Actual source code: ex45.c

slepc-3.20.2 2024-03-15
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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[] = "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:   PetscFunctionBeginUser;
 31:   PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));

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

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

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

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

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

 64:   PetscCall(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++) PetscCall(MatSetValue(B,i,j+d,1.0,INSERT_VALUES));
 68:   }
 69:   PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY));
 70:   PetscCall(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:   PetscCall(SVDCreate(PETSC_COMM_WORLD,&svd));

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

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

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

 96:   PetscCall(SVDSolve(svd));
 97:   PetscCall(SVDGetIterationNumber(svd,&its));
 98:   PetscCall(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:   PetscCall(SVDGetType(svd,&type));
104:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type));
105:   PetscCall(SVDGetDimensions(svd,&nsv,NULL,NULL));
106:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested generalized singular values: %" PetscInt_FMT "\n",nsv));
107:   PetscCall(SVDGetTolerances(svd,&tol,&maxit));
108:   PetscCall(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:   PetscCall(SVDGetConverged(svd,&nconv));
118:   PetscCall(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:     PetscCall(MatCreateVecs(A,&x,&u));
126:     PetscCall(MatCreateVecs(B,NULL,&v));
127:     aux[0] = u;
128:     aux[1] = v;
129:     PetscCall(VecCreateNest(PETSC_COMM_WORLD,2,NULL,aux,&uv));

131:     PetscCall(VecDuplicateVecs(u,nconv,&U));
132:     PetscCall(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:       PetscCall(SVDGetSingularTriplet(svd,i,&sigma,uv,x));

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

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

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

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

174:   /*
175:      Free work space
176:   */
177:   PetscCall(SVDDestroy(&svd));
178:   PetscCall(MatDestroy(&A));
179:   PetscCall(MatDestroy(&B));
180:   PetscCall(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*/