Actual source code: ex40.c

slepc-main 2024-11-15
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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[] = "Checking the definite property in quadratic symmetric eigenproblem.\n\n"
 12:   "The command line options are:\n"
 13:   "  -n <n> ... dimension of the matrices.\n"
 14:   "  -transform... whether to transform to a hyperbolic problem or not.\n"
 15:   "  -nonhyperbolic... to test with a modified (definite) problem that is not hyperbolic.\n\n";

 17: #include <slepcpep.h>

 19: /*
 20:   This example is based on spring.c, for fixed values mu=1,tau=10,kappa=5

 22:   The transformations are based on the method proposed in [Niendorf and Voss, LAA 2010].
 23: */

 25: PetscErrorCode QEPDefiniteTransformGetMatrices(PEP,PetscBool,PetscReal,PetscReal,Mat[3]);
 26: PetscErrorCode QEPDefiniteTransformMap(PetscBool,PetscReal,PetscReal,PetscInt,PetscScalar*,PetscBool);
 27: PetscErrorCode QEPDefiniteCheckError(Mat*,PEP,PetscBool,PetscReal,PetscReal);
 28: PetscErrorCode TransformMatricesMoebius(Mat[3],MatStructure,PetscReal,PetscReal,PetscReal,PetscReal,Mat[3]);

 30: int main(int argc,char **argv)
 31: {
 32:   Mat            M,C,K,*Op,A[3],At[3],B[3]; /* problem matrices */
 33:   PEP            pep;        /* polynomial eigenproblem solver context */
 34:   ST             st;         /* spectral transformation context */
 35:   KSP            ksp;
 36:   PC             pc;
 37:   PEPProblemType type;
 38:   PetscBool      terse,transform=PETSC_FALSE,nohyp=PETSC_FALSE;
 39:   PetscInt       n=100,Istart,Iend,i,def=0,hyp;
 40:   PetscReal      muu=1,tau=10,kappa=5,inta,intb;
 41:   PetscReal      alpha,beta,xi,mu,at[2]={0.0,0.0},c=.857,s;
 42:   PetscScalar    target,targett,ats[2];

 44:   PetscFunctionBeginUser;
 45:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));

 47:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
 48:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nPEP example that checks definite property, n=%" PetscInt_FMT "\n\n",n));

 50:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 51:      Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
 52:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 54:   /* K is a tridiagonal */
 55:   PetscCall(MatCreate(PETSC_COMM_WORLD,&K));
 56:   PetscCall(MatSetSizes(K,PETSC_DECIDE,PETSC_DECIDE,n,n));
 57:   PetscCall(MatSetFromOptions(K));

 59:   PetscCall(MatGetOwnershipRange(K,&Istart,&Iend));
 60:   for (i=Istart;i<Iend;i++) {
 61:     if (i>0) PetscCall(MatSetValue(K,i,i-1,-kappa,INSERT_VALUES));
 62:     PetscCall(MatSetValue(K,i,i,kappa*3.0,INSERT_VALUES));
 63:     if (i<n-1) PetscCall(MatSetValue(K,i,i+1,-kappa,INSERT_VALUES));
 64:   }

 66:   PetscCall(MatAssemblyBegin(K,MAT_FINAL_ASSEMBLY));
 67:   PetscCall(MatAssemblyEnd(K,MAT_FINAL_ASSEMBLY));

 69:   /* C is a tridiagonal */
 70:   PetscCall(MatCreate(PETSC_COMM_WORLD,&C));
 71:   PetscCall(MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,n,n));
 72:   PetscCall(MatSetFromOptions(C));

 74:   PetscCall(MatGetOwnershipRange(C,&Istart,&Iend));
 75:   for (i=Istart;i<Iend;i++) {
 76:     if (i>0) PetscCall(MatSetValue(C,i,i-1,-tau,INSERT_VALUES));
 77:     PetscCall(MatSetValue(C,i,i,tau*3.0,INSERT_VALUES));
 78:     if (i<n-1) PetscCall(MatSetValue(C,i,i+1,-tau,INSERT_VALUES));
 79:   }

