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Added CombinatoricsUtils to the util package, moving binomial 

coefficients, factorials and Stirling numbers there and adding
a combinations iterator.
JIRA: MATH-1025

git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@1517203 13f79535-47bb-0310-9956-ffa450edef68
This commit is contained in:
Phil Steitz 2013-08-24 21:55:35 +00:00
parent b06d9bcfa1
commit ad35857d0f
16 changed files with 1126 additions and 590 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

5
src/changes/changes.xml
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@ -51,6 +51,11 @@ If the output is not quite correct, check for invisible trailing spaces!
</properties>
<body>
<release version="x.y" date="TBD" description="TBD">
<action dev="psteitz" type="add" issue="MATH-1025">
Added CombinatoricsUtils to the util package, moving binomial
coefficients, factorials and Stirling numbers there and adding
a combinations iterator.
</action>
<action dev="erans" type="add" issue="MATH-991">
"PolynomialSplineFunction": added method "isValidPoint" that
checks whether a point is within the interpolation range.

4
src/main/java/org/apache/commons/math3/analysis/differentiation/DSCompiler.java
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@ -26,7 +26,7 @@ import org.apache.commons.math3.exception.MathArithmeticException;
import org.apache.commons.math3.exception.MathInternalError;
import org.apache.commons.math3.exception.NotPositiveException;
import org.apache.commons.math3.exception.NumberIsTooLargeException;
import org.apache.commons.math3.util.ArithmeticUtils;
import org.apache.commons.math3.util.CombinatoricsUtils;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.MathArrays;
@ -1752,7 +1752,7 @@ public class DSCompiler {
if (orders[k] > 0) {
try {
term *= FastMath.pow(delta[k], orders[k]) /
ArithmeticUtils.factorial(orders[k]);
CombinatoricsUtils.factorial(orders[k]);
} catch (NotPositiveException e) {
// this cannot happen
throw new MathInternalError(e);

4
src/main/java/org/apache/commons/math3/analysis/interpolation/HermiteInterpolator.java
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@ -27,7 +27,7 @@ import org.apache.commons.math3.exception.MathArithmeticException;
import org.apache.commons.math3.exception.NoDataException;
import org.apache.commons.math3.exception.ZeroException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.util.ArithmeticUtils;
import org.apache.commons.math3.util.CombinatoricsUtils;
/** Polynomial interpolator using both sample values and sample derivatives.
* <p>
@ -91,7 +91,7 @@ public class HermiteInterpolator implements UnivariateDifferentiableVectorFuncti
final double[] y = value[i].clone();
if (i > 1) {
double inv = 1.0 / ArithmeticUtils.factorial(i);
double inv = 1.0 / CombinatoricsUtils.factorial(i);
for (int j = 0; j < y.length; ++j) {
y[j] *= inv;
}

4
src/main/java/org/apache/commons/math3/analysis/polynomials/PolynomialsUtils.java
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@ -22,7 +22,7 @@ import java.util.List;
import java.util.Map;
import org.apache.commons.math3.fraction.BigFraction;
import org.apache.commons.math3.util.ArithmeticUtils;
import org.apache.commons.math3.util.CombinatoricsUtils;
import org.apache.commons.math3.util.FastMath;
/**
@ -328,7 +328,7 @@ public class PolynomialsUtils {
final int[][] coeff = new int[dp1][dp1];
for (int i = 0; i < dp1; i++){
for(int j = 0; j <= i; j++){
coeff[i][j] = (int) ArithmeticUtils.binomialCoefficient(i, j);
coeff[i][j] = (int) CombinatoricsUtils.binomialCoefficient(i, j);
}
}

4
src/main/java/org/apache/commons/math3/distribution/ExponentialDistribution.java
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@ -19,8 +19,8 @@ package org.apache.commons.math3.distribution;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.OutOfRangeException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.util.CombinatoricsUtils;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.ArithmeticUtils;
import org.apache.commons.math3.util.ResizableDoubleArray;
import org.apache.commons.math3.random.RandomGenerator;
import org.apache.commons.math3.random.Well19937c;
@ -80,7 +80,7 @@ public class ExponentialDistribution extends AbstractRealDistribution {
final ResizableDoubleArray ra = new ResizableDoubleArray(20);
while (qi < 1) {
qi += FastMath.pow(LN2, i) / ArithmeticUtils.factorial(i);
qi += FastMath.pow(LN2, i) / CombinatoricsUtils.factorial(i);
ra.addElement(qi);
++i;
}

4
src/main/java/org/apache/commons/math3/distribution/PascalDistribution.java
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@ -20,7 +20,7 @@ import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.OutOfRangeException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.special.Beta;
import org.apache.commons.math3.util.ArithmeticUtils;
import org.apache.commons.math3.util.CombinatoricsUtils;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.random.RandomGenerator;
import org.apache.commons.math3.random.Well19937c;
@ -138,7 +138,7 @@ public class PascalDistribution extends AbstractIntegerDistribution {
if (x < 0) {
ret = 0.0;
} else {
ret = ArithmeticUtils.binomialCoefficientDouble(x +
ret = CombinatoricsUtils.binomialCoefficientDouble(x +
numberOfSuccesses - 1, numberOfSuccesses - 1) *
FastMath.pow(probabilityOfSuccess, numberOfSuccesses) *
FastMath.pow(1.0 - probabilityOfSuccess, x);

6
src/main/java/org/apache/commons/math3/distribution/PoissonDistribution.java
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@ -19,8 +19,8 @@ package org.apache.commons.math3.distribution;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.special.Gamma;
import org.apache.commons.math3.util.CombinatoricsUtils;
import org.apache.commons.math3.util.MathUtils;
import org.apache.commons.math3.util.ArithmeticUtils;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.random.RandomGenerator;
import org.apache.commons.math3.random.Well19937c;
@ -309,7 +309,7 @@ public class PoissonDistribution extends AbstractIntegerDistribution {
final double lambda = FastMath.floor(meanPoisson);
final double lambdaFractional = meanPoisson - lambda;
final double logLambda = FastMath.log(lambda);
final double logLambdaFactorial = ArithmeticUtils.factorialLog((int) lambda);
final double logLambdaFactorial = CombinatoricsUtils.factorialLog((int) lambda);
final long y2 = lambdaFractional < Double.MIN_VALUE ? 0 : nextPoisson(lambdaFractional);
final double delta = FastMath.sqrt(lambda * FastMath.log(32 * lambda / FastMath.PI + 1));
final double halfDelta = delta / 2;
@ -364,7 +364,7 @@ public class PoissonDistribution extends AbstractIntegerDistribution {
if (v > qr) {
continue;
}
if (v < y * logLambda - ArithmeticUtils.factorialLog((int) (y + lambda)) + logLambdaFactorial) {
if (v < y * logLambda - CombinatoricsUtils.factorialLog((int) (y + lambda)) + logLambdaFactorial) {
y = lambda + y;
break;
}

