Date: 2015-09-03T15:05:49+00:00

Actual source code: pdde_stability.c
slepc-3.6.1 2015-09-03
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2015, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.

      8:    SLEPc is free software: you can redistribute it and/or modify it under  the
      9:    terms of version 3 of the GNU Lesser General Public License as published by
     10:    the Free Software Foundation.

     12:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
     13:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
     14:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
     15:    more details.

     17:    You  should have received a copy of the GNU Lesser General  Public  License
     18:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
     19:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     20: */
     21: /*
     22:    This example implements one of the problems found at
     23:        NLEVP: A Collection of Nonlinear Eigenvalue Problems,
     24:        The University of Manchester.
     25:    The details of the collection can be found at:
     26:        [1] T. Betcke et al., "NLEVP: A Collection of Nonlinear Eigenvalue
     27:            Problems", ACM Trans. Math. Software 39(2), Article 7, 2013.

     29:    The pdde_stability problem is a complex-symmetric QEP from the stability
     30:    analysis of a discretized partial delay-differential equation. It requires
     31:    complex scalars.
     32: */

     34: static char help[] = "NLEVP problem: pdde_stability.\n\n"
     35:   "The command line options are:\n"
     36:   "  -m <m>, grid size, the matrices have dimension n=m*m.\n"
     37:   "  -c <a0,b0,a1,b1,a2,b2,phi1>, comma-separated list of 7 real parameters.\n\n";

     39: #include <slepcpep.h>

     41: #define NMAT 3

     45: /*
     46:     Function for user-defined eigenvalue ordering criterion.

     48:     Given two eigenvalues ar+i*ai and br+i*bi, the subroutine must choose
     49:     one of them as the preferred one according to the criterion.
     50:     In this example, the preferred value is the one with absolute value closest to 1.
     51: */
     52: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx)
     53: {
     54:   PetscReal aa,ab;

     57:   aa = PetscAbsReal(SlepcAbsEigenvalue(ar,ai)-1.0);
     58:   ab = PetscAbsReal(SlepcAbsEigenvalue(br,bi)-1.0);
     59:   *r = aa > ab ? 1 : (aa < ab ? -1 : 0);
     60:   return(0);
     61: }

     65: int main(int argc,char **argv)
     66: {
     67:   Mat            A[NMAT];         /* problem matrices */
     68:   PEP            pep;             /* polynomial eigenproblem solver context */
     69:   PetscInt       m=15,n,II,Istart,Iend,i,j,k;
     70:   PetscReal      h,xi,xj,c[7] = { 2, .3, -2, .2, -2, -.3, -PETSC_PI/2 };
     71:   PetscScalar    alpha,beta,gamma;
     72:   PetscBool      flg,terse;

     75:   SlepcInitialize(&argc,&argv,(char*)0,help);
     76: #if !defined(PETSC_USE_COMPLEX)
     77:   SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP, "This example requires complex scalars");
     78: #endif

     80:   PetscOptionsGetInt(NULL,"-m",&m,NULL);
     81:   n = m*m;
     82:   h = PETSC_PI/(m+1);
     83:   gamma = PetscExpScalar(PETSC_i*c[6]);
     84:   gamma = gamma/PetscAbsScalar(gamma);
     85:   k = 7;
     86:   PetscOptionsGetRealArray(NULL,"-c",c,&k,&flg);
     87:   if (flg && k!=7) SETERRQ1(PETSC_COMM_WORLD,1,"The number of parameters -c should be 7, you provided %D",k);
     88:   PetscPrintf(PETSC_COMM_WORLD,"\nPDDE stability, n=%D (m=%D)\n\n",n,m);

     90:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     91:                      Compute the polynomial matrices
     92:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     94:   /* initialize matrices */
     95:   for (i=0;i<NMAT;i++) {
     96:     MatCreate(PETSC_COMM_WORLD,&A[i]);
     97:     MatSetSizes(A[i],PETSC_DECIDE,PETSC_DECIDE,n,n);
     98:     MatSetFromOptions(A[i]);
     99:     MatSetUp(A[i]);
    100:   }
    101:   MatGetOwnershipRange(A[0],&Istart,&Iend);

    103:   /* A[1] has a pattern similar to the 2D Laplacian */
    104:   for (II=Istart;II<Iend;II++) {
    105:     i = II/m; j = II-i*m;
    106:     xi = (i+1)*h; xj = (j+1)*h;
    107:     alpha = c[0]+c[1]*PetscSinReal(xi)+gamma*(c[2]+c[3]*xi*(1.0-PetscExpReal(xi-PETSC_PI)));
    108:     beta = c[0]+c[1]*PetscSinReal(xj)-gamma*(c[2]+c[3]*xj*(1.0-PetscExpReal(xj-PETSC_PI)));
    109:     MatSetValue(A[1],II,II,alpha+beta-4.0/(h*h),INSERT_VALUES);
    110:     if (j>0) { MatSetValue(A[1],II,II-1,1.0/(h*h),INSERT_VALUES); }
    111:     if (j<m-1) { MatSetValue(A[1],II,II+1,1.0/(h*h),INSERT_VALUES); }
    112:     if (i>0) { MatSetValue(A[1],II,II-m,1.0/(h*h),INSERT_VALUES); }
    113:     if (i<m-1) { MatSetValue(A[1],II,II+m,1.0/(h*h),INSERT_VALUES); }
    114:   }

    116:   /* A[0] and A[2] are diagonal */
    117:   for (II=Istart;II<Iend;II++) {
    118:     i = II/m; j = II-i*m;
    119:     xi = (i+1)*h; xj = (j+1)*h;
    120:     alpha = c[4]+c[5]*xi*(PETSC_PI-xi);
    121:     beta = c[4]+c[5]*xj*(PETSC_PI-xj);
    122:     MatSetValue(A[0],II,II,alpha,INSERT_VALUES);
    123:     MatSetValue(A[2],II,II,beta,INSERT_VALUES);
    124:   }
    125:
    126:   /* assemble matrices */
    127:   for (i=0;i<NMAT;i++) {
    128:     MatAssemblyBegin(A[i],MAT_FINAL_ASSEMBLY);
    129:   }
    130:   for (i=0;i<NMAT;i++) {
    131:     MatAssemblyEnd(A[i],MAT_FINAL_ASSEMBLY);
    132:   }

    134:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    135:                 Create the eigensolver and solve the problem
    136:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    138:   PEPCreate(PETSC_COMM_WORLD,&pep);
    139:   PEPSetOperators(pep,NMAT,A);
    140:   PEPSetEigenvalueComparison(pep,MyEigenSort,NULL);
    141:   PEPSetDimensions(pep,4,PETSC_DEFAULT,PETSC_DEFAULT);
    142:   PEPSetFromOptions(pep);
    143:   PEPSolve(pep);

    145:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    146:                     Display solution and clean up
    147:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    148:
    149:   /* show detailed info unless -terse option is given by user */
    150:   PetscOptionsHasName(NULL,"-terse",&terse);
    151:   if (terse) {
    152:     PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL);
    153:   } else {
    154:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
    155:     PEPReasonView(pep,PETSC_VIEWER_STDOUT_WORLD);
    156:     PEPErrorView(pep,PEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD);
    157:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
    158:   }
    159:   PEPDestroy(&pep);
    160:   for (i=0;i<NMAT;i++) {
    161:     MatDestroy(&A[i]);
    162:   }
    163:   SlepcFinalize();
    164:   return 0;
    165: }