Actual source code: ex99.c
petsc-3.5.4 2015-05-23
1: static char help[] = "Test LAPACK routine DSYGV() or DSYGVX(). \n\
2: Reads PETSc matrix A and B (or create B=I), \n\
3: then computes selected eigenvalues, and optionally, eigenvectors of \n\
4: a real generalized symmetric-definite eigenproblem \n\
5: A*x = lambda*B*x \n\
6: Input parameters include\n\
7: -f0 <input_file> : first file to load (small system)\n\
8: -fA <input_file> -fB <input_file>: second files to load (larger system) \n\
9: e.g. ./ex99 -f0 $D/small -fA $D/Eigdftb/dftb_bin/diamond_xxs_A -fB $D/Eigdftb/dftb_bin/diamond_xxs_B -mat_getrow_uppertriangular,\n\
10: where $D = /home/petsc/datafiles/matrices/Eigdftb/dftb_bin\n\n";
12: /* This example only works with real numbers */
14: #include <petscmat.h>
15: #include <../src/mat/impls/sbaij/seq/sbaij.h>
16: #include <petscblaslapack.h>
18: extern PetscErrorCode CkEigenSolutions(PetscInt*,Mat*,PetscReal*,Vec*,PetscInt*,PetscInt*,PetscReal*);
22: PetscInt main(PetscInt argc,char **args)
23: {
24: Mat A,B,A_dense,B_dense,mats[2],A_sp;
25: Vec *evecs;
26: PetscViewer fd; /* viewer */
27: char file[3][PETSC_MAX_PATH_LEN]; /* input file name */
28: PetscBool flg,flgA=PETSC_FALSE,flgB=PETSC_FALSE,TestSYGVX=PETSC_TRUE;
30: PetscBool preload=PETSC_TRUE,isSymmetric;
31: PetscScalar sigma,one=1.0,*arrayA,*arrayB,*evecs_array,*work,*evals;
32: PetscMPIInt size;
33: PetscInt m,n,i,j,nevs,il,iu;
34: PetscLogStage stages[2];
35: PetscReal vl,vu,abstol=1.e-8;
36: PetscBLASInt *iwork,*ifail,lone=1,lwork,lierr,bn;
37: PetscInt ievbd_loc[2],offset=0,cklvl=2;
38: PetscReal tols[2];
39: Mat_SeqSBAIJ *sbaij;
40: PetscScalar *aa;
41: PetscInt *ai,*aj;
42: PetscInt nzeros[2],nz;
43: PetscReal ratio;
45: PetscInitialize(&argc,&args,(char*)0,help);
46: MPI_Comm_size(PETSC_COMM_WORLD,&size);
47: if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"This is a uniprocessor example only!");
48: PetscLogStageRegister("EigSolve",&stages[0]);
49: PetscLogStageRegister("EigCheck",&stages[1]);
51: /* Determine files from which we read the two matrices */
52: PetscOptionsGetString(NULL,"-f0",file[0],PETSC_MAX_PATH_LEN,&flg);
53: if (!flg) {
54: PetscOptionsGetString(NULL,"-fA",file[0],PETSC_MAX_PATH_LEN,&flgA);
55: if (!flgA) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_USER,"Must indicate binary file with the -fA or -fB options");
56: PetscOptionsGetString(NULL,"-fB",file[1],PETSC_MAX_PATH_LEN,&flgB);
57: preload = PETSC_FALSE;
58: } else {
59: PetscOptionsGetString(NULL,"-fA",file[1],PETSC_MAX_PATH_LEN,&flgA);
60: if (!flgA) preload = PETSC_FALSE; /* don't bother with second system */
61: PetscOptionsGetString(NULL,"-fB",file[2],PETSC_MAX_PATH_LEN,&flgB);
62: }
64: PetscPreLoadBegin(preload,"Load system");
65: /* Load matrices */
66: PetscViewerBinaryOpen(PETSC_COMM_WORLD,file[PetscPreLoadIt],FILE_MODE_READ,&fd);
67: MatCreate(PETSC_COMM_WORLD,&A);
68: MatSetType(A,MATSBAIJ);
69: MatLoad(A,fd);
70: PetscViewerDestroy(&fd);
71: MatGetSize(A,&m,&n);
72: if ((flgB && PetscPreLoadIt) || (flgB && !preload)) {
73: PetscViewerBinaryOpen(PETSC_COMM_WORLD,file[PetscPreLoadIt+1],FILE_MODE_READ,&fd);
74: MatCreate(PETSC_COMM_WORLD,&B);
75: MatSetType(B,MATSBAIJ);
76: MatLoad(B,fd);
77: PetscViewerDestroy(&fd);
78: } else { /* create B=I */
79: MatCreate(PETSC_COMM_WORLD,&B);
80: MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,m,n);
81: MatSetType(B,MATSEQSBAIJ);
82: MatSetFromOptions(B);
83: MatSetUp(B);
84: for (i=0; i<m; i++) {
85: MatSetValues(B,1,&i,1,&i,&one,INSERT_VALUES);
86: }
87: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
