-/*\r
- * Jalview - A Sequence Alignment Editor and Viewer\r
- * Copyright (C) 2007 AM Waterhouse, J Procter, G Barton, M Clamp, S Searle\r
- *\r
- * This program is free software; you can redistribute it and/or\r
- * modify it under the terms of the GNU General Public License\r
- * as published by the Free Software Foundation; either version 2\r
- * of the License, or (at your option) any later version.\r
- *\r
- * This program is distributed in the hope that it will be useful,\r
- * but WITHOUT ANY WARRANTY; without even the implied warranty of\r
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\r
- * GNU General Public License for more details.\r
- *\r
- * You should have received a copy of the GNU General Public License\r
- * along with this program; if not, write to the Free Software\r
- * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA\r
- */\r
-package jalview.math;\r
-\r
-import java.io.*;\r
-\r
-import jalview.util.*;\r
-\r
-/**\r
- * DOCUMENT ME!\r
- *\r
- * @author $author$\r
- * @version $Revision$\r
- */\r
-public class Matrix\r
-{\r
- /**\r
- * SMJSPUBLIC\r
- */\r
- public double[][] value;\r
-\r
- /** DOCUMENT ME!! */\r
- public int rows;\r
-\r
- /** DOCUMENT ME!! */\r
- public int cols;\r
-\r
- /** DOCUMENT ME!! */\r
- public double[] d; // Diagonal\r
-\r
- /** DOCUMENT ME!! */\r
- public double[] e; // off diagonal\r
-\r
- /**\r
- * Creates a new Matrix object.\r
- *\r
- * @param value DOCUMENT ME!\r
- * @param rows DOCUMENT ME!\r
- * @param cols DOCUMENT ME!\r
- */\r
- public Matrix(double[][] value, int rows, int cols)\r
- {\r
- this.rows = rows;\r
- this.cols = cols;\r
- this.value = value;\r
- }\r
-\r
- /**\r
- * DOCUMENT ME!\r
- *\r
- * @return DOCUMENT ME!\r
- */\r
- public Matrix transpose()\r
- {\r
- double[][] out = new double[cols][rows];\r
-\r
- for (int i = 0; i < cols; i++)\r
- {\r
- for (int j = 0; j < rows; j++)\r
- {\r
- out[i][j] = value[j][i];\r
- }\r
- }\r
-\r
- return new Matrix(out, cols, rows);\r
- }\r
-\r
- /**\r
- * DOCUMENT ME!\r
- *\r
- * @param ps DOCUMENT ME!\r
- */\r
- public void print(PrintStream ps)\r
- {\r
- for (int i = 0; i < rows; i++)\r
- {\r
- for (int j = 0; j < cols; j++)\r
- {\r
- Format.print(ps, "%8.2f", value[i][j]);\r
- }\r
-\r
- ps.println();\r
- }\r
- }\r
-\r
- /**\r
- * DOCUMENT ME!\r
- *\r
- * @param in DOCUMENT ME!\r
- *\r
- * @return DOCUMENT ME!\r
- */\r
- public Matrix preMultiply(Matrix in)\r
- {\r
- double[][] tmp = new double[in.rows][this.cols];\r
-\r
- for (int i = 0; i < in.rows; i++)\r
- {\r
- for (int j = 0; j < this.cols; j++)\r
- {\r
- tmp[i][j] = 0.0;\r
-\r
- for (int k = 0; k < in.cols; k++)\r
- {\r
- tmp[i][j] += (in.value[i][k] * this.value[k][j]);\r
- }\r
- }\r
- }\r
-\r
- return new Matrix(tmp, in.rows, this.cols);\r
- }\r
-\r
- /**\r
- * DOCUMENT ME!\r
- *\r
- * @param in DOCUMENT ME!\r
- *\r
- * @return DOCUMENT ME!\r
- */\r
- public double[] vectorPostMultiply(double[] in)\r
- {\r
- double[] out = new double[in.length];\r
-\r
- for (int i = 0; i < in.length; i++)\r
- {\r
- out[i] = 0.0;\r
-\r
- for (int k = 0; k < in.length; k++)\r
- {\r
- out[i] += (value[i][k] * in[k]);\r
- }\r
- }\r
-\r
- return out;\r
- }\r
-\r
- /**\r
- * DOCUMENT ME!\r
- *\r
- * @param in DOCUMENT ME!\r
- *\r
- * @return DOCUMENT ME!\r
- */\r
- public Matrix postMultiply(Matrix in)\r
- {\r
- double[][] out = new double[this.rows][in.cols];\r
-\r
- for (int i = 0; i < this.rows; i++)\r
- {\r
- for (int j = 0; j < in.cols; j++)\r
- {\r
- out[i][j] = 0.0;\r
-\r
- for (int k = 0; k < rows; k++)\r
- {\r
- out[i][j] = out[i][j] + (value[i][k] * in.value[k][j]);\r
- }\r
- }\r
- }\r
-\r
- return new Matrix(out, this.cols, in.rows);\r
