public void IRID90_CholeskySolve()
{
Matrix i = Matrix.Identity(3, 3);
double[][] pvals1 = { new double[] { 1.0, 1.0, 1.0 }, new double[] { 1.0, 2.0, 3.0 }, new double[] { 1.0, 3.0, 6.0 } };
Matrix m1 = new Matrix(pvals1);
CholeskyDecomposition cd1 = new CholeskyDecomposition(m1);
Matrix inv1a = cd1.Solve(i);
Matrix test1a = m1 * inv1a;
NumericAssert.AreAlmostEqual(i, test1a, "1A");
Matrix inv1b = m1.Inverse();
NumericAssert.AreAlmostEqual(inv1a, inv1b, "1B");
double[][] pvals2 = { new double[] { 25, -5, 10 }, new double[] { -5, 17, 10 }, new double[] { 10, 10, 62 } };
Matrix m2 = new Matrix(pvals2);
CholeskyDecomposition cd2 = new CholeskyDecomposition(m2);
Matrix inv2a = cd2.Solve(i);
Matrix test2a = m2 * inv2a;
NumericAssert.AreAlmostEqual(i, test2a, "2A");
Matrix inv2b = m2.Inverse();
NumericAssert.AreAlmostEqual(inv2a, inv2b, "2B");
}
public double Distance(double[] x, double[] y)
{
double[] d = new double[x.Length];
for (int i = 0; i < x.Length; i++)
{
d[i] = x[i] - y[i];
}
double[] z;
if (svd != null)
{
z = svd.Solve(d);
}
else if (chol != null)
{
z = chol.Solve(d);
}
else
{
z = precision.Dot(d);
}
double sum = 0.0;
for (int i = 0; i < d.Length; i++)
{
sum += d[i] * z[i];
}
return(Math.Abs(sum));
}
/// <summary>
/// Gets the probability density function (pdf) for
/// this distribution evaluated at point <c>x</c>.
/// </summary>
/// <param name="x">A single point in the distribution range. For a
/// univariate distribution, this should be a single
/// double value. For a multivariate distribution,
/// this should be a double array.</param>
/// <returns>
/// The probability of <c>x</c> occurring
/// in the current distribution.
/// </returns>
/// <remarks>
/// The Probability Density Function (PDF) describes the
/// probability that a given value <c>x</c> will occur.
/// </remarks>
public override double ProbabilityDensityFunction(params double[] x)
{
if (x.Length != Dimension)
{
throw new DimensionMismatchException("x", "The vector should have the same dimension as the distribution.");
}
double[] z = x.Subtract(mean);
double[] a = chol.Solve(z);
double b = a.InnerProduct(z);
// Original code:
// double r = constant * System.Math.Exp(-b/2);
// Let lnconstant = log( constant )
//
// r = constant * exp( b/2 )
//
// r = exp(log(constant) * exp( b/2 )
// r = exp(lnconstant) * exp( b/2 )
// r = exp( lnconstant + b/2 )
//
double r = Math.Exp(lnconstant - b / 2);
return(r > 1.0 ? 1.0 : r);
}
public void CholeskyDecomposition2()
{
double[][] pvals = { new double[] { 1.0, 1.0, 1.0 }, new double[] { 1.0, 2.0, 3.0 }, new double[] { 1.0, 3.0, 6.0 } };
GeneralMatrix A = new GeneralMatrix(pvals);
CholeskyDecomposition chol = A.chol();
GeneralMatrix X = chol.Solve(GeneralMatrix.Identity(3, 3));
Assert.IsTrue(GeneralTests.Check(A.Multiply(X), GeneralMatrix.Identity(3, 3)));
}
/// <summary>
/// Gets the probability density function (pdf) for
/// this distribution evaluated at point <c>x</c>.
/// </summary>
///
/// <param name="x">A single point in the distribution range.
/// For a matrix distribution, such as the Wishart's, this
/// should be a positive-definite matrix or a matrix written
/// in flat vector form.
/// </param>
///
/// <returns>
/// The probability of <c>x</c> occurring
/// in the current distribution.
/// </returns>
///
/// <remarks>
/// The Probability Density Function (PDF) describes the
/// probability that a given value <c>x</c> will occur.
/// </remarks>
///
public double LogProbabilityDensityFunction(double[,] x)
{
var chol = new CholeskyDecomposition(x);
double det = chol.Determinant;
double[,] Vx = chol.Solve(inverseScaleMatrix);
double z = -0.5 * Vx.Trace();
return(Math.Log(constant) + power * Math.Log(det) + z);
}
/// <summary>
/// Gets the probability density function (pdf) for
/// this distribution evaluated at point <c>x</c>.
/// </summary>
/// <param name="x">A single point in the distribution range. For a
/// univariate distribution, this should be a single
/// double value. For a multivariate distribution,
/// this should be a double array.</param>
/// <returns>
/// The probability of <c>x</c> occurring
/// in the current distribution.
/// </returns>
/// <remarks>
/// The Probability Density Function (PDF) describes the
/// probability that a given value <c>x</c> will occur.
/// </remarks>
public override double ProbabilityDensityFunction(params double[] x)
{
double[] z = x.Subtract(mean);
double[] a = (svd == null) ? chol.Solve(z) : svd.Solve(z);
double b = a.InnerProduct(z);
double r = constant * System.Math.Exp(-0.5 * b);
return(r > 1.0 ? 1.0 : r);
}
/// <summary>
/// Gets the probability density function (pdf) for
/// this distribution evaluated at point <c>x</c>.
/// </summary>
///
/// <param name="x">A single point in the distribution range. For a
/// univariate distribution, this should be a single
/// double value. For a multivariate distribution,
/// this should be a double array.</param>
///
/// <returns>
/// The probability of <c>x</c> occurring
/// in the current distribution.
/// </returns>
///
/// <remarks>
/// The Probability Density Function (PDF) describes the
/// probability that a given value <c>x</c> will occur.
/// </remarks>
///
public override double ProbabilityDensityFunction(params double[] x)
{
if (x.Length != Dimension)
{
throw new DimensionMismatchException("x", "The vector should have the same dimension as the distribution.");
}
double[] z = new double[mean.Length];
for (int i = 0; i < x.Length; i++)
{
z[i] = x[i] - mean[i];
}
double[] a = chol.Solve(z);
double b = 0;
for (int i = 0; i < z.Length; i++)
{
b += a[i] * z[i];
}
// Original code:
// double r = constant * System.Math.Exp(-b/2);
// Let lnconstant = log( constant )
//
// r = constant * exp( b/2 )
//
// r = exp(log(constant) * exp( b/2 )
// r = exp(lnconstant) * exp( b/2 )
// r = exp( lnconstant + b/2 )
//
double r = Math.Exp(lnconstant - b * 0.5);
return(r > 1 ? 1 : r);
}
/// <summary>
/// Gets the probability density function (pdf) for
/// this distribution evaluated at point <c>x</c>.
/// </summary>
///
/// <param name="x">A single point in the distribution range.
/// For a matrix distribution, such as the Wishart's, this
/// should be a positive-definite matrix or a matrix written
/// in flat vector form.
/// </param>
///
/// <returns>
/// The probability of <c>x</c> occurring
/// in the current distribution.
/// </returns>
///
/// <remarks>
/// The Probability Density Function (PDF) describes the
/// probability that a given value <c>x</c> will occur.
/// </remarks>
///
public double ProbabilityDensityFunction(double[,] x)
{
var chol = new CholeskyDecomposition(x);
double det = chol.Determinant;
double[,] Vx = chol.Solve(inverseScaleMatrix);
double z = -0.5 * Vx.Trace();
double a = Math.Pow(det, power);
double b = Math.Exp(z);
return(constant * a * b);
}
public void CholeskySolveExample()
{
// This is a very simple 3 X 3 problem I just wrote down to test the Cholesky solver
SymmetricMatrix S = new SymmetricMatrix(3);
S[0, 0] = 4.0;
S[1, 0] = -2.0; S[1, 1] = 5.0;
S[2, 0] = 1.0; S[2, 1] = 3.0; S[2, 2] = 6.0;
CholeskyDecomposition CD = S.CholeskyDecomposition();
ColumnVector b = new ColumnVector(9.0, 7.0, 15.0);
ColumnVector x = CD.Solve(b);
Assert.IsTrue(TestUtilities.IsNearlyEqual(S * x, b));
}
public void MatrixCholeskyDecomposition()
{
double[][] pvals =
{
new double[] { 25, -5, 10 },
new double[] { -5, 17, 10 },
new double[] { 10, 10, 62 }
};
Matrix e = new Matrix(pvals);
CholeskyDecomposition chol = e.CholeskyDecomposition;
Matrix l = chol.TriangularFactor;
Assert.That(l * Matrix.Transpose(l), NumericIs.AlmostEqualTo(e), "CholeskyDecomposition");
Matrix g = chol.Solve(Matrix.Identity(3, 3));
Assert.That(e * g, NumericIs.AlmostEqualTo(Matrix.Identity(3, 3)), "CholeskyDecomposition Solve");
}
/// <summary>
/// Choleskies the solve.
