private static void TestDgemv()
{
Skip.IfNot(TestSettings.TestMkl, TestSettings.MessageWhenSkippingMKL);
CBLAS_LAYOUT layout = CBLAS_LAYOUT.CblasColMajor;
CBLAS_TRANSPOSE transA = CBLAS_TRANSPOSE.CblasNoTrans;
double alpha = 1.0;
double beta = 0.0;
int incX = 1;
int incY = 1;
int m = RectangularFullRank10by5.NumRows;
int n = RectangularFullRank10by5.NumCols;
int ldA = m;
double[] A = Conversions.Array2DToFullColMajor(RectangularFullRank10by5.Matrix);
double[] X = RectangularFullRank10by5.Lhs5;
double[] Y = new double[m];
LapackePInvokes.Dgemv(layout, transA, m, n, alpha, A, ldA, X, incX, beta, Y, incY);
comparer.AssertEqual(RectangularFullRank10by5.Rhs10, Y);
}
public static int Dtrsv(CBLAS_UPLO Uplo, CBLAS_TRANSPOSE TransA, CBLAS_DIAG Diag, PZMath_matrix A, PZMath_vector x)
{
int M = A.RowCount;
int N = A.ColumnCount;
if (M != N)
{
PZMath_errno.ERROR("PZMath_blas::Dtrsv(), matrix must be square", PZMath_errno.PZMath_ENOTSQR);
}
else if (N != x.Size)
{
PZMath_errno.ERROR("PZMath_blas::Dtrsv(), invalid length", PZMath_errno.PZMath_EBADLEN);
}
bool nonunit = (Diag == CBLAS_DIAG.CblasNonUnit);
int ix, jx;
int i, j;
CBLAS_TRANSPOSE Trans = (TransA != CBLAS_TRANSPOSE.CblasConjTrans) ? TransA : CBLAS_TRANSPOSE.CblasTrans;
CBLAS_ORDER order = CBLAS_ORDER.CblasRowMajor;
if (N == 0)
return PZMath_errno.PZMath_SUCCESS;
/* form x := inv( A )*x */
if ((order == CBLAS_ORDER.CblasRowMajor && Trans == CBLAS_TRANSPOSE.CblasNoTrans
&& Uplo == CBLAS_UPLO.CblasUpper)
|| (order == CBLAS_ORDER.CblasColMajor && Trans == CBLAS_TRANSPOSE.CblasTrans
&& Uplo == CBLAS_UPLO.CblasLower))
{
/* backsubstitution */
ix = N - 1;
if (nonunit)
x[ix] = x[ix] / A[N - 1, N - 1];
ix--;
for (i = N - 1; i > 0 && (i-- > 0); )
{
double tmp = x[ix];
jx = ix + 1;
for (j = i + 1; j < N; j++)
{
double Aij = A[i, j];
tmp -= Aij * x[jx];
jx++;
}
if (nonunit)
{
x[ix] = tmp / A[i, i];
}
else
{
x[ix] = tmp;
}
ix--;
}
}
else if ((order == CBLAS_ORDER.CblasRowMajor && Trans == CBLAS_TRANSPOSE.CblasNoTrans
&& Uplo == CBLAS_UPLO.CblasLower)
|| (order == CBLAS_ORDER.CblasColMajor && Trans == CBLAS_TRANSPOSE.CblasTrans
&& Uplo == CBLAS_UPLO.CblasUpper))
{
/* forward substitution */
ix = 0;
if (nonunit)
{
x[ix] = x[ix] / A[0, 0];
}
ix++;
for (i = 1; i < N; i++)
{
double tmp = x[ix];
jx = 0;
for (j = 0; j < i; j++)
{
double Aij = A[i, j];
tmp -= Aij * x[jx];
jx++;
}
if (nonunit)
{
x[ix] = tmp / A[i, i];
}
else
{
x[ix] = tmp;
}
ix++;
}
}
else if ((order == CBLAS_ORDER.CblasRowMajor && Trans == CBLAS_TRANSPOSE.CblasTrans
&& Uplo == CBLAS_UPLO.CblasUpper)
|| (order == CBLAS_ORDER.CblasColMajor && Trans == CBLAS_TRANSPOSE.CblasNoTrans
&& Uplo == CBLAS_UPLO.CblasLower))
{
/* form x := inv( A' )*x */
