public override void ExecuteExample()
{
// <seealso cref="http://en.wikipedia.org/wiki/Cholesky_decomposition">Cholesky decomposition</seealso>
MathDisplay.WriteLine("<b>Cholesky factorisation</b>");
// Format matrix output to console
var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone();
formatProvider.TextInfo.ListSeparator = " ";
// Create square, symmetric, positive definite matrix
var matrix = DenseMatrix.OfArray(new[, ] {
{ 2.0, 1.0 }, { 1.0, 2.0 }
});
MathDisplay.WriteLine(@"Initial square, symmetric, positive definite matrix");
MathDisplay.WriteLine(matrix.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// Perform Cholesky decomposition
var cholesky = matrix.Cholesky();
MathDisplay.WriteLine(@"Perform Cholesky decomposition");
// 1. Lower triangular form of the Cholesky matrix
MathDisplay.WriteLine(@"1. Lower triangular form of the Cholesky matrix");
MathDisplay.WriteLine(cholesky.Factor.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 2. Reconstruct initial matrix: A = L * LT
var reconstruct = cholesky.Factor * cholesky.Factor.Transpose();
MathDisplay.WriteLine(@"2. Reconstruct initial matrix: A = L*LT");
MathDisplay.WriteLine(reconstruct.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 3. Get determinant of the matrix
MathDisplay.WriteLine(@"3. Determinant of the matrix");
MathDisplay.WriteLine(cholesky.Determinant.ToString());
MathDisplay.WriteLine();
// 4. Get log determinant of the matrix
MathDisplay.WriteLine(@"4. Log determinant of the matrix");
MathDisplay.WriteLine(cholesky.DeterminantLn.ToString());
MathDisplay.WriteLine();
// <seealso cref="http://en.wikipedia.org/wiki/Eigenvalue,_eigenvector_and_eigenspace">EVD decomposition</seealso>
MathDisplay.WriteLine("<b>Eigenvalue, eigenvector and eigenspace factorisation</b>");
// Create square symmetric matrix
matrix = DenseMatrix.OfArray(new[, ] {
{ 1.0, 2.0, 3.0 }, { 2.0, 1.0, 4.0 }, { 3.0, 4.0, 1.0 }
});
MathDisplay.WriteLine(@"Initial square symmetric matrix");
MathDisplay.WriteLine(matrix.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// Perform eigenvalue decomposition of symmetric matrix
var evd = matrix.Evd();
MathDisplay.WriteLine(@"Perform eigenvalue decomposition of symmetric matrix");
// 1. Eigen vectors
MathDisplay.WriteLine(@"1. Eigen vectors");
MathDisplay.WriteLine(evd.EigenVectors.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 2. Eigen values as a complex vector
MathDisplay.WriteLine(@"2. Eigen values as a complex vector");
MathDisplay.WriteLine(evd.EigenValues.ToString("N", formatProvider));
MathDisplay.WriteLine();
// 3. Eigen values as the block diagonal matrix
MathDisplay.WriteLine(@"3. Eigen values as the block diagonal matrix");
MathDisplay.WriteLine(evd.D.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 4. Multiply V by its transpose VT
var identity = evd.EigenVectors.TransposeAndMultiply(evd.EigenVectors);
MathDisplay.WriteLine(@"4. Multiply V by its transpose VT: V*VT = I");
MathDisplay.WriteLine(identity.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 5. Reconstruct initial matrix: A = V*D*V'
reconstruct = evd.EigenVectors * evd.D * evd.EigenVectors.Transpose();
MathDisplay.WriteLine(@"5. Reconstruct initial matrix: A = V*D*V'");
MathDisplay.WriteLine(reconstruct.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 6. Determinant of the matrix
MathDisplay.WriteLine(@"6. Determinant of the matrix");
MathDisplay.WriteLine(evd.Determinant.ToString());
MathDisplay.WriteLine();
// 7. Rank of the matrix
MathDisplay.WriteLine(@"7. Rank of the matrix");
MathDisplay.WriteLine(evd.Rank.ToString());
MathDisplay.WriteLine();
// Fill matrix by random values
var rnd = new Random(1);
for (var i = 0; i < matrix.RowCount; i++)
{
for (var j = 0; j < matrix.ColumnCount; j++)
{
matrix[i, j] = rnd.NextDouble();
}
}
MathDisplay.WriteLine(@"Fill matrix by random values");
MathDisplay.WriteLine(matrix.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// Perform eigenvalue decomposition of non-symmetric matrix
evd = matrix.Evd();
MathDisplay.WriteLine(@"Perform eigenvalue decomposition of non-symmetric matrix");
// 8. Eigen vectors
MathDisplay.WriteLine(@"8. Eigen vectors");
MathDisplay.WriteLine(evd.EigenVectors.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 9. Eigen values as a complex vector
MathDisplay.WriteLine(@"9. Eigen values as a complex vector");
MathDisplay.WriteLine(evd.EigenValues.ToString("N", formatProvider));
MathDisplay.WriteLine();
// 10. Eigen values as the block diagonal matrix
MathDisplay.WriteLine(@"10. Eigen values as the block diagonal matrix");
MathDisplay.WriteLine(evd.D.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 11. Multiply A * V
var av = matrix * evd.EigenVectors;
MathDisplay.WriteLine(@"11. Multiply A * V");
MathDisplay.WriteLine(av.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 12. Multiply V * D
var vd = evd.EigenVectors * evd.D;
MathDisplay.WriteLine(@"12. Multiply V * D");
MathDisplay.WriteLine(vd.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 13. Reconstruct non-symmetriv matrix A = V * D * Vinverse
reconstruct = evd.EigenVectors * evd.D * evd.EigenVectors.Inverse();
MathDisplay.WriteLine(@"13. Reconstruct non-symmetriv matrix A = V * D * Vinverse");
MathDisplay.WriteLine(reconstruct.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 14. Determinant of the matrix
MathDisplay.WriteLine(@"14. Determinant of the matrix");
MathDisplay.WriteLine(evd.Determinant.ToString());
MathDisplay.WriteLine();
// 15. Rank of the matrix
MathDisplay.WriteLine(@"15. Rank of the matrix");
MathDisplay.WriteLine(evd.Rank.ToString());
MathDisplay.WriteLine();
// <seealso cref="http://en.wikipedia.org/wiki/LU_decomposition">LU decomposition</seealso>
// <seealso cref="http://en.wikipedia.org/wiki/Invertible_matrix">Invertible matrix</seealso>
MathDisplay.WriteLine("<b>LU factorisation</b>");
// Create square matrix
matrix = DenseMatrix.OfArray(new[, ] {
{ 1.0, 2.0 }, { 3.0, 4.0 }
});
MathDisplay.WriteLine(@"Initial square matrix");
MathDisplay.WriteLine(matrix.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// Perform LU decomposition
var lu = matrix.LU();
MathDisplay.WriteLine(@"Perform LU decomposition");
// 1. Lower triangular factor
MathDisplay.WriteLine(@"1. Lower triangular factor");
MathDisplay.WriteLine(lu.L.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 2. Upper triangular factor
MathDisplay.WriteLine(@"2. Upper triangular factor");
MathDisplay.WriteLine(lu.U.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 3. Permutations applied to LU factorization
MathDisplay.WriteLine(@"3. Permutations applied to LU factorization");
for (var i = 0; i < lu.P.Dimension; i++)
{
if (lu.P[i] > i)
{
MathDisplay.WriteLine(@"Row {0} permuted with row {1}", lu.P[i], i);
}
}
MathDisplay.WriteLine();
// 4. Reconstruct initial matrix: PA = L * U
reconstruct = lu.L * lu.U;
// The rows of the reconstructed matrix should be permuted to get the initial matrix
reconstruct.PermuteRows(lu.P.Inverse());
MathDisplay.WriteLine(@"4. Reconstruct initial matrix: PA = L*U");
MathDisplay.WriteLine(reconstruct.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 5. Get the determinant of the matrix
MathDisplay.WriteLine(@"5. Determinant of the matrix");
MathDisplay.WriteLine(lu.Determinant.ToString());
MathDisplay.WriteLine();
// 6. Get the inverse of the matrix
var matrixInverse = lu.Inverse();
MathDisplay.WriteLine(@"6. Inverse of the matrix");
MathDisplay.WriteLine(matrixInverse.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 7. Matrix multiplied by its inverse
identity = matrix * matrixInverse;
MathDisplay.WriteLine(@"7. Matrix multiplied by its inverse ");
MathDisplay.WriteLine(identity.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// QR factorization example. Any real square matrix A (m x n) may be decomposed as A = QR where Q is an
// orthogonal matrix (m x m)
// (its columns are orthogonal unit vectors meaning QTQ = I) and R (m x n) is an upper triangular matrix
// (also called right triangular matrix).
// In this example two methods for actually computing the QR decomposition presented: by means of the
// Gram–Schmidt process and Householder transformations.
// <seealso cref="http://reference.wolfram.com/mathematica/ref/QRDecomposition.html"/>
MathDisplay.WriteLine("<b>QR factorisation</b>");
// Create 3 x 2 matrix
matrix = DenseMatrix.OfArray(new[, ] {
{ 1.0, 2.0 }, { 3.0, 4.0 }, { 5.0, 6.0 }
});
MathDisplay.WriteLine(@"Initial 3x2 matrix");
MathDisplay.WriteLine(matrix.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// Perform QR decomposition (Householder transformations)
var qr = matrix.QR();
MathDisplay.WriteLine(@"QR decomposition (Householder transformations)");
// 1. Orthogonal Q matrix
MathDisplay.WriteLine(@"1. Orthogonal Q matrix");
MathDisplay.WriteLine(qr.Q.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 2. Multiply Q matrix by its transpose gives identity matrix
MathDisplay.WriteLine(@"2. Multiply Q matrix by its transpose gives identity matrix");
MathDisplay.WriteLine(qr.Q.TransposeAndMultiply(qr.Q).ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 3. Upper triangular factor R
MathDisplay.WriteLine(@"3. Upper triangular factor R");
MathDisplay.WriteLine(qr.R.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 4. Reconstruct initial matrix: A = Q * R
reconstruct = qr.Q * qr.R;
MathDisplay.WriteLine(@"4. Reconstruct initial matrix: A = Q*R");
MathDisplay.WriteLine(reconstruct.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// Perform QR decomposition (Gram–Schmidt process)
var gramSchmidt = matrix.GramSchmidt();
MathDisplay.WriteLine(@"QR decomposition (Gram–Schmidt process)");
// 5. Orthogonal Q matrix
MathDisplay.WriteLine(@"5. Orthogonal Q matrix");
MathDisplay.WriteLine(gramSchmidt.Q.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 6. Multiply Q matrix by its transpose gives identity matrix
MathDisplay.WriteLine(@"6. Multiply Q matrix by its transpose gives identity matrix");
MathDisplay.WriteLine((gramSchmidt.Q.Transpose() * gramSchmidt.Q).ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 7. Upper triangular factor R
MathDisplay.WriteLine(@"7. Upper triangular factor R");
MathDisplay.WriteLine(gramSchmidt.R.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 8. Reconstruct initial matrix: A = Q * R
reconstruct = gramSchmidt.Q * gramSchmidt.R;
MathDisplay.WriteLine(@"8. Reconstruct initial matrix: A = Q*R");
MathDisplay.WriteLine(reconstruct.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// SVD factorization example. Suppose M is an m-by-n matrix whose entries are real numbers.
