2 * Jalview - A Sequence Alignment Editor and Viewer ($$Version-Rel$$)
3 * Copyright (C) $$Year-Rel$$ The Jalview Authors
5 * This file is part of Jalview.
7 * Jalview is free software: you can redistribute it and/or
8 * modify it under the terms of the GNU General Public License
9 * as published by the Free Software Foundation, either version 3
10 * of the License, or (at your option) any later version.
12 * Jalview is distributed in the hope that it will be useful, but
13 * WITHOUT ANY WARRANTY; without even the implied warranty
14 * of MERCHANTABILITY or FITNESS FOR A PARTICULAR
15 * PURPOSE. See the GNU General Public License for more details.
17 * You should have received a copy of the GNU General Public License
18 * along with Jalview. If not, see <http://www.gnu.org/licenses/>.
19 * The Jalview Authors are detailed in the 'AUTHORS' file.
25 import jalview.util.*;
38 public double[][] value;
47 public double[] d; // Diagonal
50 public double[] e; // off diagonal
53 * maximum number of iterations for tqli
56 int maxIter = 45; // fudge - add 15 iterations, just in case
59 * Creates a new Matrix object.
68 public Matrix(double[][] value, int rows, int cols)
78 * @return DOCUMENT ME!
80 public Matrix transpose()
82 double[][] out = new double[cols][rows];
84 for (int i = 0; i < cols; i++)
86 for (int j = 0; j < rows; j++)
88 out[i][j] = value[j][i];
92 return new Matrix(out, cols, rows);
101 public void print(PrintStream ps)
103 for (int i = 0; i < rows; i++)
105 for (int j = 0; j < cols; j++)
107 Format.print(ps, "%8.2f", value[i][j]);
120 * @return DOCUMENT ME!
122 public Matrix preMultiply(Matrix in)
124 double[][] tmp = new double[in.rows][this.cols];
126 for (int i = 0; i < in.rows; i++)
128 for (int j = 0; j < this.cols; j++)
132 for (int k = 0; k < in.cols; k++)
134 tmp[i][j] += (in.value[i][k] * this.value[k][j]);
139 return new Matrix(tmp, in.rows, this.cols);
148 * @return DOCUMENT ME!
150 public double[] vectorPostMultiply(double[] in)
152 double[] out = new double[in.length];
154 for (int i = 0; i < in.length; i++)
158 for (int k = 0; k < in.length; k++)
160 out[i] += (value[i][k] * in[k]);
173 * @return DOCUMENT ME!
175 public Matrix postMultiply(Matrix in)
177 double[][] out = new double[this.rows][in.cols];
179 for (int i = 0; i < this.rows; i++)
181 for (int j = 0; j < in.cols; j++)
185 for (int k = 0; k < rows; k++)
187 out[i][j] = out[i][j] + (value[i][k] * in.value[k][j]);
192 return new Matrix(out, this.cols, in.rows);
198 * @return DOCUMENT ME!
