Actual source code: ex116.c

  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


 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:   PetscTruth     flg,flgA=PETSC_FALSE,flgB=PETSC_FALSE,TestSYEVX=PETSC_TRUE;
 25:   PetscTruth     isSymmetric;
 26:   PetscScalar    sigma,*arrayA,*arrayB,*evecs_array,*work,*evals;
 27:   PetscMPIInt    size;
 28:   PetscInt       m,n,i,j,nevs,il,iu,cklvl=2;
 29:   PetscReal      vl,vu,abstol=1.e-8;
 30:   PetscBLASInt   *iwork,*ifail,lwork,lierr,bn;
 31:   PetscReal      tols[2];
 32:   PetscInt       nzeros[2],nz;
 33:   PetscReal      ratio;
 34: 
 35:   PetscInitialize(&argc,&args,(char *)0,help);
 36:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
 37:   if (size != 1) SETERRQ(PETSC_ERR_SUP,"This is a uniprocessor example only!");

 39:   PetscOptionsHasName(PETSC_NULL, "-test_syev", &flg);
 40:   if (flg){
 41:     TestSYEVX = PETSC_FALSE;
 42:   }

 44:   /* Determine files from which we read the two matrices */
 45:   PetscOptionsGetString(PETSC_NULL,"-f",file[0],PETSC_MAX_PATH_LEN-1,&flg);

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

 53:   /* Check whether A is symmetric */
 54:   PetscOptionsHasName(PETSC_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_ERR_USER,"A must be symmetric");
 60:     MatDestroy(Trans);
 61:   }

 63:   /* Convert aij matrix to MatSeqDense for LAPACK */
 64:   PetscTypeCompare((PetscObject)A,MATSEQDENSE,&flg);
 65:   if (!flg) {
 66:     MatConvert(A,MATSEQDENSE,MAT_INITIAL_MATRIX,&A_dense);
 67:   }

 69:   /* Solve eigenvalue problem: A*x = lambda*B*x */
 70:   /*============================================*/
 71:   lwork = PetscBLASIntCast(8*n);
 72:   bn    = PetscBLASIntCast(n);
 73:   PetscMalloc(n*sizeof(PetscScalar),&evals);
 74:   PetscMalloc(lwork*sizeof(PetscScalar),&work);
 75:   MatGetArray(A_dense,&arrayA);

 77:   if (!TestSYEVX){ /* test syev() */
 78:     printf(" LAPACKsyev: compute all %d eigensolutions...\n",m);
 79:     LAPACKsyev_("V","U",&bn,arrayA,&bn,evals,work,&lwork,&lierr);
 80:     evecs_array = arrayA;
 81:     nevs = PetscBLASIntCast(m);
 82:     il=1; iu=PetscBLASIntCast(m);
 83:   } else { /* test syevx()  */
 84:     il = 1; iu=PetscBLASIntCast((0.2*m)); /* request 1 to 20%m evalues */
 85:     printf(" LAPACKsyevx: compute %d to %d-th eigensolutions...\n",il,iu);
 86:     PetscMalloc((m*n+1)*sizeof(PetscScalar),&evecs_array);
 87:     PetscMalloc((6*n+1)*sizeof(PetscBLASInt),&iwork);
 88:     ifail = iwork + 5*n;
 89: 
 90:     /* in the case "I", vl and vu are not referenced */
 91:     vl = 0.0; vu = 8.0;
 92:     LAPACKsyevx_("V","I","U",&bn,arrayA,&bn,&vl,&vu,&il,&iu,&abstol,&nevs,evals,evecs_array,&n,work,&lwork,iwork,ifail,&lierr);
 93:     PetscFree(iwork);
 94:   }
 95:   MatRestoreArray(A,&arrayA);
 96:   if (nevs <= 0 ) SETERRQ1(PETSC_ERR_CONV_FAILED, "nev=%d, no eigensolution has found", nevs);

 98:   /* View evals */
 99:   PetscOptionsHasName(PETSC_NULL, "-eig_view", &flg);
100:   if (flg){
101:     printf(" %d evals: \n",nevs);
102:     for (i=0; i<nevs; i++) printf("%d  %G\n",i+il,evals[i]);
103:   }

