/// <summary>
/// Pre-divides matrix B by upper triangular matrix A
/// </summary>
/// <param name="B"></param>
/// <param name="A"></param>
public static void PredivideBy(Matrix B, UpperTriangularMatrix A)
{
Assert.IsTrue(A.Rows == A.Cols);
Assert.IsTrue(A.Rows == B.Rows);
Assert.IsTrue(!object.ReferenceEquals(B, A));
// Lapack is column-major, so we tell it that A is lower triangular and switch sides:
// inv(A)*B = (B'*inv(A'))'
char side = 'R', uplo = 'L', trans = 'N', diag = 'N';
double alpha = 1;
ptrdiff_t m = B.Cols, n = B.Rows;
fixed(double *sA = A.SourceArray, sB = B.SourceArray)
{
double *pA = sA, pB = sB;
dtrsm(&side, &uplo, &trans, &diag, &m, &n, &alpha, pA, &n, pB, &m);
}
}
/// <summary>
/// Set this lower triangular matrix to the transpose of an upper triangular matrix
/// </summary>
/// <param name="U">The matrix to transpose</param>
/// <returns></returns>
public LowerTriangularMatrix SetToTranspose(UpperTriangularMatrix U)
{
if (rows != U.Cols || cols != U.Rows)
{
throw new ArgumentException("Output matrix is not compatible with the transpose", "that");
}
U.CheckUpperTriangular();
// upper triangle of this is assumed to be zero
for (int i = 0; i < rows; ++i)
{
for (int j = 0; j <= i; ++j)
{
this[i, j] = U[j, i];
}
}
CheckLowerTriangular();
return(this);
}
/// <remarks>U is no longer a valid upper triangular matrix.</remarks>
public static LowerTriangularMatrix TransposeInPlace(UpperTriangularMatrix U)
{
U.CheckUpperTriangular();
LowerTriangularMatrix L = new LowerTriangularMatrix(U.Cols, U.Rows,
U.SourceArray, U.Start);
Assert.IsTrue(L.Rows == L.Cols);
for (int i = 0; i < L.Rows; ++i)
{
for (int j = 0; j < i; ++j)
{
L[i, j] = L[j, i];
L[j, i] = 0;
}
}
L.CheckLowerTriangular();
return(L);
}
/// <summary>
/// Transposes a given lower triangular matrix in place.
/// </summary>
/// <param name="L">Matrix to transpose. Contents are corrupted on exit.</param>
/// <returns>An upper triangular wrapper of L's source array.</returns>
/// <remarks>L is no longer a valid lower triangular matrix.</remarks>
public static UpperTriangularMatrix TransposeInPlace(LowerTriangularMatrix L)
{
L.CheckLowerTriangular();
UpperTriangularMatrix U = new UpperTriangularMatrix(L.Cols, L.Rows,
L.SourceArray);
Assert.IsTrue(U.Rows == U.Cols);
for (int i = 0; i < U.Rows; ++i)
{
for (int j = i + 1; j < U.Cols; ++j)
{
U[i, j] = U[j, i];
U[j, i] = 0;
}
}
U.CheckUpperTriangular();
return(U);
}