Actual source code: ex120.c
1: static char help[] = "Test LAPACK routine ZHEEV, ZHEEVX, ZHEGV and ZHEGVX. \n\
2: ZHEEV computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A. \n\n";
4: #include <petscmat.h>
5: #include <petscblaslapack.h>
7: extern PetscErrorCode CkEigenSolutions(PetscInt, Mat, PetscInt, PetscInt, PetscReal *, Vec *, PetscReal *);
9: int main(int argc, char **args)
10: {
11: Mat A, A_dense, B;
12: Vec *evecs;
13: PetscBool flg, TestZHEEV = PETSC_TRUE, TestZHEEVX = PETSC_FALSE, TestZHEGV = PETSC_FALSE, TestZHEGVX = PETSC_FALSE;
14: PetscBool isSymmetric;
15: PetscScalar *arrayA, *arrayB, *evecs_array = NULL, *work;
16: PetscReal *evals, *rwork;
17: PetscMPIInt size;
18: PetscInt m, i, j, cklvl = 2;
19: PetscReal vl, vu, abstol = 1.e-8;
20: PetscBLASInt nn, nevs, il, iu, *iwork, *ifail, lwork, lierr, bn, one = 1;
21: PetscReal tols[2];
22: PetscScalar v, sigma2;
23: PetscRandom rctx;
24: PetscReal h2, sigma1 = 100.0;
25: PetscInt dim, Ii, J, n = 6, use_random;
27: PetscFunctionBeginUser;
28: PetscCall(PetscInitialize(&argc, &args, (char *)0, help));
29: PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
30: PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only!");
32: PetscCall(PetscOptionsHasName(NULL, NULL, "-test_zheevx", &flg));
33: if (flg) {
34: TestZHEEV = PETSC_FALSE;
35: TestZHEEVX = PETSC_TRUE;
36: }
37: PetscCall(PetscOptionsHasName(NULL, NULL, "-test_zhegv", &flg));
38: if (flg) {
39: TestZHEEV = PETSC_FALSE;
40: TestZHEGV = PETSC_TRUE;
41: }
42: PetscCall(PetscOptionsHasName(NULL, NULL, "-test_zhegvx", &flg));
43: if (flg) {
44: TestZHEEV = PETSC_FALSE;
45: TestZHEGVX = PETSC_TRUE;
46: }
48: PetscCall(PetscOptionsGetReal(NULL, NULL, "-sigma1", &sigma1, NULL));
49: PetscCall(PetscOptionsGetInt(NULL, NULL, "-n", &n, NULL));
50: dim = n * n;
52: PetscCall(MatCreate(PETSC_COMM_SELF, &A));
53: PetscCall(MatSetSizes(A, PETSC_DECIDE, PETSC_DECIDE, dim, dim));
54: PetscCall(MatSetType(A, MATSEQDENSE));
55: PetscCall(MatSetFromOptions(A));
56: PetscCall(MatSetUp(A));
58: PetscCall(PetscOptionsHasName(NULL, NULL, "-norandom", &flg));
59: if (flg) use_random = 0;
60: else use_random = 1;
61: if (use_random) {
62: PetscCall(PetscRandomCreate(PETSC_COMM_SELF, &rctx));
63: PetscCall(PetscRandomSetFromOptions(rctx));
64: PetscCall(PetscRandomSetInterval(rctx, 0.0, PETSC_i));
65: } else {
66: sigma2 = 10.0 * PETSC_i;
67: }
68: h2 = 1.0 / ((n + 1) * (n + 1));
69: for (Ii = 0; Ii < dim; Ii++) {
70: v = -1.0;
71: i = Ii / n;
72: j = Ii - i * n;
73: if (i > 0) {
74: J = Ii - n;
75: PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, ADD_VALUES));
76: }
77: if (i < n - 1) {
78: J = Ii + n;
79: PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, ADD_VALUES));
80: }
81: if (j > 0) {
82: J = Ii - 1;
83: PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, ADD_VALUES));
84: }
85: if (j < n - 1) {
86: J = Ii + 1;
