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.
23 import jalview.util.Format;
24 import jalview.util.MessageManager;
26 import java.io.PrintStream;
39 public double[][] value;
48 public double[] d; // Diagonal
51 public double[] e; // off diagonal
54 * maximum number of iterations for tqli
57 int maxIter = 45; // fudge - add 15 iterations, just in case
60 * Creates a new Matrix object.
69 public Matrix(double[][] value, int rows, int cols)
79 * @return DOCUMENT ME!
81 public Matrix transpose()
83 double[][] out = new double[cols][rows];
85 for (int i = 0; i < cols; i++)
87 for (int j = 0; j < rows; j++)
89 out[i][j] = value[j][i];
93 return new Matrix(out, cols, rows);
102 public void print(PrintStream ps)
104 for (int i = 0; i < rows; i++)
106 for (int j = 0; j < cols; j++)
108 Format.print(ps, "%8.2f", value[i][j]);
121 * @return DOCUMENT ME!
123 public Matrix preMultiply(Matrix in)
125 double[][] tmp = new double[in.rows][this.cols];
127 for (int i = 0; i < in.rows; i++)
129 for (int j = 0; j < this.cols; j++)
133 for (int k = 0; k < in.cols; k++)
135 tmp[i][j] += (in.value[i][k] * this.value[k][j]);
140 return new Matrix(tmp, in.rows, this.cols);
149 * @return DOCUMENT ME!
151 public double[] vectorPostMultiply(double[] in)
153 double[] out = new double[in.length];
155 for (int i = 0; i < in.length; i++)
159 for (int k = 0; k < in.length; k++)
161 out[i] += (value[i][k] * in[k]);
174 * @return DOCUMENT ME!
176 public Matrix postMultiply(Matrix in)
178 double[][] out = new double[this.rows][in.cols];
180 for (int i = 0; i < this.rows; i++)
182 for (int j = 0; j < in.cols; j++)
186 for (int k = 0; k < rows; k++)
188 out[i][j] = out[i][j] + (value[i][k] * in.value[k][j]);
193 return new Matrix(out, this.cols, in.rows);
199 * @return DOCUMENT ME!
203 double[][] newmat = new double[rows][cols];
205 for (int i = 0; i < rows; i++)
207 for (int j = 0; j < cols; j++)
209 newmat[i][j] = value[i][j];
213 return new Matrix(newmat, rows, cols);
233 this.d = new double[rows];
234 this.e = new double[rows];
236 for (i = n; i >= 2; i--)
244 for (k = 1; k <= l; k++)
246 scale += Math.abs(value[i - 1][k - 1]);
251 e[i - 1] = value[i - 1][l - 1];
255 for (k = 1; k <= l; k++)
257 value[i - 1][k - 1] /= scale;
258 h += (value[i - 1][k - 1] * value[i - 1][k - 1]);
261 f = value[i - 1][l - 1];
265 g = -1.0 * Math.sqrt(h);
272 e[i - 1] = scale * g;
274 value[i - 1][l - 1] = f - g;
277 for (j = 1; j <= l; j++)
279 value[j - 1][i - 1] = value[i - 1][j - 1] / h;
282 for (k = 1; k <= j; k++)
284 g += (value[j - 1][k - 1] * value[i - 1][k - 1]);
287 for (k = j + 1; k <= l; k++)
289 g += (value[k - 1][j - 1] * value[i - 1][k - 1]);
293 f += (e[j - 1] * value[i - 1][j - 1]);
298 for (j = 1; j <= l; j++)
300 f = value[i - 1][j - 1];
301 g = e[j - 1] - (hh * f);
304 for (k = 1; k <= j; k++)
306 value[j - 1][k - 1] -= ((f * e[k - 1]) + (g * value[i - 1][k - 1]));
313 e[i - 1] = value[i - 1][l - 1];
322 for (i = 1; i <= n; i++)
328 for (j = 1; j <= l; j++)
332 for (k = 1; k <= l; k++)
334 g += (value[i - 1][k - 1] * value[k - 1][j - 1]);
337 for (k = 1; k <= l; k++)
339 value[k - 1][j - 1] -= (g * value[k - 1][i - 1]);
344 d[i - 1] = value[i - 1][i - 1];
345 value[i - 1][i - 1] = 1.0;
347 for (j = 1; j <= l; j++)
349 value[j - 1][i - 1] = 0.0;
350 value[i - 1][j - 1] = 0.0;
358 public void tqli() throws Exception
378 for (i = 2; i <= n; i++)
385 for (l = 1; l <= n; l++)
391 for (m = l; m <= (n - 1); m++)
393 dd = Math.abs(d[m - 1]) + Math.abs(d[m]);
395 if ((Math.abs(e[m - 1]) + dd) == dd)
407 throw new Exception(MessageManager.formatMessage(
408 "exception.matrix_too_many_iteration", new String[] {
409 "tqli", Integer.valueOf(maxIter).toString() }));
413 // System.out.println("Iteration " + iter);
416 g = (d[l] - d[l - 1]) / (2.0 * e[l - 1]);
417 r = Math.sqrt((g * g) + 1.0);
418 g = d[m - 1] - d[l - 1] + (e[l - 1] / (g + sign(r, g)));
423 for (i = m - 1; i >= l; i--)
428 if (Math.abs(f) >= Math.abs(g))
431 r = Math.sqrt((c * c) + 1.0);
439 r = Math.sqrt((s * s) + 1.0);
446 r = ((d[i - 1] - g) * s) + (2.0 * c * b);
451 for (k = 1; k <= n; k++)
454 value[k - 1][i] = (s * value[k - 1][i - 1]) + (c * f);
455 value[k - 1][i - 1] = (c * value[k - 1][i - 1]) - (s * f);
459 d[l - 1] = d[l - 1] - p;
484 this.d = new double[rows];
485 this.e = new double[rows];
487 for (i = n - 1; i >= 1; i--)
495 for (k = 0; k < l; k++)
497 scale += Math.abs(value[i][k]);
