Date: 2015-09-03T15:05:13+00:00

Actual source code: ex6f.F
slepc-3.6.1 2015-09-03
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      1: !  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      2: !  SLEPc - Scalable Library for Eigenvalue Problem Computations
      3: !  Copyright (c) 2002-2015, Universitat Politecnica de Valencia, Spain
      4: !
      5: !  This file is part of SLEPc.
      6: !
      7: !  SLEPc is free software: you can redistribute it and/or modify it under  the
      8: !  terms of version 3 of the GNU Lesser General Public License as published by
      9: !  the Free Software Foundation.
     10: !
     11: !  SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
     12: !  WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
     13: !  FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
     14: !  more details.
     15: !
     16: !  You  should have received a copy of the GNU Lesser General  Public  License
     17: !  along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
     18: !  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     19: !
     20: !  Program usage: mpirun -np n ex6f [-help] [-m <m>] [all SLEPc options]
     21: !
     22: !  Description: This example solves the eigensystem arising in the Ising
     23: !  model for ferromagnetic materials. The file mvmisg.f must be linked
     24: !  together. Information about the model can be found at the following
     25: !  site http://math.nist.gov/MatrixMarket/data/NEP
     26: !
     27: !  The command line options are:
     28: !    -m <m>, where <m> is the number of 2x2 blocks, i.e. matrix size N=2*m
     29: !
     30: ! ----------------------------------------------------------------------
     31: !
     32:       program main
     33:       implicit none

     35: #include <petsc/finclude/petscsys.h>
     36: #include <petsc/finclude/petscvec.h>
     37: #include <petsc/finclude/petscmat.h>
     38: #include <petsc/finclude/petscviewer.h>
     39: #include <slepc/finclude/slepcsys.h>
     40: #include <slepc/finclude/slepceps.h>

     42: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     43: !     Declarations
     44: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     45: !
     46: !  Variables:
     47: !     A     operator matrix
     48: !     eps   eigenproblem solver context

     50:       Mat            A
     51:       EPS            eps
     52:       EPSType        tname
     53:       PetscReal      tol
     54:       PetscInt       N, m
     55:       PetscInt       nev, maxit, its
     56:       PetscMPIInt    sz, rank
     57:       PetscErrorCode ierr
     58:       PetscBool      flg, terse

     60: !     This is the routine to use for matrix-free approach
     61: !
     62:       external MatIsing_Mult

     64: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     65: !     Beginning of program
     66: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

     68:       call SlepcInitialize(PETSC_NULL_CHARACTER,ierr)
     69: #if defined(PETSC_USE_COMPLEX)
     70:       write(*,*) 'This example requires real numbers.'
     71:       goto 999
     72: #endif
     73:       call MPI_Comm_size(PETSC_COMM_WORLD,sz,ierr)
     74:       call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)
     75:       if (sz .ne. 1) then
     76:          if (rank .eq. 0) then
     77:             write(*,*) 'This is a uniprocessor example only!'
     78:          endif
     79:          SETERRQ(PETSC_COMM_WORLD,1,' ',ierr)
     80:       endif
     81:       m = 30
     82:       call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-m',m,flg,ierr)
     83:       N = 2*m

     85:       if (rank .eq. 0) then
     86:         write(*,*)
     87:         write(*,'(A,I6,A)') 'Ising Model Eigenproblem, m=',m,', (N=2*m)'
     88:         write(*,*)
     89:       endif

     91: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     92: !     Register the matrix-vector subroutine for the operator that defines
     93: !     the eigensystem, Ax=kx
     94: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

     96:       call MatCreateShell(PETSC_COMM_WORLD,N,N,N,N,PETSC_NULL_OBJECT,   &
     97:      &                    A,ierr)
     98:       call MatShellSetOperation(A,MATOP_MULT,MatIsing_Mult,ierr)

    100: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    101: !     Create the eigensolver and display info
    102: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    104: !     ** Create eigensolver context
    105:       call EPSCreate(PETSC_COMM_WORLD,eps,ierr)

    107: !     ** Set operators. In this case, it is a standard eigenvalue problem
    108:       call EPSSetOperators(eps,A,PETSC_NULL_OBJECT,ierr)
    109:       call EPSSetProblemType(eps,EPS_NHEP,ierr)

    111: !     ** Set solver parameters at runtime
    112:       call EPSSetFromOptions(eps,ierr)

