private static void TestEquality()
{
// Equals(SkylineMatrix)
var full1 = Matrix.CreateFromArray(SparsePosDef10by10.Matrix);
var skyline1 = SkylineMatrix.CreateFromArrays(SparsePosDef10by10.Order,
SparsePosDef10by10.SkylineValues, SparsePosDef10by10.SkylineDiagOffsets, true, true);
Assert.True(full1.Equals(skyline1));
// Equals(CsrMatrix)
var full2 = Matrix.CreateFromArray(SparseRectangular10by5.Matrix);
var csr2 = CsrMatrix.CreateFromArrays(SparseRectangular10by5.NumRows, SparseRectangular10by5.NumCols,
SparseRectangular10by5.CsrValues, SparseRectangular10by5.CsrColIndices, SparseRectangular10by5.CsrRowOffsets,
true);
Assert.True(full2.Equals(csr2));
// Equals(CscMatrix)
var full3 = Matrix.CreateFromArray(SparseRectangular10by5.Matrix);
var csc3 = CscMatrix.CreateFromArrays(SparseRectangular10by5.NumRows, SparseRectangular10by5.NumCols,
SparseRectangular10by5.CscValues, SparseRectangular10by5.CscRowIndices, SparseRectangular10by5.CscColOffsets,
true);
Assert.True(full3.Equals(csc3));
}
private static void TestMatrixVectorMultiplicationIntoResult(LinearAlgebraProviderChoice providers)
{
TestSettings.RunMultiproviderTest(providers, delegate()
{
// The result vectors will first be set to some non zero values to make sure that the result overwrites
// them instead of being added to them.
// MultiplyIntoResult() - untransposed
var A = CscMatrix.CreateFromArrays(SparseRectangular10by5.NumRows, SparseRectangular10by5.NumCols,
SparseRectangular10by5.CscValues, SparseRectangular10by5.CscRowIndices, SparseRectangular10by5.CscColOffsets,
true);
var x5 = Vector.CreateFromArray(SparseRectangular10by5.Lhs5);
var b10Expected = Vector.CreateFromArray(SparseRectangular10by5.Rhs10);
Vector b10Computed = Vector.CreateWithValue(SparseRectangular10by5.NumRows, 1.0);
//Vector bComputed = Vector.CreateZero(SparseRectangular10by5.NumRows);
A.MultiplyIntoResult(x5, b10Computed, false);
comparer.AssertEqual(b10Expected, b10Computed);
// MultiplyIntoResult() - transposed
var x10 = Vector.CreateFromArray(SparseRectangular10by5.Lhs10);
var b5Expected = Vector.CreateFromArray(SparseRectangular10by5.Rhs5);
Vector b5Computed = Vector.CreateWithValue(SparseRectangular10by5.NumCols, 1.0);
A.MultiplyIntoResult(x10, b5Computed, true);
comparer.AssertEqual(b5Expected, b5Computed);
});
}
private static void TestSparseRectangularCSC()
{
var matrix = CscMatrix.CreateFromArrays(SparseRectangular10by5.NumRows, SparseRectangular10by5.NumCols,
SparseRectangular10by5.CscValues, SparseRectangular10by5.CscRowIndices, SparseRectangular10by5.CscColOffsets,
true);
TestWriteOperation(matrix, SparseRectangular10by5.FullFormatPath);
}
private static void TestMatrixCopy()
{
var full = Matrix.CreateFromArray(SparseRectangular10by5.Matrix);
var csc = CscMatrix.CreateFromArrays(SparseRectangular10by5.NumRows, SparseRectangular10by5.NumCols,
SparseRectangular10by5.CscValues, SparseRectangular10by5.CscRowIndices, SparseRectangular10by5.CscColOffsets,
true);
comparer.AssertEqual(full, csc.CopyToFullMatrix());
}
private static void TestEquality()
{
var full = Matrix.CreateFromArray(SparseRectangular10by5.Matrix);
var csc = CscMatrix.CreateFromArrays(SparseRectangular10by5.NumRows, SparseRectangular10by5.NumCols,
SparseRectangular10by5.CscValues, SparseRectangular10by5.CscRowIndices, SparseRectangular10by5.CscColOffsets,
true);
Assert.True(csc.Equals(full));
}
private static void TestClear()
{
var zero = Matrix.CreateZero(SparseRectangular10by5.NumRows, SparseRectangular10by5.NumCols);
var csc = CscMatrix.CreateFromArrays(SparseRectangular10by5.NumRows, SparseRectangular10by5.NumCols,
SparseRectangular10by5.CscValues, SparseRectangular10by5.CscRowIndices, SparseRectangular10by5.CscColOffsets,
true);
csc.Clear();
comparer.AssertEqual(zero, csc);
}
private static void TestSparseRectangularCSC()
{
// The reference file has been written by iterating the entries in CSC order.
