import java.io.PrintStream;
/**
- * DOCUMENT ME!
- *
- * @author $author$
- * @version $Revision$
+ * A class to model rectangular matrices of double values and operations on them
*/
-public class Matrix
+public class Matrix implements MatrixI
{
- /**
- * SMJSPUBLIC
+ /*
+ * the cell values in row-major order
*/
- public double[][] value;
+ private double[][] value;
- /** DOCUMENT ME!! */
- public int rows;
+ /*
+ * the number of rows
+ */
+ protected int rows;
- /** DOCUMENT ME!! */
- public int cols;
+ /*
+ * the number of columns
+ */
+ protected int cols;
- /** DOCUMENT ME!! */
- public double[] d; // Diagonal
+ protected double[] d; // Diagonal
- /** DOCUMENT ME!! */
- public double[] e; // off diagonal
+ protected double[] e; // off diagonal
/**
* maximum number of iterations for tqli
*
*/
- int maxIter = 45; // fudge - add 15 iterations, just in case
+ private static final int maxIter = 45; // fudge - add 15 iterations, just in
+ // case
+
+ /**
+ * Default constructor
+ */
+ public Matrix()
+ {
+
+ }
/**
- * Creates a new Matrix object.
+ * Creates a new Matrix object containing a copy of the supplied array values.
+ * For example
*
- * @param value
- * DOCUMENT ME!
- * @param rows
- * DOCUMENT ME!
- * @param cols
- * DOCUMENT ME!
+ * <pre>
+ * new Matrix(new double[][] {{2, 3, 4}, {5, 6, 7})
+ * constructs
+ * (2 3 4)
+ * (5 6 7)
+ * </pre>
+ *
+ * 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];
}
}
- return new Matrix(out, cols, rows);
+ return new Matrix(out);
}
/**
*
* @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();
}
/**
- * 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)
{
}
/**
- * 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.
+ * <p>
+ * 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;
for (i = n; i >= 2; i--)
{
- l = i - 1;
+ final int l = i - 1;
h = 0.0;
scale = 0.0;
{
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)
{
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;
for (i = 1; i <= n; i++)
{
- l = i - 1;
+ final int l = i - 1;
if (d[i - 1] != 0.0)
{
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;
double s;
double r;
double p;
- ;
double g;
double f;
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
{
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));
}
}
}
}
+ @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!
*/
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
{
}
/**
- * 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)
{
}
/**
- * 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;
*
* @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]);
}
}
*
* @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;
+ }
+ }
+ }
}
}
git://source.jalview.org / jalview.git / blobdiff