Date: 2022-03-31T15:29:33+00:00

Actual source code: test1.c
slepc-3.17.0 2022-03-31
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      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:   SlepcInitialize(&argc,&argv,(char*)0,help);
     48:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     49:   PetscPrintf(PETSC_COMM_WORLD,"\n1-D Nonlinear Eigenproblem, n=%" PetscInt_FMT "\n\n",n);
     50:   ctx.h = 1.0/(PetscReal)n;
     51:   ctx.kappa = 1.0;

     53:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     54:                Prepare nonlinear eigensolver context
     55:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     57:   NEPCreate(PETSC_COMM_WORLD,&nep);

     59:   /*
     60:      Create Function and Jacobian matrices; set evaluation routines
     61:   */

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

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

     79:   NEPSetFromOptions(nep);

     81:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     82:                       Solve the eigensystem
     83:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     85:   NEPSolve(nep);

     87:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     88:                     Display solution and clean up
     89:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     91:   /* show detailed info unless -terse option is given by user */
     92:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
     93:   if (terse) NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
     94:   else {
     95:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
     96:     NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
     97:     NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
     98:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
     99:   }

    101:   NEPDestroy(&nep);
    102:   MatDestroy(&F);
    103:   MatDestroy(&J);
    104:   SlepcFinalize();
    105:   return 0;
    106: }

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

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

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

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

    141:   /*
    142:      Interior grid points
    143:   */
    144:   for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
    145:     j[0] = i-1; j[1] = i; j[2] = i+1;
    146:     A[0] = A[2] = -d-lambda*h/6.0; A[1] = 2.0*(d-lambda*h/3.0);
    147:     MatSetValues(fun,1,&i,3,j,A,INSERT_VALUES);
    148:   }

    150:   /*
    151:      Boundary points
    152:   */
    153:   if (FirstBlock) {
    154:     i = 0;
    155:     j[0] = 0; j[1] = 1;
    156:     A[0] = 2.0*(d-lambda*h/3.0); A[1] = -d-lambda*h/6.0;
    157:     MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES);
    158:   }

    160:   if (LastBlock) {
    161:     i = n-1;
    162:     j[0] = n-2; j[1] = n-1;
    163:     A[0] = -d-lambda*h/6.0; A[1] = d-lambda*h/3.0+lambda*c;
    164:     MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES);
    165:   }

    167:   /*
    168:      Assemble matrix
    169:   */
    170:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
    171:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
    172:   if (fun != B) {
    173:     MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY);
    174:     MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY);
    175:   }
    176:   PetscFunctionReturn(0);
    177: }

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

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

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

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

    211:   /*
    212:      Interior grid points
    213:   */
    214:   for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
    215:     j[0] = i-1; j[1] = i; j[2] = i+1;
    216:     A[0] = A[2] = -h/6.0; A[1] = -2.0*h/3.0;
    217:     MatSetValues(jac,1,&i,3,j,A,INSERT_VALUES);
    218:   }

    220:   /*
    221:      Boundary points
    222:   */
    223:   if (FirstBlock) {
    224:     i = 0;
    225:     j[0] = 0; j[1] = 1;
    226:     A[0] = -2.0*h/3.0; A[1] = -h/6.0;
    227:     MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES);
    228:   }

    230:   if (LastBlock) {
    231:     i = n-1;
    232:     j[0] = n-2; j[1] = n-1;
    233:     A[0] = -h/6.0; A[1] = -h/3.0-c*c;
    234:     MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES);
    235:   }

    237:   /*
    238:      Assemble matrix
    239:   */
    240:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
    241:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
    242:   PetscFunctionReturn(0);
    243: }

    245: /*TEST

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

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

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

    274: TEST*/