+++ /dev/null
-package jalview.math;
-
-import static org.testng.Assert.assertEquals;
-import static org.testng.Assert.assertFalse;
-import static org.testng.Assert.assertNotSame;
-import static org.testng.Assert.assertNull;
-import static org.testng.Assert.assertTrue;
-import static org.testng.Assert.fail;
-
-import java.util.Arrays;
-import java.util.Random;
-
-import org.testng.annotations.Test;
-import org.testng.internal.junit.ArrayAsserts;
-
-public class MatrixTest
-{
- final static double DELTA = 0.000001d;
-
- @Test(groups = "Timing")
- public void testPreMultiply_timing()
- {
- int rows = 50; // increase to stress test timing
- int cols = 100;
- double[][] d1 = new double[rows][cols];
- double[][] d2 = new double[cols][rows];
- Matrix m1 = new Matrix(d1);
- Matrix m2 = new Matrix(d2);
- long start = System.currentTimeMillis();
- m1.preMultiply(m2);
- long elapsed = System.currentTimeMillis() - start;
- System.out.println(rows + "x" + cols
- + " multiplications of double took " + elapsed + "ms");
- }
-
- @Test(groups = "Functional")
- public void testPreMultiply()
- {
- Matrix m1 = new Matrix(new double[][] { { 2, 3, 4 } }); // 1x3
- Matrix m2 = new Matrix(new double[][] { { 5 }, { 6 }, { 7 } }); // 3x1
-
- /*
- * 1x3 times 3x1 is 1x1
- * 2x5 + 3x6 + 4*7 = 56
- */
- 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.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(
- groups = "Functional",
- expectedExceptions = { IllegalArgumentException.class })
- public void testPreMultiply_tooManyColumns()
- {
- Matrix m1 = new Matrix(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 Matrix(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");
- }
-
-
- private boolean matrixEquals(Matrix m1, Matrix m2) {
- 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")
- public void testPostMultiply()
- {
- /*
- * Square matrices
- * (2 3) . (10 100)
- * (4 5) (1000 10000)
- * =
- * (3020 30200)
- * (5040 50400)
- */
- 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.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 } });
- m2 = new Matrix(new double[][] { { 10, 100, 1000 } });
- m3 = m1.postMultiply(m2);
- 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.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
- * (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 Matrix(new double[][] { { 2, 3, 4 } });
- m2 = new Matrix(new double[][] { { 5, 4 }, { 6, 3 }, { 7, 2 } });
- m3 = m1.postMultiply(m2);
- 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.height(), 1);
- assertEquals(m3.width(), 2);
- assertEquals(m3.getRow(0)[0], 56d);
- assertEquals(m3.getRow(0)[1], 25d);
- }
-
- @Test(groups = "Functional")
- public void testCopy()
- {
- Random r = new Random();
- int rows = 5;
- int cols = 11;
- double[][] in = new double[rows][cols];
-
- for (int i = 0; i < rows; i++)
- {
- for (int j = 0; j < cols; j++)
- {
- in[i][j] = r.nextDouble();
- }
- }
- Matrix m1 = new Matrix(in);
-
- Matrix m2 = (Matrix) m1.copy();
- assertNotSame(m1, m2);
- assertTrue(matrixEquals(m1, m2));
- assertNull(m2.d);
- assertNull(m2.e);
-
- /*
- * now add d and e vectors and recopy
- */
- m1.d = Arrays.copyOf(in[2], in[2].length);
- m1.e = Arrays.copyOf(in[4], in[4].length);
- m2 = (Matrix) m1.copy();
- assertNotSame(m2.d, m1.d);
- assertNotSame(m2.e, m1.e);
- assertEquals(m2.d, m1.d);
- assertEquals(m2.e, m1.e);
- }
-
- /**
- * main method extracted from Matrix
- *
- * @param args
- */
- public static void main(String[] args) throws Exception
