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BLAS

Introduction

The BLAS (Basic Linear Algebra Subprograms) are high-quality routines for performing basic vector and matrix operations. Level 1 BLAS are for vector-vector operations. Level 2 BLAS are for matrix-vector operations. Level 3 BLAS are for matrix-matrix operations.

NEC Numeric Library Collection contains the BLAS libraries of the sequential version and the OpenMP version. If the environment variable OMP_NUM_THREADS is set to np, then the OpenMP version will run on np threads. If OMP_NUM_THREADS is not set, the OpenMP version will run on mp threads, where mp is the maximum number of processes in the resource group.

How to use BLAS

The BLAS Routine List contains one-line summaries of the subprograms in BLAS.
Compiling and Linking tells how to compile and link with the BLAS library.

BLAS Routine List

^† `?` indicates prefix which must be filled with a combination of:
`S = REAL(kind=4)`, `D = REAL(kind=8)`, `C = COMPLEX(kind=4)`, `Z = COMPLEX(kind=8)`, `H = REAL(kind=2) (IEEE binary16 format)`, `B = REAL(kind=2) (bfloat16 format)`
	Name^†	Prefixes	Description
Level 1 BLAS	`?ROTG` `SROTG` `DROTG` `CROTG` `ZROTG`	`S D C Z`	Generate plane rotation
	`?ROTMG` `SROTMG` `DROTMG`	`S D`	Generate modified plane rotation
	`?ROT` `SROT` `DROT` `CROT` `ZROT` `CSROT` `ZDROT`	`S D C Z CS ZD`	Apply plane rotation
	`?ROTM` `SROTM` `DROTM`	`S D`	Apply modified plane rotation
	`?SWAP` `SSWAP` `DSWAP` `CSWAP` `ZSWAP`	`S D C Z`	Swap vectors
	`?SCAL` `SSCAL` `DSCAL` `CSCAL` `ZSCAL` `CSSCAL` `ZDSCAL`	`S D C Z CS ZD`	Scale vector
	`?COPY` `SCOPY` `DCOPY` `CCOPY` `ZCOPY`	`S D C Z`	Copy vector
	`?AXPY` `SAXPY` `DAXPY` `CAXPY` `ZAXPY`	`S D C Z`	Vector scale and add
	`?DOT` `SDOT` `DDOT` `SDSDOT` `DSDOT`	`S D SDS DS`	Dot product, real
	`?DOTU` `CDOTU` `ZDOTU`	`C Z`	Dot product, complex
	`?DOTC` `CDOTC` `ZDOTC`	`C Z`	Dot product, complex, conjugate first vector
	`?NRM2` `SNRM2` `DNRM2` `SCNRM2` `DZNRM2`	`S D SC DZ`	Euclidean norm
	`?ASUM` `SASUM` `DASUM` `SCASUM` `DZASUM`	`S D SC DZ`	Sum absolute values
	`I?AMAX` `ISAMAX` `IDAMAX` `ICAMAX` `IZAMAX`	`S D C Z`	Index of maximum absolute value
Level 2 BLAS	`?GEMV` `SGEMV` `DGEMV` `CGEMV` `ZGEMV` `HGEMV` `BGEMV`	`S D C Z H B`	General matrix-vector multiplication Note: HGEMV and BGEMV are only included in the BLAS library for Vector Engine 3 or later.
	`?GBMV` `SGBMV` `DGBMV` `CGBMV` `ZGBMV`	`S D C Z`	General banded matrix-vector multiplication
	`?HEMV` `CHEMV` `ZHEMV`	`C Z`	Hermitian matrix-vector multiplication
	`?HBMV` `CHBMV` `ZHBMV`	`C Z`	Hermitian banded matrix-vector multiplication
	`?HPMV` `CHPMV` `ZHPMV`	`C Z`	Hermitian packed matrix-vector multiplication
	`?SYMV` `SSYMV` `DSYMV` `CSYMV` `ZSYMV`	`S D C Z`	Symmetric matrix-vector multiplication
	`?SBMV` `SSBMV` `DSBMV`	`S D`	Symmetric banded matrix-vector multiplication