/// </summary>
/// <param name="matrix1">The matrix1.</param>
/// <param name="matrix2">The matrix2.</param>
/// <param name="matrixResult">The matrix result.</param>
/// <returns></returns>
public static RelationalOperation CholeskySolve(NumericMatrixFactor matrix1, NumericMatrixFactor matrix2, out NumericMatrixFactor matrixResult)
{
var values1 = matrix1.Coefficients;
var cMatrix1 = new NumericMatrixFactor(matrix1, new VariableFactor('C', 1), null);
var values2 = matrix2.Coefficients;
var cMatrix2 = new NumericMatrixFactor(matrix2, new VariableFactor('C', 1), null);
var solver = new CholeskyDecomposition(values1.AsSpan2D());
var values3 = solver.Solve(values2).Items;
matrixResult = new NumericMatrixFactor(values3, false);
var equation = new RelationalOperation(
ComparisonOperators.Equals,
new NomialExpression(
new ProductTerm(new NumericFactor(1), cMatrix1, cMatrix2)
),
new ProductTerm(new NumericFactor(1), matrixResult)
);
return(equation);
}
/// <summary>
/// Gets the probability density function (pdf) for
/// this distribution evaluated at point <c>x</c>.
/// </summary>
///
/// <param name="x">A single point in the distribution range.</param>
///
/// <returns>
/// The probability of <c>x</c> occurring
/// in the current distribution.
/// </returns>
///
/// <remarks>
/// The Probability Density Function (PDF) describes the
/// probability that a given value <c>x</c> will occur.
/// </remarks>
///
public override double ProbabilityDensityFunction(double[] x)
{
// http://www.buch-kromann.dk/tine/nonpar/Nonparametric_Density_Estimation_multidim.pdf
// http://sfb649.wiwi.hu-berlin.de/fedc_homepage/xplore/ebooks/html/spm/spmhtmlnode18.html
double sum = 0;
CholeskyDecomposition chol = new CholeskyDecomposition(smoothing);
double[] delta = new double[Dimension];
for (int i = 0; i < samples.Length; i++)
{
for (int j = 0; j < x.Length; j++)
{
delta[j] = (x[j] - samples[i][j]);
}
sum += kernel.Function(chol.Solve(delta));
}
return(sum / (samples.Length * determinant));
}
public static Double[,] Inverse(Double[,] matrix)
{
var rows = matrix.GetLength(0);
var cols = matrix.GetLength(1);
var target = Helpers.One(cols);
if (cols < 24)
{
var lu = new LUDecomposition(matrix);
return(lu.Solve(target));
}
else if (Helpers.IsSymmetric(matrix))
{
var cho = new CholeskyDecomposition(matrix);
return(cho.Solve(target));
}
else
{
var qr = QRDecomposition.Create(matrix);
return(qr.Solve(target));
}
}
public double Mahalanobis(double[] x)
{
if (x.Length != Dimension)
{
throw new DimensionMismatchException("x", "The vector should have the same dimension as the distribution.");
}
var z = new double[mean.Length];
for (int i = 0; i < x.Length; i++)
{
z[i] = x[i] - mean[i];
}
double[] a = (chol == null) ? svd.Solve(z) : chol.Solve(z);
double b = 0;
for (int i = 0; i < z.Length; i++)
{
b += a[i] * z[i];
}
return(b);
}
public void AllTests()
{
Matrix A, B, C, Z, O, I, R, S, X, SUB, M, T, SQ, DEF, SOL;
double tmp;
double[] columnwise = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 };
double[] rowwise = { 1.0, 4.0, 7.0, 10.0, 2.0, 5.0, 8.0, 11.0, 3.0, 6.0, 9.0, 12.0 };
double[][] avals = { new double[] { 1.0, 4.0, 7.0, 10.0 }, new double[] { 2.0, 5.0, 8.0, 11.0 }, new double[] { 3.0, 6.0, 9.0, 12.0 } };
double[][] rankdef = avals;
double[][] tvals = { new double[] { 1.0, 2.0, 3.0 }, new double[] { 4.0, 5.0, 6.0 }, new double[] { 7.0, 8.0, 9.0 }, new double[] { 10.0, 11.0, 12.0 } };
double[][] subavals = { new double[] { 5.0, 8.0, 11.0 }, new double[] { 6.0, 9.0, 12.0 } };
double[][] pvals = { new double[] { 25, -5, 10 }, new double[] { -5, 17, 10 }, new double[] { 10, 10, 62 } };
double[][] ivals = { new double[] { 1.0, 0.0, 0.0, 0.0 }, new double[] { 0.0, 1.0, 0.0, 0.0 }, new double[] { 0.0, 0.0, 1.0, 0.0 } };
double[][] evals = { new double[] { 0.0, 1.0, 0.0, 0.0 }, new double[] { 1.0, 0.0, 2e-7, 0.0 }, new double[] { 0.0, -2e-7, 0.0, 1.0 }, new double[] { 0.0, 0.0, 1.0, 0.0 } };
double[][] square = { new double[] { 166.0, 188.0, 210.0 }, new double[] { 188.0, 214.0, 240.0 }, new double[] { 210.0, 240.0, 270.0 } };
double[][] sqSolution = { new double[] { 13.0 }, new double[] { 15.0 } };
double[][] condmat = { new double[] { 1.0, 3.0 }, new double[] { 7.0, 9.0 } };
int rows = 3, cols = 4;
int invalidld = 5; /* should trigger bad shape for construction with val */
int validld = 3; /* leading dimension of intended test Matrices */
int nonconformld = 4; /* leading dimension which is valid, but nonconforming */
int ib = 1, ie = 2, jb = 1, je = 3; /* index ranges for sub Matrix */
int[] rowindexset = new int[] { 1, 2 };
int[] badrowindexset = new int[] { 1, 3 };
int[] columnindexset = new int[] { 1, 2, 3 };
int[] badcolumnindexset = new int[] { 1, 2, 4 };
double columnsummax = 33.0;
double rowsummax = 30.0;
double sumofdiagonals = 15;
double sumofsquares = 650;
#region Testing constructors and constructor-like methods
// Constructors and constructor-like methods:
// double[], int
// double[,]
// int, int
// int, int, double
// int, int, double[,]
// Create(double[,])
// Random(int,int)
// Identity(int)
try
{
// check that exception is thrown in packed constructor with invalid length
A = new Matrix(columnwise, invalidld);
Assert.Fail("Catch invalid length in packed constructor: exception not thrown for invalid input");
}
catch (ArgumentException) { }
A = new Matrix(columnwise, validld);
B = new Matrix(avals);
tmp = B[0, 0];
avals[0][0] = 0.0;
C = B - A;
avals[0][0] = tmp;
B = Matrix.Create(avals);
tmp = B[0, 0];
avals[0][0] = 0.0;
Assert.AreEqual((tmp - B[0, 0]), 0.0, "Create");
avals[0][0] = columnwise[0];
I = new Matrix(ivals);
NumericAssert.AreAlmostEqual(I, Matrix.Identity(3, 4), "Identity");
#endregion
#region Testing access methods
// Access Methods:
// getColumnDimension()
// getRowDimension()
// getArray()
// getArrayCopy()
// getColumnPackedCopy()
// getRowPackedCopy()
// get(int,int)
// GetMatrix(int,int,int,int)
// GetMatrix(int,int,int[])
// GetMatrix(int[],int,int)
// GetMatrix(int[],int[])
// set(int,int,double)
// SetMatrix(int,int,int,int,Matrix)
// SetMatrix(int,int,int[],Matrix)
// SetMatrix(int[],int,int,Matrix)
// SetMatrix(int[],int[],Matrix)
// Various get methods
B = new Matrix(avals);
Assert.AreEqual(B.RowCount, rows, "getRowDimension");
Assert.AreEqual(B.ColumnCount, cols, "getColumnDimension");
B = new Matrix(avals);
double[][] barray = (Matrix)B;
Assert.AreSame(barray, avals, "getArray");
barray = B.Clone();
Assert.AreNotSame(barray, avals, "getArrayCopy");
NumericAssert.AreAlmostEqual(new Matrix(barray), B, "getArrayCopy II");
// double[] bpacked = B.ColumnPackedCopy;
// try
// {
// check(bpacked, columnwise);
// try_success("getColumnPackedCopy... ", "");
// }
// catch (System.SystemException e)
// {
// errorCount = try_failure(errorCount, "getColumnPackedCopy... ", "data not successfully (deep) copied by columns");
// System.Console.Out.WriteLine(e.Message);
// }
// bpacked = B.RowPackedCopy;
// try
// {
// check(bpacked, rowwise);
// try_success("getRowPackedCopy... ", "");
// }
// catch (System.SystemException e)
// {
// errorCount = try_failure(errorCount, "getRowPackedCopy... ", "data not successfully (deep) copied by rows");
// System.Console.Out.WriteLine(e.Message);
// }
try
{
tmp = B[B.RowCount, B.ColumnCount - 1];
Assert.Fail("get(int,int): OutOfBoundsException expected but not thrown");
}
catch (IndexOutOfRangeException) { }
try
{
tmp = B[B.RowCount - 1, B.ColumnCount];
Assert.Fail("get(int,int): OutOfBoundsException expected but not thrown II");
}
catch (IndexOutOfRangeException) { }
Assert.AreEqual(B[B.RowCount - 1, B.ColumnCount - 1], avals[B.RowCount - 1][B.ColumnCount - 1], "get(int,int)");
SUB = new Matrix(subavals);
