intro_blas3(3S)
INTRO_BLAS3 - Introduction to matrix-matrix linear algebra subprograms
As shipped in IRIX 6.5.15. Added in IRIX 6.5.15.
NAME INTRO_BLAS3 - Introduction to matrix-matrix linear algebra subprograms IMPLEMENTATION See individual man pages for operating system and hardware availability. DESCRIPTION The Level 3 Basic Linear Algebra Subprograms (Level 3 BLAS) consist of routines that perform matrix-matrix operations. These routines are written to run optimally on all SGI systems. The following data types are used in these routines: * Single precision: Fortran "real" data type, C/C++ "float" data type, 32-bit floating point; these routine names begin with S. * Single precision complex: Fortran "complex" data type, C/C++ "scsl_complex" data type (defined in <scsl_blas.h>), C++ STL "complex<float>" data type (defined in <complex.h>), two 32-bit floating point reals; these routine names begin with C. * Double precision: Fortran "double precision" data type, C/C++ "double" data type, 64-bit floating point; these routine names begin with D. * Double precision complex: Fortran "double complex" data type, C/C++ "scsl_zomplex" data type (defined in <scsl_blas.h>), C++ STL "complex<double>" data type (defined in <complex.h>), two 64-bit floating point doubles; these routine names begin with Z. Often little or no difference exists between these versions, other than the data types of some inputs and outputs. In this case, the routines are described on the same man page, and that man page is named after the single precision or single precision complex routine. NOTE: SCSL supports two different C interfaces to the BLAS: * The C interface described in this man page and in individual BLAS man pages follows the same conventions used for the C interface to the SCSL signal processing library. * SCSL also supports the C interface to the legacy BLAS set forth by the BLAS Technical Forum. This interface supports row-major storage of multidimensional arrays; see INTRO_CBLAS(3S) for details. By default, the integer arguments are 4 bytes (32 bits) in size; this is the size obtained when one links to the SCSL library with -lscs or -lscs_mp. Another version of SCSL is available, however, in which integers are 8 bytes (64 bits). This version allows the user access to larger memory sizes and helps when porting legacy Cray codes. It can be loaded by using either the -lscs_i8 or -lscs_i8_mp link option. Note that any program may use only one of the two versions; 4-byte integer and 8-byte integer library calls cannot be mixed. C/C++ function prototypes for Level 2 BLAS routines are provided in <scsl_blas.h>, when using the default 4-byte integers, and <scsl_blas_i8.h>, when using 8-byte integers. These header files define the complex types scsl_complex and scsl_zomplex, which are used in the prototypes. Alternatively, C++ programs may declare arguments using the types complex<float> and complex<double> from the standard template library. But if these types are used, <complex.h> must be included before <scsl_blas.h> (or <scsl_blas_i8.h>). Note, though, that both complex types are equivalent: they simply represent (real, imaginary) pairs of floating point numbers stored contiguously in memory. With the proper casts, you can simply pass arrays of floating point data to the routines where complex arguments are expected. Casts, however, can be avoided. The header files <scsl_blas.h> and <scsl_blas.h> directly support the use of user-defined complex types or disabling prototype checking for complex arguments completely. By defining the symbol SCSL_VOID_ARGS before including <scsl_blas.h> or <scsl_blas_i8.h> all complex arguments will be prototyped as void *. To define the symbol SCSL_VOID_ARGS at compile time use the -D compiler option (i.e., -DSCSL_VOID_ARGS) or use an explicit #define SCSL_VOID_ARGS in the source code. This allows the use of any complex data structure without warnings from the compiler, provided the structure is as described above; that is: 1. The real and imaginary components must be contiguous in memory. 