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The BLAS (Basic Linear Algebra Subprograms) are routines that provide standard building blocks for performing basic vector and matrix operations. The Level 1 BLAS perform scalar, vector and vector-vector operations, the Level 2 BLAS perform matrix-vector operations, and the Level 3 BLAS perform matrix-matrix operations. Because the BLAS are efficient, portable, and widely available, they are commonly used in the development of high quality linear algebra software, LAPACK for example.
Acknowledgments:
This material is based upon work supported by the National Science Foundation under Grant No. ASC-9313958 and DOE Grant No. DE-FG03-94ER25219. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF) or the Department of Energy (DOE).
History
Discover the great history behind BLAS. On April 2004 an oral history interview was conducted as part of the SIAM project on the history of software for scientific computing and numerical analysis. This interview is being conducted with Professor Jack Dongarra in his office at the University of Tennessee. The interviewer is Thomas Haigh. |
Software:
Licensing:
The reference BLAS is a freely-available software package. It is available from netlib via anonymous ftp and the World Wide Web. Thus, it can be included in commercial software packages (and has been). We only ask that proper credit be given to the authors.
Like all software, it is copyrighted. It is not trademarked, but we do ask the following:
If you modify the source for these routines we ask that you change the name of the routine and comment the changes made to the original.
We will gladly answer any questions regarding the software. If a modification is done, however, it is the responsibility of the person who modified the routine to provide support.
REFERENCE BLAS Version 3.8.0
Download blas-3.8.0.tgz
Updated November 2017
CBLAS
Level 3 BLAS tuned for single processors with caches
Downlaod ssgemmbased.tgz
Written by Kagstrom B., Ling P., and Van Loan C.
High Performance GEMM-Based Level-3 BLAS Webpage - Fortran (High Performance Computing II, 1991, North-Holland)
Extended precision Level 2 BLAS routines
BLAS for windows
The reference BLAS is included inside the LAPACK package. Please refer tools built under Windows using Cmake the cross-platform, open-source build system. The new build system was developed in collaboration with Kitware Inc.
A dedicated website (http://icl.cs.utk.edu/lapack-for-windows/lapack/) is available for Windows users.
You will find information about your configuration need.
You will be able to download BLAS pre-built libraries.
GIT Access
The LAPACK GIT (http://github.com/Reference-LAPACK) repositories are to open for read-only for our users. The latest version of BLAS is included in LAPACK package.
lapack - LAPACK development repository : http://github.com/Reference-LAPACK/lapack
lapack-release - LAPACK official release branches : http://github.com/Reference-LAPACK/lapack-release
lapack-www - LAPACK website : http://github.com/Reference-LAPACK/lapack-www
Please use our LAPACK development repository to get the latest bug fixed, submit issues or pull requests.
The netlib family and its cousins
Basic Linear Algebra Subprograms (BLAS) | |
CLAPACK (no longer maintained) | EISPACK (no longer maintained) |
Support
If you have any issue (install, performance), just post your questions on the the LAPACK User Forum. You can also send us an email at lapack@icl.utk.edu
1 3/8 In Decimal
Documentation
BLAS Technical Forum
The BLAS Technical Forum standard is a specification of a set of kernel routines for linear algebra, historically called the Basic Linear Algebra Subprograms. http://www.netlib.org/blas/blast-forum/
Optimized BLAS Library
Machine-specific optimized BLAS libraries are available for a variety of computer architectures. These optimized BLAS libraries are provided by the computer vendor or by an independent software vendor (ISV) . For further details, please see our FAQs.
Alternatively, the user can download ATLAS to automatically generate an optimized BLAS library for his architecture. Some prebuilt optimized BLAS libraries are also available from the ATLAS site.
If all else fails, the user can download a Fortran77 reference implementation of the BLAS from netlib. However, keep in mind that this is a reference implementation and is not optimized.
BLAS vendor library List Last updated: July 20, 2005
BLAS Routines
LEVEL 1
SINGLE
SROTG - setup Givens rotation
SROTMG - setup modified Givens rotation
SROT - apply Givens rotation
SROTM - apply modified Givens rotation
SSWAP - swap x and y
SSCAL - x = a*x
SCOPY - copy x into y
SAXPY - y = a*x + y
SDOT - dot product
SDSDOT - dot product with extended precision accumulation
SNRM2 - Euclidean norm
SCNRM2- Euclidean norm
SASUM - sum of absolute values
ISAMAX - index of max abs value
DOUBLE
DROTG - setup Givens rotation
Wolf forms 2 2 1 – create php web forms. DROTMG - setup modified Givens rotation
DROT - apply Givens rotation
DROTM - apply modified Givens rotation
DSWAP - swap x and y
DSCAL - x = a*x
DCOPY - copy x into y
DAXPY - y = a*x + y Boom 3d 1 3 4 player games.
