* @author $author$
* @version $Revision$
*/
-public class Matrix
+public class Matrix implements MatrixI
{
- /**
- * SMJSPUBLIC
+ /*
+ * the [row][column] values in the matrix
*/
- 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. For example
*
* <pre>
- * new Matrix(new double[][] {{2, 3}, {4, 5}, 2, 2)
+ * new Matrix(new double[][] {{2, 3, 4}, {5, 6, 7})
* constructs
- * (2 3)
- * (4 5)
+ * (2 3 4)
+ * (5 6 7)
* </pre>
*
* Note that ragged arrays (with not all rows, or columns, of the same
*
* @param values
* the matrix values in row-major order
- * @param rows
- * @param cols
*/
- public Matrix(double[][] values, int rows, int cols)
+ public Matrix(double[][] values)
{
- this.rows = rows;
- this.cols = cols;
+ this.rows = values.length;
+ if (rows > 0)
+ {
+ this.cols = values[0].length;
+ }
this.value = values;
}
/**
- * Returns a new matrix which is the transposes of this one
+ * Returns a new matrix which is the transpose of this one
*
* @return DOCUMENT ME!
*/
- 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();
* 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)
{
- if (in.cols != this.rows)
+ if (in.width() != rows)
{
throw new IllegalArgumentException("Can't pre-multiply " + this.rows
- + " rows by " + in.cols + " columns");
+ + " rows by " + in.width() + " columns");
}
- double[][] tmp = new double[in.rows][this.cols];
+ 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);
}
/**
* number of columns in the multiplicand (this)
* @see #preMultiply(Matrix)
*/
- public Matrix postMultiply(Matrix in)
+ @Override
+ public MatrixI postMultiply(MatrixI in)
{
- if (in.rows != this.cols)
+ if (in.height() != this.cols)
{
throw new IllegalArgumentException("Can't post-multiply " + this.cols
- + " columns by " + in.rows + " rows");
+ + " columns by " + in.height() + " rows");
}
return in.preMultiply(this);
}
*
* @return
*/
- public Matrix copy()
+ @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);
- // for (int j = 0; j < cols; j++)
- // {
- // newmat[i][j] = value[i][j];
- // }
}
- 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(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] = 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]);
+ // 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 = 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;
+ // value[i - 1][l - 1] = f - g;
+ setValue(i - 1, l - 1, f - g);
+ // System.out.println(String.format("%d %d %f %f %f %f %f %.5e", i,
+ // l,
+ // scale, f, g, h, getValue(i - 1, l - 1), checksum()));
f = 0.0;
for (j = 1; j <= l; j++)
{
- value[j - 1][i - 1] = value[i - 1][j - 1] / h;
+ // 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 += (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 += (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] * 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 = 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]));
+ // 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] = 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 += (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]);
+ // 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] = 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;
+ // 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;
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 = 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];
+ }
+
+ public void setValue(int i, int j, double val)
+ {
+ value[i][j] = val;
+ }
+
/**
* DOCUMENT ME!
*/
}
/**
- * 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)
{
*
* @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;
+ }
}
--- /dev/null
+package jalview.math;
+
+import java.io.PrintStream;
+
+public interface MatrixI
+{
+ /**
+ * Answers the number of columns
+ *
+ * @return
+ */
+ int width();
+
+ /**
+ * Answers the number of rows
+ *
+ * @return
+ */
+ int height();
+
+ /**
+ * Answers the value at row i, column j
+ *
+ * @param i
+ * @param j
+ * @return
+ */
+ double getValue(int i, int j);
+
+ /**
+ * Answers a copy of the values in the i'th row
+ *
+ * @return
+ */
+ double[] getRow(int i);
+
+ MatrixI copy();
+
+ MatrixI transpose();
+
+ MatrixI preMultiply(MatrixI m);
+
+ MatrixI postMultiply(MatrixI m);
+
+ double[] getD();
+
+ double[] getE();
+
+ void print(PrintStream ps, String format);
+
+ void printD(PrintStream ps, String format);
+
+ void printE(PrintStream ps, String format);
+
+ void tqli() throws Exception;
+
+ void tred();
+
+}
--- /dev/null
+package jalview.math;
+
+import jalview.ext.android.SparseDoubleArray;
+
+/**
+ * A variant of Matrix intended for use for sparse (mostly zero) matrices. This
+ * class uses a SparseDoubleArray to hold each row of the matrix. The sparse
+ * array only stores non-zero values. This gives a smaller memory footprint, and
+ * fewer matrix calculation operations, for mostly zero matrices.
