BLAS2
Level 2 Basic Linear Algebra Subprograms

BLAS2 is a FORTRAN77 library which implements the Level 2 BLAS, or Basic Linear Algebra Subprograms.

The BLAS are a small core library of linear algebra utilities, which can be highly optimized for various architectures. Software that relies on the BLAS is thus highly portable, and will typically run very efficiently.

The Level 2 BLAS are designed to handle a variety of matrix-vector operations.

Languages:

BLAS2 is available in a FORTRAN90 version and a FORTRAN77 version.

Related Data and Programs:

BLAS1, a FORTRAN77 library which handles vector-vector operations.

BLAS3, a FORTRAN77 library which handles matrix-matrix operations.

LAPACK_EXAMPLES, a FORTRAN77 program which demonstrates the use of the LAPACK linear algebra library.

LINPACK, a FORTRAN77 library which is a linear algebra package built on top of the BLAS.

Reference:

1. Edward Anderson, Zhaojun Bai, Christian Bischof, Susan Blackford, James Demmel, Jack Dongarra, Jeremy Du Croz, Anne Greenbaum, Sven Hammarling, Alan McKenney, Danny Sorensen,
   LAPACK User's Guide,
   Third Edition,
   SIAM, 1999,
   ISBN: 0898714478,
   LC: QA76.73.F25L36.
2. Thomas Coleman, Charles vanLoan,
   Handbook for Matrix Computations,
   SIAM, 1988,
   ISBN13: 978-0-898712-27-8,
   LC: QA188.C65.
3. Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart,
   LINPACK User's Guide,
   SIAM, 1979,
   ISBN13: 978-0-898711-72-1,
   LC: QA214.L56.
4. Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,
   Algorithm 539: Basic Linear Algebra Subprograms for Fortran Usage,
   ACM Transactions on Mathematical Software,
   Volume 5, Number 3, September 1979, pages 308-323.

Source Code:

• blas2.f, the vector code;
• blas2.sh, commands to compile the source code;

Examples and Tests:

• blas2_prb.f, a calling program;
• blas2_prb.sh, commands to compile, link, load and run the calling program;
• blas2_prb_output.txt, the sample output.

List of Routines:

