public void Hilbert()
{
var matrix = GetHilbertMatrix4();
var decomposition = new QRDecomposition(matrix);
var matrixQ = decomposition.LeftFactorMatrix;
Assert.AreEqual(matrixQ[0, 0], -0.84, 0.01);
Assert.AreEqual(matrixQ[0, 1], 0.52, 0.01);
Assert.AreEqual(matrixQ[0, 2], -0.15, 0.01);
Assert.AreEqual(matrixQ[0, 3], 0.03, 0.01);
Assert.AreEqual(matrixQ[1, 0], -0.42, 0.01);
Assert.AreEqual(matrixQ[1, 1], -0.44, 0.01);
Assert.AreEqual(matrixQ[1, 2], 0.73, 0.01);
Assert.AreEqual(matrixQ[1, 3], -0.32, 0.01);
Assert.AreEqual(matrixQ[2, 0], -0.28, 0.01);
Assert.AreEqual(matrixQ[2, 1], -0.53, 0.01);
Assert.AreEqual(matrixQ[2, 2], -0.14, 0.01);
Assert.AreEqual(matrixQ[2, 3], 0.79, 0.01);
Assert.AreEqual(matrixQ[3, 0], -0.21, 0.01);
Assert.AreEqual(matrixQ[3, 1], -0.50, 0.01);
Assert.AreEqual(matrixQ[3, 2], -0.65, 0.01);
Assert.AreEqual(matrixQ[3, 3], -0.53, 0.01);
}
public void Hilbert()
{
var matrix = GetHilbertMatrix4();
var decomposition = new QRDecomposition(matrix);
var matrixR = decomposition.RightFactorMatrix;
var matrixH = decomposition.H;
Assert.AreEqual(matrixR[0, 0], -1.19, 0.01);
Assert.AreEqual(matrixR[0, 1], -0.67, 0.01);
Assert.AreEqual(matrixR[0, 2], -0.47, 0.01);
Assert.AreEqual(matrixR[0, 3], -0.37, 0.01);
Assert.AreEqual(matrixR[1, 0], 0);
Assert.AreEqual(matrixR[1, 1], -0.12, 0.01);
Assert.AreEqual(matrixR[1, 2], -0.13, 0.01);
Assert.AreEqual(matrixR[1, 3], -0.12, 0.01);
Assert.AreEqual(matrixR[2, 0], 0);
Assert.AreEqual(matrixR[2, 1], 0);
Assert.AreEqual(matrixR[2, 2], -0.01, 0.01);
Assert.AreEqual(matrixR[2, 3], -0.01, 0.01);
Assert.AreEqual(matrixR[3, 0], 0);
Assert.AreEqual(matrixR[3, 1], 0);
Assert.AreEqual(matrixR[3, 2], 0);
Assert.AreEqual(matrixR[3, 3], -0.0001, 0.0001);
}
public void ExceptionDifferentRowCount()
{
var matrixA = new Matrix(2, 2);
matrixA[0, 0] = 0;
matrixA[0, 1] = 0;
matrixA[1, 0] = 1;
matrixA[1, 1] = 0;
var matrixB = new Matrix(2, 2);
matrixB[0, 0] = 0;
matrixB[0, 1] = 0;
matrixB[1, 0] = 0;
matrixB[1, 1] = 1;
var qrDecomposition = new QRDecomposition(matrixA);
qrDecomposition.Solve(matrixB);
}
/// <summary>
/// Calculates the LHS solution vector if the matrix is square or the least squares solution otherwise.