// Then there exists a factorization of the form M = UΣVT where:
// - U is an m-by-m unitary matrix;
// - Σ is m-by-n diagonal matrix with nonnegative real numbers on the diagonal;
// - VT denotes transpose of V, an n-by-n unitary matrix;
// Such a factorization is called a singular-value decomposition of M. A common convention is to order the diagonal
// entries Σ(i,i) in descending order. In this case, the diagonal matrix Σ is uniquely determined
// by M (though the matrices U and V are not). The diagonal entries of Σ are known as the singular values of M.
// <seealso cref="http://reference.wolfram.com/mathematica/ref/SingularValueDecomposition.html"/>
MathDisplay.WriteLine("<b>SVD factorisation</b>");
// Create square matrix
matrix = DenseMatrix.OfArray(new[, ] {
{ 4.0, 1.0 }, { 3.0, 2.0 }
});
MathDisplay.WriteLine(@"Initial square matrix");
MathDisplay.WriteLine(matrix.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// Perform full SVD decomposition
var svd = matrix.Svd();
MathDisplay.WriteLine(@"Perform full SVD decomposition");
// 1. Left singular vectors
MathDisplay.WriteLine(@"1. Left singular vectors");
MathDisplay.WriteLine(svd.U.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 2. Singular values as vector
MathDisplay.WriteLine(@"2. Singular values as vector");
MathDisplay.WriteLine(svd.S.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 3. Singular values as diagonal matrix
MathDisplay.WriteLine(@"3. Singular values as diagonal matrix");
MathDisplay.WriteLine(svd.W.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 4. Right singular vectors
MathDisplay.WriteLine(@"4. Right singular vectors");
MathDisplay.WriteLine(svd.VT.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 5. Multiply U matrix by its transpose
var identinty = svd.U * svd.U.Transpose();
MathDisplay.WriteLine(@"5. Multiply U matrix by its transpose");
MathDisplay.WriteLine(identinty.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 6. Multiply V matrix by its transpose
identinty = svd.VT.TransposeAndMultiply(svd.VT);
MathDisplay.WriteLine(@"6. Multiply V matrix by its transpose");
MathDisplay.WriteLine(identinty.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 7. Reconstruct initial matrix: A = U*Σ*VT
reconstruct = svd.U * svd.W * svd.VT;
MathDisplay.WriteLine(@"7. Reconstruct initial matrix: A = U*S*VT");
MathDisplay.WriteLine(reconstruct.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 8. Condition Number of the matrix
MathDisplay.WriteLine(@"8. Condition Number of the matrix");
MathDisplay.WriteLine(svd.ConditionNumber.ToString());
MathDisplay.WriteLine();
// 9. Determinant of the matrix
MathDisplay.WriteLine(@"9. Determinant of the matrix");
MathDisplay.WriteLine(svd.Determinant.ToString());
MathDisplay.WriteLine();
// 10. 2-norm of the matrix
MathDisplay.WriteLine(@"10. 2-norm of the matrix");
MathDisplay.WriteLine(svd.L2Norm.ToString());
MathDisplay.WriteLine();
// 11. Rank of the matrix
MathDisplay.WriteLine(@"11. Rank of the matrix");
MathDisplay.WriteLine(svd.Rank.ToString());
MathDisplay.WriteLine();
// Perform partial SVD decomposition, without computing the singular U and VT vectors
svd = matrix.Svd(false);
MathDisplay.WriteLine(@"Perform partial SVD decomposition, without computing the singular U and VT vectors");
// 12. Singular values as vector
MathDisplay.WriteLine(@"12. Singular values as vector");
MathDisplay.WriteLine(svd.S.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 13. Singular values as diagonal matrix
MathDisplay.WriteLine(@"13. Singular values as diagonal matrix");
MathDisplay.WriteLine(svd.W.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 14. Access to left singular vectors when partial SVD decomposition was performed
try {
MathDisplay.WriteLine(@"14. Access to left singular vectors when partial SVD decomposition was performed");
MathDisplay.WriteLine(svd.U.ToString("#0.00\t", formatProvider));
} catch (Exception ex) {
MathDisplay.WriteLine(ex.Message);
MathDisplay.WriteLine();
}
// 15. Access to right singular vectors when partial SVD decomposition was performed
try {
MathDisplay.WriteLine(@"15. Access to right singular vectors when partial SVD decomposition was performed");
MathDisplay.WriteLine(svd.VT.ToString("#0.00\t", formatProvider));
} catch (Exception ex) {
MathDisplay.WriteLine(ex.Message);
MathDisplay.WriteLine();
}
}
public override void ExecuteExample()
{
// <a href="http://en.wikipedia.org/wiki/Binomial_distribution">Binomial distribution</a>
MathDisplay.WriteLine("<b>Binomial distribution</b>");
// 1. Initialize the new instance of the Binomial distribution class with parameters P = 0.2, N = 20
var binomial = new Binomial(0.2, 20);
MathDisplay.WriteLine(@"1. Initialize the new instance of the Binomial distribution class with parameters P = {0}, N = {1}", binomial.P, binomial.N);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", binomial);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", binomial.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", binomial.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", binomial.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Entropy
MathDisplay.WriteLine(@"{0} - Entropy", binomial.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", binomial.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", binomial.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", binomial.Mean.ToString(" #0.00000;-#0.00000"));
// Median
MathDisplay.WriteLine(@"{0} - Median", binomial.Median.ToString(" #0.00000;-#0.00000"));
// Mode
MathDisplay.WriteLine(@"{0} - Mode", binomial.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", binomial.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", binomial.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
MathDisplay.WriteLine(@"{0} - Skewness", binomial.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the Binomial distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the Binomial distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(binomial.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Bernoulli_distribution">Bernoulli distribution</a>
MathDisplay.WriteLine("<b>Bernoulli distribution</b>");
// 1. Initialize the new instance of the Bernoulli distribution class with parameter P = 0.2
var bernoulli = new Bernoulli(0.2);
MathDisplay.WriteLine(@"1. Initialize the new instance of the Bernoulli distribution class with parameter P = {0}", bernoulli.P);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", bernoulli);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", bernoulli.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", bernoulli.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", bernoulli.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Entropy
MathDisplay.WriteLine(@"{0} - Entropy", bernoulli.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", bernoulli.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", bernoulli.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", bernoulli.Mean.ToString(" #0.00000;-#0.00000"));
// Mode
MathDisplay.WriteLine(@"{0} - Mode", bernoulli.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", bernoulli.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", bernoulli.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
MathDisplay.WriteLine(@"{0} - Skewness", bernoulli.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the Bernoulli distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the Bernoulli distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(bernoulli.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Categorical_distribution">Categorical distribution</a>
MathDisplay.WriteLine("<b>Categorical distribution</b>");
// 1. Initialize the new instance of the Categorical distribution class with parameters P = (0.1, 0.2, 0.25, 0.45)
var binomialC = new Categorical(new[] { 0.1, 0.2, 0.25, 0.45 });
MathDisplay.WriteLine(@"1. Initialize the new instance of the Categorical distribution class with parameters P = (0.1, 0.2, 0.25, 0.45)");
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", binomialC);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", binomialC.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", binomialC.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", binomialC.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Entropy
MathDisplay.WriteLine(@"{0} - Entropy", binomialC.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", binomialC.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", binomialC.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", binomialC.Mean.ToString(" #0.00000;-#0.00000"));
// Median
MathDisplay.WriteLine(@"{0} - Median", binomialC.Median.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", binomialC.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", binomialC.StdDev.ToString(" #0.00000;-#0.00000"));
// 3. Generate 10 samples of the Categorical distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the Categorical distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(binomialC.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Conway%E2%80%93Maxwell%E2%80%93Poisson_distribution">ConwayMaxwellPoisson distribution</a>
MathDisplay.WriteLine("<b>Conway Maxwell Poisson distribution</b>");
// 1. Initialize the new instance of the ConwayMaxwellPoisson distribution class with parameters Lambda = 2, Nu = 1
var conwayMaxwellPoisson = new ConwayMaxwellPoisson(2, 1);
MathDisplay.WriteLine(@"1. Initialize the new instance of the ConwayMaxwellPoisson distribution class with parameters Lambda = {0}, Nu = {1}", conwayMaxwellPoisson.Lambda, conwayMaxwellPoisson.Nu);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", conwayMaxwellPoisson);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", conwayMaxwellPoisson.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", conwayMaxwellPoisson.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", conwayMaxwellPoisson.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", conwayMaxwellPoisson.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", conwayMaxwellPoisson.Mean.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", conwayMaxwellPoisson.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", conwayMaxwellPoisson.StdDev.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the ConwayMaxwellPoisson distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the ConwayMaxwellPoisson distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(conwayMaxwellPoisson.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Discrete_uniform">DiscreteUniform distribution</a>
MathDisplay.WriteLine("<b>Discrete Uniform distribution</b>");
// 1. Initialize the new instance of the DiscreteUniform distribution class with parameters LowerBound = 2, UpperBound = 10
var discreteUniform = new DiscreteUniform(2, 10);
MathDisplay.WriteLine(@"1. Initialize the new instance of the DiscreteUniform distribution class with parameters LowerBound = {0}, UpperBound = {1}", discreteUniform.LowerBound, discreteUniform.UpperBound);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", discreteUniform);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", discreteUniform.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", discreteUniform.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", discreteUniform.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Entropy
MathDisplay.WriteLine(@"{0} - Entropy", discreteUniform.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", discreteUniform.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", discreteUniform.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", discreteUniform.Mean.ToString(" #0.00000;-#0.00000"));
// Median
MathDisplay.WriteLine(@"{0} - Median", discreteUniform.Median.ToString(" #0.00000;-#0.00000"));
// Mode
MathDisplay.WriteLine(@"{0} - Mode", discreteUniform.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", discreteUniform.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", discreteUniform.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
MathDisplay.WriteLine(@"{0} - Skewness", discreteUniform.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the DiscreteUniform distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the DiscreteUniform distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(discreteUniform.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Geometric_distribution">Geometric distribution</a>