202 double[][] newmat = new double[rows][cols];
204 for (int i = 0; i < rows; i++)
206 for (int j = 0; j < cols; j++)
208 newmat[i][j] = value[i][j];
212 return new Matrix(newmat, rows, cols);
232 this.d = new double[rows];
233 this.e = new double[rows];
235 for (i = n; i >= 2; i--)
243 for (k = 1; k <= l; k++)
245 scale += Math.abs(value[i - 1][k - 1]);
250 e[i - 1] = value[i - 1][l - 1];
254 for (k = 1; k <= l; k++)
256 value[i - 1][k - 1] /= scale;
257 h += (value[i - 1][k - 1] * value[i - 1][k - 1]);
260 f = value[i - 1][l - 1];
264 g = -1.0 * Math.sqrt(h);
271 e[i - 1] = scale * g;
273 value[i - 1][l - 1] = f - g;
276 for (j = 1; j <= l; j++)
278 value[j - 1][i - 1] = value[i - 1][j - 1] / h;
281 for (k = 1; k <= j; k++)
283 g += (value[j - 1][k - 1] * value[i - 1][k - 1]);
286 for (k = j + 1; k <= l; k++)
288 g += (value[k - 1][j - 1] * value[i - 1][k - 1]);
292 f += (e[j - 1] * value[i - 1][j - 1]);
297 for (j = 1; j <= l; j++)
299 f = value[i - 1][j - 1];
300 g = e[j - 1] - (hh * f);
303 for (k = 1; k <= j; k++)
305 value[j - 1][k - 1] -= ((f * e[k - 1]) + (g * value[i - 1][k - 1]));
312 e[i - 1] = value[i - 1][l - 1];
321 for (i = 1; i <= n; i++)
327 for (j = 1; j <= l; j++)
331 for (k = 1; k <= l; k++)
333 g += (value[i - 1][k - 1] * value[k - 1][j - 1]);
336 for (k = 1; k <= l; k++)
338 value[k - 1][j - 1] -= (g * value[k - 1][i - 1]);
343 d[i - 1] = value[i - 1][i - 1];
344 value[i - 1][i - 1] = 1.0;
346 for (j = 1; j <= l; j++)
348 value[j - 1][i - 1] = 0.0;
349 value[i - 1][j - 1] = 0.0;
357 public void tqli() throws Exception
377 for (i = 2; i <= n; i++)
384 for (l = 1; l <= n; l++)
390 for (m = l; m <= (n - 1); m++)
392 dd = Math.abs(d[m - 1]) + Math.abs(d[m]);
394 if ((Math.abs(e[m - 1]) + dd) == dd)
406 throw new Exception(MessageManager.formatMessage("exception.matrix_too_many_iteration", new String[]{"tqli", Integer.valueOf(maxIter).toString()}));
410 // System.out.println("Iteration " + iter);
413 g = (d[l] - d[l - 1]) / (2.0 * e[l - 1]);
414 r = Math.sqrt((g * g) + 1.0);
415 g = d[m - 1] - d[l - 1] + (e[l - 1] / (g + sign(r, g)));
420 for (i = m - 1; i >= l; i--)
425 if (Math.abs(f) >= Math.abs(g))
428 r = Math.sqrt((c * c) + 1.0);
436 r = Math.sqrt((s * s) + 1.0);
443 r = ((d[i - 1] - g) * s) + (2.0 * c * b);
448 for (k = 1; k <= n; k++)
451 value[k - 1][i] = (s * value[k - 1][i - 1]) + (c * f);
452 value[k - 1][i - 1] = (c * value[k - 1][i - 1]) - (s * f);
456 d[l - 1] = d[l - 1] - p;
481 this.d = new double[rows];
482 this.e = new double[rows];
484 for (i = n - 1; i >= 1; i--)
492 for (k = 0; k < l; k++)
494 scale += Math.abs(value[i][k]);
503 for (k = 0; k < l; k++)
505 value[i][k] /= scale;
506 h += (value[i][k] * value[i][k]);
513 g = -1.0 * Math.sqrt(h);
525 for (j = 0; j < l; j++)
527 value[j][i] = value[i][j] / h;
530 for (k = 0; k < j; k++)
532 g += (value[j][k] * value[i][k]);
535 for (k = j; k < l; k++)
537 g += (value[k][j] * value[i][k]);
541 f += (e[j] * value[i][j]);
546 for (j = 0; j < l; j++)
552 for (k = 0; k < j; k++)
554 value[j][k] -= ((f * e[k]) + (g * value[i][k]));
570 for (i = 0; i < n; i++)
576 for (j = 0; j < l; j++)
580 for (k = 0; k < l; k++)
582 g += (value[i][k] * value[k][j]);
585 for (k = 0; k < l; k++)
587 value[k][j] -= (g * value[k][i]);
595 for (j = 0; j < l; j++)
606 public void tqli2() throws Exception
626 for (i = 2; i <= n; i++)
633 for (l = 1; l <= n; l++)
639 for (m = l; m <= (n - 1); m++)
641 dd = Math.abs(d[m - 1]) + Math.abs(d[m]);
643 if ((Math.abs(e[m - 1]) + dd) == dd)
655 throw new Exception(MessageManager.formatMessage("exception.matrix_too_many_iteration", new String[]{"tqli2", Integer.valueOf(maxIter).toString()}));
659 // System.out.println("Iteration " + iter);
662 g = (d[l] - d[l - 1]) / (2.0 * e[l - 1]);
663 r = Math.sqrt((g * g) + 1.0);
664 g = d[m - 1] - d[l - 1] + (e[l - 1] / (g + sign(r, g)));
669 for (i = m - 1; i >= l; i--)
674 if (Math.abs(f) >= Math.abs(g))
677 r = Math.sqrt((c * c) + 1.0);
685 r = Math.sqrt((s * s) + 1.0);
692 r = ((d[i - 1] - g) * s) + (2.0 * c * b);
697 for (k = 1; k <= n; k++)
700 value[k - 1][i] = (s * value[k - 1][i - 1]) + (c * f);
701 value[k - 1][i - 1] = (c * value[k - 1][i - 1]) - (s * f);
705 d[l - 1] = d[l - 1] - p;
721 * @return DOCUMENT ME!
