Java Code Examples for org.apache.commons.math3.util.ArithmeticUtils#binomialCoefficient()

/**
 * Generates all combinations of items in the input of the given length.
 *
 * @param input   Input to generate the combinations from.
 * @param length  Number of items per combination.
 * @return All combinations of length in the input.
 */
public static <T> Set<List<T>> getAllItemCombinations(T[] input, int length) {
  if (length > input.length) {
    throw new IllegalArgumentException("Length must not be larger than the length of the input.");
  }
  if (input == null || input.length == 0) {
    return new HashSet<>();
  }
  long totalCombinations = ArithmeticUtils.binomialCoefficient(input.length, length);
  if (totalCombinations > Integer.MAX_VALUE) {
    throw new IllegalArgumentException("Too many combinations for the given input and length");
  }
  Set<List<T>> allCombinations = new HashSet<>((int) totalCombinations);
  computeAllItemCombinationsRecursive(input, allCombinations, null, 0, length);
  return allCombinations;
}
 

@Test
public void testSize() {
    for (int i = 0; i < 6; ++i) {
        for (int j = 0; j < 6; ++j) {
            long expected = ArithmeticUtils.binomialCoefficient(i + j, i);
            Assert.assertEquals(expected, DSCompiler.getCompiler(i, j).getSize());
            Assert.assertEquals(expected, DSCompiler.getCompiler(j, i).getSize());
        }
    }
}
 

@Test
public void testJacobiEvaluationAt1() {
    for (int v = 0; v < 10; ++v) {
        for (int w = 0; w < 10; ++w) {
            for (int i = 0; i < 10; ++i) {
                PolynomialFunction jacobi = PolynomialsUtils.createJacobiPolynomial(i, v, w);
                double binomial = ArithmeticUtils.binomialCoefficient(v + i, i);
                Assert.assertTrue(Precision.equals(binomial, jacobi.value(1.0), 1));
            }
        }
    }
}
 

/**
 * Returns the {@code (i, j)} entry of the inverse Hilbert matrix. Exact
 * arithmetic is used; in case of overflow, an exception is thrown.
 *
 * @param i Row index (starts at 0).
 * @param j Column index (starts at 0).
 * @return The coefficient of the inverse Hilbert matrix.
 */
public long getEntry(final int i, final int j) {
    long val = i + j + 1;
    long aux = ArithmeticUtils.binomialCoefficient(n + i, n - j - 1);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    aux = ArithmeticUtils.binomialCoefficient(n + j, n - i - 1);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    aux = ArithmeticUtils.binomialCoefficient(i + j, i);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    return ((i + j) & 1) == 0 ? val : -val;
}
 

@Test
public void testJacobiEvaluationAt1() {
    for (int v = 0; v < 10; ++v) {
        for (int w = 0; w < 10; ++w) {
            for (int i = 0; i < 10; ++i) {
                PolynomialFunction jacobi = PolynomialsUtils.createJacobiPolynomial(i, v, w);
                double binomial = ArithmeticUtils.binomialCoefficient(v + i, i);
                Assert.assertTrue(Precision.equals(binomial, jacobi.value(1.0), 1));
            }
        }
    }
}
 

/**
 * Returns the {@code (i, j)} entry of the inverse Hilbert matrix. Exact
 * arithmetic is used; in case of overflow, an exception is thrown.
 *
 * @param i Row index (starts at 0).
 * @param j Column index (starts at 0).
 * @return The coefficient of the inverse Hilbert matrix.
 */
public long getEntry(final int i, final int j) {
    long val = i + j + 1;
    long aux = ArithmeticUtils.binomialCoefficient(n + i, n - j - 1);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    aux = ArithmeticUtils.binomialCoefficient(n + j, n - i - 1);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    aux = ArithmeticUtils.binomialCoefficient(i + j, i);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    return ((i + j) & 1) == 0 ? val : -val;
}
 

@Test
public void testJacobiEvaluationAt1() {
    for (int v = 0; v < 10; ++v) {
        for (int w = 0; w < 10; ++w) {
            for (int i = 0; i < 10; ++i) {
                PolynomialFunction jacobi = PolynomialsUtils.createJacobiPolynomial(i, v, w);
                double binomial = ArithmeticUtils.binomialCoefficient(v + i, i);
                Assert.assertTrue(Precision.equals(binomial, jacobi.value(1.0), 1));
            }
        }
    }
}
 

