public void Create_RebonatoJaeckelExample2_BenchmarkResult()
{
int n = 3;
var rawCorrelationMatrix = new DenseMatrix(n, n, new[] { 1.0, 0.9, 0.7, 0.9, 1.0, 0.3, 0.7, 0.3, 1.0 });
OrdinaryMultiDimOptimizer multiDimOptimizer = new PowellOptimizer();
var matrixDecomposer = new SapMatrixDecomposer(multiDimOptimizer);
PseudoSqrtMatrixDecomposer.State state;
var b = matrixDecomposer.Create(rawCorrelationMatrix, out state);
int expectedRank = 2;
Assert.That(state.Rank, Is.EqualTo(expectedRank), String.Format("Rank should be {0}, but was {1}.", expectedRank, state.Rank));
var actual = b * b.T;
var expected = new DenseMatrix(n, n, new[] {
1.0, 0.89458, 0.69662,
0.89458, 1.0, 0.30254,
0.69662, 0.30254, 1.0
});
Assert.That(actual.Data, Is.EqualTo(expected.Data).AsCollection.Within(1E-4));
}
public void Create_RebonatoJaeckelExample1_BenchmarkResult()
{
int n = 3;
var rawCorrelationMatrix = new DenseMatrix(n, n, new[] {
1.0, 0.9, 0.7,
0.9, 1.0, 0.4,
0.7, 0.4, 1.0
});
OrdinaryMultiDimOptimizer multiDimOptimizer = new PowellOptimizer();
var matrixDecomposer = new SapMatrixDecomposer(multiDimOptimizer);
PseudoSqrtMatrixDecomposer.State state;
var actual = matrixDecomposer.Create(rawCorrelationMatrix, out state);
Assert.That(state.Rank, Is.EqualTo(n), String.Format("Rank should be {0}, but was {1}.", n, state.Rank));
var expected = new DenseMatrix(n, n, new[] { // the values taken from the reference are re-ordered and some columns are multiplied with -1.0
0.13192, -0.10021, -0.05389,
-0.08718, -0.45536, 0.63329,
-0.98742, -0.88465, -0.77203
});
Assert.That(actual.Data, Is.EqualTo(expected.Data).AsCollection.Within(1E-4));
}
public void GetParametricMatrix_BrigoExample1Rank4Opt_BenchmarkResult()
{
var theta = new[] {
1.6844, 1.6088, 1.4688, 1.4435, 1.5051, 1.6365, 1.6981, 1.6728, 1.5328, 1.4571,
1.7328, 1.6828, 1.5810, 1.4708, 1.3957, 1.3957, 1.4708, 1.5810, 1.6828, 1.7328,
1.2775, 1.2965, 1.3444, 1.4267, 1.5203, 1.6213, 1.7149, 1.7972, 1.8451, 1.8640
};
int n = 10;
int rank = 4;
var b = new DenseMatrix(n, rank);
SapMatrixDecomposer.GetParametricMatrix(theta, b);
var actual = b * b.T;
var expected = new DenseMatrix(n, n, new[] {
1.0, 0.9957, 0.9633, 0.9267, 0.8999, 0.8867, 0.8752, 0.8598, 0.8346, 0.8136,
0.9957, 1.0, 0.9839, 0.9559, 0.9295, 0.9078, 0.8893, 0.8715, 0.8524, 0.8346,
0.9633, 0.9839, 1.0, 0.9904, 0.9673, 0.9317, 0.9012, 0.8796, 0.8715, 0.8598,
0.9267, 0.9559, 0.9904, 1.0, 0.9911, 0.9603, 0.9276, 0.9012, 0.8893, 0.8752,
0.8999, 0.9295, 0.9673, 0.9911, 1.0, 0.9865, 0.9603, 0.9317, 0.9078, 0.8867,
0.8867, 0.9078, 0.9317, 0.9603, 0.9865, 1.0, 0.9911, 0.9673, 0.9295, 0.8999,
0.8752, 0.8893, 0.9012, 0.9276, 0.9603, 0.9911, 1.0, 0.9904, 0.9559, 0.9267,