252
src/main/java/org/apache/commons/math3/util/ArithmeticUtils.java
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@ -17,7 +17,6 @@
package org.apache.commons.math3.util;
import java.math.BigInteger;
import java.util.concurrent.atomic.AtomicReference;
import org.apache.commons.math3.exception.MathArithmeticException;
import org.apache.commons.math3.exception.NotPositiveException;
@ -33,19 +32,6 @@ import org.apache.commons.math3.exception.util.LocalizedFormats;
*/
public final class ArithmeticUtils {
/** All long-representable factorials */
static final long[] FACTORIALS = new long[] {
1l, 1l, 2l,
6l, 24l, 120l,
720l, 5040l, 40320l,
362880l, 3628800l, 39916800l,
479001600l, 6227020800l, 87178291200l,
1307674368000l, 20922789888000l, 355687428096000l,
6402373705728000l, 121645100408832000l, 2432902008176640000l };
/** Stirling numbers of the second kind. */
static final AtomicReference<long[][]> STIRLING_S2 = new AtomicReference<long[][]> (null);
/** Private constructor. */
private ArithmeticUtils() {
super();
@ -109,61 +95,11 @@ public final class ArithmeticUtils {
* @throws NumberIsTooLargeException if {@code k > n}.
* @throws MathArithmeticException if the result is too large to be
* represented by a long integer.
* @deprecated use {@link CombinatoricsUtils#binomialCoefficient(int, int)}
*/
public static long binomialCoefficient(final int n, final int k)
throws NotPositiveException, NumberIsTooLargeException, MathArithmeticException {
ArithmeticUtils.checkBinomial(n, k);
if ((n == k) || (k == 0)) {
return 1;
}
if ((k == 1) || (k == n - 1)) {
return n;
}
// Use symmetry for large k
if (k > n / 2) {
return binomialCoefficient(n, n - k);
}
// We use the formula
// (n choose k) = n! / (n-k)! / k!
// (n choose k) == ((n-k+1)*...*n) / (1*...*k)
// which could be written
// (n choose k) == (n-1 choose k-1) * n / k
long result = 1;
if (n <= 61) {
// For n <= 61, the naive implementation cannot overflow.
int i = n - k + 1;
for (int j = 1; j <= k; j++) {
result = result * i / j;
i++;
}
} else if (n <= 66) {
// For n > 61 but n <= 66, the result cannot overflow,
// but we must take care not to overflow intermediate values.
int i = n - k + 1;
for (int j = 1; j <= k; j++) {
// We know that (result * i) is divisible by j,
// but (result * i) may overflow, so we split j:
// Filter out the gcd, d, so j/d and i/d are integer.
// result is divisible by (j/d) because (j/d)
// is relative prime to (i/d) and is a divisor of
// result * (i/d).
final long d = gcd(i, j);
result = (result / (j / d)) * (i / d);
i++;
}
} else {
// For n > 66, a result overflow might occur, so we check
// the multiplication, taking care to not overflow
// unnecessary.
int i = n - k + 1;
for (int j = 1; j <= k; j++) {
final long d = gcd(i, j);
result = mulAndCheck(result / (j / d), i / d);
i++;
}
}
return result;
return CombinatoricsUtils.binomialCoefficient(n, k);
}
/**
@ -190,29 +126,11 @@ public final class ArithmeticUtils {
* @throws NumberIsTooLargeException if {@code k > n}.
* @throws MathArithmeticException if the result is too large to be
* represented by a long integer.
* @deprecated use {@link CombinatoricsUtils#binomialCoefficientDouble(int, int)}
*/
public static double binomialCoefficientDouble(final int n, final int k)
throws NotPositiveException, NumberIsTooLargeException, MathArithmeticException {
ArithmeticUtils.checkBinomial(n, k);
if ((n == k) || (k == 0)) {
return 1d;
}
if ((k == 1) || (k == n - 1)) {
return n;
}
if (k > n/2) {
return binomialCoefficientDouble(n, n - k);
}
if (n < 67) {
return binomialCoefficient(n,k);
}
double result = 1d;
for (int i = 1; i <= k; i++) {
result *= (double)(n - k + i) / (double)i;
}
return FastMath.floor(result + 0.5);
return CombinatoricsUtils.binomialCoefficientDouble(n, k);
}
/**
@ -235,53 +153,11 @@ public final class ArithmeticUtils {
* @throws NumberIsTooLargeException if {@code k > n}.
* @throws MathArithmeticException if the result is too large to be
* represented by a long integer.
* @deprecated use {@link CombinatoricsUtils#binomialCoefficientLog(int, int)}
*/
public static double binomialCoefficientLog(final int n, final int k)
throws NotPositiveException, NumberIsTooLargeException, MathArithmeticException {
ArithmeticUtils.checkBinomial(n, k);
if ((n == k) || (k == 0)) {
return 0;
}
if ((k == 1) || (k == n - 1)) {
return FastMath.log(n);
}
/*
* For values small enough to do exact integer computation,
* return the log of the exact value
*/
if (n < 67) {
return FastMath.log(binomialCoefficient(n,k));
}
/*
* Return the log of binomialCoefficientDouble for values that will not
* overflow binomialCoefficientDouble
*/
if (n < 1030) {
return FastMath.log(binomialCoefficientDouble(n, k));
}
if (k > n / 2) {
return binomialCoefficientLog(n, n - k);
}
/*
* Sum logs for values that could overflow
*/
double logSum = 0;
// n!/(n-k)!
for (int i = n - k + 1; i <= n; i++) {
logSum += FastMath.log(i);
}
// divide by k!
for (int i = 2; i <= k; i++) {
logSum -= FastMath.log(i);
}
return logSum;
return CombinatoricsUtils.binomialCoefficientLog(n, k);
}
/**
@ -307,16 +183,10 @@ public final class ArithmeticUtils {
* @throws NotPositiveException if {@code n < 0}.
* @throws MathArithmeticException if {@code n > 20}: The factorial value is too
* large to fit in a {@code long}.
* @deprecated use {@link CombinatoricsUtils#factorial(int)}
*/
public static long factorial(final int n) throws NotPositiveException, MathArithmeticException {
if (n < 0) {
throw new NotPositiveException(LocalizedFormats.FACTORIAL_NEGATIVE_PARAMETER,
n);
}
if (n > 20) {
throw new MathArithmeticException();
}
return FACTORIALS[n];
return CombinatoricsUtils.factorial(n);
}
/**
@ -331,16 +201,10 @@ public final class ArithmeticUtils {
* @param n Argument.
* @return {@code n!}
* @throws NotPositiveException if {@code n < 0}.
* @deprecated use {@link CombinatoricsUtils#factorialDouble(int)}
*/
public static double factorialDouble(final int n) throws NotPositiveException {
if (n < 0) {
throw new NotPositiveException(LocalizedFormats.FACTORIAL_NEGATIVE_PARAMETER,
n);
}
if (n < 21) {
return FACTORIALS[n];
}
return FastMath.floor(FastMath.exp(ArithmeticUtils.factorialLog(n)) + 0.5);
return CombinatoricsUtils.factorialDouble(n);
}
/**
@ -349,20 +213,10 @@ public final class ArithmeticUtils {
* @param n Argument.
* @return {@code n!}
* @throws NotPositiveException if {@code n < 0}.
* @deprecated use {@link CombinatoricsUtils#factorialLog(int)}
*/
public static double factorialLog(final int n) throws NotPositiveException {
if (n < 0) {
throw new NotPositiveException(LocalizedFormats.FACTORIAL_NEGATIVE_PARAMETER,
n);
}
if (n < 21) {
return FastMath.log(FACTORIALS[n]);
}
double logSum = 0;
for (int i = 2; i <= n; i++) {
logSum += FastMath.log(i);
}
return logSum;
return CombinatoricsUtils.factorialLog(n);
}
/**
@ -968,71 +822,11 @@ public final class ArithmeticUtils {
* @throws MathArithmeticException if some overflow happens, typically for n exceeding 25 and
* k between 20 and n-2 (S(n,n-1) is handled specifically and does not overflow)
* @since 3.1
* @deprecated use {@link CombinatoricsUtils#stirlingS2(int, int)}
*/
public static long stirlingS2(final int n, final int k)
throws NotPositiveException, NumberIsTooLargeException, MathArithmeticException {
if (k < 0) {
throw new NotPositiveException(k);
}
if (k > n) {
throw new NumberIsTooLargeException(k, n, true);
}
long[][] stirlingS2 = STIRLING_S2.get();
if (stirlingS2 == null) {
// the cache has never been initialized, compute the first numbers
// by direct recurrence relation
// as S(26,9) = 11201516780955125625 is larger than Long.MAX_VALUE
// we must stop computation at row 26
final int maxIndex = 26;
stirlingS2 = new long[maxIndex][];
stirlingS2[0] = new long[] { 1l };
for (int i = 1; i < stirlingS2.length; ++i) {
stirlingS2[i] = new long[i + 1];
stirlingS2[i][0] = 0;
stirlingS2[i][1] = 1;
stirlingS2[i][i] = 1;
for (int j = 2; j < i; ++j) {
stirlingS2[i][j] = j * stirlingS2[i - 1][j] + stirlingS2[i - 1][j - 1];
}
}
// atomically save the cache
STIRLING_S2.compareAndSet(null, stirlingS2);
}
if (n < stirlingS2.length) {
// the number is in the small cache
return stirlingS2[n][k];
} else {
// use explicit formula to compute the number without caching it
if (k == 0) {
return 0;
} else if (k == 1 || k == n) {
return 1;
} else if (k == 2) {
return (1l << (n - 1)) - 1l;
} else if (k == n - 1) {
return binomialCoefficient(n, 2);
} else {
// definition formula: note that this may trigger some overflow
long sum = 0;
long sign = ((k & 0x1) == 0) ? 1 : -1;
for (int j = 1; j <= k; ++j) {
sign = -sign;
sum += sign * binomialCoefficient(k, j) * pow(j, n);
if (sum < 0) {
// there was an overflow somewhere
throw new MathArithmeticException(LocalizedFormats.ARGUMENT_OUTSIDE_DOMAIN,
n, 0, stirlingS2.length - 1);
}
}
return sum / factorial(k);
}
}
return CombinatoricsUtils.stirlingS2(n, k);
}
@ -1082,24 +876,6 @@ public final class ArithmeticUtils {
return ret;
}
/**
* Check binomial preconditions.
*
* @param n Size of the set.
* @param k Size of the subsets to be counted.
* @throws NotPositiveException if {@code n < 0}.
* @throws NumberIsTooLargeException if {@code k > n}.
*/
private static void checkBinomial(final int n, final int k) throws NumberIsTooLargeException, NotPositiveException {
if (n < k) {
throw new NumberIsTooLargeException(LocalizedFormats.BINOMIAL_INVALID_PARAMETERS_ORDER,
k, n, true);
}
if (n < 0) {
throw new NotPositiveException(LocalizedFormats.BINOMIAL_NEGATIVE_PARAMETER, n);
}
}
/**
* Returns true if the argument is a power of two.
*