506 for (k = 0; k < l; k++)
508 value[i][k] /= scale;
509 h += (value[i][k] * value[i][k]);
516 g = -1.0 * Math.sqrt(h);
528 for (j = 0; j < l; j++)
530 value[j][i] = value[i][j] / h;
533 for (k = 0; k < j; k++)
535 g += (value[j][k] * value[i][k]);
538 for (k = j; k < l; k++)
540 g += (value[k][j] * value[i][k]);
544 f += (e[j] * value[i][j]);
549 for (j = 0; j < l; j++)
555 for (k = 0; k < j; k++)
557 value[j][k] -= ((f * e[k]) + (g * value[i][k]));
573 for (i = 0; i < n; i++)
579 for (j = 0; j < l; j++)
583 for (k = 0; k < l; k++)
585 g += (value[i][k] * value[k][j]);
588 for (k = 0; k < l; k++)
590 value[k][j] -= (g * value[k][i]);
598 for (j = 0; j < l; j++)
609 public void tqli2() throws Exception
629 for (i = 2; i <= n; i++)
636 for (l = 1; l <= n; l++)
642 for (m = l; m <= (n - 1); m++)
644 dd = Math.abs(d[m - 1]) + Math.abs(d[m]);
646 if ((Math.abs(e[m - 1]) + dd) == dd)
658 throw new Exception(MessageManager.formatMessage(
659 "exception.matrix_too_many_iteration", new String[] {
660 "tqli2", Integer.valueOf(maxIter).toString() }));
664 // System.out.println("Iteration " + iter);
667 g = (d[l] - d[l - 1]) / (2.0 * e[l - 1]);
668 r = Math.sqrt((g * g) + 1.0);
669 g = d[m - 1] - d[l - 1] + (e[l - 1] / (g + sign(r, g)));
674 for (i = m - 1; i >= l; i--)
679 if (Math.abs(f) >= Math.abs(g))
682 r = Math.sqrt((c * c) + 1.0);
690 r = Math.sqrt((s * s) + 1.0);
697 r = ((d[i - 1] - g) * s) + (2.0 * c * b);
702 for (k = 1; k <= n; k++)
705 value[k - 1][i] = (s * value[k - 1][i - 1]) + (c * f);
706 value[k - 1][i - 1] = (c * value[k - 1][i - 1]) - (s * f);
710 d[l - 1] = d[l - 1] - p;
726 * @return DOCUMENT ME!
728 public double sign(double a, double b)
746 * @return DOCUMENT ME!
748 public double[] getColumn(int n)
750 double[] out = new double[rows];
752 for (int i = 0; i < rows; i++)
754 out[i] = value[i][n];
766 public void printD(PrintStream ps)
768 for (int j = 0; j < rows; j++)
770 Format.print(ps, "%15.4e", d[j]);
780 public void printE(PrintStream ps)
782 for (int j = 0; j < rows; j++)
784 Format.print(ps, "%15.4e", e[j]);
794 public static void main(String[] args) throws Exception
796 int n = Integer.parseInt(args[0]);
797 double[][] in = new double[n][n];
799 for (int i = 0; i < n; i++)
801 for (int j = 0; j < n; j++)
803 in[i][j] = (double) Math.random();
807 Matrix origmat = new Matrix(in, n, n);
809 // System.out.println(" --- Original matrix ---- ");
810 // / origmat.print(System.out);
811 // System.out.println();
812 // System.out.println(" --- transpose matrix ---- ");
813 Matrix trans = origmat.transpose();
815 // trans.print(System.out);
816 // System.out.println();
817 // System.out.println(" --- OrigT * Orig ---- ");
818 Matrix symm = trans.postMultiply(origmat);
820 // symm.print(System.out);
821 // System.out.println();
822 // Copy the symmetric matrix for later
823 // Matrix origsymm = symm.copy();
825 // This produces the tridiagonal transformation matrix
826 // long tstart = System.currentTimeMillis();
829 // long tend = System.currentTimeMillis();
831 // System.out.println("Time take for tred = " + (tend-tstart) + "ms");
832 // System.out.println(" ---Tridiag transform matrix ---");
833 // symm.print(System.out);
834 // System.out.println();
835 // System.out.println(" --- D vector ---");
836 // symm.printD(System.out);
837 // System.out.println();
838 // System.out.println(" --- E vector ---");
839 // symm.printE(System.out);
840 // System.out.println();
841 // Now produce the diagonalization matrix
842 // tstart = System.currentTimeMillis();
844 // tend = System.currentTimeMillis();
846 // System.out.println("Time take for tqli = " + (tend-tstart) + " ms");
847 // System.out.println(" --- New diagonalization matrix ---");
848 // symm.print(System.out);
849 // System.out.println();
850 // System.out.println(" --- D vector ---");
851 // symm.printD(System.out);
852 // System.out.println();
853 // System.out.println(" --- E vector ---");
854 // symm.printE(System.out);
855 // System.out.println();
856 // System.out.println(" --- First eigenvector --- ");
857 // double[] eigenv = symm.getColumn(0);
858 // for (int i=0; i < eigenv.length;i++) {
859 // Format.print(System.out,"%15.4f",eigenv[i]);
861 // System.out.println();
862 // double[] neigenv = origsymm.vectorPostMultiply(eigenv);
863 // for (int i=0; i < neigenv.length;i++) {
864 // Format.print(System.out,"%15.4f",neigenv[i]/symm.d[0]);
866 // System.out.println();