0.8598, 0.8715, 0.8796, 0.9012, 0.9317, 0.9673, 0.9904, 1.0, 0.9839, 0.9633,
0.8346, 0.8524, 0.8715, 0.8893, 0.9078, 0.9295, 0.9559, 0.9839, 1.0, 0.9957,
0.8136, 0.8346, 0.8598, 0.8752, 0.8867, 0.8999, 0.9267, 0.9633, 0.9957, 1.0
});
Assert.That(actual.Data, Is.EqualTo(expected.Data).AsCollection.Within(1E-4));
}
public void GetParametricMatrix_BrigoExample1Rank2Opt_BenchmarkResult()
{
var theta = new[] { 1.2367, 1.2812, 1.3319, 1.3961, 1.4947, 1.6469, 1.7455, 1.8097, 1.8604, 1.9049 };
int n = 10;
int rank = 2;
var b = new DenseMatrix(n, rank);
SapMatrixDecomposer.GetParametricMatrix(theta, b);
var actual = b * b.T;
var expected = new DenseMatrix(n, n, new[] {
1.0, 0.9990, 0.9955, 0.9873, 0.9669, 0.9170, 0.8733, 0.8403, 0.8117, 0.7849,
0.9990, 1.0, 0.9987, 0.9934, 0.9773, 0.9339, 0.8941, 0.8636, 0.8369, 0.8117,
0.9955, 0.9987, 1.0, 0.9979, 0.9868, 0.9508, 0.9157, 0.8880, 0.8636, 0.8403,
0.9873, 0.9934, 0.9979, 1.0, 0.9951, 0.9687, 0.9396, 0.9157, 0.8941, 0.8733,
0.9669, 0.9773, 0.9868, 0.9951, 1.0, 0.9885, 0.9687, 0.9508, 0.9339, 0.9170,
0.9170, 0.9339, 0.9508, 0.9687, 0.9885, 1.0, 0.9951, 0.9868, 0.9773, 0.9669,
0.8733, 0.8941, 0.9157, 0.9396, 0.9687, 0.9951, 1.0, 0.9979, 0.9934, 0.9873,
0.8403, 0.8636, 0.8880, 0.9157, 0.9508, 0.9868, 0.9979, 1.0, 0.9987, 0.9955,
0.8117, 0.8369, 0.8636, 0.8941, 0.9339, 0.9773, 0.9934, 0.9987, 1.0, 0.9990,
0.7849, 0.8117, 0.8403, 0.8733, 0.9170, 0.9669, 0.9873, 0.9955, 0.9990, 1.0
});
Assert.That(actual.Data, Is.EqualTo(expected.Data).AsCollection.Within(1E-4));
}
public void GetParametricMatrix_Test_BenchmarkMatrix()
{
int n = 3;
int rank = 2;
var expected = new DenseMatrix(n, rank, new[] { // matrix B taken from the reference
0.99805, 0.86434, 0.73974,
0.06238, 0.50292, -0.67290
});
var theta = new double[n * (rank - 1)];
SapMatrixDecomposer.GetAngleParameter(expected, theta);
var actual = new DenseMatrix(n, rank);
SapMatrixDecomposer.GetParametricMatrix(theta, actual);
Assert.That(actual.Data, Is.EqualTo(expected.Data).AsCollection.Within(1E-4));
}
public void GetAngleParameter_ParametricMatrix_BenchmarkParameter()
{
var expected = new[] { // original parameter \theta
1.6844, 1.6088, 1.4688, 1.4435, 1.5051, 1.6365, 1.6981, 1.6728, 1.5328, 1.4571,
1.7328, 1.6828, 1.5810, 1.4708, 1.3957, 1.3957, 1.4708, 1.5810, 1.6828, 1.7328,
1.2775, 1.2965, 1.3444, 1.4267, 1.5203, 1.6213, 1.7149, 1.7972, 1.8451, 1.8640
};
int n = 10;
int rank = 4;
var b = new DenseMatrix(n, rank);
SapMatrixDecomposer.GetParametricMatrix(expected, b); // b = B(\theta)
var actual = new double[n * (rank - 1)];
SapMatrixDecomposer.GetAngleParameter(b, actual); // determine \theta* such that B(\theta*) = b
Assert.That(actual, Is.EqualTo(expected).AsCollection.Within(1E-4));
}