- }\r
-\r
- /**\r
- * DOCUMENT ME!\r
- *\r
- * @return DOCUMENT ME!\r
- */\r
- public Matrix copy()\r
- {\r
- double[][] newmat = new double[rows][cols];\r
-\r
- for (int i = 0; i < rows; i++)\r
- {\r
- for (int j = 0; j < cols; j++)\r
- {\r
- newmat[i][j] = value[i][j];\r
- }\r
- }\r
-\r
- return new Matrix(newmat, rows, cols);\r
- }\r
-\r
- /**\r
- * DOCUMENT ME!\r
- */\r
- public void tred()\r
- {\r
- int n = rows;\r
- int l;\r
- int k;\r
- int j;\r
- int i;\r
-\r
- double scale;\r
- double hh;\r
- double h;\r
- double g;\r
- double f;\r
-\r
- this.d = new double[rows];\r
- this.e = new double[rows];\r
-\r
- for (i = n; i >= 2; i--)\r
- {\r
- l = i - 1;\r
- h = 0.0;\r
- scale = 0.0;\r
-\r
- if (l > 1)\r
- {\r
- for (k = 1; k <= l; k++)\r
- {\r
- scale += Math.abs(value[i - 1][k - 1]);\r
- }\r
-\r
- if (scale == 0.0)\r
- {\r
- e[i - 1] = value[i - 1][l - 1];\r
- }\r
- else\r
- {\r
- for (k = 1; k <= l; k++)\r
- {\r
- value[i - 1][k - 1] /= scale;\r
- h += (value[i - 1][k - 1] * value[i - 1][k - 1]);\r
- }\r
-\r
- f = value[i - 1][l - 1];\r
-\r
- if (f > 0)\r
- {\r
- g = -1.0 * Math.sqrt(h);\r
- }\r
- else\r
- {\r
- g = Math.sqrt(h);\r
- }\r
-\r
- e[i - 1] = scale * g;\r
- h -= (f * g);\r
- value[i - 1][l - 1] = f - g;\r
- f = 0.0;\r
-\r
- for (j = 1; j <= l; j++)\r
- {\r
- value[j - 1][i - 1] = value[i - 1][j - 1] / h;\r
- g = 0.0;\r
-\r
- for (k = 1; k <= j; k++)\r
- {\r
- g += (value[j - 1][k - 1] * value[i - 1][k - 1]);\r
- }\r
-\r
- for (k = j + 1; k <= l; k++)\r
- {\r
- g += (value[k - 1][j - 1] * value[i - 1][k - 1]);\r
- }\r
-\r
- e[j - 1] = g / h;\r
- f += (e[j - 1] * value[i - 1][j - 1]);\r
- }\r
-\r
- hh = f / (h + h);\r
-\r
- for (j = 1; j <= l; j++)\r
- {\r
- f = value[i - 1][j - 1];\r
- g = e[j - 1] - (hh * f);\r
- e[j - 1] = g;\r
-\r
- for (k = 1; k <= j; k++)\r
- {\r
- value[j - 1][k - 1] -= ( (f * e[k - 1]) +\r
- (g * value[i - 1][k - 1]));\r
- }\r
- }\r
- }\r
- }\r
- else\r
- {\r
- e[i - 1] = value[i - 1][l - 1];\r
- }\r
-\r
- d[i - 1] = h;\r
- }\r
-\r
- d[0] = 0.0;\r
- e[0] = 0.0;\r
-\r
- for (i = 1; i <= n; i++)\r
- {\r
- l = i - 1;\r
-\r
- if (d[i - 1] != 0.0)\r
- {\r
- for (j = 1; j <= l; j++)\r
- {\r
- g = 0.0;\r
-\r
- for (k = 1; k <= l; k++)\r
- {\r
- g += (value[i - 1][k - 1] * value[k - 1][j - 1]);\r
- }\r
-\r
- for (k = 1; k <= l; k++)\r
- {\r
- value[k - 1][j - 1] -= (g * value[k - 1][i - 1]);\r
- }\r
- }\r
- }\r
-\r
- d[i - 1] = value[i - 1][i - 1];\r
- value[i - 1][i - 1] = 1.0;\r
-\r
- for (j = 1; j <= l; j++)\r
- {\r
- value[j - 1][i - 1] = 0.0;\r
- value[i - 1][j - 1] = 0.0;\r
- }\r
- }\r
- }\r
-\r
- /**\r
- * DOCUMENT ME!\r
- */\r
- public void tqli()\r
- {\r
- int n = rows;\r
-\r
- int m;\r
- int l;\r
- int iter;\r
- int i;\r
- int k;\r
- double s;\r
- double r;\r
- double p;\r
- ;\r
-\r
- double g;\r
- double f;\r
- double dd;\r
- double c;\r
- double b;\r
-\r
- for (i = 2; i <= n; i++)\r
- {\r
- e[i - 2] = e[i - 1];\r
- }\r
-\r
- e[n - 1] = 0.0;\r
-\r
- for (l = 1; l <= n; l++)\r
- {\r
- iter = 0;\r
-\r
- do\r
- {\r
- for (m = l; m <= (n - 1); m++)\r
- {\r
- dd = Math.abs(d[m - 1]) + Math.abs(d[m]);\r
-\r
- if ( (Math.abs(e[m - 1]) + dd) == dd)\r
- {\r
- break;\r
- }\r
- }\r
-\r
- if (m != l)\r
- {\r
- iter++;\r
-\r
- if (iter == 30)\r
- {\r
- System.err.print("Too many iterations in tqli");\r
- System.exit(0); // JBPNote - should this really be here ???\r
- }\r
- else\r
- {\r
- // System.out.println("Iteration " + iter);\r
- }\r
-\r
- g = (d[l] - d[l - 1]) / (2.0 * e[l - 1]);\r
- r = Math.sqrt( (g * g) + 1.0);\r
- g = d[m - 1] - d[l - 1] + (e[l - 1] / (g + sign(r, g)));\r
- c = 1.0;\r
- s = c;\r
- p = 0.0;\r
-\r
- for (i = m - 1; i >= l; i--)\r
- {\r
