Actual source code: pdde_stability.c

      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.
      7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
      8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      9: */
     10: /*
     11:    This example implements one of the problems found at
     12:        NLEVP: A Collection of Nonlinear Eigenvalue Problems,
     13:        The University of Manchester.
     14:    The details of the collection can be found at:
     15:        [1] T. Betcke et al., "NLEVP: A Collection of Nonlinear Eigenvalue
     16:            Problems", ACM Trans. Math. Software 39(2), Article 7, 2013.

     18:    The pdde_stability problem is a complex-symmetric QEP from the stability
     19:    analysis of a discretized partial delay-differential equation. It requires
     20:    complex scalars.
     21: */

     23: static char help[] = "Stability analysis of a discretized partial delay-differential equation.\n\n"
     24:   "The command line options are:\n"
     25:   "  -m <m>, grid size, the matrices have dimension n=m*m.\n"
     26:   "  -c <a0,b0,a1,b1,a2,b2,phi1>, comma-separated list of 7 real parameters.\n\n";

     28: #include <slepcpep.h>

     30: #define NMAT 3

     32: /*
     33:     Function for user-defined eigenvalue ordering criterion.

     35:     Given two eigenvalues ar+i*ai and br+i*bi, the subroutine must choose
     36:     one of them as the preferred one according to the criterion.
     37:     In this example, the preferred value is the one with absolute value closest to 1.
     38: */
     39: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx)
     40: {
     41:   PetscReal aa,ab;

     43:   PetscFunctionBeginUser;
     44:   aa = PetscAbsReal(SlepcAbsEigenvalue(ar,ai)-PetscRealConstant(1.0));
     45:   ab = PetscAbsReal(SlepcAbsEigenvalue(br,bi)-PetscRealConstant(1.0));
     46:   *r = aa > ab ? 1 : (aa < ab ? -1 : 0);
     47:   PetscFunctionReturn(PETSC_SUCCESS);
     48: }

     50: int main(int argc,char **argv)
     51: {
     52:   Mat            A[NMAT];         /* problem matrices */
     53:   PEP            pep;             /* polynomial eigenproblem solver context */
     54:   PetscInt       m=15,n,II,Istart,Iend,i,j,k;
     55:   PetscReal      h,xi,xj,c[7] = { 2, .3, -2, .2, -2, -.3, -PETSC_PI/2 };
     56:   PetscScalar    alpha,beta,gamma;
     57:   PetscBool      flg,terse;

     59:   PetscFunctionBeginUser;
     60:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
     61: #if !defined(PETSC_USE_COMPLEX)
     62:   SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"This example requires complex scalars");
     63: #endif

     65:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL));
     66:   n = m*m;
     67:   h = PETSC_PI/(m+1);
     68:   gamma = PetscExpScalar(PETSC_i*c[6]);
     69:   gamma = gamma/PetscAbsScalar(gamma);
     70:   k = 7;
     71:   PetscCall(PetscOptionsGetRealArray(NULL,NULL,"-c",c,&k,&flg));
     72:   PetscCheck(!flg || k==7,PETSC_COMM_WORLD,PETSC_ERR_USER,"The number of parameters -c should be 7, you provided %" PetscInt_FMT,k);
     73:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nPDDE stability, n=%" PetscInt_FMT " (m=%" PetscInt_FMT ")\n\n",n,m));

     75:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     76:                      Compute the polynomial matrices
     77:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     79:   /* initialize matrices */
     80:   for (i=0;i<NMAT;i++) {
     81:     PetscCall(MatCreate(PETSC_COMM_WORLD,&A[i]));
     82:     PetscCall(MatSetSizes(A[i],PETSC_DECIDE,PETSC_DECIDE,n,n));
     83:     PetscCall(MatSetFromOptions(A[i]));
     84:   }
     85:   PetscCall(MatGetOwnershipRange(A[0],&Istart,&Iend));

     87:   /* A[1] has a pattern similar to the 2D Laplacian */
     88:   for (II=Istart;II<Iend;II++) {
     89:     i = II/m; j = II-i*m;
     90:     xi = (i+1)*h; xj = (j+1)*h;
     91:     alpha = c[0]+c[1]*PetscSinReal(xi)+gamma*(c[2]+c[3]*xi*(1.0-PetscExpReal(xi-PETSC_PI)));
     92:     beta = c[0]+c[1]*PetscSinReal(xj)-gamma*(c[2]+c[3]*xj*(1.0-PetscExpReal(xj-PETSC_PI)));
     93:     PetscCall(MatSetValue(A[1],II,II,alpha+beta-4.0/(h*h),INSERT_VALUES));
     94:     if (j>0) PetscCall(MatSetValue(A[1],II,II-1,1.0/(h*h),INSERT_VALUES));
     95:     if (j<m-1) PetscCall(MatSetValue(A[1],II,II+1,1.0/(h*h),INSERT_VALUES));
     96:     if (i>0) PetscCall(MatSetValue(A[1],II,II-m,1.0/(h*h),INSERT_VALUES));
     97:     if (i<m-1) PetscCall(MatSetValue(A[1],II,II+m,1.0/(h*h),INSERT_VALUES));
     98:   }

    100:   /* A[0] and A[2] are diagonal */
    101:   for (II=Istart;II<Iend;II++) {
    102:     i = II/m; j = II-i*m;
    103:     xi = (i+1)*h; xj = (j+1)*h;
    104:     alpha = c[4]+c[5]*xi*(PETSC_PI-xi);
    105:     beta = c[4]+c[5]*xj*(PETSC_PI-xj);
    106:     PetscCall(MatSetValue(A[0],II,II,alpha,INSERT_VALUES));
    107:     PetscCall(MatSetValue(A[2],II,II,beta,INSERT_VALUES));
    108:   }

    110:   /* assemble matrices */
    111:   for (i=0;i<NMAT;i++) PetscCall(MatAssemblyBegin(A[i],MAT_FINAL_ASSEMBLY));
    112:   for (i=0;i<NMAT;i++) PetscCall(MatAssemblyEnd(A[i],MAT_FINAL_ASSEMBLY));

    114:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    115:                 Create the eigensolver and solve the problem
    116:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    118:   PetscCall(PEPCreate(PETSC_COMM_WORLD,&pep));
    119:   PetscCall(PEPSetOperators(pep,NMAT,A));
    120:   PetscCall(PEPSetEigenvalueComparison(pep,MyEigenSort,NULL));
    121:   PetscCall(PEPSetDimensions(pep,4,PETSC_DETERMINE,PETSC_DETERMINE));
    122:   PetscCall(PEPSetFromOptions(pep));
    123:   PetscCall(PEPSolve(pep));

    125:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    126:                     Display solution and clean up
    127:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    129:   /* show detailed info unless -terse option is given by user */
    130:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
    131:   if (terse) PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL));
    132:   else {
    133:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
    134:     PetscCall(PEPConvergedReasonView(pep,PETSC_VIEWER_STDOUT_WORLD));
    135:     PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD));
    136:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
    137:   }
    138:   PetscCall(PEPDestroy(&pep));
    139:   for (i=0;i<NMAT;i++) PetscCall(MatDestroy(&A[i]));
    140:   PetscCall(SlepcFinalize());
    141:   return 0;
    142: }

    144: /*TEST

    146:    build:
    147:       requires: complex

    149:    test:
    150:       suffix: 1
    151:       args: -pep_type {{toar qarnoldi linear}} -pep_ncv 25 -terse
    152:       requires: complex double

    154: TEST*/