2 * Jalview - A Sequence Alignment Editor and Viewer (Version 2.4)
3 * Copyright (C) 2008 AM Waterhouse, J Procter, G Barton, M Clamp, S Searle
5 * This program is free software; you can redistribute it and/or
6 * modify it under the terms of the GNU General Public License
7 * as published by the Free Software Foundation; either version 2
8 * of the License, or (at your option) any later version.
10 * This program is distributed in the hope that it will be useful,
11 * but WITHOUT ANY WARRANTY; without even the implied warranty of
12 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
13 * GNU General Public License for more details.
15 * You should have received a copy of the GNU General Public License
16 * along with this program; if not, write to the Free Software
17 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA
23 import jalview.util.*;
36 public double[][] value;
45 public double[] d; // Diagonal
48 public double[] e; // off diagonal
51 * Creates a new Matrix object.
60 public Matrix(double[][] value, int rows, int cols)
70 * @return DOCUMENT ME!
72 public Matrix transpose()
74 double[][] out = new double[cols][rows];
76 for (int i = 0; i < cols; i++)
78 for (int j = 0; j < rows; j++)
80 out[i][j] = value[j][i];
84 return new Matrix(out, cols, rows);
93 public void print(PrintStream ps)
95 for (int i = 0; i < rows; i++)
97 for (int j = 0; j < cols; j++)
99 Format.print(ps, "%8.2f", value[i][j]);
112 * @return DOCUMENT ME!
114 public Matrix preMultiply(Matrix in)
116 double[][] tmp = new double[in.rows][this.cols];
118 for (int i = 0; i < in.rows; i++)
120 for (int j = 0; j < this.cols; j++)
124 for (int k = 0; k < in.cols; k++)
126 tmp[i][j] += (in.value[i][k] * this.value[k][j]);
131 return new Matrix(tmp, in.rows, this.cols);
140 * @return DOCUMENT ME!
142 public double[] vectorPostMultiply(double[] in)
144 double[] out = new double[in.length];
146 for (int i = 0; i < in.length; i++)
150 for (int k = 0; k < in.length; k++)
152 out[i] += (value[i][k] * in[k]);
165 * @return DOCUMENT ME!
167 public Matrix postMultiply(Matrix in)
169 double[][] out = new double[this.rows][in.cols];
171 for (int i = 0; i < this.rows; i++)
173 for (int j = 0; j < in.cols; j++)
177 for (int k = 0; k < rows; k++)
179 out[i][j] = out[i][j] + (value[i][k] * in.value[k][j]);
184 return new Matrix(out, this.cols, in.rows);
190 * @return DOCUMENT ME!
194 double[][] newmat = new double[rows][cols];
196 for (int i = 0; i < rows; i++)
198 for (int j = 0; j < cols; j++)
200 newmat[i][j] = value[i][j];
204 return new Matrix(newmat, rows, cols);
224 this.d = new double[rows];
225 this.e = new double[rows];
227 for (i = n; i >= 2; i--)
235 for (k = 1; k <= l; k++)
237 scale += Math.abs(value[i - 1][k - 1]);
242 e[i - 1] = value[i - 1][l - 1];
246 for (k = 1; k <= l; k++)
248 value[i - 1][k - 1] /= scale;
249 h += (value[i - 1][k - 1] * value[i - 1][k - 1]);
