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ng_lapack.hpp
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#ifndef FILE_NG_LAPACK
#define FILE_NG_LAPACK
// #include <mkl_cblas.h>
/****************************************************************************/
/* File: ng_lapack.hpp */
/* Author: Joachim Schoeberl */
/* Date: 21. Nov. 2004 */
/****************************************************************************/
namespace ngbla
{
class T_Lapack { };
static constexpr T_Lapack Lapack;
template <typename TA>
class LapackExpr : public Expr<LapackExpr<TA> >
{
const TA & a;
public:
LapackExpr (const TA & aa) : a(aa) { ; }
const TA & A() const { return a; }
size_t Height() const { return a.Height(); }
size_t Width() const { return a.Width(); }
};
template <typename TA>
INLINE LapackExpr<TA> operator| (const Expr<TA> & a, T_Lapack /* tl */)
{
return LapackExpr<TA> (a.Spec());
}
template <typename TOP, typename T, typename TB>
class assign_trait<TOP, T, LapackExpr<TB>, int>
{
public:
static INLINE T & Assign (MatExpr<T> & self, const Expr<LapackExpr<TB>> & v)
{
#ifdef LAPACK
if constexpr (std::is_same_v<TOP,typename MatExpr<T>::As>)
LapackMultAdd (v.Spec().A().A(), v.Spec().A().B(), 1.0, self.Spec(), 0.0);
if constexpr (std::is_same_v<TOP,typename MatExpr<T>::AsAdd>)
LapackMultAdd (v.Spec().A().A(), v.Spec().A().B(), 1.0, self.Spec(), 1.0);
if constexpr (std::is_same_v<TOP,typename MatExpr<T>::AsSub>)
LapackMultAdd (v.Spec().A().A(), v.Spec().A().B(), -1.0, self.Spec(), 1.0);
return self.Spec();
#else // LAPACK
throw Exception("No Lapack");
#endif // LAPACK
}
};
#ifdef LAPACK
extern "C" {
#ifdef MKL_ILP64
typedef long int integer;
#else
typedef int integer;
#endif
// typedef char logical;
typedef integer logical;
typedef float real;
typedef double doublereal;
typedef Complex doublecomplex;
typedef complex<float> singlecomplex;
// Windows SDK defines VOID in the file WinNT.h
#ifndef VOID
typedef void VOID;
#endif
typedef int ftnlen;
typedef int L_fp; // ?
#include "clapack.h"
}
// Interface to lapack functions
NGS_DLL_HEADER int sgemm(char *transa, char *transb, integer *m, integer *
n, integer *k, real *alpha, real *a, integer *lda,
real *b, integer *ldb, real *beta, real *c__,
integer *ldc);
NGS_DLL_HEADER int dgemm(char *transa, char *transb, integer *m, integer *
n, integer *k, doublereal *alpha, doublereal *a, integer *lda,
doublereal *b, integer *ldb, doublereal *beta, doublereal *c__,
integer *ldc);
NGS_DLL_HEADER int sgemm(char *transa, char *transb, integer *m, integer *
n, integer *k, real *alpha, real *a, integer *lda,
real *b, integer *ldb, real *beta, real *c__,
integer *ldc);
NGS_DLL_HEADER int zgemm(char *transa, char *transb, integer *m, integer *
n, integer *k, doublecomplex *alpha, doublecomplex *a, integer *lda,
doublecomplex *b, integer *ldb, doublecomplex *beta, doublecomplex *
c__, integer *ldc);
NGS_DLL_HEADER int dger(integer *m, integer *n, doublereal *alpha,
doublereal *x, integer *incx, doublereal *y, integer *incy,
doublereal *a, integer *lda);
