public void StabilityMeanVariance()
{
// Test around 10^9, potential stability issues
var gaussian = new Distributions.Normal(1e+9, 2)
{
RandomSource = new Numerics.Random.MersenneTwister(100)
};
AssertHelpers.AlmostEqual(1e+9, gaussian.Samples().Take(10000).Mean(), 11);
AssertHelpers.AlmostEqual(4d, gaussian.Samples().Take(10000).Variance(), 1);
AssertHelpers.AlmostEqual(2d, gaussian.Samples().Take(10000).StandardDeviation(), 2);
}
public static Vector GenerateRandomDenseVector(int order)
{
// Fill a matrix with standard random numbers.
var normal = new Distributions.Normal();
normal.RandomSource = new Random.MersenneTwister(1);
var v = new DenseVector(order);
for (int i = 0; i < order; i++)
{
v[i] = normal.Sample();
}
// Generate a matrix which is positive definite.
return v;
}
public static Vector <float> GenerateRandomUserDefinedVector(int order)
{
// Fill a matrix with standard random numbers.
var normal = new Distributions.Normal();
normal.RandomSource = new Numerics.Random.MersenneTwister(1);
var v = new UserDefinedVector(order);
for (int i = 0; i < order; i++)
{
v[i] = (float)normal.Sample();
}
// Generate a matrix which is positive definite.
return(v);
}
public static Matrix GenerateRandomPositiveDefiniteDenseMatrix(int order)
{
// Fill a matrix with standard random numbers.
var normal = new Distributions.Normal();
normal.RandomSource = new Random.MersenneTwister(1);
var A = new DenseMatrix(order);
for (int i = 0; i < order; i++)
{
for (int j = 0; j < order; j++)
{
A[i, j] = normal.Sample();
}
}
// Generate a matrix which is positive definite.
return A.Transpose() * A;
}
public static Matrix GenerateRandomDenseMatrix(int row, int col)
{
// Fill a matrix with standard random numbers.
var normal = new Distributions.Normal();
normal.RandomSource = new Random.MersenneTwister(1);
var A = new DenseMatrix(row, col);
for (int i = 0; i < row; i++)
{
for (int j = 0; j < col; j++)
{
A[i, j] = normal.Sample();
}
}
// Generate a matrix which is positive definite.
return A;
}
public void StabilityMeanVariance()
{
// Test around 10^9, potential stability issues
var gaussian = new Distributions.Normal(1e+9, 2, new MersenneTwister(100));
AssertHelpers.AlmostEqual(1e+9, Statistics.Mean(gaussian.Samples().Take(10000)), 11);
AssertHelpers.AlmostEqual(4d, Statistics.Variance(gaussian.Samples().Take(10000)), 1);
AssertHelpers.AlmostEqual(2d, Statistics.StandardDeviation(gaussian.Samples().Take(10000)), 2);
AssertHelpers.AlmostEqual(1e+9, ArrayStatistics.Mean(gaussian.Samples().Take(10000).ToArray()), 11);
AssertHelpers.AlmostEqual(4d, ArrayStatistics.Variance(gaussian.Samples().Take(10000).ToArray()), 1);
AssertHelpers.AlmostEqual(2d, ArrayStatistics.StandardDeviation(gaussian.Samples().Take(10000).ToArray()), 2);
AssertHelpers.AlmostEqual(1e+9, StreamingStatistics.Mean(gaussian.Samples().Take(10000)), 11);
AssertHelpers.AlmostEqual(4d, StreamingStatistics.Variance(gaussian.Samples().Take(10000)), 1);
AssertHelpers.AlmostEqual(2d, StreamingStatistics.StandardDeviation(gaussian.Samples().Take(10000)), 2);
}
public static Vector <Complex> GenerateRandomDenseVector(int order)
{
// Fill a matrix with standard random numbers.
var normal = new Distributions.Normal
{
RandomSource = new Numerics.Random.MersenneTwister(1)
};
var v = new DenseVector(order);
for (var i = 0; i < order; i++)
{
v[i] = new Complex(normal.Sample(), normal.Sample());
}
// Generate a matrix which is positive definite.
return(v);
}
public static Matrix<Complex> GenerateRandomDenseMatrix(int row, int col)
{
// Fill a matrix with standard random numbers.
var normal = new Distributions.Normal
{
RandomSource = new Random.MersenneTwister(1)
};
var matrixA = new DenseMatrix(row, col);
for (var i = 0; i < row; i++)
{
for (var j = 0; j < col; j++)
{
matrixA[i, j] = new Complex(normal.Sample(), normal.Sample());
}
}
// Generate a matrix which is positive definite.
return matrixA;
}
public static Matrix <float> GenerateRandomDenseMatrix(int row, int col)
{
// Fill a matrix with standard random numbers.