 81:   PetscCall(MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY));
 82:   PetscCall(MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY));

 84:   /* M is a diagonal matrix */
 85:   PetscCall(MatCreate(PETSC_COMM_WORLD,&M));
 86:   PetscCall(MatSetSizes(M,PETSC_DECIDE,PETSC_DECIDE,n,n));
 87:   PetscCall(MatSetFromOptions(M));
 88:   PetscCall(MatGetOwnershipRange(M,&Istart,&Iend));
 89:   for (i=Istart;i<Iend;i++) PetscCall(MatSetValue(M,i,i,muu,INSERT_VALUES));
 90:   PetscCall(MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY));
 91:   PetscCall(MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY));

 93:   PetscCall(PetscOptionsGetBool(NULL,NULL,"-nonhyperbolic",&nohyp,NULL));
 94:   A[0] = K; A[1] = C; A[2] = M;
 95:   if (nohyp) {
 96:     s = c*.6;
 97:     PetscCall(TransformMatricesMoebius(A,UNKNOWN_NONZERO_PATTERN,c,s,-s,c,At));
 98:     for (i=0;i<3;i++) PetscCall(MatDestroy(&A[i]));
 99:     Op = At;
100:   } else Op = A;

102:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
103:                 Create the eigensolver and solve the problem
104:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

106:   /*
107:      Create eigensolver context
108:   */
109:   PetscCall(PEPCreate(PETSC_COMM_WORLD,&pep));
110:   PetscCall(PEPSetProblemType(pep,PEP_HERMITIAN));
111:   PetscCall(PEPSetType(pep,PEPSTOAR));
112:   /*
113:      Set operators and set problem type
114:   */
115:   PetscCall(PEPSetOperators(pep,3,Op));

117:   /*
118:      Set shift-and-invert with Cholesky; select MUMPS if available
119:   */
120:   PetscCall(PEPGetST(pep,&st));
121:   PetscCall(STGetKSP(st,&ksp));
122:   PetscCall(KSPSetType(ksp,KSPPREONLY));
123:   PetscCall(KSPGetPC(ksp,&pc));
124:   PetscCall(PCSetType(pc,PCCHOLESKY));

126:   /*
127:      Use MUMPS if available.
128:      Note that in complex scalars we cannot use MUMPS for spectrum slicing,
129:      because MatGetInertia() is not available in that case.
130:   */
131: #if defined(PETSC_HAVE_MUMPS) && !defined(PETSC_USE_COMPLEX)
132:   PetscCall(PCFactorSetMatSolverType(pc,MATSOLVERMUMPS));
133:   /*
134:      Add several MUMPS options (see ex43.c for a better way of setting them in program):
135:      '-st_mat_mumps_icntl_13 1': turn off ScaLAPACK for matrix inertia
136:   */
137:   PetscCall(PetscOptionsInsertString(NULL,"-st_mat_mumps_icntl_13 1 -st_mat_mumps_icntl_24 1 -st_mat_mumps_cntl_3 1e-12"));
138: #endif

140:   /*
141:      Set solver parameters at runtime
142:   */
143:   PetscCall(PEPSetFromOptions(pep));

145:   PetscCall(PetscOptionsGetBool(NULL,NULL,"-transform",&transform,NULL));
146:   if (transform) {
147:     /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
148:                     Check if the problem is definite
149:        - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
150:     PetscCall(PEPCheckDefiniteQEP(pep,&xi,&mu,&def,&hyp));
151:     switch (def) {
152:       case 1:
153:         if (hyp==1) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Hyperbolic Problem xi=%g\n",(double)xi));
154:         else PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Definite Problem xi=%g mu=%g\n",(double)xi,(double)mu));
155:         break;
156:       case -1:
157:         PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Not Definite Problem\n"));
158:         break;
159:       default:
160:         PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Cannot determine definiteness\n"));
161:         break;
162:     }