MathDisplay.WriteLine("<b>Geometric distribution</b>");
// 1. Initialize the new instance of the Geometric distribution class with parameter P = 0.2
var geometric = new Geometric(0.2);
MathDisplay.WriteLine(@"1. Initialize the new instance of the Geometric distribution class with parameter P = {0}", geometric.P);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", geometric);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", geometric.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", geometric.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", geometric.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Entropy
MathDisplay.WriteLine(@"{0} - Entropy", geometric.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", geometric.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", geometric.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", geometric.Mean.ToString(" #0.00000;-#0.00000"));
// Median
MathDisplay.WriteLine(@"{0} - Median", geometric.Median.ToString(" #0.00000;-#0.00000"));
// Mode
MathDisplay.WriteLine(@"{0} - Mode", geometric.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", geometric.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", geometric.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
MathDisplay.WriteLine(@"{0} - Skewness", geometric.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the Geometric distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the Geometric distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(geometric.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Hypergeometric_distribution">Hypergeometric distribution</a>
MathDisplay.WriteLine("<b>Hypergeometric distribution</b>");
// 1. Initialize the new instance of the Hypergeometric distribution class with parameters PopulationSize = 10, M = 2, N = 8
var hypergeometric = new Hypergeometric(30, 15, 10);
MathDisplay.WriteLine(@"1. Initialize the new instance of the Hypergeometric distribution class with parameters Population = {0}, Success = {1}, Draws = {2}", hypergeometric.Population, hypergeometric.Success, hypergeometric.Draws);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", hypergeometric);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", hypergeometric.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", hypergeometric.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", hypergeometric.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", hypergeometric.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", hypergeometric.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", hypergeometric.Mean.ToString(" #0.00000;-#0.00000"));
// Mode
MathDisplay.WriteLine(@"{0} - Mode", hypergeometric.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", hypergeometric.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", hypergeometric.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
MathDisplay.WriteLine(@"{0} - Skewness", hypergeometric.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the Hypergeometric distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the Hypergeometric distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(hypergeometric.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Negative_binomial">NegativeBinomial distribution</a>
MathDisplay.WriteLine("<b>Negative Binomial distribution</b>");
// 1. Initialize the new instance of the NegativeBinomial distribution class with parameters P = 0.2, R = 20
var negativeBinomial = new NegativeBinomial(20, 0.2);
MathDisplay.WriteLine(@"1. Initialize the new instance of the NegativeBinomial distribution class with parameters P = {0}, N = {1}", negativeBinomial.P, negativeBinomial.R);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", negativeBinomial);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", negativeBinomial.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", negativeBinomial.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", negativeBinomial.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", negativeBinomial.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", negativeBinomial.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", negativeBinomial.Mean.ToString(" #0.00000;-#0.00000"));
// Mode
MathDisplay.WriteLine(@"{0} - Mode", negativeBinomial.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", negativeBinomial.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", negativeBinomial.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
MathDisplay.WriteLine(@"{0} - Skewness", negativeBinomial.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the NegativeBinomial distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the NegativeBinomial distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(negativeBinomial.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Poisson_distribution">Poisson distribution</a>
MathDisplay.WriteLine("<b>Poisson distribution</b>");
// 1. Initialize the new instance of the Poisson distribution class with parameter Lambda = 1
var poisson = new Poisson(1);
MathDisplay.WriteLine(@"1. Initialize the new instance of the Poisson distribution class with parameter Lambda = {0}", poisson.Lambda);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", poisson);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", poisson.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", poisson.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", poisson.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Entropy
MathDisplay.WriteLine(@"{0} - Entropy", poisson.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", poisson.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", poisson.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", poisson.Mean.ToString(" #0.00000;-#0.00000"));
// Median
MathDisplay.WriteLine(@"{0} - Median", poisson.Median.ToString(" #0.00000;-#0.00000"));
// Mode
MathDisplay.WriteLine(@"{0} - Mode", poisson.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", poisson.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", poisson.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
MathDisplay.WriteLine(@"{0} - Skewness", poisson.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the Poisson distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the Poisson distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(poisson.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Zipf_distribution">Zipf distribution</a>
MathDisplay.WriteLine("<b>Zipf distribution</b>");
// 1. Initialize the new instance of the Zipf distribution class with parameters S = 5, N = 10
var zipf = new Zipf(5, 10);
MathDisplay.WriteLine(@"1. Initialize the new instance of the Zipf distribution class with parameters S = {0}, N = {1}", zipf.S, zipf.N);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", zipf);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", zipf.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", zipf.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", zipf.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Entropy
MathDisplay.WriteLine(@"{0} - Entropy", zipf.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", zipf.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", zipf.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", zipf.Mean.ToString(" #0.00000;-#0.00000"));
// Mode
MathDisplay.WriteLine(@"{0} - Mode", zipf.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", zipf.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", zipf.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
MathDisplay.WriteLine(@"{0} - Skewness", zipf.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the Zipf distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the Zipf distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(zipf.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
}
/// <summary>
/// Examples of generic function sampling and quantization providers
/// </summary>
public override void ExecuteExample()
{
MathDisplay.WriteLine("<b>Chebyshev sampling</b>");
// 1. Get 20 samples of f(x) = (x * x) / 2 at the roots of the Chebyshev polynomial of the first kind within interval [0, 10]
var roots = FindRoots.ChebychevPolynomialFirstKind(20, 0, 10);
var result = Generate.Map <double, double>(roots, Function);
MathDisplay.WriteLine(@"1. Get 20 samples of f(x) = (x * x) / 2 at the roots of the Chebyshev polynomial of
the first kind within interval [0, 10]");
for (var i = 0; i < result.Length; i++)
{
MathDisplay.Write(result[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 2. Get 20 samples of f(x) = (x * x) / 2 at the roots of the Chebyshev polynomial of the second kind within interval [0, 10]
roots = FindRoots.ChebychevPolynomialSecondKind(20, 0, 10);
result = Generate.Map <double, double>(roots, Function);
MathDisplay.WriteLine(@"2. Get 20 samples of f(x) = (x * x) / 2 at the roots of the Chebyshev polynomial of
the second kind within interval [0, 10]");
for (var i = 0; i < result.Length; i++)
{
MathDisplay.Write(result[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.WriteLine("<b>Equidistant sampling</b>");
// 1. Get 11 samples of f(x) = (x * x) / 2 equidistant within interval [-5, 5]
result = Generate.LinearSpacedMap <double>(11, -5, 5, Function);
MathDisplay.WriteLine(@"1. Get 11 samples of f(x) = (x * x) / 2 equidistant within interval [-5, 5]");
for (var i = 0; i < result.Length; i++)
{
MathDisplay.Write(result[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 2. Get 10 samples of f(x) = (x * x) / 2 equidistant starting at x=1 with step = 0.5 and retrieve sample points
double[] samplePoints = Generate.LinearSpaced(10, 1.0, 5.5);
result = Generate.Map <double, double>(samplePoints, Function);
MathDisplay.WriteLine(@"2. Get 10 samples of f(x) = (x * x) / 2 equidistant starting at x=1 with step = 0.5
and retrieve sample points");
MathDisplay.Write(@"Points: ");
for (var i = 0; i < samplePoints.Length; i++)
{
MathDisplay.Write(samplePoints[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.Write(@"Values: ");
for (var i = 0; i < result.Length; i++)
{
MathDisplay.Write(result[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 3. Get 10 samples of f(x) = (x * x) / 2 equidistant within period = 10 and period offset = 5
result = Generate.PeriodicMap <double>(10, Function, 10, 1.0, 10, 5);
MathDisplay.WriteLine(@"3. Get 10 samples of f(x) = (x * x) / 2 equidistant within period = 10 and period offset = 5");
for (var i = 0; i < result.Length; i++)
{
MathDisplay.Write(result[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.WriteLine("<b>Random sampling</b>");
// 1. Get 10 random samples of f(x) = (x * x) / 2 using continuous uniform distribution on [-10, 10]
var uniform = new ContinuousUniform(-10, 10);
result = Generate.RandomMap <double>(10, uniform, Function);
MathDisplay.WriteLine(@" 1. Get 10 random samples of f(x) = (x * x) / 2 using continuous uniform
distribution on [-10, 10]");
for (var i = 0; i < result.Length; i++)
{
MathDisplay.Write(result[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 2. Get 10 random samples of f(x) = (x * x) / 2 using Exponential(1) distribution and retrieve sample points
var exponential = new Exponential(1);
samplePoints = Generate.Random(10, exponential);
result = Generate.Map <double, double>(samplePoints, Function);
MathDisplay.WriteLine(@"2. Get 10 random samples of f(x) = (x * x) / 2 using Exponential(1) distribution
and retrieve sample points");
MathDisplay.Write(@"Points: ");
for (var i = 0; i < samplePoints.Length; i++)
{
MathDisplay.Write(samplePoints[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.Write(@"Values: ");
for (var i = 0; i < result.Length; i++)
{
MathDisplay.Write(result[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 3. Get 10 random samples of f(x, y) = (x * y) / 2 using ChiSquare(10) distribution
var chiSquare = new ChiSquared(10);
result = Generate.RandomMap2 <double>(10, chiSquare, TwoDomainFunction);
MathDisplay.WriteLine(@" 3. Get 10 random samples of f(x, y) = (x * y) / 2 using ChiSquare(10) distribution");
for (var i = 0; i < result.Length; i++)
{
MathDisplay.Write(result[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
}
/// <summary>
/// Executes the example.
