public void QrDecompositionConstructorTest2()
{
double[][] value =
{
new double[] { 1 },
new double[] { 2 },
new double[] { 3 }
};
var target = new JaggedQrDecomposition(value);
// Decomposition Identity
var Q = target.OrthogonalFactor;
var QQt = Matrix.Dot(Q.Transpose(), Q);
Assert.IsTrue(Matrix.IsEqual(QQt, Jagged.Identity(1), 1e-6));
double[][] reverse = target.Reverse();
Assert.IsTrue(Matrix.IsEqual(value, reverse, 1e-6));
// Linear system solving
double[][] B = Matrix.ColumnVector(new double[] { 4, 5, 6 }).ToJagged();
double[][] expected = Jagged.ColumnVector(new double[] { 2.285714285714286 });
double[][] actual = target.Solve(B);
Assert.IsTrue(Matrix.IsEqual(expected, actual, 0.0000000000001));
double[][] R = target.UpperTriangularFactor;
actual = value.Dot(R.Inverse());
Assert.IsTrue(Matrix.IsEqual(Q, actual, 0.0000000000001));
}
public void QrDecompositionConstructorTest()
{
double[][] value =
{
new double[] { 2, -1, 0 },
new double[] { -1, 2, -1 },
new double[] { 0, -1, 2 }
};
var target = new JaggedQrDecomposition(value);
// Decomposition Identity
var Q = target.OrthogonalFactor;
var QQt = Matrix.Dot(Q, Q.Transpose());
Assert.IsTrue(Matrix.IsEqual(QQt, Jagged.Identity(3), 1e-6));
Assert.IsTrue(Matrix.IsEqual(value, target.Reverse(), 1e-6));
// Linear system solving
double[][] B = Matrix.ColumnVector(new double[] { 1, 2, 3 }).ToJagged();
double[][] expected = Matrix.ColumnVector(new double[] { 2.5, 4.0, 3.5 }).ToJagged();
double[][] actual = target.Solve(B);
Assert.IsTrue(Matrix.IsEqual(expected, actual, 0.0000000000001));
}
public void solve_for_diagonal()
{
double[][] value =
{
new double[] { 2, -1, 0 },
new double[] { -1, 2, -1 },
new double[] { 0, -1, 2 }
};
double[] b = { 1, 2, 3 };
double[][] expected =
{
new double[] { 0.75, 1, 0.75 },
new double[] { 0.50, 2, 1.50 },
new double[] { 0.25, 1, 2.25 }
};
var target = new JaggedQrDecomposition(value);
double[][] actual = target.SolveForDiagonal(b);
Assert.IsTrue(Matrix.IsEqual(expected, actual, 1e-10));
Assert.IsTrue(Matrix.IsEqual(value.Transpose(), target.Reverse(), 1e-6));
}
public void InverseTest()
{
double[][] value =
{
new double[] { 2, -1, 0 },
new double[] { -1, 2, -1 },
new double[] { 0, -1, 2 }
};
double[][] expected =
{
new double[] { 0.7500, 0.5000, 0.2500 },
new double[] { 0.5000, 1.0000, 0.5000 },
new double[] { 0.2500, 0.5000, 0.7500 },
};
var target = new JaggedQrDecomposition(value);
double[][] actual = target.Inverse();
Assert.IsTrue(Matrix.IsEqual(expected, actual, 1e-10));
Assert.IsTrue(Matrix.IsEqual(value, target.Reverse(), 1e-4));
target = new JaggedQrDecomposition(value.Transpose(), true);
actual = target.Inverse();
Assert.IsTrue(Matrix.IsEqual(expected, actual, 1e-10));
Assert.IsTrue(Matrix.IsEqual(value.Transpose(), target.Reverse(), 1e-4));
}
public void full_decomposition()
{
double[][] value =
{
new double[] { 1 },
new double[] { 2 },
new double[] { 3 }
};
var target = new JaggedQrDecomposition(value, economy: false);
// Decomposition Identity
var Q = target.OrthogonalFactor;
var QtQ = Matrix.Dot(Q.Transpose(), Q);
Assert.IsTrue(Matrix.IsEqual(QtQ, Jagged.Identity(3), 1e-6));
double[][] reverse = target.Reverse();
Assert.IsTrue(Matrix.IsEqual(value, reverse, 1e-6));
// Linear system solving
double[][] B = Matrix.ColumnVector(new double[] { 4, 5, 6 }).ToJagged();
double[][] expected = Jagged.ColumnVector(new double[] { 2.285714285714286 });
double[][] actual = target.Solve(B);
Assert.IsTrue(Matrix.IsEqual(expected, actual, 0.0000000000001));
var QQt = Matrix.Dot(Q, Q.Transpose());
Assert.IsTrue(Matrix.IsEqual(QQt, Jagged.Identity(3), 1e-6));
}
public void QrDecompositionConstructorTest()
{
double[][] value =
{
new double[] { 2, -1, 0 },
new double[] { -1, 2, -1 },
new double[] { 0, -1, 2 }
};
var target = new JaggedQrDecomposition(value);
// Decomposition Identity
var Q = target.OrthogonalFactor;
var QQt = Matrix.Multiply(Q, Q.Transpose());
Assert.IsTrue(Matrix.IsEqual(QQt, Matrix.JaggedIdentity(3), 1e-6));
Assert.IsTrue(Matrix.IsEqual(value, target.Reverse(), 1e-6));