+ *
+ * @author gmcarstairs
+ */
+public class SparseMatrix extends Matrix
+{
+ /*
+ * we choose columns for the sparse arrays as this allows
+ * optimisation of the preMultiply() method used in PCA.run()
+ */
+ SparseDoubleArray[] sparseColumns;
+
+ /**
+ * Constructor given data in [row][column] order
+ *
+ * @param v
+ */
+ public SparseMatrix(double[][] v)
+ {
+ rows = v.length;
+ if (rows > 0) {
+ cols = v[0].length;
+ }
+ sparseColumns = new SparseDoubleArray[cols];
+
+ /*
+ * transpose v[row][col] into [col][row] order
+ */
+ for (int col = 0; col < cols; col++)
+ {
+ SparseDoubleArray sparseColumn = new SparseDoubleArray();
+ sparseColumns[col] = sparseColumn;
+ for (int row = 0; row < rows; row++)
+ {
+ double value = v[row][col];
+ if (value != 0d)
+ {
+ sparseColumn.put(row, value);
+ }
+ }
+ }
+ }
+
+ /**
+ * Answers the value at row i, column j
+ */
+ @Override
+ public double getValue(int i, int j)
+ {
+ return sparseColumns[j].get(i);
+ }
+
+ /**
+ * Sets the value at row i, column j to val
+ */
+ @Override
+ public void setValue(int i, int j, double val)
+ {
+ if (val == 0d)
+ {
+ sparseColumns[j].delete(i);
+ }
+ else
+ {
+ sparseColumns[j].put(i, val);
+ }
+ }
+
+ @Override
+ public double[] getColumn(int i)
+ {
+ double[] col = new double[height()];
+
+ SparseDoubleArray vals = sparseColumns[i];
+ for (int nonZero = 0; nonZero < vals.size(); nonZero++)
+ {
+ col[vals.keyAt(nonZero)] = vals.valueAt(nonZero);
+ }
+ return col;
+ }
+
+ @Override
+ public MatrixI copy()
+ {
+ double[][] vals = new double[height()][width()];
+ for (int i = 0; i < height(); i++)
+ {
+ vals[i] = getRow(i);
+ }
+ return new SparseMatrix(vals);
+ }
+
+ @Override
+ public MatrixI transpose()
+ {
+ double[][] out = new double[cols][rows];
+
+ /*
+ * for each column...
+ */
+ for (int i = 0; i < cols; i++)
+ {
+ /*
+ * put non-zero values into the corresponding row
+ * of the transposed matrix
+ */
+ SparseDoubleArray vals = sparseColumns[i];
+ for (int nonZero = 0; nonZero < vals.size(); nonZero++)
+ {
+ out[i][vals.keyAt(nonZero)] = vals.valueAt(nonZero);
+ }
+ }
+
+ return new SparseMatrix(out);
+ }
+
+ /**
+ * Answers a new matrix which is the product in.this. If the product contains
+ * less than 20% non-zero values, it is returned as a SparseMatrix, else as a
+ * Matrix.
+ * <p>
+ * This method is optimised for the sparse arrays which store column values
+ * for a SparseMatrix. Note that postMultiply is not so optimised. That would
+ * require redundantly also storing sparse arrays for the rows, which has not
+ * been done. Currently only preMultiply is used in Jalview.