/// </summary>
/// <seealso cref="http://en.wikipedia.org/wiki/Random_number_generation">Random number generation</seealso>
/// <seealso cref="http://en.wikipedia.org/wiki/Linear_congruential_generator">Linear congruential generator</seealso>
/// <seealso cref="http://en.wikipedia.org/wiki/Mersenne_twister">Mersenne twister</seealso>
/// <seealso cref="http://en.wikipedia.org/wiki/Lagged_Fibonacci_generator">Lagged Fibonacci generator</seealso>
/// <seealso cref="http://en.wikipedia.org/wiki/Xorshift">Xorshift</seealso>
public override void ExecuteExample()
{
// All RNG classes in MathNet have the following counstructors:
// - RNG(int seed, bool threadSafe): initializes a new instance using a specific seed value and thread
// safe property
// - RNG(int seed): initializes a new instance using a specific seed value. Thread safe property is set
// to Control.ThreadSafeRandomNumberGenerators
// - RNG(bool threadSafe) : initializes a new instance with the seed value set to DateTime.Now.Ticks and
// specific thread safe property
// - RNG(bool threadSafe) : initializes a new instance with the seed value set to DateTime.Now.Ticks and
// thread safe property set to Control.ThreadSafeRandomNumberGenerators
// All RNG classes in MathNet have next methods to produce random values:
// - double[] NextDouble(int n): returns an "n"-size array of uniformly distributed random doubles in
// the interval [0.0,1.0];
// - int Next(): returns a nonnegative random number;
// - int Next(int maxValue): returns a random number less then a specified maximum;
// - int Next(int minValue, int maxValue): returns a random number within a specified range;
// - void NextBytes(byte[] buffer): fills the elements of a specified array of bytes with random numbers;
// All RNG classes in MathNet have next extension methods to produce random values:
// - long NextInt64(): returns a nonnegative random number less than "Int64.MaxValue";
// - int NextFullRangeInt32(): returns a random number of the full Int32 range;
// - long NextFullRangeInt64(): returns a random number of the full Int64 range;
// - decimal NextDecimal(): returns a nonnegative decimal floating point random number less than 1.0;
// 1. Multiplicative congruential generator using a modulus of 2^31-1 and a multiplier of 1132489760
var mcg31M1 = new Mcg31m1(1);
MathDisplay.WriteLine(@"1. Generate 10 random double values using Multiplicative congruential generator with a
modulus of 2^31-1 and a multiplier of 1132489760");
var randomValues = mcg31M1.NextDoubles(10);
for (var i = 0; i < randomValues.Length; i++)
{
MathDisplay.Write(randomValues[i].ToString("N") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 2. Multiplicative congruential generator using a modulus of 2^59 and a multiplier of 13^13
var mcg59 = new Mcg59(1);
MathDisplay.WriteLine(@"2. Generate 10 random integer values using Multiplicative congruential generator with a
modulus of 2^59 and a multiplier of 13^13");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(mcg59.Next() + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 3. Random number generator using Mersenne Twister 19937 algorithm
var mersenneTwister = new MersenneTwister(1);
MathDisplay.WriteLine(@"3. Generate 10 random integer values less then 100 using Mersenne Twister 19937 algorithm");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(mersenneTwister.Next(100) + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 4. Multiple recursive generator with 2 components of order 3
var mrg32K3A = new Mrg32k3a(1);
MathDisplay.WriteLine(@"4. Generate 10 random integer values in range [50;100] using multiple recursive generator
with 2 components of order 3");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(mrg32K3A.Next(50, 100) + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 5. Parallel Additive Lagged Fibonacci pseudo-random number generator
var palf = new Palf(1);
MathDisplay.WriteLine(@"5. Generate 10 random bytes using Parallel Additive Lagged Fibonacci pseudo-random number
generator");
var bytes = new byte[10];
palf.NextBytes(bytes);
for (var i = 0; i < bytes.Length; i++)
{
MathDisplay.Write(bytes[i] + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 6. A random number generator based on "System.Security.Cryptography.RandomNumberGenerator" class in
// the .NET library
var systemCrypto = new CryptoRandomSource();
MathDisplay.WriteLine(@"6. Generate 10 random decimal values using RNG based on
'System.Security.Cryptography.RandomNumberGenerator'");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(systemCrypto.NextDecimal().ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 7. Wichmann-Hill’s 1982 combined multiplicative congruential generator
var rngWh1982 = new WH1982();
MathDisplay.WriteLine(@"7. Generate 10 random full Int32 range values using Wichmann-Hill’s 1982 combined
multiplicative congruential generator");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(rngWh1982.NextFullRangeInt32() + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 8. Wichmann-Hill’s 2006 combined multiplicative congruential generator.
var rngWh2006 = new WH2006();
MathDisplay.WriteLine(@"8. Generate 10 random full Int64 range values using Wichmann-Hill’s 2006 combined
multiplicative congruential generator");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(rngWh2006.NextFullRangeInt32() + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 9. Multiply-with-carry Xorshift pseudo random number generator
var xorshift = new Xorshift();
MathDisplay.WriteLine(@"9. Generate 10 random nonnegative values less than Int64.MaxValue using
Multiply-with-carry Xorshift pseudo random number generator");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(xorshift.NextInt64() + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
}
public override void ExecuteExample()
{
MathDisplay.WriteLine("<b>Linear interpolation between points</b>");
// 1. Generate 20 samples of the function x*x-2*x on interval [0, 10]
MathDisplay.WriteLine(@"1. Generate 20 samples of the function x*x-2*x on interval [0, 10]");
double[] points = Generate.LinearSpaced(20, 0, 10);
var values = Generate.Map <double, double>(points, TargetFunction1);
MathDisplay.WriteLine();
// 2. Create a linear spline interpolation based on arbitrary points
var method = Interpolate.Linear(points, values);
MathDisplay.WriteLine(@"2. Create a linear spline interpolation based on arbitrary points");
MathDisplay.WriteLine();
// 3. Check if interpolation support integration
MathDisplay.WriteLine(@"3. Support integration = {0}", method.SupportsIntegration);
MathDisplay.WriteLine();
// 4. Check if interpolation support differentiation
MathDisplay.WriteLine(@"4. Support differentiation = {0}", method.SupportsDifferentiation);
MathDisplay.WriteLine();
// 5. Differentiate at point 5.2
MathDisplay.WriteLine(@"5. Differentiate at point 5.2 = {0}", method.Differentiate(5.2));
MathDisplay.WriteLine();
// 6. Integrate at point 5.2
MathDisplay.WriteLine(@"6. Integrate at point 5.2 = {0}", method.Integrate(5.2));
MathDisplay.WriteLine();
// 7. Interpolate ten random points and compare to function results
MathDisplay.WriteLine(@"7. Interpolate ten random points and compare to function results");
var rng = new MersenneTwister(1);
for (var i = 0; i < 10; i++)
{
// Generate random value from [0, 10]
var point = rng.NextDouble() * 10;
MathDisplay.WriteLine(
@"Interpolate at {0} = {1}. Function({0}) = {2}",
point.ToString("N05"),
method.Interpolate(point).ToString("N05"),
TargetFunction1(point).ToString("N05"));
}
MathDisplay.WriteLine();
// <seealso cref="http://en.wikipedia.org/wiki/Spline_interpolation">Spline interpolation</seealso>
MathDisplay.WriteLine("<b>Akima spline interpolation</b>");
// 1. Generate 10 samples of the function x*x-2*x on interval [0, 10]
MathDisplay.WriteLine(@"1. Generate 10 samples of the function x*x-2*x on interval [0, 10]");
points = Generate.LinearSpaced(10, 0, 10);
values = Generate.Map <double, double>(points, TargetFunction1);
MathDisplay.WriteLine();
// 2. Create akima spline interpolation
method = CubicSpline.InterpolateAkima(points, values);
MathDisplay.WriteLine(@"2. Create akima spline interpolation based on arbitrary points");
MathDisplay.WriteLine();
// 3. Check if interpolation supports integration
MathDisplay.WriteLine(@"3. Support integration = {0}", ((IInterpolation)method).SupportsIntegration);
MathDisplay.WriteLine();
// 4. Check if interpolation support differentiation
MathDisplay.WriteLine(@"4. Support differentiation = {0}", ((IInterpolation)method).SupportsDifferentiation);
MathDisplay.WriteLine();
// 5. Differentiate at point 5.2
MathDisplay.WriteLine(@"5. Differentiate at point 5.2 = {0}", method.Differentiate(5.2));
MathDisplay.WriteLine();
// 6. Integrate at point 5.2
MathDisplay.WriteLine(@"6. Integrate at point 5.2 = {0}", method.Integrate(5.2));
MathDisplay.WriteLine();
// 7. Interpolate ten random points and compare to function results
MathDisplay.WriteLine(@"7. Interpolate ten random points and compare to function results");
rng = new MersenneTwister(1);
for (var i = 0; i < 10; i++)
{
// Generate random value from [0, 10]
var point = rng.NextDouble() * 10;
MathDisplay.WriteLine(
@"Interpolate at {0} = {1}. Function({0}) = {2}",
point.ToString("N05"),
method.Interpolate(point).ToString("N05"),
TargetFunction1(point).ToString("N05"));
}
MathDisplay.WriteLine();
MathDisplay.WriteLine("<b>Barycentric rational interpolation without poles</b>");
// 1. Generate 10 samples of the function 1/(1+x*x) on interval [-5, 5]
MathDisplay.WriteLine(@"1. Generate 10 samples of the function 1/(1+x*x) on interval [-5, 5]");
points = Generate.LinearSpaced(10, -5, 5);
values = Generate.Map <double, double>(points, TargetFunctionWithoutPolesEx);
MathDisplay.WriteLine();
// 2. Create a floater hormann rational pole-free interpolation based on arbitrary points
// This method is used by default when create an interpolation using Interpolate.Common method
method = Interpolate.RationalWithoutPoles(points, values);
MathDisplay.WriteLine(@"2. Create a floater hormann rational pole-free interpolation based on arbitrary points");
MathDisplay.WriteLine();
// 3. Check if interpolation support integration
MathDisplay.WriteLine(@"3. Support integration = {0}", method.SupportsIntegration);
MathDisplay.WriteLine();
// 4. Check if interpolation support differentiation
MathDisplay.WriteLine(@"4. Support differentiation = {0}", method.SupportsDifferentiation);
MathDisplay.WriteLine();
// 5. Interpolate ten random points and compare to function results
MathDisplay.WriteLine(@"5. Interpolate ten random points and compare to function results");
rng = new MersenneTwister(1);
for (var i = 0; i < 10; i++)
{
// Generate random value from [0, 5]
var point = rng.NextDouble() * 5;
MathDisplay.WriteLine(
