--- /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, 0.00001d);
+
+ /*
+ * 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, 0.00001d);
+
+ /*
+ * 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, 0.00001d);
+ }
+
+ @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
+ */
+ 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 SparseMatrix(d1);
+ assertMatricesMatch(m1, m2, 0.00001d); // sanity check
+ m1.tred();
+ m2.tred();
+ assertMatricesMatch(m1, m2, 0.00001d);
+ }
+
+ private void assertMatricesMatch(MatrixI m1, MatrixI m2, double delta)
+ {
+ 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(), delta);
+ 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, 0.00001d);
+
+ m1.tqli();
+ m2.tqli();
+ assertMatricesMatch(m1, m2, 0.00001d);
+ }
+
+ /**
+ * 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)
+ {
+ /*
+ * 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;
+
+ }
+
+ /**
+ * 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);
+ }
+
+ /**
+ * 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 SparseMatrix(d);
+ Matrix m2 = new SparseMatrix(d1);
+ assertMatricesMatch(m1, m2, 1.0e16); // sanity check
+ m1.tred();
+ m2.tred();
+ assertMatricesMatch(m1, m2, 0.00001d);
+ }
+}
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