Quick Reference Guide to the BLAS

Level 1 BLAS

                   dim scalar vector   vector   scalars              5-element prefixes
                                                                     array

SUBROUTINE _ROTG (                                      A, B, C, S )          S, D
SUBROUTINE _ROTMG(                              D1, D2, A, B,        PARAM )  S, D
SUBROUTINE _ROT  ( N,         X, INCX, Y, INCY,               C, S )          S, D
SUBROUTINE _ROTM ( N,         X, INCX, Y, INCY,                      PARAM )  S, D
SUBROUTINE _SWAP ( N,         X, INCX, Y, INCY )                              S, D, C, Z
SUBROUTINE _SCAL ( N,  ALPHA, X, INCX )                                       S, D, C, Z, CS, ZD
SUBROUTINE _COPY ( N,         X, INCX, Y, INCY )                              S, D, C, Z
SUBROUTINE _AXPY ( N,  ALPHA, X, INCX, Y, INCY )                              S, D, C, Z
FUNCTION   _DOT  ( N,         X, INCX, Y, INCY )                              S, D, DS
FUNCTION   _DOTU ( N,         X, INCX, Y, INCY )                              C, Z
FUNCTION   _DOTC ( N,         X, INCX, Y, INCY )                              C, Z
FUNCTION   __DOT ( N,  ALPHA, X, INCX, Y, INCY )                              SDS
FUNCTION   _NRM2 ( N,         X, INCX )                                       S, D, SC, DZ
FUNCTION   _ASUM ( N,         X, INCX )                                       S, D, SC, DZ
FUNCTION   I_AMAX( N,         X, INCX )                                       S, D, C, Z

Name	Operation	Prefixes
_ROTG	Generate plane rotation	S, D
_ROTMG	Generate modified plane rotation	S, D
_ROT	Apply plane rotation	S, D
_ROTM	Apply modified plane rotation	S, D
_SWAP	$x \leftrightarrow y$	S, D, C, Z
_SCAL	$x \leftarrow \alpha x$	S, D, C, Z, CS, ZD
_COPY	$y \leftarrow x$	S, D, C, Z
_AXPY	$y \leftarrow \alpha x + y$	S, D, C, Z
_DOT	$dot \leftarrow x ^ {T} y$	S, D, DS
_DOTU	$dot \leftarrow x ^ {T} y$	C, Z
_DOTC	$dot \leftarrow x ^ {H} y$	C, Z
__DOT	$dot \leftarrow \alpha + x ^ {T} y$	SDS
_NRM2	$nrm2 \leftarrow \vert\vert x \vert\vert _ {2}$	S, D, SC, DZ
_ASUM	$asum \leftarrow \vert\vert re( x ) \vert\vert _ {1} + \vert\vert im( x ) \vert\vert _ {1}$	S, D, SC, DZ
I_AMAX	$amax \leftarrow 1^{st} k \ni \vert re( x _ {k} ) \vert + \vert im( x _ {k} ) \vert$	S, D, C, Z
	= max( | re( x i ) | + | im( x i ) | )

Level 2 BLAS

        options            dim   b-width scalar matrix  vector   scalar vector   prefixes

_GEMV (        TRANS,      M, N,         ALPHA, A, LDA, X, INCX, BETA,  Y, INCY ) S, D, C, Z
_GBMV (        TRANS,      M, N, KL, KU, ALPHA, A, LDA, X, INCX, BETA,  Y, INCY ) S, D, C, Z
_HEMV ( UPLO,                 N,         ALPHA, A, LDA, X, INCX, BETA,  Y, INCY ) C, Z
_HBMV ( UPLO,                 N, K,      ALPHA, A, LDA, X, INCX, BETA,  Y, INCY ) C, Z
_HPMV ( UPLO,                 N,         ALPHA, AP,     X, INCX, BETA,  Y, INCY ) C, Z
_SYMV ( UPLO,                 N,         ALPHA, A, LDA, X, INCX, BETA,  Y, INCY ) S, D
_SBMV ( UPLO,                 N, K,      ALPHA, A, LDA, X, INCX, BETA,  Y, INCY ) S, D
_SPMV ( UPLO,                 N,         ALPHA, AP,     X, INCX, BETA,  Y, INCY ) S, D
_TRMV ( UPLO, TRANS, DIAG,    N,                A, LDA, X, INCX )                 S, D, C, Z
_TBMV ( UPLO, TRANS, DIAG,    N, K,             A, LDA, X, INCX )                 S, D, C, Z
_TPMV ( UPLO, TRANS, DIAG,    N,                AP,     X, INCX )                 S, D, C, Z
_TRSV ( UPLO, TRANS, DIAG,    N,                A, LDA, X, INCX )                 S, D, C, Z
_TBSV ( UPLO, TRANS, DIAG,    N, K,             A, LDA, X, INCX )                 S, D, C, Z
_TPSV ( UPLO, TRANS, DIAG,    N,                AP,     X, INCX )                 S, D, C, Z

