2 * Jalview - A Sequence Alignment Editor and Viewer (Version 2.8.1)
3 * Copyright (C) 2014 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 of the License, or (at your option) any later version.
11 * Jalview is distributed in the hope that it will be useful, but
12 * WITHOUT ANY WARRANTY; without even the implied warranty
13 * of MERCHANTABILITY or FITNESS FOR A PARTICULAR
14 * PURPOSE. See the GNU General Public License for more details.
16 * You should have received a copy of the GNU General Public License along with Jalview. If not, see <http://www.gnu.org/licenses/>.
17 * The Jalview Authors are detailed in the 'AUTHORS' file.
23 import jalview.util.*;
36 public double[][] value;
45 public double[] d; // Diagonal
48 public double[] e; // off diagonal
51 * maximum number of iterations for tqli
54 int maxIter = 45; // fudge - add 15 iterations, just in case
57 * Creates a new Matrix object.
66 public Matrix(double[][] value, int rows, int cols)
76 * @return DOCUMENT ME!
78 public Matrix transpose()
80 double[][] out = new double[cols][rows];
82 for (int i = 0; i < cols; i++)
84 for (int j = 0; j < rows; j++)
86 out[i][j] = value[j][i];
90 return new Matrix(out, cols, rows);
99 public void print(PrintStream ps)
101 for (int i = 0; i < rows; i++)
103 for (int j = 0; j < cols; j++)
105 Format.print(ps, "%8.2f", value[i][j]);
118 * @return DOCUMENT ME!
120 public Matrix preMultiply(Matrix in)
122 double[][] tmp = new double[in.rows][this.cols];
124 for (int i = 0; i < in.rows; i++)
126 for (int j = 0; j < this.cols; j++)
130 for (int k = 0; k < in.cols; k++)
132 tmp[i][j] += (in.value[i][k] * this.value[k][j]);
137 return new Matrix(tmp, in.rows, this.cols);
146 * @return DOCUMENT ME!
148 public double[] vectorPostMultiply(double[] in)
150 double[] out = new double[in.length];
152 for (int i = 0; i < in.length; i++)
156 for (int k = 0; k < in.length; k++)
158 out[i] += (value[i][k] * in[k]);
171 * @return DOCUMENT ME!
173 public Matrix postMultiply(Matrix in)
175 double[][] out = new double[this.rows][in.cols];
177 for (int i = 0; i < this.rows; i++)
179 for (int j = 0; j < in.cols; j++)
183 for (int k = 0; k < rows; k++)
185 out[i][j] = out[i][j] + (value[i][k] * in.value[k][j]);
190 return new Matrix(out, this.cols, in.rows);
196 * @return DOCUMENT ME!
200 double[][] newmat = new double[rows][cols];
202 for (int i = 0; i < rows; i++)
204 for (int j = 0; j < cols; j++)
206 newmat[i][j] = value[i][j];
210 return new Matrix(newmat, rows, cols);
230 this.d = new double[rows];
231 this.e = new double[rows];
233 for (i = n; i >= 2; i--)
241 for (k = 1; k <= l; k++)
243 scale += Math.abs(value[i - 1][k - 1]);
248 e[i - 1] = value[i - 1][l - 1];
252 for (k = 1; k <= l; k++)
254 value[i - 1][k - 1] /= scale;
255 h += (value[i - 1][k - 1] * value[i - 1][k - 1]);
258 f = value[i - 1][l - 1];
262 g = -1.0 * Math.sqrt(h);
269 e[i - 1] = scale * g;
271 value[i - 1][l - 1] = f - g;
274 for (j = 1; j <= l; j++)
276 value[j - 1][i - 1] = value[i - 1][j - 1] / h;
279 for (k = 1; k <= j; k++)
281 g += (value[j - 1][k - 1] * value[i - 1][k - 1]);
284 for (k = j + 1; k <= l; k++)
286 g += (value[k - 1][j - 1] * value[i - 1][k - 1]);
