Actual source code: test10.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: */

     11: static char help[] = "Tests multiple calls to NEPSolve() with different matrix size.\n\n"
     12:   "The command line options are:\n"
     13:   "  -n <n>, where <n> = number of grid subdivisions.\n"
     14:   "  -tau <tau>, where <tau> is the delay parameter.\n"
     15:   "  -split <0/1>, to select the split form in the problem definition (enabled by default).\n";

     17: /* Based on ex22.c (delay) */

     19: #include <slepcnep.h>

     21: /*
     22:    User-defined application context
     23: */
     24: typedef struct {
     25:   PetscScalar tau;
     26:   PetscReal   a;
     27: } ApplicationCtx;

     29: /*
     30:    Create problem matrices in split form
     31: */
     32: PetscErrorCode BuildSplitMatrices(PetscInt n,PetscReal a,Mat *Id,Mat *A,Mat *B)
     33: {
     34:   PetscInt       i,Istart,Iend;
     35:   PetscReal      h,xi;
     36:   PetscScalar    b;

     38:   PetscFunctionBeginUser;
     39:   h = PETSC_PI/(PetscReal)(n+1);

     41:   /* Identity matrix */
     42:   PetscCall(MatCreateConstantDiagonal(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,1.0,Id));
     43:   PetscCall(MatSetOption(*Id,MAT_HERMITIAN,PETSC_TRUE));

     45:   /* A = 1/h^2*tridiag(1,-2,1) + a*I */
     46:   PetscCall(MatCreate(PETSC_COMM_WORLD,A));
     47:   PetscCall(MatSetSizes(*A,PETSC_DECIDE,PETSC_DECIDE,n,n));
     48:   PetscCall(MatSetFromOptions(*A));
     49:   PetscCall(MatGetOwnershipRange(*A,&Istart,&Iend));
     50:   for (i=Istart;i<Iend;i++) {
     51:     if (i>0) PetscCall(MatSetValue(*A,i,i-1,1.0/(h*h),INSERT_VALUES));
     52:     if (i<n-1) PetscCall(MatSetValue(*A,i,i+1,1.0/(h*h),INSERT_VALUES));
     53:     PetscCall(MatSetValue(*A,i,i,-2.0/(h*h)+a,INSERT_VALUES));
     54:   }
     55:   PetscCall(MatAssemblyBegin(*A,MAT_FINAL_ASSEMBLY));
     56:   PetscCall(MatAssemblyEnd(*A,MAT_FINAL_ASSEMBLY));
     57:   PetscCall(MatSetOption(*A,MAT_HERMITIAN,PETSC_TRUE));

     59:   /* B = diag(b(xi)) */
     60:   PetscCall(MatCreate(PETSC_COMM_WORLD,B));
     61:   PetscCall(MatSetSizes(*B,PETSC_DECIDE,PETSC_DECIDE,n,n));
     62:   PetscCall(MatSetFromOptions(*B));
     63:   PetscCall(MatGetOwnershipRange(*B,&Istart,&Iend));
     64:   for (i=Istart;i<Iend;i++) {
     65:     xi = (i+1)*h;
     66:     b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
     67:     PetscCall(MatSetValue(*B,i,i,b,INSERT_VALUES));
     68:   }
     69:   PetscCall(MatAssemblyBegin(*B,MAT_FINAL_ASSEMBLY));
     70:   PetscCall(MatAssemblyEnd(*B,MAT_FINAL_ASSEMBLY));
     71:   PetscCall(MatSetOption(*B,MAT_HERMITIAN,PETSC_TRUE));
     72:   PetscFunctionReturn(PETSC_SUCCESS);
     73: }

     75: /*
     76:    Compute Function matrix  T(lambda)
     77: */
     78: PetscErrorCode FormFunction(NEP nep,PetscScalar lambda,Mat fun,Mat B,void *ctx)
     79: {
     80:   ApplicationCtx *user = (ApplicationCtx*)ctx;
     81:   PetscInt       i,n,Istart,Iend;
     82:   PetscReal      h,xi;
     83:   PetscScalar    b;

     85:   PetscFunctionBeginUser;
     86:   PetscCall(MatGetSize(fun,&n,NULL));
     87:   h = PETSC_PI/(PetscReal)(n+1);
     88:   PetscCall(MatGetOwnershipRange(fun,&Istart,&Iend));
     89:   for (i=Istart;i<Iend;i++) {
     90:     if (i>0) PetscCall(MatSetValue(fun,i,i-1,1.0/(h*h),INSERT_VALUES));
     91:     if (i<n-1) PetscCall(MatSetValue(fun,i,i+1,1.0/(h*h),INSERT_VALUES));
     92:     xi = (i+1)*h;
     93:     b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
     94:     PetscCall(MatSetValue(fun,i,i,-lambda-2.0/(h*h)+user->a+PetscExpScalar(-user->tau*lambda)*b,INSERT_VALUES));
     95:   }
     96:   PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY));
     97:   PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY));
     98:   if (fun != B) {
     99:     PetscCall(MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY));
    100:     PetscCall(MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY));
    101:   }
    102:   PetscFunctionReturn(PETSC_SUCCESS);
    103: }