// Linear system solving
double[][] B = Matrix.ColumnVector(new double[] { 1, 2, 3 }).ToJagged();
double[][] expected = Matrix.ColumnVector(new double[] { 2.5, 4.0, 3.5 }).ToJagged();
double[][] actual = target.Solve(B);
Assert.IsTrue(Matrix.IsEqual(expected, actual, 0.0000000000001));
}
public void SolveTest2()
{
// Example from Lecture notes for MATHS 370: Advanced Numerical Methods
// http://www.math.auckland.ac.nz/~sharp/370/qr-solving.pdf
double[,] value =
{
{ 1, 0, 0 },
{ 1, 7, 49 },
{ 1, 14, 196 },
{ 1, 21, 441 },
{ 1, 28, 784 },
{ 1, 35, 1225 },
};
// Matrices
{
double[,] b =
{
{ 4 },
{ 1 },
{ 0 },
{ 0 },
{ 2 },
{ 5 },
};
double[,] expected =
{
{ 3.9286 },
{ -0.5031 },
{ 0.0153 },
};
var target = new QrDecomposition(value);
double[,] actual = target.Solve(b);
Assert.IsTrue(Matrix.IsEqual(expected, actual, atol: 1e-4));
Assert.IsTrue(Matrix.IsEqual(value, target.Reverse(), 1e-6));
var target2 = new JaggedQrDecomposition(value.ToJagged());
double[][] actual2 = target2.Solve(b.ToJagged());
Assert.IsTrue(Matrix.IsEqual(expected, actual2, atol: 1e-4));
Assert.IsTrue(Matrix.IsEqual(value, target2.Reverse(), 1e-6));
}
// Vectors
{
double[] b = { 4, 1, 0, 0, 2, 5 };
double[] expected = { 3.9286, -0.5031, 0.0153 };
var target = new QrDecomposition(value);
double[] actual = target.Solve(b);
Assert.IsTrue(Matrix.IsEqual(expected, actual, atol: 1e-4));
}
}
public void SolveTest()
{
double[][] value =
{
new double[] { 2, -1, 0 },
new double[] { -1, 2, -1 },
new double[] { 0, -1, 2 }
};
double[] b = { 1, 2, 3 };
double[] expected = { 2.5000, 4.0000, 3.5000 };
var target = new JaggedQrDecomposition(value);
double[] actual = target.Solve(b);
Assert.IsTrue(Matrix.IsEqual(expected, actual, 1e-10));
Assert.IsTrue(Matrix.IsEqual(value.Transpose(), target.Reverse(), 1e-6));
}
public void SolveTest2()
{
// Example from Lecture notes for MATHS 370: Advanced Numerical Methods
// http://www.math.auckland.ac.nz/~sharp/370/qr-solving.pdf
double[,] value =
{
{ 1, 0, 0 },
{ 1, 7, 49 },
{ 1, 14, 196 },
{ 1, 21, 441 },
{ 1, 28, 784 },
{ 1, 35, 1225 },
};
// Matrices
{
double[,] b =
{
{ 4 },
{ 1 },
{ 0 },
{ 0 },
{ 2 },
{ 5 },
};
double[,] expected =
{
{ 3.9286 },
{ -0.5031 },
{ 0.0153 },
};
var target = new QrDecomposition(value);
double[,] actual = target.Solve(b);
Assert.IsTrue(Matrix.IsEqual(expected, actual, atol: 1e-4));
Assert.IsTrue(Matrix.IsEqual(value, target.Reverse(), 1e-6));
var target2 = new JaggedQrDecomposition(value.ToJagged());
double[][] actual2 = target2.Solve(b.ToJagged());
Assert.IsTrue(Matrix.IsEqual(expected, actual2, atol: 1e-4));
Assert.IsTrue(Matrix.IsEqual(value, target2.Reverse(), 1e-6));
}
// Vectors
{
double[] b = { 4, 1, 0, 0, 2, 5 };
double[] expected = { 3.9286, -0.5031, 0.0153 };
var target = new QrDecomposition(value);
double[] actual = target.Solve(b);
Assert.IsTrue(Matrix.IsEqual(expected, actual, atol: 1e-4));
}
}
public void InverseTest()
{
double[][] value =
{
new double[] { 2, -1, 0 },
new double[] { -1, 2, -1 },
new double[] { 0, -1, 2 }
};
double[][] expected =
{
new double[] { 0.7500, 0.5000, 0.2500},
new double[] { 0.5000, 1.0000, 0.5000},
new double[] { 0.2500, 0.5000, 0.7500},
};
var target = new JaggedQrDecomposition(value);
double[][] actual = target.Inverse();
Assert.IsTrue(Matrix.IsEqual(expected, actual, 1e-10));
Assert.IsTrue(Matrix.IsEqual(value, target.Reverse(), 1e-4));
target = new JaggedQrDecomposition(value.Transpose(), true);
actual = target.Inverse();
Assert.IsTrue(Matrix.IsEqual(expected, actual, 1e-10));
Assert.IsTrue(Matrix.IsEqual(value.Transpose(), target.Reverse(), 1e-4));
}
public void SolveTest()
{
double[][] value =
{
new double[] { 2, -1, 0 },
new double[] { -1, 2, -1 },
new double[] { 0, -1, 2 }
};
double[] b = { 1, 2, 3 };
double[] expected = { 2.5000, 4.0000, 3.5000 };
var target = new JaggedQrDecomposition(value);
double[] actual = target.Solve(b);
Assert.IsTrue(Matrix.IsEqual(expected, actual, 1e-10));
Assert.IsTrue(Matrix.IsEqual(value.Transpose(), target.Reverse(), 1e-6));
}