+ */
+ @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];
+
+ long count = 0L;
+ 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]
+ * we only need to use non-zero values from the column
+ */
+ SparseDoubleArray vals = sparseColumns[j];
+ boolean added = false;
+ for (int nonZero = 0; nonZero < vals.size(); nonZero++)
+ {
+ int myRow = vals.keyAt(nonZero);
+ double myValue = vals.valueAt(nonZero);
+ tmp[i][j] += (in.getValue(i, myRow) * myValue);
+ added = true;
+ }
+ if (added && tmp[i][j] != 0d)
+ {
+ count++; // non-zero entry in product
+ }
+ }
+ }
+
+ /*
+ * heuristic rule - if product is more than 80% zero
+ * then construct a SparseMatrix, else a Matrix
+ */
+ if (count * 5 < in.height() * cols)
+ {
+ return new SparseMatrix(tmp);
+ }
+ else
+ {
+ return new Matrix(tmp);
+ }
+ }
+
+ @Override
+ protected double divideValue(int i, int j, double divisor)
+ {
+ if (divisor == 0d)
+ {
+ return getValue(i, j);
+ }
+ double v = sparseColumns[j].multiply(i, 1 / divisor);
+ return v;
+ }
+
+ @Override
+ protected double addValue(int i, int j, double addend)
+ {
+ double v = sparseColumns[j].add(i, addend);
+ return v;
+ }
+
+ /**
+ * Returns the fraction of the whole matrix size that is actually modelled in
+ * sparse arrays (normally, the non-zero values)
+ *
+ * @return
+ */
+ public float getFillRatio()
+ {
+ long count = 0L;
+ for (SparseDoubleArray col : sparseColumns)
+ {
+ count += col.size();
+ }
+ return count / (float) (height() * width());
+ }
+}
int cols = 1000;
double[][] d1 = new double[rows][cols];
double[][] d2 = new double[cols][rows];
- Matrix m1 = new Matrix(d1, rows, cols);
- Matrix m2 = new Matrix(d2, cols, rows);
+ Matrix m1 = new Matrix(d1);
+ Matrix m2 = new Matrix(d2);
long start = System.currentTimeMillis();
m1.preMultiply(m2);
long elapsed = System.currentTimeMillis() - start;
@Test(groups = "Functional")
public void testPreMultiply()
{
- Matrix m1 = new Matrix(new double[][] { { 2, 3, 4 } }, 1, 3); // 1x3
- Matrix m2 = new Matrix(new double[][] { { 5 }, { 6 }, { 7 } }, 3, 1); // 3x1
+ MatrixI m1 = new Matrix(new double[][] { { 2, 3, 4 } }); // 1x3
+ MatrixI m2 = new Matrix(new double[][] { { 5 }, { 6 }, { 7 } }); // 3x1
/*
* 1x3 times 3x1 is 1x1
* 2x5 + 3x6 + 4*7 = 56
*/
- Matrix m3 = m2.preMultiply(m1);
- assertEquals(m3.rows, 1);
- assertEquals(m3.cols, 1);
- assertEquals(m3.value[0][0], 56d);
+ MatrixI m3 = m2.preMultiply(m1);
+ assertEquals(m3.height(), 1);
+ assertEquals(m3.width(), 1);
+ assertEquals(m3.getValue(0, 0), 56d);
/*
* 3x1 times 1x3 is 3x3
*/
m3 = m1.preMultiply(m2);
- assertEquals(m3.rows, 3);
- assertEquals(m3.cols, 3);
- assertEquals(Arrays.toString(m3.value[0]), "[10.0, 15.0, 20.0]");
- assertEquals(Arrays.toString(m3.value[1]), "[12.0, 18.0, 24.0]");
- assertEquals(Arrays.toString(m3.value[2]), "[14.0, 21.0, 28.0]");
+ assertEquals(m3.height(), 3);
+ assertEquals(m3.width(), 3);
+ assertEquals(Arrays.toString(m3.getRow(0)), "[10.0, 15.0, 20.0]");
+ assertEquals(Arrays.toString(m3.getRow(1)), "[12.0, 18.0, 24.0]");
+ assertEquals(Arrays.toString(m3.getRow(2)), "[14.0, 21.0, 28.0]");
}
@Test(
expectedExceptions = { IllegalArgumentException.class })
public void testPreMultiply_tooManyColumns()
