Actual source code: dsnhepts.c
slepc-3.17.2 2022-08-09
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain
6: This file is part of SLEPc.
7: SLEPc is distributed under a 2-clause BSD license (see LICENSE).
8: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
9: */
11: #include <slepc/private/dsimpl.h>
12: #include <slepcblaslapack.h>
14: typedef struct {
15: PetscScalar *wr,*wi; /* eigenvalues of B */
16: } DS_NHEPTS;
18: PetscErrorCode DSAllocate_NHEPTS(DS ds,PetscInt ld)
19: {
20: DS_NHEPTS *ctx = (DS_NHEPTS*)ds->data;
22: DSAllocateMat_Private(ds,DS_MAT_A);
23: DSAllocateMat_Private(ds,DS_MAT_B);
24: DSAllocateMat_Private(ds,DS_MAT_Q);
25: DSAllocateMat_Private(ds,DS_MAT_Z);
26: PetscFree(ds->perm);
27: PetscMalloc1(ld,&ds->perm);
28: PetscLogObjectMemory((PetscObject)ds,ld*sizeof(PetscInt));
29: PetscMalloc1(ld,&ctx->wr);
30: PetscLogObjectMemory((PetscObject)ds,ld*sizeof(PetscScalar));
31: #if !defined(PETSC_USE_COMPLEX)
32: PetscMalloc1(ld,&ctx->wi);
33: PetscLogObjectMemory((PetscObject)ds,ld*sizeof(PetscScalar));
34: #endif
35: PetscFunctionReturn(0);
36: }
38: PetscErrorCode DSView_NHEPTS(DS ds,PetscViewer viewer)
39: {
40: PetscViewerFormat format;
42: PetscViewerGetFormat(viewer,&format);
43: if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) PetscFunctionReturn(0);
44: DSViewMat(ds,viewer,DS_MAT_A);
45: DSViewMat(ds,viewer,DS_MAT_B);
46: if (ds->state>DS_STATE_INTERMEDIATE) {
47: DSViewMat(ds,viewer,DS_MAT_Q);
48: DSViewMat(ds,viewer,DS_MAT_Z);
49: }
50: if (ds->mat[DS_MAT_X]) DSViewMat(ds,viewer,DS_MAT_X);
51: if (ds->mat[DS_MAT_Y]) DSViewMat(ds,viewer,DS_MAT_Y);
52: PetscFunctionReturn(0);
53: }
55: static PetscErrorCode DSVectors_NHEPTS_Eigen_Some(DS ds,PetscInt *k,PetscReal *rnorm,PetscBool left)
56: {
57: PetscInt i;
58: PetscBLASInt mm=1,mout,info,ld,n,*select,inc=1,cols=1,zero=0;
59: PetscScalar sone=1.0,szero=0.0;
60: PetscReal norm,done=1.0;
61: PetscBool iscomplex = PETSC_FALSE;
62: PetscScalar *A,*Q,*X,*Y;
64: PetscBLASIntCast(ds->n,&n);
65: PetscBLASIntCast(ds->ld,&ld);
66: if (left) {
67: A = ds->mat[DS_MAT_B];
68: Q = ds->mat[DS_MAT_Z];
69: X = ds->mat[DS_MAT_Y];
70: } else {
71: A = ds->mat[DS_MAT_A];
72: Q = ds->mat[DS_MAT_Q];
73: X = ds->mat[DS_MAT_X];
74: }
75: DSAllocateWork_Private(ds,0,0,ld);
76: select = ds->iwork;
77: for (i=0;i<n;i++) select[i] = (PetscBLASInt)PETSC_FALSE;
79: /* compute k-th eigenvector Y of A */
80: Y = X+(*k)*ld;
81: select[*k] = (PetscBLASInt)PETSC_TRUE;
82: #if !defined(PETSC_USE_COMPLEX)
83: if ((*k)<n-1 && A[(*k)+1+(*k)*ld]!=0.0) iscomplex = PETSC_TRUE;
84: mm = iscomplex? 2: 1;
85: if (iscomplex) select[(*k)+1] = (PetscBLASInt)PETSC_TRUE;
86: DSAllocateWork_Private(ds,3*ld,0,0);
87: PetscStackCallBLAS("LAPACKtrevc",LAPACKtrevc_("R","S",select,&n,A,&ld,Y,&ld,Y,&ld,&mm,&mout,ds->work,&info));
88: #else
89: DSAllocateWork_Private(ds,2*ld,ld,0);
90: PetscStackCallBLAS("LAPACKtrevc",LAPACKtrevc_("R","S",select,&n,A,&ld,Y,&ld,Y,&ld,&mm,&mout,ds->work,ds->rwork,&info));
91: #endif
92: SlepcCheckLapackInfo("trevc",info);
95: /* accumulate and normalize eigenvectors */
96: if (ds->state>=DS_STATE_CONDENSED) {
