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lapack

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 philip
Machine Version Module Name
None Available N/A N/A
▶ 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):

  1. ~/.bash_profile (anything sent to STDOUT or STDERR will cause things like rsync to break)
  2. ~/.bashrc (interactive login only)
  3. ~/.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]
 **********************************************/
#include 

extern 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]
 **********************************************/
#include 

extern 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: June 12 2015 16:24:59.