public void HouseholderTransformationTridiagonalizeTest()
{
// first matrix
Matrix matrix = new Matrix(new[, ] {
{ 4.0, 1, -2, 2 }, { 1, 2, 0, 1 }, { -2, 0, 3, -2 }, { 2, 1, -2, -1 }
});
Matrix expected = new Matrix(new[, ] {
{ 4, -3, 0, 0 }, { -3, 10.0 / 3, -5.0 / 3, 0 }, { 0, -5.0 / 3, -33.0 / 25, 68.0 / 75 }, { 0, 0, 68.0 / 75, 149.0 / 75 }
});
Matrix result = HouseholderTransformation.Tridiagonalize(matrix);
for (Int32 rowIndex = 0; rowIndex < matrix.NumberOfRows; rowIndex++)
{
for (Int32 columnIndex = 0; columnIndex < matrix.NumberOfColumns; columnIndex++)
{
result[rowIndex, columnIndex].ShouldBe(expected[rowIndex, columnIndex], 0.01);
}
}
// second matrix
matrix = new Matrix(new[, ] {
{ 4.0, 2, 2, 1 }, { 2, -3, 1, 1 }, { 2, 1, 3, 1 }, { 1, 1, 1, 2 }
});
expected = new Matrix(new[, ] {
{ 4, -3, 0, 0 }, { -3, 2, 3.1623, 0 }, { 0, 3.1623, -1.4, -0.2 }, { 0, 0, -0.2, 1.4 }
});
result = HouseholderTransformation.Tridiagonalize(matrix);
for (Int32 rowIndex = 0; rowIndex < matrix.NumberOfRows; rowIndex++)
{
for (Int32 columnIndex = 0; columnIndex < matrix.NumberOfColumns; columnIndex++)
{
result[rowIndex, columnIndex].ShouldBe(expected[rowIndex, columnIndex], 0.01);
}
}
// exceptions
Should.Throw <ArgumentNullException>(() => HouseholderTransformation.Tridiagonalize(null));
Should.Throw <ArgumentException>(() => HouseholderTransformation.Tridiagonalize(new Matrix(2, 3)));
Should.Throw <ArgumentException>(() => HouseholderTransformation.Tridiagonalize(MatrixFactory.CreateSquare(1, 2, 3, 4)));
}
public void HouseholderTransformationComputeTest()
{
// first vector
HouseholderTransformation transformation = new HouseholderTransformation(new Vector(new Double[] { 1, 1, 1, 1 }));
transformation.Compute();
Matrix resultH = transformation.H;
Matrix expectedH = new Matrix(new[, ] {
{ 0.5, 0.5, 0.5, 0.5 }, { 0.5, 0.5, -0.5, -0.5 }, { 0.5, -0.5, 0.5, -0.5 }, { 0.5, -0.5, -0.5, 0.5 }
});
resultH.NumberOfColumns.ShouldBe(expectedH.NumberOfColumns);
resultH.NumberOfRows.ShouldBe(expectedH.NumberOfRows);
for (Int32 rowIndex = 0; rowIndex < resultH.NumberOfRows; rowIndex++)
{
for (Int32 columnIndex = 0; columnIndex < resultH.NumberOfColumns; columnIndex++)
{
resultH[rowIndex, columnIndex].ShouldBe(expectedH[rowIndex, columnIndex], 0.01);
}
}
// second vector
transformation = new HouseholderTransformation(new Double[] { 1, -1 });
transformation.Compute();
resultH = transformation.H;
expectedH = new Matrix(new[, ] {
{ 1 / Math.Sqrt(2), -1 / Math.Sqrt(2) }, { -1 / Math.Sqrt(2), -1 / Math.Sqrt(2) }
});
resultH.NumberOfColumns.ShouldBe(expectedH.NumberOfColumns);
resultH.NumberOfRows.ShouldBe(expectedH.NumberOfRows);
for (Int32 rowIndex = 0; rowIndex < resultH.NumberOfRows; rowIndex++)
{
for (Int32 columnIndex = 0; columnIndex < resultH.NumberOfColumns; columnIndex++)
{
resultH[rowIndex, columnIndex].ShouldBe(expectedH[rowIndex, columnIndex], 0.01);
}
}
}
public void HouseholderTridiagonalizeTest()
{
Matrix matrix = MatrixFactory.CreateSquare(4, 1, -2, 2,
1, 2, 0, 1,
-2, 0, 3, -2,
2, 1, -2, -1);
Matrix expected = MatrixFactory.CreateSquare(4, -3, 0, 0,
-3, 10.0 / 3, -5.0 / 3, 0,
0, -5.0 / 3, -33.0 / 25, 68.0 / 75,
0, 0, 68.0 / 75, 149.0 / 75);
Matrix tridiag = HouseholderTransformation.Tridiagonalize(matrix);
for (Int32 j = 0; j < matrix.NumberOfRows; j++)
{
for (Int32 k = 0; k < matrix.NumberOfColumns; k++)
{
Assert.AreEqual(expected[j, k], tridiag[j, k], 0.01);
}
}
}