try
{
M = B.GetMatrix(ib, ie + B.RowCount + 1, jb, je);
Assert.Fail("GetMatrix(int,int,int,int): IndexOutOfBoundsException expected but not thrown");
}
catch (IndexOutOfRangeException) { }
try
{
M = B.GetMatrix(ib, ie, jb, je + B.ColumnCount + 1);
Assert.Fail("GetMatrix(int,int,int,int): IndexOutOfBoundsException expected but not thrown II");
}
catch (IndexOutOfRangeException) { }
M = B.GetMatrix(ib, ie, jb, je);
NumericAssert.AreAlmostEqual(SUB, M, "GetMatrix(int,int,int,int)");
try
{
M = B.GetMatrix(ib, ie, badcolumnindexset);
Assert.Fail("GetMatrix(int,int,int[]): IndexOutOfBoundsException expected but not thrown");
}
catch (IndexOutOfRangeException) { }
try
{
M = B.GetMatrix(ib, ie + B.RowCount + 1, columnindexset);
Assert.Fail("GetMatrix(int,int,int[]): IndexOutOfBoundsException expected but not thrown II");
}
catch (IndexOutOfRangeException) { }
M = B.GetMatrix(ib, ie, columnindexset);
NumericAssert.AreAlmostEqual(SUB, M, "GetMatrix(int,int,int[])");
try
{
M = B.GetMatrix(badrowindexset, jb, je);
Assert.Fail("GetMatrix(int[],int,int): IndexOutOfBoundsException expected but not thrown");
}
catch (IndexOutOfRangeException) { }
try
{
M = B.GetMatrix(rowindexset, jb, je + B.ColumnCount + 1);
Assert.Fail("GetMatrix(int[],int,int): IndexOutOfBoundsException expected but not thrown II");
}
catch (IndexOutOfRangeException) { }
M = B.GetMatrix(rowindexset, jb, je);
NumericAssert.AreAlmostEqual(SUB, M, "GetMatrix(int[],int,int)");
try
{
M = B.GetMatrix(badrowindexset, columnindexset);
Assert.Fail("GetMatrix(int[],int[]): IndexOutOfBoundsException expected but not thrown");
}
catch (IndexOutOfRangeException) { }
try
{
M = B.GetMatrix(rowindexset, badcolumnindexset);
Assert.Fail("GetMatrix(int[],int[]): IndexOutOfBoundsException expected but not thrown II");
}
catch (IndexOutOfRangeException) { }
M = B.GetMatrix(rowindexset, columnindexset);
NumericAssert.AreAlmostEqual(SUB, M, "GetMatrix(int[],int[])");
// Various set methods:
try
{
B[B.RowCount, B.ColumnCount - 1] = 0.0;
Assert.Fail("set(int,int,double): IndexOutOfBoundsException expected but not thrown");
}
catch (IndexOutOfRangeException) { }
try
{
B[B.RowCount - 1, B.ColumnCount] = 0.0;
Assert.Fail("set(int,int,double): IndexOutOfBoundsException expected but not thrown II");
}
catch (IndexOutOfRangeException) { }
B[ib, jb] = 0.0;
tmp = B[ib, jb];
NumericAssert.AreAlmostEqual(tmp, 0.0, "set(int,int,double)");
M = new Matrix(2, 3, 0.0);
try
{
B.SetMatrix(ib, ie + B.RowCount + 1, jb, je, M);
Assert.Fail("SetMatrix(int,int,int,int,Matrix): IndexOutOfBoundsException expected but not thrown");
}
catch (IndexOutOfRangeException) { }
try
{
B.SetMatrix(ib, ie, jb, je + B.ColumnCount + 1, M);
Assert.Fail("SetMatrix(int,int,int,int,Matrix): IndexOutOfBoundsException expected but not thrown II");
}
catch (IndexOutOfRangeException) { }
B.SetMatrix(ib, ie, jb, je, M);
NumericAssert.AreAlmostEqual(M - B.GetMatrix(ib, ie, jb, je), M, "SetMatrix(int,int,int,int,Matrix)");
B.SetMatrix(ib, ie, jb, je, SUB);
try
{
B.SetMatrix(ib, ie + B.RowCount + 1, columnindexset, M);
Assert.Fail("SetMatrix(int,int,int[],Matrix): IndexOutOfBoundsException expected but not thrown");
}
catch (IndexOutOfRangeException) { }
try
{
B.SetMatrix(ib, ie, badcolumnindexset, M);
Assert.Fail("SetMatrix(int,int,int[],Matrix): IndexOutOfBoundsException expected but not thrown II");
}
catch (IndexOutOfRangeException) { }
B.SetMatrix(ib, ie, columnindexset, M);
NumericAssert.AreAlmostEqual(M - B.GetMatrix(ib, ie, columnindexset), M, "SetMatrix(int,int,int[],Matrix)");
B.SetMatrix(ib, ie, jb, je, SUB);
try
{
B.SetMatrix(rowindexset, jb, je + B.ColumnCount + 1, M);
Assert.Fail("SetMatrix(int[],int,int,Matrix): IndexOutOfBoundsException expected but not thrown");
}
catch (IndexOutOfRangeException) { }
try
{
B.SetMatrix(badrowindexset, jb, je, M);
Assert.Fail("SetMatrix(int[],int,int,Matrix): IndexOutOfBoundsException expected but not thrown II");
}
catch (IndexOutOfRangeException) { }
B.SetMatrix(rowindexset, jb, je, M);
NumericAssert.AreAlmostEqual(M - B.GetMatrix(rowindexset, jb, je), M, "SetMatrix(int[],int,int,Matrix)");
B.SetMatrix(ib, ie, jb, je, SUB);
try
{
B.SetMatrix(rowindexset, badcolumnindexset, M);
Assert.Fail("SetMatrix(int[],int[],Matrix): IndexOutOfBoundsException expected but not thrown");
}
catch (IndexOutOfRangeException) { }
try
{
B.SetMatrix(badrowindexset, columnindexset, M);
Assert.Fail("SetMatrix(int[],int[],Matrix): IndexOutOfBoundsException expected but not thrown");
}
catch (IndexOutOfRangeException) { }
B.SetMatrix(rowindexset, columnindexset, M);
NumericAssert.AreAlmostEqual(M - B.GetMatrix(rowindexset, columnindexset), M, "SetMatrix(int[],int[],Matrix)");
#endregion
#region Testing array-like methods
// Array-like methods:
// Subtract
// SubtractEquals
// Add
// AddEquals
// ArrayLeftDivide
// ArrayLeftDivideEquals
// ArrayRightDivide
// ArrayRightDivideEquals
// arrayTimes
// ArrayMultiplyEquals
// uminus
S = new Matrix(columnwise, nonconformld);
R = Matrix.Random(A.RowCount, A.ColumnCount);
A = R;
try
{
S = A - S;
Assert.Fail("Subtract conformance check: nonconformance not raised");
}
catch (ArgumentException) { }
Assert.AreEqual((A - R).Norm1(), 0.0, "Subtract: difference of identical Matrices is nonzero,\nSubsequent use of Subtract should be suspect");
A = R.Clone();
A.Subtract(R);
Z = new Matrix(A.RowCount, A.ColumnCount);
try
{
A.Subtract(S);
Assert.Fail("SubtractEquals conformance check: nonconformance not raised");
}
catch (ArgumentException) { }
Assert.AreEqual((A - Z).Norm1(), 0.0, "SubtractEquals: difference of identical Matrices is nonzero,\nSubsequent use of Subtract should be suspect");
A = R.Clone();
B = Matrix.Random(A.RowCount, A.ColumnCount);
C = A - B;
try
{
S = A + S;
Assert.Fail("Add conformance check: nonconformance not raised");
}
catch (ArgumentException) { }
NumericAssert.AreAlmostEqual(C + B, A, "Add");
C = A - B;
C.Add(B);
try
{
A.Add(S);
Assert.Fail("AddEquals conformance check: nonconformance not raised");
}
catch (ArgumentException) { }
NumericAssert.AreAlmostEqual(C, A, "AddEquals");
A = ((Matrix)R.Clone());
A.UnaryMinus();
NumericAssert.AreAlmostEqual(A + R, Z, "UnaryMinus");
A = (Matrix)R.Clone();
O = new Matrix(A.RowCount, A.ColumnCount, 1.0);
try
{
Matrix.ArrayDivide(A, S);
Assert.Fail("ArrayRightDivide conformance check: nonconformance not raised");
}
catch (ArgumentException) { }
C = Matrix.ArrayDivide(A, R);
NumericAssert.AreAlmostEqual(C, O, "ArrayRightDivide");
try
{
A.ArrayDivide(S);
Assert.Fail("ArrayRightDivideEquals conformance check: nonconformance not raised");
}
catch (ArgumentException) { }
A.ArrayDivide(R);
NumericAssert.AreAlmostEqual(A, O, "ArrayRightDivideEquals");
A = (Matrix)R.Clone();
B = Matrix.Random(A.RowCount, A.ColumnCount);
try
{
S = Matrix.ArrayMultiply(A, S);
Assert.Fail("arrayTimes conformance check: nonconformance not raised");
}
catch (ArgumentException) { }
C = Matrix.ArrayMultiply(A, B);
C.ArrayDivide(B);
NumericAssert.AreAlmostEqual(C, A, "arrayTimes");
try
{
A.ArrayMultiply(S);
Assert.Fail("ArrayMultiplyEquals conformance check: nonconformance not raised");
}
catch (ArgumentException) { }
A.ArrayMultiply(B);
A.ArrayDivide(B);
NumericAssert.AreAlmostEqual(A, R, "ArrayMultiplyEquals");
#endregion
#region Testing linear algebra methods
// LA methods:
// Transpose
// Multiply
// Condition
// Rank
// Determinant
// trace
// Norm1
// norm2
// normF
// normInf
// Solve
// solveTranspose
// Inverse
// chol
// Eigen
// lu
// qr
// svd
A = new Matrix(columnwise, 3);
T = new Matrix(tvals);
T = Matrix.Transpose(A);
NumericAssert.AreAlmostEqual(Matrix.Transpose(A), T, "Transpose");
NumericAssert.AreAlmostEqual(A.Norm1(), columnsummax, "Norm1");