87: PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, ADD_VALUES));
88: }
89: if (use_random) PetscCall(PetscRandomGetValue(rctx, &sigma2));
90: v = 4.0 - sigma1 * h2;
91: PetscCall(MatSetValues(A, 1, &Ii, 1, &Ii, &v, ADD_VALUES));
92: }
93: /* make A complex Hermitian */
94: v = sigma2 * h2;
95: Ii = 0;
96: J = 1;
97: PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, ADD_VALUES));
98: v = -sigma2 * h2;
99: PetscCall(MatSetValues(A, 1, &J, 1, &Ii, &v, ADD_VALUES));
100: if (use_random) PetscCall(PetscRandomDestroy(&rctx));
101: PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
102: PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
103: m = n = dim;
105: /* Check whether A is symmetric */
106: PetscCall(PetscOptionsHasName(NULL, NULL, "-check_symmetry", &flg));
107: if (flg) {
108: Mat Trans;
109: PetscCall(MatTranspose(A, MAT_INITIAL_MATRIX, &Trans));
110: PetscCall(MatEqual(A, Trans, &isSymmetric));
111: PetscCheck(isSymmetric, PETSC_COMM_SELF, PETSC_ERR_USER, "A must be symmetric");
112: PetscCall(MatDestroy(&Trans));
113: }
115: /* Convert aij matrix to MatSeqDense for LAPACK */
116: PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQDENSE, &flg));
117: if (flg) {
118: PetscCall(MatDuplicate(A, MAT_COPY_VALUES, &A_dense));
119: } else {
120: PetscCall(MatConvert(A, MATSEQDENSE, MAT_INITIAL_MATRIX, &A_dense));
121: }
123: PetscCall(MatCreate(PETSC_COMM_SELF, &B));
124: PetscCall(MatSetSizes(B, PETSC_DECIDE, PETSC_DECIDE, dim, dim));
125: PetscCall(MatSetType(B, MATSEQDENSE));
126: PetscCall(MatSetFromOptions(B));
127: PetscCall(MatSetUp(B));
128: v = 1.0;
129: for (Ii = 0; Ii < dim; Ii++) PetscCall(MatSetValues(B, 1, &Ii, 1, &Ii, &v, ADD_VALUES));
131: /* Solve standard eigenvalue problem: A*x = lambda*x */
132: /*===================================================*/
133: PetscCall(PetscBLASIntCast(2 * n, &lwork));
134: PetscCall(PetscBLASIntCast(n, &bn));
135: PetscCall(PetscMalloc1(n, &evals));
136: PetscCall(PetscMalloc1(lwork, &work));
137: PetscCall(MatDenseGetArray(A_dense, &arrayA));
139: if (TestZHEEV) { /* test zheev() */
140: PetscCall(PetscPrintf(PETSC_COMM_WORLD, " LAPACKsyev: compute all %" PetscInt_FMT " eigensolutions...\n", m));
141: PetscCall(PetscMalloc1(3 * n - 2, &rwork));
142: LAPACKsyev_("V", "U", &bn, arrayA, &bn, evals, work, &lwork, rwork, &lierr);
143: PetscCall(PetscFree(rwork));
145: evecs_array = arrayA;
146: nevs = m;
147: il = 1;
148: iu = m;
149: }
150: if (TestZHEEVX) {
151: il = 1;
152: PetscCall(PetscBLASIntCast((0.2 * m), &iu));
153: PetscCall(PetscPrintf(PETSC_COMM_WORLD, " LAPACKsyevx: compute %d to %d-th eigensolutions...\n", il, iu));
154: PetscCall(PetscMalloc1(m * n + 1, &evecs_array));
155: PetscCall(PetscMalloc1(7 * n + 1, &rwork));
156: PetscCall(PetscMalloc1(5 * n + 1, &iwork));
157: PetscCall(PetscMalloc1(n + 1, &ifail));
159: /* in the case "I", vl and vu are not referenced */
160: vl = 0.0;
161: vu = 8.0;
