Actual source code: ex45.c

slepc-3.17.0 2022-03-31
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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;

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

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

 39:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 40:                           Build the matrices
 41:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

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

 71:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 72:           Create the singular value solver and set various options
 73:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 75:   /*
 76:      Create singular value solver context
 77:   */
 78:   SVDCreate(PETSC_COMM_WORLD,&svd);

 80:   /*
 81:      Set operators and problem type
 82:   */
 83:   SVDSetOperators(svd,A,B);
 84:   SVDSetProblemType(svd,SVD_GENERALIZED);

 86:   /*
 87:      Set solver parameters at runtime
 88:   */
 89:   SVDSetFromOptions(svd);

 91:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 92:                       Solve the singular value system
 93:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

 99:   /*
100:      Optional: Get some information from the solver and display it
101:   */
102:   SVDGetType(svd,&type);
103:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
104:   SVDGetDimensions(svd,&nsv,NULL,NULL);
105:   PetscPrintf(PETSC_COMM_WORLD," Number of requested singular values: %" PetscInt_FMT "\n",nsv);
106:   SVDGetTolerances(svd,&tol,&maxit);
107:   PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%" PetscInt_FMT "\n",(double)tol,maxit);

109:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
110:                     Display solution and clean up
111:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

113:   /*
114:      Get number of converged singular triplets
115:   */
116:   SVDGetConverged(svd,&nconv);
117:   PetscPrintf(PETSC_COMM_WORLD," Number of converged approximate singular triplets: %" PetscInt_FMT "\n\n",nconv);

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

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

133:     /*
134:        Display singular values and errors relative to the norms
135:     */
136:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,
137:          "          sigma           ||r||/||[A;B]||\n"
138:          "  --------------------- ------------------\n"));
139:     for (i=0;i<nconv;i++) {
140:       /*
141:          Get converged singular triplets: i-th singular value is stored in sigma
142:       */
143:       SVDGetSingularTriplet(svd,i,&sigma,uv,x);

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

149:       /*
150:          Compute the error associated to each singular triplet
151:       */
152:       SVDComputeError(svd,i,SVD_ERROR_NORM,&error);

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

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

173:   /*
174:      Free work space
175:   */
176:   SVDDestroy(&svd);
177:   MatDestroy(&A);
178:   MatDestroy(&B);
179:   SlepcFinalize();
180:   return 0;
181: }

183: /*TEST

185:    testset:
186:       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"
187:       requires: double
188:       test:
189:          args: -svd_type lapack -m 20 -n 10 -p 6
190:          suffix: 1
191:       test:
192:          args: -svd_type lapack -m 15 -n 20 -p 10 -svd_smallest
193:          suffix: 2
194:       test:
195:          args: -svd_type lapack -m 15 -n 20 -p 21
196:          suffix: 3
197:       test:
198:          args: -svd_type lapack -m 20 -n 15 -p 21
199:          suffix: 4

201:    testset:
202:       args: -m 25 -n 20 -p 21 -svd_smallest -svd_nsv 4
203:       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"
204:       requires: double
205:       output_file: output/ex45_5.out
206:       test:
207:          args: -svd_type trlanczos -svd_ncv 8 -svd_trlanczos_gbidiag {{upper lower}}
208:          suffix: 5
209:       test:
210:          args: -svd_type cross -svd_ncv 10 -svd_cross_explicitmatrix {{0 1}}
211:          suffix: 5_cross
212:       test:
213:          args: -svd_type cyclic -svd_ncv 12 -svd_cyclic_explicitmatrix {{0 1}}
214:          suffix: 5_cyclic
215:          requires: !complex

217:    testset:
218:       args: -m 15 -n 20 -p 21 -svd_nsv 4 -svd_ncv 9
219:       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"
220:       requires: double
221:       output_file: output/ex45_6.out
222:       test:
223:          args: -svd_type trlanczos -svd_trlanczos_gbidiag {{single upper lower}} -svd_trlanczos_locking {{0 1}}
224:          suffix: 6
225:       test:
226:          args: -svd_type cross -svd_cross_explicitmatrix {{0 1}}
227:          suffix: 6_cross
228:       test:
229:          args: -svd_type cyclic -svd_cyclic_explicitmatrix {{0 1}}
230:          suffix: 6_cyclic

232:    testset:
233:       args: -m 20 -n 15 -p 21 -svd_nsv 4 -svd_ncv 9
234:       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"
235:       requires: double
236:       output_file: output/ex45_7.out
237:       test:
238:          args: -svd_type trlanczos -svd_trlanczos_gbidiag {{single upper lower}} -svd_trlanczos_restart 0.4
239:          suffix: 7
240:       test:
241:          args: -svd_type cross -svd_cross_explicitmatrix {{0 1}}
242:          suffix: 7_cross
243:       test:
244:          args: -svd_type cyclic -svd_cyclic_explicitmatrix {{0 1}}
245:          suffix: 7_cyclic

247: TEST*/