Actual source code: test29.c

slepc-3.23.3 2025-09-08
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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[] = "Illustrates the computation of left eigenvectors for generalized eigenproblems.\n\n"
 12:   "The command line options are:\n"
 13:   "  -f1 <filename> -f2 <filename>, PETSc binary files containing A and B\n\n";

 15: #include <slepceps.h>

 17: /*
 18:    User-defined routines
 19: */
 20: PetscErrorCode ComputeResidualNorm(Mat,Mat,PetscBool,PetscScalar,PetscScalar,Vec,Vec,Vec*,PetscReal*);
 21: PetscErrorCode CheckBiorthogonality(Vec*,Vec*,PetscScalar*,PetscInt,Mat,PetscReal*);

 23: int main(int argc,char **argv)
 24: {
 25:   Mat            A,B;
 26:   EPS            eps;
 27:   EPSType        type;
 28:   PetscInt       i,nconv;
 29:   PetscBool      twosided,flg;
 30:   PetscReal      nrmr,nrml=0.0,re,im,lev;
 31:   PetscScalar    *kr,*ki;
 32:   Vec            t,*xr,*xi,*yr,*yi,*z;
 33:   char           filename[PETSC_MAX_PATH_LEN];
 34:   PetscViewer    viewer;

 36:   PetscFunctionBeginUser;
 37:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));

 39:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 40:         Load the matrices that define the eigensystem, Ax=kBx
 41:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 43:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nGeneralized eigenproblem stored in file.\n\n"));
 44:   PetscCall(PetscOptionsGetString(NULL,NULL,"-f1",filename,sizeof(filename),&flg));
 45:   PetscCheck(flg,PETSC_COMM_WORLD,PETSC_ERR_USER_INPUT,"Must indicate a file name for matrix A with the -f1 option");

 47: #if defined(PETSC_USE_COMPLEX)
 48:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Reading COMPLEX matrices from binary files...\n"));
 49: #else
 50:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Reading REAL matrices from binary files...\n"));
 51: #endif
 52:   PetscCall(PetscViewerBinaryOpen(PETSC_COMM_WORLD,filename,FILE_MODE_READ,&viewer));
 53:   PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
 54:   PetscCall(MatSetFromOptions(A));
 55:   PetscCall(MatLoad(A,viewer));
 56:   PetscCall(PetscViewerDestroy(&viewer));

 58:   PetscCall(PetscOptionsGetString(NULL,NULL,"-f2",filename,sizeof(filename),&flg));
 59:   if (flg) {
 60:     PetscCall(PetscViewerBinaryOpen(PETSC_COMM_WORLD,filename,FILE_MODE_READ,&viewer));
 61:     PetscCall(MatCreate(PETSC_COMM_WORLD,&B));
 62:     PetscCall(MatSetFromOptions(B));
 63:     PetscCall(MatLoad(B,viewer));
 64:     PetscCall(PetscViewerDestroy(&viewer));
 65:   } else {
 66:     PetscCall(PetscPrintf(PETSC_COMM_WORLD," Matrix B was not provided, setting B=I\n\n"));
 67:     B = NULL;
 68:   }
 69:   PetscCall(MatCreateVecs(A,NULL,&t));

 71:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 72:                 Create the eigensolver and set various options
 73:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 75:   PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));
 76:   PetscCall(EPSSetOperators(eps,A,B));

 78:   /* use a two-sided algorithm to compute left eigenvectors as well */
 79:   PetscCall(EPSSetTwoSided(eps,PETSC_TRUE));

 81:   /* allow user to change settings at run time */
 82:   PetscCall(EPSSetFromOptions(eps));
 83:   PetscCall(EPSGetTwoSided(eps,&twosided));

 85:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 86:                       Solve the eigensystem
 87:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 89:   PetscCall(EPSSolve(eps));

 91:   /*
 92:      Optional: Get some information from the solver and display it
 93:   */
 94:   PetscCall(EPSGetType(eps,&type));
 95:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type));

 97:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 98:                     Display solution and clean up
 99:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