NGS_DLL_HEADER int dgetrf(integer* n, integer* m, double* a, integer* lda, integer* ipiv, integer* info);
NGS_DLL_HEADER int dgetri(integer* n, double* a, integer* lda, integer* ipiv,
double* hwork, integer* lwork, integer* info);
NGS_DLL_HEADER int dgetrs(char *trans, integer *n, integer *nrhs,
doublereal *a, integer *lda, integer *ipiv, doublereal *b, integer *
ldb, integer *info);
inline int gemm(char *transa, char *transb, integer *m, integer *
n, integer *k, real *alpha, real *a, integer *lda,
real *b, integer *ldb, real *beta, real *c__,
integer *ldc)
{
return sgemm (transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c__, ldc);
}
inline int gemm(char *transa, char *transb, integer *m, integer *
n, integer *k, doublereal *alpha, doublereal *a, integer *lda,
doublereal *b, integer *ldb, doublereal *beta, doublereal *c__,
integer *ldc)
{
return dgemm (transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c__, ldc);
}
inline int gemm(char *transa, char *transb, integer *m, integer *
n, integer *k, doublecomplex *alpha, doublecomplex *a, integer *lda,
doublecomplex *b, integer *ldb, doublecomplex *beta, doublecomplex *
c__, integer *ldc)
{
return zgemm (transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c__, ldc);
}
// BLAS 1
inline double LapackDot (FlatVector<double> x, FlatVector<double> y)
{
integer n = x.Size();
integer incx = 1;
integer incy = 1;
return ddot_ (&n, &x(0), &incx, &y(0), &incy);
}
// BLAS 2
/*
extern "C"
void dgemv_ (char & trans, int & m, int & n, double & alpha, double & a, int & lda, double & x, int & incx,
double & beta, double & y, int & incy);
*/
inline void LapackMultAx (ngbla::FlatMatrix<double> a,
ngbla::FlatVector<double> x,
ngbla::FlatVector<double> y)
{
char trans = 'T';
integer m = a.Width();
integer n = a.Height();
double alpha = 1;
integer lda = max(size_t(1), a.Width());
integer incx = 1;
double beta = 0;
integer incy = 1;
dgemv_ (&trans, &m, &n, &alpha, &a(0,0), &lda, &x(0), &incx, &beta, &y(0), &incy);
}
inline void LapackMultAx (ngbla::FlatMatrix<Complex> a,
ngbla::FlatVector<Complex> x,
ngbla::FlatVector<Complex> y)
{
char trans = 'T';
integer m = a.Width();
integer n = a.Height();
Complex alpha(1,0);
integer lda = max(size_t(1), a.Width());
integer incx = 1;
Complex beta(0, 0);
integer incy = 1;
zgemv_ (&trans, &m, &n, &alpha, &a(0,0), &lda, &x(0), &incx, &beta, &y(0), &incy);
}
inline void LapackMultAtx (ngbla::FlatMatrix<double> a,
ngbla::FlatVector<double> x,
ngbla::FlatVector<double> y)
{
char trans = 'N';
integer m = a.Width();
integer n = a.Height();
double alpha = 1;
integer lda = max(size_t(1), a.Width());
integer incx = 1;
double beta = 0;
integer incy = 1;
dgemv_ (&trans, &m, &n, &alpha, &a(0,0), &lda, &x(0), &incx, &beta, &y(0), &incy);
}
inline void LapackAddxyt (ngbla::FlatMatrix<double> a,
double fac,
ngbla::FlatVector<double> x,
ngbla::FlatVector<double> y)
{
integer m = a.Width();
integer n = a.Height();
double alpha = fac;
integer lda = max(size_t(1), a.Width());
integer incx = 1;
integer incy = 1;
dger (&m, &n, &alpha, &y(0), &incx, &x(0), &incy, &a(0,0), &lda);
