Actual source code: ex99.c
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: #include petscmat.h
13: #include ../src/mat/impls/sbaij/seq/sbaij.h
14: #include petscblaslapack.h
20: PetscInt main(PetscInt argc,char **args)
21: {
22: Mat A,B,A_dense,B_dense,mats[2],A_sp;
23: Vec *evecs;
24: PetscViewer fd; /* viewer */
25: char file[3][PETSC_MAX_PATH_LEN]; /* input file name */
26: PetscTruth flg,flgA=PETSC_FALSE,flgB=PETSC_FALSE,TestSYGVX=PETSC_TRUE;
28: PetscTruth preload=PETSC_TRUE,isSymmetric;
29: PetscScalar sigma,one=1.0,*arrayA,*arrayB,*evecs_array,*work,*evals;
30: PetscMPIInt size;
31: PetscInt m,n,i,j,nevs,il,iu;
32: PetscLogStage stages[2];
33: PetscReal vl,vu,abstol=1.e-8;
34: PetscBLASInt *iwork,*ifail,lone=1,lwork,lierr,bn;
35: PetscInt ievbd_loc[2],offset=0,cklvl=2;
36: PetscReal tols[2];
37: Mat_SeqSBAIJ *sbaij;
38: PetscScalar *aa;
39: PetscInt *ai,*aj;
40: PetscInt nzeros[2],nz;
41: PetscReal ratio;
42:
43: PetscInitialize(&argc,&args,(char *)0,help);
44: MPI_Comm_size(PETSC_COMM_WORLD,&size);
45: if (size != 1) SETERRQ(PETSC_ERR_SUP,"This is a uniprocessor example only!");
46: PetscLogStageRegister("EigSolve",&stages[0]);
47: PetscLogStageRegister("EigCheck",&stages[1]);
49: /* Determine files from which we read the two matrices */
50: PetscOptionsGetString(PETSC_NULL,"-f0",file[0],PETSC_MAX_PATH_LEN-1,&flg);
51: if (!flg) {
52: PetscOptionsGetString(PETSC_NULL,"-fA",file[0],PETSC_MAX_PATH_LEN-1,&flgA);
53: if (!flgA) SETERRQ(PETSC_ERR_USER,"Must indicate binary file with the -fA or -fB options");
54: PetscOptionsGetString(PETSC_NULL,"-fB",file[1],PETSC_MAX_PATH_LEN-1,&flgB);
55: preload = PETSC_FALSE;
56: } else {
57: PetscOptionsGetString(PETSC_NULL,"-fA",file[1],PETSC_MAX_PATH_LEN-1,&flgA);
58: if (!flgA) {preload = PETSC_FALSE;} /* don't bother with second system */
59: PetscOptionsGetString(PETSC_NULL,"-fB",file[2],PETSC_MAX_PATH_LEN-1,&flgB);
60: }
62: PreLoadBegin(preload,"Load system");
63: /* Load matrices */
64: PetscViewerBinaryOpen(PETSC_COMM_WORLD,file[PreLoadIt],FILE_MODE_READ,&fd);
65: MatLoad(fd,MATSBAIJ,&A);
66: PetscViewerDestroy(fd);
67: MatGetSize(A,&m,&n);
68: if ((flgB && PreLoadIt) || (flgB && !preload)){
69: PetscViewerBinaryOpen(PETSC_COMM_WORLD,file[PreLoadIt+1],FILE_MODE_READ,&fd);
70: MatLoad(fd,MATSBAIJ,&B);
71: PetscViewerDestroy(fd);
72: } else { /* create B=I */
73: MatCreate(PETSC_COMM_WORLD,&B);
74: MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,m,n);
75: MatSetType(B,MATSEQSBAIJ);
76: MatSetFromOptions(B);
77: for (i=0; i<m; i++) {
78: MatSetValues(B,1,&i,1,&i,&one,INSERT_VALUES);
79: }
80: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
81: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
82: }
83:
84: /* Add a shift to A */
85: PetscOptionsGetScalar(PETSC_NULL,"-mat_sigma",&sigma,&flg);
86: if(flg) {
87: MatAXPY(A,sigma,B,DIFFERENT_NONZERO_PATTERN); /* A <- sigma*B + A */
88: }
90: /* Check whether A is symmetric */
91: PetscOptionsHasName(PETSC_NULL, "-check_symmetry", &flg);
92: if (flg) {
93: Mat Trans;
94: MatTranspose(A,MAT_INITIAL_MATRIX, &Trans);
95: MatEqual(A, Trans, &isSymmetric);
96: if (!isSymmetric) SETERRQ(PETSC_ERR_USER,"A must be symmetric");
97: MatDestroy(Trans);
