public void BinomialCoefficientTest()
{
// n is negative
{
string STR_EXCEPT_PAR_MUST_BE_NON_NEGATIVE =
(string)Reflector.ExecuteStaticMember(
typeof(ImplementationServices),
"GetResourceString",
new string[] { "STR_EXCEPT_PAR_MUST_BE_NON_NEGATIVE" });
ArgumentExceptionAssert.Throw(
() =>
{
SpecialFunctions.BinomialCoefficient(
n: -1,
k: 0);
},
expectedType: typeof(ArgumentOutOfRangeException),
expectedPartialMessage: STR_EXCEPT_PAR_MUST_BE_NON_NEGATIVE,
expectedParameterName: "n");
}
// k is negative
{
string STR_EXCEPT_PAR_MUST_BE_NON_NEGATIVE =
(string)Reflector.ExecuteStaticMember(
typeof(ImplementationServices),
"GetResourceString",
new string[] { "STR_EXCEPT_PAR_MUST_BE_NON_NEGATIVE" });
ArgumentExceptionAssert.Throw(
() =>
{
SpecialFunctions.BinomialCoefficient(
n: 0,
k: -1);
},
expectedType: typeof(ArgumentOutOfRangeException),
expectedPartialMessage: STR_EXCEPT_PAR_MUST_BE_NON_NEGATIVE,
expectedParameterName: "k");
}
// n < k
{
string STR_EXCEPT_PAR_MUST_BE_NOT_GREATER_THAN_OTHER =
string.Format(
(string)Reflector.ExecuteStaticMember(
typeof(ImplementationServices),
"GetResourceString",
new string[] { "STR_EXCEPT_PAR_MUST_BE_NOT_GREATER_THAN_OTHER" }),
"k",
"n");
ArgumentExceptionAssert.Throw(
() =>
{
SpecialFunctions.BinomialCoefficient(
n: 3,
k: 4);
},
expectedType: typeof(ArgumentOutOfRangeException),
expectedPartialMessage: STR_EXCEPT_PAR_MUST_BE_NOT_GREATER_THAN_OTHER,
expectedParameterName: "k");
}
// valid input
{
var n = new int[]
{
0,
1,
2,
10,
20
};
var k = new int[]
{
0,
1,
2,
7,
8
};
var expected = new double[]
{
1.0,
1.0,
1.0,
120.0,
125970.0
};
var actual = new double[5];
for (int i = 0; i < n.Length; i++)
{
actual[i] =
SpecialFunctions.BinomialCoefficient(n[i], k[i]);
}
DoubleArrayAssert.AreEqual(
expected: expected,
actual: actual,
delta: 1e-8);
}
}
/// <summary>
/// Tests that method
/// <see cref="RandomSampling.NextDoubleMatrix"/>
/// terminates successfully as expected.
/// </summary>
/// <param name="testableRandomSampling">
/// The testable random sampling providing the instance
/// on which to invoke the methods to test and their expected
/// behaviors.
/// </param>
/// <param name="numberOfSamples">
/// The number of samples to draw.
/// </param>
/// <param name="delta">The required accuracy.
/// Defaults to <c>.01</c>.</param>
public static void Succeed(
TestableRandomSampling testableRandomSampling,
int numberOfSamples,
double delta = .01)
{
var randomSampling = testableRandomSampling.RandomSampling;
// Generate samples
var samples = DoubleMatrix.Dense(
numberOfSamples,
randomSampling.PopulationSize);
for (int i = 0; i < numberOfSamples; i++)
{
samples[i, ":"] = randomSampling.NextDoubleMatrix();
}
// Compute the actual inclusion probabilities
DoubleMatrix actualInclusionProbabilities =
DoubleMatrix.Dense(randomSampling.PopulationSize, 1);
var sampleIndexes = IndexCollection.Default(numberOfSamples - 1);
for (int j = 0; j < randomSampling.PopulationSize; j++)
{
var samplesContainingUnit =
IndexPartition.Create(
sampleIndexes,
(i) => { return(samples[i, j] == 1.0); });
actualInclusionProbabilities[j] =
(double)samplesContainingUnit[true].Count
/
(double)numberOfSamples;
}
// Check the number of distinct generated samples
var distinctSamples =
IndexPartition.Create(samples.AsRowCollection());
int numberOfDistinctSamples =
distinctSamples.Count;
Assert.AreEqual(
SpecialFunctions.BinomialCoefficient(
randomSampling.PopulationSize,
randomSampling.SampleSize),
numberOfDistinctSamples);
// Check that the Chebyshev Inequality holds true
// for each inclusion probability
var expectedInclusionProbabilities =
testableRandomSampling.InclusionProbabilities;
for (int j = 0; j < randomSampling.PopulationSize; j++)
{
ProbabilityDistributionTest.CheckChebyshevInequality(
new BernoulliDistribution(expectedInclusionProbabilities[j]),
actualInclusionProbabilities[j],
numberOfSamples,
delta);
}
// Check how good the actual inclusion probabilities fit
// the expected ones
ProbabilityDistributionTest.CheckGoodnessOfFit(
expectedInclusionProbabilities,
actualInclusionProbabilities,
testableRandomSampling.GoodnessOfFitCriticalValue);
}