164:     /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
165:       Transform the QEP to have a definite inner product in the linearization
166:        - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
167:     if (def==1) {
168:       PetscCall(QEPDefiniteTransformGetMatrices(pep,hyp==1?PETSC_TRUE:PETSC_FALSE,xi,mu,B));
169:       PetscCall(PEPSetOperators(pep,3,B));
170:       PetscCall(PEPGetTarget(pep,&target));
171:       targett = target;
172:       PetscCall(QEPDefiniteTransformMap(hyp==1?PETSC_TRUE:PETSC_FALSE,xi,mu,1,&targett,PETSC_FALSE));
173:       PetscCall(PEPSetTarget(pep,targett));
174:       PetscCall(PEPGetProblemType(pep,&type));
175:       PetscCall(PEPSetProblemType(pep,PEP_HYPERBOLIC));
176:       PetscCall(PEPSTOARGetLinearization(pep,&alpha,&beta));
177:       PetscCall(PEPSTOARSetLinearization(pep,1.0,0.0));
178:       PetscCall(PEPGetInterval(pep,&inta,&intb));
179:       if (inta!=intb) {
180:         ats[0] = inta; ats[1] = intb;
181:         PetscCall(QEPDefiniteTransformMap(hyp==1?PETSC_TRUE:PETSC_FALSE,xi,mu,2,ats,PETSC_FALSE));
182:         at[0] = PetscRealPart(ats[0]); at[1] = PetscRealPart(ats[1]);
183:         if (at[0]<at[1]) PetscCall(PEPSetInterval(pep,at[0],at[1]));
184:         else PetscCall(PEPSetInterval(pep,PETSC_MIN_REAL,at[1]));
185:       }
186:     }
187:   }

189:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
190:                       Solve the eigensystem
191:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
192:   PetscCall(PEPSolve(pep));

194:   /* show detailed info unless -terse option is given by user */
195:   if (def!=1) {
196:     PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
197:     if (terse) PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL));
198:     else {
199:       PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
200:       PetscCall(PEPConvergedReasonView(pep,PETSC_VIEWER_STDOUT_WORLD));
201:       PetscCall(PEPErrorView(pep,PEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
202:       PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
203:     }
204:   } else {
205:     /* Map the solution */
206:     PetscCall(PEPConvergedReasonView(pep,PETSC_VIEWER_STDOUT_WORLD));
207:     PetscCall(QEPDefiniteCheckError(Op,pep,hyp==1?PETSC_TRUE:PETSC_FALSE,xi,mu));
208:     for (i=0;i<3;i++) PetscCall(MatDestroy(B+i));
209:   }
210:   if (at[0]>at[1]) {
211:     PetscCall(PEPSetInterval(pep,at[0],PETSC_MAX_REAL));
212:     PetscCall(PEPSolve(pep));
213:     PetscCall(PEPConvergedReasonView(pep,PETSC_VIEWER_STDOUT_WORLD));
214:     /* Map the solution */
215:     PetscCall(QEPDefiniteCheckError(Op,pep,hyp==1?PETSC_TRUE:PETSC_FALSE,xi,mu));
216:   }
217:   if (def==1) {
218:     PetscCall(PEPSetTarget(pep,target));
219:     PetscCall(PEPSetProblemType(pep,type));
220:     PetscCall(PEPSTOARSetLinearization(pep,alpha,beta));
221:     if (inta!=intb) PetscCall(PEPSetInterval(pep,inta,intb));
222:   }

224:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
225:                     Clean up
226:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
227:   PetscCall(PEPDestroy(&pep));
228:   for (i=0;i<3;i++) PetscCall(MatDestroy(Op+i));
229:   PetscCall(SlepcFinalize());
230:   return 0;
231: }

233: /* ------------------------------------------------------------------- */
234: /*
235:   QEPDefiniteTransformMap_Initial - map a scalar value with a certain Moebius transform

237:                    a theta + b
238:          lambda = --------------
239:                    c theta + d