@"Interpolate at {0} = {1}. Function({0}) = {2}",
point.ToString("N05"),
method.Interpolate(point).ToString("N05"),
TargetFunctionWithoutPolesEx(point).ToString("N05"));
}
MathDisplay.WriteLine();
MathDisplay.WriteLine("<b>Rational interpolation with poles</b>");
// 1. Generate 20 samples of the function f(x) = x on interval [-5, 5]
MathDisplay.WriteLine(@"1. Generate 20 samples of the function f(x) = x on interval [-5, 5]");
points = Generate.LinearSpaced(20, -5, 5);
values = Generate.Map <double, double>(points, TargetFunctionWithPolesEx);
MathDisplay.WriteLine();
// 2. Create a burlish stoer rational interpolation based on arbitrary points
method = Interpolate.RationalWithPoles(points, values);
MathDisplay.WriteLine(@"2. Create a burlish stoer rational interpolation based on arbitrary points");
MathDisplay.WriteLine();
// 3. Check if interpolation support integration
MathDisplay.WriteLine(@"3. Support integration = {0}", method.SupportsIntegration);
MathDisplay.WriteLine();
// 4. Check if interpolation support differentiation
MathDisplay.WriteLine(@"4. Support differentiation = {0}", method.SupportsDifferentiation);
MathDisplay.WriteLine();
// 5. Interpolate ten random points and compare to function results
MathDisplay.WriteLine(@"5. Interpolate ten random points and compare to function results");
rng = new MersenneTwister(1);
for (var i = 0; i < 10; i++)
{
// Generate random value from [0, 5]
var point = rng.Next(0, 5);
MathDisplay.WriteLine(
@"Interpolate at {0} = {1}. Function({0}) = {2}",
point.ToString("N05"),
method.Interpolate(point).ToString("N05"),
TargetFunctionWithPolesEx(point).ToString("N05"));
}
MathDisplay.WriteLine();
}
public override void ExecuteExample()
{
// <seealso cref="http://en.wikipedia.org/wiki/Biconjugate_gradient_stabilized_method">Biconjugate gradient stabilized method</seealso>
MathDisplay.WriteLine("<b>Biconjugate gradient stabilised iterative solver</b>");
// Format matrix output to console
var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone();
formatProvider.TextInfo.ListSeparator = " ";
// Solve next system of linear equations (Ax=b):
// 5*x + 2*y - 4*z = -7
// 3*x - 7*y + 6*z = 38
// 4*x + 1*y + 5*z = 43
// Create matrix "A" with coefficients
var matrixA = DenseMatrix.OfArray(new[, ] {
{ 5.00, 2.00, -4.00 }, { 3.00, -7.00, 6.00 }, { 4.00, 1.00, 5.00 }
});
MathDisplay.WriteLine(@"Matrix 'A' with coefficients");
MathDisplay.WriteLine(matrixA.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// Create vector "b" with the constant terms.
var vectorB = new DenseVector(new[] { -7.0, 38.0, 43.0 });
MathDisplay.WriteLine(@"Vector 'b' with the constant terms");
MathDisplay.WriteLine(vectorB.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// Create stop criteria to monitor an iterative calculation. There are next available stop criteria:
// - DivergenceStopCriterion: monitors an iterative calculation for signs of divergence;
// - FailureStopCriterion: monitors residuals for NaN's;
// - IterationCountStopCriterion: monitors the numbers of iteration steps;
// - ResidualStopCriterion: monitors residuals if calculation is considered converged;
// Stop calculation if 1000 iterations reached during calculation
var iterationCountStopCriterion = new IterationCountStopCriterion <double>(1000);
// Stop calculation if residuals are below 1E-10 --> the calculation is considered converged
var residualStopCriterion = new ResidualStopCriterion <double>(1e-10);
// Create monitor with defined stop criteria
var monitor = new Iterator <double>(iterationCountStopCriterion, residualStopCriterion);
// Create Bi-Conjugate Gradient Stabilized solver
var solverBiCgStab = new BiCgStab();
// 1. Solve the matrix equation
var resultX = matrixA.SolveIterative(vectorB, solverBiCgStab, monitor);
MathDisplay.WriteLine(@"1. Solve the matrix equation");
MathDisplay.WriteLine();
// 2. Check solver status of the iterations.
// Solver has property IterationResult which contains the status of the iteration once the calculation is finished.
// Possible values are:
// - CalculationCancelled: calculation was cancelled by the user;
// - CalculationConverged: calculation has converged to the desired convergence levels;
// - CalculationDiverged: calculation diverged;
// - CalculationFailure: calculation has failed for some reason;
// - CalculationIndetermined: calculation is indetermined, not started or stopped;
// - CalculationRunning: calculation is running and no results are yet known;
// - CalculationStoppedWithoutConvergence: calculation has been stopped due to reaching the stopping limits, but that convergence was not achieved;
MathDisplay.WriteLine(@"2. Solver status of the iterations");
MathDisplay.WriteLine(monitor.Status.ToString());
MathDisplay.WriteLine();
// 3. Solution result vector of the matrix equation
MathDisplay.WriteLine(@"3. Solution result vector of the matrix equation");
MathDisplay.WriteLine(resultX.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 4. Verify result. Multiply coefficient matrix "A" by result vector "x"
var reconstructVecorB = matrixA * resultX;
MathDisplay.WriteLine(@"4. Multiply coefficient matrix 'A' by result vector 'x'");
MathDisplay.WriteLine(reconstructVecorB.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
MathDisplay.WriteLine("<b>Generalized product biconjugate gradient solver</b>");
// Solve next system of linear equations (Ax=b):
// 5*x + 2*y - 4*z = -7
// 3*x - 7*y + 6*z = 38
// 4*x + 1*y + 5*z = 43
// Create matrix "A" with coefficients
matrixA = DenseMatrix.OfArray(new[, ] {
{ 5.00, 2.00, -4.00 }, { 3.00, -7.00, 6.00 }, { 4.00, 1.00, 5.00 }
});
MathDisplay.WriteLine(@"Matrix 'A' with coefficients");
MathDisplay.WriteLine(matrixA.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// Create vector "b" with the constant terms.
vectorB = new DenseVector(new[] { -7.0, 38.0, 43.0 });
MathDisplay.WriteLine(@"Vector 'b' with the constant terms");
MathDisplay.WriteLine(vectorB.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// Create stop criteria to monitor an iterative calculation. There are next available stop criteria:
// - DivergenceStopCriterion: monitors an iterative calculation for signs of divergence;
// - FailureStopCriterion: monitors residuals for NaN's;
// - IterationCountStopCriterion: monitors the numbers of iteration steps;
// - ResidualStopCriterion: monitors residuals if calculation is considered converged;
// Stop calculation if 1000 iterations reached during calculation
iterationCountStopCriterion = new IterationCountStopCriterion <double>(1000);
// Stop calculation if residuals are below 1E-10 --> the calculation is considered converged
residualStopCriterion = new ResidualStopCriterion <double>(1e-10);
// Create monitor with defined stop criteria
monitor = new Iterator <double>(iterationCountStopCriterion, residualStopCriterion);
// Create Generalized Product Bi-Conjugate Gradient solver
var solverGpBiCg = new GpBiCg();
// 1. Solve the matrix equation
resultX = matrixA.SolveIterative(vectorB, solverGpBiCg, monitor);
MathDisplay.WriteLine(@"1. Solve the matrix equation");
MathDisplay.WriteLine();
// 2. Check solver status of the iterations.
// Solver has property IterationResult which contains the status of the iteration once the calculation is finished.
// Possible values are:
// - CalculationCancelled: calculation was cancelled by the user;
// - CalculationConverged: calculation has converged to the desired convergence levels;
// - CalculationDiverged: calculation diverged;
// - CalculationFailure: calculation has failed for some reason;
// - CalculationIndetermined: calculation is indetermined, not started or stopped;
// - CalculationRunning: calculation is running and no results are yet known;
// - CalculationStoppedWithoutConvergence: calculation has been stopped due to reaching the stopping limits, but that convergence was not achieved;
MathDisplay.WriteLine(@"2. Solver status of the iterations");
MathDisplay.WriteLine(monitor.Status.ToString());
MathDisplay.WriteLine();
// 3. Solution result vector of the matrix equation
MathDisplay.WriteLine(@"3. Solution result vector of the matrix equation");
MathDisplay.WriteLine(resultX.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 4. Verify result. Multiply coefficient matrix "A" by result vector "x"
reconstructVecorB = matrixA * resultX;
MathDisplay.WriteLine(@"4. Multiply coefficient matrix 'A' by result vector 'x'");
MathDisplay.WriteLine(reconstructVecorB.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
MathDisplay.WriteLine("<b>Composite linear equation solver</b>");
// Solve next system of linear equations (Ax=b):
// 5*x + 2*y - 4*z = -7
// 3*x - 7*y + 6*z = 38
// 4*x + 1*y + 5*z = 43
// Create matrix "A" with coefficients
matrixA = DenseMatrix.OfArray(new[, ] {
{ 5.00, 2.00, -4.00 }, { 3.00, -7.00, 6.00 }, { 4.00, 1.00, 5.00 }
});
MathDisplay.WriteLine(@"Matrix 'A' with coefficients");
MathDisplay.WriteLine(matrixA.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// Create vector "b" with the constant terms.
vectorB = new DenseVector(new[] { -7.0, 38.0, 43.0 });
MathDisplay.WriteLine(@"Vector 'b' with the constant terms");
MathDisplay.WriteLine(vectorB.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// Create stop criteria to monitor an iterative calculation. There are next available stop criteria:
// - DivergenceStopCriterion: monitors an iterative calculation for signs of divergence;
// - FailureStopCriterion: monitors residuals for NaN's;
// - IterationCountStopCriterion: monitors the numbers of iteration steps;
// - ResidualStopCriterion: monitors residuals if calculation is considered converged;
// Stop calculation if 1000 iterations reached during calculation
iterationCountStopCriterion = new IterationCountStopCriterion <double>(1000);
// Stop calculation if residuals are below 1E-10 --> the calculation is considered converged
residualStopCriterion = new ResidualStopCriterion <double>(1e-10);
// Create monitor with defined stop criteria
monitor = new Iterator <double>(iterationCountStopCriterion, residualStopCriterion);
// Load all suitable solvers from current assembly. Below (see UserBiCgStab) there is a custom user-defined solver
// "class UserBiCgStab : IIterativeSolverSetup<double>" which derives from the regular BiCgStab solver. However users can
// create any other solver and solver setup classes that implement IIterativeSolverSetup<T> and load the assembly that
// contains them using the following function:
var solverComp = new CompositeSolver(SolverSetup <double> .LoadFromAssembly(Assembly.GetExecutingAssembly()));
// 1. Solve the linear system
resultX = matrixA.SolveIterative(vectorB, solverComp, monitor);
MathDisplay.WriteLine(@"1. Solve the matrix equation");
MathDisplay.WriteLine();
// 2. Check solver status of the iterations.