162: PetscCall(PetscBLASIntCast(n, &nn));
163: LAPACKsyevx_("V", "I", "U", &bn, arrayA, &bn, &vl, &vu, &il, &iu, &abstol, &nevs, evals, evecs_array, &nn, work, &lwork, rwork, iwork, ifail, &lierr);
164: PetscCall(PetscFree(iwork));
165: PetscCall(PetscFree(ifail));
166: PetscCall(PetscFree(rwork));
167: }
168: if (TestZHEGV) {
169: PetscCall(PetscPrintf(PETSC_COMM_WORLD, " LAPACKsygv: compute all %" PetscInt_FMT " eigensolutions...\n", m));
170: PetscCall(PetscMalloc1(3 * n + 1, &rwork));
171: PetscCall(MatDenseGetArray(B, &arrayB));
172: LAPACKsygv_(&one, "V", "U", &bn, arrayA, &bn, arrayB, &bn, evals, work, &lwork, rwork, &lierr);
173: evecs_array = arrayA;
174: nevs = m;
175: il = 1;
176: iu = m;
177: PetscCall(MatDenseRestoreArray(B, &arrayB));
178: PetscCall(PetscFree(rwork));
179: }
180: if (TestZHEGVX) {
181: il = 1;
182: PetscCall(PetscBLASIntCast((0.2 * m), &iu));
183: PetscCall(PetscPrintf(PETSC_COMM_WORLD, " LAPACKsygv: compute %d to %d-th eigensolutions...\n", il, iu));
184: PetscCall(PetscMalloc1(m * n + 1, &evecs_array));
185: PetscCall(PetscMalloc1(6 * n + 1, &iwork));
186: ifail = iwork + 5 * n;
187: PetscCall(PetscMalloc1(7 * n + 1, &rwork));
188: PetscCall(MatDenseGetArray(B, &arrayB));
189: vl = 0.0;
190: vu = 8.0;
191: PetscCall(PetscBLASIntCast(n, &nn));
192: LAPACKsygvx_(&one, "V", "I", "U", &bn, arrayA, &bn, arrayB, &bn, &vl, &vu, &il, &iu, &abstol, &nevs, evals, evecs_array, &nn, work, &lwork, rwork, iwork, ifail, &lierr);
193: PetscCall(MatDenseRestoreArray(B, &arrayB));
194: PetscCall(PetscFree(iwork));
195: PetscCall(PetscFree(rwork));
196: }
197: PetscCall(MatDenseRestoreArray(A_dense, &arrayA));
198: PetscCheck(nevs > 0, PETSC_COMM_SELF, PETSC_ERR_CONV_FAILED, "nev=%d, no eigensolution has found", nevs);
200: /* View evals */
201: PetscCall(PetscOptionsHasName(NULL, NULL, "-eig_view", &flg));
202: if (flg) {
203: PetscCall(PetscPrintf(PETSC_COMM_WORLD, " %d evals: \n", nevs));
204: for (i = 0; i < nevs; i++) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%" PetscInt_FMT " %g\n", i + il, (double)evals[i]));
205: }
207: /* Check residuals and orthogonality */
208: PetscCall(PetscMalloc1(nevs + 1, &evecs));
209: for (i = 0; i < nevs; i++) {
210: PetscCall(VecCreate(PETSC_COMM_SELF, &evecs[i]));
211: PetscCall(VecSetSizes(evecs[i], PETSC_DECIDE, n));
212: PetscCall(VecSetFromOptions(evecs[i]));
213: PetscCall(VecPlaceArray(evecs[i], evecs_array + i * n));
214: }
216: tols[0] = PETSC_SQRT_MACHINE_EPSILON;
217: tols[1] = PETSC_SQRT_MACHINE_EPSILON;
218: PetscCall(CkEigenSolutions(cklvl, A, il - 1, iu - 1, evals, evecs, tols));
219: for (i = 0; i < nevs; i++) PetscCall(VecDestroy(&evecs[i]));
220: PetscCall(PetscFree(evecs));
222: /* Free work space. */
223: if (TestZHEEVX || TestZHEGVX) PetscCall(PetscFree(evecs_array));
224: PetscCall(PetscFree(evals));
225: PetscCall(PetscFree(work));
226: PetscCall(MatDestroy(&A_dense));