- f = s * e[i - 1];\r
- b = c * e[i - 1];\r
-\r
- if (Math.abs(f) >= Math.abs(g))\r
- {\r
- c = g / f;\r
- r = Math.sqrt( (c * c) + 1.0);\r
- e[i] = f * r;\r
- s = 1.0 / r;\r
- c *= s;\r
- }\r
- else\r
- {\r
- s = f / g;\r
- r = Math.sqrt( (s * s) + 1.0);\r
- e[i] = g * r;\r
- c = 1.0 / r;\r
- s *= c;\r
- }\r
-\r
- g = d[i] - p;\r
- r = ( (d[i - 1] - g) * s) + (2.0 * c * b);\r
- p = s * r;\r
- d[i] = g + p;\r
- g = (c * r) - b;\r
-\r
- for (k = 1; k <= n; k++)\r
- {\r
- f = value[k - 1][i];\r
- value[k - 1][i] = (s * value[k - 1][i - 1]) +\r
- (c * f);\r
- value[k - 1][i - 1] = (c * value[k - 1][i - 1]) -\r
- (s * f);\r
- }\r
- }\r
-\r
- d[l - 1] = d[l - 1] - p;\r
- e[l - 1] = g;\r
- e[m - 1] = 0.0;\r
- }\r
- }\r
- while (m != l);\r
- }\r
- }\r
-\r
- /**\r
- * DOCUMENT ME!\r
- */\r
- public void tred2()\r
- {\r
- int n = rows;\r
- int l;\r
- int k;\r
- int j;\r
- int i;\r
-\r
- double scale;\r
- double hh;\r
- double h;\r
- double g;\r
- double f;\r
-\r
- this.d = new double[rows];\r
- this.e = new double[rows];\r
-\r
- for (i = n - 1; i >= 1; i--)\r
- {\r
- l = i - 1;\r
- h = 0.0;\r
- scale = 0.0;\r
-\r
- if (l > 0)\r
- {\r
- for (k = 0; k < l; k++)\r
- {\r
- scale += Math.abs(value[i][k]);\r
- }\r
-\r
- if (scale == 0.0)\r
- {\r
- e[i] = value[i][l];\r
- }\r
- else\r
- {\r
- for (k = 0; k < l; k++)\r
- {\r
- value[i][k] /= scale;\r
- h += (value[i][k] * value[i][k]);\r
- }\r
-\r
- f = value[i][l];\r
-\r
- if (f > 0)\r
- {\r
- g = -1.0 * Math.sqrt(h);\r
- }\r
- else\r
- {\r
- g = Math.sqrt(h);\r
- }\r
-\r
- e[i] = scale * g;\r
- h -= (f * g);\r
- value[i][l] = f - g;\r
- f = 0.0;\r
-\r
- for (j = 0; j < l; j++)\r
- {\r
- value[j][i] = value[i][j] / h;\r
- g = 0.0;\r
-\r
- for (k = 0; k < j; k++)\r
- {\r
- g += (value[j][k] * value[i][k]);\r
- }\r
-\r
- for (k = j; k < l; k++)\r
- {\r
- g += (value[k][j] * value[i][k]);\r
- }\r
-\r
- e[j] = g / h;\r
- f += (e[j] * value[i][j]);\r
- }\r
-\r
- hh = f / (h + h);\r
-\r
- for (j = 0; j < l; j++)\r
- {\r
- f = value[i][j];\r
- g = e[j] - (hh * f);\r
- e[j] = g;\r
-\r
- for (k = 0; k < j; k++)\r
- {\r
- value[j][k] -= ( (f * e[k]) + (g * value[i][k]));\r
- }\r
- }\r
- }\r
- }\r
- else\r
- {\r
- e[i] = value[i][l];\r
- }\r
-\r
- d[i] = h;\r
- }\r
-\r
- d[0] = 0.0;\r
- e[0] = 0.0;\r
-\r
- for (i = 0; i < n; i++)\r
- {\r
- l = i - 1;\r
-\r
- if (d[i] != 0.0)\r
- {\r
- for (j = 0; j < l; j++)\r
- {\r
- g = 0.0;\r
-\r
- for (k = 0; k < l; k++)\r
- {\r
- g += (value[i][k] * value[k][j]);\r
- }\r
-\r
- for (k = 0; k < l; k++)\r
- {\r
- value[k][j] -= (g * value[k][i]);\r
- }\r
- }\r
- }\r
-\r
- d[i] = value[i][i];\r
- value[i][i] = 1.0;\r
-\r
- for (j = 0; j < l; j++)\r
- {\r
- value[j][i] = 0.0;\r
- value[i][j] = 0.0;\r
- }\r
- }\r
- }\r
-\r
- /**\r
- * DOCUMENT ME!\r
- */\r
- public void tqli2()\r
- {\r
- int n = rows;\r
-\r
- int m;\r
- int l;\r
- int iter;\r
- int i;\r
- int k;\r
- double s;\r
- double r;\r
- double p;\r
- ;\r
-\r
- double g;\r
- double f;\r
- double dd;\r
- double c;\r
- double b;\r
-\r
- for (i = 2; i <= n; i++)\r
- {\r
- e[i - 2] = e[i - 1];\r
- }\r
-\r
- e[n - 1] = 0.0;\r
-\r
- for (l = 1; l <= n; l++)\r
- {\r
- iter = 0;\r
-\r
- do\r
- {\r
- for (m = l; m <= (n - 1); m++)\r
- {\r
- dd = Math.abs(d[m - 1]) + Math.abs(d[m]);\r
-\r
- if ( (Math.abs(e[m - 1]) + dd) == dd)\r
- {\r
- break;\r
- }\r
- }\r
-\r
- if (m != l)\r
- {\r
- iter++;\r
-\r
- if (iter == 30)\r
- {\r
- System.err.print("Too many iterations in tqli");\r
- System.exit(0); // JBPNote - same as above - not a graceful exit!\r
- }\r
- else\r
- {\r
- // System.out.println("Iteration " + iter);\r
- }\r
-\r
- g = (d[l] - d[l - 1]) / (2.0 * e[l - 1]);\r
- r = Math.sqrt( (g * g) + 1.0);\r