88: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
89: }
91: /* Add a shift to A */
92: PetscOptionsGetScalar(NULL,"-mat_sigma",&sigma,&flg);
93: if (flg) {
94: MatAXPY(A,sigma,B,DIFFERENT_NONZERO_PATTERN); /* A <- sigma*B + A */
95: }
97: /* Check whether A is symmetric */
98: PetscOptionsHasName(NULL, "-check_symmetry", &flg);
99: if (flg) {
100: Mat Trans;
101: MatTranspose(A,MAT_INITIAL_MATRIX, &Trans);
102: MatEqual(A, Trans, &isSymmetric);
103: if (!isSymmetric) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"A must be symmetric");
104: MatDestroy(&Trans);
105: if (flgB && PetscPreLoadIt) {
106: MatTranspose(B,MAT_INITIAL_MATRIX, &Trans);
107: MatEqual(B, Trans, &isSymmetric);
108: if (!isSymmetric) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"B must be symmetric");
109: MatDestroy(&Trans);
110: }
111: }
113: /* View small entries of A */
114: PetscOptionsHasName(NULL, "-Asp_view", &flg);
115: if (flg) {
116: MatCreate(PETSC_COMM_SELF,&A_sp);
117: MatSetSizes(A_sp,PETSC_DECIDE,PETSC_DECIDE,m,n);
118: MatSetType(A_sp,MATSEQSBAIJ);
120: tols[0] = 1.e-6, tols[1] = 1.e-9;
121: sbaij = (Mat_SeqSBAIJ*)A->data;
122: ai = sbaij->i;
123: aj = sbaij->j;
124: aa = sbaij->a;
125: nzeros[0] = nzeros[1] = 0;
126: for (i=0; i<m; i++) {
127: nz = ai[i+1] - ai[i];
128: for (j=0; j<nz; j++) {
129: if (PetscAbsScalar(*aa)<tols[0]) {
130: MatSetValues(A_sp,1,&i,1,aj,aa,INSERT_VALUES);
131: nzeros[0]++;
132: }
133: if (PetscAbsScalar(*aa)<tols[1]) nzeros[1]++;
134: aa++; aj++;
135: }
136: }
137: MatAssemblyBegin(A_sp,MAT_FINAL_ASSEMBLY);
138: MatAssemblyEnd(A_sp,MAT_FINAL_ASSEMBLY);
140: MatDestroy(&A_sp);
142: ratio = (PetscReal)nzeros[0]/sbaij->nz;
143: PetscPrintf(PETSC_COMM_SELF," %D matrix entries < %g, ratio %g of %d nonzeros\n",nzeros[0],(double)tols[0],(double)ratio,sbaij->nz);
144: PetscPrintf(PETSC_COMM_SELF," %D matrix entries < %g\n",nzeros[1],(double)tols[1]);
145: }
147: /* Convert aij matrix to MATSEQDENSE for LAPACK */
148: PetscObjectTypeCompare((PetscObject)A,MATSEQDENSE,&flg);
149: if (!flg) {
150: MatConvert(A,MATSEQDENSE,MAT_INITIAL_MATRIX,&A_dense);
151: }
152: PetscObjectTypeCompare((PetscObject)B,MATSEQDENSE,&flg);
153: if (!flg) {MatConvert(B,MATSEQDENSE,MAT_INITIAL_MATRIX,&B_dense);}
155: /* Solve eigenvalue problem: A*x = lambda*B*x */
156: /*============================================*/
157: PetscBLASIntCast(8*n,&lwork);
158: PetscBLASIntCast(n,&bn);
159: PetscMalloc1(n,&evals);
160: PetscMalloc1(lwork,&work);
161: MatDenseGetArray(A_dense,&arrayA);
162: MatDenseGetArray(B_dense,&arrayB);
164: if (!TestSYGVX) { /* test sygv() */
165: evecs_array = arrayA;
166: LAPACKsygv_(&lone,"V","U",&bn,arrayA,&bn,arrayB,&bn,evals,work,&lwork,&lierr);
167: nevs = m;
168: il =1;
169: } else { /* test sygvx() */
170: il = 1;
171: PetscBLASIntCast(.6*m,&iu);
172: PetscMalloc1((m*n+1),&evecs_array);
173: PetscMalloc1((6*n+1),&iwork);
174: ifail = iwork + 5*n;
175: if (PetscPreLoadIt) {PetscLogStagePush(stages[0]);}
176: /* in the case "I", vl and vu are not referenced */
177: LAPACKsygvx_(&lone,"V","I","U",&bn,arrayA,&bn,arrayB,&bn,&vl,&vu,&il,&iu,&abstol,&nevs,evals,evecs_array,&n,work,&lwork,iwork,ifail,&lierr);
178: if (PetscPreLoadIt) PetscLogStagePop();
179: PetscFree(iwork);
180: }
181: MatDenseRestoreArray(A_dense,&arrayA);
182: MatDenseRestoreArray(B_dense,&arrayB);
184: if (nevs <= 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_CONV_FAILED, "nev=%d, no eigensolution has found", nevs);
185: /* View evals */
186: PetscOptionsHasName(NULL, "-eig_view", &flg);
187: if (flg) {
188: printf(" %d evals: \n",nevs);
