Actual source code: ex116.c

petsc-3.7.3 2016-08-01
Report Typos and Errors
  1: static char help[] = "Test LAPACK routine DSYEV() or DSYEVX(). \n\
  2: Reads PETSc matrix A \n\
  3: then computes selected eigenvalues, and optionally, eigenvectors of \n\
  4: a real generalized symmetric-definite eigenproblem \n\
  5:  A*x = lambda*x \n\
  6: Input parameters include\n\
  7:   -f <input_file> : file to load\n\
  8: e.g. ./ex116 -f /home/petsc/datafiles/matrices/small  \n\n";

 10: #include <petscmat.h>
 11: #include <petscblaslapack.h>

 13: extern PetscErrorCode CkEigenSolutions(PetscInt,Mat,PetscInt,PetscInt,PetscReal*,Vec*,PetscReal*);

 17: PetscInt main(PetscInt argc,char **args)
 18: {
 19:   Mat            A,A_dense;
 20:   Vec            *evecs;
 21:   PetscViewer    fd;                /* viewer */
 22:   char           file[1][PETSC_MAX_PATH_LEN];     /* input file name */
 23:   PetscBool      flg,TestSYEVX=PETSC_TRUE;
 25:   PetscBool      isSymmetric;
 26:   PetscScalar    *arrayA,*evecs_array,*work,*evals;
 27:   PetscMPIInt    size;
 28:   PetscInt       m,n,i,nevs,il,iu,cklvl=2;
 29:   PetscReal      vl,vu,abstol=1.e-8;
 30:   PetscBLASInt   *iwork,*ifail,lwork,lierr,bn;
 31:   PetscReal      tols[2];

 33:   PetscInitialize(&argc,&args,(char*)0,help);
 34:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
 35:   if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"This is a uniprocessor example only!");

 37:   PetscOptionsHasName(NULL,NULL, "-test_syev", &flg);
 38:   if (flg) {
 39:     TestSYEVX = PETSC_FALSE;
 40:   }

 42:   /* Determine files from which we read the two matrices */
 43:   PetscOptionsGetString(NULL,NULL,"-f",file[0],PETSC_MAX_PATH_LEN,&flg);

 45:   /* Load matrix A */
 46:   PetscViewerBinaryOpen(PETSC_COMM_WORLD,file[0],FILE_MODE_READ,&fd);
 47:   MatCreate(PETSC_COMM_WORLD,&A);
 48:   MatSetType(A,MATSEQAIJ);
 49:   MatLoad(A,fd);
 50:   PetscViewerDestroy(&fd);
 51:   MatGetSize(A,&m,&n);

 53:   /* Check whether A is symmetric */
 54:   PetscOptionsHasName(NULL,NULL, "-check_symmetry", &flg);
 55:   if (flg) {
 56:     Mat Trans;
 57:     MatTranspose(A,MAT_INITIAL_MATRIX, &Trans);
 58:     MatEqual(A, Trans, &isSymmetric);
 59:     if (!isSymmetric) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"A must be symmetric");
 60:     MatDestroy(&Trans);
 61:   }

 63:   /* Solve eigenvalue problem: A_dense*x = lambda*B*x */
 64:   /*==================================================*/
 65:   /* Convert aij matrix to MatSeqDense for LAPACK */
 66:   MatConvert(A,MATSEQDENSE,MAT_INITIAL_MATRIX,&A_dense);

 68:   PetscBLASIntCast(8*n,&lwork);
 69:   PetscBLASIntCast(n,&bn);
 70:   PetscMalloc1(n,&evals);
 71:   PetscMalloc1(lwork,&work);
 72:   MatDenseGetArray(A_dense,&arrayA);

 74:   if (!TestSYEVX) { /* test syev() */
 75:     printf(" LAPACKsyev: compute all %D eigensolutions...\n",m);
 76:     LAPACKsyev_("V","U",&bn,arrayA,&bn,evals,work,&lwork,&lierr);
 77:     evecs_array = arrayA;
 78:     PetscBLASIntCast(m,&nevs);
 79:     il          = 1;
 80:     PetscBLASIntCast(m,&iu);
 81:   } else { /* test syevx()  */
 82:     il   = 1;
 83:     PetscBLASIntCast(0.2*m,&iu);
 84:     printf(" LAPACKsyevx: compute %D to %D-th eigensolutions...\n",il,iu);
 85:     PetscMalloc1(m*n+1,&evecs_array);
 86:     PetscMalloc1(6*n+1,&iwork);
 87:     ifail = iwork + 5*n;

