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];
31: PetscFunctionBeginUser;
32: PetscCall(PetscInitialize(&argc, &args, NULL, help));
33: PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
34: PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only!");
36: PetscCall(PetscOptionsHasName(NULL, NULL, "-test_syev", &flg));
37: if (flg) TestSYEVX = PETSC_FALSE;
39: /* Determine files from which we read the two matrices */
40: PetscCall(PetscOptionsGetString(NULL, NULL, "-f", file[0], sizeof(file[0]), &flg));
42: /* Load matrix A */
43: PetscCall(PetscViewerBinaryOpen(PETSC_COMM_WORLD, file[0], FILE_MODE_READ, &fd));
44: PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
45: PetscCall(MatSetType(A, MATSEQAIJ));
46: PetscCall(MatLoad(A, fd));
47: PetscCall(PetscViewerDestroy(&fd));
48: PetscCall(MatGetSize(A, &m, &n));
50: /* Check whether A is symmetric */
51: PetscCall(PetscOptionsHasName(NULL, NULL, "-check_symmetry", &flg));
52: if (flg) {
53: Mat Trans;
54: PetscCall(MatTranspose(A, MAT_INITIAL_MATRIX, &Trans));
55: PetscCall(MatEqual(A, Trans, &isSymmetric));
56: PetscCheck(isSymmetric, PETSC_COMM_SELF, PETSC_ERR_USER, "A must be symmetric");
57: PetscCall(MatDestroy(&Trans));
58: }
60: /* Solve eigenvalue problem: A_dense*x = lambda*B*x */
61: /*==================================================*/
62: /* Convert aij matrix to MatSeqDense for LAPACK */
63: PetscCall(MatConvert(A, MATSEQDENSE, MAT_INITIAL_MATRIX, &A_dense));
65: PetscCall(PetscBLASIntCast(8 * n, &lwork));
66: PetscCall(PetscBLASIntCast(n, &bn));
67: PetscCall(PetscMalloc1(n, &evals));
68: PetscCall(PetscMalloc1(lwork, &work));
69: PetscCall(MatDenseGetArray(A_dense, &arrayA));
71: if (!TestSYEVX) { /* test syev() */
72: PetscCall(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: PetscCall(PetscBLASIntCast(m, &nevs));
76: il = 1;
77: PetscCall(PetscBLASIntCast(m, &iu));
78: } else { /* test syevx() */
79: il = 1;
80: PetscCall(PetscBLASIntCast(0.2 * m, &iu));
81: PetscCall(PetscBLASIntCast(n, &in));
82: PetscCall(PetscPrintf(PETSC_COMM_SELF, " LAPACKsyevx: compute %" PetscBLASInt_FMT " to %" PetscBLASInt_FMT "-th eigensolutions...\n", il, iu));
83: PetscCall(PetscMalloc1(m * n + 1, &evecs_array));
84: PetscCall(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: PetscCall(PetscFree(iwork));
92: }
93: PetscCall(MatDenseRestoreArray(A_dense, &arrayA));
94: PetscCheck(nevs > 0, PETSC_COMM_SELF, PETSC_ERR_CONV_FAILED, "nev=%" PetscBLASInt_FMT ", no eigensolution has found", nevs);
96: /* View eigenvalues */
97: PetscCall(PetscOptionsHasName(NULL, NULL, "-eig_view", &flg));
98: if (flg) {
99: PetscCall(PetscPrintf(PETSC_COMM_SELF, " %" PetscBLASInt_FMT " evals: \n", nevs));
100: for (i = 0; i < nevs; i++) PetscCall(PetscPrintf(PETSC_COMM_SELF, "%" PetscInt_FMT " %g\n", (PetscInt)(i + il), (double)evals[i]));
101: }
103: /* Check residuals and orthogonality */
104: PetscCall(PetscMalloc1(nevs + 1, &evecs));
105: for (i = 0; i < nevs; i++) {
106: PetscCall(VecCreate(PETSC_COMM_SELF, &evecs[i]));
107: PetscCall(VecSetSizes(evecs[i], PETSC_DECIDE, n));
108: PetscCall(VecSetFromOptions(evecs[i]));
109: PetscCall(VecPlaceArray(evecs[i], evecs_array + i * n));
110: }
112: tols[0] = tols[1] = PETSC_SQRT_MACHINE_EPSILON;
113: PetscCall(CkEigenSolutions(cklvl, A, il - 1, iu - 1, evals, evecs, tols));
115: /* Free work space. */
116: for (i = 0; i < nevs; i++) PetscCall(VecDestroy(&evecs[i]));
117: PetscCall(PetscFree(evecs));
118: PetscCall(MatDestroy(&A_dense));
119: PetscCall(PetscFree(work));
120: if (TestSYEVX) PetscCall(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: PetscCall(MatConvert(A, MATSEQDENSE, MAT_INITIAL_MATRIX, &A_dense));
135: PetscCall(PetscBLASIntCast(PetscMin(m, n), &minMN));
136: PetscCall(PetscBLASIntCast(PetscMax(m, n), &maxMN));