DDOT - dot product
DSDOT - dot product with extended precision accumulation
DNRM2 - Euclidean norm
DZNRM2 - Euclidean norm
DASUM - sum of absolute values
IDAMAX - index of max abs value
COMPLEX
CROTG - setup Givens rotation
CSROT - apply Givens rotation
CSWAP - swap x and y
CSCAL - x = a*x
CSSCAL - x = a*x
CCOPY - copy x into y
CAXPY - y = a*x + y
CDOTU - dot product
CDOTC - dot product, conjugating the first vector
SCASUM - sum of absolute values
ICAMAX - index of max abs value
DOUBLE COMLPEX
ZROTG - setup Givens rotation
ZDROTF - apply Givens rotation
ZSWAP - swap x and y
ZSCAL - x = a*x
ZDSCAL - x = a*x
ZCOPY - copy x into y
ZAXPY - y = a*x + y
ZDOTU - dot product
ZDOTC - dot product, conjugating the first vector
DZASUM - sum of absolute values
IZAMAX - index of max abs value
Motrix Mac
The reference BLAS is a freely-available software package. It is available from netlib via anonymous ftp and the World Wide Web. Thus, it can be included in commercial software packages (and has been). We only ask that proper credit be given to the authors.
Like all software, it is copyrighted. It is not trademarked, but we do ask the following:
If you modify the source for these routines we ask that you change the name of the routine and comment the changes made to the original.
We will gladly answer any questions regarding the software. If a modification is done, however, it is the responsibility of the person who modified the routine to provide support.
REFERENCE BLAS Version 3.8.0
Download blas-3.8.0.tgz
Updated November 2017
CBLAS
Level 3 BLAS tuned for single processors with caches
Downlaod ssgemmbased.tgz
Written by Kagstrom B., Ling P., and Van Loan C.
High Performance GEMM-Based Level-3 BLAS Webpage - Fortran (High Performance Computing II, 1991, North-Holland)
Extended precision Level 2 BLAS routines
BLAS for windows
The reference BLAS is included inside the LAPACK package. Please refer tools built under Windows using Cmake the cross-platform, open-source build system. The new build system was developed in collaboration with Kitware Inc.
A dedicated website (http://icl.cs.utk.edu/lapack-for-windows/lapack/) is available for Windows users.
You will find information about your configuration need.
You will be able to download BLAS pre-built libraries.
GIT Access
The LAPACK GIT (http://github.com/Reference-LAPACK) repositories are to open for read-only for our users. The latest version of BLAS is included in LAPACK package.
lapack - LAPACK development repository : http://github.com/Reference-LAPACK/lapack
lapack-release - LAPACK official release branches : http://github.com/Reference-LAPACK/lapack-release
lapack-www - LAPACK website : http://github.com/Reference-LAPACK/lapack-www
Please use our LAPACK development repository to get the latest bug fixed, submit issues or pull requests.
The netlib family and its cousins
Basic Linear Algebra Subprograms (BLAS) | |
CLAPACK (no longer maintained) | EISPACK (no longer maintained) |
Support
If you have any issue (install, performance), just post your questions on the the LAPACK User Forum. You can also send us an email at lapack@icl.utk.edu
1 3/8 In Decimal
Documentation
BLAS Technical Forum
The BLAS Technical Forum standard is a specification of a set of kernel routines for linear algebra, historically called the Basic Linear Algebra Subprograms. http://www.netlib.org/blas/blast-forum/
Optimized BLAS Library
Machine-specific optimized BLAS libraries are available for a variety of computer architectures. These optimized BLAS libraries are provided by the computer vendor or by an independent software vendor (ISV) . For further details, please see our FAQs.
Alternatively, the user can download ATLAS to automatically generate an optimized BLAS library for his architecture. Some prebuilt optimized BLAS libraries are also available from the ATLAS site.
If all else fails, the user can download a Fortran77 reference implementation of the BLAS from netlib. However, keep in mind that this is a reference implementation and is not optimized.