 89:     /* in the case "I", vl and vu are not referenced */
 90:     vl = 0.0; vu = 8.0;
 91:     LAPACKsyevx_("V","I","U",&bn,arrayA,&bn,&vl,&vu,&il,&iu,&abstol,&nevs,evals,evecs_array,&n,work,&lwork,iwork,ifail,&lierr);
 92:     PetscFree(iwork);
 93:   }
 94:   MatDenseRestoreArray(A_dense,&arrayA);
 95:   if (nevs <= 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_CONV_FAILED, "nev=%D, no eigensolution has found", nevs);

 97:   /* View eigenvalues */
 98:   PetscOptionsHasName(NULL,NULL, "-eig_view", &flg);
 99:   if (flg) {
100:     printf(" %D evals: \n",nevs);
101:     for (i=0; i<nevs; i++) printf("%D  %g\n",i+il,(double)evals[i]);
102:   }

104:   /* Check residuals and orthogonality */
105:   PetscMalloc1(nevs+1,&evecs);
106:   for (i=0; i<nevs; i++) {
107:     VecCreate(PETSC_COMM_SELF,&evecs[i]);
108:     VecSetSizes(evecs[i],PETSC_DECIDE,n);
109:     VecSetFromOptions(evecs[i]);
110:     VecPlaceArray(evecs[i],evecs_array+i*n);
111:   }

113:   tols[0] = tols[1] = PETSC_SQRT_MACHINE_EPSILON;
114:   CkEigenSolutions(cklvl,A,il-1,iu-1,evals,evecs,tols);

116:   /* Free work space. */
117:   for (i=0; i<nevs; i++) { VecDestroy(&evecs[i]);}
118:   PetscFree(evecs);
119:   MatDestroy(&A_dense);
120:   PetscFree(work);
121:   if (TestSYEVX) {PetscFree(evecs_array);}

123:   /* Compute SVD: A_dense = U*SIGMA*transpose(V),
124:      JOBU=JOBV='S':  the first min(m,n) columns of U and V are returned in the arrayU and arrayV; */
125:   /*==============================================================================================*/
126:   {
127:     /* Convert aij matrix to MatSeqDense for LAPACK */
128:     PetscScalar  *arrayU,*arrayVT,*arrayErr,alpha=1.0,beta=-1.0;
129:     Mat          Err;
130:     PetscBLASInt minMN,maxMN;
131:     PetscInt     j;
132:     PetscReal    norm;

134:     MatConvert(A,MATSEQDENSE,MAT_INITIAL_MATRIX,&A_dense);

136:     minMN = PetscMin(m,n);
137:     maxMN = PetscMax(m,n);
138:     lwork = 5*minMN + maxMN;
139:     PetscMalloc4(m*minMN,&arrayU,m*minMN,&arrayVT,m*minMN,&arrayErr,lwork,&work);

141:     /* Create matrix Err for checking error */
142:     MatCreate(PETSC_COMM_WORLD,&Err);
143:     MatSetSizes(Err,PETSC_DECIDE,PETSC_DECIDE,m,minMN);
144:     MatSetType(Err,MATSEQDENSE);
145:     MatSeqDenseSetPreallocation(Err,(PetscScalar*)arrayErr);

147:     /* Save A to arrayErr for checking accuracy later. arrayA will be destroyed by LAPACKgesvd_() */
148:     MatDenseGetArray(A_dense,&arrayA);
149:     PetscMemcpy(arrayErr,arrayA,sizeof(PetscScalar)*m*minMN);

151:     /* Compute A = U*SIGMA*VT */
152:     LAPACKgesvd_("S","S",&m,&n,arrayA,&m,evals,arrayU,&minMN,arrayVT,&minMN,work,&lwork,&lierr);
153:     MatDenseRestoreArray(A_dense,&arrayA);
154:     if (!lierr) {
155:       printf(" 1st 10 of %d singular values: \n",minMN);
156:       for (i=0; i<10; i++) printf("%D  %g\n",i,(double)evals[i]);
157:     } else {
158:       printf("LAPACKgesvd_ fails!");
159:     }