137: PetscCall(PetscBLASIntCast(5 * minMN + maxMN, &lwork));
138: PetscCall(PetscMalloc4(m * minMN, &arrayU, m * minMN, &arrayVT, m * minMN, &arrayErr, lwork, &work));
140: /* Create matrix Err for checking error */
141: PetscCall(MatCreate(PETSC_COMM_WORLD, &Err));
142: PetscCall(MatSetSizes(Err, PETSC_DECIDE, PETSC_DECIDE, m, minMN));
143: PetscCall(MatSetType(Err, MATSEQDENSE));
144: PetscCall(MatSeqDenseSetPreallocation(Err, (PetscScalar *)arrayErr));
146: /* Save A to arrayErr for checking accuracy later. arrayA will be destroyed by LAPACKgesvd_() */
147: PetscCall(MatDenseGetArray(A_dense, &arrayA));
148: PetscCall(PetscArraycpy(arrayErr, arrayA, m * minMN));
150: PetscCall(PetscBLASIntCast(m, &im));
151: PetscCall(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: PetscCall(MatDenseRestoreArray(A_dense, &arrayA));
155: if (!lierr) {
156: PetscCall(PetscPrintf(PETSC_COMM_SELF, " 1st 10 of %" PetscBLASInt_FMT " singular values: \n", minMN));
157: for (i = 0; i < 10; i++) PetscCall(PetscPrintf(PETSC_COMM_SELF, "%" PetscInt_FMT " %g\n", i, (double)evals[i]));
158: } else {
159: PetscCall(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: PetscCall(MatNorm(Err, NORM_FROBENIUS, &norm));
170: PetscCall(PetscPrintf(PETSC_COMM_SELF, " || U*Sigma*VT - A || = %g\n", (double)norm));
172: PetscCall(PetscFree4(arrayU, arrayVT, arrayErr, work));
173: PetscCall(PetscFree(evals));
174: PetscCall(MatDestroy(&A_dense));
175: PetscCall(MatDestroy(&Err));
176: }
178: PetscCall(MatDestroy(&A));
179: PetscCall(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: PetscFunctionBegin;
203: nev = iu - il;
204: if (nev <= 0) PetscFunctionReturn(PETSC_SUCCESS);
206: /*ierr = VecView(evec[0],PETSC_VIEWER_STDOUT_WORLD);*/
207: PetscCall(VecDuplicate(evec[0], &vt1));
208: PetscCall(VecDuplicate(evec[0], &vt2));
210: switch (cklvl) {
211: case 2:
212: dot_max = 0.0;
213: for (i = il; i < iu; i++) {
214: PetscCall(VecCopy(evec[i], vt1));
215: for (j = il; j < iu; j++) {
216: PetscCall(VecDot(evec[j], vt1, &dot));
217: if (j == i) {
218: dot = PetscAbsScalar(dot - 1);
219: } else {
220: dot = PetscAbsScalar(dot);
221: }
222: if (dot > dot_max) dot_max = dot;
223: if (dot > tols[1]) {
224: PetscCall(VecNorm(evec[i], NORM_INFINITY, &norm));
225: PetscCall(PetscPrintf(PETSC_COMM_SELF, "|delta(%" PetscInt_FMT ",%" PetscInt_FMT ")|: %g, norm: %g\n", i, j, (double)dot, (double)norm));
226: }
227: }
228: }
229: PetscCall(PetscPrintf(PETSC_COMM_SELF, " max|(x_j^T*x_i) - delta_ji|: %g\n", (double)dot_max));
231: case 1:
232: norm_max = 0.0;
233: for (i = il; i < iu; i++) {
234: PetscCall(MatMult(A, evec[i], vt1));
235: PetscCall(VecCopy(evec[i], vt2));
236: tmp = -eval[i];
237: PetscCall(VecAXPY(vt1, tmp, vt2));
238: PetscCall(VecNorm(vt1, NORM_INFINITY, &norm));
239: norm = PetscAbsScalar(norm);
240: if (norm > norm_max) norm_max = norm;
241: /* sniff, and bark if necessary */
242: if (norm > tols[0]) PetscCall(PetscPrintf(PETSC_COMM_SELF, " residual violation: %" PetscInt_FMT ", resi: %g\n", i, (double)norm));
243: }
244: PetscCall(PetscPrintf(PETSC_COMM_SELF, " max_resi: %g\n", (double)norm_max));
245: break;
246: default:
247: PetscCall(PetscPrintf(PETSC_COMM_SELF, "Error: cklvl=%" PetscInt_FMT " is not supported \n", cklvl));
248: }
249: PetscCall(VecDestroy(&vt2));
250: PetscCall(VecDestroy(&vt1));
251: PetscFunctionReturn(PETSC_SUCCESS);
252: }
254: /*TEST
256: build:
257: requires: !complex
259: test:
260: requires: datafilespath !complex double !defined(PETSC_USE_64BIT_INDICES)
261: args: -f ${DATAFILESPATH}/matrices/small
262: output_file: output/ex116_1.out
264: test:
265: suffix: 2
266: requires: datafilespath !complex double !defined(PETSC_USE_64BIT_INDICES)
267: args: -f ${DATAFILESPATH}/matrices/small -test_syev -check_symmetry
269: TEST*/