X-Git-Url: http://source.jalview.org/gitweb/?a=blobdiff_plain;f=src%2Fjalview%2Fmath%2FMatrix.java;h=b22bf4e1d27558fc09c6e59e64a45733f12d75cf;hb=187269da0130408d24901c88acb10c217f6284f9;hp=06177f55b72af1a4f8a9190cc43b7bf22d1876e3;hpb=174230b4233d9ce80f94527768d2cd2f76da11ab;p=jalview.git
diff --git a/src/jalview/math/Matrix.java b/src/jalview/math/Matrix.java
index 06177f5..b22bf4e 100755
--- a/src/jalview/math/Matrix.java
+++ b/src/jalview/math/Matrix.java
@@ -1,852 +1,1025 @@
-/*
-* Jalview - A Sequence Alignment Editor and Viewer
-* Copyright (C) 2006 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 jalview.util.*;
-
-import java.io.*;
-
-
-/**
- * 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();
- }
-}
+/*
+ * Jalview - A Sequence Alignment Editor and Viewer ($$Version-Rel$$)
+ * Copyright (C) $$Year-Rel$$ The Jalview Authors
+ *
+ * This file is part of Jalview.
+ *
+ * Jalview 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 3
+ * of the License, or (at your option) any later version.
+ *
+ * Jalview 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 Jalview. If not, see .
+ * The Jalview Authors are detailed in the 'AUTHORS' file.
+ */
+package jalview.math;
+
+import jalview.util.Format;
+import jalview.util.MessageManager;
+
+import java.io.PrintStream;
+import java.util.Arrays;
+
+/**
+ * A class to model rectangular matrices of double values and operations on them
+ */
+public class Matrix implements MatrixI
+{
+ /*
+ * maximum number of iterations for tqli
+ */
+ private static final int MAX_ITER = 45;
+ // fudge - add 15 iterations, just in case
+
+ /*
+ * the number of rows
+ */
+ final protected int rows;
+
+ /*
+ * the number of columns
+ */
+ final protected int cols;
+
+ /*
+ * the cell values in row-major order
+ */
+ private double[][] value;
+
+ protected double[] d; // Diagonal
+
+ protected double[] e; // off diagonal
+
+ /**
+ * Constructor given number of rows and columns
+ *
+ * @param colCount
+ * @param rowCount
+ */
+ protected Matrix(int rowCount, int colCount)
+ {
+ rows = rowCount;
+ cols = colCount;
+ }
+
+ /**
+ * Creates a new Matrix object containing a copy of the supplied array values.
+ * For example
+ *
+ *
+ * new Matrix(new double[][] {{2, 3, 4}, {5, 6, 7})
+ * constructs
+ * (2 3 4)
+ * (5 6 7)
+ *
+ *
+ * Note that ragged arrays (with not all rows, or columns, of the same
+ * length), are not supported by this class. They can be constructed, but
+ * results of operations on them are undefined and may throw exceptions.
+ *
+ * @param values
+ * the matrix values in row-major order
+ */
+ public Matrix(double[][] values)
+ {
+ this.rows = values.length;
+ this.cols = this.rows == 0 ? 0 : values[0].length;
+
+ /*
+ * make a copy of the values array, for immutability
+ */
+ this.value = new double[rows][];
+ int i = 0;
+ for (double[] row : values)
+ {
+ if (row != null)
+ {
+ value[i] = new double[row.length];
+ System.arraycopy(row, 0, value[i], 0, row.length);
+ }
+ i++;
+ }
+ }
+
+ @Override
+ public MatrixI 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);
+ }
+
+ /**
+ * DOCUMENT ME!
+ *
+ * @param ps
+ * DOCUMENT ME!
+ * @param format
+ */
+ @Override
+ public void print(PrintStream ps, String format)
+ {
+ for (int i = 0; i < rows; i++)
+ {
+ for (int j = 0; j < cols; j++)
+ {
+ Format.print(ps, format, getValue(i, j));
+ }
+
+ ps.println();
+ }
+ }
+
+ @Override
+ public MatrixI preMultiply(MatrixI in)
+ {
+ if (in.width() != rows)
+ {
+ throw new IllegalArgumentException("Can't pre-multiply " + this.rows
+ + " rows by " + in.width() + " columns");
+ }
+ double[][] tmp = new double[in.height()][this.cols];
+
+ for (int i = 0; i < in.height(); i++)
+ {
+ for (int j = 0; j < this.cols; j++)
+ {
+ /*
+ * result[i][j] is the vector product of
+ * in.row[i] and this.column[j]
+ */
+ for (int k = 0; k < in.width(); k++)
+ {
+ tmp[i][j] += (in.getValue(i, k) * this.value[k][j]);
+ }
+ }
+ }
+
+ return new Matrix(tmp);
+ }
+
+ /**
+ *
+ * @param in
+ *
+ * @return
+ */
+ 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;
+ }
+
+ @Override
+ public MatrixI postMultiply(MatrixI in)
+ {
+ if (in.height() != this.cols)
+ {
+ throw new IllegalArgumentException("Can't post-multiply " + this.cols
+ + " columns by " + in.height() + " rows");
+ }
+ return in.preMultiply(this);
+ }
+
+ @Override
+ public MatrixI copy()
+ {
+ double[][] newmat = new double[rows][cols];
+
+ for (int i = 0; i < rows; i++)
+ {
+ System.arraycopy(value[i], 0, newmat[i], 0, value[i].length);
+ }
+
+ Matrix m = new Matrix(newmat);
+ if (this.d != null)
+ {
+ m.d = Arrays.copyOf(this.d, this.d.length);
+ }
+ if (this.e != null)
+ {
+ m.e = Arrays.copyOf(this.e, this.e.length);
+ }
+
+ return m;
+ }
+
+ /**
+ * DOCUMENT ME!