101:   /*
102:      Get number of converged approximate eigenpairs
103:   */
104:   PetscCall(EPSGetConverged(eps,&nconv));
105:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of converged eigenpairs: %" PetscInt_FMT "\n\n",nconv));
106:   PetscCall(PetscMalloc2(nconv,&kr,nconv,&ki));
107:   PetscCall(VecDuplicateVecs(t,3,&z));
108:   PetscCall(VecDuplicateVecs(t,nconv,&xr));
109:   PetscCall(VecDuplicateVecs(t,nconv,&xi));
110:   if (twosided) {
111:     PetscCall(VecDuplicateVecs(t,nconv,&yr));
112:     PetscCall(VecDuplicateVecs(t,nconv,&yi));
113:   }

115:   if (nconv>0) {
116:     /*
117:        Display eigenvalues and relative errors
118:     */
119:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,
120:          "           k            ||Ax-kBx||         ||y'A-y'Bk||\n"
121:          "   ---------------- ------------------ ------------------\n"));

123:     for (i=0;i<nconv;i++) {
124:       /*
125:         Get converged eigenpairs: i-th eigenvalue is stored in kr (real part) and
126:         ki (imaginary part)
127:       */
128:       PetscCall(EPSGetEigenpair(eps,i,&kr[i],&ki[i],xr[i],xi[i]));
129:       if (twosided) PetscCall(EPSGetLeftEigenvector(eps,i,yr[i],yi[i]));
130:       /*
131:          Compute the residual norms associated to each eigenpair
132:       */
133:       PetscCall(ComputeResidualNorm(A,B,PETSC_FALSE,kr[i],ki[i],xr[i],xi[i],z,&nrmr));
134:       if (twosided) PetscCall(ComputeResidualNorm(A,B,PETSC_TRUE,kr[i],ki[i],yr[i],yi[i],z,&nrml));

136: #if defined(PETSC_USE_COMPLEX)
137:       re = PetscRealPart(kr[i]);
138:       im = PetscImaginaryPart(kr[i]);
139: #else
140:       re = kr[i];
141:       im = ki[i];
142: #endif
143:       if (im!=0.0) PetscCall(PetscPrintf(PETSC_COMM_WORLD," %8f%+8fi %12g       %12g\n",(double)re,(double)im,(double)nrmr,(double)nrml));
144:       else PetscCall(PetscPrintf(PETSC_COMM_WORLD,"   %12f       %12g       %12g\n",(double)re,(double)nrmr,(double)nrml));
145:     }
146:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n"));
147:     /*
148:        Check bi-orthogonality of eigenvectors
149:     */
150:     if (twosided) {
151:       PetscCall(CheckBiorthogonality(xr,yr,ki,nconv,B,&lev));
152:       if (lev<100*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"  Level of bi-orthogonality of eigenvectors < 100*eps\n\n"));
153:       else PetscCall(PetscPrintf(PETSC_COMM_WORLD,"  Level of bi-orthogonality of eigenvectors: %g\n\n",(double)lev));
154:     }
155:   }

157:   PetscCall(EPSDestroy(&eps));
158:   PetscCall(MatDestroy(&A));
159:   PetscCall(MatDestroy(&B));
160:   PetscCall(VecDestroy(&t));
161:   PetscCall(PetscFree2(kr,ki));
162:   PetscCall(VecDestroyVecs(3,&z));
163:   PetscCall(VecDestroyVecs(nconv,&xr));
164:   PetscCall(VecDestroyVecs(nconv,&xi));
165:   if (twosided) {
166:     PetscCall(VecDestroyVecs(nconv,&yr));
167:     PetscCall(VecDestroyVecs(nconv,&yi));
168:   }
169:   PetscCall(SlepcFinalize());
170:   return 0;
171: }

173: /*
174:    ComputeResidualNorm - Computes the norm of the residual vector
175:    associated with an eigenpair.