// Therefore it cannot be used for checking with a CSR matrix.
var matrix = CscMatrix.CreateFromArrays(SparseRectangular10by5.NumRows, SparseRectangular10by5.NumCols,
SparseRectangular10by5.CscValues, SparseRectangular10by5.CscRowIndices, SparseRectangular10by5.CscColOffsets,
true);
TestWriteOperation(matrix, SparseRectangular10by5.CoordinateFormatPath);
}
private static void TestGetRow()
{
var matrix = CscMatrix.CreateFromArrays(SparseRectangular10by5.NumRows, SparseRectangular10by5.NumCols,
SparseRectangular10by5.CscValues, SparseRectangular10by5.CscRowIndices, SparseRectangular10by5.CscColOffsets,
true);
for (int i = 0; i < SparseRectangular10by5.NumRows; ++i)
{
Vector rowExpected = DenseStrategies.GetRow(matrix, i);
Vector rowComputed = matrix.GetRow(i);
comparer.AssertEqual(rowExpected, rowComputed);
}
}
private static void TestGetColumn()
{
var matrix = CscMatrix.CreateFromArrays(SparseRectangular10by5.NumRows, SparseRectangular10by5.NumCols,
SparseRectangular10by5.CscValues, SparseRectangular10by5.CscRowIndices, SparseRectangular10by5.CscColOffsets,
true);
for (int j = 0; j < SparseRectangular10by5.NumCols; ++j)
{
Vector colExpected = DenseStrategies.GetColumn(matrix, j);
Vector colComputed = matrix.GetColumn(j);
comparer.AssertEqual(colExpected, colComputed);
}
}
internal static CscMatrix GetSubmatrixCsc(double[] skyValues, int[] skyDiagOffsets, int[] rowsToKeep, int[] colsToKeep)
{
if ((rowsToKeep.Length == 0) || (colsToKeep.Length == 0))
{
return(CscMatrix.CreateFromArrays(rowsToKeep.Length, colsToKeep.Length, new double[0], new int[0],
new int[1] {
0
}, false));
}
var submatrix = DokColMajor.CreateEmpty(rowsToKeep.Length, colsToKeep.Length);
for (int subCol = 0; subCol < colsToKeep.Length; ++subCol)
{
int col = colsToKeep[subCol];
int diagOffset = skyDiagOffsets[col];
int colHeight = skyDiagOffsets[col + 1] - diagOffset - 1; // excluding diagonal
for (int subRow = 0; subRow < rowsToKeep.Length; ++subRow)
{
int row = rowsToKeep[subRow];
if (row <= col)
{
int entryHeight = col - row; // excluding diagonal
if (entryHeight <= colHeight) // inside stored non zero pattern
{
double val = skyValues[diagOffset + entryHeight];
if (val != 0.0)
{
submatrix[subRow, subCol] = val; // Skyline format stores many unnecessary zeros.
}
}
}
else // Transpose row <-> col. The cached column height and offset must be recalculated.
{
int transposedDiagOffset = skyDiagOffsets[row];
int transposedColHeight = skyDiagOffsets[row + 1] - transposedDiagOffset - 1; // excluding diagonal
int entryHeight = row - col; // excluding diagonal
if (entryHeight <= transposedColHeight) // inside stored non zero pattern
{
double val = skyValues[transposedDiagOffset + entryHeight];
if (val != 0.0)
{
submatrix[subRow, subCol] = val; // Skyline format stores many unnecessary zeros.
}
}
}
}
}
return(submatrix.BuildCscMatrix(true));
}
private static void TestSymmSystemSolution()
{
double pivotTolerance = 0.5;
int order = SparseSymm5by5.Order;
var csc = CscMatrix.CreateFromArrays(order, order, SparseSymm5by5.CscValues, SparseSymm5by5.CscRowIndices,
SparseSymm5by5.CscColOffsets, true);
var xExpected = Vector.CreateWithValue(order, 1.0);
var b = csc.Multiply(xExpected);
var factor = LUCSparseNet.Factorize(order, csc.NumNonZeros, csc.RawValues, csc.RawRowIndices, csc.RawColOffsets,
pivotTolerance);
Vector xComputed = factor.SolveLinearSystem(b);
comparer.AssertEqual(xExpected, xComputed);
}
[Fact] //TODO: If the explicit transposition becomes abstracted behind a provider, then this should also be a Theory
private static void TestTransposition()
{
var matrix = CscMatrix.CreateFromArrays(SparseRectangular10by5.NumRows, SparseRectangular10by5.NumCols,
SparseRectangular10by5.CscValues, SparseRectangular10by5.CscRowIndices, SparseRectangular10by5.CscColOffsets,
true);
var transposeExpected = Matrix.CreateFromArray(MatrixOperations.Transpose(SparseRectangular10by5.Matrix));