    114: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    115: !     Solve the eigensystem
    116: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    118:       call EPSSolve(eps,ierr)
    119:       call EPSGetIterationNumber(eps,its,ierr)
    120:       if (rank .eq. 0) then
    121:         write(*,'(A,I4)') ' Number of iterations of the method: ', its
    122:       endif

    124: !     ** Optional: Get some information from the solver and display it
    125:       call EPSGetType(eps,tname,ierr)
    126:       if (rank .eq. 0) then
    127:         write(*,'(A,A)') ' Solution method: ', tname
    128:       endif
    129:       call EPSGetDimensions(eps,nev,PETSC_NULL_INTEGER,                 &
    130:      &                      PETSC_NULL_INTEGER,ierr)
    131:       if (rank .eq. 0) then
    132:         write(*,'(A,I2)') ' Number of requested eigenvalues:', nev
    133:       endif
    134:       call EPSGetTolerances(eps,tol,maxit,ierr)
    135:       if (rank .eq. 0) then
    136:         write(*,'(A,1PE10.4,A,I6)') ' Stopping condition: tol=', tol,   &
    137:      &                              ', maxit=', maxit
    138:       endif

    140: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    141: !     Display solution and clean up
    142: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    144: !     ** show detailed info unless -terse option is given by user
    145:       call PetscOptionsHasName(PETSC_NULL_CHARACTER,'-terse',terse,ierr)
    146:       if (terse) then
    147:         call EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_NULL_OBJECT,ierr)
    148:       else
    149:         call PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,           &
    150:      &                   PETSC_VIEWER_ASCII_INFO_DETAIL,ierr)
    151:         call EPSReasonView(eps,PETSC_VIEWER_STDOUT_WORLD,ierr)
    152:         call EPSErrorView(eps,EPS_ERROR_RELATIVE,                       &
    153:      &                   PETSC_VIEWER_STDOUT_WORLD,ierr)
    154:         call PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD,ierr)
    155:       endif
    156:       call EPSDestroy(eps,ierr)
    157:       call MatDestroy(A,ierr)

    159: #if defined(PETSC_USE_COMPLEX)
    160:  999  continue
    161: #endif
    162:       call SlepcFinalize(ierr)
    163:       end

    165: ! -------------------------------------------------------------------
    166: !
    167: !   MatIsing_Mult - user provided matrix-vector multiply
    168: !
    169: !   Input Parameters:
    170: !   A - matrix
    171: !   x - input vector
    172: !
    173: !   Output Parameter:
    174: !   y - output vector
    175: !
    176:       subroutine MatIsing_Mult(A,x,y,ierr)
    177:       implicit none

    179: #include <petsc/finclude/petscsys.h>
    180: #include <petsc/finclude/petscvec.h>
    181: #include <petsc/finclude/petscmat.h>

    183:       Mat            A
    184:       Vec            x,y
    185:       PetscInt       trans,one,N
    186:       PetscScalar    x_array(1),y_array(1)
    187:       PetscOffset    i_x,i_y
    188:       PetscErrorCode ierr

    190: !     The actual routine for the matrix-vector product
    191:       external mvmisg

    193:       call MatGetSize(A,N,PETSC_NULL_INTEGER,ierr)
    194:       call VecGetArrayRead(x,x_array,i_x,ierr)
    195:       call VecGetArray(y,y_array,i_y,ierr)

    197:       trans = 0
    198:       one = 1
    199:       call mvmisg(trans,N,one,x_array(i_x+1),N,y_array(i_y+1),N)

    201:       call VecRestoreArrayRead(x,x_array,i_x,ierr)
    202:       call VecRestoreArray(y,y_array,i_y,ierr)

    204:       return
    205:       end

    207: ! -------------------------------------------------------------------
    208: !     The actual routine for the matrix-vector product
    209: !     See http://math.nist.gov/MatrixMarket/data/NEP/mvmisg/mvmisg.html