- g = d[m - 1] - d[l - 1] + (e[l - 1] / (g + sign(r, g)));\r
- c = 1.0;\r
- s = c;\r
- p = 0.0;\r
-\r
- for (i = m - 1; i >= l; i--)\r
- {\r
- f = s * e[i - 1];\r
- b = c * e[i - 1];\r
-\r
- if (Math.abs(f) >= Math.abs(g))\r
- {\r
- c = g / f;\r
- r = Math.sqrt( (c * c) + 1.0);\r
- e[i] = f * r;\r
- s = 1.0 / r;\r
- c *= s;\r
- }\r
- else\r
- {\r
- s = f / g;\r
- r = Math.sqrt( (s * s) + 1.0);\r
- e[i] = g * r;\r
- c = 1.0 / r;\r
- s *= c;\r
- }\r
-\r
- g = d[i] - p;\r
- r = ( (d[i - 1] - g) * s) + (2.0 * c * b);\r
- p = s * r;\r
- d[i] = g + p;\r
- g = (c * r) - b;\r
-\r
- for (k = 1; k <= n; k++)\r
- {\r
- f = value[k - 1][i];\r
- value[k - 1][i] = (s * value[k - 1][i - 1]) +\r
- (c * f);\r
- value[k - 1][i - 1] = (c * value[k - 1][i - 1]) -\r
- (s * f);\r
- }\r
- }\r
-\r
- d[l - 1] = d[l - 1] - p;\r
- e[l - 1] = g;\r
- e[m - 1] = 0.0;\r
- }\r
- }\r
- while (m != l);\r
- }\r
- }\r
-\r
- /**\r
- * DOCUMENT ME!\r
- *\r
- * @param a DOCUMENT ME!\r
- * @param b DOCUMENT ME!\r
- *\r
- * @return DOCUMENT ME!\r
- */\r
- public double sign(double a, double b)\r
- {\r
- if (b < 0)\r
- {\r
- return -Math.abs(a);\r
- }\r
- else\r
- {\r
- return Math.abs(a);\r
- }\r
- }\r
-\r
- /**\r
- * DOCUMENT ME!\r
- *\r
- * @param n DOCUMENT ME!\r
- *\r
- * @return DOCUMENT ME!\r
- */\r
- public double[] getColumn(int n)\r
- {\r
- double[] out = new double[rows];\r
-\r
- for (int i = 0; i < rows; i++)\r
- {\r
- out[i] = value[i][n];\r
- }\r
-\r
- return out;\r
- }\r
-\r
- /**\r
- * DOCUMENT ME!\r
- *\r
- * @param ps DOCUMENT ME!\r
- */\r
- public void printD(PrintStream ps)\r
- {\r
- for (int j = 0; j < rows; j++)\r
- {\r
- Format.print(ps, "%15.4e", d[j]);\r
- }\r
- }\r
-\r
- /**\r
- * DOCUMENT ME!\r
- *\r
- * @param ps DOCUMENT ME!\r
- */\r
- public void printE(PrintStream ps)\r
- {\r
- for (int j = 0; j < rows; j++)\r
- {\r
- Format.print(ps, "%15.4e", e[j]);\r
- }\r
- }\r
-\r
- /**\r
- * DOCUMENT ME!\r
- *\r
- * @param args DOCUMENT ME!\r
- */\r
- public static void main(String[] args)\r
- {\r
- int n = Integer.parseInt(args[0]);\r
- double[][] in = new double[n][n];\r
-\r
- for (int i = 0; i < n; i++)\r
- {\r
- for (int j = 0; j < n; j++)\r
- {\r
- in[i][j] = (double) Math.random();\r
- }\r
- }\r
-\r
- Matrix origmat = new Matrix(in, n, n);\r
-\r
- // System.out.println(" --- Original matrix ---- ");\r
- /// origmat.print(System.out);\r
- //System.out.println();\r
- //System.out.println(" --- transpose matrix ---- ");\r
- Matrix trans = origmat.transpose();\r
-\r
- //trans.print(System.out);\r
- //System.out.println();\r
- //System.out.println(" --- OrigT * Orig ---- ");\r
- Matrix symm = trans.postMultiply(origmat);\r
-\r
- //symm.print(System.out);\r
- //System.out.println();\r
- // Copy the symmetric matrix for later\r
- //Matrix origsymm = symm.copy();\r
-\r
- // This produces the tridiagonal transformation matrix\r
- //long tstart = System.currentTimeMillis();\r
- symm.tred();\r
-\r
- //long tend = System.currentTimeMillis();\r
-\r
- //System.out.println("Time take for tred = " + (tend-tstart) + "ms");\r
- //System.out.println(" ---Tridiag transform matrix ---");\r
- //symm.print(System.out);\r
- //System.out.println();\r
- //System.out.println(" --- D vector ---");\r
- //symm.printD(System.out);\r
- //System.out.println();\r
- //System.out.println(" --- E vector ---");\r
- //symm.printE(System.out);\r
- //System.out.println();\r
- // Now produce the diagonalization matrix\r
- //tstart = System.currentTimeMillis();\r
- symm.tqli();\r
- //tend = System.currentTimeMillis();\r
-\r
- //System.out.println("Time take for tqli = " + (tend-tstart) + " ms");\r
- //System.out.println(" --- New diagonalization matrix ---");\r