        options            dim   scalar vector   vector   matrix  prefixes

_GER  (                    M, N, ALPHA, X, INCX, Y, INCY, A, LDA ) S, D
_GERU (                    M, N, ALPHA, X, INCX, Y, INCY, A, LDA ) C, Z
_GERC (                    M, N, ALPHA, X, INCX, Y, INCY, A, LDA ) C, Z
_HER  ( UPLO,                 N, ALPHA, X, INCX,          A, LDA ) C, Z
_HPR  ( UPLO,                 N, ALPHA, X, INCX,          AP )     C, Z
_HER2 ( UPLO,                 N, ALPHA, X, INCX, Y, INCY, A, LDA ) C, Z
_HPR2 ( UPLO,                 N, ALPHA, X, INCX, Y, INCY, AP )     C, Z
_SYR  ( UPLO,                 N, ALPHA, X, INCX,          A, LDA ) S, D
_SPR  ( UPLO,                 N, ALPHA, X, INCX,          AP )     S, D
_SYR2 ( UPLO,                 N, ALPHA, X, INCX, Y, INCY, A, LDA ) S, D
_SPR2 ( UPLO,                 N, ALPHA, X, INCX, Y, INCY, AP )     S, D

Level 3 BLAS

        options                          dim      scalar matrix  matrix  scalar matrix  prefixes

_GEMM (             TRANSA, TRANSB,      M, N, K, ALPHA, A, LDA, B, LDB, BETA,  C, LDC ) S, D, C, Z
_SYMM ( SIDE, UPLO,                      M, N,    ALPHA, A, LDA, B, LDB, BETA,  C, LDC ) S, D, C, Z
_HEMM ( SIDE, UPLO,                      M, N,    ALPHA, A, LDA, B, LDB, BETA,  C, LDC ) C, Z
_SYRK (       UPLO, TRANS,                  N, K, ALPHA, A, LDA,         BETA,  C, LDC ) S, D, C, Z
_HERK (       UPLO, TRANS,                  N, K, ALPHA, A, LDA,         BETA,  C, LDC ) C, Z
_SYR2K(       UPLO, TRANS,                  N, K, ALPHA, A, LDA, B, LDB, BETA,  C, LDC ) S, D, C, Z
_HER2K(       UPLO, TRANS,                  N, K, ALPHA, A, LDA, B, LDB, BETA,  C, LDC ) C, Z
_TRMM ( SIDE, UPLO, TRANSA,        DIAG, M, N,    ALPHA, A, LDA, B, LDB )                S, D, C, Z
_TRSM ( SIDE, UPLO, TRANSA,        DIAG, M, N,    ALPHA, A, LDA, B, LDB )                S, D, C, Z

Name	Operation	Prefixes
_GEMV	$y \leftarrow \alpha A x + \beta y , y \leftarrow \alpha A ^ {T} x + \beta y , y \leftarrow \alpha A ^{H} x + \beta y , A - m \times n$	S, D, C, Z
_GBMV	$y \leftarrow \alpha A x + \beta y , y \leftarrow \alpha A ^ {T} x + \beta y , y \leftarrow \alpha A ^{H} x + \beta y , A - m \times n$	S, D, C, Z
_HEMV	$y \leftarrow \alpha A x + \beta y$	C, Z
_HBMV	$y \leftarrow \alpha A x + \beta y$	C, Z
_HPMV	$y \leftarrow \alpha A x + \beta y$	C, Z
_SYMV	$y \leftarrow \alpha A x + \beta y$	S, D
_SBMV	$y \leftarrow \alpha A x + \beta y$	S, D
_SPMV	$y \leftarrow \alpha A x + \beta y$	S, D
_TRMV	$x \leftarrow A x, x \leftarrow A ^{T} x, x \leftarrow A ^ {H} x$	S, D, C, Z
_TBMV	$x \leftarrow A x, x \leftarrow A ^{T} x, x \leftarrow A ^ {H} x$	S, D, C, Z
_TPMV	$x \leftarrow A x, x \leftarrow A ^{T} x, x \leftarrow A ^ {H} x$	S, D, C, Z
_TRSV	$x \leftarrow A ^{-1} x, x \leftarrow A ^{-T} x, x \leftarrow A ^ {-H} x$	S, D, C, Z
_TBSV	$x \leftarrow A ^{-1} x, x \leftarrow A ^{-T} x, x \leftarrow A ^ {-H} x$	S, D, C, Z
_TPSV	$x \leftarrow A ^{-1} x, x \leftarrow A ^{-T} x, x \leftarrow A ^ {-H} x$	S, D, C, Z
_GER	$A \leftarrow \alpha x y ^{T} + A , A - m \times n$	S, D
_GERU	$A \leftarrow \alpha x y ^{T} + A , A - m \times n$	C, Z
_GERC	$A \leftarrow \alpha x y ^{H} + A , A - m \times n$	C, Z
_HER	$A \leftarrow \alpha x x ^{H} + A$	C, Z
_HPR	$A \leftarrow \alpha x x ^{H} + A$	C, Z
_HER2	$A \leftarrow \alpha x y ^{H} + y ( \alpha x ) ^ {H} + A$	C, Z
_HPR2	$A \leftarrow \alpha x y ^{H} + y ( \alpha x ) ^ {H} + A$	C, Z
_SYR	$A \leftarrow \alpha x x ^{T} + A$	S, D
_SPR	$A \leftarrow \alpha x x ^{T} + A$	S, D
_SYR2	$A \leftarrow \alpha x y ^{T} + \alpha y x ^ {T} + A$	S, D
_SPR2	$A \leftarrow \alpha x y ^{T} + \alpha y x ^ {T} + A$	S, D

