Module document_func

BLAS Wrapper Structs

Document of BLAS wrappers is on-going work.

Terms of the following table is

• Prototype: Prototype of BLAS wrappers.
  • For users, prototype is NOT designed to be used by API caller. One may wish to call generic structs (such as GEMM<F>) or directly call specialization (such as DGEMM).
  • For documents and structure of BLAS wrapper, please refer to hyperlinks of prototype (on docs.rs). We also refer LAPACK document.
• Num Trait: Trait bound that could be applied on generics.
• Generic: Generic structs of BLAS wrapper. This is designed to be called by API user. For example of GEMM<F>, this is type alias of GEMM_Builder<F>.
• Specialization: Specialization structs of BLAS wrapper. This is designed to be called by API user, and have the same subroutine name to (legacy) BLAS.

Abbrivations

• symm: Symmetric
• hermi: Hermitian
• tri: Triangular

Level 3 BLAS

BLAS	Prototype	Num Trait	Generic	f32	f64	c32	c64	Description
gemm	GEMM_<F>	GEMMNum	GEMM<F>	SGEMM	DGEMM	CGEMM	ZGEMM	general matrix-matrix multiply
symm	SYMM_<F>	SYMMNum	SYMM<F>	SSYMM	DSYMM	CSYMM	ZSYMM	symm matrix-matrix multiply
hemm	HEMM_<F>	HEMMNum	HEMM<F>			CHEMM	ZHEMM	hermi matrix-matrix multiply
syrk	SYRK_<F>	SYRKNum	SYRK<F>	SSYRK	DSYRK	CSYRK	ZSYRK	symm rank-k update
herk	HERK_<F>	HERKNum	HERK<F>			CHERK	ZHERK	hermi rank-k update
syr2k	SYR2K_<F>	SYR2KNum	SYR2K<F>	SSYR2K	DSYR2K	CSYR2K	ZSYR2K	symm rank-2k update
her2k	HER2K_<F>	HER2KNum	HER2K<F>			CHER2K	ZHER2K	hermi rank-2k update
trmm	TRMM_<F>	TRMMNum	TRMM<F>	STRMM	DTRMM	CTRMM	ZTRMM	tri matrix-matrix multiply
trsm	TRSM_<F>	TRSMNum	TRSM<F>	STRSM	DTRSM	CTRSM	ZTRSM	tri matrix-matrix solve

Level 3 BLAS (extensions)

BLAS	Prototype	Num Trait	Generic	f32	f64	c32	c64	Description
gemmt	[GEMMT_<F>]	[GEMMTNum]	[GEMMT<F>]	[SGEMMT]	[DGEMMT]	[CGEMMT]	[ZGEMMT]	general matrix-matrix multiply, tri update

Level 2 BLAS (full)

BLAS	Prototype	Num Trait	Generic	f32	f64	c32	c64	Description
gemv	GEMV_<F>	GEMVNum	GEMV<F>	SGEMV	DGEMV	CGEMV	ZGEMV	general matrix-vector multiply
ger	GER_<F>	GERNum	GER<F>	SGER	DGER	CGERU	ZGERU	general matrix rank-1 update
gerc	GERC_<F>	GERCNum	GERC<F>			CGERC	ZGERC	general matrix rank-1 update
{sy,he}mv	HEMV_<F>	HEMVNum	HEMV<F>	SSYMV	DSYMV	CHEMV	ZHEMV	symm/hermi matrix-vector multiply
{sy,he}r	HER_<F>	HERNum	HER<F>	SSYR	DSYR	CHER	ZHER	symm/hermi rank-1 update
{sy,he}r2	HER2_<F>	HER2Num	HER2<F>	SSYR2	DSYR2	CHER2	ZHER2	symm/hermi rank-2 update
trmv	TRMV_<F>	TRMVNum	TRMV<F>	STRMV	DTRMV	CTRMV	ZTRMV	tri matrix-vector multiply
trsv	TRSV_<F>	TRSVNum	TRSV<F>	STRSV	DTRSV	CTRSV	ZTRSV	tri matrix-vector solve

Level 2 BLAS (packed)

BLAS	Prototype	Num Trait	Generic	f32	f64	c32	c64	Description
{sp,hp}mv	HPMV_<F>	HPMVNum	HPMV<F>	SSPMV	DSPMV	CHPMV	ZHPMV	symm/hermi matrix-vector multiply
{sp,hp}r	HPR_<F>	HPRNum	HPR<F>	SSPR	DSPR	CHPR	ZHPR	symm/hermi rank-1 update
{sp,hp}r2	HPR2_<F>	HPR2Num	HPR2<F>	SSPR2	DSPR2	CHPR2	ZHPR2	symm/hermi rank-2 update
tpmv	TPMV_<F>	TPMVNum	TPMV<F>	STPMV	DTPMV	CTPMV	ZTPMV	tri matrix-vector multiply
tpsv	TPSV_<F>	TPSVNum	TPSV<F>	STPSV	DTPSV	CTPSV	ZTPSV	tri matrix-vector solve

Level 2 BLAS (banded)

BLAS	Prototype	Num Trait	Generic	f32	f64	c32	c64	Description
gbmv	GBMV_<F>	GBMVNum	GBMV<F>	SGBMV	DGBMV	CGBMV	ZGBMV	general matrix-vector multiply
{sb,hb}mv	HBMV_<F>	HBMVNum	HBMV<F>	SSBMV	DSBMV	CHBMV	ZHBMV	symm/hermi matrix-vector multiply
tbmv	TBMV_<F>	TBMVNum	TBMV<F>	STBMV	DTBMV	CTBMV	ZTBMV	tri matrix-vector multiply
tbsv	TBSV_<F>	TBSVNum	TBSV<F>	STBSV	DTBSV	CTBSV	ZTBSV	tri matrix-vector solve

Level 1 BLAS

BLAS	Prototype	Num Trait	Generic	f32	f64	c32	c64	Description
asum	ASUM_<F>	ASUMNum	ASUM<F>	SASUM	DASUM	SCASUM	DZASUM	$\sum_i \big( \vert \mathrm{re} ( x_i ) \vert + \vert \mathrm{im} ( x_i ) \vert \big)$
nrm2	NRM2_<F>	NRM2Num	NRM2<F>	SNRM2	DNRM2	SCNRM2	DZASUM	$\Vert \boldsymbol{x} \Vert_2$
iamax	IAMAX_<F>	IAMAXNum	IAMAX<F>	ISAMAX	IDAMAX	ICAMAX	IZAMAX	$\arg \max_i \big( \vert \mathrm{re} ( x_i ) \vert + \vert \mathrm{im} ( x_i ) \vert \big)$