- //symm.print(System.out);\r
- //System.out.println();\r
- //System.out.println(" --- D vector ---");\r
- //symm.printD(System.out);\r
- //System.out.println();\r
- //System.out.println(" --- E vector ---");\r
- //symm.printE(System.out);\r
- //System.out.println();\r
- //System.out.println(" --- First eigenvector --- ");\r
- //double[] eigenv = symm.getColumn(0);\r
- //for (int i=0; i < eigenv.length;i++) {\r
- // Format.print(System.out,"%15.4f",eigenv[i]);\r
- // }\r
- //System.out.println();\r
- //double[] neigenv = origsymm.vectorPostMultiply(eigenv);\r
- //for (int i=0; i < neigenv.length;i++) {\r
- // Format.print(System.out,"%15.4f",neigenv[i]/symm.d[0]);\r
- //}\r
- //System.out.println();\r
- }\r
-}\r
+/*
+ * Jalview - A Sequence Alignment Editor and Viewer (Version 2.4)
+ * Copyright (C) 2008 AM Waterhouse, J Procter, G Barton, M Clamp, S Searle
+ *
+ * This program is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU General Public License
+ * as published by the Free Software Foundation; either version 2
+ * of the License, or (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA
+ */
+package jalview.math;
+
+import java.io.*;
+
+import jalview.util.*;
+
+/**
+ * DOCUMENT ME!
+ *
+ * @author $author$
+ * @version $Revision$
+ */
+public class Matrix
+{
+ /**
+ * SMJSPUBLIC
+ */
+ public double[][] value;
+
+ /** DOCUMENT ME!! */
+ public int rows;
+
+ /** DOCUMENT ME!! */
+ public int cols;
+
+ /** DOCUMENT ME!! */
+ public double[] d; // Diagonal
+
+ /** DOCUMENT ME!! */
+ public double[] e; // off diagonal
+
+ /**
+ * Creates a new Matrix object.
+ *
+ * @param value
+ * DOCUMENT ME!
+ * @param rows
+ * DOCUMENT ME!
+ * @param cols
+ * DOCUMENT ME!
+ */
+ public Matrix(double[][] value, int rows, int cols)
+ {
+ this.rows = rows;
+ this.cols = cols;
+ this.value = value;
+ }
+
+ /**
+ * DOCUMENT ME!
+ *
+ * @return DOCUMENT ME!
+ */
+ public Matrix transpose()
+ {
+ double[][] out = new double[cols][rows];
+
+ for (int i = 0; i < cols; i++)
+ {
+ for (int j = 0; j < rows; j++)
+ {
+ out[i][j] = value[j][i];
+ }
+ }
+
+ return new Matrix(out, cols, rows);
+ }
+
+ /**
+ * DOCUMENT ME!
+ *
+ * @param ps
+ * DOCUMENT ME!
+ */
+ public void print(PrintStream ps)
+ {
+ for (int i = 0; i < rows; i++)
+ {
+ for (int j = 0; j < cols; j++)
+ {
+ Format.print(ps, "%8.2f", value[i][j]);
+ }
+
+ ps.println();
+ }
+ }
+
+ /**
+ * DOCUMENT ME!
+ *
+ * @param in
+ * DOCUMENT ME!
+ *
+ * @return DOCUMENT ME!
+ */
+ public Matrix preMultiply(Matrix in)
+ {
+ double[][] tmp = new double[in.rows][this.cols];
+
+ for (int i = 0; i < in.rows; i++)
+ {
+ for (int j = 0; j < this.cols; j++)
+ {
+ tmp[i][j] = 0.0;
+
+ for (int k = 0; k < in.cols; k++)
+ {
+ tmp[i][j] += (in.value[i][k] * this.value[k][j]);
+ }
+ }
+ }
+
+ return new Matrix(tmp, in.rows, this.cols);
+ }
+
+ /**
+ * DOCUMENT ME!
+ *
+ * @param in
+ * DOCUMENT ME!
+ *
+ * @return DOCUMENT ME!
+ */
+ public double[] vectorPostMultiply(double[] in)
+ {
+ double[] out = new double[in.length];
+
+ for (int i = 0; i < in.length; i++)
+ {
+ out[i] = 0.0;
+
+ for (int k = 0; k < in.length; k++)
+ {
+ out[i] += (value[i][k] * in[k]);
+ }
+ }
+
+ return out;
+ }
+
+ /**
+ * DOCUMENT ME!
+ *
+ * @param in
+ * DOCUMENT ME!
+ *
+ * @return DOCUMENT ME!
+ */
+ public Matrix postMultiply(Matrix in)
+ {
+ double[][] out = new double[this.rows][in.cols];
+
+ for (int i = 0; i < this.rows; i++)
+ {
+ for (int j = 0; j < in.cols; j++)
+ {
+ out[i][j] = 0.0;
+
+ for (int k = 0; k < rows; k++)
+ {
+ out[i][j] = out[i][j] + (value[i][k] * in.value[k][j]);
+ }
+ }
+ }
+
+ return new Matrix(out, this.cols, in.rows);
+ }
+
+ /**
+ * DOCUMENT ME!