+ */
+ @Override
+ public void tred()
+ {
+ int n = rows;
+ 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--)
+ {
+ final int l = i - 1;
+ h = 0.0;
+ scale = 0.0;
+
+ if (l > 1)
+ {
+ for (k = 1; k <= l; k++)
+ {
+ double v = Math.abs(getValue(i - 1, k - 1));
+ scale += v;
+ }
+
+ if (scale == 0.0)
+ {
+ e[i - 1] = getValue(i - 1, l - 1);
+ }
+ else
+ {
+ for (k = 1; k <= l; k++)
+ {
+ double v = divideValue(i - 1, k - 1, scale);
+ h += v * v;
+ }
+
+ f = getValue(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);
+ setValue(i - 1, l - 1, f - g);
+ f = 0.0;
+
+ for (j = 1; j <= l; j++)
+ {
+ double val = getValue(i - 1, j - 1) / h;
+ setValue(j - 1, i - 1, val);
+ g = 0.0;
+
+ for (k = 1; k <= j; k++)
+ {
+ g += (getValue(j - 1, k - 1) * getValue(i - 1, k - 1));
+ }
+
+ for (k = j + 1; k <= l; k++)
+ {
+ g += (getValue(k - 1, j - 1) * getValue(i - 1, k - 1));
+ }
+
+ e[j - 1] = g / h;
+ f += (e[j - 1] * getValue(i - 1, j - 1));
+ }
+
+ hh = f / (h + h);
+
+ for (j = 1; j <= l; j++)
+ {
+ f = getValue(i - 1, j - 1);
+ g = e[j - 1] - (hh * f);
+ e[j - 1] = g;
+
+ for (k = 1; k <= j; k++)
+ {
+ double val = (f * e[k - 1]) + (g * getValue(i - 1, k - 1));
+ addValue(j - 1, k - 1, -val);
+ }
+ }
+ }
+ }
+ else
+ {
+ e[i - 1] = getValue(i - 1, l - 1);
+ }
+
+ d[i - 1] = h;
+ }
+
+ d[0] = 0.0;
+ e[0] = 0.0;
+
+ for (i = 1; i <= n; i++)
+ {
+ final int 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 += (getValue(i - 1, k - 1) * getValue(k - 1, j - 1));
+ }
+
+ for (k = 1; k <= l; k++)
+ {
+ addValue(k - 1, j - 1, -(g * getValue(k - 1, i - 1)));
+ }
+ }
+ }
+
+ d[i - 1] = getValue(i - 1, i - 1);
+ setValue(i - 1, i - 1, 1.0);
+
+ for (j = 1; j <= l; j++)
+ {
+ setValue(j - 1, i - 1, 0.0);
+ setValue(i - 1, j - 1, 0.0);
+ }
+ }
+ }
+
+ /**
+ * Adds f to the value at [i, j] and returns the new value
+ *
+ * @param i
+ * @param j
+ * @param f
+ */
+ protected double addValue(int i, int j, double f)
+ {
+ double v = value[i][j] + f;
+ value[i][j] = v;
+ return v;
+ }
+
+ /**
+ * Divides the value at [i, j] by divisor and returns the new value. If d is
+ * zero, returns the unchanged value.
+ *
+ * @param i
+ * @param j
+ * @param divisor
+ * @return
+ */
+ protected double divideValue(int i, int j, double divisor)
+ {
+ if (divisor == 0d)
+ {
+ return getValue(i, j);
+ }
+ double v = value[i][j];
+ v = v / divisor;
+ value[i][j] = v;
+ return v;
+ }
+
+ /**
+ * DOCUMENT ME!