290 f += (e[j - 1] * value[i - 1][j - 1]);
295 for (j = 1; j <= l; j++)
297 f = value[i - 1][j - 1];
298 g = e[j - 1] - (hh * f);
301 for (k = 1; k <= j; k++)
303 value[j - 1][k - 1] -= ((f * e[k - 1]) + (g * value[i - 1][k - 1]));
310 e[i - 1] = value[i - 1][l - 1];
319 for (i = 1; i <= n; i++)
325 for (j = 1; j <= l; j++)
329 for (k = 1; k <= l; k++)
331 g += (value[i - 1][k - 1] * value[k - 1][j - 1]);
334 for (k = 1; k <= l; k++)
336 value[k - 1][j - 1] -= (g * value[k - 1][i - 1]);
341 d[i - 1] = value[i - 1][i - 1];
342 value[i - 1][i - 1] = 1.0;
344 for (j = 1; j <= l; j++)
346 value[j - 1][i - 1] = 0.0;
347 value[i - 1][j - 1] = 0.0;
355 public void tqli() throws Exception
375 for (i = 2; i <= n; i++)
382 for (l = 1; l <= n; l++)
388 for (m = l; m <= (n - 1); m++)
390 dd = Math.abs(d[m - 1]) + Math.abs(d[m]);
392 if ((Math.abs(e[m - 1]) + dd) == dd)
404 throw new Exception("Too many iterations in tqli ("+maxIter+")");
408 // System.out.println("Iteration " + iter);
411 g = (d[l] - d[l - 1]) / (2.0 * e[l - 1]);
412 r = Math.sqrt((g * g) + 1.0);
413 g = d[m - 1] - d[l - 1] + (e[l - 1] / (g + sign(r, g)));
418 for (i = m - 1; i >= l; i--)
423 if (Math.abs(f) >= Math.abs(g))
426 r = Math.sqrt((c * c) + 1.0);
434 r = Math.sqrt((s * s) + 1.0);
441 r = ((d[i - 1] - g) * s) + (2.0 * c * b);
446 for (k = 1; k <= n; k++)
449 value[k - 1][i] = (s * value[k - 1][i - 1]) + (c * f);
450 value[k - 1][i - 1] = (c * value[k - 1][i - 1]) - (s * f);
454 d[l - 1] = d[l - 1] - p;
479 this.d = new double[rows];
480 this.e = new double[rows];
482 for (i = n - 1; i >= 1; i--)
490 for (k = 0; k < l; k++)
492 scale += Math.abs(value[i][k]);
501 for (k = 0; k < l; k++)
503 value[i][k] /= scale;
504 h += (value[i][k] * value[i][k]);
511 g = -1.0 * Math.sqrt(h);
523 for (j = 0; j < l; j++)
525 value[j][i] = value[i][j] / h;
528 for (k = 0; k < j; k++)
530 g += (value[j][k] * value[i][k]);
533 for (k = j; k < l; k++)
535 g += (value[k][j] * value[i][k]);
539 f += (e[j] * value[i][j]);
544 for (j = 0; j < l; j++)
550 for (k = 0; k < j; k++)
552 value[j][k] -= ((f * e[k]) + (g * value[i][k]));
568 for (i = 0; i < n; i++)
574 for (j = 0; j < l; j++)
578 for (k = 0; k < l; k++)
580 g += (value[i][k] * value[k][j]);
583 for (k = 0; k < l; k++)
585 value[k][j] -= (g * value[k][i]);
593 for (j = 0; j < l; j++)
604 public void tqli2() throws Exception
624 for (i = 2; i <= n; i++)
631 for (l = 1; l <= n; l++)
637 for (m = l; m <= (n - 1); m++)
639 dd = Math.abs(d[m - 1]) + Math.abs(d[m]);
641 if ((Math.abs(e[m - 1]) + dd) == dd)
653 throw new Exception ("Too many iterations in tqli2 (max is "+maxIter+")");
657 // System.out.println("Iteration " + iter);
660 g = (d[l] - d[l - 1]) / (2.0 * e[l - 1]);
661 r = Math.sqrt((g * g) + 1.0);
662 g = d[m - 1] - d[l - 1] + (e[l - 1] / (g + sign(r, g)));
667 for (i = m - 1; i >= l; i--)
672 if (Math.abs(f) >= Math.abs(g))
675 r = Math.sqrt((c * c) + 1.0);
683 r = Math.sqrt((s * s) + 1.0);
690 r = ((d[i - 1] - g) * s) + (2.0 * c * b);
695 for (k = 1; k <= n; k++)
698 value[k - 1][i] = (s * value[k - 1][i - 1]) + (c * f);
699 value[k - 1][i - 1] = (c * value[k - 1][i - 1]) - (s * f);
703 d[l - 1] = d[l - 1] - p;
719 * @return DOCUMENT ME!