637
src/main/java/org/apache/commons/math3/util/CombinatoricsUtils.java Normal file
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@ -0,0 +1,637 @@
/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math3.util;
import java.util.Iterator;
import java.util.NoSuchElementException;
import java.util.concurrent.atomic.AtomicReference;
import org.apache.commons.math3.exception.MathArithmeticException;
import org.apache.commons.math3.exception.NotPositiveException;
import org.apache.commons.math3.exception.NumberIsTooLargeException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
/**
* Combinatorial utilities.
*
* @version $Id$
* @since 3.3
*/
public final class CombinatoricsUtils {
/** All long-representable factorials */
static final long[] FACTORIALS = new long[] {
1l, 1l, 2l,
6l, 24l, 120l,
720l, 5040l, 40320l,
362880l, 3628800l, 39916800l,
479001600l, 6227020800l, 87178291200l,
1307674368000l, 20922789888000l, 355687428096000l,
6402373705728000l, 121645100408832000l, 2432902008176640000l };
/** Stirling numbers of the second kind. */
static final AtomicReference<long[][]> STIRLING_S2 = new AtomicReference<long[][]> (null);
/** Private constructor. */
private CombinatoricsUtils() {
super();
}
/**
* Returns an exact representation of the <a
* href="http://mathworld.wolfram.com/BinomialCoefficient.html"> Binomial
* Coefficient</a>, "{@code n choose k}", the number of
* {@code k}-element subsets that can be selected from an
* {@code n}-element set.
* <p>
* <Strong>Preconditions</strong>:
* <ul>
* <li> {@code 0 <= k <= n } (otherwise
* {@code IllegalArgumentException} is thrown)</li>
* <li> The result is small enough to fit into a {@code long}. The
* largest value of {@code n} for which all coefficients are
* {@code < Long.MAX_VALUE} is 66. If the computed value exceeds
* {@code Long.MAX_VALUE} an {@code ArithMeticException} is
* thrown.</li>
* </ul></p>
*
* @param n the size of the set
* @param k the size of the subsets to be counted
* @return {@code n choose k}
* @throws NotPositiveException if {@code n < 0}.
* @throws NumberIsTooLargeException if {@code k > n}.
* @throws MathArithmeticException if the result is too large to be
* represented by a long integer.
*/
public static long binomialCoefficient(final int n, final int k)
throws NotPositiveException, NumberIsTooLargeException, MathArithmeticException {
CombinatoricsUtils.checkBinomial(n, k);
if ((n == k) || (k == 0)) {
return 1;
}
if ((k == 1) || (k == n - 1)) {
return n;
}
// Use symmetry for large k
if (k > n / 2) {
return binomialCoefficient(n, n - k);
}
// We use the formula
// (n choose k) = n! / (n-k)! / k!
// (n choose k) == ((n-k+1)*...*n) / (1*...*k)
// which could be written
// (n choose k) == (n-1 choose k-1) * n / k
long result = 1;
if (n <= 61) {
// For n <= 61, the naive implementation cannot overflow.
int i = n - k + 1;
for (int j = 1; j <= k; j++) {
result = result * i / j;
i++;
}
} else if (n <= 66) {
// For n > 61 but n <= 66, the result cannot overflow,
// but we must take care not to overflow intermediate values.
int i = n - k + 1;
for (int j = 1; j <= k; j++) {
// We know that (result * i) is divisible by j,
// but (result * i) may overflow, so we split j:
// Filter out the gcd, d, so j/d and i/d are integer.
// result is divisible by (j/d) because (j/d)
// is relative prime to (i/d) and is a divisor of
// result * (i/d).
final long d = ArithmeticUtils.gcd(i, j);
result = (result / (j / d)) * (i / d);
i++;
}
} else {
// For n > 66, a result overflow might occur, so we check
// the multiplication, taking care to not overflow
// unnecessary.
int i = n - k + 1;
for (int j = 1; j <= k; j++) {
final long d = ArithmeticUtils.gcd(i, j);
result = ArithmeticUtils.mulAndCheck(result / (j / d), i / d);
i++;
}
}
return result;
}
/**
* Returns a {@code double} representation of the <a
* href="http://mathworld.wolfram.com/BinomialCoefficient.html"> Binomial
* Coefficient</a>, "{@code n choose k}", the number of
* {@code k}-element subsets that can be selected from an
* {@code n}-element set.
* <p>
* <Strong>Preconditions</strong>:
* <ul>
* <li> {@code 0 <= k <= n } (otherwise
* {@code IllegalArgumentException} is thrown)</li>
* <li> The result is small enough to fit into a {@code double}. The
* largest value of {@code n} for which all coefficients are <
* Double.MAX_VALUE is 1029. If the computed value exceeds Double.MAX_VALUE,
* Double.POSITIVE_INFINITY is returned</li>
* </ul></p>
*
* @param n the size of the set
* @param k the size of the subsets to be counted
* @return {@code n choose k}
* @throws NotPositiveException if {@code n < 0}.
* @throws NumberIsTooLargeException if {@code k > n}.
* @throws MathArithmeticException if the result is too large to be
* represented by a long integer.
*/
public static double binomialCoefficientDouble(final int n, final int k)
throws NotPositiveException, NumberIsTooLargeException, MathArithmeticException {
CombinatoricsUtils.checkBinomial(n, k);
if ((n == k) || (k == 0)) {
return 1d;
}
if ((k == 1) || (k == n - 1)) {
return n;
}
if (k > n/2) {
return binomialCoefficientDouble(n, n - k);
}
if (n < 67) {
return binomialCoefficient(n,k);
}
double result = 1d;
for (int i = 1; i <= k; i++) {
result *= (double)(n - k + i) / (double)i;
}
return FastMath.floor(result + 0.5);
}
/**
* Returns the natural {@code log} of the <a
* href="http://mathworld.wolfram.com/BinomialCoefficient.html"> Binomial
* Coefficient</a>, "{@code n choose k}", the number of
* {@code k}-element subsets that can be selected from an
* {@code n}-element set.
* <p>
* <Strong>Preconditions</strong>:
* <ul>
* <li> {@code 0 <= k <= n } (otherwise
* {@code IllegalArgumentException} is thrown)</li>
* </ul></p>
*
* @param n the size of the set
* @param k the size of the subsets to be counted
* @return {@code n choose k}
* @throws NotPositiveException if {@code n < 0}.
* @throws NumberIsTooLargeException if {@code k > n}.
* @throws MathArithmeticException if the result is too large to be
* represented by a long integer.
*/
public static double binomialCoefficientLog(final int n, final int k)
throws NotPositiveException, NumberIsTooLargeException, MathArithmeticException {
CombinatoricsUtils.checkBinomial(n, k);
if ((n == k) || (k == 0)) {
return 0;
}
if ((k == 1) || (k == n - 1)) {
return FastMath.log(n);
}
/*
* For values small enough to do exact integer computation,
* return the log of the exact value
*/
if (n < 67) {
return FastMath.log(binomialCoefficient(n,k));
}
/*
* Return the log of binomialCoefficientDouble for values that will not
* overflow binomialCoefficientDouble
*/
if (n < 1030) {
return FastMath.log(binomialCoefficientDouble(n, k));
}
if (k > n / 2) {
return binomialCoefficientLog(n, n - k);
}
/*
* Sum logs for values that could overflow
*/
double logSum = 0;
// n!/(n-k)!
for (int i = n - k + 1; i <= n; i++) {
logSum += FastMath.log(i);
}
// divide by k!
for (int i = 2; i <= k; i++) {
logSum -= FastMath.log(i);
}
return logSum;
}
/**
* Returns n!. Shorthand for {@code n} <a
* href="http://mathworld.wolfram.com/Factorial.html"> Factorial</a>, the
* product of the numbers {@code 1,...,n}.
* <p>
* <Strong>Preconditions</strong>:
* <ul>
* <li> {@code n >= 0} (otherwise
* {@code IllegalArgumentException} is thrown)</li>
* <li> The result is small enough to fit into a {@code long}. The
* largest value of {@code n} for which {@code n!} <
* Long.MAX_VALUE} is 20. If the computed value exceeds {@code Long.MAX_VALUE}
* an {@code ArithMeticException } is thrown.</li>
* </ul>
* </p>
*
* @param n argument
* @return {@code n!}
* @throws MathArithmeticException if the result is too large to be represented
* by a {@code long}.
* @throws NotPositiveException if {@code n < 0}.
* @throws MathArithmeticException if {@code n > 20}: The factorial value is too
* large to fit in a {@code long}.
*/
public static long factorial(final int n) throws NotPositiveException, MathArithmeticException {
if (n < 0) {
throw new NotPositiveException(LocalizedFormats.FACTORIAL_NEGATIVE_PARAMETER,
n);
}
if (n > 20) {
throw new MathArithmeticException();
}
return FACTORIALS[n];
}
/**
* Compute n!, the<a href="http://mathworld.wolfram.com/Factorial.html">
* factorial</a> of {@code n} (the product of the numbers 1 to n), as a
* {@code double}.
* The result should be small enough to fit into a {@code double}: The
* largest {@code n} for which {@code n! < Double.MAX_VALUE} is 170.
* If the computed value exceeds {@code Double.MAX_VALUE},
* {@code Double.POSITIVE_INFINITY} is returned.
*
* @param n Argument.
* @return {@code n!}
* @throws NotPositiveException if {@code n < 0}.