2. Sequential array elements must also be contiguous in memory. While this allows the use of non-standard complex types without generating compiler warnings, it has the disadvantage that the compiler will not catch type mismatches. Strong type checking can be enabled employing user-defined complex types instead of SCSL's standard complex types. To do this, define SCSL_USER_COMPLEX_T=my_complex and SCSL_USER_ZOMPLEX_T=my_zomplex, where my_complex and my_zomplex are the names of user-defined complex types. These complex types must be defined before including the <scsl_blas.h> (or <scsl_blas_i8.h>) header file. Array Storage Multidimensoinal arrays passed as arguments to BLAS routines must be stored in column-major order, the storage convention used in Fortran programs. C and C++ users must explicitly store multidimensional arrays column-by-column. One way to do this is to reverse the order of array dimensions with respect to the Fortran declaration (e.g., x(ldx,n) in Fortran versus x[n][ldx] in C/C++). Because of the prototypes used in <scsl_blas.h>, the array should be cast as a pointer to the appropriate type when passed as an argument to a BLAS routine in order to avoid potential compiler type mismatch errors or warning messages. C and C++ users who want to employ row-major storage for multidimensional arrays when calling the BLAS routines should consult the INTRO_CBLAS(3S) man page. Man page naming The man(1) command can find a man page online by either the real, complex, double precision, or double complex name. The following table describes the naming conventions for these routines: ------------------------------------------------------------- Single Double Single Double Precision Precision Precision Precision Complex Complex ------------------------------------------------------------- form: Sname Dname Cname Zname example: SGEMM DGEMM CGEMM ZGEMM ------------------------------------------------------------- List of Level 3 Basic Linear The following list describes these routines. The list is in alphabetic order, except that a Hermitian matrix routine (any routine whose name begins with CH) is grouped next to equivalent symmetric matrix routines (whose names begin with SS or CS). This is because the Hermitian property is a type of symmetry. Each routine marked with an asterisk (*) is an extension to the standard set of Level 3 BLAS routines. * SGEMM, DGEMM, CGEMM, ZGEMM: Multiplies a real or complex general matrix by a real or complex general matrix. C <- alpha op(A)op(B) + beta C where op(X) = X or T op(X) = X or H op(X) = X (CGEMM/ZGEMM only) * CGEMM3M*, ZGEMM3M*: Multiplies a complex general matrix by a complex general matrix, using 3 real matrix multiplications and 5 matrix additions. C <- alpha op(A)op(B) + beta C where op(X) = X or T op(X) = X or H op(X) = X * DGEMMS*: Multiplies a double precision general matrix by a double precision general matrix, using a variation of Strassen's algorithm. C <- alpha op(A)op(B) + beta C where op(X) = X or T op(X) = X * SSYMM, DSYMM, CSYMM, ZSYMM: Multiplies a real or complex general matrix by a real or complex symmetric matrix. C <- alpha AB + beta C or C <- alpha BA + beta C * CHEMM, ZHEMM: Multiplies a complex general matrix by a Hermitian matrix. C <- alpha AB + beta C or C <- alpha BA + beta C * SSYR2K, DSYR2K, CSYR2K, ZSYR2K: Performs symmetric rank 2k update of a real or complex symmetric matrix. T T C <- alpha AB + alpha BA + beta C or T C <- alpha A B + alpha B A + beta C * CHER2K, ZHER2K: Performs Hermitian rank 2k update of a complex Hermitian matrix. H H C <- alpha AB + alpha BA + beta C or H H C <- alpha A B + alpha B A + beta C * SSYRK, DSYRK, CSYRK, ZSYRK: Performs symmetric rank k update of a real or complex symmetric matrix. T C <- alpha AA + beta C or T C <- alpha A A + beta C * CHERK, ZHERK: Performs Hermitian rank k update of a complex Hermitian matrix. H C <- alpha AA + beta C or H C <- alpha A A + beta C * STRMM, DTRMM, CTRMM, ZTRMM: Multiplies a real or complex general matrix by a real or complex triangular matrix. B <- alpha op(A)B or B <- alpha B op(A) where op(A) = A or T op(A) = A or H op(A) = A (CTRMM/ZTRMM only) * STRSM, DTRSM, CTRSM, ZTRSM: Solves a real or complex triangular system of equations with multiple right-hand sides. -1 B <- alpha op(A) B or -1 B <- alpha B op(A) where op(A) = A or T op(A) = A or H op(A) = A (CTRSM/ZTRSM only) NOTES SCSL does not currently support reshaped arrays. SEE ALSO Dongarra, J., J. Du Croz, I. Duff, and S. Hammarling,"A Set of Level 3 Basic Linear Algebra Subprograms," ACM Transactions on Mathematical Software, Vol. 16, No. 1, March 1990, pp. 1 - 17. INTRO_SCSL(3S), INTRO_BLAS1(3S), INTRO_BLAS2(3S), INTRO_CBLAS(3S)