}
template <typename SCAL>
inline void BASE_LapackMult (SliceMatrix<SCAL> a, bool transa,
SliceMatrix<SCAL> b, bool transb,
SliceMatrix<SCAL> c)
{
char transa_ = transa ? 'T' : 'N';
char transb_ = transb ? 'T' : 'N';
integer n = c.Width();
integer m = c.Height();
if (n == 0 || m == 0) return;
integer k = transa ? a.Height() : a.Width();
SCAL alpha = 1.0;
SCAL beta = 0;
integer lda = max(size_t(1), a.Dist());
integer ldb = max(size_t(1), b.Dist());
integer ldc = max(size_t(1), c.Dist());
gemm (&transb_, &transa_, &n, &m, &k, &alpha,
&b(0,0), &ldb, &a(0,0), &lda, &beta, &c(0,0), &ldc);
}
template <typename SCAL>
inline void BASE_LapackMultAdd (SliceMatrix<SCAL> a, bool transa,
SliceMatrix<SCAL> b, bool transb,
SCAL aalpha,
SliceMatrix<SCAL> c,
SCAL abeta)
{
char transa_ = transa ? 'T' : 'N';
char transb_ = transb ? 'T' : 'N';
integer n = c.Width();
integer m = c.Height();
if (n == 0 || m == 0) return;
integer k = transa ? a.Height() : a.Width();
SCAL alpha = aalpha;
SCAL beta = abeta;
integer lda = max(size_t(1), a.Dist());
integer ldb = max(size_t(1), b.Dist());
integer ldc = max(size_t(1), c.Dist());
gemm (&transb_, &transa_, &n, &m, &k, &alpha,
&b(0,0), &ldb, &a(0,0), &lda, &beta, &c(0,0), &ldc);
}
template <typename TA, typename TB, typename TC>
inline void LapackMult (const TA & a,
const TB & b,
const TC & c)
{ BASE_LapackMult<typename TC::TSCAL> (a, false, b, false, c); }
template <typename TA, typename TB, typename TC>
inline void LapackMult (const TA & a,
TransExpr<TB> b,
const TC & c)
{ BASE_LapackMult<typename TC::TSCAL> (a, false, b.A(), true, c); }
template <typename TA, typename TB, typename TC>
inline void LapackMult (TransExpr<TA> a,
const TB & b,
const TC & c)
{ BASE_LapackMult<typename TC::TSCAL> (a.A(), true, b, false, c); }
template <typename TA, typename TB, typename TC>
inline void LapackMult (TransExpr<TA> a,
TransExpr<TB> b,
const TC & c)
{ BASE_LapackMult<typename TC::TSCAL> (a.A(), true, b.A(), true, c); }
/*
inline void LapackMult (SliceMatrix<double> a,
SliceMatrix<double> b,
SliceMatrix<double> c)
{ BASE_LapackMult<double> (a, false, b, false, c); }
template <typename TA>
inline void LapackMult (SliceMatrix<double> a,
TransExpr<TA> b,
SliceMatrix<double> c)
{ BASE_LapackMult<double> (a, false, b.A(), true, c); }
template <typename TA>
inline void LapackMult (TransExpr<TA> a,
SliceMatrix<double> b,
SliceMatrix<double> c)
{ BASE_LapackMult<double> (a.A(), true, b, false, c); }
template <typename TA, typename TB>
inline void LapackMult (TransExpr<TA> a,
TransExpr<TB> b,
SliceMatrix<double> c)
{ BASE_LapackMult<double> (a.A(), true, b.A(), true, c); }
*/
/*
inline void LapackMult (SliceMatrix<Complex> a,
SliceMatrix<Complex> b,
SliceMatrix<Complex> c)
{ BASE_LapackMult<Complex> (a, false, b, false, c); }
template <typename TA>
inline void LapackMult (SliceMatrix<Complex> a,
TransExpr<TA> b,
SliceMatrix<Complex> c)
{ BASE_LapackMult<Complex> (a, false, b.A(), true, c); }
template <typename TA>
inline void LapackMult (TransExpr<TA> a,
SliceMatrix<Complex> b,