// Solver has property IterationResult which contains the status of the iteration once the calculation is finished.
// Possible values are:
// - CalculationCancelled: calculation was cancelled by the user;
// - CalculationConverged: calculation has converged to the desired convergence levels;
// - CalculationDiverged: calculation diverged;
// - CalculationFailure: calculation has failed for some reason;
// - CalculationIndetermined: calculation is indetermined, not started or stopped;
// - CalculationRunning: calculation is running and no results are yet known;
// - CalculationStoppedWithoutConvergence: calculation has been stopped due to reaching the stopping limits, but that convergence was not achieved;
MathDisplay.WriteLine(@"2. Solver status of the iterations");
MathDisplay.WriteLine(monitor.Status.ToString());
MathDisplay.WriteLine();
// 3. Solution result vector of the matrix equation
MathDisplay.WriteLine(@"3. Solution result vector of the matrix equation");
MathDisplay.WriteLine(resultX.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 4. Verify result. Multiply coefficient matrix "A" by result vector "x"
reconstructVecorB = matrixA * resultX;
MathDisplay.WriteLine(@"4. Multiply coefficient matrix 'A' by result vector 'x'");
MathDisplay.WriteLine(reconstructVecorB.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
MathDisplay.WriteLine("<b>Multiple-Lanczos biconjugate gradient stabilised iterative solver</b>");
// Solve next system of linear equations (Ax=b):
// 5*x + 2*y - 4*z = -7
// 3*x - 7*y + 6*z = 38
// 4*x + 1*y + 5*z = 43
// Create matrix "A" with coefficients
matrixA = DenseMatrix.OfArray(new[, ] {
{ 5.00, 2.00, -4.00 }, { 3.00, -7.00, 6.00 }, { 4.00, 1.00, 5.00 }
});
MathDisplay.WriteLine(@"Matrix 'A' with coefficients");
MathDisplay.WriteLine(matrixA.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// Create vector "b" with the constant terms.
vectorB = new DenseVector(new[] { -7.0, 38.0, 43.0 });
MathDisplay.WriteLine(@"Vector 'b' with the constant terms");
MathDisplay.WriteLine(vectorB.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// Create stop criteria to monitor an iterative calculation. There are next available stop criteria:
// - DivergenceStopCriterion: monitors an iterative calculation for signs of divergence;
// - FailureStopCriterion: monitors residuals for NaN's;
// - IterationCountStopCriterion: monitors the numbers of iteration steps;
// - ResidualStopCriterion: monitors residuals if calculation is considered converged;
// Stop calculation if 1000 iterations reached during calculation
iterationCountStopCriterion = new IterationCountStopCriterion <double>(1000);
// Stop calculation if residuals are below 1E-10 --> the calculation is considered converged
residualStopCriterion = new ResidualStopCriterion <double>(1e-10);
// Create monitor with defined stop criteria
monitor = new Iterator <double>(iterationCountStopCriterion, residualStopCriterion);
// Create Multiple-Lanczos Bi-Conjugate Gradient Stabilized solver
var solverLanczos = new MlkBiCgStab();
// 1. Solve the matrix equation
resultX = matrixA.SolveIterative(vectorB, solverLanczos, monitor);
MathDisplay.WriteLine(@"1. Solve the matrix equation");
MathDisplay.WriteLine();
// 2. Check solver status of the iterations.
// Solver has property IterationResult which contains the status of the iteration once the calculation is finished.
// Possible values are:
// - CalculationCancelled: calculation was cancelled by the user;
// - CalculationConverged: calculation has converged to the desired convergence levels;
// - CalculationDiverged: calculation diverged;
// - CalculationFailure: calculation has failed for some reason;
// - CalculationIndetermined: calculation is indetermined, not started or stopped;
// - CalculationRunning: calculation is running and no results are yet known;
// - CalculationStoppedWithoutConvergence: calculation has been stopped due to reaching the stopping limits, but that convergence was not achieved;
MathDisplay.WriteLine(@"2. Solver status of the iterations");
MathDisplay.WriteLine(monitor.Status.ToString());
MathDisplay.WriteLine();
// 3. Solution result vector of the matrix equation
MathDisplay.WriteLine(@"3. Solution result vector of the matrix equation");
MathDisplay.WriteLine(resultX.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 4. Verify result. Multiply coefficient matrix "A" by result vector "x"
reconstructVecorB = matrixA * resultX;
MathDisplay.WriteLine(@"4. Multiply coefficient matrix 'A' by result vector 'x'");
MathDisplay.WriteLine(reconstructVecorB.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
MathDisplay.WriteLine("<b>Transpose freee quasi-minimal residual iterative solver</b>");
// Solve next system of linear equations (Ax=b):
// 5*x + 2*y - 4*z = -7
// 3*x - 7*y + 6*z = 38
// 4*x + 1*y + 5*z = 43
// Create matrix "A" with coefficients
matrixA = DenseMatrix.OfArray(new[, ] {
{ 5.00, 2.00, -4.00 }, { 3.00, -7.00, 6.00 }, { 4.00, 1.00, 5.00 }
});
MathDisplay.WriteLine(@"Matrix 'A' with coefficients");
MathDisplay.WriteLine(matrixA.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// Create vector "b" with the constant terms.
vectorB = new DenseVector(new[] { -7.0, 38.0, 43.0 });
MathDisplay.WriteLine(@"Vector 'b' with the constant terms");
MathDisplay.WriteLine(vectorB.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// Create stop criteria to monitor an iterative calculation. There are next available stop criteria:
// - DivergenceStopCriterion: monitors an iterative calculation for signs of divergence;
// - FailureStopCriterion: monitors residuals for NaN's;
// - IterationCountStopCriterion: monitors the numbers of iteration steps;
// - ResidualStopCriterion: monitors residuals if calculation is considered converged;
// Stop calculation if 1000 iterations reached during calculation
iterationCountStopCriterion = new IterationCountStopCriterion <double>(1000);
// Stop calculation if residuals are below 1E-10 --> the calculation is considered converged
residualStopCriterion = new ResidualStopCriterion <double>(1e-10);
// Create monitor with defined stop criteria
monitor = new Iterator <double>(iterationCountStopCriterion, residualStopCriterion);
// Create Transpose Free Quasi-Minimal Residual solver
var solverTFQMR = new TFQMR();
// 1. Solve the matrix equation
resultX = matrixA.SolveIterative(vectorB, solverTFQMR, monitor);
MathDisplay.WriteLine(@"1. Solve the matrix equation");
MathDisplay.WriteLine();
// 2. Check solver status of the iterations.
// Solver has property IterationResult which contains the status of the iteration once the calculation is finished.
// Possible values are:
// - CalculationCancelled: calculation was cancelled by the user;
// - CalculationConverged: calculation has converged to the desired convergence levels;
// - CalculationDiverged: calculation diverged;
// - CalculationFailure: calculation has failed for some reason;
// - CalculationIndetermined: calculation is indetermined, not started or stopped;
// - CalculationRunning: calculation is running and no results are yet known;
// - CalculationStoppedWithoutConvergence: calculation has been stopped due to reaching the stopping limits, but that convergence was not achieved;
MathDisplay.WriteLine(@"2. Solver status of the iterations");
MathDisplay.WriteLine(monitor.Status.ToString());
MathDisplay.WriteLine();
// 3. Solution result vector of the matrix equation
MathDisplay.WriteLine(@"3. Solution result vector of the matrix equation");
MathDisplay.WriteLine(resultX.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 4. Verify result. Multiply coefficient matrix "A" by result vector "x"
reconstructVecorB = matrixA * resultX;
MathDisplay.WriteLine(@"4. Multiply coefficient matrix 'A' by result vector 'x'");
MathDisplay.WriteLine(reconstructVecorB.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
}
/// <summary>
/// Executes the example.