241:   Input:
242:     xi,mu: real values such that Q(xi)<0 and Q(mu)>0
243:     hyperbolic: if true the problem is assumed hyperbolic (mu is not used)
244:   Input/Output:
245:     val (array of length n)
246:     if backtransform=true returns lambda from theta, else returns theta from lambda
247: */
248: static PetscErrorCode QEPDefiniteTransformMap_Initial(PetscBool hyperbolic,PetscReal xi,PetscReal mu,PetscInt n,PetscScalar *val,PetscBool backtransform)
249: {
250:   PetscInt  i;
251:   PetscReal a,b,c,d,s;

253:   PetscFunctionBegin;
254:   if (hyperbolic) { a = 1.0; b = xi; c =0.0; d = 1.0; }
255:   else { a = mu; b = mu*xi-1; c = 1.0; d = xi+mu; }
256:   if (!backtransform) { s = a; a = -d; d = -s; }
257:   for (i=0;i<n;i++) {
258:     if (PetscRealPart(val[i]) >= PETSC_MAX_REAL || PetscRealPart(val[i]) <= PETSC_MIN_REAL) val[i] = a/c;
259:     else if (val[i] == -d/c) val[i] = PETSC_MAX_REAL;
260:     else val[i] = (a*val[i]+b)/(c*val[i]+d);
261:   }
262:   PetscFunctionReturn(PETSC_SUCCESS);
263: }

265: /* ------------------------------------------------------------------- */
266: /*
267:   QEPDefiniteTransformMap - perform the mapping if the problem is hyperbolic, otherwise
268:   modify the value of xi in advance
269: */
270: PetscErrorCode QEPDefiniteTransformMap(PetscBool hyperbolic,PetscReal xi,PetscReal mu,PetscInt n,PetscScalar *val,PetscBool backtransform)
271: {
272:   PetscReal      xit;
273:   PetscScalar    alpha;

275:   PetscFunctionBegin;
276:   xit = xi;
277:   if (!hyperbolic) {
278:     alpha = xi;
279:     PetscCall(QEPDefiniteTransformMap_Initial(PETSC_FALSE,0.0,mu,1,&alpha,PETSC_FALSE));
280:     xit = PetscRealPart(alpha);
281:   }
282:   PetscCall(QEPDefiniteTransformMap_Initial(hyperbolic,xit,mu,n,val,backtransform));
283:   PetscFunctionReturn(PETSC_SUCCESS);
284: }

286: /* ------------------------------------------------------------------- */
287: /*
288:   TransformMatricesMoebius - transform the coefficient matrices of a QEP

290:   Input:
291:     A: coefficient matrices of the original QEP
292:     a,b,c,d: parameters of the Moebius transform
293:     str: structure flag for MatAXPY operations
294:   Output:
295:     B: transformed matrices
296: */
297: PetscErrorCode TransformMatricesMoebius(Mat A[3],MatStructure str,PetscReal a,PetscReal b,PetscReal c,PetscReal d,Mat B[3])
298: {
299:   PetscInt       i,k;
300:   PetscReal      cf[9];

302:   PetscFunctionBegin;
303:   for (i=0;i<3;i++) PetscCall(MatDuplicate(A[2],MAT_COPY_VALUES,&B[i]));
304:   /* Ct = b*b*A+b*d*B+d*d*C */
305:   cf[0] = d*d; cf[1] = b*d; cf[2] = b*b;
306:   /* Bt = 2*a*b*A+(b*c+a*d)*B+2*c*d*C*/
307:   cf[3] = 2*c*d; cf[4] = b*c+a*d; cf[5] = 2*a*b;
308:   /* At = a*a*A+a*c*B+c*c*C */
309:   cf[6] = c*c; cf[7] = a*c; cf[8] = a*a;
310:   for (k=0;k<3;k++) {
311:     PetscCall(MatScale(B[k],cf[k*3+2]));
312:     for (i=0;i<2;i++) PetscCall(MatAXPY(B[k],cf[3*k+i],A[i],str));
313:   }
314:   PetscFunctionReturn(PETSC_SUCCESS);
315: }

317: /* ------------------------------------------------------------------- */
318: /*
319:   QEPDefiniteTransformGetMatrices - given a PEP of degree 2, transform the three
320:   matrices with TransformMatricesMoebius