BLAS vendor library List Last updated: July 20, 2005
BLAS Routines
LEVEL 1
SINGLE
SROTG - setup Givens rotation
SROTMG - setup modified Givens rotation
SROT - apply Givens rotation
SROTM - apply modified Givens rotation
SSWAP - swap x and y
SSCAL - x = a*x
SCOPY - copy x into y
SAXPY - y = a*x + y
SDOT - dot product
SDSDOT - dot product with extended precision accumulation
SNRM2 - Euclidean norm
SCNRM2- Euclidean norm
SASUM - sum of absolute values
ISAMAX - index of max abs value
DOUBLE
DROTG - setup Givens rotation
Wolf forms 2 2 1 – create php web forms. DROTMG - setup modified Givens rotation
DROT - apply Givens rotation
DROTM - apply modified Givens rotation
DSWAP - swap x and y
DSCAL - x = a*x
DCOPY - copy x into y
DAXPY - y = a*x + y Boom 3d 1 3 4 player games.
DDOT - dot product
DSDOT - dot product with extended precision accumulation
DNRM2 - Euclidean norm
DZNRM2 - Euclidean norm
DASUM - sum of absolute values
IDAMAX - index of max abs value
COMPLEX
CROTG - setup Givens rotation
CSROT - apply Givens rotation
CSWAP - swap x and y
CSCAL - x = a*x
CSSCAL - x = a*x
CCOPY - copy x into y
CAXPY - y = a*x + y
CDOTU - dot product
CDOTC - dot product, conjugating the first vector
SCASUM - sum of absolute values
ICAMAX - index of max abs value
DOUBLE COMLPEX
ZROTG - setup Givens rotation
ZDROTF - apply Givens rotation
ZSWAP - swap x and y
ZSCAL - x = a*x
ZDSCAL - x = a*x
ZCOPY - copy x into y
ZAXPY - y = a*x + y
ZDOTU - dot product
ZDOTC - dot product, conjugating the first vector
DZASUM - sum of absolute values
IZAMAX - index of max abs value
Motrix Mac
LEVEL 2
Single
SGEMV - matrix vector multiply
SGBMV - banded matrix vector multiply
SSYMV - symmetric matrix vector multiply
SSBMV - symmetric banded matrix vector multiply
SSPMV - symmetric packed matrix vector multiply
STRMV - triangular matrix vector multiply
STBMV - triangular banded matrix vector multiply
STPMV - triangular packed matrix vector multiply
STRSV - solving triangular matrix problems
STBSV - solving triangular banded matrix problems
STPSV - solving triangular packed matrix problems
SGER - performs the rank 1 operation A := alpha*x*y' + A
SSYR - performs the symmetric rank 1 operation A := alpha*x*x' + A
SSPR - symmetric packed rank 1 operation A := alpha*x*x' + A
SSYR2 - performs the symmetric rank 2 operation, A := alpha*x*y' + alpha*y*x' + A
SSPR2 - performs the symmetric packed rank 2 operation, A := alpha*x*y' + alpha*y*x' + A
Double
DGEMV - matrix vector multiply
DGBMV - banded matrix vector multiply
DSYMV - symmetric matrix vector multiply
DSBMV - symmetric banded matrix vector multiply
DSPMV - symmetric packed matrix vector multiply
DTRMV - triangular matrix vector multiply
DTBMV - triangular banded matrix vector multiply
DTPMV - triangular packed matrix vector multiply
DTRSV - solving triangular matrix problems
DTBSV - solving triangular banded matrix problems
DTPSV - solving triangular packed matrix problems
DGER - performs the rank 1 operation A := alpha*x*y' + A
DSYR - performs the symmetric rank 1 operation A := alpha*x*x' + A
DSPR - symmetric packed rank 1 operation A := alpha*x*x' + A
DSYR2 - performs the symmetric rank 2 operation, A := alpha*x*y' + alpha*y*x' + A
DSPR2 - performs the symmetric packed rank 2 operation, A := alpha*x*y' + alpha*y*x' + A
Complex
CGEMV - matrix vector multiply
CGBMV - banded matrix vector multiply
CHEMV - hermitian matrix vector multiply
CHBMV - hermitian banded matrix vector multiply
CHPMV - hermitian packed matrix vector multiply
CTRMV - triangular matrix vector multiply
CTBMV - triangular banded matrix vector multiply
CTPMV - triangular packed matrix vector multiply
CTRSV - solving triangular matrix problems
CTBSV - solving triangular banded matrix problems
CTPSV - solving triangular packed matrix problems
