DXML(3dxml) — Subroutines

Digital

Name

dxml − A library of linear algebra and signal processing routines

Description

Digital Extended Math Library (DXML) for Digital UNIX is a set of computationally intensive mathematical subroutines that is optimized for Alpha AXP platforms. DXML includes four component libraries covering the areas of:

•Basic Linear Algebra (BLAS): includes array-math, BLAS 1, BLAS 1E, BLAS 1S, BLAS 2 and BLAS 3.

•Linear and Eigen System Solvers (LAPACK)

•Sparse Linear System Solvers: includes direct and iterative solvers

•Signal Processing: includes FFTs, cos/sin transforms, convolution, correlations and digital filters

Most routines are available in both real and complex versions, as well as in both single and double precision.

Further details about DXML are provided in the manpages for the following sub-components:

Sub-componentFunction

array-math (3dxml)Standard math functions operating on arrays

blas1 (3dxml)Vector-vector linear algebra subprograms

blas1e (3dxml)Enhancements to BLAS 1

blas1s (3dxml)Sparse version of BLAS 1

blas2 (3dxml)Matrix-vector linear algebra subprograms

blas3 (3dxml)Matrix-matrix linear algebra subprograms

lapack (3dxml)Dense linear system solvers and eigensolvers

iterative-solvers (3dxml)Sparse iterative linear system solvers

skyline-solvers (3dxml)Direct solver for skyline matrices

signal-processing (3dxml)FFTs, cos/sin transforms, convolution, correlation, filters

random-numbers (3dxml)Random number generator subprograms

sorts (3dxml)Sort subprograms

Parallel routines

DXML includes a parallel version of the library for SMP configuration. The parallel library contains the exact same set of subroutines with the same name and calling standards with a subset of the routines parallelized to take advantage of additional CPUs. The following routines are parallelized in this version of DXML:

{S,D,C,Z}GEMV BLAS2

{S,D,C,Z}GEMM BLAS3

{S,D,C,Z}GETRF LAPACK
{S,D,C,Z}POTRF

{S,D,C,Z}FFT Signal Processing - 1D
{S,D,C,Z}FFT_APPLY
{S,D,C,Z}FFT_INIT
{S,D,C,Z}FFT_EXIT

{S,D,C,Z}FFT_2D Signal Processing - 2D
{S,D,C,Z}FFT_INIT_2D
{S,D,C,Z}FFT_APPLY_2D
{S,D,C,Z}FFT_EXIT_2D

{S,D,C,Z}FFT_3D Signal Processing - 3D
{S,D,C,Z}FFT_INIT_3D
{S,D,C,Z}FFT_APPLY_3D
{S,D,C,Z}FFT_EXIT_3D

DITSOL_DRIVER Iterative Solvers

DITSOL_PBCG
DITSOL_PCG
DITSOL_PCGS
DITSOL_PGMRES
DITSOL_PLSCG
DITSOL_PTFQMR

DMATVEC_GENR
DMATVEC_SDIA
DMATVEC_UDIA

DCREATE_DIAG_GENR
DCREATE_DIAG_SDIA
DCREATE_DIAG_UDIA

DAPPLY_DIAG_ALL

DCREATE_POLY_GENR
DCREATE_POLY_SDIA
DCREATE_POLY_UDIA

DAPPLY_POLY_GENR
DAPPLY_POLY_SDIA
DAPPLY_POLY_UDIA

DSSKYF Skyline Solvers
DUSKYF

Linking with DXML

To compile and link a Fortran program, my_prog.f, that contains calls to DXML routines:

f77 my_prog.f -ldxml

To compile and link a C program, my_prog.c, that contains calls to DXML routines:

cc -migrate my_prog.c -ldxml

By using the -migrate flag you take advantage of the DEC C compilation environment.

To compile and link a Fortran program with the parallel version of DXML:

f77 my_prog.f -ldxmlp

Executing parallel programs

Before executing programs linked with the parallel version of DXML two environment variables need to be set.

The PARALLEL environment variable must be set to a numeric value defining the number of threads to be used. The number of parallel threads is usually equal to the number of processors on the system.

The KMP_STACKSIZE environment variable must be set to a numeric value. KMP_STACKSIZE defines the size of each thread’s private stack. The value must be at least 262144 which defines a 256K byte private stack.

Eg.

> setenv PARALLEL 3

> setenv KMP_STACKSIZE 262144