97: PetscArraycpy(ds->work,Y,mout*ld);
98: PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&sone,Q,&ld,ds->work,&inc,&szero,Y,&inc));
99: #if !defined(PETSC_USE_COMPLEX)
100: if (iscomplex) PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&sone,Q,&ld,ds->work+ld,&inc,&szero,Y+ld,&inc));
101: #endif
102: cols = 1;
103: norm = BLASnrm2_(&n,Y,&inc);
104: #if !defined(PETSC_USE_COMPLEX)
105: if (iscomplex) {
106: norm = SlepcAbsEigenvalue(norm,BLASnrm2_(&n,Y+ld,&inc));
107: cols = 2;
108: }
109: #endif
110: PetscStackCallBLAS("LAPACKlascl",LAPACKlascl_("G",&zero,&zero,&norm,&done,&n,&cols,Y,&ld,&info));
111: SlepcCheckLapackInfo("lascl",info);
112: }
114: /* set output arguments */
115: if (iscomplex) (*k)++;
116: if (rnorm) {
117: if (iscomplex) *rnorm = SlepcAbsEigenvalue(Y[n-1],Y[n-1+ld]);
118: else *rnorm = PetscAbsScalar(Y[n-1]);
119: }
120: PetscFunctionReturn(0);
121: }
123: static PetscErrorCode DSVectors_NHEPTS_Eigen_All(DS ds,PetscBool left)
124: {
125: PetscInt i;
126: PetscBLASInt n,ld,mout,info,inc=1,cols,zero=0;
127: PetscBool iscomplex;
128: PetscScalar *A,*Q,*X;
129: PetscReal norm,done=1.0;
130: const char *back;
132: PetscBLASIntCast(ds->n,&n);
133: PetscBLASIntCast(ds->ld,&ld);
134: if (left) {
135: A = ds->mat[DS_MAT_B];
136: Q = ds->mat[DS_MAT_Z];
137: X = ds->mat[DS_MAT_Y];
138: } else {
139: A = ds->mat[DS_MAT_A];
140: Q = ds->mat[DS_MAT_Q];
141: X = ds->mat[DS_MAT_X];
142: }
143: if (ds->state>=DS_STATE_CONDENSED) {
144: /* DSSolve() has been called, backtransform with matrix Q */
145: back = "B";
146: PetscArraycpy(X,Q,ld*ld);
147: } else back = "A";
148: #if !defined(PETSC_USE_COMPLEX)
149: DSAllocateWork_Private(ds,3*ld,0,0);
150: PetscStackCallBLAS("LAPACKtrevc",LAPACKtrevc_("R",back,NULL,&n,A,&ld,X,&ld,X,&ld,&n,&mout,ds->work,&info));
151: #else
152: DSAllocateWork_Private(ds,2*ld,ld,0);
153: PetscStackCallBLAS("LAPACKtrevc",LAPACKtrevc_("R",back,NULL,&n,A,&ld,X,&ld,X,&ld,&n,&mout,ds->work,ds->rwork,&info));
154: #endif
155: SlepcCheckLapackInfo("trevc",info);
157: /* normalize eigenvectors */
158: for (i=0;i<n;i++) {
159: iscomplex = (i<n-1 && A[i+1+i*ld]!=0.0)? PETSC_TRUE: PETSC_FALSE;
160: cols = 1;
161: norm = BLASnrm2_(&n,X+i*ld,&inc);
162: #if !defined(PETSC_USE_COMPLEX)
163: if (iscomplex) {
164: norm = SlepcAbsEigenvalue(norm,BLASnrm2_(&n,X+(i+1)*ld,&inc));
165: cols = 2;
166: }
167: #endif
168: PetscStackCallBLAS("LAPACKlascl",LAPACKlascl_("G",&zero,&zero,&norm,&done,&n,&cols,X+i*ld,&ld,&info));
169: SlepcCheckLapackInfo("lascl",info);
170: if (iscomplex) i++;
171: }
172: PetscFunctionReturn(0);
173: }
175: PetscErrorCode DSVectors_NHEPTS(DS ds,DSMatType mat,PetscInt *j,PetscReal *rnorm)
176: {
177: switch (mat) {
178: case DS_MAT_X:
180: if (j) DSVectors_NHEPTS_Eigen_Some(ds,j,rnorm,PETSC_FALSE);
181: else DSVectors_NHEPTS_Eigen_All(ds,PETSC_FALSE);
182: break;
183: case DS_MAT_Y:
185: if (j) DSVectors_NHEPTS_Eigen_Some(ds,j,rnorm,PETSC_TRUE);
186: else DSVectors_NHEPTS_Eigen_All(ds,PETSC_TRUE);
187: break;
188: case DS_MAT_U:
189: case DS_MAT_V:
190: SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
191: default:
192: SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