252 f = value[i - 1][l - 1];
256 g = -1.0 * Math.sqrt(h);
263 e[i - 1] = scale * g;
265 value[i - 1][l - 1] = f - g;
268 for (j = 1; j <= l; j++)
270 value[j - 1][i - 1] = value[i - 1][j - 1] / h;
273 for (k = 1; k <= j; k++)
275 g += (value[j - 1][k - 1] * value[i - 1][k - 1]);
278 for (k = j + 1; k <= l; k++)
280 g += (value[k - 1][j - 1] * value[i - 1][k - 1]);
284 f += (e[j - 1] * value[i - 1][j - 1]);
289 for (j = 1; j <= l; j++)
291 f = value[i - 1][j - 1];
292 g = e[j - 1] - (hh * f);
295 for (k = 1; k <= j; k++)
297 value[j - 1][k - 1] -= ((f * e[k - 1]) + (g * value[i - 1][k - 1]));
304 e[i - 1] = value[i - 1][l - 1];
313 for (i = 1; i <= n; i++)
319 for (j = 1; j <= l; j++)
323 for (k = 1; k <= l; k++)
325 g += (value[i - 1][k - 1] * value[k - 1][j - 1]);
328 for (k = 1; k <= l; k++)
330 value[k - 1][j - 1] -= (g * value[k - 1][i - 1]);
335 d[i - 1] = value[i - 1][i - 1];
336 value[i - 1][i - 1] = 1.0;
338 for (j = 1; j <= l; j++)
340 value[j - 1][i - 1] = 0.0;
341 value[i - 1][j - 1] = 0.0;
369 for (i = 2; i <= n; i++)
376 for (l = 1; l <= n; l++)
382 for (m = l; m <= (n - 1); m++)
384 dd = Math.abs(d[m - 1]) + Math.abs(d[m]);
386 if ((Math.abs(e[m - 1]) + dd) == dd)
398 System.err.print("Too many iterations in tqli");
399 System.exit(0); // JBPNote - should this really be here ???
403 // System.out.println("Iteration " + iter);
406 g = (d[l] - d[l - 1]) / (2.0 * e[l - 1]);
407 r = Math.sqrt((g * g) + 1.0);
408 g = d[m - 1] - d[l - 1] + (e[l - 1] / (g + sign(r, g)));
413 for (i = m - 1; i >= l; i--)
418 if (Math.abs(f) >= Math.abs(g))
421 r = Math.sqrt((c * c) + 1.0);
429 r = Math.sqrt((s * s) + 1.0);
436 r = ((d[i - 1] - g) * s) + (2.0 * c * b);
441 for (k = 1; k <= n; k++)
444 value[k - 1][i] = (s * value[k - 1][i - 1]) + (c * f);
445 value[k - 1][i - 1] = (c * value[k - 1][i - 1]) - (s * f);
449 d[l - 1] = d[l - 1] - p;
474 this.d = new double[rows];
475 this.e = new double[rows];
477 for (i = n - 1; i >= 1; i--)
485 for (k = 0; k < l; k++)
487 scale += Math.abs(value[i][k]);
496 for (k = 0; k < l; k++)
498 value[i][k] /= scale;
499 h += (value[i][k] * value[i][k]);
506 g = -1.0 * Math.sqrt(h);
518 for (j = 0; j < l; j++)
520 value[j][i] = value[i][j] / h;
523 for (k = 0; k < j; k++)
525 g += (value[j][k] * value[i][k]);
528 for (k = j; k < l; k++)
530 g += (value[k][j] * value[i][k]);
534 f += (e[j] * value[i][j]);
539 for (j = 0; j < l; j++)
545 for (k = 0; k < j; k++)
547 value[j][k] -= ((f * e[k]) + (g * value[i][k]));
563 for (i = 0; i < n; i++)
569 for (j = 0; j < l; j++)
573 for (k = 0; k < l; k++)
575 g += (value[i][k] * value[k][j]);
578 for (k = 0; k < l; k++)
580 value[k][j] -= (g * value[k][i]);
588 for (j = 0; j < l; j++)
619 for (i = 2; i <= n; i++)
626 for (l = 1; l <= n; l++)
632 for (m = l; m <= (n - 1); m++)
634 dd = Math.abs(d[m - 1]) + Math.abs(d[m]);
636 if ((Math.abs(e[m - 1]) + dd) == dd)