177:    Input Parameters:
178:      trans - whether A' must be used instead of A
179:      kr,ki - eigenvalue
180:      xr,xi - eigenvector
181:      z     - three work vectors (the second one not referenced in complex scalars)
182: */
183: PetscErrorCode ComputeResidualNorm(Mat A,Mat B,PetscBool trans,PetscScalar kr,PetscScalar ki,Vec xr,Vec xi,Vec *z,PetscReal *norm)
184: {
185:   Vec            u,w=NULL;
186:   PetscScalar    alpha;
187: #if !defined(PETSC_USE_COMPLEX)
188:   Vec            v;
189:   PetscReal      ni,nr;
190: #endif
191:   PetscErrorCode (*matmult)(Mat,Vec,Vec) = trans? MatMultHermitianTranspose: MatMult;

193:   PetscFunctionBegin;
194:   u = z[0];
195:   if (B) w = z[2];

197: #if !defined(PETSC_USE_COMPLEX)
198:   v = z[1];
199:   if (ki == 0 || PetscAbsScalar(ki) < PetscAbsScalar(kr*PETSC_MACHINE_EPSILON)) {
200: #endif
201:     PetscCall((*matmult)(A,xr,u));                          /* u=A*x */
202:     if (PetscAbsScalar(kr) > PETSC_MACHINE_EPSILON) {
203:       if (B) PetscCall((*matmult)(B,xr,w));             /* w=B*x */
204:       else w = xr;
205:       alpha = trans? -PetscConj(kr): -kr;
206:       PetscCall(VecAXPY(u,alpha,w));                        /* u=A*x-k*B*x */
207:     }
208:     PetscCall(VecNorm(u,NORM_2,norm));
209: #if !defined(PETSC_USE_COMPLEX)
210:   } else {
211:     PetscCall((*matmult)(A,xr,u));                          /* u=A*xr */
212:     if (SlepcAbsEigenvalue(kr,ki) > PETSC_MACHINE_EPSILON) {
213:       if (B) PetscCall((*matmult)(B,xr,v));             /* v=B*xr */
214:       else PetscCall(VecCopy(xr,v));
215:       PetscCall(VecAXPY(u,-kr,v));                          /* u=A*xr-kr*B*xr */
216:       if (B) PetscCall((*matmult)(B,xi,w));             /* w=B*xi */
217:       else w = xi;
218:       PetscCall(VecAXPY(u,trans?-ki:ki,w));                 /* u=A*xr-kr*B*xr+ki*B*xi */
219:     }
220:     PetscCall(VecNorm(u,NORM_2,&nr));
221:     PetscCall((*matmult)(A,xi,u));                          /* u=A*xi */
222:     if (SlepcAbsEigenvalue(kr,ki) > PETSC_MACHINE_EPSILON) {
223:       PetscCall(VecAXPY(u,-kr,w));                          /* u=A*xi-kr*B*xi */
224:       PetscCall(VecAXPY(u,trans?ki:-ki,v));                 /* u=A*xi-kr*B*xi-ki*B*xr */
225:     }
226:     PetscCall(VecNorm(u,NORM_2,&ni));
227:     *norm = SlepcAbsEigenvalue(nr,ni);
228:   }
229: #endif
230:   PetscFunctionReturn(PETSC_SUCCESS);
231: }

233: /*
234:    CheckOrthogonality - Similar to VecCheckOrthogonality but taking into account complex eigenvalues.

236:    Input Parameters:
237:      V - right eigenvectors
238:      W - left eigenvectors
239:      eigi - imaginary part of eigenvalues (only to check if the corresponding vector is complex)
240:      n - number of V,W vectors
241:      B - matrix defining the inner product
242:    Output Parameter:
243:      lev - level of bi-orthogonality
244: */
245: PetscErrorCode CheckBiorthogonality(Vec *V,Vec *W,PetscScalar *ki,PetscInt n,Mat B,PetscReal *lev)
246: {
247:   PetscInt       i,j;
248:   PetscScalar    val1;
249:   PetscBool      wcmplx;
250:   Vec            wr;
251: #if !defined(PETSC_USE_COMPLEX)
252:   Vec            wi;
253:   PetscScalar    val2,dotr,doti;
254: #endif