SliceMatrix<Complex> c)
{ BASE_LapackMult<Complex> (a.A(), true, b, false, c); }
template <typename TA, typename TB>
inline void LapackMult (TransExpr<TA> a,
TransExpr<TB> b,
SliceMatrix<Complex> c)
{ BASE_LapackMult<Complex> (a.A(), true, b.A(), true, c); }
*/
inline void LapackMultAdd (SliceMatrix<float> a,
SliceMatrix<float> b,
float alpha,
SliceMatrix<float> c,
float beta)
{ BASE_LapackMultAdd<float> (a, false, b, false, alpha, c, beta); }
inline void LapackMultAdd (SliceMatrix<double> a,
SliceMatrix<double> b,
double alpha,
SliceMatrix<double> c,
double beta)
{ BASE_LapackMultAdd<double> (a, false, b, false, alpha, c, beta); }
inline void LapackMultAdd (SliceMatrix<double,ColMajor> a,
SliceMatrix<double> b,
double alpha,
SliceMatrix<double> c,
double beta)
{ BASE_LapackMultAdd<double> (Trans(a), true, b, false, alpha, c, beta); }
inline void LapackMultAdd (SliceMatrix<double> a,
SliceMatrix<double,ColMajor> b,
double alpha,
SliceMatrix<double> c,
double beta)
{ BASE_LapackMultAdd<double> (a, false, Trans(b), true, alpha, c, beta); }
inline void LapackMultAdd (SliceMatrix<double,ColMajor> a,
SliceMatrix<double,ColMajor> b,
double alpha,
SliceMatrix<double> c,
double beta)
{ BASE_LapackMultAdd<double> (Trans(a), true, Trans(b), true, alpha, c, beta); }
/*
template <typename TA>
inline void LapackMultAdd (SliceMatrix<double> a,
TransExpr<TA> b,
double alpha,
SliceMatrix<double> c,
double beta = 1.0)
{ BASE_LapackMultAdd<double> (a, false, b.A(), true, alpha, c, beta); }
template <typename TA>
inline void LapackMultAdd (TransExpr<TA> a,
SliceMatrix<double> b,
double alpha,
SliceMatrix<double> c,
double beta = 1.0)
{ BASE_LapackMultAdd<double> (a.A(), true, b, false, alpha, c, beta); }
template <typename TA, typename TB>
inline void LapackMultAdd (TransExpr<TA> a,
TransExpr<TB> b,
double alpha,
SliceMatrix<double> c,
double beta = 1.0)
{ BASE_LapackMultAdd<double> (a.A(), true, b.A(), true, alpha, c, beta); }
*/
inline void LapackMultAdd (SliceMatrix<Complex> a,
SliceMatrix<Complex> b,
Complex alpha,
SliceMatrix<Complex> c,
Complex beta = 1.0)
{ BASE_LapackMultAdd<Complex> (a, false, b, false, alpha, c, beta); }
inline void LapackMultAdd (SliceMatrix<Complex,ColMajor> a,
SliceMatrix<Complex> b,
Complex alpha,
SliceMatrix<Complex> c,
Complex beta)
{ BASE_LapackMultAdd<Complex> (Trans(a), true, b, false, alpha, c, beta); }
inline void LapackMultAdd (SliceMatrix<Complex> a,
SliceMatrix<Complex,ColMajor> b,
Complex alpha,
SliceMatrix<Complex> c,
Complex beta)
{ BASE_LapackMultAdd<Complex> (a, false, Trans(b), true, alpha, c, beta); }
inline void LapackMultAdd (SliceMatrix<Complex,ColMajor> a,
SliceMatrix<Complex,ColMajor> b,
Complex alpha,
SliceMatrix<Complex> c,
Complex beta)
{ BASE_LapackMultAdd<Complex> (Trans(a), true, Trans(b), true, alpha, c, beta); }
template <typename TA>
inline void LapackMultAdd (SliceMatrix<Complex> a,
TransExpr<TA> b,
Complex alpha,
SliceMatrix<Complex> c,
Complex beta = 1.0)
{ BASE_LapackMultAdd<Complex> (a, false, b.A(), true, alpha, c, beta); }
template <typename TA>