+ *
+ * @return DOCUMENT ME!
+ */
+ public Matrix copy()
+ {
+ double[][] newmat = new double[rows][cols];
+
+ for (int i = 0; i < rows; i++)
+ {
+ for (int j = 0; j < cols; j++)
+ {
+ newmat[i][j] = value[i][j];
+ }
+ }
+
+ return new Matrix(newmat, rows, cols);
+ }
+
+ /**
+ * DOCUMENT ME!
+ */
+ public void tred()
+ {
+ int n = rows;
+ int l;
+ int k;
+ int j;
+ int i;
+
+ double scale;
+ double hh;
+ double h;
+ double g;
+ double f;
+
+ this.d = new double[rows];
+ this.e = new double[rows];
+
+ for (i = n; i >= 2; i--)
+ {
+ l = i - 1;
+ h = 0.0;
+ scale = 0.0;
+
+ if (l > 1)
+ {
+ for (k = 1; k <= l; k++)
+ {
+ scale += Math.abs(value[i - 1][k - 1]);
+ }
+
+ if (scale == 0.0)
+ {
+ e[i - 1] = value[i - 1][l - 1];
+ }
+ else
+ {
+ for (k = 1; k <= l; k++)
+ {
+ value[i - 1][k - 1] /= scale;
+ h += (value[i - 1][k - 1] * value[i - 1][k - 1]);
+ }
+
+ f = value[i - 1][l - 1];
+
+ if (f > 0)
+ {
+ g = -1.0 * Math.sqrt(h);
+ }
+ else
+ {
+ g = Math.sqrt(h);
+ }
+
+ e[i - 1] = scale * g;
+ h -= (f * g);
+ value[i - 1][l - 1] = f - g;
+ f = 0.0;
+
+ for (j = 1; j <= l; j++)
+ {
+ value[j - 1][i - 1] = value[i - 1][j - 1] / h;
+ g = 0.0;
+
+ for (k = 1; k <= j; k++)
+ {
+ g += (value[j - 1][k - 1] * value[i - 1][k - 1]);
+ }
+
+ for (k = j + 1; k <= l; k++)
+ {
+ g += (value[k - 1][j - 1] * value[i - 1][k - 1]);
+ }
+
+ e[j - 1] = g / h;
+ f += (e[j - 1] * value[i - 1][j - 1]);
+ }
+
+ hh = f / (h + h);
+
+ for (j = 1; j <= l; j++)
+ {
+ f = value[i - 1][j - 1];
+ g = e[j - 1] - (hh * f);
+ e[j - 1] = g;
+
+ for (k = 1; k <= j; k++)
+ {
+ value[j - 1][k - 1] -= ((f * e[k - 1]) + (g * value[i - 1][k - 1]));
+ }
+ }
+ }
+ }
+ else
+ {
+ e[i - 1] = value[i - 1][l - 1];
+ }
+
+ d[i - 1] = h;
+ }
+
+ d[0] = 0.0;
+ e[0] = 0.0;
+
+ for (i = 1; i <= n; i++)
+ {
+ l = i - 1;
+
+ if (d[i - 1] != 0.0)
+ {
+ for (j = 1; j <= l; j++)
+ {
+ g = 0.0;
+
+ for (k = 1; k <= l; k++)
+ {
+ g += (value[i - 1][k - 1] * value[k - 1][j - 1]);
+ }
+
+ for (k = 1; k <= l; k++)
+ {
+ value[k - 1][j - 1] -= (g * value[k - 1][i - 1]);
+ }
+ }
+ }
+
+ d[i - 1] = value[i - 1][i - 1];
+ value[i - 1][i - 1] = 1.0;
+
+ for (j = 1; j <= l; j++)
+ {
+ value[j - 1][i - 1] = 0.0;
+ value[i - 1][j - 1] = 0.0;
+ }
+ }
+ }
+
+ /**
+ * DOCUMENT ME!
+ */
+ public void tqli()
+ {
+ int n = rows;
+
+ int m;
+ int l;
+ int iter;
+ int i;
+ int k;
+ double s;
+ double r;
+ double p;
+ ;
+
+ double g;
+ double f;
+ double dd;
+ double c;
+ double b;
+
+ for (i = 2; i <= n; i++)
+ {
+ e[i - 2] = e[i - 1];
+ }
+
+ e[n - 1] = 0.0;
+
+ for (l = 1; l <= n; l++)
+ {
+ iter = 0;
+
+ do
+ {
+ for (m = l; m <= (n - 1); m++)
+ {
+ dd = Math.abs(d[m - 1]) + Math.abs(d[m]);
+
+ if ((Math.abs(e[m - 1]) + dd) == dd)
+ {
+ break;
+ }
+ }
+
+ if (m != l)
+ {
+ iter++;
+
+ if (iter == 30)
+ {
+ System.err.print("Too many iterations in tqli");
+ System.exit(0); // JBPNote - should this really be here ???