98: if (flgB && PreLoadIt){
99: MatTranspose(B,MAT_INITIAL_MATRIX, &Trans);
100: MatEqual(B, Trans, &isSymmetric);
101: if (!isSymmetric) SETERRQ(PETSC_ERR_USER,"B must be symmetric");
102: MatDestroy(Trans);
103: }
104: }
106: /* View small entries of A */
107: PetscOptionsHasName(PETSC_NULL, "-Asp_view", &flg);
108: if (flg){
109: MatCreate(PETSC_COMM_SELF,&A_sp);
110: MatSetSizes(A_sp,PETSC_DECIDE,PETSC_DECIDE,m,n);
111: MatSetType(A_sp,MATSEQSBAIJ);
113: tols[0] = 1.e-6, tols[1] = 1.e-9;
114: sbaij = (Mat_SeqSBAIJ*)A->data;
115: ai = sbaij->i;
116: aj = sbaij->j;
117: aa = sbaij->a;
118: nzeros[0] = nzeros[1] = 0;
119: for (i=0; i<m; i++) {
120: nz = ai[i+1] - ai[i];
121: for (j=0; j<nz; j++){
122: if (PetscAbsScalar(*aa)<tols[0]) {
123: MatSetValues(A_sp,1,&i,1,aj,aa,INSERT_VALUES);
124: nzeros[0]++;
125: }
126: if (PetscAbsScalar(*aa)<tols[1]) nzeros[1]++;
127: aa++; aj++;
128: }
129: }
130: MatAssemblyBegin(A_sp,MAT_FINAL_ASSEMBLY);
131: MatAssemblyEnd(A_sp,MAT_FINAL_ASSEMBLY);
133: MatDestroy(A_sp);
135: ratio = (PetscReal)nzeros[0]/sbaij->nz;
136: PetscPrintf(PETSC_COMM_SELF," %d matrix entries < %e, ratio %G of %d nonzeros\n",nzeros[0],tols[0],ratio,sbaij->nz);
137: PetscPrintf(PETSC_COMM_SELF," %d matrix entries < %e\n",nzeros[1],tols[1]);
138: }
140: /* Convert aij matrix to MatSeqDense for LAPACK */
141: PetscTypeCompare((PetscObject)A,MATSEQDENSE,&flg);
142: if (!flg) {
143: MatConvert(A,MATSEQDENSE,MAT_INITIAL_MATRIX,&A_dense);
144: }
145: PetscTypeCompare((PetscObject)B,MATSEQDENSE,&flg);
146: if (!flg) {MatConvert(B,MATSEQDENSE,MAT_INITIAL_MATRIX,&B_dense);}
148: /* Solve eigenvalue problem: A*x = lambda*B*x */
149: /*============================================*/
150: lwork = PetscBLASIntCast(8*n);
151: bn = PetscBLASIntCast(n);
152: PetscMalloc(n*sizeof(PetscScalar),&evals);
153: PetscMalloc(lwork*sizeof(PetscScalar),&work);
154: MatGetArray(A_dense,&arrayA);
155: MatGetArray(B_dense,&arrayB);
157: if (!TestSYGVX){ /* test sygv() */
158: evecs_array = arrayA;
159: LAPACKsygv_(&lone,"V","U",&bn,arrayA,&bn,arrayB,&bn,evals,work,&lwork,&lierr);
160: nevs = m;
161: il=1;
162: } else { /* test sygvx() */
163: il = 1; iu=PetscBLASIntCast(.6*m); /* request 1 to 60%m evalues */
164: PetscMalloc((m*n+1)*sizeof(PetscScalar),&evecs_array);
165: PetscMalloc((6*n+1)*sizeof(PetscBLASInt),&iwork);
166: ifail = iwork + 5*n;
167: if(PreLoadIt){PetscLogStagePush(stages[0]);}
168: /* in the case "I", vl and vu are not referenced */
169: 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);
170: if(PreLoadIt){PetscLogStagePop();}
171: PetscFree(iwork);
172: }
173: MatRestoreArray(A,&arrayA);
174: MatRestoreArray(B,&arrayB);
176: if (nevs <= 0 ) SETERRQ1(PETSC_ERR_CONV_FAILED, "nev=%d, no eigensolution has found", nevs);
177: /* View evals */
178: PetscOptionsHasName(PETSC_NULL, "-eig_view", &flg);
179: if (flg){
180: printf(" %d evals: \n",nevs);
181: for (i=0; i<nevs; i++) printf("%d %G\n",i+il,evals[i]);
182: }
184: /* Check residuals and orthogonality */
185: if(PreLoadIt){
186: mats[0] = A; mats[1] = B;
187: one = (PetscInt)one;
188: PetscMalloc((nevs+1)*sizeof(Vec),&evecs);
189: for (i=0; i<nevs; i++){
190: VecCreate(PETSC_COMM_SELF,&evecs[i]);
191: VecSetSizes(evecs[i],PETSC_DECIDE,n);