NumericAssert.AreAlmostEqual(A.NormInf(), rowsummax, "NormInf");
NumericAssert.AreAlmostEqual(A.NormF(), Math.Sqrt(sumofsquares), "NormF");
NumericAssert.AreAlmostEqual(A.Trace(), sumofdiagonals, "Trace");
NumericAssert.AreAlmostEqual(A.GetMatrix(0, A.RowCount - 1, 0, A.RowCount - 1).Determinant(), 0.0, "Determinant");
SQ = new Matrix(square);
NumericAssert.AreAlmostEqual(A * Matrix.Transpose(A), SQ, "Multiply(Matrix)");
NumericAssert.AreAlmostEqual(0.0 * A, Z, "Multiply(double)");
A = new Matrix(columnwise, 4);
QRDecomposition QR = A.QRDecomposition;
R = QR.R;
NumericAssert.AreAlmostEqual(A, QR.Q * R, "QRDecomposition");
SingularValueDecomposition SVD = A.SingularValueDecomposition;
NumericAssert.AreAlmostEqual(A, SVD.LeftSingularVectors * (SVD.S * Matrix.Transpose(SVD.RightSingularVectors)), "SingularValueDecomposition");
DEF = new Matrix(rankdef);
NumericAssert.AreAlmostEqual(DEF.Rank(), Math.Min(DEF.RowCount, DEF.ColumnCount) - 1, "Rank");
B = new Matrix(condmat);
SVD = B.SingularValueDecomposition;
double[] singularvalues = SVD.SingularValues;
NumericAssert.AreAlmostEqual(B.Condition(), singularvalues[0] / singularvalues[Math.Min(B.RowCount, B.ColumnCount) - 1], "Condition");
int n = A.ColumnCount;
A = A.GetMatrix(0, n - 1, 0, n - 1);
A[0, 0] = 0.0;
LUDecomposition LU = A.LUDecomposition;
NumericAssert.AreAlmostEqual(A.GetMatrix(LU.Pivot, 0, n - 1), LU.L * LU.U, "LUDecomposition");
X = A.Inverse();
NumericAssert.AreAlmostEqual(A * X, Matrix.Identity(3, 3), "Inverse");
O = new Matrix(SUB.RowCount, 1, 1.0);
SOL = new Matrix(sqSolution);
SQ = SUB.GetMatrix(0, SUB.RowCount - 1, 0, SUB.RowCount - 1);
NumericAssert.AreAlmostEqual(SQ.Solve(SOL), O, "Solve");
A = new Matrix(pvals);
CholeskyDecomposition Chol = A.CholeskyDecomposition;
Matrix L = Chol.TriangularFactor;
NumericAssert.AreAlmostEqual(A, L * Matrix.Transpose(L), "CholeskyDecomposition");
X = Chol.Solve(Matrix.Identity(3, 3));
NumericAssert.AreAlmostEqual(A * X, Matrix.Identity(3, 3), "CholeskyDecomposition Solve");
EigenvalueDecomposition Eig = A.EigenvalueDecomposition;
Matrix D = Eig.BlockDiagonal;
Matrix V = Eig.EigenVectors;
NumericAssert.AreAlmostEqual(A * V, V * D, "EigenvalueDecomposition (symmetric)");
A = new Matrix(evals);
Eig = A.EigenvalueDecomposition;
D = Eig.BlockDiagonal;
V = Eig.EigenVectors;
NumericAssert.AreAlmostEqual(A * V, V * D, "EigenvalueDecomposition (nonsymmetric)");
#endregion
}
public override IVector Apply(IMatrix A, IVector b, IVector x)
{
double[] xs = (double[])decomp.Solve(
new Matrix(Blas.Default.GetArrayCopy(b), b.Length));
return(Blas.Default.SetVector(xs, x));
}
/// <summary>An exception is thrown at the end of the process,
/// if any error is encountered.</summary>
[Test] public void AllTests()
{
Matrix A, B, C, Z, O, I, R, S, X, SUB, M, T, SQ, DEF, SOL;
int errorCount = 0;
int warningCount = 0;
double tmp;
double[] columnwise = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 };
double[] rowwise = { 1.0, 4.0, 7.0, 10.0, 2.0, 5.0, 8.0, 11.0, 3.0, 6.0, 9.0, 12.0 };
double[,] avals = { { 1.0, 4.0, 7.0, 10.0 }, { 2.0, 5.0, 8.0, 11.0 }, { 3.0, 6.0, 9.0, 12.0 } };
double[,] rankdef = avals;
double[,] tvals = { { 1.0, 2.0, 3.0 }, { 4.0, 5.0, 6.0 }, { 7.0, 8.0, 9.0 }, { 10.0, 11.0, 12.0 } };
double[,] subavals = { { 5.0, 8.0, 11.0 }, { 6.0, 9.0, 12.0 } };
double[,] pvals = { { 1.0, 1.0, 1.0 }, { 1.0, 2.0, 3.0 }, { 1.0, 3.0, 6.0 } };
double[,] ivals = { { 1.0, 0.0, 0.0, 0.0 }, { 0.0, 1.0, 0.0, 0.0 }, { 0.0, 0.0, 1.0, 0.0 } };
double[,] evals = { { 0.0, 1.0, 0.0, 0.0 }, { 1.0, 0.0, 2e-7, 0.0 }, { 0.0, -2e-7, 0.0, 1.0 }, { 0.0, 0.0, 1.0, 0.0 } };
double[,] square = { { 166.0, 188.0, 210.0 }, { 188.0, 214.0, 240.0 }, { 210.0, 240.0, 270.0 } };
double[,] sqSolution = { { 13.0 }, { 15.0 } };
double[,] condmat = { { 1.0, 3.0 }, { 7.0, 9.0 } };
int rows = 3, cols = 4;
int invalidld = 5; /* should trigger bad shape for construction with val */
int validld = 3; /* leading dimension of intended test Matrices */
int nonconformld = 4; /* leading dimension which is valid, but nonconforming */
int ib = 1, ie = 2, jb = 1, je = 3; /* index ranges for sub Matrix */
int[] rowindexset = new int[] { 1, 2 };
int[] badrowindexset = new int[] { 1, 3 };
int[] columnindexset = new int[] { 1, 2, 3 };
int[] badcolumnindexset = new int[] { 1, 2, 4 };
double columnsummax = 33.0;
double rowsummax = 30.0;
double sumofdiagonals = 15;
double sumofsquares = 650;
// Constructors and constructor-like methods:
// double[], int
// double[,]
// int, int
// int, int, double
// int, int, double[,]
// Create(double[,])
// Random(int,int)
// Identity(int)
print("\nTesting constructors and constructor-like methods...\n");
try
{
// check that exception is thrown in packed constructor with invalid length
A = new Matrix(columnwise, invalidld);
errorCount = try_failure(errorCount, "Catch invalid length in packed constructor... ", "exception not thrown for invalid input");
}
catch (System.ArgumentException e)
{
try_success("Catch invalid length in packed constructor... ", e.Message);
}
A = new Matrix(columnwise, validld);
B = new Matrix(avals);
tmp = B[0, 0];
avals[0, 0] = 0.0;
C = B - A;
avals[0, 0] = tmp;
B = Matrix.Create(avals);
tmp = B[0, 0];
avals[0, 0] = 0.0;
if ((tmp - B[0, 0]) != 0.0)
{
// check that Create behaves properly
errorCount = try_failure(errorCount, "Create... ", "Copy not effected... data visible outside");
}
else
{
try_success("Create... ", "");
}
avals[0, 0] = columnwise[0];
I = new Matrix(ivals);
try
{
check(I, Matrix.Identity(3, 4));
try_success("Identity... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "Identity... ", "Identity Matrix not successfully created");
System.Console.Out.WriteLine(e.Message);
}
// Access Methods:
// getColumnDimension()
// getRowDimension()
// getArray()
// getArrayCopy()
// getColumnPackedCopy()
// getRowPackedCopy()
// get(int,int)
// GetMatrix(int,int,int,int)
// GetMatrix(int,int,int[])
// GetMatrix(int[],int,int)
// GetMatrix(int[],int[])
// set(int,int,double)
// SetMatrix(int,int,int,int,Matrix)
// SetMatrix(int,int,int[],Matrix)
// SetMatrix(int[],int,int,Matrix)
// SetMatrix(int[],int[],Matrix)
print("\nTesting access methods...\n");
// Various get methods
B = new Matrix(avals);
if (B.RowCount != rows)
{
errorCount = try_failure(errorCount, "getRowDimension... ", "");
}
else
{
try_success("getRowDimension... ", "");
}
if (B.ColumnCount != cols)
{
errorCount = try_failure(errorCount, "getColumnDimension... ", "");
}
else
{
try_success("getColumnDimension... ", "");
}
B = new Matrix(avals);
double[,] barray = (Matrix)B;
if (barray != avals)
{
errorCount = try_failure(errorCount, "getArray... ", "");
}
else
{
try_success("getArray... ", "");
}
barray = (Matrix)B.Clone();
if (barray == avals)
{
errorCount = try_failure(errorCount, "getArrayCopy... ", "data not (deep) copied");
}
try
{
check(barray, avals);
try_success("getArrayCopy... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "getArrayCopy... ", "data not successfully (deep) copied");
System.Console.Out.WriteLine(e.Message);
}
// double[] bpacked = B.ColumnPackedCopy;
// try
// {
// check(bpacked, columnwise);
// try_success("getColumnPackedCopy... ", "");
// }
// catch (System.SystemException e)
// {
// errorCount = try_failure(errorCount, "getColumnPackedCopy... ", "data not successfully (deep) copied by columns");
// System.Console.Out.WriteLine(e.Message);
// }
// bpacked = B.RowPackedCopy;
// try
// {
// check(bpacked, rowwise);
// try_success("getRowPackedCopy... ", "");
// }
// catch (System.SystemException e)
// {
// errorCount = try_failure(errorCount, "getRowPackedCopy... ", "data not successfully (deep) copied by rows");
// System.Console.Out.WriteLine(e.Message);