Name	Operation	Prefixes
_GEMM	$C \leftarrow \alpha op(A)op(B) + \beta C, op(X) = X, X ^{T}, X ^{H}, C - m \times n$	S, D, C, Z
_SYMM	$C \leftarrow \alpha AB + \beta C, C \leftarrow \alpha BA + \beta C, C - m \times n, A = A ^{T}$	S, D, C, Z
_HEMM	$C \leftarrow \alpha AB + \beta C, C \leftarrow \alpha BA + \beta C, C - m \times n, A = A ^{H}$	C, Z
_SYRK	$C \leftarrow \alpha AA ^{T} + \beta C, C \leftarrow \alpha A ^{T} A + \beta C, C - n \times n$	S, D, C, Z
_HERK	$C \leftarrow \alpha AA ^{H} + \beta C, C \leftarrow \alpha A ^{H} A + \beta C, C - n \times n$	C, Z
_SYR2K	$C \leftarrow \alpha AB ^{T} + \alpha BA ^{T} + \beta C, C \leftarrow \alpha A ^{T} B + \alpha B ^{T} A + \beta C, C - n \times n$	S, D, C, Z
_HER2K	$C \leftarrow \alpha AB ^{H} + \bar{\alpha} BA ^{H} + \beta C, C \leftarrow \alpha A ^{H} B + \bar{\alpha} B ^{H} A + \beta C, C - n \times n$	C, Z
_TRMM	$B \leftarrow \alpha op(A)B, B \leftarrow \alpha B op(A), op(A) = A, A ^{T}, A ^{H}, B - m \times n$	S, D, C, Z
_TRSM	$B \leftarrow \alpha op(A ^{-1} )B, B \leftarrow \alpha B op(A ^{-1} ), op(A) = A, A ^{T}, A ^{H}, B - m \times n$	S, D, C, Z

Notes

Meaning of prefixes

S - REAL	C - COMPLEX
D - DOUBLE PRECISION	Z - COMPLEX*16	(this may not be supported
		by all machines)

For the Level 2 BLAS a set of extended-precision routines with the prefixes ES, ED, EC, EZ may also be available.

Level 1 BLAS

In addition to the listed routines there are two further extended-precision dot product routines DQDOTI and DQDOTA.

Level 2 and Level 3 BLAS

Matrix types

GE - GEneral	GB - General Band
SY - SYmmetric	SB - Symmetric Band	SP - Symmetric Packed
HE - HErmitian	HB - Hermitian Band	HP - Hermitian Packed
TR - TRiangular	TB - Triangular Band	TP - Triangular Packed

Options

Arguments describing options are declared as CHARACTER*1 and may be passed as character strings.

TRANS	= ` No transpose', ` Transpose', ` Conjugate transpose' ( X, X T, XC )
UPLO	= ` Upper triangular', ` Lower triangular'
DIAG	= ` Non-unit triangular', ` Unit triangular'
SIDE	= ` Left', ` Right' (A or op(A) on the left, or A or op(A) on the right)

For real matrices, TRANS = `T' and TRANS = `C' have the same meaning.
For Hermitian matrices, TRANS = `T' is not allowed.
For complex symmetric matrices, TRANS = `H' is not allowed.