+ }
+ else
+ {
+ // System.out.println("Iteration " + iter);
+ }
+
+ g = (d[l] - d[l - 1]) / (2.0 * e[l - 1]);
+ r = Math.sqrt((g * g) + 1.0);
+ g = d[m - 1] - d[l - 1] + (e[l - 1] / (g + sign(r, g)));
+ c = 1.0;
+ s = c;
+ p = 0.0;
+
+ for (i = m - 1; i >= l; i--)
+ {
+ f = s * e[i - 1];
+ b = c * e[i - 1];
+
+ if (Math.abs(f) >= Math.abs(g))
+ {
+ c = g / f;
+ r = Math.sqrt((c * c) + 1.0);
+ e[i] = f * r;
+ s = 1.0 / r;
+ c *= s;
+ }
+ else
+ {
+ s = f / g;
+ r = Math.sqrt((s * s) + 1.0);
+ e[i] = g * r;
+ c = 1.0 / r;
+ s *= c;
+ }
+
+ g = d[i] - p;
+ r = ((d[i - 1] - g) * s) + (2.0 * c * b);
+ p = s * r;
+ d[i] = g + p;
+ g = (c * r) - b;
+
+ for (k = 1; k <= n; k++)
+ {
+ f = value[k - 1][i];
+ value[k - 1][i] = (s * value[k - 1][i - 1]) + (c * f);
+ value[k - 1][i - 1] = (c * value[k - 1][i - 1]) - (s * f);
+ }
+ }
+
+ d[l - 1] = d[l - 1] - p;
+ e[l - 1] = g;
+ e[m - 1] = 0.0;
+ }
+ } while (m != l);
+ }
+ }
+
+ /**
+ * DOCUMENT ME!
+ */
+ public void tred2()
+ {
+ int n = rows;
+ int l;
+ int k;
+ int j;
+ int i;
+
+ double scale;
+ double hh;
+ double h;
+ double g;
+ double f;
+
+ this.d = new double[rows];
+ this.e = new double[rows];
+
+ for (i = n - 1; i >= 1; i--)
+ {
+ l = i - 1;
+ h = 0.0;
+ scale = 0.0;
+
+ if (l > 0)
+ {
+ for (k = 0; k < l; k++)
+ {
+ scale += Math.abs(value[i][k]);
+ }
+
+ if (scale == 0.0)
+ {
+ e[i] = value[i][l];
+ }
+ else
+ {
+ for (k = 0; k < l; k++)
+ {
+ value[i][k] /= scale;
+ h += (value[i][k] * value[i][k]);
+ }
+
+ f = value[i][l];
+
+ if (f > 0)
+ {
+ g = -1.0 * Math.sqrt(h);
+ }
+ else
+ {
+ g = Math.sqrt(h);
+ }
+
+ e[i] = scale * g;
+ h -= (f * g);
+ value[i][l] = f - g;
+ f = 0.0;
+
+ for (j = 0; j < l; j++)
+ {
+ value[j][i] = value[i][j] / h;
+ g = 0.0;
+
+ for (k = 0; k < j; k++)
+ {
+ g += (value[j][k] * value[i][k]);
+ }
+
+ for (k = j; k < l; k++)
+ {
+ g += (value[k][j] * value[i][k]);
+ }
+
+ e[j] = g / h;
+ f += (e[j] * value[i][j]);
+ }
+
+ hh = f / (h + h);
+
+ for (j = 0; j < l; j++)
+ {
+ f = value[i][j];
+ g = e[j] - (hh * f);
+ e[j] = g;
+
+ for (k = 0; k < j; k++)
+ {
+ value[j][k] -= ((f * e[k]) + (g * value[i][k]));
+ }
+ }
+ }
+ }
+ else
+ {
+ e[i] = value[i][l];
+ }
+
+ d[i] = h;
+ }
+
+ d[0] = 0.0;
+ e[0] = 0.0;
+
+ for (i = 0; i < n; i++)
+ {
+ l = i - 1;
+
+ if (d[i] != 0.0)
+ {
+ for (j = 0; j < l; j++)
+ {
+ g = 0.0;
+
+ for (k = 0; k < l; k++)
+ {
+ g += (value[i][k] * value[k][j]);
+ }
+
+ for (k = 0; k < l; k++)
+ {
+ value[k][j] -= (g * value[k][i]);
+ }
+ }
+ }
+
+ d[i] = value[i][i];
+ value[i][i] = 1.0;
+
+ for (j = 0; j < l; j++)
+ {
+ value[j][i] = 0.0;
+ value[i][j] = 0.0;
+ }
+ }
+ }
+
+ /**
+ * DOCUMENT ME!
+ */
+ public void tqli2()
+ {
+ int n = rows;
+
+ int m;
+ int l;
+ int iter;
+ int i;
+ int k;
+ double s;
+ double r;
+ double p;
+ ;
+
+ double g;
+ double f;
+ double dd;
+ double c;
+ double b;
+
+ for (i = 2; i <= n; i++)
+ {
+ e[i - 2] = e[i - 1];
+ }
+
+ e[n - 1] = 0.0;
+
+ for (l = 1; l <= n; l++)
+ {
+ iter = 0;
+
+ do
+ {
+ for (m = l; m <= (n - 1); m++)
+ {
+ dd = Math.abs(d[m - 1]) + Math.abs(d[m]);
+
+ if ((Math.abs(e[m - 1]) + dd) == dd)
+ {
+ break;
+ }
+ }
+
+ if (m != l)
+ {
+ iter++;
+
+ if (iter == 30)
+ {
+ System.err.print("Too many iterations in tqli");
+ System.exit(0); // JBPNote - same as above - not a graceful exit!