/// </summary>
public override void ExecuteExample()
{
// <seealso cref="http://en.wikipedia.org/wiki/Beta_function">Beta function</seealso>
MathDisplay.WriteLine("<b>Beta fuction</b>");
// 1. Compute the Beta function at z = 1.0, w = 3.0
MathDisplay.WriteLine(@"1. Compute the Beta function at z = 1.0, w = 3.0");
MathDisplay.WriteLine(SpecialFunctions.Beta(1.0, 3.0).ToString());
MathDisplay.WriteLine();
// 2. Compute the logarithm of the Beta function at z = 1.0, w = 3.0
MathDisplay.WriteLine(@"2. Compute the logarithm of the Beta function at z = 1.0, w = 3.0");
MathDisplay.WriteLine(SpecialFunctions.BetaLn(1.0, 3.0).ToString());
MathDisplay.WriteLine();
// 3. Compute the Beta incomplete function at z = 1.0, w = 3.0, x = 0.7
MathDisplay.WriteLine(@"3. Compute the Beta incomplete function at z = 1.0, w = 3.0, x = 0.7");
MathDisplay.WriteLine(SpecialFunctions.BetaIncomplete(1.0, 3.0, 0.7).ToString());
MathDisplay.WriteLine();
// 4. Compute the Beta incomplete function at z = 1.0, w = 3.0, x = 1.0
MathDisplay.WriteLine(@"4. Compute the Beta incomplete function at z = 1.0, w = 3.0, x = 1.0");
MathDisplay.WriteLine(SpecialFunctions.BetaIncomplete(1.0, 3.0, 1.0).ToString());
MathDisplay.WriteLine();
// 5. Compute the Beta regularized function at z = 1.0, w = 3.0, x = 0.7
MathDisplay.WriteLine(@"5. Compute the Beta regularized function at z = 1.0, w = 3.0, x = 0.7");
MathDisplay.WriteLine(SpecialFunctions.BetaRegularized(1.0, 3.0, 0.7).ToString());
MathDisplay.WriteLine();
// 6. Compute the Beta regularized function at z = 1.0, w = 3.0, x = 1.0
MathDisplay.WriteLine(@"6. Compute the Beta regularized function at z = 1.0, w = 3.0, x = 1.0");
MathDisplay.WriteLine(SpecialFunctions.BetaRegularized(1.0, 3.0, 1.0).ToString());
MathDisplay.WriteLine();
MathDisplay.WriteLine("<b>Common functions</b>");
// 1. Calculate the Digamma function at point 5.0
// <seealso cref="http://en.wikipedia.org/wiki/Digamma_function">Digamma function</seealso>
MathDisplay.WriteLine(@"1. Calculate the Digamma function at point 5.0");
MathDisplay.WriteLine(SpecialFunctions.DiGamma(5.0).ToString());
MathDisplay.WriteLine();
// 2. Calculate the inverse Digamma function at point 1.5
MathDisplay.WriteLine(@"2. Calculate the inverse Digamma function at point 1.5");
MathDisplay.WriteLine(SpecialFunctions.DiGammaInv(1.5).ToString());
MathDisplay.WriteLine();
// 3. Calculate the 10'th Harmonic number
// <seealso cref="http://en.wikipedia.org/wiki/Harmonic_number">Harmonic number</seealso>
MathDisplay.WriteLine(@"3. Calculate the 10'th Harmonic number");
MathDisplay.WriteLine(SpecialFunctions.Harmonic(10).ToString());
MathDisplay.WriteLine();
// 4. Calculate the generalized harmonic number of order 10 of 3.0.
// <seealso cref="http://en.wikipedia.org/wiki/Harmonic_number#Generalized_harmonic_numbers">Generalized harmonic numbers</seealso>
MathDisplay.WriteLine(@"4. Calculate the generalized harmonic number of order 10 of 3.0");
MathDisplay.WriteLine(SpecialFunctions.GeneralHarmonic(10, 3.0).ToString());
MathDisplay.WriteLine();
// 5. Calculate the logistic function of 3.0
// <seealso cref="http://en.wikipedia.org/wiki/Logistic_function">Logistic function</seealso>
MathDisplay.WriteLine(@"5. Calculate the logistic function of 3.0");
MathDisplay.WriteLine(SpecialFunctions.Logistic(3.0).ToString());
MathDisplay.WriteLine();
// 6. Calculate the logit function of 0.3
// <seealso cref="http://en.wikipedia.org/wiki/Logit">Logit function</seealso>
MathDisplay.WriteLine(@"6. Calculate the logit function of 0.3");
MathDisplay.WriteLine(SpecialFunctions.Logit(0.3).ToString());
MathDisplay.WriteLine();
// <seealso cref="http://en.wikipedia.org/wiki/Error_function">Error function</seealso>
MathDisplay.WriteLine("<b>Error function</b>");
// 1. Calculate the error function at point 2
MathDisplay.WriteLine(@"1. Calculate the error function at point 2");
MathDisplay.WriteLine(SpecialFunctions.Erf(2).ToString());
MathDisplay.WriteLine();
// 2. Sample 10 values of the error function in [-1.0; 1.0]
MathDisplay.WriteLine(@"2. Sample 10 values of the error function in [-1.0; 1.0]");
var data = Generate.LinearSpacedMap <double>(10, -1.0, 1.0, SpecialFunctions.Erf);
for (var i = 0; i < data.Length; i++)
{
MathDisplay.Write(data[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 3. Calculate the complementary error function at point 2
MathDisplay.WriteLine(@"3. Calculate the complementary error function at point 2");
MathDisplay.WriteLine(SpecialFunctions.Erfc(2).ToString());
MathDisplay.WriteLine();
// 4. Sample 10 values of the complementary error function in [-1.0; 1.0]
MathDisplay.WriteLine(@"4. Sample 10 values of the complementary error function in [-1.0; 1.0]");
data = Generate.LinearSpacedMap <double>(10, -1.0, 1.0, SpecialFunctions.Erfc);
for (var i = 0; i < data.Length; i++)
{
MathDisplay.Write(data[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 5. Calculate the inverse error function at point z=0.5
MathDisplay.WriteLine(@"5. Calculate the inverse error function at point z=0.5");
MathDisplay.WriteLine(SpecialFunctions.ErfInv(0.5).ToString());
MathDisplay.WriteLine();
// 6. Sample 10 values of the inverse error function in [-1.0; 1.0]
MathDisplay.WriteLine(@"6. Sample 10 values of the inverse error function in [-1.0; 1.0]");
data = Generate.LinearSpacedMap <double>(10, -1.0, 1.0, SpecialFunctions.ErfInv);
for (var i = 0; i < data.Length; i++)
{
MathDisplay.Write(data[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 7. Calculate the complementary inverse error function at point z=0.5
MathDisplay.WriteLine(@"7. Calculate the complementary inverse error function at point z=0.5");
MathDisplay.WriteLine(SpecialFunctions.ErfcInv(0.5).ToString());
MathDisplay.WriteLine();
// 8. Sample 10 values of the complementary inverse error function in [-1.0; 1.0]
MathDisplay.WriteLine(@"8. Sample 10 values of the complementary inverse error function in [-1.0; 1.0]");
data = Generate.LinearSpacedMap <double>(10, -1.0, 1.0, SpecialFunctions.ErfcInv);
for (var i = 0; i < data.Length; i++)
{
MathDisplay.Write(data[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
// <seealso cref="http://en.wikipedia.org/wiki/Factorial">Factorial</seealso>
MathDisplay.WriteLine("<b>Factorial</b>");
// 1. Compute the factorial of 5
MathDisplay.WriteLine(@"1. Compute the factorial of 5");
MathDisplay.WriteLine(SpecialFunctions.Factorial(5).ToString("N"));
MathDisplay.WriteLine();
// 2. Compute the logarithm of the factorial of 5
MathDisplay.WriteLine(@"2. Compute the logarithm of the factorial of 5");
MathDisplay.WriteLine(SpecialFunctions.FactorialLn(5).ToString("N"));
MathDisplay.WriteLine();
// <seealso cref="http://en.wikipedia.org/wiki/Binomial_coefficient">Binomial coefficient</seealso>
MathDisplay.WriteLine("<b>Binomial coefficient</b>");
// 3. Compute the binomial coefficient: 10 choose 8
MathDisplay.WriteLine(@"3. Compute the binomial coefficient: 10 choose 8");
MathDisplay.WriteLine(SpecialFunctions.Binomial(10, 8).ToString("N"));
MathDisplay.WriteLine();
// 4. Compute the logarithm of the binomial coefficient: 10 choose 8
MathDisplay.WriteLine(@"4. Compute the logarithm of the binomial coefficient: 10 choose 8");
MathDisplay.WriteLine(SpecialFunctions.BinomialLn(10, 8).ToString("N"));
MathDisplay.WriteLine();
// <seealso cref="http://en.wikipedia.org/wiki/Multinomial_theorem#Multinomial_coefficients">Multinomial coefficients</seealso>
MathDisplay.WriteLine("<b>Multinomial coefficient</b>");
// 5. Compute the multinomial coefficient: 10 choose 2, 3, 5
MathDisplay.WriteLine(@"5. Compute the multinomial coefficient: 10 choose 2, 3, 5");
MathDisplay.WriteLine(SpecialFunctions.Multinomial(10, new[] { 2, 3, 5 }).ToString("N"));
MathDisplay.WriteLine();
// <seealso cref="http://en.wikipedia.org/wiki/Gamma_function">Gamma function</seealso>
MathDisplay.WriteLine("<b>Gamma function</b>");
// 1. Compute the Gamma function of 10
MathDisplay.WriteLine(@"1. Compute the Gamma function of 10");
MathDisplay.WriteLine(SpecialFunctions.Gamma(10).ToString("N"));
MathDisplay.WriteLine();
// 2. Compute the logarithm of the Gamma function of 10
MathDisplay.WriteLine(@"2. Compute the logarithm of the Gamma function of 10");
MathDisplay.WriteLine(SpecialFunctions.GammaLn(10).ToString("N"));
MathDisplay.WriteLine();
// 3. Compute the lower incomplete gamma(a, x) function at a = 10, x = 14
MathDisplay.WriteLine(@"3. Compute the lower incomplete gamma(a, x) function at a = 10, x = 14");
MathDisplay.WriteLine(SpecialFunctions.GammaLowerIncomplete(10, 14).ToString("N"));
MathDisplay.WriteLine();
// 4. Compute the lower incomplete gamma(a, x) function at a = 10, x = 100
MathDisplay.WriteLine(@"4. Compute the lower incomplete gamma(a, x) function at a = 10, x = 100");
MathDisplay.WriteLine(SpecialFunctions.GammaLowerIncomplete(10, 100).ToString("N"));
MathDisplay.WriteLine();
// 5. Compute the upper incomplete gamma(a, x) function at a = 10, x = 0
MathDisplay.WriteLine(@"5. Compute the upper incomplete gamma(a, x) function at a = 10, x = 0");
MathDisplay.WriteLine(SpecialFunctions.GammaUpperIncomplete(10, 0).ToString("N"));
MathDisplay.WriteLine();
// 6. Compute the upper incomplete gamma(a, x) function at a = 10, x = 10
MathDisplay.WriteLine(@"6. Compute the upper incomplete gamma(a, x) function at a = 10, x = 100");
MathDisplay.WriteLine(SpecialFunctions.GammaLowerIncomplete(10, 10).ToString("N"));
MathDisplay.WriteLine();
// 7. Compute the lower regularized gamma(a, x) function at a = 10, x = 14
MathDisplay.WriteLine(@"7. Compute the lower regularized gamma(a, x) function at a = 10, x = 14");
MathDisplay.WriteLine(SpecialFunctions.GammaLowerRegularized(10, 14).ToString("N"));
MathDisplay.WriteLine();
// 8. Compute the lower regularized gamma(a, x) function at a = 10, x = 100
MathDisplay.WriteLine(@"8. Compute the lower regularized gamma(a, x) function at a = 10, x = 100");
MathDisplay.WriteLine(SpecialFunctions.GammaLowerRegularized(10, 100).ToString("N"));
MathDisplay.WriteLine();
// 9. Compute the upper regularized gamma(a, x) function at a = 10, x = 0
MathDisplay.WriteLine(@"9. Compute the upper regularized gamma(a, x) function at a = 10, x = 0");
MathDisplay.WriteLine(SpecialFunctions.GammaUpperRegularized(10, 0).ToString("N"));
MathDisplay.WriteLine();
// 10. Compute the upper regularized gamma(a, x) function at a = 10, x = 10
MathDisplay.WriteLine(@"10. Compute the upper regularized gamma(a, x) function at a = 10, x = 100");
MathDisplay.WriteLine(SpecialFunctions.GammaUpperRegularized(10, 10).ToString("N"));
MathDisplay.WriteLine();
MathDisplay.WriteLine("<b>Numerical stability</b>");
// 1. Compute numerically stable exponential of 10 minus one
MathDisplay.WriteLine(@"1. Compute numerically stable exponential of 4.2876 minus one");
MathDisplay.WriteLine(SpecialFunctions.ExponentialMinusOne(4.2876).ToString());
MathDisplay.WriteLine();
// 2. Compute regular System.Math exponential of 15.28 minus one
MathDisplay.WriteLine(@"2. Compute regular System.Math exponential of 4.2876 minus one ");
MathDisplay.WriteLine((Math.Exp(4.2876) - 1).ToString());
MathDisplay.WriteLine();
// 3. Compute numerically stable hypotenuse of a right angle triangle with a = 5, b = 3
MathDisplay.WriteLine(@"3. Compute numerically stable hypotenuse of a right angle triangle with a = 5, b = 3");
MathDisplay.WriteLine(SpecialFunctions.Hypotenuse(5, 3).ToString());
MathDisplay.WriteLine();
}
/// <summary>
/// Execute example
/// </summary>
/// <seealso cref="http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient">Pearson
/// product-moment correlation coefficient</seealso>
public override void ExecuteExample()
{
// 1. Initialize the new instance of the ChiSquare distribution class with parameter dof = 5.
