Actual source code: dsnep.c
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: PetscInt nf; /* number of functions in f[] */
16: FN f[DS_NUM_EXTRA]; /* functions defining the nonlinear operator */
17: PetscInt max_mid; /* maximum minimality index */
18: PetscInt nnod; /* number of nodes for quadrature rules */
19: PetscInt spls; /* number of sampling columns for quadrature rules */
20: PetscInt Nit; /* number of refinement iterations */
21: PetscReal rtol; /* tolerance of Newton refinement */
22: RG rg; /* region for contour integral */
23: PetscLayout map; /* used to distribute work among MPI processes */
24: DSNEPMatrixFunctionFn *computematrix; /* user-provided compute matrix function */
25: void *computematrixctx; /* context for the compute matrix function */
26: PetscCtxDestroyFn *computematrixdestroy; /* context destroy function */
27: } DS_NEP;
29: /*
30: DSNEPComputeMatrix - Build the matrix associated with a nonlinear operator
31: T(lambda) or its derivative T'(lambda), given the parameter lambda, where
32: T(lambda) = sum_i E_i*f_i(lambda). The result is written in mat.
33: */
34: static PetscErrorCode DSNEPComputeMatrix(DS ds,PetscScalar lambda,PetscBool deriv,DSMatType mat)
35: {
36: DS_NEP *ctx = (DS_NEP*)ds->data;
37: PetscScalar *T,alpha;
38: const PetscScalar *E;
39: PetscInt i,ld,n;
40: PetscBLASInt k,inc=1;
42: PetscFunctionBegin;
43: PetscCall(PetscLogEventBegin(DS_Other,ds,0,0,0));
44: if (ctx->computematrix) PetscCall((*ctx->computematrix)(ds,lambda,deriv,mat,ctx->computematrixctx));
45: else {
46: PetscCall(DSGetDimensions(ds,&n,NULL,NULL,NULL));
47: PetscCall(DSGetLeadingDimension(ds,&ld));
48: PetscCall(PetscBLASIntCast(ld*n,&k));
49: PetscCall(MatDenseGetArray(ds->omat[mat],&T));
50: PetscCall(PetscArrayzero(T,k));
51: for (i=0;i<ctx->nf;i++) {
52: if (deriv) PetscCall(FNEvaluateDerivative(ctx->f[i],lambda,&alpha));
53: else PetscCall(FNEvaluateFunction(ctx->f[i],lambda,&alpha));
54: PetscCall(MatDenseGetArrayRead(ds->omat[DSMatExtra[i]],&E));
55: PetscCallBLAS("BLASaxpy",BLASaxpy_(&k,&alpha,E,&inc,T,&inc));
56: PetscCall(MatDenseRestoreArrayRead(ds->omat[DSMatExtra[i]],&E));
57: }
58: PetscCall(MatDenseRestoreArray(ds->omat[mat],&T));
59: }
60: PetscCall(PetscLogEventEnd(DS_Other,ds,0,0,0));
61: PetscFunctionReturn(PETSC_SUCCESS);
62: }
64: static PetscErrorCode DSAllocate_NEP(DS ds,PetscInt ld)
65: {
66: DS_NEP *ctx = (DS_NEP*)ds->data;
67: PetscInt i;
69: PetscFunctionBegin;
70: PetscCall(DSAllocateMat_Private(ds,DS_MAT_X));
71: for (i=0;i<ctx->nf;i++) PetscCall(DSAllocateMat_Private(ds,DSMatExtra[i]));
72: PetscCall(PetscFree(ds->perm));
73: PetscCall(PetscMalloc1(ld*ctx->max_mid,&ds->perm));
74: PetscFunctionReturn(PETSC_SUCCESS);
75: }
77: static PetscErrorCode DSView_NEP(DS ds,PetscViewer viewer)
78: {
79: DS_NEP *ctx = (DS_NEP*)ds->data;
80: PetscViewerFormat format;
81: PetscInt i;
82: const char *methodname[] = {
83: "Successive Linear Problems",
84: "Contour Integral"
85: };
86: const int nmeth=PETSC_STATIC_ARRAY_LENGTH(methodname);
88: PetscFunctionBegin;
89: PetscCall(PetscViewerGetFormat(viewer,&format));
90: if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
91: if (ds->method<nmeth) PetscCall(PetscViewerASCIIPrintf(viewer,"solving the problem with: %s\n",methodname[ds->method]));
92: #if PetscDefined(USE_COMPLEX)
93: if (ds->method==1) { /* contour integral method */
94: PetscCall(PetscViewerASCIIPrintf(viewer,"number of integration points: %" PetscInt_FMT "\n",ctx->nnod));
95: PetscCall(PetscViewerASCIIPrintf(viewer,"maximum minimality index: %" PetscInt_FMT "\n",ctx->max_mid));
96: if (ctx->spls) PetscCall(PetscViewerASCIIPrintf(viewer,"number of sampling columns for quadrature: %" PetscInt_FMT "\n",ctx->spls));
97: if (ctx->Nit) PetscCall(PetscViewerASCIIPrintf(viewer,"doing iterative refinement (%" PetscInt_FMT " its, tolerance %g)\n",ctx->Nit,(double)ctx->rtol));