{
- Matrix m1 = new Matrix(new double[][] { { 2, 3, 4 }, { 3, 4, 5 } }, 2,
- 3); // 2x3
+ Matrix m1 = new Matrix(new double[][] { { 2, 3, 4 }, { 3, 4, 5 } }); // 2x3
/*
* 2x3 times 2x3 invalid operation -
expectedExceptions = { IllegalArgumentException.class })
public void testPreMultiply_tooFewColumns()
{
- Matrix m1 = new Matrix(new double[][] { { 2, 3, 4 }, { 3, 4, 5 } }, 2,
- 3); // 2x3
+ Matrix m1 = new Matrix(new double[][] { { 2, 3, 4 }, { 3, 4, 5 } }); // 2x3
/*
* 3x2 times 3x2 invalid operation -
private boolean matrixEquals(Matrix m1, Matrix m2) {
- return Arrays.deepEquals(m1.value, m2.value);
+ if (m1.width() != m2.width() || m1.height() != m2.height())
+ {
+ return false;
+ }
+ for (int i = 0; i < m1.height(); i++)
+ {
+ if (!Arrays.equals(m1.getRow(i), m2.getRow(i)))
+ {
+ return false;
+ }
+ }
+ return true;
}
@Test(groups = "Functional")
* (3020 30200)
* (5040 50400)
*/
- Matrix m1 = new Matrix(new double[][] { { 2, 3 }, { 4, 5 } }, 2, 2);
- Matrix m2 = new Matrix(new double[][] { { 10, 100 }, { 1000, 10000 } },
- 2, 2);
- Matrix m3 = m1.postMultiply(m2);
- assertEquals(Arrays.toString(m3.value[0]), "[3020.0, 30200.0]");
- assertEquals(Arrays.toString(m3.value[1]), "[5040.0, 50400.0]");
+ MatrixI m1 = new Matrix(new double[][] { { 2, 3 }, { 4, 5 } });
+ MatrixI m2 = new Matrix(new double[][] { { 10, 100 }, { 1000, 10000 } });
+ MatrixI m3 = m1.postMultiply(m2);
+ assertEquals(Arrays.toString(m3.getRow(0)), "[3020.0, 30200.0]");
+ assertEquals(Arrays.toString(m3.getRow(1)), "[5040.0, 50400.0]");
/*
* also check m2.preMultiply(m1) - should be same as m1.postMultiply(m2)
*/
m3 = m2.preMultiply(m1);
- assertEquals(Arrays.toString(m3.value[0]), "[3020.0, 30200.0]");
- assertEquals(Arrays.toString(m3.value[1]), "[5040.0, 50400.0]");
+ assertEquals(Arrays.toString(m3.getRow(0)), "[3020.0, 30200.0]");
+ assertEquals(Arrays.toString(m3.getRow(1)), "[5040.0, 50400.0]");
/*
* m1 has more rows than columns
* (2).(10 100 1000) = (20 200 2000)
* (3) (30 300 3000)
*/
- m1 = new Matrix(new double[][] { { 2 }, { 3 } }, 2, 1);
- m2 = new Matrix(new double[][] { { 10, 100, 1000 } }, 1, 3);
+ m1 = new Matrix(new double[][] { { 2 }, { 3 } });
+ m2 = new Matrix(new double[][] { { 10, 100, 1000 } });
m3 = m1.postMultiply(m2);
- assertEquals(m3.rows, 2);
- assertEquals(m3.cols, 3);
- assertEquals(Arrays.toString(m3.value[0]), "[20.0, 200.0, 2000.0]");
- assertEquals(Arrays.toString(m3.value[1]), "[30.0, 300.0, 3000.0]");
+ assertEquals(m3.height(), 2);
+ assertEquals(m3.width(), 3);
+ assertEquals(Arrays.toString(m3.getRow(0)), "[20.0, 200.0, 2000.0]");
+ assertEquals(Arrays.toString(m3.getRow(1)), "[30.0, 300.0, 3000.0]");
m3 = m2.preMultiply(m1);
- assertEquals(m3.rows, 2);
- assertEquals(m3.cols, 3);
- assertEquals(Arrays.toString(m3.value[0]), "[20.0, 200.0, 2000.0]");
- assertEquals(Arrays.toString(m3.value[1]), "[30.0, 300.0, 3000.0]");
+ assertEquals(m3.height(), 2);
+ assertEquals(m3.width(), 3);
+ assertEquals(Arrays.toString(m3.getRow(0)), "[20.0, 200.0, 2000.0]");
+ assertEquals(Arrays.toString(m3.getRow(1)), "[30.0, 300.0, 3000.0]");
/*
* m1 has more columns than rows
* [0, 0] = 2*5 + 3*6 + 4*7 = 56
* [0, 1] = 2*4 + 3*3 + 4*2 = 25
*/