648 System.err.print("Too many iterations in tqli");
649 System.exit(0); // JBPNote - same as above - not a graceful exit!
653 // System.out.println("Iteration " + iter);
656 g = (d[l] - d[l - 1]) / (2.0 * e[l - 1]);
657 r = Math.sqrt((g * g) + 1.0);
658 g = d[m - 1] - d[l - 1] + (e[l - 1] / (g + sign(r, g)));
663 for (i = m - 1; i >= l; i--)
668 if (Math.abs(f) >= Math.abs(g))
671 r = Math.sqrt((c * c) + 1.0);
679 r = Math.sqrt((s * s) + 1.0);
686 r = ((d[i - 1] - g) * s) + (2.0 * c * b);
691 for (k = 1; k <= n; k++)
694 value[k - 1][i] = (s * value[k - 1][i - 1]) + (c * f);
695 value[k - 1][i - 1] = (c * value[k - 1][i - 1]) - (s * f);
699 d[l - 1] = d[l - 1] - p;
715 * @return DOCUMENT ME!
717 public double sign(double a, double b)
735 * @return DOCUMENT ME!
737 public double[] getColumn(int n)
739 double[] out = new double[rows];
741 for (int i = 0; i < rows; i++)
743 out[i] = value[i][n];
755 public void printD(PrintStream ps)
757 for (int j = 0; j < rows; j++)
759 Format.print(ps, "%15.4e", d[j]);
769 public void printE(PrintStream ps)
771 for (int j = 0; j < rows; j++)
773 Format.print(ps, "%15.4e", e[j]);
783 public static void main(String[] args)
785 int n = Integer.parseInt(args[0]);
786 double[][] in = new double[n][n];
788 for (int i = 0; i < n; i++)
790 for (int j = 0; j < n; j++)
792 in[i][j] = (double) Math.random();
796 Matrix origmat = new Matrix(in, n, n);
798 // System.out.println(" --- Original matrix ---- ");
799 // / origmat.print(System.out);
800 // System.out.println();
801 // System.out.println(" --- transpose matrix ---- ");
802 Matrix trans = origmat.transpose();
804 // trans.print(System.out);
805 // System.out.println();
806 // System.out.println(" --- OrigT * Orig ---- ");
807 Matrix symm = trans.postMultiply(origmat);
809 // symm.print(System.out);
810 // System.out.println();
811 // Copy the symmetric matrix for later
812 // Matrix origsymm = symm.copy();
814 // This produces the tridiagonal transformation matrix
815 // long tstart = System.currentTimeMillis();
818 // long tend = System.currentTimeMillis();
820 // System.out.println("Time take for tred = " + (tend-tstart) + "ms");
821 // System.out.println(" ---Tridiag transform matrix ---");
822 // symm.print(System.out);
823 // System.out.println();
824 // System.out.println(" --- D vector ---");
825 // symm.printD(System.out);
826 // System.out.println();
827 // System.out.println(" --- E vector ---");
828 // symm.printE(System.out);
829 // System.out.println();
830 // Now produce the diagonalization matrix
831 // tstart = System.currentTimeMillis();
833 // tend = System.currentTimeMillis();
835 // System.out.println("Time take for tqli = " + (tend-tstart) + " ms");
836 // System.out.println(" --- New diagonalization matrix ---");
837 // symm.print(System.out);
838 // System.out.println();
839 // System.out.println(" --- D vector ---");
840 // symm.printD(System.out);
841 // System.out.println();
842 // System.out.println(" --- E vector ---");
843 // symm.printE(System.out);
844 // System.out.println();
845 // System.out.println(" --- First eigenvector --- ");
846 // double[] eigenv = symm.getColumn(0);
847 // for (int i=0; i < eigenv.length;i++) {
848 // Format.print(System.out,"%15.4f",eigenv[i]);
850 // System.out.println();
851 // double[] neigenv = origsymm.vectorPostMultiply(eigenv);
852 // for (int i=0; i < neigenv.length;i++) {
853 // Format.print(System.out,"%15.4f",neigenv[i]/symm.d[0]);
855 // System.out.println();