// }
try
{
tmp = B[B.RowCount, B.ColumnCount - 1];
errorCount = try_failure(errorCount, "get(int,int)... ", "OutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e)
{
System.Console.Out.WriteLine(e.Message);
try
{
tmp = B[B.RowCount - 1, B.ColumnCount];
errorCount = try_failure(errorCount, "get(int,int)... ", "OutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e1)
{
try_success("get(int,int)... OutofBoundsException... ", "");
System.Console.Out.WriteLine(e1.Message);
}
}
catch (System.ArgumentException e1)
{
errorCount = try_failure(errorCount, "get(int,int)... ", "OutOfBoundsException expected but not thrown");
System.Console.Out.WriteLine(e1.Message);
}
try
{
if (B[B.RowCount - 1, B.ColumnCount - 1] != avals[B.RowCount - 1, B.ColumnCount - 1])
{
errorCount = try_failure(errorCount, "get(int,int)... ", "Matrix entry (i,j) not successfully retreived");
}
else
{
try_success("get(int,int)... ", "");
}
}
catch (System.IndexOutOfRangeException e)
{
errorCount = try_failure(errorCount, "get(int,int)... ", "Unexpected ArrayIndexOutOfBoundsException");
System.Console.Out.WriteLine(e.Message);
}
SUB = new Matrix(subavals);
try
{
M = B.GetMatrix(ib, ie + B.RowCount + 1, jb, je);
errorCount = try_failure(errorCount, "GetMatrix(int,int,int,int)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e)
{
System.Console.Out.WriteLine(e.Message);
try
{
M = B.GetMatrix(ib, ie, jb, je + B.ColumnCount + 1);
errorCount = try_failure(errorCount, "GetMatrix(int,int,int,int)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e1)
{
try_success("GetMatrix(int,int,int,int)... ArrayIndexOutOfBoundsException... ", "");
System.Console.Out.WriteLine(e1.Message);
}
}
catch (System.ArgumentException e1)
{
errorCount = try_failure(errorCount, "GetMatrix(int,int,int,int)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
System.Console.Out.WriteLine(e1.Message);
}
try
{
M = B.GetMatrix(ib, ie, jb, je);
try
{
check(SUB, M);
try_success("GetMatrix(int,int,int,int)... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "GetMatrix(int,int,int,int)... ", "submatrix not successfully retreived");
System.Console.Out.WriteLine(e.Message);
}
}
catch (System.IndexOutOfRangeException e)
{
errorCount = try_failure(errorCount, "GetMatrix(int,int,int,int)... ", "Unexpected ArrayIndexOutOfBoundsException");
System.Console.Out.WriteLine(e.Message);
}
try
{
M = B.GetMatrix(ib, ie, badcolumnindexset);
errorCount = try_failure(errorCount, "GetMatrix(int,int,int[])... ", "ArrayIndexOutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e)
{
System.Console.Out.WriteLine(e.Message);
try
{
M = B.GetMatrix(ib, ie + B.RowCount + 1, columnindexset);
errorCount = try_failure(errorCount, "GetMatrix(int,int,int[])... ", "ArrayIndexOutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e1)
{
try_success("GetMatrix(int,int,int[])... ArrayIndexOutOfBoundsException... ", "");
System.Console.Out.WriteLine(e1.Message);
}
}
catch (System.ArgumentException e1)
{
errorCount = try_failure(errorCount, "GetMatrix(int,int,int[])... ", "ArrayIndexOutOfBoundsException expected but not thrown");
System.Console.Out.WriteLine(e1.Message);
}
try
{
M = B.GetMatrix(ib, ie, columnindexset);
try
{
check(SUB, M);
try_success("GetMatrix(int,int,int[])... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "GetMatrix(int,int,int[])... ", "submatrix not successfully retreived");
System.Console.Out.WriteLine(e.Message);
}
}
catch (System.IndexOutOfRangeException e)
{
errorCount = try_failure(errorCount, "GetMatrix(int,int,int[])... ", "Unexpected ArrayIndexOutOfBoundsException");
System.Console.Out.WriteLine(e.Message);
}
try
{
M = B.GetMatrix(badrowindexset, jb, je);
errorCount = try_failure(errorCount, "GetMatrix(int[],int,int)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e)
{
System.Console.Out.WriteLine(e.Message);
try
{
M = B.GetMatrix(rowindexset, jb, je + B.ColumnCount + 1);
errorCount = try_failure(errorCount, "GetMatrix(int[],int,int)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e1)
{
try_success("GetMatrix(int[],int,int)... ArrayIndexOutOfBoundsException... ", "");
System.Console.Out.WriteLine(e1.Message);
}
}
catch (System.ArgumentException e1)
{
errorCount = try_failure(errorCount, "GetMatrix(int[],int,int)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
System.Console.Out.WriteLine(e1.Message);
}
try
{
M = B.GetMatrix(rowindexset, jb, je);
try
{
check(SUB, M);
try_success("GetMatrix(int[],int,int)... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "GetMatrix(int[],int,int)... ", "submatrix not successfully retreived");
System.Console.Out.WriteLine(e.Message);
}
}
catch (System.IndexOutOfRangeException e)
{
errorCount = try_failure(errorCount, "GetMatrix(int[],int,int)... ", "Unexpected ArrayIndexOutOfBoundsException");
System.Console.Out.WriteLine(e.Message);
}
try
{
M = B.GetMatrix(badrowindexset, columnindexset);
errorCount = try_failure(errorCount, "GetMatrix(int[],int[])... ", "ArrayIndexOutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e)
{
System.Console.Out.WriteLine(e.Message);
try
{
M = B.GetMatrix(rowindexset, badcolumnindexset);
errorCount = try_failure(errorCount, "GetMatrix(int[],int[])... ", "ArrayIndexOutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e1)
{
try_success("GetMatrix(int[],int[])... ArrayIndexOutOfBoundsException... ", "");
System.Console.Out.WriteLine(e1.Message);
}
}
catch (System.ArgumentException e1)
{
errorCount = try_failure(errorCount, "GetMatrix(int[],int[])... ", "ArrayIndexOutOfBoundsException expected but not thrown");
System.Console.Out.WriteLine(e1.Message);
}
try
{
M = B.GetMatrix(rowindexset, columnindexset);
try
{
check(SUB, M);
try_success("GetMatrix(int[],int[])... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "GetMatrix(int[],int[])... ", "submatrix not successfully retreived");
System.Console.Out.WriteLine(e.Message);
}
}
catch (System.IndexOutOfRangeException e)
{
errorCount = try_failure(errorCount, "GetMatrix(int[],int[])... ", "Unexpected ArrayIndexOutOfBoundsException");
System.Console.Out.WriteLine(e.Message);
}
// Various set methods:
try
{
B[B.RowCount, B.ColumnCount - 1] = 0.0;
errorCount = try_failure(errorCount, "set(int,int,double)... ", "OutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e)
{
System.Console.Out.WriteLine(e.Message);
try
{
B[B.RowCount - 1, B.ColumnCount] = 0.0;
errorCount = try_failure(errorCount, "set(int,int,double)... ", "OutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e1)
{
try_success("set(int,int,double)... OutofBoundsException... ", "");
System.Console.Out.WriteLine(e1.Message);
}
}
catch (System.ArgumentException e1)
{
errorCount = try_failure(errorCount, "set(int,int,double)... ", "OutOfBoundsException expected but not thrown");
System.Console.Out.WriteLine(e1.Message);
}
try
{
B[ib, jb] = 0.0;
tmp = B[ib, jb];
try
{
check(tmp, 0.0);
try_success("set(int,int,double)... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "set(int,int,double)... ", "Matrix element not successfully set");
System.Console.Out.WriteLine(e.Message);
}
}
catch (System.IndexOutOfRangeException e1)
{
errorCount = try_failure(errorCount, "set(int,int,double)... ", "Unexpected ArrayIndexOutOfBoundsException");
System.Console.Out.WriteLine(e1.Message);
}
M = new Matrix(2, 3, 0.0);
try
{
B.SetMatrix(ib, ie + B.RowCount + 1, jb, je, M);
errorCount = try_failure(errorCount, "SetMatrix(int,int,int,int,Matrix)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e)
{
System.Console.Out.WriteLine(e.Message);
try
{
B.SetMatrix(ib, ie, jb, je + B.ColumnCount + 1, M);
errorCount = try_failure(errorCount, "SetMatrix(int,int,int,int,Matrix)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e1)
{