*/
public static double factorialDouble(final int n) throws NotPositiveException {
if (n < 0) {
throw new NotPositiveException(LocalizedFormats.FACTORIAL_NEGATIVE_PARAMETER,
n);
}
if (n < 21) {
return FACTORIALS[n];
}
return FastMath.floor(FastMath.exp(CombinatoricsUtils.factorialLog(n)) + 0.5);
}
/**
* Compute the natural logarithm of the factorial of {@code n}.
*
* @param n Argument.
* @return {@code n!}
* @throws NotPositiveException if {@code n < 0}.
*/
public static double factorialLog(final int n) throws NotPositiveException {
if (n < 0) {
throw new NotPositiveException(LocalizedFormats.FACTORIAL_NEGATIVE_PARAMETER,
n);
}
if (n < 21) {
return FastMath.log(FACTORIALS[n]);
}
double logSum = 0;
for (int i = 2; i <= n; i++) {
logSum += FastMath.log(i);
}
return logSum;
}
/**
* Returns the <a
* href="http://mathworld.wolfram.com/StirlingNumberoftheSecondKind.html">
* Stirling number of the second kind</a>, "{@code S(n,k)}", the number of
* ways of partitioning an {@code n}-element set into {@code k} non-empty
* subsets.
* <p>
* The preconditions are {@code 0 <= k <= n } (otherwise
* {@code NotPositiveException} is thrown)
* </p>
* @param n the size of the set
* @param k the number of non-empty subsets
* @return {@code S(n,k)}
* @throws NotPositiveException if {@code k < 0}.
* @throws NumberIsTooLargeException if {@code k > n}.
* @throws MathArithmeticException if some overflow happens, typically for n exceeding 25 and
* k between 20 and n-2 (S(n,n-1) is handled specifically and does not overflow)
* @since 3.1
*/
public static long stirlingS2(final int n, final int k)
throws NotPositiveException, NumberIsTooLargeException, MathArithmeticException {
if (k < 0) {
throw new NotPositiveException(k);
}
if (k > n) {
throw new NumberIsTooLargeException(k, n, true);
}
long[][] stirlingS2 = STIRLING_S2.get();
if (stirlingS2 == null) {
// the cache has never been initialized, compute the first numbers
// by direct recurrence relation
// as S(26,9) = 11201516780955125625 is larger than Long.MAX_VALUE
// we must stop computation at row 26
final int maxIndex = 26;
stirlingS2 = new long[maxIndex][];
stirlingS2[0] = new long[] { 1l };
for (int i = 1; i < stirlingS2.length; ++i) {
stirlingS2[i] = new long[i + 1];
stirlingS2[i][0] = 0;
stirlingS2[i][1] = 1;
stirlingS2[i][i] = 1;
for (int j = 2; j < i; ++j) {
stirlingS2[i][j] = j * stirlingS2[i - 1][j] + stirlingS2[i - 1][j - 1];
}
}
// atomically save the cache
STIRLING_S2.compareAndSet(null, stirlingS2);
}
if (n < stirlingS2.length) {
// the number is in the small cache
return stirlingS2[n][k];
} else {
// use explicit formula to compute the number without caching it
if (k == 0) {
return 0;
} else if (k == 1 || k == n) {
return 1;
} else if (k == 2) {
return (1l << (n - 1)) - 1l;
} else if (k == n - 1) {
return binomialCoefficient(n, 2);
} else {
// definition formula: note that this may trigger some overflow
long sum = 0;
long sign = ((k & 0x1) == 0) ? 1 : -1;
for (int j = 1; j <= k; ++j) {
sign = -sign;
sum += sign * binomialCoefficient(k, j) * ArithmeticUtils.pow(j, n);
if (sum < 0) {
// there was an overflow somewhere
throw new MathArithmeticException(LocalizedFormats.ARGUMENT_OUTSIDE_DOMAIN,
n, 0, stirlingS2.length - 1);
}
}
return sum / factorial(k);
}
}
}
/**
* Returns an Iterator whose range is the k-element subsets of {0, ..., n - 1}
* represented as {@code int[]} arrays.
* <p>
* The arrays returned by the iterator are sorted in descending order and
* they are visited in lexicographic order with significance from right to
* left. For example, combinationsIterator(4, 2) returns an Iterator that
* will generate the following sequence of arrays on successive calls to
* {@code next()}:<br/>
* {@code [0, 1], [0, 2], [1, 2], [0, 3], [1, 3], [2, 3]}
* </p>
* If {@code k == 0} an Iterator containing an empty array is returned and
* if {@code k == n} an Iterator containing [0, ..., n -1] is returned.
*
* @param n size of the set from which subsets are selected
* @param k size of the subsets to be enumerated
* @return an Iterator over the k-sets in n
* @throws NotPositiveException if {@code n < 0}.
* @throws NumberIsTooLargeException if {@code k > n}.
*/
public static Iterator<int[]> combinationsIterator(int n, int k) {
checkBinomial(n, k);
if (k == 0) {
return new SingletonIterator(new int[]{});
}
if (k == n) {
// TODO: once getNatural is extracted from RandomDataGenerator, use it
final int[] natural = new int[n];
for (int i = 0; i < n; i++) {
natural[i] = i;
}
return new SingletonIterator(natural);
}
return new LexicographicCombinationIterator(n, k);
}
/**
* Lexicographic combinations iterator.
* <p>
* Implementation follows Algorithm T in <i>The Art of Computer Programming</i>
* Internet Draft (PRE-FASCICLE 3A), "A Draft of Section 7.2.1.3 Generating All
* Combinations</a>, D. Knuth, 2004.</p>
* <p>
* The degenerate cases {@code k == 0} and {@code k == n} are NOT handled by this
* implementation. If constructor arguments satisfy {@code k == 0}
* or {@code k >= n}, no exception is generated, but the iterator is empty.
* </p>
*
*/
private static class LexicographicCombinationIterator implements Iterator<int[]> {
/** Size of subsets returned by the iterator */
private final int k;
/**
* c[1], ..., c[k] stores the next combination; c[k + 1], c[k + 2] are
* sentinels.
* <p>
* Note that c[0] is "wasted" but this makes it a little easier to
* follow the code.
* </p>
*/
private final int[] c;
/** Return value for {@link #hasNext()} */
private boolean more = true;
/** Marker: smallest index such that c[j + 1] > j */
private int j;
/**
* Construct a CombinationIterator to enumerate k-sets from n.
* <p>
* NOTE: If {@code k === 0} or {@code k >= n}, the Iterator will be empty
* (that is, {@link #hasNext()} will return {@code false} immediately.
* </p>
*
* @param n size of the set from which subsets are enumerated
* @param k size of the subsets to enumerate
*/
public LexicographicCombinationIterator(int n, int k) {
this.k = k;
c = new int[k + 3];
if (k == 0 || k >= n) {
more = false;
return;
}
// Initialize c to start with lexicographically first k-set
for (int i = 1; i <= k; i++) {
c[i] = i - 1;
}
// Initialize sentinels
c[k + 1] = n;
c[k + 2] = 0;
j = k; // Set up invariant: j is smallest index such that c[j + 1] > j
}
/**
* {@inheritDoc}
*/
public boolean hasNext() {
return more;
}
/**
* {@inheritDoc}
*/
public int[] next() {
if (!more) {
throw new NoSuchElementException();
}
// Copy return value (prepared by last activation)
final int[] ret = new int[k];
System.arraycopy(c, 1, ret, 0, k);
//final int[] ret = MathArrays.copyOf(c, k + 1);
// Prepare next iteration
// T2 and T6 loop
int x = 0;
if (j > 0) {
x = j;
c[j] = x;
j--;
return ret;
}
// T3
if (c[1] + 1 < c[2]) {
c[1] = c[1] + 1;
return ret;
} else {
j = 2;
}
// T4
boolean stepDone = false;
while (!stepDone) {
c[j - 1] = j - 2;
x = c[j] + 1;
if (x == c[j + 1]) {
j++;
} else {
stepDone = true;
}
}
// T5
if (j > k) {
more = false;
return ret;
}
// T6
c[j] = x;
j--;
return ret;
}
/**
* Not supported.
*/
public void remove() {
throw new UnsupportedOperationException();
}
}
/**
* Iterator with just one element to handle degenerate cases (full array,
* empty array) for combination iterator.
*/
private static class SingletonIterator implements Iterator<int[]> {
/** Singleton array */
private final int[] singleton;
/** True on initialization, false after first call to next */
private boolean more = true;
/**
* Create a singleton iterator providing the given array.
* @param singleton array returned by the iterator
*/
public SingletonIterator(final int[] singleton) {
this.singleton = singleton;
}
/** @return True until next is called the first time, then false */
public boolean hasNext() {
return more;
}
/** @return the singleton in first activation; throws NSEE thereafter */
public int[] next() {
if (more) {
more = false;
return singleton;
} else {
throw new NoSuchElementException();
}
}
/** Not supported */
public void remove() {
throw new UnsupportedOperationException();
}
}
/**
* Check binomial preconditions.
*
* @param n Size of the set.
* @param k Size of the subsets to be counted.
* @throws NotPositiveException if {@code n < 0}.
* @throws NumberIsTooLargeException if {@code k > n}.
*/
private static void checkBinomial(final int n, final int k) throws NumberIsTooLargeException, NotPositiveException {
if (n < k) {
throw new NumberIsTooLargeException(LocalizedFormats.BINOMIAL_INVALID_PARAMETERS_ORDER,
k, n, true);
}
if (n < 0) {
throw new NotPositiveException(LocalizedFormats.BINOMIAL_NEGATIVE_PARAMETER, n);
}
}
}