    105: /*
    106:    Compute Jacobian matrix  T'(lambda)
    107: */
    108: PetscErrorCode FormJacobian(NEP nep,PetscScalar lambda,Mat jac,void *ctx)
    109: {
    110:   ApplicationCtx *user = (ApplicationCtx*)ctx;
    111:   PetscInt       i,n,Istart,Iend;
    112:   PetscReal      h,xi;
    113:   PetscScalar    b;

    115:   PetscFunctionBeginUser;
    116:   PetscCall(MatGetSize(jac,&n,NULL));
    117:   h = PETSC_PI/(PetscReal)(n+1);
    118:   PetscCall(MatGetOwnershipRange(jac,&Istart,&Iend));
    119:   for (i=Istart;i<Iend;i++) {
    120:     xi = (i+1)*h;
    121:     b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
    122:     PetscCall(MatSetValue(jac,i,i,-1.0-user->tau*PetscExpScalar(-user->tau*lambda)*b,INSERT_VALUES));
    123:   }
    124:   PetscCall(MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY));
    125:   PetscCall(MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY));
    126:   PetscFunctionReturn(PETSC_SUCCESS);
    127: }

    129: int main(int argc,char **argv)
    130: {
    131:   NEP            nep;             /* nonlinear eigensolver context */
    132:   Mat            Id,A,B,J,F;      /* problem matrices */
    133:   FN             f1,f2,f3;        /* functions to define the nonlinear operator */
    134:   ApplicationCtx ctx;             /* user-defined context */
    135:   Mat            mats[3];
    136:   FN             funs[3];
    137:   PetscScalar    coeffs[2];
    138:   PetscInt       n=128;
    139:   PetscReal      tau=0.001,a=20;
    140:   PetscBool      split=PETSC_TRUE;

    142:   PetscFunctionBeginUser;
    143:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
    144:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
    145:   PetscCall(PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL));
    146:   PetscCall(PetscOptionsGetBool(NULL,NULL,"-split",&split,NULL));
    147:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%" PetscInt_FMT ", tau=%g\n\n",n,(double)tau));

    149:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    150:               Create nonlinear eigensolver and set options
    151:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    153:   PetscCall(NEPCreate(PETSC_COMM_WORLD,&nep));
    154:   PetscCall(NEPSetTolerances(nep,1e-9,PETSC_CURRENT));

    156:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    157:                       First solve
    158:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    160:   if (split) {
    161:     PetscCall(BuildSplitMatrices(n,a,&Id,&A,&B));
    162:     /* f1=-lambda */
    163:     PetscCall(FNCreate(PETSC_COMM_WORLD,&f1));
    164:     PetscCall(FNSetType(f1,FNRATIONAL));
    165:     coeffs[0] = -1.0; coeffs[1] = 0.0;
    166:     PetscCall(FNRationalSetNumerator(f1,2,coeffs));
    167:     /* f2=1.0 */
    168:     PetscCall(FNCreate(PETSC_COMM_WORLD,&f2));
    169:     PetscCall(FNSetType(f2,FNRATIONAL));
    170:     coeffs[0] = 1.0;
    171:     PetscCall(FNRationalSetNumerator(f2,1,coeffs));
    172:     /* f3=exp(-tau*lambda) */
    173:     PetscCall(FNCreate(PETSC_COMM_WORLD,&f3));
    174:     PetscCall(FNSetType(f3,FNEXP));
    175:     PetscCall(FNSetScale(f3,-tau,1.0));
    176:     mats[0] = A;  funs[0] = f2;
    177:     mats[1] = Id; funs[1] = f1;
    178:     mats[2] = B;  funs[2] = f3;
    179:     PetscCall(NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN));
    180:   } else {
    181:     /* callback form  */
    182:     ctx.tau = tau;
    183:     ctx.a   = a;
    184:     PetscCall(MatCreate(PETSC_COMM_WORLD,&F));
    185:     PetscCall(MatSetSizes(F,PETSC_DECIDE,PETSC_DECIDE,n,n));
    186:     PetscCall(MatSetFromOptions(F));
    187:     PetscCall(MatSeqAIJSetPreallocation(F,3,NULL));
    188:     PetscCall(MatMPIAIJSetPreallocation(F,3,NULL,1,NULL));
    189:     PetscCall(NEPSetFunction(nep,F,F,FormFunction,&ctx));
    190:     PetscCall(MatCreate(PETSC_COMM_WORLD,&J));
    191:     PetscCall(MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,n,n));
    192:     PetscCall(MatSetFromOptions(J));
    193:     PetscCall(MatSeqAIJSetPreallocation(J,3,NULL));
    194:     PetscCall(MatMPIAIJSetPreallocation(F,3,NULL,1,NULL));
    195:     PetscCall(NEPSetJacobian(nep,J,FormJacobian,&ctx));
    196:   }

