public void Test2()
{
// Every transpose(A)*A is SPD if A has full column rank and m > n.
MatrixD a = new MatrixD(new double[, ] {
{ 1, 2, 3 },
{ 4, 5, 6 },
{ 7, 8, 9 },
{ 10, 11, -12 }
});
//MatrixD a = new MatrixD(new double[,] { { 1, 2},
// { 4, 5},
// { 7, 8}});
a = a.Transposed * a;
CholeskyDecompositionD d = new CholeskyDecompositionD(a);
Assert.AreEqual(true, d.IsSymmetricPositiveDefinite);
MatrixD l = d.L;
Assert.AreEqual(0, l[0, 1]);
Assert.AreEqual(0, l[0, 2]);
Assert.AreEqual(0, l[1, 2]);
Assert.IsTrue(MatrixD.AreNumericallyEqual(a, l * l.Transposed));
}
public void Test1()
{
MatrixD a = new MatrixD(new double[,] { { 2, -1, 0},
{ -1, 2, -1},
{ 0, -1, 2} });
CholeskyDecompositionD d = new CholeskyDecompositionD(a);
Assert.AreEqual(true, d.IsSymmetricPositiveDefinite);
MatrixD l = d.L;
Assert.AreEqual(0, l[0, 1]);
Assert.AreEqual(0, l[0, 2]);
Assert.AreEqual(0, l[1, 2]);
Assert.IsTrue(MatrixD.AreNumericallyEqual(a, l * l.Transposed));
Assert.IsTrue(MatrixD.AreNumericallyEqual(a, l * l.Transposed));
// Check solving of linear equations.
MatrixD x = new MatrixD(new double[,] { { 1, 2},
{ 3, 4},
{ 5, 6} });
MatrixD b = a * x;
Assert.IsTrue(MatrixD.AreNumericallyEqual(x, d.SolveLinearEquations(b)));
}
public void Test1()
{
MatrixD a = new MatrixD(new double[, ] {
{ 2, -1, 0 },
{ -1, 2, -1 },
{ 0, -1, 2 }
});
CholeskyDecompositionD d = new CholeskyDecompositionD(a);
Assert.AreEqual(true, d.IsSymmetricPositiveDefinite);
MatrixD l = d.L;
Assert.AreEqual(0, l[0, 1]);
Assert.AreEqual(0, l[0, 2]);
Assert.AreEqual(0, l[1, 2]);
Assert.IsTrue(MatrixD.AreNumericallyEqual(a, l * l.Transposed));
Assert.IsTrue(MatrixD.AreNumericallyEqual(a, l * l.Transposed));
// Check solving of linear equations.
MatrixD x = new MatrixD(new double[, ] {
{ 1, 2 },
{ 3, 4 },
{ 5, 6 }
});
MatrixD b = a * x;
Assert.IsTrue(MatrixD.AreNumericallyEqual(x, d.SolveLinearEquations(b)));
}
public void TestRandomRectangularA()
{
RandomHelper.Random = new Random(1);
// Every transpose(A) * A is SPD if A has full column rank and m>n.
for (int i = 0; i < 100; i++)
{
// Create A.
MatrixD a = new MatrixD(10, 3);
RandomHelper.Random.NextMatrixD(a, 0, 1);
QRDecompositionD d = new QRDecompositionD(a);
MatrixD b = new MatrixD(10, 1);
RandomHelper.Random.NextMatrixD(b, 0, 1);
MatrixD x = d.SolveLinearEquations(b);
Assert.IsTrue(MatrixD.AreNumericallyEqual(a, d.Q * d.R));
Assert.IsTrue(MatrixD.AreNumericallyEqual(a, d.Q * d.R)); // Second time with the cached values.
// Check solving of linear equations.
if (d.HasNumericallyFullRank)
{
// Compare with Least squares solution (Gauss-Transformation and Cholesky).
MatrixD spdMatrix = a.Transposed * a;
CholeskyDecompositionD ch = new CholeskyDecompositionD(spdMatrix);
MatrixD x2 = ch.SolveLinearEquations(a.Transposed * b);
Assert.IsTrue(MatrixD.AreNumericallyEqual(x, x2, 0.0001f));
}
MatrixD h = d.H; // Just call this one to see if it runs through.
