--- /dev/null
+package jalview.math;
+
+import static org.testng.Assert.assertEquals;
+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 = 0.0001d;
+
+ @Test(groups = "Timing")
+ public void testPreMultiply_timing()
+ {
+ int rows = 500;
+ int cols = 1000;
+ 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();
+ assertTrue(matrixEquals(m1, m2));
+ }
+
+ /**
+ * 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);
+ }
+
+ 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);
+ }
+}
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