4
src/test/java/org/apache/commons/math3/analysis/differentiation/DSCompilerTest.java
View File

@ -22,7 +22,7 @@ import java.util.HashMap;
import java.util.Map;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.util.ArithmeticUtils;
import org.apache.commons.math3.util.CombinatoricsUtils;
import org.junit.Assert;
import org.junit.Test;
@ -36,7 +36,7 @@ public class DSCompilerTest {
public void testSize() {
for (int i = 0; i < 6; ++i) {
for (int j = 0; j < 6; ++j) {
long expected = ArithmeticUtils.binomialCoefficient(i + j, i);
long expected = CombinatoricsUtils.binomialCoefficient(i + j, i);
Assert.assertEquals(expected, DSCompiler.getCompiler(i, j).getSize());
Assert.assertEquals(expected, DSCompiler.getCompiler(j, i).getSize());
}

5
src/test/java/org/apache/commons/math3/analysis/differentiation/DerivativeStructureTest.java
View File

@ -27,6 +27,7 @@ import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.NumberIsTooLargeException;
import org.apache.commons.math3.random.Well1024a;
import org.apache.commons.math3.util.ArithmeticUtils;
import org.apache.commons.math3.util.CombinatoricsUtils;
import org.apache.commons.math3.util.FastMath;
import org.junit.Assert;
import org.junit.Test;
@ -175,7 +176,7 @@ public class DerivativeStructureTest extends ExtendedFieldElementAbstractTest<De
DerivativeStructure r = new DerivativeStructure(1, 6, 0, x).reciprocal();
Assert.assertEquals(1 / x, r.getValue(), 1.0e-15);
for (int i = 1; i < r.getOrder(); ++i) {
double expected = ArithmeticUtils.pow(-1, i) * ArithmeticUtils.factorial(i) /
double expected = ArithmeticUtils.pow(-1, i) * CombinatoricsUtils.factorial(i) /
FastMath.pow(x, i + 1);
Assert.assertEquals(expected, r.getPartialDerivative(i), 1.0e-15 * FastMath.abs(expected));
}
@ -651,7 +652,7 @@ public class DerivativeStructureTest extends ExtendedFieldElementAbstractTest<De
DerivativeStructure log = new DerivativeStructure(1, maxOrder, 0, x).log();
Assert.assertEquals(FastMath.log(x), log.getValue(), epsilon[0]);
for (int n = 1; n <= maxOrder; ++n) {
double refDer = -ArithmeticUtils.factorial(n - 1) / FastMath.pow(-x, n);
double refDer = -CombinatoricsUtils.factorial(n - 1) / FastMath.pow(-x, n);
Assert.assertEquals(refDer, log.getPartialDerivative(n), epsilon[n]);
}
}

4
src/test/java/org/apache/commons/math3/analysis/polynomials/PolynomialsUtilsTest.java
View File

@ -18,7 +18,7 @@ package org.apache.commons.math3.analysis.polynomials;
import org.apache.commons.math3.analysis.UnivariateFunction;
import org.apache.commons.math3.analysis.integration.IterativeLegendreGaussIntegrator;
import org.apache.commons.math3.util.ArithmeticUtils;
import org.apache.commons.math3.util.CombinatoricsUtils;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.Precision;
import org.junit.Assert;
@ -289,7 +289,7 @@ public class PolynomialsUtilsTest {
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);
double binomial = CombinatoricsUtils.binomialCoefficient(v + i, i);
Assert.assertTrue(Precision.equals(binomial, jacobi.value(1.0), 1));
}
}

7
src/test/java/org/apache/commons/math3/linear/InverseHilbertMatrix.java
View File

@ -18,6 +18,7 @@ package org.apache.commons.math3.linear;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.util.ArithmeticUtils;
import org.apache.commons.math3.util.CombinatoricsUtils;
/**
* This class implements inverses of Hilbert Matrices as
@ -54,11 +55,11 @@ public class InverseHilbertMatrix
*/
public long getEntry(final int i, final int j) {
long val = i + j + 1;
long aux = ArithmeticUtils.binomialCoefficient(n + i, n - j - 1);
long aux = CombinatoricsUtils.binomialCoefficient(n + i, n - j - 1);
val = ArithmeticUtils.mulAndCheck(val, aux);
aux = ArithmeticUtils.binomialCoefficient(n + j, n - i - 1);
aux = CombinatoricsUtils.binomialCoefficient(n + j, n - i - 1);
val = ArithmeticUtils.mulAndCheck(val, aux);
aux = ArithmeticUtils.binomialCoefficient(i + j, i);
aux = CombinatoricsUtils.binomialCoefficient(i + j, i);
val = ArithmeticUtils.mulAndCheck(val, aux);
val = ArithmeticUtils.mulAndCheck(val, aux);
return ((i + j) & 1) == 0 ? val : -val;

332
src/test/java/org/apache/commons/math3/util/ArithmeticUtilsTest.java
View File