• CGBMV SY:=alpha*A*SX+beta*SY, A a complex band matrix.
• CGEMV SY:=alpha*A*SX+beta*SY, A a complex rectangular matrix.
• CGERC A:=A+alpha*SX*CONJUGATE-TRANSPOSE(SY), rank 1 update, A a complex general matrix.
• CGERU A:=A+alpha*SX*TRANSPOSE(SY), rank 1 update, A a complex general matrix.
• CHBMV SY:=alpha*A*SX+beta*SY, A a complex Hermitian band matrix.
• CHEMV SY:=alpha*A*SX+beta*SY, A a complex Hermitian matrix.
• CHER A:=A+alpha*SX*TRANSPOSE(SX), A a complex Hermitian matrix.
• CHER2 A:=A+alpha*SX*TRANSPOSE(SY)+alpha*SY*TRANSPOSE(SX), A a complex Hermitian matrix.
• CHPMV SY:=alpha*A*SX+beta*SY, A a complex Hermitian packed matrix.
• CHPR A:=A+alpha*SX*TRANSPOSE(SX), A a complex Hermitian packed matrix.
• CHPR2 A:=A+alpha*SX*TRANSPOSE(SY)+alpha*SY*TRANSPOSE(SX), A complex Hermitian packed matrix.
• CSBMV SY:=alpha*A*SX+beta*SY, A a complex symmetric band matrix.
• CSPMV SY:=alpha*A*SX+beta*SY, A a packed complex symmetric matrix.
• CSPR A:=A+alpha*SX*TRANSPOSE(SX), A a complex symmetric packed matrix.
• CSPR2 A:=A+alpha*SX*TRANSPOSE(SY)+alpha*SY*TRANSPOSE(SX), A packed complex symmetric matrix.
• CSYMV SY:=alpha*A*SX+beta*SY, A a complex symmetric matrix.
• CSYR A:=A+alpha*SX*TRANSPOSE(SX), A a complex symmetric matrix.
• CSYR2 A:=A+alpha*SX*TRANSPOSE(SY)+alpha*SY*TRANSPOSE(SX), A complex symmetric matrix.
• CTBMV SX:=A*SX, A a complex triangular band matrix.
• CTBSV SX:=INVERSE(A)*SX, A a complex triangular band matrix.
• CTPMV SX:=A*SX, A a packed complex symmetric matrix.
• CTPSV SX:=INVERSE(A)*SX, A a packed complex symmetric matrix.
• CTRMV SX:=A*SX, A a complex triangular matrix.
• CTRSV SX:=INVERSE(A)*SX, A a complex triangular matrix.
• DGBMV SY:=alpha*A*SX+beta*SY, A a double precision band matrix.
• DGEMV SY:=alpha*A*SX+beta*SY, A a double precision rectangular matrix.
• DGER A:=A+alpha*SX*TRANSPOSE(SY), rank 1 update, A a double precision general matrix.
• DSBMV SY:=alpha*A*SX+beta*SY, A a double precision symmetric band matrix.
• DSPMV SY:=alpha*A*SX+beta*SY, A a packed double precision symmetric matrix.
• DSPR A:=A+alpha*SX*TRANSPOSE(SX), A a packed double precision symmetric matrix.
• DSPR2 A:=A+alpha*SX*TRANSPOSE(SY)+alpha*SY*TRANSPOSE(SX), A packed double precision symmetric matrix.
• DSYMV SY:=alpha*A*SX+beta*SY, A a double precision symmetric matrix.
• DSYR A:=A+alpha*SX*TRANSPOSE(SX), A a double precision symmetric matrix.
• DSYR2 A:=A+alpha*SX*TRANSPOSE(SY)+alpha*SY*TRANSPOSE(SX), A a double precision symmetric matrix.
• DTBMV SX:=A*SX, A a double precision triangular band matrix.
• DTBSV SX:=INVERSE(A)*SX, A a double precision triangular band matrix.
• DTPMV SX:=A*SX, A a packed double precision symmetric matrix.
• DTPSV SX:=INVERSE(A)*SX, A a packed double precision symmetric matrix.
• DTRMV SX:=A*SX, A a double precision triangular matrix.
• DTRSV SX:=INVERSE(A)*SX, A a double precision triangular matrix.
• SGBMV SY:=alpha*A*SX+beta*SY, A a real band matrix.
• SGEMV SY:=alpha*A*SX+beta*SY, A a real rectangular matrix.
• SGER A:=A+alpha*SX*TRANSPOSE(SY), rank 1 update, A a real general matrix.
• SSBMV SY:=alpha*A*SX+beta*SY, A a real symmetric band matrix.
• SSPMV SY:=alpha*A*SX+beta*SY, A a packed realn symmetric matrix.
• SSPR A:=A+alpha*SX*TRANSPOSE(SX), A a packed real symmetric matrix.
• SSPR2 A:=A+alpha*SX*TRANSPOSE(SY)+alpha*SY*TRANSPOSE(SX), A packed real symmetric matrix.
• SSYMV SY:=alpha*A*SX+beta*SY, A a real symmetric matrix.
• SSYR A:=A+alpha*SX*TRANSPOSE(SX), A a real symmetric matrix.
• SSYR2 A:=A+alpha*SX*TRANSPOSE(SY)+alpha*SY*TRANSPOSE(SX), A a real symmetric matrix.
• STBMV SX:=A*SX, A a real triangular band matrix.
• STBSV SX:=INVERSE(A)*SX, A a real triangular band matrix.
• STPMV SX:=A*SX, A a packed real symmetric matrix.
• STPSV SX:=INVERSE(A)*SX, A a packed real symmetric matrix.
• STRMV SX:=A*SX, A a real triangular matrix.
• STRSV SX:=INVERSE(A)*SX, A a real triangular matrix.
• ZGBMV SY:=alpha*A*SX+beta*SY, A a double complex band matrix.
• ZGEMV SY:=alpha*A*SX+beta*SY, A a double complex rectangular matrix.
• ZGERC A:=A+alpha*SX*CONJUGATE-TRANSPOSE(SY), rank 1 update, A a double complex general matrix.
• ZGERU A:=A+alpha*SX*TRANSPOSE(SY), rank 1 update, A a double complex general matrix.
• ZHBMV SY:=alpha*A*SX+beta*SY, A a double complex Hermitian band matrix.
• ZHEMV SY:=alpha*A*SX+beta*SY, A a double complex Hermitian matrix.
• ZHER A:=A+alpha*SX*TRANSPOSE(SX), A a double complex Hermitian matrix.
• ZHER2 A:=A+alpha*SX*TRANSPOSE(SY)+alpha*SY*TRANSPOSE(SX), A a double complex Hermitian matrix.
• ZHPMV SY:=alpha*A*SX+beta*SY, A a double complex Hermitian packed matrix.
• ZHPR A:=A+alpha*SX*TRANSPOSE(SX), A a double complex Hermitian packed matrix.
• ZHPR2 A:=A+alpha*SX*TRANSPOSE(SY)+alpha*SY*TRANSPOSE(SX), A double complex Hermitian packed matrix.
• ZSBMV SY:=alpha*A*SX+beta*SY, A a double complex symmetric band matrix.
• ZSPMV SY:=alpha*A*SX+beta*SY, A a packed double complex symmetric matrix.
• ZSPR A:=A+alpha*SX*TRANSPOSE(SX), A a double complex symmetric packed matrix.
• ZSPR2 A:=A+alpha*SX*TRANSPOSE(SY)+alpha*SY*TRANSPOSE(SX), A packed double complex symmetric matrix.
• ZSYMV SY:=alpha*A*SX+beta*SY, A a double complex symmetric matrix.
• ZSYR A:=A+alpha*SX*TRANSPOSE(SX), A a double complex symmetric matrix.
• ZSYR2 A:=A+alpha*SX*TRANSPOSE(SY)+alpha*SY*TRANSPOSE(SX), A double complex symmetric matrix.
• ZTBMV SX:=A*SX, A a double complex triangular band matrix.
• ZTBSV SX:=INVERSE(A)*SX, A a double complex triangular band matrix.
• ZTPMV SX:=A*SX, A a packed double complex symmetric matrix.
• ZTPSV SX:=INVERSE(A)*SX, A a packed double complex symmetric matrix.
• ZTRMV SX:=A*SX, A a double complex triangular matrix.
• ZTRSV SX:=INVERSE(A)*SX, A a double complex triangular matrix.

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