Engine bridge into LAPACK for RR / CC dense linear algebra. More...

#include "aring-RR.hpp"
#include "aring-CC.hpp"
#include "aring-RRR.hpp"
#include "aring-CCC.hpp"
#include "dmat.hpp"

Classes
class	Lapack
	Static-method namespace bridging the engine's RR / CC / RRR / CCC dense matrices and LAPACK / BLAS routines. More...

Typedefs
typedef DMat< M2::ARingRRR >	DMatRRR
typedef DMat< M2::ARingCCC >	DMatCCC
typedef DMat< M2::ARingRR >	DMatRR
typedef DMat< M2::ARingCC >	DMatCC

Functions
int	dgesv_ (int n, int nrhs, double a, int lda, int ipiv, double b, int ldb, int info)
int	dgeev_ (char n, char n2, int size, double M, int size1, double E, double E2, double , int , double , int , double , int , int )
int	dsyev_ (char n, char n2, int size, double M, int lda, double eig, double work, int wsize, int *info)
void	dgetrf_ (const int rows, const int cols, double A, const int ld, int ipiv, int info)
int	dgesvd_ (char jobU, char jobV, int rows, int cols, double A, int ldA, double Sigma, double U, int ldU, double VT, int ldVT, double work, int lwork, int info)
int	dgesdd_ (char jobU, int rows, int cols, double A, int ldA, double Sigma, double U, int ldU, double VT, int ldVT, double work, int lwork, int iwork, int info)
int	dgels_ (char job, int rows, int cols, int nhrs, double A, int ldA, double b, int ldb, double work, int lwork, int *info)
int	dgelss_ (int rows, int cols, int nhrs, double A, int ldA, double b, int ldb, double Sigma, double rcond, int rank, double work, int lwork, int *info)
int	dgeqrf_ (int m, int n, double A, int lda, double tau, double work, int lwork, int info)
int	dorgqr_ (int m, int n, int k, double A, int lda, double tau, double work, int lwork, int *info)
int	zgeqrf_ (int m, int n, double A, int lda, double tau, double work, int lwork, int info)
int	zungqr_ (int m, int n, int k, double A, int lda, double tau, double work, int lwork, int *info)
void	cblas_daxpy (const int n, const double a, const double x, const int incx, double y, const int incy)
void	cblas_dgemm (const int Order, const int TransA, const int TransB, const int M, const int N, const int K, const double alpha, const double A, const int lda, const double B, const int ldb, const double beta, double *C, const int ldc)
void	cblas_dscal (const int n, const double a, double *x, const int incx)
int	zgesv_ (int n, int nrhs, double a, int lda, int ipiv, double b, int ldb, int info)
int	zgeev_ (char n, char n2, int size, double M, int size1, double E, double l, int lsize, double r, int rsize, double w, int wsize, double rwork, int info)
int	zheev_ (char n, char n2, int size, double M, int lda, double eig, double w, int wsize, double rwork, int info)
int	zgetrf_ (int rows, int cols, double M, int ld, int ipiv, int info)
int	zgesvd_ (char jobU, char jobV, int rows, int cols, double A, int ldA, double Sigma, double U, int ldU, double VT, int ldVT, double w, int lwork, double rwork, int *info)
int	zgesdd_ (char jobU, int rows, int cols, double A, int ldA, double Sigma, double U, int ldU, double VT, int ldVT, double w, int lwork, double rwork, int iwork, int *info)
int	zgels_ (char job, int rows, int cols, int nhrs, double A, int ldA, double b, int ldb, double work, int lwork, int *info)
int	zgelss_ (int rows, int cols, int nhrs, double A, int ldA, double b, int ldb, double Sigma, double rcond, int rank, double work, int lwork, double rwork, int info)
void	cblas_zgemm (const int Order, const int TransA, const int TransB, const int M, const int N, const int K, const void alpha, const void A, const int lda, const void B, const int ldb, const void beta, void *C, const int ldc)

Detailed Description

Engine bridge into LAPACK for RR / CC dense linear algebra.

Note: AI-generated documentation. Verify against the source before relying on it.

Defines the four DMat<R> aliases the LAPACK path uses (DMatRR, DMatCC, DMatRRR, DMatCCC) and declares the Fortran ABI prototypes (dgesv_, dgeev_, dsyev_, dgetrf_, dgesvd_, zgesv_, zgeev_, ...) that the implementation forwards into for linear solve, LU, QR, SVD, eigenvalue, and least-squares work. Engine callers reach those routines through the static Lapack class declared further down: LU, solve, solve_triangular (real only), eigenvalues / eigenvectors, the real-symmetric eigenvalues_symmetric / eigenvectors_symmetric, the complex-hermitian eigenvalues_hermitian / eigenvectors_hermitian (separate methods, not a unified suffix), SVD / SVD_divide_conquer, least_squares / least_squares_deficient, and QR, each overloaded once for the hardware-precision aliases (DMatRR / DMatCC) and once for the MPFR-precision aliases (DMatRRR / DMatCCC); the MPFR overloads copy through double / complex<double> element by element, so the answer carries hardware precision regardless of the input ring.

The library is detected at configure time — the autotools macro M2/m4/ax_lapack.m4 resolves to whatever LAPACK build is available (system reference LAPACK, Apple Accelerate, OpenBLAS, ...). The neighbouring eigen.hpp covers the Eigen3-backed path used for the genuine MPFR-precision computations and as the #ifdef NO_LAPACK fallback for the hardware-precision aliases.

See also: dmat.hpp; eigen.hpp; aring-RR.hpp; aring-CC.hpp

Definition in file lapack.hpp.

Classes

Typedefs

Functions

Detailed Description