+ }
+ else
+ {
+ // System.out.println("Iteration " + iter);
+ }
+
+ g = (d[l] - d[l - 1]) / (2.0 * e[l - 1]);
+ r = Math.sqrt((g * g) + 1.0);
+ g = d[m - 1] - d[l - 1] + (e[l - 1] / (g + sign(r, g)));
+ c = 1.0;
+ s = c;
+ p = 0.0;
+
+ for (i = m - 1; i >= l; i--)
+ {
+ f = s * e[i - 1];
+ b = c * e[i - 1];
+
+ if (Math.abs(f) >= Math.abs(g))
+ {
+ c = g / f;
+ r = Math.sqrt((c * c) + 1.0);
+ e[i] = f * r;
+ s = 1.0 / r;
+ c *= s;
+ }
+ else
+ {
+ s = f / g;
+ r = Math.sqrt((s * s) + 1.0);
+ e[i] = g * r;
+ c = 1.0 / r;
+ s *= c;
+ }
+
+ g = d[i] - p;
+ r = ((d[i - 1] - g) * s) + (2.0 * c * b);
+ p = s * r;
+ d[i] = g + p;
+ g = (c * r) - b;
+
+ for (k = 1; k <= n; k++)
+ {
+ f = value[k - 1][i];
+ value[k - 1][i] = (s * value[k - 1][i - 1]) + (c * f);
+ value[k - 1][i - 1] = (c * value[k - 1][i - 1]) - (s * f);
+ }
+ }
+
+ d[l - 1] = d[l - 1] - p;
+ e[l - 1] = g;
+ e[m - 1] = 0.0;
+ }
+ } while (m != l);
+ }
+ }
+
+ /**
+ * DOCUMENT ME!
+ *
+ * @param a
+ * DOCUMENT ME!
+ * @param b
+ * DOCUMENT ME!
+ *
+ * @return DOCUMENT ME!
+ */
+ public double sign(double a, double b)
+ {
+ if (b < 0)
+ {
+ return -Math.abs(a);
+ }
+ else
+ {
+ return Math.abs(a);
+ }
+ }
+
+ /**
+ * DOCUMENT ME!
+ *
+ * @param n
+ * DOCUMENT ME!
+ *
+ * @return DOCUMENT ME!
+ */
+ public double[] getColumn(int n)
+ {
+ double[] out = new double[rows];
+
+ for (int i = 0; i < rows; i++)
+ {
+ out[i] = value[i][n];
+ }
+
+ return out;
+ }
+
+ /**
+ * DOCUMENT ME!
+ *
+ * @param ps
+ * DOCUMENT ME!
+ */
+ public void printD(PrintStream ps)
+ {
+ for (int j = 0; j < rows; j++)
+ {
+ Format.print(ps, "%15.4e", d[j]);
+ }
+ }
+
+ /**
+ * DOCUMENT ME!
+ *
+ * @param ps
+ * DOCUMENT ME!
+ */
+ public void printE(PrintStream ps)
+ {
+ for (int j = 0; j < rows; j++)
+ {
+ Format.print(ps, "%15.4e", e[j]);
+ }
+ }
+
+ /**
+ * DOCUMENT ME!
+ *
+ * @param args
+ * DOCUMENT ME!
+ */
+ public static void main(String[] args)
+ {
+ int n = Integer.parseInt(args[0]);
+ double[][] in = new double[n][n];
+
+ for (int i = 0; i < n; i++)
+ {
+ for (int j = 0; j < n; j++)
+ {
+ in[i][j] = (double) Math.random();
+ }
+ }
+
+ Matrix origmat = new Matrix(in, n, n);
+
+ // System.out.println(" --- Original matrix ---- ");
+ // / origmat.print(System.out);
+ // System.out.println();
+ // System.out.println(" --- transpose matrix ---- ");
+ Matrix trans = origmat.transpose();
+
+ // trans.print(System.out);
+ // System.out.println();
+ // System.out.println(" --- OrigT * Orig ---- ");
+ Matrix symm = trans.postMultiply(origmat);
+
+ // symm.print(System.out);
+ // System.out.println();
+ // Copy the symmetric matrix for later
+ // Matrix origsymm = symm.copy();
+
+ // This produces the tridiagonal transformation matrix
+ // long tstart = System.currentTimeMillis();
+ symm.tred();
+
+ // long tend = System.currentTimeMillis();
+
+ // System.out.println("Time take for tred = " + (tend-tstart) + "ms");
+ // System.out.println(" ---Tridiag transform matrix ---");
+ // symm.print(System.out);
+ // System.out.println();
+ // System.out.println(" --- D vector ---");
+ // symm.printD(System.out);
+ // System.out.println();
+ // System.out.println(" --- E vector ---");
+ // symm.printE(System.out);
+ // System.out.println();
+ // Now produce the diagonalization matrix
+ // tstart = System.currentTimeMillis();
+ symm.tqli();
+ // tend = System.currentTimeMillis();
+
+ // System.out.println("Time take for tqli = " + (tend-tstart) + " ms");
+ // System.out.println(" --- New diagonalization matrix ---");
+ // symm.print(System.out);
+ // System.out.println();
+ // System.out.println(" --- D vector ---");
+ // symm.printD(System.out);
+ // System.out.println();
+ // System.out.println(" --- E vector ---");
+ // symm.printE(System.out);
+ // System.out.println();
+ // System.out.println(" --- First eigenvector --- ");
+ // double[] eigenv = symm.getColumn(0);
+ // for (int i=0; i < eigenv.length;i++) {
+ // Format.print(System.out,"%15.4f",eigenv[i]);
+ // }
+ // System.out.println();
+ // double[] neigenv = origsymm.vectorPostMultiply(eigenv);
+ // for (int i=0; i < neigenv.length;i++) {
+ // Format.print(System.out,"%15.4f",neigenv[i]/symm.d[0]);
+ // }
+ // System.out.println();
+ }
+}
git://source.jalview.org / jalview.git / blobdiff