- m1 = new Matrix(new double[][] { { 2, 3, 4 } }, 1, 3);
- m2 = new Matrix(new double[][] { { 5, 4 }, { 6, 3 }, { 7, 2 } }, 3, 2);
+ m1 = new Matrix(new double[][] { { 2, 3, 4 } });
+ m2 = new Matrix(new double[][] { { 5, 4 }, { 6, 3 }, { 7, 2 } });
m3 = m1.postMultiply(m2);
- assertEquals(m3.rows, 1);
- assertEquals(m3.cols, 2);
- assertEquals(m3.value[0][0], 56d);
- assertEquals(m3.value[0][1], 25d);
+ assertEquals(m3.height(), 1);
+ assertEquals(m3.width(), 2);
+ assertEquals(m3.getRow(0)[0], 56d);
+ assertEquals(m3.getRow(0)[1], 25d);
/*
* and check premultiply equivalent
*/
m3 = m2.preMultiply(m1);
- assertEquals(m3.rows, 1);
- assertEquals(m3.cols, 2);
- assertEquals(m3.value[0][0], 56d);
- assertEquals(m3.value[0][1], 25d);
+ assertEquals(m3.height(), 1);
+ assertEquals(m3.width(), 2);
+ assertEquals(m3.getRow(0)[0], 56d);
+ assertEquals(m3.getRow(0)[1], 25d);
}
/**
}
}
- Matrix origmat = new Matrix(in, n, n);
+ Matrix origmat = new Matrix(in);
// System.out.println(" --- Original matrix ---- ");
// / origmat.print(System.out);
// System.out.println();
// System.out.println(" --- transpose matrix ---- ");
- Matrix trans = origmat.transpose();
+ MatrixI trans = origmat.transpose();
// trans.print(System.out);
// System.out.println();
// System.out.println(" --- OrigT * Orig ---- ");
- Matrix symm = trans.postMultiply(origmat);
+ MatrixI symm = trans.postMultiply(origmat);
// symm.print(System.out);
// System.out.println();
// }
// System.out.println();
}
+
+ @Test(groups = "Timing")
+ public void testSign()
+ {
+ assertEquals(Matrix.sign(-1, -2), -1d);
+ assertEquals(Matrix.sign(-1, 2), 1d);
+ assertEquals(Matrix.sign(-1, 0), 1d);
+ assertEquals(Matrix.sign(1, -2), -1d);
+ assertEquals(Matrix.sign(1, 2), 1d);
+ assertEquals(Matrix.sign(1, 0), 1d);
+ }
}
--- /dev/null
+package jalview.math;
+
+import static org.testng.Assert.assertEquals;
+import static org.testng.Assert.assertFalse;
+import static org.testng.Assert.assertTrue;
+import static org.testng.Assert.fail;
+
+import java.util.Random;
+
+import org.testng.annotations.Test;
+import org.testng.internal.junit.ArrayAsserts;
+
+public class SparseMatrixTest
+{
+ final static double DELTA = 0.0001d;
+
+ Random r = new Random(1729);
+
+ @Test(groups = "Functional")
+ public void testConstructor()
+ {
+ MatrixI m1 = new SparseMatrix(
+ new double[][] { { 2, 0, 4 }, { 0, 6, 0 } });
+ assertEquals(m1.getValue(0, 0), 2d);
+ assertEquals(m1.getValue(0, 1), 0d);
+ assertEquals(m1.getValue(0, 2), 4d);
+ assertEquals(m1.getValue(1, 0), 0d);
+ assertEquals(m1.getValue(1, 1), 6d);
+ assertEquals(m1.getValue(1, 2), 0d);
+ }
+
+ @Test(groups = "Functional")
+ public void testTranspose()
+ {
+ MatrixI m1 = new SparseMatrix(
+ new double[][] { { 2, 0, 4 }, { 5, 6, 0 } });
+ MatrixI m2 = m1.transpose();
+ assertTrue(m2 instanceof SparseMatrix);
+ assertEquals(m2.height(), 3);
+ assertEquals(m2.width(), 2);
+ assertEquals(m2.getValue(0, 0), 2d);
+ assertEquals(m2.getValue(0, 1), 5d);
+ assertEquals(m2.getValue(1, 0), 0d);
+ assertEquals(m2.getValue(1, 1), 6d);
+ assertEquals(m2.getValue(2, 0), 4d);
+ assertEquals(m2.getValue(2, 1), 0d);
+ }
+ @Test(groups = "Functional")
+ public void testPreMultiply()