var chiSquare = new ChiSquared(5);
MathDisplay.WriteLine(@"1. Initialize the new instance of the ChiSquare distribution class with parameter DegreesOfFreedom = {0}", chiSquare.DegreesOfFreedom);
MathDisplay.WriteLine(@"{0} distributuion properties:", chiSquare);
MathDisplay.WriteLine(@"{0} - Largest element", chiSquare.Maximum.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine(@"{0} - Smallest element", chiSquare.Minimum.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine(@"{0} - Mean", chiSquare.Mean.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine(@"{0} - Median", chiSquare.Median.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine(@"{0} - Mode", chiSquare.Mode.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine(@"{0} - Variance", chiSquare.Variance.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine(@"{0} - Standard deviation", chiSquare.StdDev.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine(@"{0} - Skewness", chiSquare.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 2. Generate 1000 samples of the ChiSquare(5) distribution
MathDisplay.WriteLine(@"2. Generate 1000 samples of the ChiSquare(5) distribution");
var data = new double[1000];
for (var i = 0; i < data.Length; i++)
{
data[i] = chiSquare.Sample();
}
// 3. Get basic statistics on set of generated data using extention methods
MathDisplay.WriteLine(@"3. Get basic statistics on set of generated data using extention methods");
MathDisplay.WriteLine(@"{0} - Largest element", data.Maximum().ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine(@"{0} - Smallest element", data.Minimum().ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine(@"{0} - Mean", data.Mean().ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine(@"{0} - Median", data.Median().ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine(@"{0} - Biased population variance", data.PopulationVariance().ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine(@"{0} - Variance", data.Variance().ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine(@"{0} - Standard deviation", data.StandardDeviation().ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine(@"{0} - Biased sample standard deviation", data.PopulationStandardDeviation().ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 4. Compute the basic statistics of data set using DescriptiveStatistics class
MathDisplay.WriteLine(@"4. Compute the basic statistics of data set using DescriptiveStatistics class");
var descriptiveStatistics = new DescriptiveStatistics(data);
MathDisplay.WriteLine(@"{0} - Kurtosis", descriptiveStatistics.Kurtosis.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine(@"{0} - Largest element", descriptiveStatistics.Maximum.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine(@"{0} - Smallest element", descriptiveStatistics.Minimum.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine(@"{0} - Mean", descriptiveStatistics.Mean.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine(@"{0} - Variance", descriptiveStatistics.Variance.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine(@"{0} - Standard deviation", descriptiveStatistics.StandardDeviation.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine(@"{0} - Skewness", descriptiveStatistics.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// Generate 1000 samples of the ChiSquare(2.5) distribution
var chiSquareB = new ChiSquared(2);
var dataB = new double[1000];
for (var i = 0; i < data.Length; i++)
{
dataB[i] = chiSquareB.Sample();
}
// 5. Correlation coefficient between 1000 samples of ChiSquare(5) and ChiSquare(2.5)
MathDisplay.WriteLine(@"5. Correlation coefficient between 1000 samples of ChiSquare(5) and ChiSquare(2.5) is {0}", Correlation.Pearson(data, dataB).ToString("N04"));
MathDisplay.WriteLine(@"6. Ranked correlation coefficient between 1000 samples of ChiSquare(5) and ChiSquare(2.5) is {0}", Correlation.Spearman(data, dataB).ToString("N04"));
MathDisplay.WriteLine();
// 6. Correlation coefficient between 1000 samples of f(x) = x * 2 and f(x) = x * x
data = Generate.LinearSpacedMap(1000, 0, 100, x => x * 2);
dataB = Generate.LinearSpacedMap(1000, 0, 100, x => x * x);
MathDisplay.WriteLine(@"7. Correlation coefficient between 1000 samples of f(x) = x * 2 and f(x) = x * x is {0}", Correlation.Pearson(data, dataB).ToString("N04"));
MathDisplay.WriteLine(@"8. Ranked correlation coefficient between 1000 samples of f(x) = x * 2 and f(x) = x * x is {0}", Correlation.Spearman(data, dataB).ToString("N04"));
MathDisplay.WriteLine();
}
/// <summary>
/// Executes the example.
/// </summary>
public override void ExecuteExample()
{
// 1. Find out whether the provided number is an even number
MathDisplay.WriteLine(@"1. Find out whether the provided number is an even number");
MathDisplay.WriteLine(@"{0} is even = {1}. {2} is even = {3}", 1, Euclid.IsEven(1), 2, 2.IsEven());
MathDisplay.WriteLine();
// 2. Find out whether the provided number is an odd number
MathDisplay.WriteLine(@"2. Find out whether the provided number is an odd number");
MathDisplay.WriteLine(@"{0} is odd = {1}. {2} is odd = {3}", 1, 1.IsOdd(), 2, Euclid.IsOdd(2));
MathDisplay.WriteLine();
// 3. Find out whether the provided number is a perfect power of two
MathDisplay.WriteLine(@"2. Find out whether the provided number is a perfect power of two");
MathDisplay.WriteLine(
@"{0} is power of two = {1}. {2} is power of two = {3}",
5,
5.IsPowerOfTwo(),
16,
Euclid.IsPowerOfTwo(16));
MathDisplay.WriteLine();
// 4. Find the closest perfect power of two that is larger or equal to 97
MathDisplay.WriteLine(@"4. Find the closest perfect power of two that is larger or equal to 97");
MathDisplay.WriteLine(97.CeilingToPowerOfTwo().ToString());
MathDisplay.WriteLine();
// 5. Raise 2 to the 16
MathDisplay.WriteLine(@"5. Raise 2 to the 16");
MathDisplay.WriteLine(16.PowerOfTwo().ToString());
MathDisplay.WriteLine();
// 6. Find out whether the number is a perfect square
MathDisplay.WriteLine(@"6. Find out whether the number is a perfect square");
MathDisplay.WriteLine(
@"{0} is perfect square = {1}. {2} is perfect square = {3}",
37,
37.IsPerfectSquare(),
81,
Euclid.IsPerfectSquare(81));
MathDisplay.WriteLine();
// 7. Compute the greatest common divisor of 32 and 36
MathDisplay.WriteLine(@"7. Returns the greatest common divisor of 32 and 36");
MathDisplay.WriteLine(Euclid.GreatestCommonDivisor(32, 36).ToString());
MathDisplay.WriteLine();
// 8. Compute the greatest common divisor of 492, -984, 123, 246
MathDisplay.WriteLine(@"8. Returns the greatest common divisor of 492, -984, 123, 246");
MathDisplay.WriteLine(Euclid.GreatestCommonDivisor(492, -984, 123, 246).ToString());
MathDisplay.WriteLine();
// 9. Compute the extended greatest common divisor "z", such that 45*x + 18*y = z
MathDisplay.WriteLine(@"9. Compute the extended greatest common divisor Z, such that 45*x + 18*y = Z");
long x, y;
var z = Euclid.ExtendedGreatestCommonDivisor(45, 18, out x, out y);
MathDisplay.WriteLine(@"z = {0}, x = {1}, y = {2}. 45*{1} + 18*{2} = {0}", z, x, y);
MathDisplay.WriteLine();
// 10. Compute the least common multiple of 16 and 12
MathDisplay.WriteLine(@"10. Compute the least common multiple of 16 and 12");
MathDisplay.WriteLine(Euclid.LeastCommonMultiple(16, 12).ToString());
MathDisplay.WriteLine();
}