- {
- 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] = Math.random();
- }
- }
-
- Matrix origmat = new Matrix(in);
-
- // System.out.println(" --- Original matrix ---- ");
- // / origmat.print(System.out);
- // System.out.println();
- // System.out.println(" --- transpose matrix ---- ");
- MatrixI trans = origmat.transpose();
-
- // trans.print(System.out);
- // System.out.println();
- // System.out.println(" --- OrigT * Orig ---- ");
- MatrixI 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();
- }
-
- @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);
- }
-
- /**
- * Helper method to make values for a sparse, pseudo-random symmetric matrix
- *
- * @param rows
- * @param cols
- * @param occupancy
- * one in 'occupancy' entries will be non-zero
- * @return
- */
- public double[][] getSparseValues(int rows, int cols, int occupancy)
- {
- Random r = new Random(1729);
-
- /*
- * generate whole number values between -12 and +12
- * (to mimic score matrices used in Jalview)
- */
- double[][] d = new double[rows][cols];
- int m = 0;
- for (int i = 0; i < rows; i++)
- {
- if (++m % occupancy == 0)
- {
- d[i][i] = r.nextInt() % 13; // diagonal
- }
- for (int j = 0; j < i; j++)
- {
- if (++m % occupancy == 0)
- {
- d[i][j] = r.nextInt() % 13;
- d[j][i] = d[i][j];
- }
- }
- }
- return d;
-
- }
-
- /**
- * Verify that the results of method tred() are the same if the calculation is
- * redone
- */
- @Test(groups = "Functional")
- public void testTred_reproducible()
- {
- /*
- * make a pseudo-random symmetric matrix as required for tred/tqli
- */
- int rows = 10;
- 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 Matrix(d1);
- assertMatricesMatch(m1, m2); // sanity check
- m1.tred();
- m2.tred();
- assertMatricesMatch(m1, m2);
- }
-
- public static 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("D vector", m1.getD(), m2.getD(),
- 0.00001d);
- ArrayAsserts.assertArrayEquals("E vector", m1.getE(), m2.getE(),
- 0.00001d);
- }
-
- @Test(groups = "Functional")
- public void testFindMinMax()
- {
- /*
- * empty matrix case
- */
- Matrix m = new Matrix(new double[][] { {} });
- assertNull(m.findMinMax());
-
- /*
- * normal case
- */
- double[][] vals = new double[2][];
- vals[0] = new double[] {7d, 1d, -2.3d};
- vals[1] = new double[] {-12d, 94.3d, -102.34d};
- m = new Matrix(vals);
- double[] minMax = m.findMinMax();
- assertEquals(minMax[0], -102.34d);
- assertEquals(minMax[1], 94.3d);
- }
-
- @Test(groups = { "Functional", "Timing" })
- public void testFindMinMax_timing()
- {
- Random r = new Random();
- int size = 1000; // increase to stress test timing
- double[][] vals = new double[size][size];
- double max = -Double.MAX_VALUE;
- double min = Double.MAX_VALUE;
- for (int i = 0; i < size; i++)
- {
- vals[i] = new double[size];
- for (int j = 0; j < size; j++)
- {
- // use nextLong rather than nextDouble to include negative values
- double d = r.nextLong();
- if (d > max)
- {
- max = d;
- }
- if (d < min)
- {
- min = d;
- }
- vals[i][j] = d;
- }
- }
- Matrix m = new Matrix(vals);
- long now = System.currentTimeMillis();
- double[] minMax = m.findMinMax();
- System.out.println(String.format("findMinMax for %d x %d took %dms",
- size, size, (System.currentTimeMillis() - now)));
- assertEquals(minMax[0], min);
- assertEquals(minMax[1], max);
- }
-
- /**
- * Test range reversal with maximum value becoming zero
- */
- @Test(groups = "Functional")
- public void testReverseRange_maxToZero()
- {
- Matrix m1 = new Matrix(
