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 $DATAFILESPATH/matrices/small  \n\n";

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

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

 15: int main(int argc, char **args)
 16: {
 17:   Mat           A, A_dense;
 18:   Vec          *evecs;
 19:   PetscViewer   fd;                          /* viewer */
 20:   char          file[1][PETSC_MAX_PATH_LEN]; /* input file name */
 21:   PetscBool     flg, TestSYEVX = PETSC_TRUE;
 22:   PetscBool     isSymmetric;
 23:   PetscScalar  *arrayA, *evecs_array, *work, *evals;
 24:   PetscMPIInt   size;
 25:   PetscInt      m, n, i, cklvl = 2;
 26:   PetscBLASInt  nevs, il, iu, in;
 27:   PetscReal     vl, vu, abstol = 1.e-8;
 28:   PetscBLASInt *iwork, *ifail, lwork, lierr, bn;
 29:   PetscReal     tols[2];

 32:   PetscInitialize(&argc, &args, (char *)0, help);
 33:   MPI_Comm_size(PETSC_COMM_WORLD, &size);

 36:   PetscOptionsHasName(NULL, NULL, "-test_syev", &flg);
 37:   if (flg) TestSYEVX = PETSC_FALSE;

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

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

 50:   /* Check whether A is symmetric */
 51:   PetscOptionsHasName(NULL, NULL, "-check_symmetry", &flg);
 52:   if (flg) {
 53:     Mat Trans;
 54:     MatTranspose(A, MAT_INITIAL_MATRIX, &Trans);
 55:     MatEqual(A, Trans, &isSymmetric);
 57:     MatDestroy(&Trans);
 58:   }

 60:   /* Solve eigenvalue problem: A_dense*x = lambda*B*x */
 61:   /*==================================================*/
 62:   /* Convert aij matrix to MatSeqDense for LAPACK */
 63:   MatConvert(A, MATSEQDENSE, MAT_INITIAL_MATRIX, &A_dense);

 65:   PetscBLASIntCast(8 * n, &lwork);
 66:   PetscBLASIntCast(n, &bn);
 67:   PetscMalloc1(n, &evals);
 68:   PetscMalloc1(lwork, &work);
 69:   MatDenseGetArray(A_dense, &arrayA);

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

 87:     /* in the case "I", vl and vu are not referenced */
 88:     vl = 0.0;
 89:     vu = 8.0;
 90:     LAPACKsyevx_("V", "I", "U", &bn, arrayA, &bn, &vl, &vu, &il, &iu, &abstol, &nevs, evals, evecs_array, &in, work, &lwork, iwork, ifail, &lierr);
 91:     PetscFree(iwork);
 92:   }
 93:   MatDenseRestoreArray(A_dense, &arrayA);

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

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

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

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

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

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

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

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

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

150:     PetscBLASIntCast(m, &im);
151:     PetscBLASIntCast(n, &in);
152:     /* Compute A = U*SIGMA*VT */
153:     LAPACKgesvd_("S", "S", &im, &in, arrayA, &im, evals, arrayU, &minMN, arrayVT, &minMN, work, &lwork, &lierr);
154:     MatDenseRestoreArray(A_dense, &arrayA);
155:     if (!lierr) {
156:       PetscPrintf(PETSC_COMM_SELF, " 1st 10 of %" PetscBLASInt_FMT " singular values: \n", minMN);
157:       for (i = 0; i < 10; i++) PetscPrintf(PETSC_COMM_SELF, "%" PetscInt_FMT "  %g\n", i, (double)evals[i]);
158:     } else {
159:       PetscPrintf(PETSC_COMM_SELF, "LAPACKgesvd_ fails!");
160:     }

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

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

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

202:   nev = iu - il;
203:   if (nev <= 0) return 0;

205:   /*VecView(evec[0],PETSC_VIEWER_STDOUT_WORLD);*/
206:   VecDuplicate(evec[0], &vt1);
207:   VecDuplicate(evec[0], &vt2);

209:   switch (cklvl) {
210:   case 2:
211:     dot_max = 0.0;
212:     for (i = il; i < iu; i++) {
213:       VecCopy(evec[i], vt1);
214:       for (j = il; j < iu; j++) {
215:         VecDot(evec[j], vt1, &dot);
216:         if (j == i) {
217:           dot = PetscAbsScalar(dot - 1);
218:         } else {
219:           dot = PetscAbsScalar(dot);
220:         }
221:         if (dot > dot_max) dot_max = dot;
222:         if (dot > tols[1]) {
223:           VecNorm(evec[i], NORM_INFINITY, &norm);
224:           PetscPrintf(PETSC_COMM_SELF, "|delta(%" PetscInt_FMT ",%" PetscInt_FMT ")|: %g, norm: %g\n", i, j, (double)dot, (double)norm);
225:         }
226:       }
227:     }
228:     PetscPrintf(PETSC_COMM_SELF, "    max|(x_j^T*x_i) - delta_ji|: %g\n", (double)dot_max);

230:   case 1:
231:     norm_max = 0.0;
232:     for (i = il; i < iu; i++) {
233:       MatMult(A, evec[i], vt1);
234:       VecCopy(evec[i], vt2);
235:       tmp = -eval[i];
236:       VecAXPY(vt1, tmp, vt2);
237:       VecNorm(vt1, NORM_INFINITY, &norm);
238:       norm = PetscAbsScalar(norm);
239:       if (norm > norm_max) norm_max = norm;
240:       /* sniff, and bark if necessary */
241:       if (norm > tols[0]) PetscPrintf(PETSC_COMM_SELF, "  residual violation: %" PetscInt_FMT ", resi: %g\n", i, (double)norm);
242:     }
243:     PetscPrintf(PETSC_COMM_SELF, "    max_resi:                    %g\n", (double)norm_max);
244:     break;
245:   default:
246:     PetscPrintf(PETSC_COMM_SELF, "Error: cklvl=%" PetscInt_FMT " is not supported \n", cklvl);
247:   }
248:   VecDestroy(&vt2);
249:   VecDestroy(&vt1);
250:   return 0;
251: }

253: /*TEST

255:    build:
256:       requires: !complex

258:    test:
259:       requires: datafilespath !complex double !defined(PETSC_USE_64BIT_INDICES)
260:       args: -f ${DATAFILESPATH}/matrices/small
261:       output_file: output/ex116_1.out

263:    test:
264:       suffix: 2
265:       requires: datafilespath !complex double !defined(PETSC_USE_64BIT_INDICES)
266:       args: -f ${DATAFILESPATH}/matrices/small -test_syev -check_symmetry

268: TEST*/