+ {
+ MatrixI m1 = new SparseMatrix(new double[][] { { 2, 3, 4 } }); // 1x3
+ MatrixI m2 = new SparseMatrix(new double[][] { { 5 }, { 6 }, { 7 } }); // 3x1
+
+ /*
+ * 1x3 times 3x1 is 1x1
+ * 2x5 + 3x6 + 4*7 = 56
+ */
+ MatrixI m3 = m2.preMultiply(m1);
+ assertFalse(m3 instanceof SparseMatrix);
+ assertEquals(m3.height(), 1);
+ assertEquals(m3.width(), 1);
+ assertEquals(m3.getValue(0, 0), 56d);
+
+ /*
+ * 3x1 times 1x3 is 3x3
+ */
+ m3 = m1.preMultiply(m2);
+ assertEquals(m3.height(), 3);
+ assertEquals(m3.width(), 3);
+ assertEquals(m3.getValue(0, 0), 10d);
+ assertEquals(m3.getValue(0, 1), 15d);
+ assertEquals(m3.getValue(0, 2), 20d);
+ assertEquals(m3.getValue(1, 0), 12d);
+ assertEquals(m3.getValue(1, 1), 18d);
+ assertEquals(m3.getValue(1, 2), 24d);
+ assertEquals(m3.getValue(2, 0), 14d);
+ assertEquals(m3.getValue(2, 1), 21d);
+ assertEquals(m3.getValue(2, 2), 28d);
+ }
+
+ @Test(
+ groups = "Functional",
+ expectedExceptions = { IllegalArgumentException.class })
+ public void testPreMultiply_tooManyColumns()
+ {
+ Matrix m1 = new SparseMatrix(
+ new double[][] { { 2, 3, 4 }, { 3, 4, 5 } }); // 2x3
+
+ /*
+ * 2x3 times 2x3 invalid operation -
+ * multiplier has more columns than multiplicand has rows
+ */
+ m1.preMultiply(m1);
+ fail("Expected exception");
+ }
+
+ @Test(
+ groups = "Functional",
+ expectedExceptions = { IllegalArgumentException.class })
+ public void testPreMultiply_tooFewColumns()
+ {
+ Matrix m1 = new SparseMatrix(
+ new double[][] { { 2, 3, 4 }, { 3, 4, 5 } }); // 2x3
+
+ /*
+ * 3x2 times 3x2 invalid operation -
+ * multiplier has more columns than multiplicand has row
+ */
+ m1.preMultiply(m1);
+ fail("Expected exception");
+ }
+
+ @Test(groups = "Functional")
+ public void testPostMultiply()
+ {
+ /*
+ * Square matrices
+ * (2 3) . (10 100)
+ * (4 5) (1000 10000)
+ * =
+ * (3020 30200)
+ * (5040 50400)
+ */
+ MatrixI m1 = new SparseMatrix(new double[][] { { 2, 3 }, { 4, 5 } });
+ MatrixI m2 = new SparseMatrix(new double[][] { { 10, 100 },
+ { 1000, 10000 } });
+ MatrixI m3 = m1.postMultiply(m2);
+ assertEquals(m3.getValue(0, 0), 3020d);
+ assertEquals(m3.getValue(0, 1), 30200d);
+ assertEquals(m3.getValue(1, 0), 5040d);
+ assertEquals(m3.getValue(1, 1), 50400d);
+
+ /*
+ * also check m2.preMultiply(m1) - should be same as m1.postMultiply(m2)
+ */
+ MatrixI m4 = m2.preMultiply(m1);
+ assertMatricesMatch(m3, m4);
+
+ /*
+ * m1 has more rows than columns
+ * (2).(10 100 1000) = (20 200 2000)
+ * (3) (30 300 3000)
+ */
+ m1 = new SparseMatrix(new double[][] { { 2 }, { 3 } });
+ m2 = new SparseMatrix(new double[][] { { 10, 100, 1000 } });
+ m3 = m1.postMultiply(m2);
+ assertEquals(m3.height(), 2);
+ assertEquals(m3.width(), 3);
+ assertEquals(m3.getValue(0, 0), 20d);
+ assertEquals(m3.getValue(0, 1), 200d);
+ assertEquals(m3.getValue(0, 2), 2000d);
+ assertEquals(m3.getValue(1, 0), 30d);
+ assertEquals(m3.getValue(1, 1), 300d);
+ assertEquals(m3.getValue(1, 2), 3000d);
+
+ m4 = m2.preMultiply(m1);
+ assertMatricesMatch(m3, m4);
+
+ /*
+ * m1 has more columns than rows
+ * (2 3 4) . (5 4) = (56 25)
+ * (6 3)
+ * (7 2)
+ * [0, 0] = 2*5 + 3*6 + 4*7 = 56
+ * [0, 1] = 2*4 + 3*3 + 4*2 = 25
+ */
+ m1 = new SparseMatrix(new double[][] { { 2, 3, 4 } });