var normal = new Distributions.Normal();
normal.RandomSource = new Numerics.Random.MersenneTwister(1);
var matrixA = new DenseMatrix(row, col);
for (int i = 0; i < row; i++)
{
for (int j = 0; j < col; j++)
{
matrixA[i, j] = (float)normal.Sample();
}
}
// Generate a matrix which is positive definite.
return(matrixA);
}
public static Matrix <float> GenerateRandomPositiveDefiniteUserDefinedMatrix(int order)
{
// Fill a matrix with standard random numbers.
var normal = new Distributions.Normal();
normal.RandomSource = new Numerics.Random.MersenneTwister(1);
var matrixA = new UserDefinedMatrix(order);
for (int i = 0; i < order; i++)
{
for (int j = 0; j < order; j++)
{
matrixA[i, j] = (float)normal.Sample();
}
}
// Generate a matrix which is positive definite.
return(matrixA.Transpose() * matrixA);
}
public static Matrix <Complex> GenerateRandomPositiveDefiniteHermitianUserDefinedMatrix(int order)
{
// Fill a matrix with standard random numbers.
var normal = new Distributions.Normal
{
RandomSource = new Numerics.Random.MersenneTwister(1)
};
var matrixA = new UserDefinedMatrix(order);
for (var i = 0; i < order; i++)
{
for (var j = 0; j < order; j++)
{
matrixA[i, j] = new Complex(normal.Sample(), normal.Sample());
}
}
// Generate a Hermitian matrix which is positive definite.
return(matrixA.ConjugateTranspose() * matrixA);
}
public static Matrix <Complex> GenerateRandomUserDefinedMatrix(int row, int col)
{
// Fill a matrix with standard random numbers.
var normal = new Distributions.Normal
{
RandomSource = new Numerics.Random.MersenneTwister(1)
};
var matrixA = new UserDefinedMatrix(row, col);
for (var i = 0; i < row; i++)
{
for (var j = 0; j < col; j++)
{
matrixA[i, j] = new Complex(normal.Sample(), normal.Sample());
}
}
// Generate a matrix which is positive definite.
return(matrixA);
}
public void StabilityMeanVariance()
{
// Test around 10^9, potential stability issues
var gaussian = new Distributions.Normal(1e+9, 2)
{
RandomSource = new Numerics.Random.MersenneTwister(100)
};
AssertHelpers.AlmostEqual(1e+9, gaussian.Samples().Take(10000).Mean(), 11);
AssertHelpers.AlmostEqual(4d, gaussian.Samples().Take(10000).Variance(), 1);
AssertHelpers.AlmostEqual(2d, gaussian.Samples().Take(10000).StandardDeviation(), 2);
}
public void StabilityMeanVariance()
{
// Test around 10^9, potential stability issues
var gaussian = new Distributions.Normal(1e+9, 2, new MersenneTwister(100));
AssertHelpers.AlmostEqual(1e+9, Statistics.Mean(gaussian.Samples().Take(10000)), 11);
AssertHelpers.AlmostEqual(4d, Statistics.Variance(gaussian.Samples().Take(10000)), 1);
AssertHelpers.AlmostEqual(2d, Statistics.StandardDeviation(gaussian.Samples().Take(10000)), 2);
AssertHelpers.AlmostEqual(1e+9, ArrayStatistics.Mean(gaussian.Samples().Take(10000).ToArray()), 11);
AssertHelpers.AlmostEqual(4d, ArrayStatistics.Variance(gaussian.Samples().Take(10000).ToArray()), 1);
AssertHelpers.AlmostEqual(2d, ArrayStatistics.StandardDeviation(gaussian.Samples().Take(10000).ToArray()), 2);
AssertHelpers.AlmostEqual(1e+9, StreamingStatistics.Mean(gaussian.Samples().Take(10000)), 11);
AssertHelpers.AlmostEqual(4d, StreamingStatistics.Variance(gaussian.Samples().Take(10000)), 1);
AssertHelpers.AlmostEqual(2d, StreamingStatistics.StandardDeviation(gaussian.Samples().Take(10000)), 2);
}
public static Matrix<Complex> GenerateRandomPositiveDefiniteHermitianDenseMatrix(int order)
{
// Fill a matrix with standard random numbers.
var normal = new Distributions.Normal
{
RandomSource = new Random.MersenneTwister(1)
};
var matrixA = new DenseMatrix(order);
for (var i = 0; i < order; i++)
{
for (var j = 0; j < order; j++)
{
matrixA[i, j] = new Complex(normal.Sample(), normal.Sample());
}
}
// Generate a Hermitian matrix which is positive definite.
return matrixA.ConjugateTranspose() * matrixA;
}
public static Vector<Complex> GenerateRandomUserDefinedVector(int order)
{
// Fill a matrix with standard random numbers.
var normal = new Distributions.Normal
{
RandomSource = new Random.MersenneTwister(1)
};
var v = new UserDefinedVector(order);
for (var i = 0; i < order; i++)
{
v[i] = new Complex(normal.Sample(), normal.Sample());
}
// Generate a matrix which is positive definite.
return v;
}