105:   /* Check residuals and orthogonality */
106:   PetscMalloc((nevs+1)*sizeof(Vec),&evecs);
107:   for (i=0; i<nevs; i++){
108:     VecCreate(PETSC_COMM_SELF,&evecs[i]);
109:     VecSetSizes(evecs[i],PETSC_DECIDE,n);
110:     VecSetFromOptions(evecs[i]);
111:     VecPlaceArray(evecs[i],evecs_array+i*n);
112:   }
113: 
114:   tols[0] = 1.e-8;  tols[1] = 1.e-8;
115:   CkEigenSolutions(cklvl,A,il-1,iu-1,evals,evecs,tols);
116:   for (i=0; i<nevs; i++){ VecDestroy(evecs[i]);}
117:   PetscFree(evecs);
118: 
119:   /* Free work space. */
120:   if (TestSYEVX){PetscFree(evecs_array);}
121: 
122:   PetscFree(evals);
123:   PetscFree(work);

125:   MatDestroy(A_dense);
126:   MatDestroy(A);
127:   PetscFinalize();
128:   return 0;
129: }
130: /*------------------------------------------------
131:   Check the accuracy of the eigen solution
132:   ----------------------------------------------- */
133: /*
134:   input: 
135:      cklvl      - check level: 
136:                     1: check residual
137:                     2: 1 and check B-orthogonality locally 
138:      A          - matrix 
139:      il,iu      - lower and upper index bound of eigenvalues 
140:      eval, evec - eigenvalues and eigenvectors stored in this process
141:      tols[0]    - reporting tol_res: || A * evec[i] - eval[i]*evec[i] ||
142:      tols[1]    - reporting tol_orth: evec[i]^T*evec[j] - delta_ij
143: */
144: #undef DEBUG_CkEigenSolutions
147: PetscErrorCode CkEigenSolutions(PetscInt cklvl,Mat A,PetscInt il,PetscInt iu,PetscReal *eval,Vec *evec,PetscReal *tols)
148: {
149:   PetscInt     ierr,i,j,nev;
150:   Vec          vt1,vt2; /* tmp vectors */
151:   PetscReal    norm,tmp,dot,norm_max,dot_max;

154:   nev = iu - il;
155:   if (nev <= 0) return(0);

157:   //VecView(evec[0],PETSC_VIEWER_STDOUT_WORLD);
158:   VecDuplicate(evec[0],&vt1);
159:   VecDuplicate(evec[0],&vt2);

161:   switch (cklvl){
162:   case 2:
163:     dot_max = 0.0;
164:     for (i = il; i<iu; i++){
165:       //printf("ck %d-th\n",i);
166:       VecCopy(evec[i], vt1);
167:       for (j=il; j<iu; j++){
168:         VecDot(evec[j],vt1,&dot);
169:         if (j == i){
170:           dot = PetscAbsScalar(dot - 1.0);
171:         } else {
172:           dot = PetscAbsScalar(dot);
173:         }
174:         if (dot > dot_max) dot_max = dot;
175: #ifdef DEBUG_CkEigenSolutions
176:         if (dot > tols[1] ) {
177:           VecNorm(evec[i],NORM_INFINITY,&norm);
178:           PetscPrintf(PETSC_COMM_SELF,"|delta(%d,%d)|: %G, norm: %G\n",i,j,dot,norm);
179:         }
180: #endif
181:       }
182:     }
183:     PetscPrintf(PETSC_COMM_SELF,"    max|(x_j^T*x_i) - delta_ji|: %G\n",dot_max);

185:   case 1:
186:     norm_max = 0.0;
187:     for (i = il; i< iu; i++){
188:       MatMult(A, evec[i], vt1);
189:       VecCopy(evec[i], vt2);
190:       tmp  = -eval[i];
191:       VecAXPY(vt1,tmp,vt2);
192:       VecNorm(vt1, NORM_INFINITY, &norm);
193:       norm = PetscAbsScalar(norm);
194:       if (norm > norm_max) norm_max = norm;
195: #ifdef DEBUG_CkEigenSolutions
196:       /* sniff, and bark if necessary */
197:       if (norm > tols[0]){
198:         printf( "  residual violation: %d, resi: %g\n",i, norm);
199:       }
200: #endif
201:     }
202:     PetscPrintf(PETSC_COMM_SELF,"    max_resi:                    %G\n", norm_max);
203:    break;
204:   default:
205:     PetscPrintf(PETSC_COMM_SELF,"Error: cklvl=%d is not supported \n",cklvl);
206:   }
207:   VecDestroy(vt2);
208:   VecDestroy(vt1);
209:   return(0);
210: }