    211:       SUBROUTINE MVMISG( TRANS, N, M, X, LDX, Y, LDY )
    212: !     ..
    213: !     .. Scalar Arguments ..
    214:       PetscInt     LDY, LDX, M, N, TRANS
    215: !     ..
    216: !     .. Array Arguments ..
    217:       PetscScalar  Y( LDY, * ), X( LDX, * )
    218: !     ..
    219: !
    220: !  Purpose
    221: !  =======
    222: !
    223: !  Compute
    224: !
    225: !               Y(:,1:M) = op(A)*X(:,1:M)
    226: !
    227: !  where op(A) is A or A' (the transpose of A). The A is the Ising
    228: !  matrix.
    229: !
    230: !  Arguments
    231: !  =========
    232: !
    233: !  TRANS   (input) INTEGER
    234: !          If TRANS = 0, compute Y(:,1:M) = A*X(:,1:M)
    235: !          If TRANS = 1, compute Y(:,1:M) = A'*X(:,1:M)
    236: !
    237: !  N       (input) INTEGER
    238: !          The order of the matrix A. N has to be an even number.
    239: !
    240: !  M       (input) INTEGER
    241: !          The number of columns of X to multiply.
    242: !
    243: !  X       (input) DOUBLE PRECISION array, dimension ( LDX, M )
    244: !          X contains the matrix (vectors) X.
    245: !
    246: !  LDX     (input) INTEGER
    247: !          The leading dimension of array X, LDX >= max( 1, N )
    248: !
    249: !  Y       (output) DOUBLE PRECISION array, dimension (LDX, M )
    250: !          contains the product of the matrix op(A) with X.
    251: !
    252: !  LDY     (input) INTEGER
    253: !          The leading dimension of array Y, LDY >= max( 1, N )
    254: !
    255: !  ===================================================================
    256: !
    257: !
    258: #include <petsc/finclude/petscsys.h>

    260: !     .. Local Variables ..
    261:       PetscInt    I, K
    262:       PetscReal   ALPHA, BETA
    263:       PetscReal   COSA, COSB, SINA
    264:       PetscReal   SINB, TEMP, TEMP1
    265: !
    266: !     .. Intrinsic functions ..
    267:       INTRINSIC   COS, SIN
    268: !
    269:       ALPHA = PETSC_PI/4
    270:       BETA = PETSC_PI/4
    271:       COSA = COS( ALPHA )
    272:       SINA = SIN( ALPHA )
    273:       COSB = COS( BETA )
    274:       SINB = SIN( BETA )
    275: !
    276:       IF ( TRANS.EQ.0 ) THEN
    277: !
    278: !     Compute Y(:,1:M) = A*X(:,1:M)

    280:          DO 30 K = 1, M
    281: !
    282:             Y( 1, K ) = COSB*X( 1, K ) - SINB*X( N, K )
    283:             DO 10 I = 2, N-1, 2
    284:                Y( I, K )   =  COSB*X( I, K ) + SINB*X( I+1, K )
    285:                Y( I+1, K ) = -SINB*X( I, K ) + COSB*X( I+1, K )
    286:    10       CONTINUE
    287:             Y( N, K ) = SINB*X( 1, K ) + COSB*X( N, K )
    288: !
    289:             DO 20 I = 1, N, 2
    290:                TEMP        =  COSA*Y( I, K ) + SINA*Y( I+1, K )
    291:                Y( I+1, K ) = -SINA*Y( I, K ) + COSA*Y( I+1, K )
    292:                Y( I, K )   = TEMP
    293:    20       CONTINUE
    294: !
    295:    30    CONTINUE
    296: !
    297:       ELSE IF ( TRANS.EQ.1 ) THEN
    298: !
    299: !        Compute Y(:1:M) = A'*X(:,1:M)
    300: !
    301:          DO 60 K = 1, M
    302: !
    303:             DO 40 I = 1, N, 2
    304:                Y( I, K )   =  COSA*X( I, K ) - SINA*X( I+1, K )
    305:                Y( I+1, K ) =  SINA*X( I, K ) + COSA*X( I+1, K )
    306:    40       CONTINUE
    307:             TEMP  = COSB*Y(1,K) + SINB*Y(N,K)
    308:             DO 50 I = 2, N-1, 2
    309:                TEMP1       =  COSB*Y( I, K ) - SINB*Y( I+1, K )
    310:                Y( I+1, K ) =  SINB*Y( I, K ) + COSB*Y( I+1, K )
    311:                Y( I, K )   =  TEMP1
    312:    50       CONTINUE
    313:             Y( N, K ) = -SINB*Y( 1, K ) + COSB*Y( N, K )
    314:             Y( 1, K ) = TEMP
    315: !
    316:    60    CONTINUE
    317: !
    318:       END IF
    319: !
    320:       RETURN
    321: !
    322: !     END OF MVMISG
    323:       END