+ */
+ @Override
+ public void tqli() throws Exception
+ {
+ 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 == MAX_ITER)
+ {
+ throw new Exception(MessageManager.formatMessage(
+ "exception.matrix_too_many_iteration", new String[]
+ { "tqli", Integer.valueOf(MAX_ITER).toString() }));
+ }
+ 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 = getValue(k - 1, i);
+ setValue(k - 1, i, (s * getValue(k - 1, i - 1)) + (c * f));
+ setValue(k - 1, i - 1,
+ (c * getValue(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);
+ }
+ }
+
+ @Override
+ public double getValue(int i, int j)
+ {
+ return value[i][j];
+ }
+
+ @Override
+ public void setValue(int i, int j, double val)
+ {
+ value[i][j] = val;
+ }
+
+ /**
+ * 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() throws Exception
+ {
+ 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 == MAX_ITER)
+ {
+ throw new Exception(MessageManager.formatMessage(
+ "exception.matrix_too_many_iteration", new String[]
+ { "tqli2", Integer.valueOf(MAX_ITER).toString() }));
+ }
+ 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);
+ }
+ }
+
+ /**
+ * Answers the first argument with the sign of the second argument
+ *
+ * @param a
+ * @param b
+ *
+ * @return
+ */
+ static double sign(double a, double b)
+ {
+ if (b < 0)
+ {
+ return -Math.abs(a);
+ }
+ else
+ {
+ return Math.abs(a);
+ }
+ }
+
+ /**
+ * Returns an array containing the values in the specified column
+ *
+ * @param col
+ *
+ * @return
+ */
+ public double[] getColumn(int col)
+ {
+ double[] out = new double[rows];
+
+ for (int i = 0; i < rows; i++)
+ {
+ out[i] = value[i][col];
+ }
+
+ return out;
+ }
+
+ /**
+ * DOCUMENT ME!
+ *
+ * @param ps
+ * DOCUMENT ME!
+ * @param format
+ */
+ @Override
+ public void printD(PrintStream ps, String format)
+ {
+ for (int j = 0; j < rows; j++)
+ {
+ Format.print(ps, format, d[j]);
+ }
+ }
+
+ /**
+ * DOCUMENT ME!
+ *
+ * @param ps
+ * DOCUMENT ME!
+ * @param format
+ * TODO
+ */
+ @Override
+ public void printE(PrintStream ps, String format)
+ {
+ for (int j = 0; j < rows; j++)
+ {
+ Format.print(ps, format, e[j]);
+ }
+ }
+
+ @Override
+ public double[] getD()
+ {
+ return d;
+ }
+
+ @Override
+ public double[] getE()
+ {
+ return e;
+ }
+
+ @Override
+ public int height()
+ {
+ return rows;
+ }
+
+ @Override
+ public int width()
+ {
+ return cols;
+ }
+
+ @Override
+ public double[] getRow(int i)
+ {
+ double[] row = new double[cols];
+ System.arraycopy(value[i], 0, row, 0, cols);
+ return row;
+ }
+
+ /**
+ * Returns a length 2 array of {minValue, maxValue} of all values in the
+ * matrix. Returns null if the matrix is null or empty.
+ *
+ * @return
+ */
+ double[] findMinMax()
+ {
+ if (value == null)
+ {
+ return null;
+ }
+ double min = Double.MAX_VALUE;
+ double max = -Double.MAX_VALUE;
+ boolean empty = true;
+ for (double[] row : value)
+ {
+ if (row != null)
+ {
+ for (double x : row)
+ {
+ empty = false;
+ if (x > max)
+ {
+ max = x;
+ }
+ if (x < min)
+ {
+ min = x;
+ }
+ }
+ }
+ }
+ return empty ? null : new double[] { min, max };
+ }
+
+ /**
+ * {@inheritDoc}
+ */
+ @Override
+ public void reverseRange(boolean maxToZero)
+ {
+ if (value == null)
+ {
+ return;
+ }
+ double[] minMax = findMinMax();
+ if (minMax == null)
+ {
+ return; // empty matrix
+ }
+ double subtractFrom = maxToZero ? minMax[1] : minMax[0] + minMax[1];
+
+ for (double[] row : value)
+ {
+ if (row != null)
+ {
+ int j = 0;
+ for (double x : row)
+ {
+ row[j] = subtractFrom - x;
+ j++;
+ }
+ }
+ }
+ }
+
+ /**
+ * Multiplies every entry in the matrix by the given value.
+ *
+ * @param
+ */
+ @Override
+ public void multiply(double by)
+ {
+ for (double[] row : value)
+ {
+ if (row != null)
+ {
+ for (int i = 0; i < row.length; i++)
+ {
+ row[i] *= by;
+ }
+ }
+ }
+ }
+
+ @Override
+ public void setD(double[] v)
+ {
+ d = v;
+ }
+
+ @Override
+ public void setE(double[] v)
+ {
+ e = v;
+ }
+
+ public double getTotal()
+ {
+ double d = 0d;
+ for (int i = 0; i < this.height(); i++)
+ {
+ for (int j = 0; j < this.width(); j++)
+ {
+ d += value[i][j];
+ }
+ }
+ return d;
+ }
+
+ /**
+ * {@inheritDoc}
+ */
+ @Override
+ public boolean equals(MatrixI m2, double delta)
+ {
+ if (m2 == null || this.height() != m2.height()
+ || this.width() != m2.width())
+ {
+ return false;
+ }
+ for (int i = 0; i < this.height(); i++)
+ {
+ for (int j = 0; j < this.width(); j++)
+ {
+ double diff = this.getValue(i, j) - m2.getValue(i, j);
+ if (Math.abs(diff) > delta)
+ {
+ return false;
+ }
+ }
+ }
+ return true;
+ }
+}