192: VecSetFromOptions(evecs[i]);
193: VecPlaceArray(evecs[i],evecs_array+i*n);
194: }
195:
196: ievbd_loc[0] = 0; ievbd_loc[1] = nevs-1;
197: tols[0] = 1.e-8; tols[1] = 1.e-8;
198: PetscLogStagePush(stages[1]);
199: CkEigenSolutions(&cklvl,mats,evals,evecs,ievbd_loc,&offset,tols);
200: PetscLogStagePop();
201: for (i=0; i<nevs; i++){ VecDestroy(evecs[i]);}
202: PetscFree(evecs);
203: }
204:
205: /* Free work space. */
206: if (TestSYGVX){PetscFree(evecs_array);}
207:
208: PetscFree(evals);
209: PetscFree(work);
211: MatDestroy(A_dense);
212: MatDestroy(B_dense);
213: MatDestroy(B);
214: MatDestroy(A);
216: PreLoadEnd();
217: PetscFinalize();
218: return 0;
219: }
220: /*------------------------------------------------
221: Check the accuracy of the eigen solution
222: ----------------------------------------------- */
223: /*
224: input:
225: cklvl - check level:
226: 1: check residual
227: 2: 1 and check B-orthogonality locally
228: mats - matrix pencil
229: eval, evec - eigenvalues and eigenvectors stored in this process
230: ievbd_loc - local eigenvalue bounds, see eigc()
231: offset - see eigc()
232: tols[0] - reporting tol_res: || A evec[i] - eval[i] B evec[i]||
233: tols[1] - reporting tol_orth: evec[i] B evec[j] - delta_ij
234: */
235: #undef DEBUG_CkEigenSolutions
238: PetscErrorCode CkEigenSolutions(PetscInt *fcklvl,Mat *mats,
239: PetscReal *eval,Vec *evec,PetscInt *ievbd_loc,PetscInt *offset,
240: PetscReal *tols)
241: {
242: PetscInt ierr,cklvl=*fcklvl,nev_loc,i,j;
243: Mat A=mats[0], B=mats[1];
244: Vec vt1,vt2; /* tmp vectors */
245: PetscReal norm,tmp,dot,norm_max,dot_max;
248: nev_loc = ievbd_loc[1] - ievbd_loc[0];
249: if (nev_loc == 0) return(0);
251: nev_loc += (*offset);
252: VecDuplicate(evec[*offset],&vt1);
253: VecDuplicate(evec[*offset],&vt2);
255: switch (cklvl){
256: case 2:
257: dot_max = 0.0;
258: for (i = *offset; i<nev_loc; i++){
259: MatMult(B, evec[i], vt1);
260: for (j=i; j<nev_loc; j++){
261: VecDot(evec[j],vt1,&dot);
262: if (j == i){
263: dot = PetscAbsScalar(dot - 1.0);
264: } else {
265: dot = PetscAbsScalar(dot);
266: }
267: if (dot > dot_max) dot_max = dot;
268: #ifdef DEBUG_CkEigenSolutions
269: if (dot > tols[1] ) {
270: VecNorm(evec[i],NORM_INFINITY,&norm);
271: PetscPrintf(PETSC_COMM_SELF,"|delta(%d,%d)|: %G, norm: %G\n",i,j,dot,norm);
272: }
273: #endif
274: } /* for (j=i; j<nev_loc; j++) */
275: }
276: PetscPrintf(PETSC_COMM_SELF," max|(x_j*B*x_i) - delta_ji|: %G\n",dot_max);
278: case 1:
279: norm_max = 0.0;
280: for (i = *offset; i< nev_loc; i++){
281: MatMult(A, evec[i], vt1);
282: MatMult(B, evec[i], vt2);
283: tmp = -eval[i];
284: VecAXPY(vt1,tmp,vt2);
285: VecNorm(vt1, NORM_INFINITY, &norm);
286: norm = PetscAbsScalar(norm);
287: if (norm > norm_max) norm_max = norm;
288: #ifdef DEBUG_CkEigenSolutions
289: /* sniff, and bark if necessary */
290: if (norm > tols[0]){
291: printf( " residual violation: %d, resi: %g\n",i, norm);
292: }
293: #endif
294: }
295:
296: PetscPrintf(PETSC_COMM_SELF," max_resi: %G\n", norm_max);
297:
298: break;
299: default:
300: PetscPrintf(PETSC_COMM_SELF,"Error: cklvl=%d is not supported \n",cklvl);
301: }
302: VecDestroy(vt2);
303: VecDestroy(vt1);
304: return(0);
305: }