inline void LapackMultAdd (TransExpr<TA> a,
SliceMatrix<Complex> b,
Complex alpha,
SliceMatrix<Complex> c,
Complex beta)
{ BASE_LapackMultAdd<Complex> (a.A(), true, b, false, alpha, c, beta); }
template <typename TA, typename TB>
inline void LapackMultAdd (TransExpr<TA> a,
TransExpr<TB> b,
Complex alpha,
SliceMatrix<Complex> c,
Complex beta)
{ BASE_LapackMultAdd<Complex> (a.A(), true, b.A(), true, alpha, c, beta); }
template <typename TA, typename TB, typename Talpha, typename Tc, typename Tbeta>
inline void LapackMultAdd (MinusExpr<TA> a,
const TB & b,
Talpha alpha,
const Tc & c,
Tbeta beta)
{ LapackMultAdd (a.A(), b, -alpha, c, beta); }
// we don't have a lapack function for that
void LapackMultAdd (SliceMatrix<double> a,
SliceMatrix<Complex,ColMajor> b,
Complex alpha,
SliceMatrix<Complex> c,
Complex beta);
// ---> moved implementation to ng_blas
/*
{
if (beta == 0.0)
c = alpha * (a * b);
else
{
c *= beta;
c += alpha * (a * b);
}
// BASE_LapackMultAdd<double> (Trans(a), true, Trans(b), true, alpha, c, beta);
}
*/
template <typename TA, typename TB, typename ALPHA, typename BETA, typename TC>
inline void LapackMultAdd (TA a,
TB b,
ALPHA alpha,
SliceMatrix<TC,ColMajor> c,
BETA beta)
{
LapackMultAdd (Trans(b), Trans(a), alpha, Trans(c), beta);
}
/*
// old-style function names, new driver
inline void LapackMultABt (SliceMatrix<double> a,
SliceMatrix<double> b,
SliceMatrix<double> c)
{ BASE_LapackMult (a, false, b, true, c); }
inline void LapackMultABt (SliceMatrix<Complex> a,
SliceMatrix<Complex> b,
SliceMatrix<Complex> c)
{ BASE_LapackMult (a, false, b, true, c); }
inline void LapackMultAB (SliceMatrix<double> a,
SliceMatrix<double> b,
SliceMatrix<double> c)
{ BASE_LapackMult (a, false, b, false, c); }
inline void LapackMultAB (SliceMatrix<Complex> a,
SliceMatrix<Complex> b,
SliceMatrix<Complex> c)
{ BASE_LapackMult (a, false, b, false, c); }
inline void LapackMultAtB (SliceMatrix<double> a,
SliceMatrix<double> b,
SliceMatrix<double> c)
{ BASE_LapackMult (a, true, b, false, c); }
inline void LapackMultAtB (SliceMatrix<Complex> a,
SliceMatrix<Complex> b,
SliceMatrix<Complex> c)
{ BASE_LapackMult (a, true, b, false, c); }
inline void LapackMultAtBt (SliceMatrix<double> a,
SliceMatrix<double> b,
SliceMatrix<double> c)
{ BASE_LapackMult (a, true, b, true, c); }
inline void LapackMultAtBt (SliceMatrix<Complex> a,
SliceMatrix<Complex> b,
SliceMatrix<Complex> c)
{ BASE_LapackMult (a, true, b, true, c); }
*/
// old functions for compatibility
inline void LapackMultABt (SliceMatrix<double> a,
SliceMatrix<double> b,
SliceMatrix<double> c)
{
char transa = 'T';
char transb = 'N';
integer m = c.Height();
integer n = c.Width();
integer k = a.Width();
double alpha = 1.0;
double beta = 0;
integer lda = max(size_t(1), a.Dist());
integer ldb = max(size_t(1), b.Dist());
integer ldc = max(size_t(1), c.Dist());
dgemm (&transa, &transb, &n, &m, &k, &alpha, &b(0,0), &ldb, &a(0,0), &lda, &beta, &c(0,0), &ldc);
}
inline void LapackMultAB (SliceMatrix<double> a,
SliceMatrix<double> b,
SliceMatrix<double> c)
{
char transa = 'N';
char transb = 'N';
