Actual source code: test16.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[] = "Illustrates use of NEPSetEigenvalueComparison().\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 MyEigenSort(PetscScalar,PetscScalar,PetscScalar,PetscScalar,PetscInt*,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;               /* Function matrix */
 43:   ApplicationCtx ctx;             /* user-defined context */
 44:   PetscScalar    target;
 45:   RG             rg;
 46:   PetscInt       n=128;
 47:   PetscBool      terse;

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

 56:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 57:                Prepare nonlinear eigensolver context
 58:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

 69:   PetscCall(NEPSetType(nep,NEPNLEIGS));
 70:   PetscCall(NEPGetRG(nep,&rg));
 71:   PetscCall(RGSetType(rg,RGINTERVAL));
 72: #if defined(PETSC_USE_COMPLEX)
 73:   PetscCall(RGIntervalSetEndpoints(rg,2.0,400.0,-0.001,0.001));
 74: #else
 75:   PetscCall(RGIntervalSetEndpoints(rg,2.0,400.0,0,0));
 76: #endif
 77:   PetscCall(NEPSetTarget(nep,25.0));
 78:   PetscCall(NEPSetEigenvalueComparison(nep,MyEigenSort,&target));
 79:   PetscCall(NEPSetTolerances(nep,PETSC_SMALL,PETSC_CURRENT));
 80:   PetscCall(NEPSetFromOptions(nep));
 81:   PetscCall(NEPGetTarget(nep,&target));

 83:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 84:               Solve the eigensystem and display the solution
 85:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 87:   PetscCall(NEPSolve(nep));

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

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

105: /* ------------------------------------------------------------------- */
106: /*
107:    FormFunction - Computes Function matrix  T(lambda)

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

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

126:   PetscFunctionBeginUser;
127:   /*
128:      Compute Function entries and insert into matrix
129:   */
130:   PetscCall(MatGetSize(fun,&n,NULL));
131:   PetscCall(MatGetOwnershipRange(fun,&Istart,&Iend));
132:   if (Istart==0) FirstBlock=PETSC_TRUE;
133:   if (Iend==n) LastBlock=PETSC_TRUE;
134:   h = user->h;
135:   c = user->kappa/(lambda-user->kappa);
136:   d = n;

138:   /*
139:      Interior grid points
140:   */
141:   for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
142:     j[0] = i-1; j[1] = i; j[2] = i+1;
143:     A[0] = A[2] = -d-lambda*h/6.0; A[1] = 2.0*(d-lambda*h/3.0);
144:     PetscCall(MatSetValues(fun,1,&i,3,j,A,INSERT_VALUES));
145:   }

147:   /*
148:      Boundary points
149:   */
150:   if (FirstBlock) {
151:     i = 0;
152:     j[0] = 0; j[1] = 1;
153:     A[0] = 2.0*(d-lambda*h/3.0); A[1] = -d-lambda*h/6.0;
154:     PetscCall(MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES));
155:   }

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

164:   /*
165:      Assemble matrix
166:   */
167:   PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY));
168:   PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY));
169:   if (fun != B) {
170:     PetscCall(MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY));
171:     PetscCall(MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY));
172:   }
173:   PetscFunctionReturn(PETSC_SUCCESS);
174: }

176: /*
177:     Function for user-defined eigenvalue ordering criterion.

179:     Given two eigenvalues ar+i*ai and br+i*bi, the subroutine must choose
180:     one of them as the preferred one according to the criterion.
181:     In this example, eigenvalues are sorted with respect to the target,
182:     but those on the right of the target are preferred.
183: */
184: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx)
185: {
186:   PetscReal   a,b;
187:   PetscScalar target = *(PetscScalar*)ctx;

189:   PetscFunctionBeginUser;
190:   if (PetscRealPart(ar-target)<0.0 && PetscRealPart(br-target)>0.0) *r = 1;
191:   else {
192:     a = SlepcAbsEigenvalue(ar-target,ai);
193:     b = SlepcAbsEigenvalue(br-target,bi);
194:     if (a>b) *r = 1;
195:     else if (a<b) *r = -1;
196:     else *r = 0;
197:   }
198:   PetscFunctionReturn(PETSC_SUCCESS);
199: }

201: /*TEST

203:    test:
204:       suffix: 1
205:       args: -nep_nev 4 -nep_ncv 8 -terse
206:       requires: double !complex

208: TEST*/