}
}
public void TestRandomSpdA()
{
RandomHelper.Random = new Random(1);
// Every transpose(A) * A is SPD if A has full column rank and m>n.
for (int i = 0; i < 100; i++)
{
VectorD column1 = new VectorD(4);
RandomHelper.Random.NextVectorD(column1, 1, 2);
VectorD column2 = new VectorD(4);
RandomHelper.Random.NextVectorD(column2, 1, 2);
// Make linearly independent.
if (column1 / column1[0] == column2 / column2[0])
{
column2[0]++;
}
// Create linearly independent third column.
VectorD column3 = column1 + column2;
column3[1]++;
// Create A.
MatrixD a = new MatrixD(4, 3);
a.SetColumn(0, column1);
a.SetColumn(1, column2);
a.SetColumn(2, column3);
MatrixD spdMatrix = a.Transposed * a;
CholeskyDecompositionD d = new CholeskyDecompositionD(spdMatrix);
Assert.AreEqual(true, d.IsSymmetricPositiveDefinite);
MatrixD l = d.L;
// Test if L is a lower triangular matrix.
for (int j = 0; j < l.NumberOfRows; j++)
{
for (int k = 0; k < l.NumberOfColumns; k++)
{
if (j < k)
{
Assert.AreEqual(0, l[j, k]);
}
}
}
Assert.IsTrue(MatrixD.AreNumericallyEqual(spdMatrix, l * l.Transposed));
// Check solving of linear equations.
MatrixD b = new MatrixD(3, 2);
RandomHelper.Random.NextMatrixD(b, 0, 1);
MatrixD x = d.SolveLinearEquations(b);
MatrixD b2 = spdMatrix * x;
Assert.IsTrue(MatrixD.AreNumericallyEqual(b, b2, 0.01f));
}
}
public void SolveLinearEquationsException1()
{
// Create A.
MatrixD a = new MatrixD(new double[,] { { 1, 2, 3 }, { 4, 5, 6 }, { 7, 8, -9 } });
CholeskyDecompositionD decomp = new CholeskyDecompositionD(a);
decomp.SolveLinearEquations(null);
}
public void TestEmptyMatrix()
{
MatrixD a = new MatrixD(2, 2);
CholeskyDecompositionD d = new CholeskyDecompositionD(a);
Assert.AreEqual(false, d.IsSymmetricPositiveDefinite);
}
public void SolveLinearEquationsException1()
{
// Create A.
MatrixD a = new MatrixD(new double[, ] {
{ 1, 2, 3 }, { 4, 5, 6 }, { 7, 8, -9 }
});
CholeskyDecompositionD decomp = new CholeskyDecompositionD(a);
decomp.SolveLinearEquations(null);
}
public void TestRectangularA()
{
MatrixD a = new MatrixD(new double[, ] {
{ 2, -1 },
{ -1, 2 },
{ 0, -1 }
});
CholeskyDecompositionD d = new CholeskyDecompositionD(a);
Assert.AreEqual(false, d.IsSymmetricPositiveDefinite);
}
public void TestNonSpdA()
{
MatrixD a = new MatrixD(new double[, ] {
{ 1, 2, 3 },
{ 2, 5, 6 },
{ 3, 6, 4 }
});
CholeskyDecompositionD d = new CholeskyDecompositionD(a);
Assert.AreEqual(false, d.IsSymmetricPositiveDefinite);
}
public void TestWithNaNValues()
{
MatrixD a = new MatrixD(new[, ] {
{ 0, 1, 2 },
{ 1, 4, 3 },
{ 5, 3, double.NaN }
});
// Any result is ok. We must only check for infinite loops!
var d = new CholeskyDecompositionD(a);
d = new CholeskyDecompositionD(new MatrixD(4, 4, double.NaN));
}
public void TestNonSymmetricA()
{
MatrixD a = new MatrixD(new double[,] { { 1, 2, 3},
{ 2, 2, 2},
{ 0, 0, 0} });
CholeskyDecompositionD d = new CholeskyDecompositionD(a);
Assert.AreEqual(false, d.IsSymmetricPositiveDefinite);
}
public void TestRandomRectangularA()
{
RandomHelper.Random = new Random(1);
// Every transpose(A) * A is SPD if A has full column rank and m>n.
for (int i = 0; i < 100; i++)
{
// Create A.