integer m = c.Height();
integer n = c.Width();
integer k = a.Width();
double alpha = 1.0;
double beta = 0;
integer lda = max(size_t(1), a.Dist());
integer ldb = max(size_t(1), b.Dist());
integer ldc = max(size_t(1), c.Dist());
dgemm (&transa, &transb, &n, &m, &k, &alpha, &b(0,0), &ldb, &a(0,0), &lda, &beta, &c(0,0), &ldc);
}
inline void LapackMultAtB (ngbla::FlatMatrix<double> a,
ngbla::FlatMatrix<double> b,
ngbla::SliceMatrix<double> c)
{
char transa = 'N';
char transb = 'T';
integer m = c.Height(); // changed n,m
integer n = c.Width();
integer k = a.Height();
double alpha = 1.0;
double beta = 0;
integer lda = max(size_t(1), a.Width());
integer ldb = max(size_t(1), b.Width());
integer ldc = max(size_t(1), c.Dist()); // c.Width();
dgemm (&transa, &transb, &n, &m, &k, &alpha, &b(0,0), &ldb, &a(0,0), &lda, &beta, &c(0,0), &ldc);
}
inline void LapackMultAtBt (ngbla::FlatMatrix<double> a,
ngbla::FlatMatrix<double> b,
ngbla::FlatMatrix<double> c)
{
char transa = 'T';
char transb = 'T';
integer m = c.Height();
integer n = c.Width();
integer k = a.Height();
double alpha = 1.0;
double beta = 0;
integer lda = max(size_t(1), a.Width());
integer ldb = max(size_t(1), b.Width());
integer ldc = max(size_t(1), c.Width());
dgemm (&transa, &transb, &n, &m, &k, &alpha, &b(0,0), &ldb, &a(0,0), &lda, &beta, &c(0,0), &ldc);
}
inline void LapackMultABt (ngbla::FlatMatrix<ngbla::Complex> a,
ngbla::FlatMatrix<ngbla::Complex> b,
ngbla::FlatMatrix<ngbla::Complex> c)
{
// c = a * Trans (b);
char transa = 'T';
char transb = 'N';
integer m = c.Height();
integer n = c.Width();
integer k = a.Width();
Complex alpha(1,0); // double alpha[2] = { 1.0, 0.0 };
Complex beta(0,0); // double beta[2] = { 0.0, 0.0 };
integer lda = max(size_t(1), a.Width());
integer ldb = max(size_t(1), b.Width());
integer ldc = max(size_t(1), c.Width());
zgemm (&transa, &transb, &n, &m, &k, &alpha,
&b(0,0), &ldb,
&a(0,0), &lda, &beta,
&c(0,0), &ldc);
}
inline void LapackMultAddABt (ngbla::FlatMatrix<double> a,
ngbla::FlatMatrix<double> b,
double fac,
ngbla::FlatMatrix<double> c)
{
char transa = 'T';
char transb = 'N';
integer m = c.Height();
integer n = c.Width();
integer k = a.Width();
double alpha = fac;
double beta = 1.0;
integer lda = max(size_t(1), a.Width());
integer ldb = max(size_t(1), b.Width());
integer ldc = max(size_t(1), c.Width());
dgemm (&transa, &transb, &n, &m, &k, &alpha, &b(0,0), &ldb, &a(0,0), &lda, &beta, &c(0,0), &ldc);
}
inline void LapackMultAddAB (ngbla::FlatMatrix<double> a,
ngbla::FlatMatrix<double> b,
double fac,
ngbla::FlatMatrix<double> c)
{
char transa = 'N';
char transb = 'N';
integer m = c.Height();
integer n = c.Width();
integer k = a.Width();
double alpha = fac;
double beta = 1.0;
integer lda = max(size_t(1), a.Width());
integer ldb = max(size_t(1), b.Width());
integer ldc = max(size_t(1), c.Width());
dgemm (&transa, &transb, &n, &m, &k, &alpha, &b(0,0), &ldb, &a(0,0), &lda, &beta, &c(0,0), &ldc);
}
inline void LapackMultAddAtB (ngbla::FlatMatrix<double> a,
ngbla::FlatMatrix<double> b,
double fac,
ngbla::FlatMatrix<double> c)