// TransposeToCSC()
CscMatrix transposeCsc = matrix.TransposeToCSC();
comparer.AssertEqual(transposeExpected, transposeCsc);
// TransposeToCSR()
CsrMatrix transposeCsr = matrix.TransposeToCSR(true);
comparer.AssertEqual(transposeExpected, transposeCsr);
}
private static void TestMatrixMatrixMultiplication(LinearAlgebraProviderChoice providers)
{
TestSettings.RunMultiproviderTest(providers, delegate()
{
var matrix5x5 = Matrix.CreateFromArray(SquareInvertible10by10.Matrix).GetSubmatrix(0, 5, 0, 5); //TODO: add a 5x5 matrix and its products
var matrix10x10 = Matrix.CreateFromArray(SquareInvertible10by10.Matrix);
var ATimesMatrix5x5 = Matrix.CreateFromArray(
MatrixOperations.MatrixTimesMatrix(SparseRectangular10by5.Matrix, matrix5x5.CopyToArray2D()));
var ATimesTransposeMatrix5x5 = Matrix.CreateFromArray(
MatrixOperations.MatrixTimesMatrix(SparseRectangular10by5.Matrix, matrix5x5.Transpose().CopyToArray2D()));
var transposeATimesMatrix10x10 = Matrix.CreateFromArray(MatrixOperations.MatrixTimesMatrix(
MatrixOperations.Transpose(SparseRectangular10by5.Matrix), matrix10x10.CopyToArray2D()));
var transposeATimesTransposeMatrix10x10 = Matrix.CreateFromArray(MatrixOperations.MatrixTimesMatrix(
MatrixOperations.Transpose(SparseRectangular10by5.Matrix), matrix10x10.Transpose().CopyToArray2D()));
var matrix10x10TimesA = Matrix.CreateFromArray(
MatrixOperations.MatrixTimesMatrix(matrix10x10.CopyToArray2D(), SparseRectangular10by5.Matrix));
var transposeMatrix10x10TimesA = Matrix.CreateFromArray(
MatrixOperations.MatrixTimesMatrix(matrix10x10.Transpose().CopyToArray2D(), SparseRectangular10by5.Matrix));
var matrix5x5TimesTransposeA = Matrix.CreateFromArray(
MatrixOperations.MatrixTimesMatrix(matrix5x5.CopyToArray2D(),
MatrixOperations.Transpose(SparseRectangular10by5.Matrix)));
var transposeMatrix5x5TimesTransposeA = Matrix.CreateFromArray(
MatrixOperations.MatrixTimesMatrix(matrix5x5.Transpose().CopyToArray2D(),
MatrixOperations.Transpose(SparseRectangular10by5.Matrix)));
var A = CscMatrix.CreateFromArrays(SparseRectangular10by5.NumRows, SparseRectangular10by5.NumCols,
SparseRectangular10by5.CscValues, SparseRectangular10by5.CscRowIndices, SparseRectangular10by5.CscColOffsets,
true);
// MultiplyRight()
comparer.AssertEqual(ATimesMatrix5x5, A.MultiplyRight(matrix5x5, false, false));
comparer.AssertEqual(ATimesTransposeMatrix5x5, A.MultiplyRight(matrix5x5, false, true));
comparer.AssertEqual(transposeATimesMatrix10x10, A.MultiplyRight(matrix10x10, true, false));
comparer.AssertEqual(transposeATimesTransposeMatrix10x10, A.MultiplyRight(matrix10x10, true, true));
// MultiplyLeft()
comparer.AssertEqual(matrix10x10TimesA, A.MultiplyLeft(matrix10x10, false, false));
comparer.AssertEqual(transposeMatrix10x10TimesA, A.MultiplyLeft(matrix10x10, false, true));
comparer.AssertEqual(matrix5x5TimesTransposeA, A.MultiplyLeft(matrix5x5, true, false));
comparer.AssertEqual(transposeMatrix5x5TimesTransposeA, A.MultiplyLeft(matrix5x5, true, true));
});
}
private static void TestMatrixVectorMultiplication(LinearAlgebraProviderChoice providers)
{
TestSettings.RunMultiproviderTest(providers, delegate()
{
// MultiplyRight() - untransposed
var A = CscMatrix.CreateFromArrays(SparseRectangular10by5.NumRows, SparseRectangular10by5.NumCols,
SparseRectangular10by5.CscValues, SparseRectangular10by5.CscRowIndices, SparseRectangular10by5.CscColOffsets,
true);
var x5 = Vector.CreateFromArray(SparseRectangular10by5.Lhs5);
var b10Expected = Vector.CreateFromArray(SparseRectangular10by5.Rhs10);
Vector b10Computed = A.Multiply(x5, false);
comparer.AssertEqual(b10Expected, b10Computed);
// MultiplyRight() - transposed
var x10 = Vector.CreateFromArray(SparseRectangular10by5.Lhs10);
var b5Expected = Vector.CreateFromArray(SparseRectangular10by5.Rhs5);
Vector b5Computed = A.Multiply(x10, true);
comparer.AssertEqual(b5Expected, b5Computed);
});
}