Actual source code: ex45.c

slepc-3.18.1 2022-11-02
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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[] = "Computes a partial generalized singular value decomposition (GSVD).\n"
 12:   "The command line options are:\n"
 13:   "  -m <m>, where <m> = number of rows of A.\n"
 14:   "  -n <n>, where <n> = number of columns of A.\n"
 15:   "  -p <p>, where <p> = number of rows of B.\n\n";

 17: #include <slepcsvd.h>

 19: int main(int argc,char **argv)
 20: {
 21:   Mat            A,B;             /* operator matrices */
 22:   Vec            u,v,x;           /* singular vectors */
 23:   SVD            svd;             /* singular value problem solver context */
 24:   SVDType        type;
 25:   Vec            uv,aux[2],*U,*V;
 26:   PetscReal      error,tol,sigma,lev1=0.0,lev2=0.0;
 27:   PetscInt       m=100,n,p=14,i,j,d,Istart,Iend,nsv,maxit,its,nconv;
 28:   PetscBool      flg,skiporth=PETSC_FALSE;

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

 33:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
 34:   PetscOptionsGetInt(NULL,NULL,"-n",&n,&flg);
 35:   if (!flg) n = m;
 36:   PetscOptionsGetInt(NULL,NULL,"-p",&p,&flg);
 37:   PetscPrintf(PETSC_COMM_WORLD,"\nGeneralized singular value decomposition, (%" PetscInt_FMT "+%" PetscInt_FMT ")x%" PetscInt_FMT "\n\n",m,p,n);
 38:   PetscOptionsGetBool(NULL,NULL,"-skiporth",&skiporth,NULL);

 40:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 41:                           Build the matrices
 42:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 44:   MatCreate(PETSC_COMM_WORLD,&A);
 45:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m,n);
 46:   MatSetFromOptions(A);
 47:   MatSetUp(A);

 49:   MatGetOwnershipRange(A,&Istart,&Iend);
 50:   for (i=Istart;i<Iend;i++) {
 51:     if (i>0 && i-1<n) MatSetValue(A,i,i-1,-1.0,INSERT_VALUES);
 52:     if (i+1<n) MatSetValue(A,i,i+1,-1.0,INSERT_VALUES);
 53:     if (i<n) MatSetValue(A,i,i,2.0,INSERT_VALUES);
 54:     if (i>n) MatSetValue(A,i,n-1,1.0,INSERT_VALUES);
 55:   }
 56:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 57:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

 59:   MatCreate(PETSC_COMM_WORLD,&B);
 60:   MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,p,n);
 61:   MatSetFromOptions(B);
 62:   MatSetUp(B);

 64:   MatGetOwnershipRange(B,&Istart,&Iend);
 65:   d = PetscMax(0,n-p);
 66:   for (i=Istart;i<Iend;i++) {
 67:     for (j=0;j<=PetscMin(i,n-1);j++) MatSetValue(B,i,j+d,1.0,INSERT_VALUES);
 68:   }
 69:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
 70:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);

 72:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 73:           Create the singular value solver and set various options
 74:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 76:   /*
 77:      Create singular value solver context
 78:   */
 79:   SVDCreate(PETSC_COMM_WORLD,&svd);

 81:   /*
 82:      Set operators and problem type
 83:   */
 84:   SVDSetOperators(svd,A,B);
 85:   SVDSetProblemType(svd,SVD_GENERALIZED);

 87:   /*
 88:      Set solver parameters at runtime
 89:   */
 90:   SVDSetFromOptions(svd);

 92:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 93:                       Solve the singular value system
 94:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 96:   SVDSolve(svd);
 97:   SVDGetIterationNumber(svd,&its);
 98:   PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %" PetscInt_FMT "\n",its);

100:   /*
101:      Optional: Get some information from the solver and display it
102:   */
103:   SVDGetType(svd,&type);
104:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
105:   SVDGetDimensions(svd,&nsv,NULL,NULL);
106:   PetscPrintf(PETSC_COMM_WORLD," Number of requested generalized singular values: %" PetscInt_FMT "\n",nsv);
107:   SVDGetTolerances(svd,&tol,&maxit);
108:   PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%" PetscInt_FMT "\n",(double)tol,maxit);

110:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
111:                     Display solution and clean up
112:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

114:   /*
115:      Get number of converged singular triplets
116:   */
117:   SVDGetConverged(svd,&nconv);
118:   PetscPrintf(PETSC_COMM_WORLD," Number of converged approximate singular triplets: %" PetscInt_FMT "\n\n",nconv);

120:   if (nconv>0) {
121:     /*
122:        Create vectors. The interface returns u and v as stacked on top of each other
123:        [u;v] so need to create a special vector (VecNest) to extract them
124:     */
125:     MatCreateVecs(A,&x,&u);
126:     MatCreateVecs(B,NULL,&v);
127:     aux[0] = u;
128:     aux[1] = v;
129:     VecCreateNest(PETSC_COMM_WORLD,2,NULL,aux,&uv);

131:     VecDuplicateVecs(u,nconv,&U);
132:     VecDuplicateVecs(v,nconv,&V);

134:     /*
135:        Display singular values and errors relative to the norms
136:     */
137:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,
138:          "          sigma           ||r||/||[A;B]||\n"
139:          "  --------------------- ------------------\n"));
140:     for (i=0;i<nconv;i++) {
141:       /*
142:          Get converged singular triplets: i-th singular value is stored in sigma
143:       */
144:       SVDGetSingularTriplet(svd,i,&sigma,uv,x);

146:       /* at this point, u and v can be used normally as individual vectors */
147:       VecCopy(u,U[i]);
148:       VecCopy(v,V[i]);

150:       /*
151:          Compute the error associated to each singular triplet
152:       */
153:       SVDComputeError(svd,i,SVD_ERROR_NORM,&error);

155:       PetscPrintf(PETSC_COMM_WORLD,"       % 6f      ",(double)sigma);
156:       PetscPrintf(PETSC_COMM_WORLD,"   % 12g\n",(double)error);
157:     }
158:     PetscPrintf(PETSC_COMM_WORLD,"\n");

160:     if (!skiporth) {
161:       VecCheckOrthonormality(U,nconv,NULL,nconv,NULL,NULL,&lev1);
162:       VecCheckOrthonormality(V,nconv,NULL,nconv,NULL,NULL,&lev2);
163:     }
164:     if (lev1+lev2<20*tol) PetscPrintf(PETSC_COMM_WORLD,"Level of orthogonality below the tolerance\n");
165:     else PetscPrintf(PETSC_COMM_WORLD,"Level of orthogonality: %g (U) %g (V)\n",(double)lev1,(double)lev2);
166:     VecDestroyVecs(nconv,&U);
167:     VecDestroyVecs(nconv,&V);
168:     VecDestroy(&x);
169:     VecDestroy(&u);
170:     VecDestroy(&v);
171:     VecDestroy(&uv);
172:   }

174:   /*
175:      Free work space
176:   */
177:   SVDDestroy(&svd);
178:   MatDestroy(&A);
179:   MatDestroy(&B);
180:   SlepcFinalize();
181:   return 0;
182: }

184: /*TEST

186:    testset:
187:       filter: grep -v "Solution method" | grep -v "Number of iterations" | sed -e "s/, maxit=1[0]*$//" | sed -e "s/[0-9]\.[0-9]*e[+-]\([0-9]*\)/removed/g"
188:       requires: double
189:       test:
190:          args: -svd_type lapack -m 20 -n 10 -p 6
191:          suffix: 1
192:       test:
193:          args: -svd_type lapack -m 15 -n 20 -p 10 -svd_smallest
194:          suffix: 2
195:       test:
196:          args: -svd_type lapack -m 15 -n 20 -p 21
197:          suffix: 3
198:       test:
199:          args: -svd_type lapack -m 20 -n 15 -p 21
200:          suffix: 4