try_success("SetMatrix(int,int,int,int,Matrix)... ArrayIndexOutOfBoundsException... ", "");
System.Console.Out.WriteLine(e1.Message);
}
}
catch (System.ArgumentException e1)
{
errorCount = try_failure(errorCount, "SetMatrix(int,int,int,int,Matrix)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
System.Console.Out.WriteLine(e1.Message);
}
try
{
B.SetMatrix(ib, ie, jb, je, M);
try
{
check(M - B.GetMatrix(ib, ie, jb, je), M);
try_success("SetMatrix(int,int,int,int,Matrix)... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "SetMatrix(int,int,int,int,Matrix)... ", "submatrix not successfully set");
System.Console.Out.WriteLine(e.Message);
}
B.SetMatrix(ib, ie, jb, je, SUB);
}
catch (System.IndexOutOfRangeException e1)
{
errorCount = try_failure(errorCount, "SetMatrix(int,int,int,int,Matrix)... ", "Unexpected ArrayIndexOutOfBoundsException");
System.Console.Out.WriteLine(e1.Message);
}
try
{
B.SetMatrix(ib, ie + B.RowCount + 1, columnindexset, M);
errorCount = try_failure(errorCount, "SetMatrix(int,int,int[],Matrix)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e)
{
System.Console.Out.WriteLine(e.Message);
try
{
B.SetMatrix(ib, ie, badcolumnindexset, M);
errorCount = try_failure(errorCount, "SetMatrix(int,int,int[],Matrix)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e1)
{
try_success("SetMatrix(int,int,int[],Matrix)... ArrayIndexOutOfBoundsException... ", "");
System.Console.Out.WriteLine(e1.Message);
}
}
catch (System.ArgumentException e1)
{
errorCount = try_failure(errorCount, "SetMatrix(int,int,int[],Matrix)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
System.Console.Out.WriteLine(e1.Message);
}
try
{
B.SetMatrix(ib, ie, columnindexset, M);
try
{
check(M - B.GetMatrix(ib, ie, columnindexset), M);
try_success("SetMatrix(int,int,int[],Matrix)... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "SetMatrix(int,int,int[],Matrix)... ", "submatrix not successfully set");
System.Console.Out.WriteLine(e.Message);
}
B.SetMatrix(ib, ie, jb, je, SUB);
}
catch (System.IndexOutOfRangeException e1)
{
errorCount = try_failure(errorCount, "SetMatrix(int,int,int[],Matrix)... ", "Unexpected ArrayIndexOutOfBoundsException");
System.Console.Out.WriteLine(e1.Message);
}
try
{
B.SetMatrix(rowindexset, jb, je + B.ColumnCount + 1, M);
errorCount = try_failure(errorCount, "SetMatrix(int[],int,int,Matrix)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e)
{
System.Console.Out.WriteLine(e.Message);
try
{
B.SetMatrix(badrowindexset, jb, je, M);
errorCount = try_failure(errorCount, "SetMatrix(int[],int,int,Matrix)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e1)
{
try_success("SetMatrix(int[],int,int,Matrix)... ArrayIndexOutOfBoundsException... ", "");
System.Console.Out.WriteLine(e1.Message);
}
}
catch (System.ArgumentException e1)
{
errorCount = try_failure(errorCount, "SetMatrix(int[],int,int,Matrix)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
System.Console.Out.WriteLine(e1.Message);
}
try
{
B.SetMatrix(rowindexset, jb, je, M);
try
{
check(M - B.GetMatrix(rowindexset, jb, je), M);
try_success("SetMatrix(int[],int,int,Matrix)... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "SetMatrix(int[],int,int,Matrix)... ", "submatrix not successfully set");
System.Console.Out.WriteLine(e.Message);
}
B.SetMatrix(ib, ie, jb, je, SUB);
}
catch (System.IndexOutOfRangeException e1)
{
errorCount = try_failure(errorCount, "SetMatrix(int[],int,int,Matrix)... ", "Unexpected ArrayIndexOutOfBoundsException");
System.Console.Out.WriteLine(e1.Message);
}
try
{
B.SetMatrix(rowindexset, badcolumnindexset, M);
errorCount = try_failure(errorCount, "SetMatrix(int[],int[],Matrix)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e)
{
System.Console.Out.WriteLine(e.Message);
try
{
B.SetMatrix(badrowindexset, columnindexset, M);
errorCount = try_failure(errorCount, "SetMatrix(int[],int[],Matrix)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e1)
{
try_success("SetMatrix(int[],int[],Matrix)... ArrayIndexOutOfBoundsException... ", "");
System.Console.Out.WriteLine(e1.Message);
}
}
catch (System.ArgumentException e1)
{
errorCount = try_failure(errorCount, "SetMatrix(int[],int[],Matrix)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
System.Console.Out.WriteLine(e1.Message);
}
try
{
B.SetMatrix(rowindexset, columnindexset, M);
try
{
check(M - B.GetMatrix(rowindexset, columnindexset), M);
try_success("SetMatrix(int[],int[],Matrix)... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "SetMatrix(int[],int[],Matrix)... ", "submatrix not successfully set");
System.Console.Out.WriteLine(e.Message);
}
}
catch (System.IndexOutOfRangeException e1)
{
errorCount = try_failure(errorCount, "SetMatrix(int[],int[],Matrix)... ", "Unexpected ArrayIndexOutOfBoundsException");
System.Console.Out.WriteLine(e1.Message);
}
// Array-like methods:
// Subtract
// SubtractEquals
// Add
// AddEquals
// ArrayLeftDivide
// ArrayLeftDivideEquals
// ArrayRightDivide
// ArrayRightDivideEquals
// arrayTimes
// ArrayMultiplyEquals
// uminus
print("\nTesting array-like methods...\n");
S = new Matrix(columnwise, nonconformld);
R = Matrix.Random(A.RowCount, A.ColumnCount);
A = R;
try
{
S = A - S;
errorCount = try_failure(errorCount, "Subtract conformance check... ", "nonconformance not raised");
}
catch (System.ArgumentException e)
{
try_success("Subtract conformance check... ", "");
System.Console.Out.WriteLine(e.Message);
}
if ((A - R).Norm1() != 0.0)
{
errorCount = try_failure(errorCount, "Subtract... ", "(difference of identical Matrices is nonzero,\nSubsequent use of Subtract should be suspect)");
}
else
{
try_success("Subtract... ", "");
}
A = (Matrix)R.Clone();
A.Subtract(R);
Z = new Matrix(A.RowCount, A.ColumnCount);
try
{
A.Subtract(S);
errorCount = try_failure(errorCount, "SubtractEquals conformance check... ", "nonconformance not raised");
}
catch (System.ArgumentException e)
{
try_success("SubtractEquals conformance check... ", "");
System.Console.Out.WriteLine(e.Message);
}
if ((A - Z).Norm1() != 0.0)
{
errorCount = try_failure(errorCount, "SubtractEquals... ", "(difference of identical Matrices is nonzero,\nSubsequent use of Subtract should be suspect)");
}
else
{
try_success("SubtractEquals... ", "");
}
A = (Matrix)R.Clone();
B = Matrix.Random(A.RowCount, A.ColumnCount);
C = A - B;
try
{
S = A + S;
errorCount = try_failure(errorCount, "Add conformance check... ", "nonconformance not raised");
}
catch (System.ArgumentException e)
{
try_success("Add conformance check... ", "");
System.Console.Out.WriteLine(e.Message);
}
try
{
check(C + B, A);
try_success("Add... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "Add... ", "(C = A - B, but C + B != A)");
System.Console.Out.WriteLine(e.Message);
}
C = A - B;
C.Add(B);
try
{
A.Add(S);
errorCount = try_failure(errorCount, "AddEquals conformance check... ", "nonconformance not raised");
}
catch (System.ArgumentException e)
{
try_success("AddEquals conformance check... ", "");
System.Console.Out.WriteLine(e.Message);
}
try
{
check(C, A);
try_success("AddEquals... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "AddEquals... ", "(C = A - B, but C = C + B != A)");
System.Console.Out.WriteLine(e.Message);
}
A = ((Matrix)R.Clone());
A.UnaryMinus();
try
{
check(A + R, Z);
try_success("UnaryMinus... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "uminus... ", "(-A + A != zeros)");
System.Console.Out.WriteLine(e.Message);
}
A = (Matrix)R.Clone();
O = new Matrix(A.RowCount, A.ColumnCount, 1.0);
try
{
Matrix.ArrayDivide(A, S);
errorCount = try_failure(errorCount, "ArrayRightDivide conformance check... ", "nonconformance not raised");
}
catch (System.ArgumentException e)
{
try_success("ArrayRightDivide conformance check... ", "");
