lapack
Table of Content
About
LAPACK is a free package of linear algebra subroutines written in Fortran that can be used to solve:
- Systems of Linear equations
- Linear least squares problems
- Eigenvalue problems
- Singular value problems
- Associated Computations
- Matrix factorizations (LU, Cholesky, QR, SVD, Schur, generalized Schur)
- Reordering of the Schur factorizations
- Estimating condition numbers
- And much more . . .
LAPACK can be used for the following types of matrices:
- Dense and band (not general sparse matrices)
- Real and complex
- Single and double precision
Versions and Availability
Module Names for lapack on smic
Machine | Version | Module Name |
---|---|---|
smic | 3.4.2 | lapack/3.4.2/INTEL-140-MVAPICH2-2.0 |
▶ Module FAQ?
The information here is applicable to LSU HPC and LONI systems.
Shells
A user may choose between using /bin/bash and /bin/tcsh. Details about each shell follows.
/bin/bash
System resource file: /etc/profile
When one access the shell, the following user files are read in if they exist (in order):
- ~/.bash_profile (anything sent to STDOUT or STDERR will cause things like rsync to break)
- ~/.bashrc (interactive login only)
- ~/.profile
When a user logs out of an interactive session, the file ~/.bash_logout is executed if it exists.
The default value of the environmental variable, PATH, is set automatically using SoftEnv. See below for more information.
/bin/tcsh
The file ~/.cshrc is used to customize the user's environment if his login shell is /bin/tcsh.
Modules
Modules is a utility which helps users manage the complex business of setting up their shell environment in the face of potentially conflicting application versions and libraries.
Default Setup
When a user logs in, the system looks for a file named .modules in their home directory. This file contains module commands to set up the initial shell environment.
Viewing Available Modules
The command
$ module avail
displays a list of all the modules available. The list will look something like:
--- some stuff deleted --- velvet/1.2.10/INTEL-14.0.2 vmatch/2.2.2 ---------------- /usr/local/packages/Modules/modulefiles/admin ----------------- EasyBuild/1.11.1 GCC/4.9.0 INTEL-140-MPICH/3.1.1 EasyBuild/1.13.0 INTEL/14.0.2 INTEL-140-MVAPICH2/2.0 --- some stuff deleted ---
The module names take the form appname/version/compiler, providing the application name, the version, and information about how it was compiled (if needed).
Managing Modules
Besides avail, there are other basic module commands to use for manipulating the environment. These include:
add/load mod1 mod2 ... modn . . . Add modules rm/unload mod1 mod2 ... modn . . Remove modules switch/swap mod . . . . . . . . . Switch or swap one module for another display/show . . . . . . . . . . List modules loaded in the environment avail . . . . . . . . . . . . . . List available module names whatis mod1 mod2 ... modn . . . . Describe listed modules
The -h option to module will list all available commands.
Module is currently available only on SuperMIC.
Usage
LAPACK is a binary library, so it is linked to your program by the
compiler during the build process by adding the -llapack
flag to the link line:
Fortran
$ ifort sample.f -llapack
Open Fortran Example?
Fortran Source
!********************************************** ! THIS EXAMPLE USES THE LAPACK ROUTINE DGESV ! TO SOLVE A SYSTEM OF LINEAR EQUATIONS AX=B ! A = [1, 2, 3; 4, 5, 6; 7, 8 10] ! B = [1, 0; 0, 1; 0, 0] ! ********************************************* program lapack_test integer ipiv(3), info, i, j double precision A(3,3), B(3,2) A(1,1)=1 A(1,2)=2 A(1,3)=3 A(2,1)=4 A(2,2)=5 A(2,3)=6 A(3,1)=7 A(3,2)=8 A(3,3)=10 B(1,1)=1 B(2,1)=0 B(3,1)=0 B(1,2)=0 B(2,2)=1 B(3,2)=0 call dgesv (3,2,A,3,ipiv,B,3,info) if(info .EQ. 0) then do i=1,3 write(*,'(2F8.3)') (B(i,j), j=1,2) enddo endif end program lapack_test
Build and Execute
$ ifort lapack_test.f90 -llapack $ ./a.out -0.667 -1.333 -0.667 3.667 1.000 -2.000
C
The LAPACK routines must be declared with extern
,
the routine name must be in lowercase, and it must be followed by
an _ (i.e. underscore):
extern void dgetrf_(int*, int*, double*, int*, int*, int*);
Be sure when calling the LAPACK routing that all arguments are passed by reference.