256:   PetscFunctionBegin;
257:   if (n<=0) PetscFunctionReturn(PETSC_SUCCESS);
258:   PetscCall(VecDuplicate(V[0],&wr));
259: #if !defined(PETSC_USE_COMPLEX)
260:   PetscCall(VecDuplicate(V[0],&wi));
261: #endif
262:   *lev = 0.0;
263:   for (i=0;i<n;i++) {
264:     wcmplx = PETSC_FALSE;
265:     PetscCall(MatMult(B,W[i],wr));
266: #if !defined(PETSC_USE_COMPLEX)
267:     if (ki[i] != 0.0) {
268:       PetscCall(MatMult(B,W[i+1],wi));
269:       wcmplx = PETSC_TRUE;
270:     }
271: #endif
272:     for (j=0;j<n;j++) {
273:       if (j==i || (wcmplx && j==i+1)) continue;
274:       PetscCall(VecDot(wr,V[j],&val1));
275: #if !defined(PETSC_USE_COMPLEX)
276:       dotr = val1;
277:       if (ki[j] != 0.0) {  /* V complex */
278:         if (wcmplx) {
279:           PetscCall(VecDot(wi,V[j+1],&val2));
280:           dotr = val1+val2;
281:           PetscCall(VecDot(wi,V[j],&val1));
282:           PetscCall(VecDot(wr,V[j+1],&val2));
283:           doti = val1-val2;
284:         } else {
285:           PetscCall(VecDot(wr,V[j+1],&val1));
286:           doti = -val1;
287:         }
288:       } else if (wcmplx) {
289:         PetscCall(VecDot(wi,V[j],&doti));
290:       } else doti = 0.0;
291:       *lev = PetscMax(*lev,SlepcAbsEigenvalue(dotr,doti));
292:       if (ki[j] != 0.0) j++;
293: #else
294:       *lev = PetscMax(*lev,PetscAbsScalar(val1));
295: #endif
296:     }
297:     if (wcmplx) i++;
298:   }
299:   PetscCall(VecDestroy(&wr));
300: #if !defined(PETSC_USE_COMPLEX)
301:   PetscCall(VecDestroy(&wi));
302: #endif
303:   PetscFunctionReturn(PETSC_SUCCESS);
304: }

306: /*TEST

308:    testset:
309:       args: -f1 ${SLEPC_DIR}/share/slepc/datafiles/matrices/bfw62a.petsc -f2 ${SLEPC_DIR}/share/slepc/datafiles/matrices/bfw62b.petsc -eps_nev 4 -st_type sinvert -eps_target -190000
310:       filter: grep -v "method" | sed -e "s/[+-]0\.0*i//g" | sed -e "s/[0-9]\.[0-9]*e[+-]\([0-9]*\)/removed/g"
311:       requires: double !complex !defined(PETSC_USE_64BIT_INDICES)
312:       test:
313:          suffix: 1
314:       test:
315:          suffix: 1_cmplxvals
316:          args: -eps_target -250000
317:       test:
318:          suffix: 1_rqi
319:          args: -eps_type power -eps_power_shift_type rayleigh -eps_nev 2 -eps_target -2000
320:       test:
321:          suffix: 1_rqi_singular
322:          args: -eps_type power -eps_power_shift_type rayleigh -eps_nev 1 -eps_target -195500

324:    test:
325:       suffix: 2
326:       args: -f1 ${DATAFILESPATH}/matrices/complex/mhd1280a.petsc -f2 ${DATAFILESPATH}/matrices/complex/mhd1280b.petsc -eps_nev 6 -eps_tol 1e-11
327:       filter: sed -e "s/-892/+892/" | sed -e "s/-759/+759/" | sed -e "s/-674/+674/" | sed -e "s/[0-9]\.[0-9]*e[+-]\([0-9]*\)/removed/g"
328:       requires: double complex datafilespath !defined(PETSC_USE_64BIT_INDICES)
329:       timeoutfactor: 2

331:    test:
332:       suffix: 3
333:       args: -f1 ${SLEPC_DIR}/share/slepc/datafiles/matrices/bfw62a.petsc -f2 ${SLEPC_DIR}/share/slepc/datafiles/matrices/bfw62b.petsc -eps_nev 4 -st_type sinvert -eps_target -250000
334:       filter: grep -v "method" | sed -e "s/[+-]0\.0*i//g" | sed -e "s/[0-9]\.[0-9]*e[+-]\([0-9]*\)/removed/g" | grep -v bi-orthog
335:       requires: double !complex !defined(PETSC_USE_64BIT_INDICES)

337: TEST*/