+ * 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[][] value, int rows, int cols)
+ public Matrix(double[][] values)
{
- this.rows = rows;
- this.cols = cols;
- this.value = value;
+ 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++;
+ }
}
/**
- * DOCUMENT ME!
+ * Returns a new matrix which is the transpose of this one
*
- * @return DOCUMENT ME!
+ * @return
*/
- public Matrix transpose()
+ @Override
+ public MatrixI transpose()
{
double[][] out = new double[cols][rows];
@@ -90,7 +121,7 @@ public class Matrix
}
}
- return new Matrix(out, cols, rows);
+ return new Matrix(out);
}
/**
@@ -98,14 +129,16 @@ public class Matrix
*
* @param ps
* DOCUMENT ME!
+ * @param format
*/
- public void print(PrintStream ps)
+ @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, "%8.2f", value[i][j]);
+ Format.print(ps, format, getValue(i, j));
}
ps.println();
@@ -113,40 +146,50 @@ public class Matrix
}
/**
- * DOCUMENT ME!
+ * 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
- * DOCUMENT ME!
*
- * @return DOCUMENT ME!
+ * @return
+ * @throws IllegalArgumentException
+ * if the number of columns in the pre-multiplier is not equal to
+ * the number of rows in the multiplicand (this)
*/
- public Matrix preMultiply(Matrix in)
+ @Override
+ public MatrixI preMultiply(MatrixI in)
{
- double[][] tmp = new double[in.rows][this.cols];
+ 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.rows; i++)
+ for (int i = 0; i < in.height(); i++)
{
for (int j = 0; j < this.cols; j++)
{
- tmp[i][j] = 0.0;
-
- for (int k = 0; k < in.cols; k++)
+ /*
+ * 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.value[i][k] * this.value[k][j]);
+ tmp[i][j] += (in.getValue(i, k) * this.value[k][j]);
}
}
}
- return new Matrix(tmp, in.rows, this.cols);
+ return new Matrix(tmp);
}
/**
- * DOCUMENT ME!
*
* @param in
- * DOCUMENT ME!
*
- * @return DOCUMENT ME!
+ * @return
*/
public double[] vectorPostMultiply(double[] in)
{
@@ -166,60 +209,56 @@ public class Matrix
}
/**
- * DOCUMENT ME!
+ * 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 - * DOCUMENT ME! * - * @return DOCUMENT ME! + * @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) */ - public Matrix postMultiply(Matrix in) + @Override + public MatrixI postMultiply(MatrixI in) { - double[][] out = new double[this.rows][in.cols]; - - for (int i = 0; i < this.rows; i++) + if (in.height() != this.cols) { - 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]); - } - } + throw new IllegalArgumentException("Can't post-multiply " + this.cols + + " columns by " + in.height() + " rows"); } - - return new Matrix(out, this.cols, in.rows); + return in.preMultiply(this); } /** - * DOCUMENT ME! + * Answers a new matrix with a copy of the values in this one * - * @return DOCUMENT ME! + * @return */ - public Matrix copy() + @Override + public MatrixI 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]; - } + System.arraycopy(value[i], 0, newmat[i], 0, value[i].length); } - return new Matrix(newmat, rows, cols); + return new Matrix(newmat); } /** * DOCUMENT ME! */ + @Override public void tred() { int n = rows; - int l; int k; int j; int i; @@ -235,7 +274,7 @@ public class Matrix for (i = n; i >= 2; i--) { - l = i - 1; + final int l = i - 1; h = 0.0; scale = 0.0; @@ -243,22 +282,23 @@ public class Matrix { for (k = 1; k <= l; k++) { - scale += Math.abs(value[i - 1][k - 1]); + double v = Math.abs(getValue(i - 1, k - 1)); + scale += v; } if (scale == 0.0) { - e[i - 1] = value[i - 1][l - 1]; + e[i - 1] = getValue(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]); + double v = divideValue(i - 1, k - 1, scale); + h += v * v; } - f = value[i - 1][l - 1]; + f = getValue(i - 1, l - 1); if (f > 0) { @@ -271,46 +311,48 @@ public class Matrix e[i - 1] = scale * g; h -= (f * g); - value[i - 1][l - 1] = f - g; + setValue(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; + double val = getValue(i - 1, j - 1) / h; + setValue(j - 1, i - 1, val); g = 0.0; for (k = 1; k <= j; k++) { - g += (value[j - 1][k - 1] * value[i - 1][k - 1]); + g += (getValue(j - 1, k - 1) * getValue(i - 1, k - 1)); } for (k = j + 1; k <= l; k++) { - g += (value[k - 1][j - 1] * value[i - 1][k - 1]); + g += (getValue(k - 1, j - 1) * getValue(i - 1, k - 1)); } e[j - 1] = g / h; - f += (e[j - 1] * value[i - 