{
char transa = 'N';
char transb = 'T';
integer m = c.Height(); // changed n,m
integer n = c.Width();
integer k = a.Height();
double alpha = fac;
double beta = 1.0;
integer lda = max(size_t(1), a.Width());
integer ldb = max(size_t(1), b.Width());
integer ldc = max(size_t(1), c.Width());
dgemm (&transa, &transb, &n, &m, &k, &alpha, &b(0,0), &ldb, &a(0,0), &lda, &beta, &c(0,0), &ldc);
}
inline void LapackMultAddABt (ngbla::FlatMatrix<ngbla::Complex> a,
ngbla::FlatMatrix<ngbla::Complex> b,
double fac,
ngbla::FlatMatrix<ngbla::Complex> c)
{
// c += fac * a * Trans (b);
char transa = 'T';
char transb = 'N';
integer m = c.Height();
integer n = c.Width();
integer k = a.Width();
Complex alpha(fac, 0);
Complex beta(1,0);
integer lda = max(size_t(1), a.Width());
integer ldb = max(size_t(1), b.Width());
integer ldc = max(size_t(1), c.Width());
zgemm (&transa, &transb, &n, &m, &k, &alpha,
&b(0,0), &ldb,
&a(0,0), &lda, &beta,
&c(0,0), &ldc);
}
inline void LapackMultAddAtB (ngbla::FlatMatrix<ngbla::Complex> a,
ngbla::FlatMatrix<ngbla::Complex> b,
double fac,
ngbla::FlatMatrix<ngbla::Complex> c)
{
// c += fac * a * Trans (b);
char transa = 'N';
char transb = 'T';
integer m = c.Height();
integer n = c.Width();
integer k = a.Height();
Complex alpha(fac, 0); // double alpha[2] = { fac, 0 };
Complex beta(1,0); // double beta[2] = { 1.0, 0 };
integer lda = max(size_t(1), a.Width());
integer ldb = max(size_t(1), b.Width());
integer ldc = max(size_t(1), c.Width());
zgemm (&transa, &transb, &n, &m, &k, &alpha,
&b(0,0), &ldb,
&a(0,0), &lda, &beta,
&c(0,0), &ldc);
}
inline void LapackMultAddAB (ngbla::FlatMatrix<ngbla::Complex> a,
ngbla::FlatMatrix<ngbla::Complex> b,
double fac,
ngbla::FlatMatrix<ngbla::Complex> c)
{
char transa = 'N';
char transb = 'N';
integer m = c.Height();
integer n = c.Width();
integer k = a.Width();
Complex alpha(fac, 0); // double alpha[2] = { fac, 0 };
Complex beta(1,0); // double beta[2] = { 1.0, 0 };
integer lda = max(size_t(1), a.Width());
integer ldb = max(size_t(1), b.Width());
integer ldc = max(size_t(1), c.Width());
zgemm (&transa, &transb, &n, &m, &k, &alpha,
&b(0,0), &ldb,
&a(0,0), &lda, &beta,
&c(0,0), &ldc);
}
/*
extern "C"
void dgetri_ (int & n, double & a, int & lda,
int & ipiv, double & work, int & lwork, int & info);
extern "C"
void dgetrf_ (int & n, int & m, double & a, int & lda,
int & ipiv, int & info);
extern "C"
void dgetrs_ (char & trans, int & n, int & nrhs,
double & a, int & lda, int & ipiv,
double & b, int & ldb, int & info);
extern "C"
void dpotrf_ (char & uplo, int & n, double & a, int & lda,
int & info);
extern "C"
void dpotrs_ (char & uplo, int & n, int & nrhs,
double & a, int & lda,
double & b, int & ldb, int & info);
*/
template <ORDERING ORD>
class LapackLU
{
Matrix <double, ORD> a;
ArrayMem<integer,100> ipiv;
public:
LapackLU (Matrix<double,ORD> _a)
: a(std::move(_a)), ipiv(a.Height())
{
integer m = a.Height();
if (m == 0) return;
integer n = a.Width();
integer lda = a.Dist();
integer info;
dgetrf(&n, &m, &a(0,0), &lda, &ipiv[0], &info);
}
template <typename Db>