/// </summary>
/// <param name="rightHandSide">The right hand side.</param>
/// <returns>Returns the LHS solution vector if the matrix is square or the least squares solution otherwise.</returns>
public Matrix Solve(Matrix rightHandSide)
{
IDecomposition decomposition;
if (IsSquare)
{
// if (IsSymmetric)
// decomposition = new CholeskyDecomposition(this);
// else
decomposition = new LUDecomposition(this);
}
else
{
decomposition = new QRDecomposition(this);
}
return(decomposition.Solve(rightHandSide));
}
public void Simple()
{
var decomposition = new QRDecomposition(GetMatrix());
var matrixQ = decomposition.LeftFactorMatrix;
Assert.AreEqual(matrixQ[0, 0], -6d / 7d, 0.0000001);
Assert.AreEqual(matrixQ[0, 1], 69d / 175d, 0.0000001);
Assert.AreEqual(matrixQ[0, 2], -58d / 175d, 0.0000001);
Assert.AreEqual(matrixQ[1, 0], -3d / 7d, 0.0000001);
Assert.AreEqual(matrixQ[1, 1], -158d / 175d, 0.0000001);
Assert.AreEqual(matrixQ[1, 2], 6d / 175d, 0.0000001);
Assert.AreEqual(matrixQ[2, 0], 2d / 7d, 0.0000001);
Assert.AreEqual(matrixQ[2, 1], -6d / 35d, 0.0000001);
Assert.AreEqual(matrixQ[2, 2], -33d / 35d, 0.0000001);
}
public void Simple()
{
var decomposition = new QRDecomposition(GetMatrix());
var matrixR = decomposition.RightFactorMatrix;
Assert.AreEqual(matrixR[0, 0], -14d, 0.0000001);
Assert.AreEqual(matrixR[0, 1], -21d, 0.0000001);
Assert.AreEqual(matrixR[0, 2], 24.571428571428569d, 0.0000001);
Assert.AreEqual(matrixR[1, 0], 0d, 0.0000001);
Assert.AreEqual(matrixR[1, 1], -175d, 0.0000001);
Assert.AreEqual(matrixR[1, 2], 63.657142857142844d, 0.0000001);
Assert.AreEqual(matrixR[2, 0], 0d, 0.0000001);
Assert.AreEqual(matrixR[2, 1], 0d, 0.0000001);
Assert.AreEqual(matrixR[2, 2], 0.11428571428571477d, 0.0000001);
}
public void ExceptionRankDeficient()
{
var matrixA = new Matrix(3, 2);
matrixA[0, 0] = 1;
matrixA[0, 1] = 2;
matrixA[1, 0] = 3;
matrixA[1, 1] = 4;
matrixA[2, 0] = 4;
matrixA[2, 1] = 2;
var matrixB = new Matrix(2, 2);
matrixB[0, 0] = 0;
matrixB[0, 1] = 0;
matrixB[1, 0] = 0;
matrixB[1, 1] = 1;
var qrDecomposition = new QRDecomposition(matrixA);
qrDecomposition.Solve(matrixB);
}
public void Simple()
{
var a = new Matrix(2, 2);
a[0, 0] = 0;
a[0, 1] = 0;
a[1, 0] = 1;
a[1, 1] = 0;
var b = new Matrix(2, 2);
b[0, 0] = 0;
b[0, 1] = 0;
b[1, 0] = 0;
b[1, 1] = 1;
var qrDecomposition = new QRDecomposition(a);
Assert.IsFalse(qrDecomposition.IsFullRank);
qrDecomposition = new QRDecomposition(b);
Assert.IsFalse(qrDecomposition.IsFullRank);
qrDecomposition = new QRDecomposition(a * b);
Assert.IsFalse(qrDecomposition.IsFullRank);
}
public void Simple()
{
var matrixA = new Matrix(3, 2);
matrixA[0, 0] = 1;
matrixA[0, 1] = 2;
matrixA[1, 0] = 3;
matrixA[1, 1] = 4;
matrixA[2, 0] = 4;
matrixA[2, 1] = 2;
var matrixB = new Matrix(3, 2);
matrixB[0, 0] = 3;
matrixB[0, 1] = 4;
matrixB[1, 0] = 4;
matrixB[1, 1] = 2;
matrixB[2, 0] = 1;
matrixB[2, 1] = 2;
var decomposition = new QRDecomposition(matrixA);
var solveMatrix = decomposition.Solve(matrixB);
Assert.AreEqual(solveMatrix.Rows, 2);
Assert.AreEqual(solveMatrix.Columns, 2);
Assert.AreEqual(solveMatrix[0, 0], -0.514285714, 0.00000001);
Assert.AreEqual(solveMatrix[0, 1], -0.057142857, 0.00000001);
Assert.AreEqual(solveMatrix[1, 0], 1.4714285714, 0.00000001);
Assert.AreEqual(solveMatrix[1, 1], 0.8857142857, 0.00000001);
}