@ -18,16 +18,11 @@ package org.apache.commons.math3.util;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.math.BigInteger;
import org.apache.commons.math3.exception.MathArithmeticException;
import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.exception.NotPositiveException;
import org.apache.commons.math3.exception.NumberIsTooLargeException;
import org.apache.commons.math3.random.RandomDataImpl;
import org.apache.commons.math3.random.RandomDataGenerator;
import org.junit.Assert;
import org.junit.Test;
@ -38,17 +33,6 @@ import org.junit.Test;
*/
public class ArithmeticUtilsTest {
/** cached binomial coefficients */
private static final List<Map<Integer, Long>> binomialCache = new ArrayList<Map<Integer, Long>>();
/** Verify that b(0,0) = 1 */
@Test
public void test0Choose0() {
Assert.assertEquals(ArithmeticUtils.binomialCoefficientDouble(0, 0), 1d, 0);
Assert.assertEquals(ArithmeticUtils.binomialCoefficientLog(0, 0), 0d, 0);
Assert.assertEquals(ArithmeticUtils.binomialCoefficient(0, 0), 1);
}
@Test
public void testAddAndCheck() {
int big = Integer.MAX_VALUE;
@ -84,214 +68,6 @@ public class ArithmeticUtilsTest {
testAddAndCheckLongFailure(-1L, min);
}
@Test
public void testBinomialCoefficient() {
long[] bcoef5 = {
1,
5,
10,
10,
5,
1 };
long[] bcoef6 = {
1,
6,
15,
20,
15,
6,
1 };
for (int i = 0; i < 6; i++) {
Assert.assertEquals("5 choose " + i, bcoef5[i], ArithmeticUtils.binomialCoefficient(5, i));
}
for (int i = 0; i < 7; i++) {
Assert.assertEquals("6 choose " + i, bcoef6[i], ArithmeticUtils.binomialCoefficient(6, i));
}
for (int n = 1; n < 10; n++) {
for (int k = 0; k <= n; k++) {
Assert.assertEquals(n + " choose " + k, binomialCoefficient(n, k), ArithmeticUtils.binomialCoefficient(n, k));
Assert.assertEquals(n + " choose " + k, binomialCoefficient(n, k), ArithmeticUtils.binomialCoefficientDouble(n, k), Double.MIN_VALUE);
Assert.assertEquals(n + " choose " + k, FastMath.log(binomialCoefficient(n, k)), ArithmeticUtils.binomialCoefficientLog(n, k), 10E-12);
}
}
int[] n = { 34, 66, 100, 1500, 1500 };
int[] k = { 17, 33, 10, 1500 - 4, 4 };
for (int i = 0; i < n.length; i++) {
long expected = binomialCoefficient(n[i], k[i]);
Assert.assertEquals(n[i] + " choose " + k[i], expected,
ArithmeticUtils.binomialCoefficient(n[i], k[i]));
Assert.assertEquals(n[i] + " choose " + k[i], expected,
ArithmeticUtils.binomialCoefficientDouble(n[i], k[i]), 0.0);
Assert.assertEquals("log(" + n[i] + " choose " + k[i] + ")", FastMath.log(expected),
ArithmeticUtils.binomialCoefficientLog(n[i], k[i]), 0.0);
}
}
@Test
public void testBinomialCoefficientFail() {
try {
ArithmeticUtils.binomialCoefficient(4, 5);
Assert.fail("expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// ignored
}
try {
ArithmeticUtils.binomialCoefficientDouble(4, 5);
Assert.fail("expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// ignored
}
try {
ArithmeticUtils.binomialCoefficientLog(4, 5);
Assert.fail("expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// ignored
}
try {
ArithmeticUtils.binomialCoefficient(-1, -2);
Assert.fail("expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// ignored
}
try {
ArithmeticUtils.binomialCoefficientDouble(-1, -2);
Assert.fail("expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// ignored
}
try {
ArithmeticUtils.binomialCoefficientLog(-1, -2);
Assert.fail("expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// ignored
}
try {
ArithmeticUtils.binomialCoefficient(67, 30);
Assert.fail("expecting MathArithmeticException");
} catch (MathArithmeticException ex) {
// ignored
}
try {
ArithmeticUtils.binomialCoefficient(67, 34);
Assert.fail("expecting MathArithmeticException");
} catch (MathArithmeticException ex) {
// ignored
}
double x = ArithmeticUtils.binomialCoefficientDouble(1030, 515);
Assert.assertTrue("expecting infinite binomial coefficient", Double
.isInfinite(x));
}
/**
* Tests correctness for large n and sharpness of upper bound in API doc
* JIRA: MATH-241
*/
@Test
public void testBinomialCoefficientLarge() throws Exception {
// This tests all legal and illegal values for n <= 200.
for (int n = 0; n <= 200; n++) {
for (int k = 0; k <= n; k++) {
long ourResult = -1;
long exactResult = -1;
boolean shouldThrow = false;
boolean didThrow = false;
try {
ourResult = ArithmeticUtils.binomialCoefficient(n, k);
} catch (MathArithmeticException ex) {
didThrow = true;
}
try {
exactResult = binomialCoefficient(n, k);
} catch (MathArithmeticException ex) {
shouldThrow = true;
}
Assert.assertEquals(n + " choose " + k, exactResult, ourResult);
Assert.assertEquals(n + " choose " + k, shouldThrow, didThrow);
Assert.assertTrue(n + " choose " + k, (n > 66 || !didThrow));
if (!shouldThrow && exactResult > 1) {
Assert.assertEquals(n + " choose " + k, 1.,
ArithmeticUtils.binomialCoefficientDouble(n, k) / exactResult, 1e-10);
Assert.assertEquals(n + " choose " + k, 1,
ArithmeticUtils.binomialCoefficientLog(n, k) / FastMath.log(exactResult), 1e-10);
}
}
}
long ourResult = ArithmeticUtils.binomialCoefficient(300, 3);
long exactResult = binomialCoefficient(300, 3);
Assert.assertEquals(exactResult, ourResult);
ourResult = ArithmeticUtils.binomialCoefficient(700, 697);
exactResult = binomialCoefficient(700, 697);
Assert.assertEquals(exactResult, ourResult);
// This one should throw
try {
ArithmeticUtils.binomialCoefficient(700, 300);
Assert.fail("Expecting MathArithmeticException");
} catch (MathArithmeticException ex) {
// Expected
}
int n = 10000;
ourResult = ArithmeticUtils.binomialCoefficient(n, 3);
exactResult = binomialCoefficient(n, 3);
Assert.assertEquals(exactResult, ourResult);
Assert.assertEquals(1, ArithmeticUtils.binomialCoefficientDouble(n, 3) / exactResult, 1e-10);
Assert.assertEquals(1, ArithmeticUtils.binomialCoefficientLog(n, 3) / FastMath.log(exactResult), 1e-10);
}
@Test
public void testFactorial() {
for (int i = 1; i < 21; i++) {
Assert.assertEquals(i + "! ", factorial(i), ArithmeticUtils.factorial(i));
Assert.assertEquals(i + "! ", factorial(i), ArithmeticUtils.factorialDouble(i), Double.MIN_VALUE);
Assert.assertEquals(i + "! ", FastMath.log(factorial(i)), ArithmeticUtils.factorialLog(i), 10E-12);
}
Assert.assertEquals("0", 1, ArithmeticUtils.factorial(0));
Assert.assertEquals("0", 1.0d, ArithmeticUtils.factorialDouble(0), 1E-14);
Assert.assertEquals("0", 0.0d, ArithmeticUtils.factorialLog(0), 1E-14);
}
@Test
public void testFactorialFail() {
try {
ArithmeticUtils.factorial(-1);
Assert.fail("expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// ignored
}
try {
ArithmeticUtils.factorialDouble(-1);
Assert.fail("expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// ignored
}
try {
ArithmeticUtils.factorialLog(-1);
Assert.fail("expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// ignored
}
try {
ArithmeticUtils.factorial(21);
Assert.fail("expecting MathArithmeticException");
} catch (MathArithmeticException ex) {
// ignored
}
Assert.assertTrue("expecting infinite factorial value", Double.isInfinite(ArithmeticUtils.factorialDouble(171)));
}
@Test
public void testGcd() {
int a = 30;
@ -350,7 +126,7 @@ public class ArithmeticUtilsTest {
for (int i = 0; i < primeList.length; i++) {
primes.add(Integer.valueOf(primeList[i]));
}
RandomDataImpl randomData = new RandomDataImpl();
RandomDataGenerator randomData = new RandomDataGenerator();
for (int i = 0; i < 20; i++) {
Object[] sample = randomData.nextSample(primes, 4);
int p1 = ((Integer) sample[0]).intValue();
@ -695,110 +471,6 @@ public class ArithmeticUtilsTest {
}
}
@Test
public void testStirlingS2() {
Assert.assertEquals(1, ArithmeticUtils.stirlingS2(0, 0));
for (int n = 1; n < 30; ++n) {
Assert.assertEquals(0, ArithmeticUtils.stirlingS2(n, 0));
Assert.assertEquals(1, ArithmeticUtils.stirlingS2(n, 1));
if (n > 2) {
Assert.assertEquals((1l << (n - 1)) - 1l, ArithmeticUtils.stirlingS2(n, 2));
Assert.assertEquals(ArithmeticUtils.binomialCoefficient(n, 2),
ArithmeticUtils.stirlingS2(n, n - 1));
}
Assert.assertEquals(1, ArithmeticUtils.stirlingS2(n, n));
}
Assert.assertEquals(536870911l, ArithmeticUtils.stirlingS2(30, 2));
Assert.assertEquals(576460752303423487l, ArithmeticUtils.stirlingS2(60, 2));
Assert.assertEquals( 25, ArithmeticUtils.stirlingS2( 5, 3));
Assert.assertEquals( 90, ArithmeticUtils.stirlingS2( 6, 3));
Assert.assertEquals( 65, ArithmeticUtils.stirlingS2( 6, 4));
Assert.assertEquals( 301, ArithmeticUtils.stirlingS2( 7, 3));
Assert.assertEquals( 350, ArithmeticUtils.stirlingS2( 7, 4));
Assert.assertEquals( 140, ArithmeticUtils.stirlingS2( 7, 5));
Assert.assertEquals( 966, ArithmeticUtils.stirlingS2( 8, 3));
Assert.assertEquals( 1701, ArithmeticUtils.stirlingS2( 8, 4));
Assert.assertEquals( 1050, ArithmeticUtils.stirlingS2( 8, 5));
Assert.assertEquals( 266, ArithmeticUtils.stirlingS2( 8, 6));
Assert.assertEquals( 3025, ArithmeticUtils.stirlingS2( 9, 3));
Assert.assertEquals( 7770, ArithmeticUtils.stirlingS2( 9, 4));
Assert.assertEquals( 6951, ArithmeticUtils.stirlingS2( 9, 5));
Assert.assertEquals( 2646, ArithmeticUtils.stirlingS2( 9, 6));
Assert.assertEquals( 462, ArithmeticUtils.stirlingS2( 9, 7));
Assert.assertEquals( 9330, ArithmeticUtils.stirlingS2(10, 3));
Assert.assertEquals(34105, ArithmeticUtils.stirlingS2(10, 4));
Assert.assertEquals(42525, ArithmeticUtils.stirlingS2(10, 5));
Assert.assertEquals(22827, ArithmeticUtils.stirlingS2(10, 6));
Assert.assertEquals( 5880, ArithmeticUtils.stirlingS2(10, 7));
Assert.assertEquals( 750, ArithmeticUtils.stirlingS2(10, 8));
}
@Test(expected=NotPositiveException.class)
public void testStirlingS2NegativeN() {
ArithmeticUtils.stirlingS2(3, -1);
}
@Test(expected=NumberIsTooLargeException.class)
public void testStirlingS2LargeK() {
ArithmeticUtils.stirlingS2(3, 4);
}
@Test(expected=MathArithmeticException.class)
public void testStirlingS2Overflow() {
ArithmeticUtils.stirlingS2(26, 9);
}
/**
* Exact (caching) recursive implementation to test against
*/
private long binomialCoefficient(int n, int k) throws MathArithmeticException {
if (binomialCache.size() > n) {
Long cachedResult = binomialCache.get(n).get(Integer.valueOf(k));
if (cachedResult != null) {
return cachedResult.longValue();
}
}
long result = -1;
if ((n == k) || (k == 0)) {
result = 1;
} else if ((k == 1) || (k == n - 1)) {
result = n;
} else {
// Reduce stack depth for larger values of n
if (k < n - 100) {
binomialCoefficient(n - 100, k);
}
if (k > 100) {
binomialCoefficient(n - 100, k - 100);
}
result = ArithmeticUtils.addAndCheck(binomialCoefficient(n - 1, k - 1),
binomialCoefficient(n - 1, k));
}
if (result == -1) {
throw new MathArithmeticException();
}
for (int i = binomialCache.size(); i < n + 1; i++) {
binomialCache.add(new HashMap<Integer, Long>());
}
binomialCache.get(n).put(Integer.valueOf(k), Long.valueOf(result));
return result;
}
/**
* Exact direct multiplication implementation to test against
*/
private long factorial(int n) {
long result = 1;
for (int i = 2; i <= n; i++) {
result *= i;
}
return result;
}
private void testAddAndCheckLongFailure(long a, long b) {
try {
ArithmeticUtils.addAndCheck(a, b);