/**
 * Returns the {@code (i, j)} entry of the inverse Hilbert matrix. Exact
 * arithmetic is used; in case of overflow, an exception is thrown.
 *
 * @param i Row index (starts at 0).
 * @param j Column index (starts at 0).
 * @return The coefficient of the inverse Hilbert matrix.
 */
public long getEntry(final int i, final int j) {
    long val = i + j + 1;
    long aux = ArithmeticUtils.binomialCoefficient(n + i, n - j - 1);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    aux = ArithmeticUtils.binomialCoefficient(n + j, n - i - 1);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    aux = ArithmeticUtils.binomialCoefficient(i + j, i);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    return ((i + j) & 1) == 0 ? val : -val;
}
 

@Test
public void testSize() {
    for (int i = 0; i < 6; ++i) {
        for (int j = 0; j < 6; ++j) {
            long expected = ArithmeticUtils.binomialCoefficient(i + j, i);
            Assert.assertEquals(expected, DSCompiler.getCompiler(i, j).getSize());
            Assert.assertEquals(expected, DSCompiler.getCompiler(j, i).getSize());
        }
    }
}
 

@Test
public void testJacobiEvaluationAt1() {
    for (int v = 0; v < 10; ++v) {
        for (int w = 0; w < 10; ++w) {
            for (int i = 0; i < 10; ++i) {
                PolynomialFunction jacobi = PolynomialsUtils.createJacobiPolynomial(i, v, w);
                double binomial = ArithmeticUtils.binomialCoefficient(v + i, i);
                Assert.assertTrue(Precision.equals(binomial, jacobi.value(1.0), 1));
            }
        }
    }
}
 

/**
 * Returns the {@code (i, j)} entry of the inverse Hilbert matrix. Exact
 * arithmetic is used; in case of overflow, an exception is thrown.
 *
 * @param i Row index (starts at 0).
 * @param j Column index (starts at 0).
 * @return The coefficient of the inverse Hilbert matrix.
 */
public long getEntry(final int i, final int j) {
    long val = i + j + 1;
    long aux = ArithmeticUtils.binomialCoefficient(n + i, n - j - 1);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    aux = ArithmeticUtils.binomialCoefficient(n + j, n - i - 1);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    aux = ArithmeticUtils.binomialCoefficient(i + j, i);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    return ((i + j) & 1) == 0 ? val : -val;
}
 

@Test
public void testSize() {
    for (int i = 0; i < 6; ++i) {
        for (int j = 0; j < 6; ++j) {
            long expected = ArithmeticUtils.binomialCoefficient(i + j, i);
            Assert.assertEquals(expected, DSCompiler.getCompiler(i, j).getSize());
            Assert.assertEquals(expected, DSCompiler.getCompiler(j, i).getSize());
        }
    }
}
 

@Test
public void testJacobiEvaluationAt1() {
    for (int v = 0; v < 10; ++v) {
        for (int w = 0; w < 10; ++w) {
            for (int i = 0; i < 10; ++i) {
                PolynomialFunction jacobi = PolynomialsUtils.createJacobiPolynomial(i, v, w);
                double binomial = ArithmeticUtils.binomialCoefficient(v + i, i);
                Assert.assertTrue(Precision.equals(binomial, jacobi.value(1.0), 1));
            }
        }
    }
}
 

/**
 * Returns the {@code (i, j)} entry of the inverse Hilbert matrix. Exact
 * arithmetic is used; in case of overflow, an exception is thrown.
 *
 * @param i Row index (starts at 0).
 * @param j Column index (starts at 0).
 * @return The coefficient of the inverse Hilbert matrix.
 */
public long getEntry(final int i, final int j) {
    long val = i + j + 1;
    long aux = ArithmeticUtils.binomialCoefficient(n + i, n - j - 1);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    aux = ArithmeticUtils.binomialCoefficient(n + j, n - i - 1);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    aux = ArithmeticUtils.binomialCoefficient(i + j, i);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    return ((i + j) & 1) == 0 ? val : -val;
}