Date: 2026-03-31T13:23:25+00:00

Actual source code: test1.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[] = "Simple 1-D nonlinear eigenproblem.\n\n"
     12:   "This is a simplified version of ex20.\n"
     13:   "The command line options are:\n"
     14:   "  -n <n>, where <n> = number of grid subdivisions.\n";

     16: /*
     17:    Solve 1-D PDE
     18:             -u'' = lambda*u
     19:    on [0,1] subject to
     20:             u(0)=0, u'(1)=u(1)*lambda*kappa/(kappa-lambda)
     21: */

     23: #include <slepcnep.h>

     25: /*
     26:    User-defined routines
     27: */
     28: PetscErrorCode FormFunction(NEP,PetscScalar,Mat,Mat,void*);
     29: PetscErrorCode FormJacobian(NEP,PetscScalar,Mat,void*);

     31: /*
     32:    User-defined application context
     33: */
     34: typedef struct {
     35:   PetscScalar kappa;   /* ratio between stiffness of spring and attached mass */
     36:   PetscReal   h;       /* mesh spacing */
     37: } ApplicationCtx;

     39: int main(int argc,char **argv)
     40: {
     41:   NEP            nep;             /* nonlinear eigensolver context */
     42:   Mat            F,J;             /* Function and Jacobian matrices */
     43:   ApplicationCtx ctx;             /* user-defined context */
     44:   PetscInt       n=128;
     45:   PetscBool      terse;

     47:   PetscFunctionBeginUser;
     48:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
     49:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     50:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n1-D Nonlinear Eigenproblem, n=%" PetscInt_FMT "\n\n",n));
     51:   ctx.h = 1.0/(PetscReal)n;
     52:   ctx.kappa = 1.0;

     54:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     55:                Prepare nonlinear eigensolver context
     56:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     58:   PetscCall(NEPCreate(PETSC_COMM_WORLD,&nep));

     60:   /*
     61:      Create Function and Jacobian matrices; set evaluation routines
     62:   */

     64:   PetscCall(MatCreate(PETSC_COMM_WORLD,&F));
     65:   PetscCall(MatSetSizes(F,PETSC_DECIDE,PETSC_DECIDE,n,n));
     66:   PetscCall(MatSetFromOptions(F));
     67:   PetscCall(MatSeqAIJSetPreallocation(F,3,NULL));
     68:   PetscCall(MatMPIAIJSetPreallocation(F,3,NULL,1,NULL));
     69:   PetscCall(NEPSetFunction(nep,F,F,FormFunction,&ctx));

     71:   PetscCall(MatCreate(PETSC_COMM_WORLD,&J));
     72:   PetscCall(MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,n,n));
     73:   PetscCall(MatSetFromOptions(J));
     74:   PetscCall(MatSeqAIJSetPreallocation(J,3,NULL));
     75:   PetscCall(MatMPIAIJSetPreallocation(F,3,NULL,1,NULL));
     76:   PetscCall(NEPSetJacobian(nep,J,FormJacobian,&ctx));

     78:   PetscCall(NEPSetFromOptions(nep));

     80:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     81:                       Solve the eigensystem
     82:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     84:   PetscCall(NEPSolve(nep));

     86:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     87:                     Display solution and clean up
     88:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     90:   /* show detailed info unless -terse option is given by user */
     91:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
     92:   if (terse) PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL));
     93:   else {
     94:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
     95:     PetscCall(NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD));
     96:     PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
     97:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
     98:   }

    100:   PetscCall(NEPDestroy(&nep));
    101:   PetscCall(MatDestroy(&F));
    102:   PetscCall(MatDestroy(&J));
    103:   PetscCall(SlepcFinalize());
    104:   return 0;
    105: }

    107: /* ------------------------------------------------------------------- */
    108: /*
    109:    FormFunction - Computes Function matrix  T(lambda)

    111:    Input Parameters:
    112: .  nep    - the NEP context
    113: .  lambda - the scalar argument
    114: .  ctx    - optional user-defined context, as set by NEPSetFunction()

    116:    Output Parameters:
    117: .  fun - Function matrix
    118: .  B   - optionally different preconditioning matrix
    119: */
    120: PetscErrorCode FormFunction(NEP nep,PetscScalar lambda,Mat fun,Mat B,void *ctx)
    121: {
    122:   ApplicationCtx *user = (ApplicationCtx*)ctx;
    123:   PetscScalar    A[3],c,d;
    124:   PetscReal      h;
    125:   PetscInt       i,n,j[3],Istart,Iend;
    126:   PetscBool      FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;

    128:   PetscFunctionBeginUser;
    129:   /*
    130:      Compute Function entries and insert into matrix
    131:   */
    132:   PetscCall(MatGetSize(fun,&n,NULL));
    133:   PetscCall(MatGetOwnershipRange(fun,&Istart,&Iend));
    134:   if (Istart==0) FirstBlock=PETSC_TRUE;
    135:   if (Iend==n) LastBlock=PETSC_TRUE;
    136:   h = user->h;
    137:   c = user->kappa/(lambda-user->kappa);
    138:   d = n;