443
src/test/java/org/apache/commons/math3/util/CombinatoricsUtilsTest.java Normal file
View File

@ -0,0 +1,443 @@
/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math3.util;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.Iterator;
import java.util.List;
import java.util.Map;
import org.apache.commons.math3.exception.MathArithmeticException;
import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.exception.NotPositiveException;
import org.apache.commons.math3.exception.NumberIsTooLargeException;
import org.junit.Assert;
import org.junit.Test;
/**
* Test cases for the {@link CombinatoricsUtils} class.
*
* @version $Id: $
*/
public class CombinatoricsUtilsTest {
/** cached binomial coefficients */
private static final List<Map<Integer, Long>> binomialCache = new ArrayList<Map<Integer, Long>>();
/** Verify that b(0,0) = 1 */
@Test
public void test0Choose0() {
Assert.assertEquals(CombinatoricsUtils.binomialCoefficientDouble(0, 0), 1d, 0);
Assert.assertEquals(CombinatoricsUtils.binomialCoefficientLog(0, 0), 0d, 0);
Assert.assertEquals(CombinatoricsUtils.binomialCoefficient(0, 0), 1);
}
@Test
public void testBinomialCoefficient() {
long[] bcoef5 = {
1,
5,
10,
10,
5,
1 };
long[] bcoef6 = {
1,
6,
15,
20,
15,
6,
1 };
for (int i = 0; i < 6; i++) {
Assert.assertEquals("5 choose " + i, bcoef5[i], CombinatoricsUtils.binomialCoefficient(5, i));
}
for (int i = 0; i < 7; i++) {
Assert.assertEquals("6 choose " + i, bcoef6[i], CombinatoricsUtils.binomialCoefficient(6, i));
}
for (int n = 1; n < 10; n++) {
for (int k = 0; k <= n; k++) {
Assert.assertEquals(n + " choose " + k, binomialCoefficient(n, k), CombinatoricsUtils.binomialCoefficient(n, k));
Assert.assertEquals(n + " choose " + k, binomialCoefficient(n, k), CombinatoricsUtils.binomialCoefficientDouble(n, k), Double.MIN_VALUE);
Assert.assertEquals(n + " choose " + k, FastMath.log(binomialCoefficient(n, k)), CombinatoricsUtils.binomialCoefficientLog(n, k), 10E-12);
}
}
int[] n = { 34, 66, 100, 1500, 1500 };
int[] k = { 17, 33, 10, 1500 - 4, 4 };
for (int i = 0; i < n.length; i++) {
long expected = binomialCoefficient(n[i], k[i]);
Assert.assertEquals(n[i] + " choose " + k[i], expected,
CombinatoricsUtils.binomialCoefficient(n[i], k[i]));
Assert.assertEquals(n[i] + " choose " + k[i], expected,
CombinatoricsUtils.binomialCoefficientDouble(n[i], k[i]), 0.0);
Assert.assertEquals("log(" + n[i] + " choose " + k[i] + ")", FastMath.log(expected),
CombinatoricsUtils.binomialCoefficientLog(n[i], k[i]), 0.0);
}
}
@Test
public void testBinomialCoefficientFail() {
try {
CombinatoricsUtils.binomialCoefficient(4, 5);
Assert.fail("expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// ignored
}
try {
CombinatoricsUtils.binomialCoefficientDouble(4, 5);
Assert.fail("expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// ignored
}
try {
CombinatoricsUtils.binomialCoefficientLog(4, 5);
Assert.fail("expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// ignored
}
try {
CombinatoricsUtils.binomialCoefficient(-1, -2);
Assert.fail("expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// ignored
}
try {
CombinatoricsUtils.binomialCoefficientDouble(-1, -2);
Assert.fail("expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// ignored
}
try {
CombinatoricsUtils.binomialCoefficientLog(-1, -2);
Assert.fail("expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// ignored
}
try {
CombinatoricsUtils.binomialCoefficient(67, 30);
Assert.fail("expecting MathArithmeticException");
} catch (MathArithmeticException ex) {
// ignored
}
try {
CombinatoricsUtils.binomialCoefficient(67, 34);
Assert.fail("expecting MathArithmeticException");
} catch (MathArithmeticException ex) {
// ignored
}
double x = CombinatoricsUtils.binomialCoefficientDouble(1030, 515);
Assert.assertTrue("expecting infinite binomial coefficient", Double
.isInfinite(x));
}
/**
* Tests correctness for large n and sharpness of upper bound in API doc
* JIRA: MATH-241
*/
@Test
public void testBinomialCoefficientLarge() throws Exception {
// This tests all legal and illegal values for n <= 200.
for (int n = 0; n <= 200; n++) {
for (int k = 0; k <= n; k++) {
long ourResult = -1;
long exactResult = -1;
boolean shouldThrow = false;
boolean didThrow = false;
try {
ourResult = CombinatoricsUtils.binomialCoefficient(n, k);
} catch (MathArithmeticException ex) {
didThrow = true;
}
try {
exactResult = binomialCoefficient(n, k);
} catch (MathArithmeticException ex) {
shouldThrow = true;
}
Assert.assertEquals(n + " choose " + k, exactResult, ourResult);
Assert.assertEquals(n + " choose " + k, shouldThrow, didThrow);
Assert.assertTrue(n + " choose " + k, (n > 66 || !didThrow));
if (!shouldThrow && exactResult > 1) {
Assert.assertEquals(n + " choose " + k, 1.,
CombinatoricsUtils.binomialCoefficientDouble(n, k) / exactResult, 1e-10);
Assert.assertEquals(n + " choose " + k, 1,
CombinatoricsUtils.binomialCoefficientLog(n, k) / FastMath.log(exactResult), 1e-10);
}
}
}
long ourResult = CombinatoricsUtils.binomialCoefficient(300, 3);
long exactResult = binomialCoefficient(300, 3);
Assert.assertEquals(exactResult, ourResult);
ourResult = CombinatoricsUtils.binomialCoefficient(700, 697);
exactResult = binomialCoefficient(700, 697);
Assert.assertEquals(exactResult, ourResult);
// This one should throw
try {
CombinatoricsUtils.binomialCoefficient(700, 300);
Assert.fail("Expecting MathArithmeticException");
} catch (MathArithmeticException ex) {
// Expected
}
int n = 10000;
ourResult = CombinatoricsUtils.binomialCoefficient(n, 3);
exactResult = binomialCoefficient(n, 3);
Assert.assertEquals(exactResult, ourResult);
Assert.assertEquals(1, CombinatoricsUtils.binomialCoefficientDouble(n, 3) / exactResult, 1e-10);
Assert.assertEquals(1, CombinatoricsUtils.binomialCoefficientLog(n, 3) / FastMath.log(exactResult), 1e-10);
}
@Test
public void testFactorial() {
for (int i = 1; i < 21; i++) {
Assert.assertEquals(i + "! ", factorial(i), CombinatoricsUtils.factorial(i));
Assert.assertEquals(i + "! ", factorial(i), CombinatoricsUtils.factorialDouble(i), Double.MIN_VALUE);
Assert.assertEquals(i + "! ", FastMath.log(factorial(i)), CombinatoricsUtils.factorialLog(i), 10E-12);
}
Assert.assertEquals("0", 1, CombinatoricsUtils.factorial(0));
Assert.assertEquals("0", 1.0d, CombinatoricsUtils.factorialDouble(0), 1E-14);
Assert.assertEquals("0", 0.0d, CombinatoricsUtils.factorialLog(0), 1E-14);
}
@Test
public void testFactorialFail() {
try {
CombinatoricsUtils.factorial(-1);
Assert.fail("expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// ignored
}
try {
CombinatoricsUtils.factorialDouble(-1);
Assert.fail("expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// ignored
}
try {
CombinatoricsUtils.factorialLog(-1);
Assert.fail("expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// ignored