227: PetscCall(MatDestroy(&A));
228: PetscCall(MatDestroy(&B));
229: PetscCall(PetscFinalize());
230: return 0;
231: }
232: /*------------------------------------------------
233: Check the accuracy of the eigen solution
234: ----------------------------------------------- */
235: /*
236: input:
237: cklvl - check level:
238: 1: check residual
239: 2: 1 and check B-orthogonality locally
240: A - matrix
241: il,iu - lower and upper index bound of eigenvalues
242: eval, evec - eigenvalues and eigenvectors stored in this process
243: tols[0] - reporting tol_res: || A * evec[i] - eval[i]*evec[i] ||
244: tols[1] - reporting tol_orth: evec[i]^T*evec[j] - delta_ij
245: */
246: PetscErrorCode CkEigenSolutions(PetscInt cklvl, Mat A, PetscInt il, PetscInt iu, PetscReal *eval, Vec *evec, PetscReal *tols)
247: {
248: PetscInt i, j, nev;
249: Vec vt1, vt2; /* tmp vectors */
250: PetscReal norm, tmp, norm_max, dot_max, rdot;
251: PetscScalar dot;
253: PetscFunctionBegin;
254: nev = iu - il;
255: if (nev <= 0) PetscFunctionReturn(PETSC_SUCCESS);
257: PetscCall(VecDuplicate(evec[0], &vt1));
258: PetscCall(VecDuplicate(evec[0], &vt2));
260: switch (cklvl) {
261: case 2:
262: dot_max = 0.0;
263: for (i = il; i < iu; i++) {
264: PetscCall(VecCopy(evec[i], vt1));
265: for (j = il; j < iu; j++) {
266: PetscCall(VecDot(evec[j], vt1, &dot));
267: if (j == i) {
268: rdot = PetscAbsScalar(dot - (PetscScalar)1.0);
269: } else {
270: rdot = PetscAbsScalar(dot);
271: }
272: if (rdot > dot_max) dot_max = rdot;
273: if (rdot > tols[1]) {
274: PetscCall(VecNorm(evec[i], NORM_INFINITY, &norm));
275: PetscCall(PetscPrintf(PETSC_COMM_SELF, "|delta(%" PetscInt_FMT ",%" PetscInt_FMT ")|: %g, norm: %g\n", i, j, (double)rdot, (double)norm));
276: }
277: }
278: }
279: PetscCall(PetscPrintf(PETSC_COMM_SELF, " max|(x_j^T*x_i) - delta_ji|: %g\n", (double)dot_max));
281: case 1:
282: norm_max = 0.0;
283: for (i = il; i < iu; i++) {
284: PetscCall(MatMult(A, evec[i], vt1));
285: PetscCall(VecCopy(evec[i], vt2));
286: tmp = -eval[i];
287: PetscCall(VecAXPY(vt1, tmp, vt2));
288: PetscCall(VecNorm(vt1, NORM_INFINITY, &norm));
289: norm = PetscAbs(norm);
290: if (norm > norm_max) norm_max = norm;
291: /* sniff, and bark if necessary */
292: if (norm > tols[0]) PetscCall(PetscPrintf(PETSC_COMM_WORLD, " residual violation: %" PetscInt_FMT ", resi: %g\n", i, (double)norm));
293: }
294: PetscCall(PetscPrintf(PETSC_COMM_SELF, " max_resi: %g\n", (double)norm_max));
295: break;
296: default:
297: PetscCall(PetscPrintf(PETSC_COMM_SELF, "Error: cklvl=%" PetscInt_FMT " is not supported \n", cklvl));
298: }
299: PetscCall(VecDestroy(&vt2));
300: PetscCall(VecDestroy(&vt1));
301: PetscFunctionReturn(PETSC_SUCCESS);
302: }
304: /*TEST
306: build:
307: requires: complex
309: test:
311: test:
312: suffix: 2
313: args: -test_zheevx
315: test:
316: suffix: 3
317: args: -test_zhegv
319: test:
320: suffix: 4
321: args: -test_zhegvx
323: TEST*/