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
Softenv Keys for lapack on supermike2
Machine | Version | Softenv Key |
---|---|---|
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.
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.
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
The command softenv will provide a list of available packages. The listing will look something like:
$ 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 ... some stuff deleted ...
Managing 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
The command soft can be used to manipulate the environment from the command line. It takes the form:
$ soft add/delete +keyword
Using this method of adding or removing keywords requires the user to pay attention to possible order dependencies. That is, best results require the user to remove keywords in the reverse order in which they were added. It is handy to test out individual keys, but can lead to trouble if changing multiple keys. Changing the .soft file and issuing the resoft is the recommended way of dealing with multiple changes.
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.