1;i>=l;i--) {
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260 if (Math.abs(f) >= Math.abs(g)) {
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262 r = Math.sqrt((c*c)+1.0);
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268 r = Math.sqrt((s*s)+1.0);
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274 r=(d[i-1]-g)*s + 2.0*c*b;
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278 for (k=1; k <= n; k++) {
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280 value[k-1][i] = s*value[k-1][i-1] + c*f;
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281 value[k-1][i-1] = c*value[k-1][i-1] - s*f;
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284 d[l-1] = d[l-1] - p;
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291 public void tred2() {
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304 this.d = new double[rows];
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305 this.e = new double[rows];
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307 for (i=n-1; i >= 1;i--) {
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313 for (k=0;k<l;k++) {
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314 scale += Math.abs(value[i][k]);
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316 if (scale == 0.0) {
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317 e[i] = value[i][l];
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319 for (k=0; k < l; k++) {
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320 value[i][k] /= scale;
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321 h += value[i][k]*value[i][k];
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325 g = -1.0*Math.sqrt(h);
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333 for (j=0; j < l; j++) {
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334 value[j][i] = value[i][j]/h;
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336 for (k= 0; k < j; k++) {
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337 g += value[j][k]*value[i][k];
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339 for (k=j; k<l;k++) {
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340 g+= value[k][j]*value[i][k];
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343 f+=e[j]*value[i][j];
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346 for (j=0;j<l;j++) {
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350 for (k=0;k<j;k++) {
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351 value[j][k] -= (f*e[k]+g*value[i][k]);
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356 e[i] = value[i][l];
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362 for (i=0;i<n;i++) {
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365 for (j=0;j<l;j++) {
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367 for (k=0;k<l;k++) {
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368 g+= value[i][k]*value[k][j];
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370 for (k=0;k<l;k++) {
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371 value[k][j] -= g*value[k][i];
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375 d[i] = value[i][i];
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377 for (j=0;j<l;j++) {
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384 public void tqli2() {
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402 for (i=2;i<=n;i++) {
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406 for (l=1;l<=n;l++) {
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409 for (m=l;m<=(n-1);m++) {
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410 dd=Math.abs(d[m-1]) + Math.abs(d[m]);
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411 if (Math.abs(e[m-1]) + dd == dd)
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417 System.err.print("Too many iterations in tqli");
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418 System.exit(0); // JBPNote - same as above - not a graceful exit!
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420 // System.out.println("Iteration " + iter);
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422 g=(d[l]-d[l-1])/(2.0*e[l-1]);
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423 r = Math.sqrt((g*g) + 1.0);
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424 g=d[m-1]-d[l-1]+e[l-1]/(g + sign(r,g));
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428 for (i=m-1;i>=l;i--) {
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431 if (Math.abs(f) >= Math.abs(g)) {
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433 r = Math.sqrt((c*c)+1.0);
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439 r = Math.sqrt((s*s)+1.0);
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445 r=(d[i-1]-g)*s + 2.0*c*b;
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449 for (k=1; k <= n; k++) {
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451 value[k-1][i] = s*value[k-1][i-1] + c*f;
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452 value[k-1][i-1] = c*value[k-1][i-1] - s*f;
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455 d[l-1] = d[l-1] - p;
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463 public double sign(double a, double b) {
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465 return -Math.abs(a);
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467 return Math.abs(a);
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471 public double[] getColumn(int n) {
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472 double[] out = new double[rows];
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473 for (int i=0;i<rows;i++) {
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474 out[i] = value[i][n];
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480 public void printD(PrintStream ps) {
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482 for (int j = 0; j < rows;j++) {
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483 Format.print(ps,"%15.4e",d[j]);
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486 public void printE(PrintStream ps) {
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488 for (int j = 0; j < rows;j++) {
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489 Format.print(ps,"%15.4e",e[j]);
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493 public static void main(String[] args) {
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494 int n = Integer.parseInt(args[0]);
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495 double[][] in = new double[n][n];
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497 for (int i = 0;i < n;i++) {
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498 for (int j = 0; j < n; j++) {
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499 in[i][j] = (double)Math.random();
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503 Matrix origmat = new Matrix(in,n,n);
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504 // System.out.println(" --- Original matrix ---- ");
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505 /// origmat.print(System.out);
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506 //System.out.println();
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508 //System.out.println(" --- transpose matrix ---- ");
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509 Matrix trans = origmat.transpose();
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510 //trans.print(System.out);
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511 //System.out.println();
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513 //System.out.println(" --- OrigT * Orig ---- ");
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515 Matrix symm = trans.postMultiply(origmat);
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516 //symm.print(System.out);
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517 //System.out.println();
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519 // Copy the symmetric matrix for later
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520 Matrix origsymm = symm.copy();
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523 // This produces the tridiagonal transformation matrix
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524 long tstart = System.currentTimeMillis();
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526 long tend = System.currentTimeMillis();
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527 //System.out.println("Time take for tred = " + (tend-tstart) + "ms");
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528 //System.out.println(" ---Tridiag transform matrix ---");
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529 //symm.print(System.out);
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530 //System.out.println();
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532 //System.out.println(" --- D vector ---");
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533 //symm.printD(System.out);
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534 //System.out.println();
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535 //System.out.println(" --- E vector ---");
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536 //symm.printE(System.out);
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537 //System.out.println();
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540 // Now produce the diagonalization matrix
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541 tstart = System.currentTimeMillis();
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543 tend = System.currentTimeMillis();
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544 //System.out.println("Time take for tqli = " + (tend-tstart) + " ms");
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546 //System.out.println(" --- New diagonalization matrix ---");
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547 //symm.print(System.out);
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548 //System.out.println();
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550 //System.out.println(" --- D vector ---");
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551 //symm.printD(System.out);
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552 //System.out.println();
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553 //System.out.println(" --- E vector ---");
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554 //symm.printE(System.out);
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555 //System.out.println();
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557 //System.out.println(" --- First eigenvector --- ");
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558 //double[] eigenv = symm.getColumn(0);
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559 //for (int i=0; i < eigenv.length;i++) {
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560 // Format.print(System.out,"%15.4f",eigenv[i]);
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562 //System.out.println();
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564 //double[] neigenv = origsymm.vectorPostMultiply(eigenv);
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566 //for (int i=0; i < neigenv.length;i++) {
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567 // Format.print(System.out,"%15.4f",neigenv[i]/symm.d[0]);
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570 //System.out.println();
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