189: for (i=0; i<nevs; i++) printf("%D %g\n",i+il,(double)evals[i]);
190: }
192: /* Check residuals and orthogonality */
193: if (PetscPreLoadIt) {
194: mats[0] = A; mats[1] = B;
195: one = (PetscInt)one;
196: PetscMalloc1((nevs+1),&evecs);
197: for (i=0; i<nevs; i++) {
198: VecCreate(PETSC_COMM_SELF,&evecs[i]);
199: VecSetSizes(evecs[i],PETSC_DECIDE,n);
200: VecSetFromOptions(evecs[i]);
201: VecPlaceArray(evecs[i],evecs_array+i*n);
202: }
204: ievbd_loc[0] = 0; ievbd_loc[1] = nevs-1;
205: tols[0] = 1.e-8; tols[1] = 1.e-8;
207: PetscLogStagePush(stages[1]);
208: CkEigenSolutions(&cklvl,mats,evals,evecs,ievbd_loc,&offset,tols);
209: PetscLogStagePop();
210: for (i=0; i<nevs; i++) { VecDestroy(&evecs[i]);}
211: PetscFree(evecs);
212: }
214: /* Free work space. */
215: if (TestSYGVX) {PetscFree(evecs_array);}
217: PetscFree(evals);
218: PetscFree(work);
220: MatDestroy(&A_dense);
221: MatDestroy(&B_dense);
222: MatDestroy(&B);
223: MatDestroy(&A);
225: PetscPreLoadEnd();
226: PetscFinalize();
227: return 0;
228: }
229: /*------------------------------------------------
230: Check the accuracy of the eigen solution
231: ----------------------------------------------- */
232: /*
233: input:
234: cklvl - check level:
235: 1: check residual
236: 2: 1 and check B-orthogonality locally
237: mats - matrix pencil
238: eval, evec - eigenvalues and eigenvectors stored in this process
239: ievbd_loc - local eigenvalue bounds, see eigc()
240: offset - see eigc()
241: tols[0] - reporting tol_res: || A evec[i] - eval[i] B evec[i]||
242: tols[1] - reporting tol_orth: evec[i] B evec[j] - delta_ij
243: */
244: #undef DEBUG_CkEigenSolutions
247: PetscErrorCode CkEigenSolutions(PetscInt *fcklvl,Mat *mats,PetscReal *eval,Vec *evec,PetscInt *ievbd_loc,PetscInt *offset,PetscReal *tols)
248: {
249: PetscInt ierr,cklvl=*fcklvl,nev_loc,i,j;
250: Mat A=mats[0], B=mats[1];
251: Vec vt1,vt2; /* tmp vectors */
252: PetscReal norm,tmp,dot,norm_max,dot_max;
255: nev_loc = ievbd_loc[1] - ievbd_loc[0];
256: if (nev_loc == 0) return(0);
258: nev_loc += (*offset);
259: VecDuplicate(evec[*offset],&vt1);
260: VecDuplicate(evec[*offset],&vt2);
262: switch (cklvl) {
263: case 2:
264: dot_max = 0.0;
265: for (i = *offset; i<nev_loc; i++) {
266: MatMult(B, evec[i], vt1);
267: for (j=i; j<nev_loc; j++) {
268: VecDot(evec[j],vt1,&dot);
269: if (j == i) {
270: dot = PetscAbsScalar(dot - 1.0);
271: } else {
272: dot = PetscAbsScalar(dot);
273: }
274: if (dot > dot_max) dot_max = dot;
275: #if defined(DEBUG_CkEigenSolutions)
276: if (dot > tols[1]) {
277: VecNorm(evec[i],NORM_INFINITY,&norm);
278: PetscPrintf(PETSC_COMM_SELF,"|delta(%D,%D)|: %g, norm: %g\n",i,j,(double)ndot,(double)nnorm);
279: }
280: #endif
281: } /* for (j=i; j<nev_loc; j++) */
282: }
283: PetscPrintf(PETSC_COMM_SELF," max|(x_j*B*x_i) - delta_ji|: %g\n",(double)dot_max);
285: case 1:
286: norm_max = 0.0;
287: for (i = *offset; i< nev_loc; i++) {
288: MatMult(A, evec[i], vt1);
289: MatMult(B, evec[i], vt2);
290: tmp = -eval[i];
291: VecAXPY(vt1,tmp,vt2);
292: VecNorm(vt1, NORM_INFINITY, &norm);
293: norm = PetscAbsScalar(norm);
294: if (norm > norm_max) norm_max = norm;
295: #if defined(DEBUG_CkEigenSolutions)
296: /* sniff, and bark if necessary */
297: if (norm > tols[0]) {
298: printf(" residual violation: %D, resi: %g\n",i, (double)nnorm);
299: }
300: #endif
301: }
303: PetscPrintf(PETSC_COMM_SELF," max_resi: %g\n", (double)norm_max);
305: break;
306: default:
307: PetscPrintf(PETSC_COMM_SELF,"Error: cklvl=%D is not supported \n",cklvl);
308: }
309: VecDestroy(&vt2);
310: VecDestroy(&vt1);
311: return(0);
312: }