193: }
194: PetscFunctionReturn(0);
195: }
197: PetscErrorCode DSSort_NHEPTS(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
198: {
199: DS_NHEPTS *ctx = (DS_NHEPTS*)ds->data;
200: PetscInt i,j,cont,id=0,*p,*idx,*idx2;
201: PetscReal s,t;
202: #if defined(PETSC_USE_COMPLEX)
203: Mat A,U;
204: #endif
207: PetscMalloc3(ds->ld,&idx,ds->ld,&idx2,ds->ld,&p);
208: DSSort_NHEP_Total(ds,ds->mat[DS_MAT_A],ds->mat[DS_MAT_Q],wr,wi);
209: #if defined(PETSC_USE_COMPLEX)
210: DSGetMat(ds,DS_MAT_B,&A);
211: MatConjugate(A);
212: DSRestoreMat(ds,DS_MAT_B,&A);
213: DSGetMat(ds,DS_MAT_Z,&U);
214: MatConjugate(U);
215: DSRestoreMat(ds,DS_MAT_Z,&U);
216: for (i=0;i<ds->n;i++) ctx->wr[i] = PetscConj(ctx->wr[i]);
217: #endif
218: DSSort_NHEP_Total(ds,ds->mat[DS_MAT_B],ds->mat[DS_MAT_Z],ctx->wr,ctx->wi);
219: /* check correct eigenvalue correspondence */
220: cont = 0;
221: for (i=0;i<ds->n;i++) {
222: if (SlepcAbsEigenvalue(ctx->wr[i]-wr[i],ctx->wi[i]-wi[i])>PETSC_SQRT_MACHINE_EPSILON) {idx2[cont] = i; idx[cont++] = i;}
223: p[i] = -1;
224: }
225: if (cont) {
226: for (i=0;i<cont;i++) {
227: t = PETSC_MAX_REAL;
228: for (j=0;j<cont;j++) if (idx2[j]!=-1 && (s=SlepcAbsEigenvalue(ctx->wr[idx[j]]-wr[idx[i]],ctx->wi[idx[j]]-wi[idx[i]]))<t) { id = j; t = s; }
229: p[idx[i]] = idx[id];
230: idx2[id] = -1;
231: }
232: for (i=0;i<ds->n;i++) if (p[i]==-1) p[i] = i;
233: DSSortWithPermutation_NHEP_Private(ds,p,ds->mat[DS_MAT_B],ds->mat[DS_MAT_Z],ctx->wr,ctx->wi);
234: }
235: #if defined(PETSC_USE_COMPLEX)
236: DSGetMat(ds,DS_MAT_B,&A);
237: MatConjugate(A);
238: DSRestoreMat(ds,DS_MAT_B,&A);
239: DSGetMat(ds,DS_MAT_Z,&U);
240: MatConjugate(U);
241: DSRestoreMat(ds,DS_MAT_Z,&U);
242: #endif
243: PetscFree3(idx,idx2,p);
244: PetscFunctionReturn(0);
245: }
247: PetscErrorCode DSUpdateExtraRow_NHEPTS(DS ds)
248: {
249: PetscInt i;
250: PetscBLASInt n,ld,incx=1;
251: PetscScalar *A,*Q,*x,*y,one=1.0,zero=0.0;
253: PetscBLASIntCast(ds->n,&n);
254: PetscBLASIntCast(ds->ld,&ld);
255: DSAllocateWork_Private(ds,2*ld,0,0);
256: x = ds->work;
257: y = ds->work+ld;
258: A = ds->mat[DS_MAT_A];
259: Q = ds->mat[DS_MAT_Q];
260: for (i=0;i<n;i++) x[i] = PetscConj(A[n+i*ld]);
261: PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx));
262: for (i=0;i<n;i++) A[n+i*ld] = PetscConj(y[i]);
263: A = ds->mat[DS_MAT_B];
264: Q = ds->mat[DS_MAT_Z];
265: for (i=0;i<n;i++) x[i] = PetscConj(A[n+i*ld]);
266: PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx));
267: for (i=0;i<n;i++) A[n+i*ld] = PetscConj(y[i]);
268: ds->k = n;
269: PetscFunctionReturn(0);
270: }
272: PetscErrorCode DSSolve_NHEPTS(DS ds,PetscScalar *wr,PetscScalar *wi)
273: {
274: DS_NHEPTS *ctx = (DS_NHEPTS*)ds->data;
276: #if !defined(PETSC_USE_COMPLEX)
278: #endif
279: DSSolve_NHEP_Private(ds,ds->mat[DS_MAT_A],ds->mat[DS_MAT_Q],wr,wi);
280: DSSolve_NHEP_Private(ds,ds->mat[DS_MAT_B],ds->mat[DS_MAT_Z],ctx->wr,ctx->wi);
281: PetscFunctionReturn(0);
282: }
284: PetscErrorCode DSSynchronize_NHEPTS(DS ds,PetscScalar eigr[],PetscScalar eigi[])
285: {
286: PetscInt ld=ds->ld,l=ds->l,k;
287: PetscMPIInt n,rank,off=0,size,ldn;