202:    testset:
203:       args: -m 25 -n 20 -p 21 -svd_smallest -svd_nsv 2
204:       filter: grep -v "Solution method" | grep -v "Number of iterations" | sed -e "s/, maxit=1[0]*$//" | sed -e "s/[0-9]\.[0-9]*e[+-]\([0-9]*\)/removed/g"
205:       requires: double
206:       output_file: output/ex45_5.out
207:       test:
208:          args: -svd_type trlanczos -svd_ncv 8 -svd_trlanczos_gbidiag {{upper lower}} -svd_trlanczos_oneside {{0 1}}
209:          suffix: 5
210:       test:
211:          args: -svd_type cross -svd_ncv 10 -svd_cross_explicitmatrix
212:          suffix: 5_cross
213:       test:
214:          args: -svd_type cross -svd_ncv 10 -svd_cross_eps_type krylovschur -svd_cross_st_type sinvert -svd_cross_eps_target 0 -svd_cross_st_ksp_type gmres -svd_cross_st_pc_type jacobi
215:          suffix: 5_cross_implicit
216:       test:
217:          args: -svd_type cyclic -svd_ncv 12 -svd_cyclic_explicitmatrix {{0 1}}
218:          suffix: 5_cyclic
219:          requires: !complex

221:    testset:
222:       args: -m 15 -n 20 -p 21 -svd_nsv 4 -svd_ncv 9
223:       filter: grep -v "Solution method" | grep -v "Number of iterations" | sed -e "s/7.884967/7.884968/" | sed -e "s/, maxit=1[0]*$//" | sed -e "s/[0-9]\.[0-9]*e[+-]\([0-9]*\)/removed/g"
224:       requires: double
225:       output_file: output/ex45_6.out
226:       test:
227:          args: -svd_type trlanczos -svd_trlanczos_gbidiag {{single upper lower}} -svd_trlanczos_locking {{0 1}} -svd_trlanczos_oneside {{0 1}}
228:          suffix: 6
229:       test:
230:          args: -svd_type cross -svd_cross_explicitmatrix {{0 1}}
231:          suffix: 6_cross

233:    test:
234:       args: -m 15 -n 20 -p 21 -svd_nsv 4 -svd_ncv 9 -svd_type cyclic -svd_cyclic_explicitmatrix {{0 1}}
235:       filter: grep -v "Number of iterations" | sed -e "s/7.884967/7.884968/" | sed -e "s/[0-9]\.[0-9]*e[+-]\([0-9]*\)/removed/g"
236:       requires: double
237:       suffix: 6_cyclic
238:       output_file: output/ex45_6_cyclic.out

240:    testset:
241:       args: -m 20 -n 15 -p 21 -svd_nsv 4 -svd_ncv 9
242:       filter: grep -v "Solution method" | grep -v "Number of iterations" | sed -e "s/, maxit=1[0]*$//" | sed -e "s/[0-9]\.[0-9]*e[+-]\([0-9]*\)/removed/g"
243:       requires: double
244:       output_file: output/ex45_7.out
245:       test:
246:          args: -svd_type trlanczos -svd_trlanczos_gbidiag {{single upper lower}} -svd_trlanczos_restart 0.4 -svd_trlanczos_oneside {{0 1}}
247:          suffix: 7
248:       test:
249:          args: -svd_type cross -svd_cross_explicitmatrix {{0 1}}
250:          suffix: 7_cross

252:    test:
253:       args: -m 20 -n 15 -p 21 -svd_nsv 4 -svd_ncv 16 -svd_type cyclic -svd_cyclic_explicitmatrix {{0 1}}
254:       filter: grep -v "Number of iterations" | sed -e "s/[0-9]\.[0-9]*e[+-]\([0-9]*\)/removed/g"
255:       requires: double
256:       suffix: 7_cyclic
257:       output_file: output/ex45_7_cyclic.out

259:    test:
260:        args: -m 25 -n 20 -p 21 -svd_smallest -svd_nsv 2 -svd_ncv 5 -svd_type trlanczos -svd_trlanczos_gbidiag {{upper lower}} -svd_trlanczos_scale {{0.1 -20}}
261:        filter: grep -v "Solution method" | grep -v "Number of iterations" | grep -v "Stopping condition" | sed -e "s/, maxit=1[0]*$//" | sed -e "s/[0-9]\.[0-9]*e[+-]\([0-9]*\)/removed/g"
262:        suffix: 8

264: TEST*/