/* forward substitution */
ix = 0;
if (nonunit)
{
x[ix] = x[ix] / A[0, 0];
}
ix++;
for (i = 1; i < N; i++)
{
double tmp = x[ix];
jx = 0;
for (j = 0; j < i; j++)
{
double Aji = A[j, i];
tmp -= Aji * x[jx];
jx++;
}
if (nonunit)
{
x[ix] = tmp / A[i, i];
}
else
{
x[ix] = tmp;
}
ix++;
}
}
else if ((order == CBLAS_ORDER.CblasRowMajor && Trans == CBLAS_TRANSPOSE.CblasTrans
&& Uplo == CBLAS_UPLO.CblasLower)
|| (order == CBLAS_ORDER.CblasColMajor && Trans == CBLAS_TRANSPOSE.CblasNoTrans
&& Uplo == CBLAS_UPLO.CblasUpper))
{
/* backsubstitution */
ix = N - 1;
if (nonunit)
{
x[ix] = x[ix] / A[(N - 1), (N - 1)];
}
ix--;
for (i = N - 1; i > 0 && (i-- > 0); )
{
double tmp = x[ix];
jx = ix + 1;
for (j = i + 1; j < N; j++)
{
double Aji = A[j, i];
tmp -= Aji * x[jx];
jx++;
}
if (nonunit)
{
x[ix] = tmp / A[i, i];
}
else
{
x[ix] = tmp;
}
ix--;
}
}
else
{
PZMath_errno.ERROR("PZMath_blas::Dtrsv(), unrecognized operation");
}
return PZMath_errno.PZMath_SUCCESS;
}
public static extern void Dgemv(CBLAS_LAYOUT layout, CBLAS_TRANSPOSE transA, int m, int n,
double alpha, double[] A, int ldA, double[] X, int incX, double beta, double[] Y, int incY); // CBLAS, rather than LAPACKE
public static extern void dMatrixMatrixProduct(CBLAS_TRANSPOSE transa, CBLAS_TRANSPOSE transb, int m, int n, int k, double[] a, double[] b, double alpha, double beta, [In, Out] double[] c);
public static extern void dMatrixVectorProduct(CBLAS_TRANSPOSE trans, int m, int n, double[] a, double alpha, double[] x, double beta, [In, Out] double[] y);
/// <summary>
/// generate a 1D matrix from a column vector
/// </summary>
/// <param name="v"></param>
/// <param name="transV"></param>
public PZMath_matrix(PZMath_vector v, CBLAS_TRANSPOSE transV)
{
if (transV == CBLAS_TRANSPOSE.CblasTrans)
// column vector
{
row = v.Size;
col = 1;
}
else
// row vector
{
row = 1;
col = v.Size;
}
offset = 0;
stride = 1;
orgrow = row;
orgcol = col;
length = orgrow * orgcol;
data = new double[length];
for (int i = 0; i < v.Size; i++)
data[i] = v[i];
}
static extern unsafe void cblas_sgemm(CBLAS_ORDER __Order, CBLAS_TRANSPOSE __TransA, CBLAS_TRANSPOSE __TransB,
int __M, int __N, int __K, float __alpha, float *__A, int __lda, float *__B, int __ldb,
float __beta, float *__C, int __ldc);
private static extern void cblas_dgemm(CBLAS_LAYOUT Layout, CBLAS_TRANSPOSE TransA, CBLAS_TRANSPOSE TransB, int m, int n, int k, double alpha, double* A,
int lda, double* B, int ldb, double beta, double* C, int ldc);
private static extern void cblas_sgemm(CBLAS_LAYOUT Layout, CBLAS_TRANSPOSE TransA,CBLAS_TRANSPOSE TransB, int m, int n,int k, float alpha, float* A,
int lda, float* B, int ldb, float beta, float* C, int ldc);