288: DS_NHEPTS *ctx = (DS_NHEPTS*)ds->data;
290: k = 2*(ds->n-l)*ld;
291: if (ds->state>DS_STATE_RAW) k += 2*(ds->n-l)*ld;
292: if (eigr) k += ds->n-l;
293: if (eigi) k += ds->n-l;
294: if (ctx->wr) k += ds->n-l;
295: if (ctx->wi) k += ds->n-l;
296: DSAllocateWork_Private(ds,k,0,0);
297: PetscMPIIntCast(k*sizeof(PetscScalar),&size);
298: PetscMPIIntCast(ds->n-l,&n);
299: PetscMPIIntCast(ld*(ds->n-l),&ldn);
300: MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank);
301: if (!rank) {
302: MPI_Pack(ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
303: MPI_Pack(ds->mat[DS_MAT_B]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
304: if (ds->state>DS_STATE_RAW) {
305: MPI_Pack(ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
306: MPI_Pack(ds->mat[DS_MAT_Z]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
307: }
308: if (eigr) MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
309: #if !defined(PETSC_USE_COMPLEX)
310: if (eigi) MPI_Pack(eigi+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
311: #endif
312: if (ctx->wr) MPI_Pack(ctx->wr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
313: if (ctx->wi) MPI_Pack(ctx->wi+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
314: }
315: MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds));
316: if (rank) {
317: MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
318: MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_B]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
319: if (ds->state>DS_STATE_RAW) {
320: MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
321: MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_Z]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
322: }
323: if (eigr) MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
324: #if !defined(PETSC_USE_COMPLEX)
325: if (eigi) MPI_Unpack(ds->work,size,&off,eigi+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
326: #endif
327: if (ctx->wr) MPI_Unpack(ds->work,size,&off,ctx->wr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
328: if (ctx->wi) MPI_Unpack(ds->work,size,&off,ctx->wi+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
329: }
330: PetscFunctionReturn(0);
331: }
333: PetscErrorCode DSGetTruncateSize_NHEPTS(DS ds,PetscInt l,PetscInt n,PetscInt *k)
334: {
335: #if !defined(PETSC_USE_COMPLEX)
336: PetscScalar *A = ds->mat[DS_MAT_A],*B = ds->mat[DS_MAT_B];
337: #endif
339: #if !defined(PETSC_USE_COMPLEX)
340: if (A[l+(*k)+(l+(*k)-1)*ds->ld] != 0.0 || B[l+(*k)+(l+(*k)-1)*ds->ld] != 0.0) {
341: if (l+(*k)<n-1) (*k)++;
342: else (*k)--;
343: }
344: #endif
345: PetscFunctionReturn(0);
346: }
348: PetscErrorCode DSTruncate_NHEPTS(DS ds,PetscInt n,PetscBool trim)
349: {
350: PetscInt i,ld=ds->ld,l=ds->l;
351: PetscScalar *A = ds->mat[DS_MAT_A],*B = ds->mat[DS_MAT_B];
353: #if defined(PETSC_USE_DEBUG)
354: /* make sure diagonal 2x2 block is not broken */
356: #endif
357: if (trim) {
358: if (ds->extrarow) { /* clean extra row */
359: for (i=l;i<ds->n;i++) { A[ds->n+i*ld] = 0.0; B[ds->n+i*ld] = 0.0; }
360: }
361: ds->l = 0;
362: ds->k = 0;
363: ds->n = n;
364: ds->t = ds->n; /* truncated length equal to the new dimension */
