Actual source code: ex24.c

slepc-3.18.0 2022-10-01
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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[] = "Spectrum folding for a standard symmetric eigenproblem.\n\n"
 12:   "The problem matrix is the 2-D Laplacian.\n\n"
 13:   "The command line options are:\n"
 14:   "  -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
 15:   "  -m <m>, where <m> = number of grid subdivisions in y dimension.\n";

 17: #include <slepceps.h>

 19: /*
 20:    User context for spectrum folding
 21: */
 22: typedef struct {
 23:   Mat       A;
 24:   Vec       w;
 25:   PetscReal target;
 26: } CTX_FOLD;

 28: /*
 29:    Auxiliary routines
 30: */
 31: PetscErrorCode MatMult_Fold(Mat,Vec,Vec);
 32: PetscErrorCode RayleighQuotient(Mat,Vec,PetscScalar*);
 33: PetscErrorCode ComputeResidualNorm(Mat,PetscScalar,Vec,PetscReal*);

 35: int main(int argc,char **argv)
 36: {
 37:   Mat            A,M,P;       /* problem matrix, shell matrix and preconditioner */
 38:   Vec            x;           /* eigenvector */
 39:   EPS            eps;         /* eigenproblem solver context */
 40:   ST             st;          /* spectral transformation */
 41:   KSP            ksp;
 42:   PC             pc;
 43:   EPSType        type;
 44:   CTX_FOLD       *ctx;
 45:   PetscInt       nconv,N,n=10,m,nloc,mloc,Istart,Iend,II,i,j;
 46:   PetscReal      *error,*evals,target=0.0,tol;
 47:   PetscScalar    lambda;
 48:   PetscBool      flag,terse,errok,hasmat;

 51:   SlepcInitialize(&argc,&argv,(char*)0,help);

 53:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 54:   PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag);
 55:   if (!flag) m=n;
 56:   PetscOptionsGetReal(NULL,NULL,"-target",&target,NULL);
 57:   N = n*m;
 58:   PetscPrintf(PETSC_COMM_WORLD,"\nSpectrum Folding, N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid) target=%f\n\n",N,n,m,(double)target);

 60:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 61:      Compute the 5-point stencil Laplacian
 62:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 64:   MatCreate(PETSC_COMM_WORLD,&A);
 65:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
 66:   MatSetFromOptions(A);
 67:   MatSetUp(A);

 69:   MatGetOwnershipRange(A,&Istart,&Iend);
 70:   for (II=Istart;II<Iend;II++) {
 71:     i = II/n; j = II-i*n;
 72:     if (i>0) MatSetValue(A,II,II-n,-1.0,INSERT_VALUES);
 73:     if (i<m-1) MatSetValue(A,II,II+n,-1.0,INSERT_VALUES);
 74:     if (j>0) MatSetValue(A,II,II-1,-1.0,INSERT_VALUES);
 75:     if (j<n-1) MatSetValue(A,II,II+1,-1.0,INSERT_VALUES);
 76:     MatSetValue(A,II,II,4.0,INSERT_VALUES);
 77:   }

 79:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 80:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
 81:   MatCreateVecs(A,&x,NULL);
 82:   MatGetLocalSize(A,&nloc,&mloc);

 84:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 85:                 Create shell matrix to perform spectrum folding
 86:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 87:   PetscNew(&ctx);
 88:   ctx->A = A;
 89:   ctx->target = target;
 90:   VecDuplicate(x,&ctx->w);

 92:   MatCreateShell(PETSC_COMM_WORLD,nloc,mloc,N,N,ctx,&M);
 93:   MatShellSetOperation(M,MATOP_MULT,(void(*)(void))MatMult_Fold);

 95:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 96:                 Create the eigensolver and set various options
 97:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 99:   EPSCreate(PETSC_COMM_WORLD,&eps);
100:   EPSSetOperators(eps,M,NULL);
101:   EPSSetProblemType(eps,EPS_HEP);
102:   EPSSetWhichEigenpairs(eps,EPS_SMALLEST_REAL);
103:   EPSSetFromOptions(eps);

105:   PetscObjectTypeCompareAny((PetscObject)eps,&flag,EPSGD,EPSJD,EPSBLOPEX,EPSLOBPCG,EPSRQCG,"");
106:   if (flag) {
107:     /*
108:        Build preconditioner specific for this application (diagonal of A^2)
109:     */
110:     MatGetRowSum(A,x);
111:     VecScale(x,-1.0);
112:     VecShift(x,20.0);
113:     MatCreate(PETSC_COMM_WORLD,&P);
114:     MatSetSizes(P,PETSC_DECIDE,PETSC_DECIDE,N,N);
115:     MatSetFromOptions(P);
116:     MatSetUp(P);
117:     MatDiagonalSet(P,x,INSERT_VALUES);
118:     /*
119:        Set diagonal preconditioner
120:     */
121:     EPSGetST(eps,&st);
122:     STSetType(st,STPRECOND);
123:     STSetPreconditionerMat(st,P);
124:     MatDestroy(&P);
125:     STGetKSP(st,&ksp);
126:     KSPGetPC(ksp,&pc);
127:     PCSetType(pc,PCJACOBI);
128:     STPrecondGetKSPHasMat(st,&hasmat);
129:     PetscPrintf(PETSC_COMM_WORLD," Preconditioned solver, hasmat=%s\n",hasmat?"true":"false");
130:   }

132:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
133:                       Solve the eigensystem
134:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

136:   EPSSolve(eps);
137:   EPSGetType(eps,&type);
138:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
139:   EPSGetTolerances(eps,&tol,NULL);

141:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
142:                     Display solution and clean up
143:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

145:   EPSGetConverged(eps,&nconv);
146:   PetscPrintf(PETSC_COMM_WORLD," Number of converged eigenpairs: %" PetscInt_FMT "\n\n",nconv);
147:   if (nconv>0) {
148:     PetscMalloc2(nconv,&evals,nconv,&error);
149:     for (i=0;i<nconv;i++) {
150:       /*  Get i-th eigenvector, compute eigenvalue approximation from
151:           Rayleigh quotient and compute residual norm */
152:       EPSGetEigenpair(eps,i,NULL,NULL,x,NULL);
153:       RayleighQuotient(A,x,&lambda);
154:       ComputeResidualNorm(A,lambda,x,&error[i]);
155: #if defined(PETSC_USE_COMPLEX)
156:       evals[i] = PetscRealPart(lambda);
157: #else
158:       evals[i] = lambda;
159: #endif
160:     }
161:     PetscOptionsHasName(NULL,NULL,"-terse",&terse);
162:     if (!terse) {
163:       PetscCall(PetscPrintf(PETSC_COMM_WORLD,
164:            "           k              ||Ax-kx||\n"
165:            "   ----------------- ------------------\n"));
166:       for (i=0;i<nconv;i++) PetscPrintf(PETSC_COMM_WORLD,"   %12f       %12.2g\n",(double)evals[i],(double)error[i]);
167:     } else {
168:       errok = PETSC_TRUE;
169:       for (i=0;i<nconv;i++) errok = (errok && error[i]<5.0*tol)? PETSC_TRUE: PETSC_FALSE;
170:       if (!errok) PetscPrintf(PETSC_COMM_WORLD," Problem: some of the first %" PetscInt_FMT " relative errors are higher than the tolerance\n\n",nconv);
171:       else {
172:         PetscPrintf(PETSC_COMM_WORLD," nconv=%" PetscInt_FMT " eigenvalues computed up to the required tolerance:",nconv);
173:         for (i=0;i<nconv;i++) PetscPrintf(PETSC_COMM_WORLD," %.5f",(double)evals[i]);
174:       }
175:     }
176:     PetscPrintf(PETSC_COMM_WORLD,"\n");
177:     PetscFree2(evals,error);
178:   }

180:   EPSDestroy(&eps);
181:   MatDestroy(&A);
182:   MatDestroy(&M);
183:   VecDestroy(&ctx->w);
184:   VecDestroy(&x);
185:   PetscFree(ctx);
186:   SlepcFinalize();
187:   return 0;
188: }

190: /*
191:     Matrix-vector product subroutine for the spectrum folding.
192:        y <-- (A-t*I)^2*x
193:  */
194: PetscErrorCode MatMult_Fold(Mat M,Vec x,Vec y)
195: {
196:   CTX_FOLD       *ctx;
197:   PetscScalar    sigma;

200:   MatShellGetContext(M,&ctx);
201:   sigma = -ctx->target;
202:   MatMult(ctx->A,x,ctx->w);
203:   VecAXPY(ctx->w,sigma,x);
204:   MatMult(ctx->A,ctx->w,y);
205:   VecAXPY(y,sigma,ctx->w);
206:   return 0;
207: }

209: /*
210:     Computes the Rayleigh quotient of a vector x
211:        r <-- x^T*A*x       (assumes x has unit norm)
212:  */
213: PetscErrorCode RayleighQuotient(Mat A,Vec x,PetscScalar *r)
214: {
215:   Vec            Ax;

218:   VecDuplicate(x,&Ax);
219:   MatMult(A,x,Ax);
220:   VecDot(Ax,x,r);
221:   VecDestroy(&Ax);
222:   return 0;
223: }

225: /*
226:     Computes the residual norm of an approximate eigenvector x, |A*x-lambda*x|
227:  */
228: PetscErrorCode ComputeResidualNorm(Mat A,PetscScalar lambda,Vec x,PetscReal *r)
229: {
230:   Vec            Ax;

233:   VecDuplicate(x,&Ax);
234:   MatMult(A,x,Ax);
235:   VecAXPY(Ax,-lambda,x);
236:   VecNorm(Ax,NORM_2,r);
237:   VecDestroy(&Ax);
238:   return 0;
239: }

241: /*TEST

243:    testset:
244:       args: -n 15 -eps_nev 1 -eps_ncv 12 -eps_max_it 1000 -eps_tol 1e-5 -terse
245:       filter: grep -v Solution
246:       test:
247:          suffix: 1
248:       test:
249:          suffix: 1_lobpcg
250:          args: -eps_type lobpcg
251:          requires: !single
252:       test:
253:          suffix: 1_gd
254:          args: -eps_type gd
255:          requires: !single

257: TEST*/