322:   Input:
323:     pep: polynomial eigenproblem to be transformed, with Q(.) being the quadratic polynomial
324:     xi,mu: real values such that Q(xi)<0 and Q(mu)>0
325:     hyperbolic: if true the problem is assumed hyperbolic (mu is not used)
326:   Output:
327:     T: coefficient matrices of the transformed polynomial
328: */
329: PetscErrorCode QEPDefiniteTransformGetMatrices(PEP pep,PetscBool hyperbolic,PetscReal xi,PetscReal mu,Mat T[3])
330: {
331:   MatStructure   str;
332:   ST             st;
333:   PetscInt       i;
334:   PetscReal      a,b,c,d;
335:   PetscScalar    xit;
336:   Mat            A[3];

338:   PetscFunctionBegin;
339:   for (i=2;i>=0;i--) PetscCall(PEPGetOperators(pep,i,&A[i]));
340:   if (hyperbolic) { a = 1.0; b = xi; c =0.0; d = 1.0; }
341:   else {
342:     xit = xi;
343:     PetscCall(QEPDefiniteTransformMap_Initial(PETSC_FALSE,0.0,mu,1,&xit,PETSC_FALSE));
344:     a = mu; b = mu*PetscRealPart(xit)-1.0; c = 1.0; d = PetscRealPart(xit)+mu;
345:   }
346:   PetscCall(PEPGetST(pep,&st));
347:   PetscCall(STGetMatStructure(st,&str));
348:   PetscCall(TransformMatricesMoebius(A,str,a,b,c,d,T));
349:   PetscFunctionReturn(PETSC_SUCCESS);
350: }

352: /* ------------------------------------------------------------------- */
353: /*
354:   Auxiliary function to compute the residual norm of an eigenpair of a QEP defined
355:   by coefficient matrices A
356: */
357: static PetscErrorCode PEPResidualNorm(Mat *A,PetscScalar kr,PetscScalar ki,Vec xr,Vec xi,Vec *z,PetscReal *norm)
358: {
359:   PetscInt       i,nmat=3;
360:   PetscScalar    vals[3];
361:   Vec            u,w;
362: #if !defined(PETSC_USE_COMPLEX)
363:   Vec            ui,wi;
364:   PetscReal      ni;
365:   PetscBool      imag;
366:   PetscScalar    ivals[3];
367: #endif

369:   PetscFunctionBegin;
370:   u = z[0]; w = z[1];
371:   PetscCall(VecSet(u,0.0));
372: #if !defined(PETSC_USE_COMPLEX)
373:   ui = z[2]; wi = z[3];
374: #endif
375:   vals[0] = 1.0;
376:   vals[1] = kr;
377:   vals[2] = kr*kr-ki*ki;
378: #if !defined(PETSC_USE_COMPLEX)
379:   ivals[0] = 0.0;
380:   ivals[1] = ki;
381:   ivals[2] = 2.0*kr*ki;
382:   if (ki == 0 || PetscAbsScalar(ki) < PetscAbsScalar(kr*PETSC_MACHINE_EPSILON))
383:     imag = PETSC_FALSE;
384:   else {
385:     imag = PETSC_TRUE;
386:     PetscCall(VecSet(ui,0.0));
387:   }
388: #endif
389:   for (i=0;i<nmat;i++) {
390:     if (vals[i]!=0.0) {
391:       PetscCall(MatMult(A[i],xr,w));
392:       PetscCall(VecAXPY(u,vals[i],w));
393:     }
394: #if !defined(PETSC_USE_COMPLEX)
395:     if (imag) {
396:       if (ivals[i]!=0 || vals[i]!=0) {
397:         PetscCall(MatMult(A[i],xi,wi));
398:         if (vals[i]==0) PetscCall(MatMult(A[i],xr,w));
399:       }
400:       if (ivals[i]!=0) {
401:         PetscCall(VecAXPY(u,-ivals[i],wi));
402:         PetscCall(VecAXPY(ui,ivals[i],w));
403:       }
404:       if (vals[i]!=0) PetscCall(VecAXPY(ui,vals[i],wi));
405:     }
406: #endif
407:   }
408:   PetscCall(VecNorm(u,NORM_2,norm));
409: #if !defined(PETSC_USE_COMPLEX)
410:   if (imag) {
411:     PetscCall(VecNorm(ui,NORM_2,&ni));
412:     *norm = SlepcAbsEigenvalue(*norm,ni);
413:   }
414: #endif
415:   PetscFunctionReturn(PETSC_SUCCESS);
416: }