System.Console.Out.WriteLine(e.Message);
}
C = Matrix.ArrayDivide(A, R);
try
{
check(C, O);
try_success("ArrayRightDivide... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "ArrayRightDivide... ", "(M./M != ones)");
System.Console.Out.WriteLine(e.Message);
}
try
{
A.ArrayDivide(S);
errorCount = try_failure(errorCount, "ArrayRightDivideEquals conformance check... ", "nonconformance not raised");
}
catch (System.ArgumentException e)
{
try_success("ArrayRightDivideEquals conformance check... ", "");
System.Console.Out.WriteLine(e.Message);
}
A.ArrayDivide(R);
try
{
check(A, O);
try_success("ArrayRightDivideEquals... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "ArrayRightDivideEquals... ", "(M./M != ones)");
System.Console.Out.WriteLine(e.Message);
}
A = (Matrix)R.Clone();
B = Matrix.Random(A.RowCount, A.ColumnCount);
try
{
S = Matrix.ArrayMultiply(A, S);
errorCount = try_failure(errorCount, "arrayTimes conformance check... ", "nonconformance not raised");
}
catch (System.ArgumentException e)
{
try_success("arrayTimes conformance check... ", "");
System.Console.Out.WriteLine(e.Message);
}
C = Matrix.ArrayMultiply(A, B);
try
{
C.ArrayDivide(B);
check(C, A);
try_success("arrayTimes... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "arrayTimes... ", "(A = R, C = A.*B, but C./B != A)");
System.Console.Out.WriteLine(e.Message);
}
try
{
A.ArrayMultiply(S);
errorCount = try_failure(errorCount, "ArrayMultiplyEquals conformance check... ", "nonconformance not raised");
}
catch (System.ArgumentException e)
{
try_success("ArrayMultiplyEquals conformance check... ", "");
System.Console.Out.WriteLine(e.Message);
}
A.ArrayMultiply(B);
try
{
A.ArrayDivide(B);
check(A, R);
try_success("ArrayMultiplyEquals... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "ArrayMultiplyEquals... ", "(A = R, A = A.*B, but A./B != R)");
System.Console.Out.WriteLine(e.Message);
}
// LA methods:
// Transpose
// Multiply
// Condition
// Rank
// Determinant
// trace
// Norm1
// norm2
// normF
// normInf
// Solve
// solveTranspose
// Inverse
// chol
// Eigen
// lu
// qr
// svd
print("\nTesting linear algebra methods...\n");
A = new Matrix(columnwise, 3);
T = new Matrix(tvals);
T = Matrix.Transpose(A);
try
{
check(Matrix.Transpose(A), T);
try_success("Transpose...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "Transpose()...", "Transpose unsuccessful");
System.Console.Out.WriteLine(e.Message);
}
Matrix.Transpose(A);
try
{
check(A.Norm1(), columnsummax);
try_success("Norm1...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "Norm1()...", "incorrect norm calculation");
System.Console.Out.WriteLine(e.Message);
}
try
{
check(A.NormInf(), rowsummax);
try_success("normInf()...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "normInf()...", "incorrect norm calculation");
System.Console.Out.WriteLine(e.Message);
}
try
{
check(A.NormF(), System.Math.Sqrt(sumofsquares));
try_success("normF...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "normF()...", "incorrect norm calculation");
System.Console.Out.WriteLine(e.Message);
}
try
{
check(A.Trace(), sumofdiagonals);
try_success("trace()...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "trace()...", "incorrect trace calculation");
System.Console.Out.WriteLine(e.Message);
}
try
{
check(A.GetMatrix(0, A.RowCount - 1, 0, A.RowCount - 1).Determinant(), 0.0);
try_success("Determinant()...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "Determinant()...", "incorrect determinant calculation");
System.Console.Out.WriteLine(e.Message);
}
SQ = new Matrix(square);
try
{
check(A * Matrix.Transpose(A), SQ);
try_success("Multiply(Matrix)...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "Multiply(Matrix)...", "incorrect Matrix-Matrix product calculation");
System.Console.Out.WriteLine(e.Message);
}
try
{
check(0.0 * A, Z);
try_success("Multiply(double)...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "Multiply(double)...", "incorrect Matrix-scalar product calculation");
System.Console.Out.WriteLine(e.Message);
}
A = new Matrix(columnwise, 4);
QRDecomposition QR = A.QRD();
R = QR.R;
try
{
check(A, QR.Q * R);
try_success("QRDecomposition...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "QRDecomposition...", "incorrect QR decomposition calculation");
System.Console.Out.WriteLine(e.Message);
}
SingularValueDecomposition SVD = A.SVD();
try
{
check(A, SVD.LeftSingularVectors * (SVD.S * Matrix.Transpose(SVD.RightSingularVectors)));
try_success("SingularValueDecomposition...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "SingularValueDecomposition...", "incorrect singular value decomposition calculation");
System.Console.Out.WriteLine(e.Message);
}
DEF = new Matrix(rankdef);
try
{
check(DEF.Rank(), System.Math.Min(DEF.RowCount, DEF.ColumnCount) - 1);
try_success("Rank()...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "Rank()...", "incorrect Rank calculation");
System.Console.Out.WriteLine(e.Message);
}
B = new Matrix(condmat);
SVD = B.SVD();
double[] singularvalues = SVD.SingularValues;
try
{
check(B.Condition(), singularvalues[0] / singularvalues[System.Math.Min(B.RowCount, B.ColumnCount) - 1]);
try_success("Condition()...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "Condition()...", "incorrect condition number calculation");
System.Console.Out.WriteLine(e.Message);
}
int n = A.ColumnCount;
A = A.GetMatrix(0, n - 1, 0, n - 1);
A[0, 0] = 0.0;
LUDecomposition LU = A.LUD();
try
{
check(A.GetMatrix(LU.Pivot, 0, n - 1), LU.L * LU.U);
try_success("LUDecomposition...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "LUDecomposition...", "incorrect LU decomposition calculation");
System.Console.Out.WriteLine(e.Message);
}
X = A.Inverse();
try
{
check(A * X, Matrix.Identity(3, 3));
try_success("Inverse()...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "Inverse()...", "incorrect Inverse calculation");
System.Console.Out.WriteLine(e.Message);
}
O = new Matrix(SUB.RowCount, 1, 1.0);
SOL = new Matrix(sqSolution);
SQ = SUB.GetMatrix(0, SUB.RowCount - 1, 0, SUB.RowCount - 1);
try
{
check(SQ.Solve(SOL), O);
try_success("Solve()...", "");
}
catch (System.ArgumentException e1)
{
errorCount = try_failure(errorCount, "Solve()...", e1.Message);
System.Console.Out.WriteLine(e1.Message);
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "Solve()...", e.Message);
System.Console.Out.WriteLine(e.Message);
}
A = new Matrix(pvals);
CholeskyDecomposition Chol = A.chol();
Matrix L = Chol.GetL();
try
{
check(A, L * Matrix.Transpose(L));
try_success("CholeskyDecomposition...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "CholeskyDecomposition...", "incorrect Cholesky decomposition calculation");
System.Console.Out.WriteLine(e.Message);
}
X = Chol.Solve(Matrix.Identity(3, 3));
try
{
check(A * X, Matrix.Identity(3, 3));
try_success("CholeskyDecomposition Solve()...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "CholeskyDecomposition Solve()...", "incorrect Choleskydecomposition Solve calculation");
System.Console.Out.WriteLine(e.Message);
}
EigenvalueDecomposition Eig = A.Eigen();
Matrix D = Eig.BlockDiagonal;
Matrix V = Eig.EigenVectors;
try
{
check(A * V, V * D);
try_success("EigenvalueDecomposition (symmetric)...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "EigenvalueDecomposition (symmetric)...", "incorrect symmetric Eigenvalue decomposition calculation");
System.Console.Out.WriteLine(e.Message);
}
A = new Matrix(evals);
Eig = A.Eigen();
D = Eig.BlockDiagonal;
V = Eig.EigenVectors;
try
{
check(A * V, V * D);
try_success("EigenvalueDecomposition (nonsymmetric)...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "EigenvalueDecomposition (nonsymmetric)...", "incorrect nonsymmetric Eigenvalue decomposition calculation");