Note: Since C matrices are stored in row major order, and Fortran matrices are stored in column major order, a transpose is necessary to go from C to Fortran order, and the result transposed again from Fortran to C order. It is more efficient to change the array indexing to take this into account.
$ icc sample.c -llapack
Open C Example?
C Source
$ cat lapack_test.c /********************************************** * THIS EXAMPLE USES THE LAPACK ROUTINE DGESV * TO SOLVE A SYSTEM OF LINEAR EQUATIONS AX=B * A = [1, 2, 3; 4, 5, 6; 7, 8 10] * B = [1, 0; 0, 1; 0, 0] **********************************************/ #includeextern void dgesv_(int*, int*, double*, int*, int*, double*, int*, int*); int main() { int n, nrhs, lda, ldb, IPIV[3], info, i; double A[3][3], B[2][3]; // Matrices must be transposed A[0][0] = 1; A[1][0] = 2; A[2][0] = 3; A[0][1] = 4; A[1][1] = 5; A[2][1] = 6; A[0][2] = 7; A[1][2] = 8; A[2][2] = 10; B[0][0] = 1; B[0][1] = 0; B[0][2] = 0; B[1][0] = 0; B[1][1] = 1; B[1][2] = 0; n = 3; nrhs = 2; lda = 3; ldb = 3; dgesv_(&n, &nrhs, (double *)A, &lda, IPIV, (double *)B, &ldb, &info); if(info == 0) { for(i = 0; i < 3; i++) printf("%8.3f %8.3f\n", B[0][i], B[1][i]); } }
Build and Execute
C++
The LAPACK routines must be declared with extern
"C"
, the routine name must be in lowercase, and it must
be followed by an _ (i.e. underscore):
extern "C" void dgetrf_(int*, int*, double*, int*, int*, int*);
Be sure when calling the LAPACK routing that all arguments are passed by reference.
Note: Since C++ matrices are stored in row major order, and Fortran matrices are stored in column major order, a transpose is necessary to go from C to Fortran order, and the result transposed again from Fortran to C order. It is more efficient to change the array indexing to take this into account.
$ icpc sample.c -llapack
Open C++ Example?
C Source
$ cat lapack_test.c /********************************************** * THIS EXAMPLE USES THE LAPACK ROUTINE DGESV * TO SOLVE A SYSTEM OF LINEAR EQUATIONS AX=B * A = [1, 2, 3; 4, 5, 6; 7, 8 10] * B = [1, 0; 0, 1; 0, 0] **********************************************/ #includeextern void dgesv_(int*, int*, double*, int*, int*, double*, int*, int*); int main() { int n, nrhs, lda, ldb, IPIV[3], info, i; double A[3][3], B[2][3]; // Matrices must be transposed A[0][0] = 1; A[1][0] = 2; A[2][0] = 3; A[0][1] = 4; A[1][1] = 5; A[2][1] = 6; A[0][2] = 7; A[1][2] = 8; A[2][2] = 10; B[0][0] = 1; B[0][1] = 0; B[0][2] = 0; B[1][0] = 0; B[1][1] = 1; B[1][2] = 0; n = 3; nrhs = 2; lda = 3; ldb = 3; dgesv_(&n, &nrhs, (double *)A, &lda, IPIV, (double *)B, &ldb, &info); if(info == 0) { for(i = 0; i < 3; i++) printf("%8.3f %8.3f\n", B[0][i], B[1][i]); } }
Build and Execute
Resources
- LAPACK Users Guide
- Individual LAPACK routines are documented in their own man page.
To get more information on a given routine, use the command:
$ man routine_name
For example, to get informantion on
dgesvd
:$ man dgesvd
Last modified: August 22 2017 15:10:53.