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* [[Media:Frontiers_of_HPC_Unified_Parallel_C.pdf|Unified Parallel C (UPC)]] (slides: overview/usage/examples)
 
* [[Media:Frontiers_of_HPC_Unified_Parallel_C.pdf|Unified Parallel C (UPC)]] (slides: overview/usage/examples)
 
* [[Using R and MPI]]
 
* [[Using R and MPI]]
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* [[Media:Parallel_Numerical_Solution_of_PDEs_with_Message_Passing.pdf|Parallel Numerical Solution of PDEs with Message Passing]] (article/tutorial)
 
 
* [[Using CRAY POINTERS in a FORTRAN 90 PROGRAM]]
 
* [[Using CRAY POINTERS in a FORTRAN 90 PROGRAM]]
 
* [[Reading from c BINARY_FILES generated by a fortran program]]
 
* [[Reading from c BINARY_FILES generated by a fortran program]]

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SOFTWARE PACKAGES USAGE

LAPACK

Solve Linear System Ax=b

As an example of using LAPACK let's consider the following identity of linear equations of order 6:

\mathbf \begin{bmatrix} 3.0 &-1. & 0.0 & 0.0 & 0.0 & 1.0 \\ -1. & 3.0 &-1. & 0.0 & 1.0 & 0.0 \\ 0.0 & -1. & 3.0 & 0.0 & 0.0 & 0.0 \\ 0.0 & 0.0 & 0.0 & 3.0 & -1. & 0.0 \\ 0.0 & 1.0 & 0.0 & -1. & 3.0 &-1. \\ 1.0 & 0.0 & 0.0 & 0.0 & -1. & 3.0 \end{bmatrix} \begin{bmatrix} 1.0 \\ 2.0 \\ 3.0 \\ 4.0 \\ 5.0 \\ 6.0 \\ \end{bmatrix} = \begin{bmatrix} 7.0 \\ 7.0 \\ 7.0 \\ 7.0 \\ 7.0 \\ 14.0 \\ \end{bmatrix}

If we write the above identity with following symbols:

Ax = b

and assume that x is unknown, then we can try to solve for x using some LAPACK subroutine. Here is how we proceed:

  • Find out what LAPACK subroutine solves the system of linear equations:
Ax = b
(subroutine dgesv is what we need).
  • Write a fortran program which defines A, b and calls dgesv to solve for x
!  file_name = solve.f90

      program solve_N6
!
!     This program solves Ax=B using LAPACK subroutine dgesv
!     A is a double precision 6 by 6 matrix defined in the program.
!     B is a double precision vector of length 6 also defined in the program.
!
      implicit none
      integer info, N, nrhs, lda, ldb
      parameter (N=6, nrhs=1, lda=N, ldb=N)
      double precision A(N,N), B(ldb,nrhs)
      integer indx(N)

      integer i, j
!
!     Defined matrix A:

      data A / 3. , -1. ,  0. ,  0. ,  0. ,  1. ,                       &
     &        -1. ,  3. , -1. ,  0. ,  1. ,  0. ,                       &
     &         0. , -1. ,  3. ,  0. ,  0. ,  0. ,                       &
     &         0. ,  0. ,  0. ,  3. , -1. ,  0. ,                       &
     &         0. ,  1. ,  0. , -1. ,  3. , -1. ,                       &
     &         1. ,  0. ,  0. ,  0. , -1. ,  3.      / 


      data B / 7. ,  7. ,  7. ,  7. ,  7. , 14. /
!
      print *,"N = ", N
      print *,"A = "
      print *,A
      print *,"B = "
      print *,B
      print *," "

      call dgesv( N, nrhs, A, lda, indx, B, ldb, info )
!
!   Parameters of dgesv
!
!   N  is the matrix size, N >= 1 . (input)
!
!   nhrs is the number of Right Sides to be solved
!          --here 1 (input)
!
!    A is the matrix in Ax = B, overwritten on output by
!         L and U -- where L*U = A (rows permuted)
!         A is double precision N by N , but with leading
!         dimension lda >= N .
!         A is input, but is different on output (in/out) .
!
!    lda is the leading dimension of A.  lda >= N .
!
!    indx , integer array dimension N, indx(i)
!      was interchanged with the ith row of A.    (output)
!
!    B  , double precision array of dimension (ldb,nhrs)
!        On input it is the right hand side(s) B, on output
!        it is the solution vector(s) x.   (in/out)
!
!    info integer, output info = 0 indicates a successful exit
!                 info <= -i, the ith argument was illegal.
!                 info = i means u(i,i) was zero so factorization
!                    not completed.
!
      print *,"X = "
      print *,B

      stop
      end
  • Write a makefile named Makefile to compile, link, and submit a job to the batch system
Make sure to include the ACML library for intel by issuing the command:
module load acml/ifort/4.4.0

before using the makefile Makefile: 

# file_name = Makefile
# Makefile for solve.f90

ROOTDIR  = $(shell pwd)

SRC = solve.f90
OBJ = $(SRC:.f90=.o)

LIBS = $(LDFLAGS) -lacml

TARGET = solve_exec

OUTPUTFILE=FORTRAN_LAPACK_SOLVE

all: $(TARGET)

$(TARGET): $(OBJ)
        $(FC) -o $@ $(CPPFLAGS) $(OBJ) $(LIBS)

$(OBJ): ${SRC}
        $(FC) $(FFLAGS) -c ${SRC}

help:;  @echo " "
        @echo "USAGE: "
        @echo "make help       To get this listing"
        @echo "make            To compile the FORTRAN LAPACK program in current environment"
        @echo "make subjob     To submit the executable to a batch queue using sqsub"
        @echo "make clean      Remove *.o and executable files"
        @echo "make list       List the compilers in current environment"
        @echo " "

list:
        @echo
        @echo "ROOTDIR:     $(ROOTDIR)"
        @echo "FC Compiler: $(FC)"
        @echo "FFLAGS:      $(FFLAGS)"
        @echo "LDFLAGS:     $(LDFLAGS)"
        @echo "OUTPUT FILE: $(OUTPUTFILE)"
        @echo " "
        @echo "LD_LIBRARY_PATH: " $(LD_LIBRARY_PATH)

clean:
        @echo "Removing *.o and executable files"
        rm -rf *.o $(TARGET)

subjob:;
        rm -rf $(OUTPUTFILE)
        sqsub -t -r 1h --mpp=2.0G  -o ${CLU}_$(OUTPUTFILE) -n 1 ./$(TARGET)

For more details on the identity of linear equations of any order N, see:

https://www.sharcnet.ca/help/index.php/Solving_Systems_of_Sparse_Linear_Equations

Also, you can find more information on modules and make utility and makefiles in the following two references:

https://www.sharcnet.ca/help/index.php/Configuring_your_software_environment_with_Modules

https://www.sharcnet.ca/help/index.php/Make_utility_and_makefiles

ScaLAPACK

PETSc_SLEPc

R

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