1][j - 1]); + f += (e[j - 1] * getValue(i - 1, j - 1)); } hh = f / (h + h); for (j = 1; j <= l; j++) { - f = value[i - 1][j - 1]; + f = getValue(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])); + double val = (f * e[k - 1]) + (g * getValue(i - 1, k - 1)); + addValue(j - 1, k - 1, -val); } } } } else { - e[i - 1] = value[i - 1][l - 1]; + e[i - 1] = getValue(i - 1, l - 1); } d[i - 1] = h; @@ -321,7 +363,7 @@ public class Matrix for (i = 1; i <= n; i++) { - l = i - 1; + final int l = i - 1; if (d[i - 1] != 0.0) { @@ -331,30 +373,66 @@ public class Matrix for (k = 1; k <= l; k++) { - g += (value[i - 1][k - 1] * value[k - 1][j - 1]); + g += (getValue(i - 1, k - 1) * getValue(k - 1, j - 1)); } for (k = 1; k <= l; k++) { - value[k - 1][j - 1] -= (g * value[k - 1][i - 1]); + addValue(k - 1, j - 1, -(g * getValue(k - 1, i - 1))); } } } - d[i - 1] = value[i - 1][i - 1]; - value[i - 1][i - 1] = 1.0; + d[i - 1] = getValue(i - 1, i - 1); + setValue(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; + 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; @@ -367,7 +445,6 @@ public class Matrix double s; double r; double p; - ; double g; double f; @@ -405,8 +482,8 @@ public class Matrix if (iter == maxIter) { throw new Exception(MessageManager.formatMessage( - "exception.matrix_too_many_iteration", new String[] { - "tqli", Integer.valueOf(maxIter).toString() })); + "exception.matrix_too_many_iteration", new String[] + { "tqli", Integer.valueOf(maxIter).toString() })); } else { @@ -450,9 +527,10 @@ public class Matrix 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); + 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)); } } @@ -464,6 +542,18 @@ public class Matrix } } + @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! */ @@ -656,8 +746,8 @@ public class Matrix if (iter == maxIter) { throw new Exception(MessageManager.formatMessage( - "exception.matrix_too_many_iteration", new String[] { - "tqli2", Integer.valueOf(maxIter).toString() })); + "exception.matrix_too_many_iteration", new String[] + { "tqli2", Integer.valueOf(maxIter).toString() })); } else { @@ -716,16 +806,14 @@ public class Matrix } /** - * DOCUMENT ME! + * Answers the first argument with the sign of the second argument * * @param a - * DOCUMENT ME! * @param b - * DOCUMENT ME! * - * @return DOCUMENT ME! + * @return */ - public double sign(double a, double b) + static double sign(double a, double b) { if (b < 0) { @@ -738,20 +826,19 @@ public class Matrix } /** - * DOCUMENT ME! + * Returns an array containing the values in the specified column * - * @param n - * DOCUMENT ME! + * @param col * - * @return DOCUMENT ME! + * @return */ - public double[] getColumn(int n) + public double[] getColumn(int col) { double[] out = new double[rows]; for (int i = 0; i < rows; i++) { - out[i] = value[i][n]; + out[i] = value[i][col]; } return out; @@ -762,12 +849,14 @@ public class Matrix * * @param ps * DOCUMENT ME! + * @param format */ - public void printD(PrintStream ps) + @Override + public void printD(PrintStream ps, String format) { for (int j = 0; j < rows; j++) { - Format.print(ps, "%15.4e", d[j]); + Format.print(ps, format, d[j]); } } @@ -776,93 +865,134 @@ public class Matrix * * @param ps * DOCUMENT ME! + * @param format + * TODO */ - public void printE(PrintStream ps) + @Override + public void printE(PrintStream ps, String format) { for (int j = 0; j < rows; j++) { - Format.print(ps, "%15.4e", e[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; + } + /** - * DOCUMENT ME! + * Returns a length 2 array of {minValue, maxValue} of all values in the + * matrix. Returns null if the matrix is null or empty. * - * @param args - * DOCUMENT ME! + * @return */ - public static void main(String[] args) throws Exception + double[] findMinMax() { - int n = Integer.parseInt(args[0]); - double[][] in = new double[n][n]; + 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 (int i = 0; i < n; i++) + for (double[] row : value) { - for (int j = 0; j < n; j++) + if (row != null) { - in[i][j] = (double) Math.random(); + int j = 0; + for (double x : row) + { + row[j] = subtractFrom - x; + j++; + } } } + } - 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(); + /** + * 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; + } + } + } } }