+ m2 = new SparseMatrix(new double[][] { { 5, 4 }, { 6, 3 }, { 7, 2 } });
+ m3 = m1.postMultiply(m2);
+ assertEquals(m3.height(), 1);
+ assertEquals(m3.width(), 2);
+ assertEquals(m3.getValue(0, 0), 56d);
+ assertEquals(m3.getValue(0, 1), 25d);
+
+ /*
+ * and check premultiply equivalent
+ */
+ m4 = m2.preMultiply(m1);
+ assertMatricesMatch(m3, m4);
+ }
+
+ @Test(groups = "Timing")
+ public void testSign()
+ {
+ assertEquals(Matrix.sign(-1, -2), -1d);
+ assertEquals(Matrix.sign(-1, 2), 1d);
+ assertEquals(Matrix.sign(-1, 0), 1d);
+ assertEquals(Matrix.sign(1, -2), -1d);
+ assertEquals(Matrix.sign(1, 2), 1d);
+ assertEquals(Matrix.sign(1, 0), 1d);
+ }
+
+ /**
+ * Verify that the results of method tred() are the same for SparseMatrix as
+ * they are for Matrix (i.e. a regression test rather than an absolute test of
+ * correctness of results)
+ */
+ @Test(groups = "Functional")
+ public void testTred_matchesMatrix()
+ {
+ /*
+ * make a pseudo-random symmetric matrix as required for tred/tqli
+ * note: test fails for matrices larger than 6x6 due to double value
+ * rounding only (random values result in very small values)
+ */
+ int rows = 6;
+ int cols = rows;
+ double[][] d = getSparseValues(rows, cols, 3);
+
+ /*
+ * make a copy of the values so m1, m2 are not
+ * sharing arrays!
+ */
+ double[][] d1 = new double[rows][cols];
+ for (int row = 0; row < rows; row++)
+ {
+ for (int col = 0; col < cols; col++)
+ {
+ d1[row][col] = d[row][col];
+ }
+ }
+ Matrix m1 = new Matrix(d);
+ Matrix m2 = new SparseMatrix(d1);
+ assertMatricesMatch(m1, m2); // sanity check
+ m1.tred();
+ m2.tred();
+ assertMatricesMatch(m1, m2);
+ }
+
+ private void assertMatricesMatch(MatrixI m1, MatrixI m2)
+ {
+ if (m1.height() != m2.height())
+ {
+ fail("height mismatch");
+ }
+ if (m1.width() != m2.width())
+ {
+ fail("width mismatch");
+ }
+ for (int row = 0; row < m1.height(); row++)
+ {
+ for (int col = 0; col < m1.width(); col++)
+ {
+ double v2 = m2.getValue(row, col);
+ double v1 = m1.getValue(row, col);
+ if (Math.abs(v1 - v2) > DELTA)
+ {
+ fail(String.format("At [%d, %d] %f != %f", row, col, v1, v2));
+ }
+ }
+ }
+ ArrayAsserts.assertArrayEquals(m1.getD(), m2.getD(), 0.00001d);
+ ArrayAsserts.assertArrayEquals(m1.getE(), m2.getE(), 0.00001d);
+ }
+
+ @Test
+ public void testGetValue()
+ {
+ double[][] d = new double[][] { { 0, 0, 1, 0, 0 }, { 2, 3, 0, 0, 0 },
+ { 4, 0, 0, 0, 5 } };
+ MatrixI m = new SparseMatrix(d);
+ for (int row = 0; row < 3; row++)
+ {
+ for (int col = 0; col < 5; col++)
+ {
+ assertEquals(m.getValue(row, col), d[row][col],
+ String.format("At [%d, %d]", row, col));
+ }
+ }
+ }
+
+ /**
+ * Verify that the results of method tqli() are the same for SparseMatrix as
+ * they are for Matrix (i.e. a regression test rather than an absolute test of
+ * correctness of results)
+ *
+ * @throws Exception
+ */
+ @Test(groups = "Functional")
+ public void testTqli_matchesMatrix() throws Exception
+ {
+ /*
+ * make a pseudo-random symmetric matrix as required for tred
+ */
+ int rows = 6;
+ int cols = rows;
+ double[][] d = getSparseValues(rows, cols, 3);
+
+ /*
+ * make a copy of the values so m1, m2 are not
+ * sharing arrays!