- new double[][] { { 2, 3.5, 4 }, { -3.4, 4, 15 } });
-
- /*
- * subtract all from max: range -3.4 to 15 becomes 18.4 to 0
- */
- m1.reverseRange(true);
- assertEquals(m1.getValue(0, 0), 13d, DELTA);
- assertEquals(m1.getValue(0, 1), 11.5d, DELTA);
- assertEquals(m1.getValue(0, 2), 11d, DELTA);
- assertEquals(m1.getValue(1, 0), 18.4d, DELTA);
- assertEquals(m1.getValue(1, 1), 11d, DELTA);
- assertEquals(m1.getValue(1, 2), 0d, DELTA);
-
- /*
- * repeat operation - range is now 0 to 18.4
- */
- m1.reverseRange(true);
- assertEquals(m1.getValue(0, 0), 5.4d, DELTA);
- assertEquals(m1.getValue(0, 1), 6.9d, DELTA);
- assertEquals(m1.getValue(0, 2), 7.4d, DELTA);
- assertEquals(m1.getValue(1, 0), 0d, DELTA);
- assertEquals(m1.getValue(1, 1), 7.4d, DELTA);
- assertEquals(m1.getValue(1, 2), 18.4d, DELTA);
- }
-
- /**
- * Test range reversal with minimum and maximum values swapped
- */
- @Test(groups = "Functional")
- public void testReverseRange_swapMinMax()
- {
- Matrix m1 = new Matrix(
- new double[][] { { 2, 3.5, 4 }, { -3.4, 4, 15 } });
-
- /*
- * swap all values in min-max range
- * = subtract from (min + max = 11.6)
- * range -3.4 to 15 becomes 18.4 to -3.4
- */
- m1.reverseRange(false);
- assertEquals(m1.getValue(0, 0), 9.6d, DELTA);
- assertEquals(m1.getValue(0, 1), 8.1d, DELTA);
- assertEquals(m1.getValue(0, 2), 7.6d, DELTA);
- assertEquals(m1.getValue(1, 0), 15d, DELTA);
- assertEquals(m1.getValue(1, 1), 7.6d, DELTA);
- assertEquals(m1.getValue(1, 2), -3.4d, DELTA);
-
- /*
- * repeat operation - original values restored
- */
- m1.reverseRange(false);
- assertEquals(m1.getValue(0, 0), 2d, DELTA);
- assertEquals(m1.getValue(0, 1), 3.5d, DELTA);
- assertEquals(m1.getValue(0, 2), 4d, DELTA);
- assertEquals(m1.getValue(1, 0), -3.4d, DELTA);
- assertEquals(m1.getValue(1, 1), 4d, DELTA);
- assertEquals(m1.getValue(1, 2), 15d, DELTA);
- }
-
- @Test(groups = "Functional")
- public void testMultiply()
- {
- Matrix m = new Matrix(new double[][] { { 2, 3.5, 4 }, { -3.4, 4, 15 } });
- m.multiply(2d);
- assertEquals(m.getValue(0, 0), 4d, DELTA);
- assertEquals(m.getValue(0, 1), 7d, DELTA);
- assertEquals(m.getValue(0, 2), 8d, DELTA);
- assertEquals(m.getValue(1, 0), -6.8d, DELTA);
- assertEquals(m.getValue(1, 1), 8d, DELTA);
- assertEquals(m.getValue(1, 2), 30d, DELTA);
- }
-
- @Test(groups = "Functional")
- public void testConstructor()
- {
- double[][] values = new double[][] { { 1, 2, 3 }, { 4, 5, 6 } };
- Matrix m = new Matrix(values);
- assertEquals(m.getValue(0, 0), 1d, DELTA);
-
- /*
- * verify the matrix has a copy of the original array
- */
- assertNotSame(values[0], m.getRow(0));
- values[0][0] = -1d;
- assertEquals(m.getValue(0, 0), 1d, DELTA); // unchanged
- }
-
- @Test(groups = "Functional")
- public void testEquals()
- {
- double[][] values = new double[][] { { 1, 2, 3 }, { 4, 5, 6 } };
- Matrix m1 = new Matrix(values);
- double[][] values2 = new double[][] { { 1, 2, 3 }, { 4, 5, 6 } };
- Matrix m2 = new Matrix(values2);
-
- double delta = 0.0001d;
- assertTrue(m1.equals(m1, delta));
- assertTrue(m1.equals(m2, delta));
- assertTrue(m2.equals(m1, delta));
-
- double[][] values3 = new double[][] { { 1, 2, 3 }, { 4, 5, 7 } };
- m2 = new Matrix(values3);
- assertFalse(m1.equals(m2, delta));
- assertFalse(m2.equals(m1, delta));
-
- // must be same shape
- values2 = new double[][] { { 1, 2, 3 } };
- m2 = new Matrix(values2);
- assertFalse(m2.equals(m1, delta));
-
- assertFalse(m1.equals(null, delta));
- }
-}
git://source.jalview.org / jalview.git / blobdiff