CGERU - performs the rank 1 operation A := alpha*x*y' + A
CGERC - performs the rank 1 operation A := alpha*x*conjg( y' ) + A
CHER - hermitian rank 1 operation A := alpha*x*conjg(x') + A
CHPR - hermitian packed rank 1 operation A := alpha*x*conjg( x' ) + A
CHER2 - hermitian rank 2 operation
CHPR2 - hermitian packed rank 2 operation
Double Complex
ZGEMV - matrix vector multiply
ZGBMV - banded matrix vector multiply
ZHEMV - hermitian matrix vector multiply
ZHBMV - hermitian banded matrix vector multiply
ZHPMV - hermitian packed matrix vector multiply
ZTRMV - triangular matrix vector multiply
ZTBMV - triangular banded matrix vector multiply
ZTPMV - triangular packed matrix vector multiply
ZTRSV - solving triangular matrix problems
ZTBSV - solving triangular banded matrix problems
ZTPSV - solving triangular packed matrix problems
ZGERU - performs the rank 1 operation A := alpha*x*y' + A
ZGERC - performs the rank 1 operation A := alpha*x*conjg( y' ) + A
ZHER - hermitian rank 1 operation A := alpha*x*conjg(x') + A
ZHPR - hermitian packed rank 1 operation A := alpha*x*conjg( x' ) + A
ZHER2 - hermitian rank 2 operation
ZHPR2 - hermitian packed rank 2 operation
LEVEL 3
Single
SGEMM - matrix matrix multiply
SSYMM - symmetric matrix matrix multiply
SSYRK - symmetric rank-k update to a matrix
SSYR2K - symmetric rank-2k update to a matrix
STRMM - triangular matrix matrix multiply
STRSM - solving triangular matrix with multiple right hand sides
Double
DGEMM - matrix matrix multiply
DSYMM - symmetric matrix matrix multiply
DSYRK - symmetric rank-k update to a matrix
DSYR2K - symmetric rank-2k update to a matrix
DTRMM - triangular matrix matrix multiply
DTRSM - solving triangular matrix with multiple right hand sides
Complex
CGEMM - matrix matrix multiply
CSYMM - symmetric matrix matrix multiply
CHEMM - hermitian matrix matrix multiply
CSYRK - symmetric rank-k update to a matrix
CHERK - hermitian rank-k update to a matrix
CSYR2K - symmetric rank-2k update to a matrix
CHER2K - hermitian rank-2k update to a matrix
CTRMM - triangular matrix matrix multiply
CTRSM - solving triangular matrix with multiple right hand sides
Double Complex
ZGEMM - matrix matrix multiply
ZSYMM - symmetric matrix matrix multiply
ZHEMM - hermitian matrix matrix multiply
ZSYRK - symmetric rank-k update to a matrix
ZHERK - hermitian rank-k update to a matrix
ZSYR2K - symmetric rank-2k update to a matrix
ZHER2K - hermitian rank-2k update to a matrix
ZTRMM - triangular matrix matrix multiply
ZTRSM - solving triangular matrix with multiple right hand sides
Extended precision Level 2 BLAS routines
SUBROUTINE ECGEMV ( TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY )
SUBROUTINE ECGBMV ( TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, BETA, Y, INCY )
SUBROUTINE ECHEMV ( UPLO, N, ALPHA, A, LDA, X, INCX,BETA, Y, INCY )
SUBROUTINE ECHBMV ( UPLO, N, K, ALPHA, A, LDA, X, INCX,BETA, Y, INCY )
SUBROUTINE ECHPMV ( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY )
SUBROUTINE ECTRMV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX )
SUBROUTINE ECTBMV ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX )
SUBROUTINE ECTPMV ( UPLO, TRANS, DIAG, N, AP, X, INCX )
SUBROUTINE ECTRSV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX )
SUBROUTINE ECTBSV ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX )
SUBROUTINE ECTPSV ( UPLO, TRANS, DIAG, N, AP, X, INCX )
SUBROUTINE ECGERU ( M, N, ALPHA, X, INCX, Y, INCY, A, LDA )
SUBROUTINE ECGERC ( M, N, ALPHA, X, INCX, Y, INCY, A, LDA )
SUBROUTINE ECHER ( UPLO, N, ALPHA, X, INCX, A, LDA )
SUBROUTINE ECHPR ( UPLO, N, ALPHA, X, INCX, AP )
SUBROUTINE ECHER2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA )
SUBROUTINE ECHPR2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, AP )
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