723 public double sign(double a, double b)
741 * @return DOCUMENT ME!
743 public double[] getColumn(int n)
745 double[] out = new double[rows];
747 for (int i = 0; i < rows; i++)
749 out[i] = value[i][n];
761 public void printD(PrintStream ps)
763 for (int j = 0; j < rows; j++)
765 Format.print(ps, "%15.4e", d[j]);
775 public void printE(PrintStream ps)
777 for (int j = 0; j < rows; j++)
779 Format.print(ps, "%15.4e", e[j]);
789 public static void main(String[] args) throws Exception
791 int n = Integer.parseInt(args[0]);
792 double[][] in = new double[n][n];
794 for (int i = 0; i < n; i++)
796 for (int j = 0; j < n; j++)
798 in[i][j] = (double) Math.random();
802 Matrix origmat = new Matrix(in, n, n);
804 // System.out.println(" --- Original matrix ---- ");
805 // / origmat.print(System.out);
806 // System.out.println();
807 // System.out.println(" --- transpose matrix ---- ");
808 Matrix trans = origmat.transpose();
810 // trans.print(System.out);
811 // System.out.println();
812 // System.out.println(" --- OrigT * Orig ---- ");
813 Matrix symm = trans.postMultiply(origmat);
815 // symm.print(System.out);
816 // System.out.println();
817 // Copy the symmetric matrix for later
818 // Matrix origsymm = symm.copy();
820 // This produces the tridiagonal transformation matrix
821 // long tstart = System.currentTimeMillis();
824 // long tend = System.currentTimeMillis();
826 // System.out.println("Time take for tred = " + (tend-tstart) + "ms");
827 // System.out.println(" ---Tridiag transform matrix ---");
828 // symm.print(System.out);
829 // System.out.println();
830 // System.out.println(" --- D vector ---");
831 // symm.printD(System.out);
832 // System.out.println();
833 // System.out.println(" --- E vector ---");
834 // symm.printE(System.out);
835 // System.out.println();
836 // Now produce the diagonalization matrix
837 // tstart = System.currentTimeMillis();
839 // tend = System.currentTimeMillis();
841 // System.out.println("Time take for tqli = " + (tend-tstart) + " ms");
842 // System.out.println(" --- New diagonalization matrix ---");
843 // symm.print(System.out);
844 // System.out.println();
845 // System.out.println(" --- D vector ---");
846 // symm.printD(System.out);
847 // System.out.println();
848 // System.out.println(" --- E vector ---");
849 // symm.printE(System.out);
850 // System.out.println();
851 // System.out.println(" --- First eigenvector --- ");
852 // double[] eigenv = symm.getColumn(0);
853 // for (int i=0; i < eigenv.length;i++) {
854 // Format.print(System.out,"%15.4f",eigenv[i]);
856 // System.out.println();
857 // double[] neigenv = origsymm.vectorPostMultiply(eigenv);
858 // for (int i=0; i < neigenv.length;i++) {
859 // Format.print(System.out,"%15.4f",neigenv[i]/symm.d[0]);
861 // System.out.println();