void Solve (VectorView<double,Db> b) const
{
/*
int dgetrs_(char *trans, integer *n, integer *nrhs,
doublereal *a, integer *lda, integer *ipiv, doublereal *b, integer *
ldb, integer *info);
*/
char transa = (ORD == ColMajor) ? 'N' : 'T';
integer n = a.Height();
integer nrhs = 1;
integer lda = a.Dist();
integer ldb = b.Size();
integer info;
dgetrs(&transa, &n, &nrhs, a.Data(), &lda, ipiv.Data(), b.Data(), &ldb, &info);
}
Matrix <double,ORD> Inverse() &&
{
double hwork;
integer lwork = -1;
integer n = a.Height();
integer lda = a.Dist();
integer info;
dgetri(&n, &a(0,0), &lda, &ipiv[0], &hwork, &lwork, &info);
lwork = integer(hwork);
ArrayMem<double,1000> work(lwork);
dgetri(&n, &a(0,0), &lda, &ipiv[0], &work[0], &lwork, &info);
return std::move(a);
}
};
inline void LapackInverse (ngbla::SliceMatrix<double> a)
{
integer m = a.Height();
if (m == 0) return;
integer n = a.Width();
integer lda = max(size_t(1), a.Dist());
ArrayMem<integer,100> ipiv(n);
integer info;
dgetrf(&n, &m, &a(0,0), &lda, &ipiv[0], &info);
double hwork;
integer lwork = -1;
dgetri(&n, &a(0,0), &lda, &ipiv[0], &hwork, &lwork, &info);
lwork = integer(hwork);
ArrayMem<double,1000> work(lwork);
dgetri(&n, &a(0,0), &lda, &ipiv[0], &work[0], &lwork, &info);
}
inline void LapackInverseSPD (ngbla::SliceMatrix<double> a)
{
integer n = a.Width();
if (n == 0) return;
integer lda = max(size_t(1), a.Dist());
integer info;
char uplo = 'U';
dpotrf_ (&uplo, &n, &a(0,0), &lda, &info);
dpotri_ (&uplo, &n, &a(0,0), &lda, &info);
for (int i = 0; i < n; i++)
for (int j = 0; j < i; j++)
a(j,i) = a(i,j);
}
/*
Compoutes B <--- B A^{-1} (trans = 'N')
Compoutes B <--- B A^{-T} (trans = 'T')
Compoutes B <--- B A^{-H} (trans = 'H')
// trans = 'N': solve A x = b^T
// trans = 'T': solve A^T x = b^T
// trans = 'C': solve A^H x = b^T
*/
inline void LapackAInvBt (ngbla::FlatMatrix<double> a, ngbla::FlatMatrix<double> b, char trans = 'N')
{
integer m = a.Height();
integer n = a.Width();
integer lda = max(size_t(1), a.Width());
integer ldb = max(size_t(1), b.Width());
integer nrhs = b.Height();
ArrayMem<integer,100> ipiv(n);
integer info;
// char uplo = 'L';
dgetrf_ (&n, &m, &a(0,0), &lda, &ipiv[0], &info);
dgetrs_ (&trans, &n, &nrhs, &a(0,0), &lda, &ipiv[0], &b(0,0), &ldb, &info);
/*
// symmetric, non-spd
int lwork = -1;
double hwork[1] = { 1.0 };
dsytrf_ (&uplo, &n, &a(0,0), &lda, &ipiv[0], &hwork[0], &lwork, &info);
lwork = int(hwork[0]);
ArrayMem<double, 1000> work(lwork);
dsytrf_ (&uplo, &n, &a(0,0), &lda, &ipiv[0], &work[0], &lwork, &info);
dsytrs_ (&uplo, &n, &nrhs, &a(0,0), &lda, &ipiv[0], &b(0,0), &ldb, &info);
*/
/*
// spd
dpotrf_ (&uplo, &n, &a(0,0), &lda, &info);
dpotrs_ (&uplo, &n, &nrhs, &a(0,0), &lda, &b(0,0), &ldb, &info);
*/
}
/*
extern "C"
void zgetri_ (int & n, double & a, int & lda,
int & ipiv, double & work, int & lwork, int & info);
extern "C"
void zgetrf_ (int & n, int & m, double & a, int & lda,
int & ipiv, int & info);
extern "C"
void zgetrs_ (char & trans, int & m, int & nrhs, double & a, int & lda,
int & ipiv,
double & b, int & ldb,
int & info);
*/