}
try {
CombinatoricsUtils.factorial(21);
Assert.fail("expecting MathArithmeticException");
} catch (MathArithmeticException ex) {
// ignored
}
Assert.assertTrue("expecting infinite factorial value", Double.isInfinite(CombinatoricsUtils.factorialDouble(171)));
}
@Test
public void testStirlingS2() {
Assert.assertEquals(1, CombinatoricsUtils.stirlingS2(0, 0));
for (int n = 1; n < 30; ++n) {
Assert.assertEquals(0, CombinatoricsUtils.stirlingS2(n, 0));
Assert.assertEquals(1, CombinatoricsUtils.stirlingS2(n, 1));
if (n > 2) {
Assert.assertEquals((1l << (n - 1)) - 1l, CombinatoricsUtils.stirlingS2(n, 2));
Assert.assertEquals(CombinatoricsUtils.binomialCoefficient(n, 2),
CombinatoricsUtils.stirlingS2(n, n - 1));
}
Assert.assertEquals(1, CombinatoricsUtils.stirlingS2(n, n));
}
Assert.assertEquals(536870911l, CombinatoricsUtils.stirlingS2(30, 2));
Assert.assertEquals(576460752303423487l, CombinatoricsUtils.stirlingS2(60, 2));
Assert.assertEquals( 25, CombinatoricsUtils.stirlingS2( 5, 3));
Assert.assertEquals( 90, CombinatoricsUtils.stirlingS2( 6, 3));
Assert.assertEquals( 65, CombinatoricsUtils.stirlingS2( 6, 4));
Assert.assertEquals( 301, CombinatoricsUtils.stirlingS2( 7, 3));
Assert.assertEquals( 350, CombinatoricsUtils.stirlingS2( 7, 4));
Assert.assertEquals( 140, CombinatoricsUtils.stirlingS2( 7, 5));
Assert.assertEquals( 966, CombinatoricsUtils.stirlingS2( 8, 3));
Assert.assertEquals( 1701, CombinatoricsUtils.stirlingS2( 8, 4));
Assert.assertEquals( 1050, CombinatoricsUtils.stirlingS2( 8, 5));
Assert.assertEquals( 266, CombinatoricsUtils.stirlingS2( 8, 6));
Assert.assertEquals( 3025, CombinatoricsUtils.stirlingS2( 9, 3));
Assert.assertEquals( 7770, CombinatoricsUtils.stirlingS2( 9, 4));
Assert.assertEquals( 6951, CombinatoricsUtils.stirlingS2( 9, 5));
Assert.assertEquals( 2646, CombinatoricsUtils.stirlingS2( 9, 6));
Assert.assertEquals( 462, CombinatoricsUtils.stirlingS2( 9, 7));
Assert.assertEquals( 9330, CombinatoricsUtils.stirlingS2(10, 3));
Assert.assertEquals(34105, CombinatoricsUtils.stirlingS2(10, 4));
Assert.assertEquals(42525, CombinatoricsUtils.stirlingS2(10, 5));
Assert.assertEquals(22827, CombinatoricsUtils.stirlingS2(10, 6));
Assert.assertEquals( 5880, CombinatoricsUtils.stirlingS2(10, 7));
Assert.assertEquals( 750, CombinatoricsUtils.stirlingS2(10, 8));
}
@Test(expected=NotPositiveException.class)
public void testStirlingS2NegativeN() {
CombinatoricsUtils.stirlingS2(3, -1);
}
@Test(expected=NumberIsTooLargeException.class)
public void testStirlingS2LargeK() {
CombinatoricsUtils.stirlingS2(3, 4);
}
@Test(expected=MathArithmeticException.class)
public void testStirlingS2Overflow() {
CombinatoricsUtils.stirlingS2(26, 9);
}
/**
* Exact (caching) recursive implementation to test against
*/
private long binomialCoefficient(int n, int k) throws MathArithmeticException {
if (binomialCache.size() > n) {
Long cachedResult = binomialCache.get(n).get(Integer.valueOf(k));
if (cachedResult != null) {
return cachedResult.longValue();
}
}
long result = -1;
if ((n == k) || (k == 0)) {
result = 1;
} else if ((k == 1) || (k == n - 1)) {
result = n;
} else {
// Reduce stack depth for larger values of n
if (k < n - 100) {
binomialCoefficient(n - 100, k);
}
if (k > 100) {
binomialCoefficient(n - 100, k - 100);
}
result = ArithmeticUtils.addAndCheck(binomialCoefficient(n - 1, k - 1),
binomialCoefficient(n - 1, k));
}
if (result == -1) {
throw new MathArithmeticException();
}
for (int i = binomialCache.size(); i < n + 1; i++) {
binomialCache.add(new HashMap<Integer, Long>());
}
binomialCache.get(n).put(Integer.valueOf(k), Long.valueOf(result));
return result;
}
/**
* Exact direct multiplication implementation to test against
*/
private long factorial(int n) {
long result = 1;
for (int i = 2; i <= n; i++) {
result *= i;
}
return result;
}
@Test
public void testCombinationsIterator() {
Iterator<int[]> combinationsIterator = CombinatoricsUtils.combinationsIterator(5, 3);
checkIterator(combinationsIterator, 5, 3);
combinationsIterator = CombinatoricsUtils.combinationsIterator(6, 4);
checkIterator(combinationsIterator, 6, 4);
combinationsIterator = CombinatoricsUtils.combinationsIterator(8, 2);
checkIterator(combinationsIterator, 8, 2);
combinationsIterator = CombinatoricsUtils.combinationsIterator(6, 1);
checkIterator(combinationsIterator, 6, 1);
combinationsIterator = CombinatoricsUtils.combinationsIterator(3, 3);
checkIterator(combinationsIterator, 3, 3);
combinationsIterator = CombinatoricsUtils.combinationsIterator(1, 1);
checkIterator(combinationsIterator, 1, 1);
combinationsIterator = CombinatoricsUtils.combinationsIterator(1, 1);
checkIterator(combinationsIterator, 1, 1);
combinationsIterator = CombinatoricsUtils.combinationsIterator(1, 0);
checkIterator(combinationsIterator, 1, 0);
combinationsIterator = CombinatoricsUtils.combinationsIterator(0, 0);
checkIterator(combinationsIterator, 0, 0);
combinationsIterator = CombinatoricsUtils.combinationsIterator(4, 2);
}
/**
* Verifies that the iterator generates a lexicographically
* increasing sequence of b(n,k) arrays, each having length k
* and each array itself increasing.
*
* Note: the lexicographic order check only works for n < 10.
*
* @param iterator
* @param n size of universe
* @param k size of subsets
*/
private void checkIterator(Iterator<int[]> iterator, int n, int k) {
long lastLex = -1;
long length = 0;
while (iterator.hasNext()) {
final int[] iterate = iterator.next();
Assert.assertEquals(k, iterate.length);
final long curLex = lexNorm(iterate);
Assert.assertTrue(curLex > lastLex);
lastLex = curLex;
length++;
for (int i = 1; i < iterate.length; i++) {
Assert.assertTrue(iterate[i] > iterate[i - 1]);
}
}
Assert.assertEquals(CombinatoricsUtils.binomialCoefficient(n, k), length);
}
@Test
public void testCombinationsIteratorFail() {
try {
CombinatoricsUtils.combinationsIterator(4, 5);
Assert.fail("expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// ignored
}
try {
CombinatoricsUtils.combinationsIterator(-1, -2);
Assert.fail("expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// ignored
}
}
/**
* Returns the value represented by the digits in the input array in reverse order.
* For example [3,2,1] returns 123.
*
* @param iterate input array
* @return lexicographic norm
*/
private long lexNorm(int[] iterate) {
long ret = 0;
for (int i = iterate.length - 1; i >= 0; i--) {
ret += iterate[i] * ArithmeticUtils.pow(10l, (long) i);
}
return ret;
}
}

1
src/test/java/org/apache/commons/math3/util/MathArraysTest.java
View File

@ -14,6 +14,7 @@
package org.apache.commons.math3.util;
import java.util.Arrays;
import java.util.Iterator;
import org.apache.commons.math3.TestUtils;
import org.apache.commons.math3.exception.DimensionMismatchException;