MatrixD a = new MatrixD(10, 3);
RandomHelper.Random.NextMatrixD(a, 0, 1);
QRDecompositionD d = new QRDecompositionD(a);
MatrixD b = new MatrixD(10, 1);
RandomHelper.Random.NextMatrixD(b, 0, 1);
MatrixD x = d.SolveLinearEquations(b);
Assert.IsTrue(MatrixD.AreNumericallyEqual(a, d.Q * d.R));
Assert.IsTrue(MatrixD.AreNumericallyEqual(a, d.Q * d.R)); // Second time with the cached values.
// Check solving of linear equations.
if (d.HasNumericallyFullRank)
{
// Compare with Least squares solution (Gauss-Transformation and Cholesky).
MatrixD spdMatrix = a.Transposed * a;
CholeskyDecompositionD ch = new CholeskyDecompositionD(spdMatrix);
MatrixD x2 = ch.SolveLinearEquations(a.Transposed * b);
Assert.IsTrue(MatrixD.AreNumericallyEqual(x, x2, 0.0001f));
}
MatrixD h = d.H; // Just call this one to see if it runs through.
}
}
public void Test2()
{
// Every transpose(A)*A is SPD if A has full column rank and m > n.
MatrixD a = new MatrixD(new double[,] { { 1, 2, 3},
{ 4, 5, 6},
{ 7, 8, 9},
{ 10, 11, -12}});
//MatrixD a = new MatrixD(new double[,] { { 1, 2},
// { 4, 5},
// { 7, 8}});
a = a.Transposed * a;
CholeskyDecompositionD d = new CholeskyDecompositionD(a);
Assert.AreEqual(true, d.IsSymmetricPositiveDefinite);
MatrixD l = d.L;
Assert.AreEqual(0, l[0, 1]);
Assert.AreEqual(0, l[0, 2]);
Assert.AreEqual(0, l[1, 2]);
Assert.IsTrue(MatrixD.AreNumericallyEqual(a, l * l.Transposed));
}
public void TestEmptyMatrix()
{
MatrixD a = new MatrixD(2, 2);
CholeskyDecompositionD d = new CholeskyDecompositionD(a);
Assert.AreEqual(false, d.IsSymmetricPositiveDefinite);
}
public void TestWithNaNValues()
{
MatrixD a = new MatrixD(new[,] {{ 0, 1, 2 },
{ 1, 4, 3 },
{ 5, 3, double.NaN}});
// Any result is ok. We must only check for infinite loops!
var d = new CholeskyDecompositionD(a);
d = new CholeskyDecompositionD(new MatrixD(4, 4, double.NaN));
}
public void TestRectangularA()
{
MatrixD a = new MatrixD(new double[,] { { 2, -1},
{ -1, 2},
{ 0, -1} });
CholeskyDecompositionD d = new CholeskyDecompositionD(a);
Assert.AreEqual(false, d.IsSymmetricPositiveDefinite);
}
public void TestRandomSpdA()
{
RandomHelper.Random = new Random(1);
// Every transpose(A) * A is SPD if A has full column rank and m>n.
for (int i = 0; i < 100; i++)
{
VectorD column1 = new VectorD(4);
RandomHelper.Random.NextVectorD(column1, 1, 2);
VectorD column2 = new VectorD(4);
RandomHelper.Random.NextVectorD(column2, 1, 2);
// Make linearly independent.
if (column1 / column1[0] == column2 / column2[0])
column2[0]++;
// Create linearly independent third column.
VectorD column3 = column1 + column2;
column3[1]++;
// Create A.
MatrixD a = new MatrixD(4, 3);
a.SetColumn(0, column1);
a.SetColumn(1, column2);
a.SetColumn(2, column3);
MatrixD spdMatrix = a.Transposed * a;
CholeskyDecompositionD d = new CholeskyDecompositionD(spdMatrix);
Assert.AreEqual(true, d.IsSymmetricPositiveDefinite);
MatrixD l = d.L;
// Test if L is a lower triangular matrix.
for (int j = 0; j < l.NumberOfRows; j++)
for (int k = 0; k < l.NumberOfColumns; k++)
if (j < k)
Assert.AreEqual(0, l[j, k]);
Assert.IsTrue(MatrixD.AreNumericallyEqual(spdMatrix, l * l.Transposed));
// Check solving of linear equations.
MatrixD b = new MatrixD(3, 2);
RandomHelper.Random.NextMatrixD(b, 0, 1);
MatrixD x = d.SolveLinearEquations(b);
MatrixD b2 = spdMatrix * x;
Assert.IsTrue(MatrixD.AreNumericallyEqual(b, b2, 0.01f));
}
}