365: } else {
366: if (ds->extrarow && ds->k==ds->n) {
367: /* copy entries of extra row to the new position, then clean last row */
368: for (i=l;i<n;i++) { A[n+i*ld] = A[ds->n+i*ld]; B[n+i*ld] = B[ds->n+i*ld]; }
369: for (i=l;i<ds->n;i++) { A[ds->n+i*ld] = 0.0; B[ds->n+i*ld] = 0.0; }
370: }
371: ds->k = (ds->extrarow)? n: 0;
372: ds->t = ds->n; /* truncated length equal to previous dimension */
373: ds->n = n;
374: }
375: PetscFunctionReturn(0);
376: }
378: PetscErrorCode DSDestroy_NHEPTS(DS ds)
379: {
380: DS_NHEPTS *ctx = (DS_NHEPTS*)ds->data;
382: if (ctx->wr) PetscFree(ctx->wr);
383: if (ctx->wi) PetscFree(ctx->wi);
384: PetscFree(ds->data);
385: PetscFunctionReturn(0);
386: }
388: PetscErrorCode DSMatGetSize_NHEPTS(DS ds,DSMatType t,PetscInt *rows,PetscInt *cols)
389: {
390: *rows = ((t==DS_MAT_A || t==DS_MAT_B) && ds->extrarow)? ds->n+1: ds->n;
391: *cols = ds->n;
392: PetscFunctionReturn(0);
393: }
395: /*MC
396: DSNHEPTS - Dense Non-Hermitian Eigenvalue Problem (special variant intended
397: for two-sided Krylov solvers).
399: Level: beginner
401: Notes:
402: Two related problems are solved, A*X = X*Lambda and B*Y = Y*Lambda', where A and
403: B are supposed to come from the Arnoldi factorizations of a certain matrix and its
404: (conjugate) transpose, respectively. Hence, in exact arithmetic the columns of Y
405: are equal to the left eigenvectors of A. Lambda is a diagonal matrix whose diagonal
406: elements are the arguments of DSSolve(). After solve, A is overwritten with the
407: upper quasi-triangular matrix T of the (real) Schur form, A*Q = Q*T, and similarly
408: another (real) Schur relation is computed, B*Z = Z*S, overwriting B.
410: In the intermediate state A and B are reduced to upper Hessenberg form.
412: When left eigenvectors DS_MAT_Y are requested, right eigenvectors of B are returned,
413: while DS_MAT_X contains right eigenvectors of A.
415: Used DS matrices:
416: + DS_MAT_A - first problem matrix obtained from Arnoldi
417: . DS_MAT_B - second problem matrix obtained from Arnoldi on the transpose
418: . DS_MAT_Q - orthogonal/unitary transformation that reduces A to Hessenberg form
419: (intermediate step) or matrix of orthogonal Schur vectors of A
420: - DS_MAT_Z - orthogonal/unitary transformation that reduces B to Hessenberg form
421: (intermediate step) or matrix of orthogonal Schur vectors of B
423: Implemented methods:
424: . 0 - Implicit QR (_hseqr)
426: .seealso: DSCreate(), DSSetType(), DSType
427: M*/
428: SLEPC_EXTERN PetscErrorCode DSCreate_NHEPTS(DS ds)
429: {
430: DS_NHEPTS *ctx;
432: PetscNewLog(ds,&ctx);
433: ds->data = (void*)ctx;
435: ds->ops->allocate = DSAllocate_NHEPTS;
436: ds->ops->view = DSView_NHEPTS;
437: ds->ops->vectors = DSVectors_NHEPTS;
438: ds->ops->solve[0] = DSSolve_NHEPTS;
439: ds->ops->sort = DSSort_NHEPTS;
440: ds->ops->synchronize = DSSynchronize_NHEPTS;
441: ds->ops->gettruncatesize = DSGetTruncateSize_NHEPTS;
442: ds->ops->truncate = DSTruncate_NHEPTS;
443: ds->ops->update = DSUpdateExtraRow_NHEPTS;
444: ds->ops->destroy = DSDestroy_NHEPTS;
445: ds->ops->matgetsize = DSMatGetSize_NHEPTS;
446: PetscFunctionReturn(0);
447: }