418: /* ------------------------------------------------------------------- */
419: /*
420:   QEPDefiniteCheckError - check and print the residual norm of a transformed PEP

422:   Input:
423:     A: coefficient matrices of the original problem
424:     pep: solver containing the computed solution of the transformed problem
425:     xi,mu,hyperbolic: parameters used in transformation
426: */
427: PetscErrorCode QEPDefiniteCheckError(Mat *A,PEP pep,PetscBool hyperbolic,PetscReal xi,PetscReal mu)
428: {
429:   PetscScalar    er,ei;
430:   PetscReal      re,im,error;
431:   Vec            vr,vi,w[4];
432:   PetscInt       i,nconv;
433:   BV             bv;
434:   char           ex[30],sep[]=" ---------------------- --------------------\n";

436:   PetscFunctionBegin;
437:   PetscCall(PetscSNPrintf(ex,sizeof(ex),"||P(k)x||/||kx||"));
438:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%s            k             %s\n%s",sep,ex,sep));
439:   PetscCall(PEPGetConverged(pep,&nconv));
440:   PetscCall(PEPGetBV(pep,&bv));
441:   PetscCall(BVCreateVec(bv,w));
442:   PetscCall(VecDuplicate(w[0],&vr));
443:   PetscCall(VecDuplicate(w[0],&vi));
444:   for (i=1;i<4;i++) PetscCall(VecDuplicate(w[0],w+i));
445:   for (i=0;i<nconv;i++) {
446:     PetscCall(PEPGetEigenpair(pep,i,&er,&ei,vr,vi));
447:     PetscCall(QEPDefiniteTransformMap(hyperbolic,xi,mu,1,&er,PETSC_TRUE));
448:     PetscCall(PEPResidualNorm(A,er,0.0,vr,vi,w,&error));
449:     error /= SlepcAbsEigenvalue(er,0.0);
450: #if defined(PETSC_USE_COMPLEX)
451:     re = PetscRealPart(er);
452:     im = PetscImaginaryPart(ei);
453: #else
454:     re = er;
455:     im = ei;
456: #endif
457:     if (im!=0.0) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"  % 9f%+9fi      %12g\n",(double)re,(double)im,(double)error));
458:     else PetscCall(PetscPrintf(PETSC_COMM_WORLD,"    % 12f           %12g\n",(double)re,(double)error));
459:   }
460:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%s",sep));
461:   for (i=0;i<4;i++) PetscCall(VecDestroy(w+i));
462:   PetscCall(VecDestroy(&vi));
463:   PetscCall(VecDestroy(&vr));
464:   PetscFunctionReturn(PETSC_SUCCESS);
465: }

467: /*TEST

469:    testset:
470:       requires: !single
471:       args: -pep_nev 3 -nonhyperbolic -pep_target 2
472:       output_file: output/ex40_1.out
473:       filter: grep -v "Definite" | sed -e "s/iterations [0-9]\([0-9]*\)/iterations xx/g" | sed -e "s/[0-9]\.[0-9]*e[+-]\([0-9]*\)/removed/g"
474:       test:
475:          suffix: 1
476:          requires: !complex
477:       test:
478:          suffix: 1_complex
479:          requires: complex !mumps
480:       test:
481:          suffix: 1_transform
482:          requires: !complex
483:          args: -transform
484:       test:
485:          suffix: 1_transform_complex
486:          requires: complex !mumps
487:          args: -transform

489: TEST*/