	`?SPMV` `SSPMV` `DSPMV`	`S D`	Symmetric packed matrix-vector multiplication
	`?TRMV` `STRMV` `DTRMV` `CTRMV` `ZTRMV`	`S D C Z`	Triangular matrix-vector multiplication
	`?TBMV` `STBMV` `DTBMV` `CTBMV` `ZTBMV`	`S D C Z`	Triangular banded matrix-vector multiplication
	`?TPMV` `STPMV` `DTPMV` `CTPMV` `ZTPMV`	`S D C Z`	Triangular packed matrix-vector multiplication
	`?TRSV` `STRSV` `DTRSV` `CTRSV` `ZTRSV`	`S D C Z`	Triangular solve
	`?TBSV` `STBSV` `DTBSV` `CTBSV` `ZTBSV`	`S D C Z`	Triangular banded solve
	`?TPSV` `STPSV` `DTPSV` `CTPSV` `ZTPSV`	`S D C Z`	Triangular packed solve
	`?GER` `SGER` `DGER`	`S D`	General rank-1 update, real
	`?GERU` `CGERU` `ZGERU`	`C Z`	General rank-1 update, complex
	`?GERC` `CGERC` `ZGERC`	`C Z`	General rank-1 update, complex, second vector conjugate
	`?HER` `CHER` `ZHER`	`C Z`	Hermitian rank-1 update
	`?HPR` `CHPR` `ZHPR`	`C Z`	Hermitian packed rank-1 update
	`?HER2` `CHER2` `ZHER2`	`C Z`	Hermitian rank-2 update
	`?HPR2` `CHPR2` `ZHPR2`	`C Z`	Hermitian packed rank-2 update
	`?SYR` `SSYR` `DSYR`	`S D`	Symmetric rank-1 update
	`?SPR` `SSPR` `DSPR`	`S D`	Symmetric packed rank-1 update
	`?SYR2` `SSYR2` `DSYR2`	`S D`	Symmetric rank-2 update
	`?SPR2` `SSPR2` `DSPR2`	`S D`	Symmetric packed rank-2 update
Level 3 BLAS	`?GEMM` `SGEMM` `DGEMM` `CGEMM` `ZGEMM` `HGEMM` `BGEMM`	`S D C Z H B`	General matrix-matrix multiplication Note: HGEMM and BGEMM are only included in the BLAS library for Vector Engine 3 or later.
	`?GEMM_BATCH_STRIDED` `SGEMM_BATCH_STRIDED` `DGEMM_BATCH_STRIDED`	`S D`	Computes groups of matrix-matrix product with general matrices
	`?GEMMT` `SGEMMT` `DGEMMT` `CGEMMT` `ZGEMMT`	`S D C Z`	General matrix-matrix multiplication (updates only the upper or lower triangular part of the result)
	`?GEMM3M` `CGEMM3M` `ZGEMM3M`	`C Z`	General complex matrix-matrix multiplication (Performance Priority Version)
	`?SYMM` `SSYMM` `DSYMM` `CSYMM` `ZSYMM`	`S D C Z`	Symmetric matrix-matrix multiplication
	`?HEMM` `CHEMM` `ZHEMM`	`C Z`	Hermitian matrix-matrix multiplication
	`?SYRK` `SSYRK` `DSYRK` `CSYRK` `ZSYRK`	`S D C Z`	Symmetric rank-k update
	`?HERK` `CHERK` `ZHERK`	`C Z`	Hermitian rank-k update
	`?SYR2K` `SSYR2K` `DSYR2K` `CSYR2K` `ZSYR2K`	`S D C Z`	Symmetric rank-2k update
	`?HER2K` `CHER2K` `ZHER2K`	`C Z`	Hermitian rank-2k update
	`?TRMM` `STRMM` `DTRMM` `CTRMM` `ZTRMM`	`S D C Z`	Triangular matrix-matrix multiply
	`?TRSM` `STRSM` `DTRSM` `CTRSM` `ZTRSM`	`S D C Z`	Triangular solve
Auxiliary Subprograms	`LSAME`		Returns .TRUE. if the first input character CA is the same letter as the second input character CB regardless of case.
	`XERBLA`		Print argument error messages
	`BLAS_INIT`		Retrieves the value of the environment variables for BLAS routines

External Link

A Quick Reference Guide for BLAS

Version Information

This manual page version: 3.0.0-230227