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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

Version and Availability

Softenv Keys for lapack on philip
Machine Version Softenv Key
philip 3.2 +lapack-3.2-intel-11.1
philip 3.2 +lapack-3.2-intel-11.1-mpich-1.2.7p1
philip 3.4.0 +lapack-3.4.0-gcc-4.1.2
philip 3.4.0 +lapack-3.4.0-gcc-4.3.2
philip 3.4.0 +lapack-3.4.0-intel-11.1
philip 3.4.0 +lapack-3.4.0-pgi-12.8
▶ Display Softenv Keys for lapack all clusters
Machine Version Softenv Key
eric 3.2 +lapack-3.2-intel-11.1
eric 3.2 +lapack-3.2-intel-11.1-mvapich-1.1
eric 3.2 +lapack-3.2-intel-11.1-mvapich2-1.4
qb 3.2 +lapack-3.2-gcc-4.3.2-mvapich-1.1
qb 3.2 +lapack-3.2-intel-11.1
qb 3.2 +lapack-3.2-intel-11.1-mvapich-1.1
qb 3.2 +lapack-3.2-intel-11.1-mvapich2-1.4
oliver 3.2 +lapack-3.2-intel-11.1
oliver 3.2 +lapack-3.2-intel-11.1-mvapich-1.1
oliver 3.2 +lapack-3.2-intel-11.1-mvapich2-1.4
louie 3.1.1 +lapack-3.1.1-gcc-3.4.6
louie 3.2 +lapack-3.2-intel-11.1
louie 3.2 +lapack-3.2-intel-11.1-mvapich-1.1
louie 3.2 +lapack-3.2-intel-11.1-mvapich2-1.4
poseidon 3.2 +lapack-3.2-intel-11.1
poseidon 3.2 +lapack-3.2-intel-11.1-mvapich-1.1
poseidon 3.2 +lapack-3.2-intel-11.1-mvapich2-1.4
painter 3.2 +lapack-3.2-intel-11.1
painter 3.2 +lapack-3.2-intel-11.1-mvapich-1.1
painter 3.2 +lapack-3.2-intel-11.1-mvapich2-1.4
philip 3.2 +lapack-3.2-intel-11.1
philip 3.2 +lapack-3.2-intel-11.1-mpich-1.2.7p1
philip 3.4.0 +lapack-3.4.0-gcc-4.1.2
philip 3.4.0 +lapack-3.4.0-gcc-4.3.2
philip 3.4.0 +lapack-3.4.0-intel-11.1
philip 3.4.0 +lapack-3.4.0-pgi-12.8
supermike2 3.4.0 +lapack-3.4.0-gcc-4.4.6
supermike2 3.4.0 +lapack-3.4.0-Intel-13.0.0
▶ Softenv FAQ?

The information here is applicable to LSU HPC and LONI systems.

Softenv

SoftEnv is a utility that is supposed to help users manage complex user environments with potentially conflicting application versions and libraries.

System Default Path

When a user logs in, the system /etc/profile or /etc/csh.cshrc (depending on login shell, and mirrored from csm:/cfmroot/etc/profile) calls /usr/local/packages/softenv-1.6.2/bin/use.softenv.sh to set up the default path via the SoftEnv database.

SoftEnv looks for a user's ~/.soft file and updates the variables and paths accordingly.

Viewing Available Packages

Using the softenv command, a user may view the list of available packages. Currently, it can not be ensured that the packages shown are actually available or working on the particular machine. Every attempt is made to present an identical environment on all of the LONI clusters, but sometimes this is not the case.

Example,

$ softenv
These are the macros available:
*   @default
These are the keywords explicitly available:
+amber-8                       Applications: 'Amber', version: 8 Amber is a
+apache-ant-1.6.5              Ant, Java based XML make system version: 1.6.
+charm-5.9                     Applications: 'Charm++', version: 5.9 Charm++
+default                       this is the default environment...nukes /etc/
+essl-4.2                      Libraries: 'ESSL', version: 4.2 ESSL is a sta
+gaussian-03                   Applications: 'Gaussian', version: 03 Gaussia
....
Listing of Available Packages

See Packages Available via SoftEnv on LSU HPC and LONI.

For a more accurate, up to date list, use the softenv command.

Caveats

Currently there are some caveats to using this tool.

  1. packages might be out of sync between what is listed and what is actually available
  2. resoft and soft utilities are not; to update the environment for now, log out and login after modifying the ~/.soft file.
Availability

softenv is available on all LSU HPC and LONI clusters to all users in both interactive login sessions (i.e., just logging into the machine) and the batch environment created by the PBS job scheduler on Linux clusters and by loadleveler on AIX clusters..

Packages Availability

This information can be viewed using the softenv command:

% softenv
Managing Environment with SoftEnv

The file ~/.soft in the user's home directory is where the different packages are managed. Add the +keyword into your .soft file. For instance, ff one wants to add the Amber Molecular Dynamics package into their environment, the end of the .soft file should look like this:

+amber-8

@default

To update the environment after modifying this file, one simply uses the resoft command:

% resoft

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 "C" 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

$ icpc lapack_test.C -llapack
$ ./a.out
 -0.677  -1.333
 -0.677   3.667
  1.000  -2.000

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: March 07 2013 12:30:04.