+ */
+ double[][] d1 = new double[rows][cols];
+ for (int row = 0; row < rows; row++)
+ {
+ for (int col = 0; col < cols; col++)
+ {
+ d1[row][col] = d[row][col];
+ }
+ }
+ Matrix m1 = new Matrix(d);
+ Matrix m2 = new SparseMatrix(d1);
+
+ // have to do tred() before doing tqli()
+ m1.tred();
+ m2.tred();
+ assertMatricesMatch(m1, m2);
+
+ m1.tqli();
+ m2.tqli();
+ assertMatricesMatch(m1, m2);
+ }
+
+ /**
+ * Helper method to make values for a sparse, pseudo-random symmetric matrix
+ *
+ * @param rows
+ * @param cols
+ * @param fraction
+ * one n fraction entries will be non-zero
+ * @return
+ */
+ public double[][] getSparseValues(int rows, int cols, int fraction)
+ {
+ double[][] d = new double[rows][cols];
+ int m = 0;
+ for (int i = 0; i < rows; i++)
+ {
+ if (++m % fraction == 0)
+ {
+ d[i][i] = r.nextDouble(); // diagonal
+ }
+ for (int j = 0; j < i; j++)
+ {
+ if (++m % fraction == 0)
+ {
+ d[i][j] = r.nextDouble();
+ d[j][i] = d[i][j];
+ }
+ }
+ }
+ return d;
+
+ }
+
+ /**
+ * Test that verifies that the result of preMultiply is a SparseMatrix if more
+ * than 80% zeroes, else a Matrix
+ */
+ @Test(groups = "Functional")
+ public void testPreMultiply_sparseProduct()
+ {
+ MatrixI m1 = new SparseMatrix(new double[][] { { 1 }, { 0 }, { 0 },
+ { 0 }, { 0 } }); // 5x1
+ MatrixI m2 = new SparseMatrix(new double[][] { { 1, 1, 1, 1 } }); // 1x4
+
+ /*
+ * m1.m2 makes a row of 4 1's, and 4 rows of zeros
+ * 20% non-zero so not 'sparse'
+ */
+ MatrixI m3 = m2.preMultiply(m1);
+ assertFalse(m3 instanceof SparseMatrix);
+
+ /*
+ * replace a 1 with a 0 in the product:
+ * it is now > 80% zero so 'sparse'
+ */
+ m2 = new SparseMatrix(new double[][] { { 1, 1, 1, 0 } });
+ m3 = m2.preMultiply(m1);
+ assertTrue(m3 instanceof SparseMatrix);
+ }
+
+ @Test(groups = "Functional")
+ public void testFillRatio()
+ {
+ SparseMatrix m1 = new SparseMatrix(new double[][] { { 2, 0, 4, 1, 0 },
+ { 0, 6, 0, 0, 0 } });
+ assertEquals(m1.getFillRatio(), 0.4f);
+ }
+}
\ No newline at end of file
git://source.jalview.org / jalview.git / commitdiff