721 public double sign(double a, double b)
739 * @return DOCUMENT ME!
741 public double[] getColumn(int n)
743 double[] out = new double[rows];
745 for (int i = 0; i < rows; i++)
747 out[i] = value[i][n];
759 public void printD(PrintStream ps)
761 for (int j = 0; j < rows; j++)
763 Format.print(ps, "%15.4e", d[j]);
773 public void printE(PrintStream ps)
775 for (int j = 0; j < rows; j++)
777 Format.print(ps, "%15.4e", e[j]);
787 public static void main(String[] args) throws Exception
789 int n = Integer.parseInt(args[0]);
790 double[][] in = new double[n][n];
792 for (int i = 0; i < n; i++)
794 for (int j = 0; j < n; j++)
796 in[i][j] = (double) Math.random();
800 Matrix origmat = new Matrix(in, n, n);
802 // System.out.println(" --- Original matrix ---- ");
803 // / origmat.print(System.out);
804 // System.out.println();
805 // System.out.println(" --- transpose matrix ---- ");
806 Matrix trans = origmat.transpose();
808 // trans.print(System.out);
809 // System.out.println();
810 // System.out.println(" --- OrigT * Orig ---- ");
811 Matrix symm = trans.postMultiply(origmat);
813 // symm.print(System.out);
814 // System.out.println();
815 // Copy the symmetric matrix for later
816 // Matrix origsymm = symm.copy();
818 // This produces the tridiagonal transformation matrix
819 // long tstart = System.currentTimeMillis();
822 // long tend = System.currentTimeMillis();
824 // System.out.println("Time take for tred = " + (tend-tstart) + "ms");
825 // System.out.println(" ---Tridiag transform matrix ---");
826 // symm.print(System.out);
827 // System.out.println();
828 // System.out.println(" --- D vector ---");
829 // symm.printD(System.out);
830 // System.out.println();
831 // System.out.println(" --- E vector ---");
832 // symm.printE(System.out);
833 // System.out.println();
834 // Now produce the diagonalization matrix
835 // tstart = System.currentTimeMillis();
837 // tend = System.currentTimeMillis();
839 // System.out.println("Time take for tqli = " + (tend-tstart) + " ms");
840 // System.out.println(" --- New diagonalization matrix ---");
841 // symm.print(System.out);
842 // System.out.println();
843 // System.out.println(" --- D vector ---");
844 // symm.printD(System.out);
845 // System.out.println();
846 // System.out.println(" --- E vector ---");
847 // symm.printE(System.out);
848 // System.out.println();
849 // System.out.println(" --- First eigenvector --- ");
850 // double[] eigenv = symm.getColumn(0);
851 // for (int i=0; i < eigenv.length;i++) {
852 // Format.print(System.out,"%15.4f",eigenv[i]);
854 // System.out.println();
855 // double[] neigenv = origsymm.vectorPostMultiply(eigenv);
856 // for (int i=0; i < neigenv.length;i++) {
857 // Format.print(System.out,"%15.4f",neigenv[i]/symm.d[0]);
859 // System.out.println();