System.Console.Out.WriteLine(e.Message);
}
print("\nTestMatrix completed.\n");
print("Total errors reported: " + System.Convert.ToString(errorCount) + "\n");
print("Total warnings reported: " + System.Convert.ToString(warningCount) + "\n");
if (errorCount > 0)
{
throw new Exception("Errors reported.");
}
}
public void Simple()
{
var matrixA = new Matrix(5, 5);
// // [ 2, 1, 1, 3, 2 ]
// // [ 1, 2, 2, 1, 1 ]
// // [ 1, 2, 9, 1, 5 ]
// // [ 3, 1, 1, 7, 1 ]
// // [ 2, 1, 5, 1, 8 ]
matrixA[0, 0] = 2;
matrixA[0, 1] = 1;
matrixA[0, 2] = 1;
matrixA[0, 3] = 3;
matrixA[0, 4] = 2;
matrixA[1, 0] = 1;
matrixA[1, 1] = 2;
matrixA[1, 2] = 2;
matrixA[1, 3] = 1;
matrixA[1, 4] = 1;
matrixA[2, 0] = 1;
matrixA[2, 1] = 2;
matrixA[2, 2] = 9;
matrixA[2, 3] = 1;
matrixA[2, 4] = 5;
matrixA[3, 0] = 3;
matrixA[3, 1] = 1;
matrixA[3, 2] = 1;
matrixA[3, 3] = 7;
matrixA[3, 4] = 1;
matrixA[4, 0] = 2;
matrixA[4, 1] = 1;
matrixA[4, 2] = 5;
matrixA[4, 3] = 1;
matrixA[4, 4] = 8;
var matrixB = new Matrix(5, 1);
matrixB[0, 0] = -2;
matrixB[1, 0] = 4;
matrixB[2, 0] = 3;
matrixB[3, 0] = -5;
matrixB[4, 0] = 1;
var decomposition = new CholeskyDecomposition(matrixA);
var solveMatrix = decomposition.Solve(matrixB);
Assert.AreEqual(solveMatrix.Rows, 5);
Assert.AreEqual(solveMatrix.Columns, 1);
Assert.IsTrue(solveMatrix[0, 0].IsSimilarTo(-629.0 / 98.0));
Assert.IsTrue(solveMatrix[1, 0].IsSimilarTo(237.0 / 49.0));
Assert.IsTrue(solveMatrix[2, 0].IsSimilarTo(-53.0 / 49.0));
Assert.IsTrue(solveMatrix[3, 0].IsSimilarTo(62.0 / 49.0));
Assert.IsTrue(solveMatrix[4, 0].IsSimilarTo(23.0 / 14.0));
}
public static void test_Matrices()
{
int N = 200;
//int N = 2500;
DenseMatrix M1 = new DenseMatrix(N, N);
SymmetricSparseMatrix M2 = new SymmetricSparseMatrix();
for (int i = 0; i < N; ++i)
{
for (int j = i; j < N; ++j)
{
if (i == j)
{
M1.Set(i, i, N);
M2.Set(i, i, N);
}
else if (j % 2 != 0)
{
double d = 1.0 / Math.Sqrt(i + j);
M1.Set(i, j, d);
M1.Set(j, i, d);
M2.Set(i, j, d);
}
}
}
double[] X = new double[N], b1 = new double[N], b2 = new double[N];
for (int i = 0; i < N; ++i)
{
X[i] = (double)i / (double)N;
}
M1.Multiply(X, b1);
M2.Multiply(X, b2);
for (int i = 0; i < N; ++i)
{
Debug.Assert(MathUtil.EpsilonEqual(b1[i], b2[i]));
}
Debug.Assert(M1.IsSymmetric());
Debug.Assert(M1.IsPositiveDefinite());
// test parallel cholesky decomposition
LocalProfiler p = new LocalProfiler();
p.Start("chol");
CholeskyDecomposition decompM = new CholeskyDecomposition(M1);
decompM.ComputeParallel();
p.Stop("chol");
//System.Console.WriteLine(p.AllTimes());
DenseMatrix LLT_M1 = decompM.L.Multiply(decompM.L.Transpose());
if (LLT_M1.EpsilonEquals(M1) == false)
{
System.Console.WriteLine("FAIL choleskyM1 did not reproduce input");
}
// test cholesky-decomp backsubstitution
Random r = new Random(31337);
double[] RealX = TestUtil.RandomScalars(N, r, new Interval1d(-10, 10));
double[] B = new double[N], SolvedX = new double[N], TmpY = new double[N];
M1.Multiply(RealX, B);
decompM.Solve(B, SolvedX, TmpY);
if (BufferUtil.DistanceSquared(RealX, SolvedX) > MathUtil.ZeroTolerance)
{
System.Console.WriteLine("FAIL choleskyM1 backsubstution did not reproduce input vector");
}
// test case from: https://people.cs.kuleuven.be/~karl.meerbergen/didactiek/h03g1a/ilu.pdf
//DenseMatrix tmp = new DenseMatrix(6, 6);
//tmp.Set(new double[] {
// 3,0,-1,-1,0,-1,
// 0,2,0,-1,0,0,
// -1,0,3,0,-1,0,
// -1,-1,0,2,0,-1,
// 0,0,-1,0,3,-1,
// -1,0,0,-1,-1,4});
//CholeskyDecomposition decompDense = new CholeskyDecomposition(tmp);
//decompDense.Compute();
//PackedSparseMatrix M1_sparse = PackedSparseMatrix.FromDense(tmp, true);
//M1_sparse.Sort();
//SparseCholeskyDecomposition decompM1_sparse = new SparseCholeskyDecomposition(M1_sparse);
//decompM1_sparse.ComputeIncomplete();
// cholesky decomposition known-result test
DenseMatrix MSym3x3 = new DenseMatrix(3, 3);
MSym3x3.Set(new double[] { 25, 15, -5, 15, 18, 0, -5, 0, 11 });
DenseMatrix MSym3x3_Chol = new DenseMatrix(3, 3);
MSym3x3_Chol.Set(new double[] { 5, 0, 0, 3, 3, 0, -1, 1, 3 });
CholeskyDecomposition decomp3x3 = new CholeskyDecomposition(MSym3x3);
decomp3x3.Compute();
if (decomp3x3.L.EpsilonEquals(MSym3x3_Chol) == false)
{
System.Console.WriteLine("FAIL cholesky3x3 incorrect result");
}
if (decomp3x3.L.Multiply(decomp3x3.L.Transpose()).EpsilonEquals(MSym3x3) == false)
{
System.Console.WriteLine("FAIL cholesky3x3 did not reproduce input");
}
// cholesky decomposition known-result test
DenseMatrix MSym4x4 = new DenseMatrix(4, 4);
MSym4x4.Set(new double[] {
18, 22, 54, 42, 22, 70, 86, 62,
54, 86, 174, 134, 42, 62, 134, 106
});
DenseMatrix MSym4x4_Chol = new DenseMatrix(4, 4);
MSym4x4_Chol.Set(new double[] {
4.24264, 0, 0, 0, 5.18545, 6.56591, 0, 0,
12.72792, 3.04604, 1.64974, 0, 9.89949, 1.62455, 1.84971, 1.39262
});
CholeskyDecomposition decomp4x4 = new CholeskyDecomposition(MSym4x4);
decomp4x4.Compute();
if (decomp4x4.L.EpsilonEquals(MSym4x4_Chol, 0.0001) == false)
{
System.Console.WriteLine("FAIL cholesky4x4 incorrect result");
}
if (decomp4x4.L.Multiply(decomp4x4.L.Transpose()).EpsilonEquals(MSym4x4) == false)
{
System.Console.WriteLine("FAIL cholesky4x4 did not reproduce input");
}
}
// the internal linear regression routine, which assumes inputs are entirely valid
private FitResult LinearRegression_Internal(int outputIndex)
{
// to do a fit, we need more data than parameters
if (Count < Dimension)
{
throw new InsufficientDataException();
}
// construct the design matrix
SymmetricMatrix D = new SymmetricMatrix(Dimension);
for (int i = 0; i < Dimension; i++)
{
for (int j = 0; j <= i; j++)
{
if (i == outputIndex)
{
if (j == outputIndex)
{
D[i, j] = Count;
}
else
{
D[i, j] = storage[j].Mean * Count;
}
}
else
{
if (j == outputIndex)
{
D[i, j] = storage[i].Mean * Count;
}
else
{
double Dij = 0.0;
for (int k = 0; k < Count; k++)
{
Dij += storage[i][k] * storage[j][k];
}
D[i, j] = Dij;
}
}
}
}
// construct the right hand side
ColumnVector b = new ColumnVector(Dimension);
for (int i = 0; i < Dimension; i++)
{
if (i == outputIndex)
{
b[i] = storage[i].Mean * Count;
}
else
{
double bi = 0.0;
for (int k = 0; k < Count; k++)
{
bi += storage[outputIndex][k] * storage[i][k];
}
b[i] = bi;
}
}
// solve the system for the linear model parameters
CholeskyDecomposition CD = D.CholeskyDecomposition();
ColumnVector parameters = CD.Solve(b);
// find total sum of squares, with dof = # points - 1 (minus one for the variance-minimizing mean)
double totalSumOfSquares = storage[outputIndex].Variance * Count;
// find remaining unexplained sum of squares, with dof = # points - # parameters
double unexplainedSumOfSquares = 0.0;
for (int r = 0; r < Count; r++)
{
double y = 0.0;
for (int c = 0; c < Dimension; c++)
{
if (c == outputIndex)
{
y += parameters[c];
}
else
{
y += parameters[c] * storage[c][r];
}
}
unexplainedSumOfSquares += MoreMath.Sqr(y - storage[outputIndex][r]);
}
int unexplainedDegreesOfFreedom = Count - Dimension;
double unexplainedVariance = unexplainedSumOfSquares / unexplainedDegreesOfFreedom;
// find explained sum of squares, with dof = # parameters - 1
double explainedSumOfSquares = totalSumOfSquares - unexplainedSumOfSquares;
int explainedDegreesOfFreedom = Dimension - 1;
double explainedVariance = explainedSumOfSquares / explainedDegreesOfFreedom;
// compute F statistic from sums of squares
double F = explainedVariance / unexplainedVariance;
Distribution fDistribution = new FisherDistribution(explainedDegreesOfFreedom, unexplainedDegreesOfFreedom);
SymmetricMatrix covariance = unexplainedVariance * CD.Inverse();
return(new FitResult(parameters, covariance, new TestResult("F", F, TestType.RightTailed, fDistribution)));
}