161:     /* Check Err = (U*Sigma*V^T - A) using BLASgemm() */
162:     /* U = U*Sigma */
163:     for (j=0; j<minMN; j++) { /* U[:,j] = sigma[j]*U[:,j] */
164:       for (i=0; i<m; i++) arrayU[j*m+i] *= evals[j];
165:     }
166:     /* Err = U*VT - A = alpha*U*VT + beta*Err */
167:     BLASgemm_("N","N",&m,&minMN,&minMN,&alpha,arrayU,&m,arrayVT,&minMN,&beta,arrayErr,&m);
168:     /*printf(" Err:\n");*/
169:     /*MatView(Err,PETSC_VIEWER_STDOUT_SELF);*/
170:     MatNorm(Err,NORM_FROBENIUS,&norm);
171:     printf(" || U*Sigma*VT - A || = %g\n",(double)norm);

173:     PetscFree4(arrayU,arrayVT,arrayErr,work);
174:     PetscFree(evals);
175:     MatDestroy(&A_dense);
176:     MatDestroy(&Err);
177:   }

179:   MatDestroy(&A);
180:   PetscFinalize();
181:   return 0;
182: }
183: /*------------------------------------------------
184:   Check the accuracy of the eigen solution
185:   ----------------------------------------------- */
186: /*
187:   input:
188:      cklvl      - check level:
189:                     1: check residual
190:                     2: 1 and check B-orthogonality locally
191:      A          - matrix
192:      il,iu      - lower and upper index bound of eigenvalues
193:      eval, evec - eigenvalues and eigenvectors stored in this process
194:      tols[0]    - reporting tol_res: || A * evec[i] - eval[i]*evec[i] ||
195:      tols[1]    - reporting tol_orth: evec[i]^T*evec[j] - delta_ij
196: */
197: #undef DEBUG_CkEigenSolutions
200: PetscErrorCode CkEigenSolutions(PetscInt cklvl,Mat A,PetscInt il,PetscInt iu,PetscReal *eval,Vec *evec,PetscReal *tols)
201: {
202:   PetscInt  ierr,i,j,nev;
203:   Vec       vt1,vt2;    /* tmp vectors */
204:   PetscReal norm,tmp,dot,norm_max,dot_max;

207:   nev = iu - il;
208:   if (nev <= 0) return(0);

210:   /*VecView(evec[0],PETSC_VIEWER_STDOUT_WORLD);*/
211:   VecDuplicate(evec[0],&vt1);
212:   VecDuplicate(evec[0],&vt2);

214:   switch (cklvl) {
215:   case 2:
216:     dot_max = 0.0;
217:     for (i = il; i<iu; i++) {
218:       VecCopy(evec[i], vt1);
219:       for (j=il; j<iu; j++) {
220:         VecDot(evec[j],vt1,&dot);
221:         if (j == i) {
222:           dot = PetscAbsScalar(dot - 1.0);
223:         } else {
224:           dot = PetscAbsScalar(dot);
225:         }
226:         if (dot > dot_max) dot_max = dot;
227: #if defined(DEBUG_CkEigenSolutions)
228:         if (dot > tols[1]) {
229:           VecNorm(evec[i],NORM_INFINITY,&norm);
230:           PetscPrintf(PETSC_COMM_SELF,"|delta(%D,%D)|: %g, norm: %g\n",i,j,(double)dot,(double)norm);
231:         }
232: #endif
233:       }
234:     }
235:     PetscPrintf(PETSC_COMM_SELF,"    max|(x_j^T*x_i) - delta_ji|: %g\n",(double)dot_max);

237:   case 1:
238:     norm_max = 0.0;
239:     for (i = il; i< iu; i++) {
240:       MatMult(A, evec[i], vt1);
241:       VecCopy(evec[i], vt2);
242:       tmp  = -eval[i];
243:       VecAXPY(vt1,tmp,vt2);
244:       VecNorm(vt1, NORM_INFINITY, &norm);
245:       norm = PetscAbsScalar(norm);
246:       if (norm > norm_max) norm_max = norm;
247: #if defined(DEBUG_CkEigenSolutions)
248:       /* sniff, and bark if necessary */
249:       if (norm > tols[0]) {
250:         printf("  residual violation: %D, resi: %g\n",i, norm);
251:       }
252: #endif
253:     }
254:     PetscPrintf(PETSC_COMM_SELF,"    max_resi:                    %g\n", (double)norm_max);
255:     break;
256:   default:
257:     PetscPrintf(PETSC_COMM_SELF,"Error: cklvl=%D is not supported \n",cklvl);
258:   }
259:   VecDestroy(&vt2);
260:   VecDestroy(&vt1);
261:   return(0);
262: }