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 |
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S, D, C, Z |
_SCAL |
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S, D, C, Z, CS, ZD |
_COPY | ![]() |
S, D, C, Z |
_AXPY |
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S, D, C, Z |
_DOT |
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S, D, DS |
_DOTU |
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C, Z |
_DOTC |
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C, Z |
__DOT |
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SDS |
_NRM2 |
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S, D, SC, DZ |
_ASUM |
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S, D, SC, DZ |
I_AMAX |
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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 |
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S, D, C, Z |
_GBMV |
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S, D, C, Z |
_HEMV |
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C, Z |
_HBMV |
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C, Z |
_HPMV |
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C, Z |
_SYMV |
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S, D |
_SBMV |
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S, D |
_SPMV |
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S, D |
_TRMV |
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S, D, C, Z |
_TBMV |
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S, D, C, Z |
_TPMV |
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S, D, C, Z |
_TRSV |
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S, D, C, Z |
_TBSV |
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S, D, C, Z |
_TPSV |
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S, D, C, Z |
_GER |
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S, D |
_GERU |
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C, Z |
_GERC |
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C, Z |
_HER |
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C, Z |
_HPR |
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C, Z |
_HER2 |
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C, Z |
_HPR2 |
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C, Z |
_SYR |
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S, D |
_SPR |
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S, D |
_SYR2 |
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S, D |
_SPR2 |
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S, D |
Name | Operation | Prefixes |
_GEMM |
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S, D, C, Z |
_SYMM |
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S, D, C, Z |
_HEMM |
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C, Z |
_SYRK |
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S, D, C, Z |
_HERK |
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C, Z |
_SYR2K |
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S, D, C, Z |
_HER2K |
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C, Z |
_TRMM |
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S, D, C, Z |
_TRSM |
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S, D, C, Z |
Notes
Meaning of prefixes
S - REAL | C - COMPLEX | |
D - DOUBLE PRECISION | Z - COMPLEX*16 | (this may not be supported |
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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) |