private static void TestFactorsLU(LinearAlgebraProviderChoice providers)
{
TestSettings.RunMultiproviderTest(providers, delegate()
{
// invertible (rank = 10)
var A1 = Matrix.CreateFromArray(SquareInvertible10by10.Matrix);
var expectedL1 = Matrix.CreateFromArray(SquareInvertible10by10.FactorL);
var expectedU1 = Matrix.CreateFromArray(SquareInvertible10by10.FactorU);
LUFactorization factorization1 = A1.FactorLU();
Matrix computedL1 = factorization1.GetFactorL();
Matrix computedU1 = factorization1.GetFactorU();
comparer.AssertEqual(expectedL1, computedL1);
comparer.AssertEqual(expectedU1, computedU1);
// singular (rank = 8)
var A2 = Matrix.CreateFromArray(SquareSingular10by10.Matrix);
var expectedL2 = Matrix.CreateFromArray(SquareSingular10by10.FactorL);
var expectedU2 = Matrix.CreateFromArray(SquareSingular10by10.FactorU);
LUFactorization factorization2 = A2.FactorLU();
Matrix computedL2 = factorization2.GetFactorL();
Matrix computedU2 = factorization2.GetFactorU();
comparer.AssertEqual(expectedL2, computedL2);
comparer.AssertEqual(expectedU2, computedU2);
// singular (rank = 9)
var A3 = Matrix.CreateFromArray(SquareSingularSingleDeficiency10by10.Matrix);
var expectedL3 = Matrix.CreateFromArray(SquareSingularSingleDeficiency10by10.FactorL);
var expectedU3 = Matrix.CreateFromArray(SquareSingularSingleDeficiency10by10.FactorU);
LUFactorization factorization3 = A3.FactorLU();
Matrix computedL3 = factorization3.GetFactorL();
Matrix computedU3 = factorization3.GetFactorU();
comparer.AssertEqual(expectedL3, computedL3);
comparer.AssertEqual(expectedU3, computedU3);
});
}
private static void TestSystemSolution(LinearAlgebraProviderChoice providers)
{
TestSettings.RunMultiproviderTest(providers, delegate()
{
// invertible (rank = 10)
var A1 = Matrix.CreateFromArray(SquareInvertible10by10.Matrix);
var b1 = Vector.CreateFromArray(SquareInvertible10by10.Rhs);
var x1Expected = Vector.CreateFromArray(SquareInvertible10by10.Lhs);
LUFactorization factorization1 = A1.FactorLU();
Vector x1Computed = factorization1.SolveLinearSystem(b1);
comparer.AssertEqual(x1Expected, x1Computed);
// singular (rank = 8)
var A2 = Matrix.CreateFromArray(SquareSingular10by10.Matrix);
var b2 = Vector.CreateFromArray(SquareSingular10by10.Rhs);
LUFactorization factorization2 = A2.FactorLU();
Assert.Throws <SingularMatrixException>(() => factorization2.SolveLinearSystem(b2));
// singular (rank = 9)
var A3 = Matrix.CreateFromArray(SquareSingularSingleDeficiency10by10.Matrix);
var b3 = Vector.CreateFromArray(SquareSingularSingleDeficiency10by10.Rhs);
LUFactorization factorization3 = A3.FactorLU();
Assert.Throws <SingularMatrixException>(() => factorization3.SolveLinearSystem(b3));
});
}
private static void TestDeterminantSingular2(LinearAlgebraProviderChoice providers)
{
TestSettings.RunMultiproviderTest(providers, delegate()
{
// singular (rank = 9)
var A = Matrix.CreateFromArray(SquareSingularSingleDeficiency10by10.Matrix);
LUFactorization factorization = A.FactorLU();
double det = factorization.CalcDeterminant();
comparer.AssertEqual(SquareSingularSingleDeficiency10by10.Determinant, det);
});
}
private static void TestDeterminantInvertiblePositive(LinearAlgebraProviderChoice providers)
{
TestSettings.RunMultiproviderTest(providers, delegate()
{
// invertible (rank = 10) with positive det
var A = Matrix.CreateFromArray(SquareInvertible10by10.Matrix);
LUFactorization factorization = A.FactorLU();
double det = factorization.CalcDeterminant();
comparer.AssertEqual(SquareInvertible10by10.Determinant, det);
});
}
private static void TestDeterminantInvertibleNegative(LinearAlgebraProviderChoice providers)
{
TestSettings.RunMultiproviderTest(providers, delegate()
{
// Switch 2 rows to make the det negative
var A = Matrix.CreateFromArray(SquareInvertible10by10.Matrix);
Vector row0 = A.GetRow(0);
Vector row9 = A.GetRow(9);
A.SetSubrow(0, row9);
A.SetSubrow(9, row0);
LUFactorization factorization = A.FactorLU();
double det = factorization.CalcDeterminant();
comparer.AssertEqual(-SquareInvertible10by10.Determinant, det);
});
}
public void LUFactTest_1500x1500()
{
var tileSize = 40;
// prepare data
var data = MatrixHelpers.Tile(Matrix<double>.DeSerializeFromFile(@"C:\Users\eh\Documents\KU\Inversion-of-Block-Tridiagonal-Matrices\Dataset\m1500x1500-a.mat"), tileSize);
Matrix<Matrix<double>> expected = MatrixHelpers.Tile(Matrix<double>.DeSerializeFromFile(@"C:\Users\eh\Documents\KU\Inversion-of-Block-Tridiagonal-Matrices\Dataset\m1500x1500-a-LUFactorize-result.mat"), tileSize);
var opData1 = new OperationResult<double>(data);
OperationResult<double> actual;
var mProducer = new LUFactorization<double>(opData1, out actual);
var pm = new Manager(mProducer);
pm.Start();
pm.Join();
MatrixHelpers.IsDone(actual);
MatrixHelpers.Diff(expected, actual.Data);
MatrixHelpers.Compare(expected, actual.Data);
}
private static void TestInversion(LinearAlgebraProviderChoice providers)
{
TestSettings.RunMultiproviderTest(providers, delegate()
{
// invertible (rank = 10)
var A1 = Matrix.CreateFromArray(SquareInvertible10by10.Matrix);
var inverseA1Expected = Matrix.CreateFromArray(SquareInvertible10by10.Inverse);
LUFactorization factorization1 = A1.FactorLU();
Matrix inverseA1Computed = factorization1.Invert(true);
comparer.AssertEqual(inverseA1Expected, inverseA1Computed);
// singular (rank = 8)
var A2 = Matrix.CreateFromArray(SquareSingular10by10.Matrix);
LUFactorization factorization2 = A2.FactorLU();
Assert.Throws <SingularMatrixException>(() => factorization2.Invert(true));
// singular (rank = 9)
var A3 = Matrix.CreateFromArray(SquareSingularSingleDeficiency10by10.Matrix);
LUFactorization factorization3 = A3.FactorLU();
Assert.Throws <SingularMatrixException>(() => factorization3.Invert(true));
});
}
public static IEnumerable<Measurement> LUFactorize()
{
foreach (int threadCount in ThreadCountGenerator())
foreach (int tileSize in TileSizeGenerator)
yield return new OneBlockMatrixMeasurement
{
TileSize = tileSize,
ThreadCount = threadCount,
Execute = (a, tc) =>
{
var opRes1 = new OperationResult<double>(a);
OperationResult<double> actual;
var producer = new LUFactorization<double>(opRes1,
out actual);
Runner(producer, tc);
}
};
}