    198:   /* Set solver parameters at runtime */
    199:   PetscCall(NEPSetFromOptions(nep));

    201:   /* Solve the eigensystem */
    202:   PetscCall(NEPSolve(nep));
    203:   PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL));

    205:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    206:                Second solve, with problem matrices of size 2*n
    207:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    209:   n *= 2;
    210:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%" PetscInt_FMT ", tau=%g\n\n",n,(double)tau));
    211:   if (split) {
    212:     PetscCall(MatDestroy(&Id));
    213:     PetscCall(MatDestroy(&A));
    214:     PetscCall(MatDestroy(&B));
    215:     PetscCall(BuildSplitMatrices(n,a,&Id,&A,&B));
    216:     mats[0] = A;
    217:     mats[1] = Id;
    218:     mats[2] = B;
    219:     PetscCall(NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN));
    220:   } else {
    221:     /* callback form  */
    222:     PetscCall(MatDestroy(&F));
    223:     PetscCall(MatDestroy(&J));
    224:     PetscCall(MatCreate(PETSC_COMM_WORLD,&F));
    225:     PetscCall(MatSetSizes(F,PETSC_DECIDE,PETSC_DECIDE,n,n));
    226:     PetscCall(MatSetFromOptions(F));
    227:     PetscCall(MatSeqAIJSetPreallocation(F,3,NULL));
    228:     PetscCall(MatMPIAIJSetPreallocation(F,3,NULL,1,NULL));
    229:     PetscCall(NEPSetFunction(nep,F,F,FormFunction,&ctx));
    230:     PetscCall(MatCreate(PETSC_COMM_WORLD,&J));
    231:     PetscCall(MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,n,n));
    232:     PetscCall(MatSetFromOptions(J));
    233:     PetscCall(MatSeqAIJSetPreallocation(J,3,NULL));
    234:     PetscCall(MatMPIAIJSetPreallocation(F,3,NULL,1,NULL));
    235:     PetscCall(NEPSetJacobian(nep,J,FormJacobian,&ctx));
    236:   }

    238:   /* Solve the eigensystem */
    239:   PetscCall(NEPSolve(nep));
    240:   PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL));

    242:   PetscCall(NEPDestroy(&nep));
    243:   if (split) {
    244:     PetscCall(MatDestroy(&Id));
    245:     PetscCall(MatDestroy(&A));
    246:     PetscCall(MatDestroy(&B));
    247:     PetscCall(FNDestroy(&f1));
    248:     PetscCall(FNDestroy(&f2));
    249:     PetscCall(FNDestroy(&f3));
    250:   } else {
    251:     PetscCall(MatDestroy(&F));
    252:     PetscCall(MatDestroy(&J));
    253:   }
    254:   PetscCall(SlepcFinalize());
    255:   return 0;
    256: }

    258: /*TEST

    260:    testset:
    261:       nsize: 2
    262:       requires: !single
    263:       output_file: output/test10_1.out
    264:       test:
    265:          suffix: 1
    266:          args: -nep_type narnoldi -nep_target 0.55
    267:       test:
    268:          suffix: 1_rii
    269:          args: -nep_type rii -nep_target 0.55 -nep_rii_hermitian -split {{0 1}}
    270:       test:
    271:          suffix: 1_narnoldi
    272:          args: -nep_type narnoldi -nep_target 0.55 -nep_narnoldi_lag_preconditioner 2
    273:       test:
    274:          suffix: 1_slp
    275:          args: -nep_type slp -nep_slp_st_pc_type redundant -split {{0 1}}
    276:       test:
    277:          suffix: 1_interpol
    278:          args: -nep_type interpol -rg_type interval -rg_interval_endpoints .5,1,-.1,.1 -nep_target .7 -nep_interpol_st_pc_type redundant
    279:       test:
    280:          suffix: 1_narnoldi_sync
    281:          args: -nep_type narnoldi -ds_parallel synchronized

    283:    testset:
    284:       args: -nep_nev 2 -rg_type interval -rg_interval_endpoints .5,15,-.1,.1 -nep_target .7
    285:       requires: !single
    286:       output_file: output/test10_2.out
    287:       filter: sed -e "s/[+-]0\.0*i//g"
    288:       test:
    289:          suffix: 2_interpol
    290:          args: -nep_type interpol -nep_interpol_pep_type jd -nep_interpol_st_pc_type sor
    291:       test:
    292:          suffix: 2_nleigs
    293:          args: -nep_type nleigs -split {{0 1}}
    294:          requires: complex
    295:       test:
    296:          suffix: 2_nleigs_real
    297:          args: -nep_type nleigs -rg_interval_endpoints .5,15 -split {{0 1}}
    298:          requires: !complex

    300:    test:
    301:       suffix: 3
    302:       requires: complex !single
    303:       args: -nep_type ciss -rg_type ellipse -rg_ellipse_center 10 -rg_ellipse_radius 9.5 -rg_ellipse_vscale 0.1 -split {{0 1}}
    304:       timeoutfactor: 2

    306: TEST*/