    140:   /*
    141:      Interior grid points
    142:   */
    143:   for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
    144:     j[0] = i-1; j[1] = i; j[2] = i+1;
    145:     A[0] = A[2] = -d-lambda*h/6.0; A[1] = 2.0*(d-lambda*h/3.0);
    146:     PetscCall(MatSetValues(fun,1,&i,3,j,A,INSERT_VALUES));
    147:   }

    149:   /*
    150:      Boundary points
    151:   */
    152:   if (FirstBlock) {
    153:     i = 0;
    154:     j[0] = 0; j[1] = 1;
    155:     A[0] = 2.0*(d-lambda*h/3.0); A[1] = -d-lambda*h/6.0;
    156:     PetscCall(MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES));
    157:   }

    159:   if (LastBlock) {
    160:     i = n-1;
    161:     j[0] = n-2; j[1] = n-1;
    162:     A[0] = -d-lambda*h/6.0; A[1] = d-lambda*h/3.0+lambda*c;
    163:     PetscCall(MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES));
    164:   }

    166:   /*
    167:      Assemble matrix
    168:   */
    169:   PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY));
    170:   PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY));
    171:   if (fun != B) {
    172:     PetscCall(MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY));
    173:     PetscCall(MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY));
    174:   }
    175:   PetscFunctionReturn(PETSC_SUCCESS);
    176: }

    178: /* ------------------------------------------------------------------- */
    179: /*
    180:    FormJacobian - Computes Jacobian matrix  T'(lambda)

    182:    Input Parameters:
    183: .  nep    - the NEP context
    184: .  lambda - the scalar argument
    185: .  ctx    - optional user-defined context, as set by NEPSetJacobian()

    187:    Output Parameters:
    188: .  jac - Jacobian matrix
    189: .  B   - optionally different preconditioning matrix
    190: */
    191: PetscErrorCode FormJacobian(NEP nep,PetscScalar lambda,Mat jac,void *ctx)
    192: {
    193:   ApplicationCtx *user = (ApplicationCtx*)ctx;
    194:   PetscScalar    A[3],c;
    195:   PetscReal      h;
    196:   PetscInt       i,n,j[3],Istart,Iend;
    197:   PetscBool      FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;

    199:   PetscFunctionBeginUser;
    200:   /*
    201:      Compute Jacobian entries and insert into matrix
    202:   */
    203:   PetscCall(MatGetSize(jac,&n,NULL));
    204:   PetscCall(MatGetOwnershipRange(jac,&Istart,&Iend));
    205:   if (Istart==0) FirstBlock=PETSC_TRUE;
    206:   if (Iend==n) LastBlock=PETSC_TRUE;
    207:   h = user->h;
    208:   c = user->kappa/(lambda-user->kappa);

    210:   /*
    211:      Interior grid points
    212:   */
    213:   for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
    214:     j[0] = i-1; j[1] = i; j[2] = i+1;
    215:     A[0] = A[2] = -h/6.0; A[1] = -2.0*h/3.0;
    216:     PetscCall(MatSetValues(jac,1,&i,3,j,A,INSERT_VALUES));
    217:   }

    219:   /*
    220:      Boundary points
    221:   */
    222:   if (FirstBlock) {
    223:     i = 0;
    224:     j[0] = 0; j[1] = 1;
    225:     A[0] = -2.0*h/3.0; A[1] = -h/6.0;
    226:     PetscCall(MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES));
    227:   }

    229:   if (LastBlock) {
    230:     i = n-1;
    231:     j[0] = n-2; j[1] = n-1;
    232:     A[0] = -h/6.0; A[1] = -h/3.0-c*c;
    233:     PetscCall(MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES));
    234:   }

    236:   /*
    237:      Assemble matrix
    238:   */
    239:   PetscCall(MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY));
    240:   PetscCall(MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY));
    241:   PetscFunctionReturn(PETSC_SUCCESS);
    242: }

    244: /*TEST

    246:    testset:
    247:       args: -nep_type {{rii slp}} -nep_target 21 -terse -nep_view_vectors ::ascii_info
    248:       filter: sed -e "s/\(0x[0-9a-fA-F]*\)/objectid/" | sed -e "s/[+-]0\.0*i//g"
    249:       test:
    250:          suffix: 1_real
    251:          requires: !single !complex
    252:       test:
    253:          suffix: 1
    254:          requires: !single complex

    256:    testset:
    257:       args: -nep_type {{rii slp}} -nep_target 21 -terse
    258:       filter: sed -e "s/[+-]0\.0*i//"
    259:       output_file: output/test3_1.out
    260:       test:
    261:          suffix: 2_cuda
    262:          args: -mat_type aijcusparse
    263:          requires: cuda !single
    264:       test:
    265:          suffix: 2_hip
    266:          args: -mat_type aijhipsparse
    267:          requires: hip !single

    269:    testset:
    270:       args: -nep_type slp -nep_two_sided -nep_target 21 -terse -nep_view_vectors ::ascii_info
    271:       filter: sed -e "s/\(0x[0-9a-fA-F]*\)/objectid/"
    272:       test:
    273:          suffix: 3_real
    274:          requires: !single !complex
    275:       test:
    276:          suffix: 3
    277:          requires: !single complex

    279: TEST*/