/* * 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; /** * A class to model rectangular matrices of double values and operations on them */ public class Matrix implements MatrixI { /* * the cell values in row-major order */ private double[][] value; /* * the number of rows */ protected int rows; /* * the number of columns */ protected int cols; protected double[] d; // Diagonal protected double[] e; // off diagonal /** * maximum number of iterations for tqli * */ private static final int maxIter = 45; // fudge - add 15 iterations, just in // case /** * Default constructor */ public Matrix() { } /** * 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++; } } /** * Returns a new matrix which is the transpose of this one * * @return */ @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(); } } /** * Returns a new matrix which is the result of premultiplying this matrix by * the supplied argument. If this of size AxB (A rows and B columns), and the * argument is CxA (C rows and A columns), the result is of size CxB. * * @param in * * @return * @throws IllegalArgumentException * if the number of columns in the pre-multiplier is not equal to * the number of rows in the multiplicand (this) */ @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; } /** * Returns a new matrix which is the result of postmultiplying this matrix by * the supplied argument. If this of size AxB (A rows and B columns), and the * argument is BxC (B rows and C columns), the result is of size AxC. *

* This method simply returns the result of in.preMultiply(this) * * @param in * * @return * @throws IllegalArgumentException * if the number of rows in the post-multiplier is not equal to the * number of columns in the multiplicand (this) * @see #preMultiply(Matrix) */ @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); } /** * Answers a new matrix with a copy of the values in this one * * @return */ @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); } return new Matrix(newmat); } /** * 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 == maxIter) { throw new Exception(MessageManager.formatMessage( "exception.matrix_too_many_iteration", new String[] { "tqli", Integer.valueOf(maxIter).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 == maxIter) { throw new Exception(MessageManager.formatMessage( "exception.matrix_too_many_iteration", new String[] { "tqli2", Integer.valueOf(maxIter).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; } } } } }