98: PetscCall(RGView(ctx->rg,viewer));
99: }
100: #endif
101: if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) PetscCall(PetscViewerASCIIPrintf(viewer,"number of functions: %" PetscInt_FMT "\n",ctx->nf));
102: PetscFunctionReturn(PETSC_SUCCESS);
103: }
104: for (i=0;i<ctx->nf;i++) {
105: PetscCall(FNView(ctx->f[i],viewer));
106: PetscCall(DSViewMat(ds,viewer,DSMatExtra[i]));
107: }
108: if (ds->state>DS_STATE_INTERMEDIATE) PetscCall(DSViewMat(ds,viewer,DS_MAT_X));
109: PetscFunctionReturn(PETSC_SUCCESS);
110: }
112: static PetscErrorCode DSVectors_NEP(DS ds,DSMatType mat,PetscInt *j,PetscReal *rnorm)
113: {
114: PetscFunctionBegin;
115: PetscCheck(!rnorm,PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
116: switch (mat) {
117: case DS_MAT_X:
118: break;
119: case DS_MAT_Y:
120: SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
121: default:
122: SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
123: }
124: PetscFunctionReturn(PETSC_SUCCESS);
125: }
127: static PetscErrorCode DSSort_NEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *dummy)
128: {
129: DS_NEP *ctx = (DS_NEP*)ds->data;
130: PetscInt n,l,i,*perm,lds;
131: PetscScalar *Q;
133: PetscFunctionBegin;
134: if (!ds->sc) PetscFunctionReturn(PETSC_SUCCESS);
135: if (!ds->method) PetscFunctionReturn(PETSC_SUCCESS); /* SLP computes just one eigenvalue */
136: n = ds->n*ctx->max_mid;
137: lds = ds->ld*ctx->max_mid;
138: l = ds->l;
139: perm = ds->perm;
140: for (i=0;i<n;i++) perm[i] = i;
141: if (rr) PetscCall(DSSortEigenvalues_Private(ds,rr,ri,perm,PETSC_FALSE));
142: else PetscCall(DSSortEigenvalues_Private(ds,wr,NULL,perm,PETSC_FALSE));
143: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q));
144: for (i=l;i<ds->t;i++) Q[i+i*lds] = wr[perm[i]];
145: for (i=l;i<ds->t;i++) wr[i] = Q[i+i*lds];
146: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q));
147: /* n != ds->n */
148: PetscCall(DSPermuteColumns_Private(ds,0,ds->t,ds->n,DS_MAT_X,perm));
149: PetscFunctionReturn(PETSC_SUCCESS);
150: }
152: #if defined(SLEPC_MISSING_LAPACK_GGEV3)
153: #define LAPGEEV "ggev"
154: #else
155: #define LAPGEEV "ggev3"
156: #endif
158: static PetscErrorCode DSSolve_NEP_SLP(DS ds,PetscScalar *wr,PetscScalar *wi)
159: {
160: PetscScalar *A,*B,*W,*X,*work,*alpha,*beta,a;
161: PetscScalar sigma,lambda,mu,re,re2,sone=1.0,szero=0.0;
162: PetscBLASInt n,ld,lwork,one=1,zero=0;
163: PetscInt it,pos,j,maxit=100,result;
164: PetscReal norm,tol,done=1.0;
165: #if !PetscDefined(USE_COMPLEX)
166: PetscReal *alphai,im,im2;
167: #endif
169: PetscFunctionBegin;
170: PetscCall(PetscBLASIntCast(ds->n,&n));
171: PetscCall(PetscBLASIntCast(ds->ld,&ld));
172: PetscCall(DSAllocateMat_Private(ds,DS_MAT_A));
173: PetscCall(DSAllocateMat_Private(ds,DS_MAT_B));
174: PetscCall(DSAllocateMat_Private(ds,DS_MAT_W));
175: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
176: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_B],&B));
177: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_W],&W));
178: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_X],&X));
180: /* workspace query and memory allocation */
181: lwork = -1;
182: #if PetscDefined(USE_COMPLEX)
183: PetscCallLAPACKInfo("LAPACK" LAPGEEV,LAPACKggevalt_("N","V",&n,A,&ld,B,&ld,NULL,NULL,NULL,&ld,W,&ld,&a,&lwork,NULL,&info));
184: PetscCall(PetscBLASIntCast((PetscInt)PetscRealPart(a),&lwork));
185: PetscCall(DSAllocateWork_Private(ds,lwork+2*ds->n,8*ds->n,0));
186: alpha = ds->work;
187: beta = ds->work + ds->n;
188: work = ds->work + 2*ds->n;
189: #else
190: PetscCallLAPACKInfo("LAPACK" LAPGEEV,LAPACKggevalt_("N","V",&n,A,&ld,B,&ld,NULL,NULL,NULL,NULL,&ld,W,&ld,&a,&lwork,&info));
191: PetscCall(PetscBLASIntCast((PetscInt)a,&lwork));
192: PetscCall(DSAllocateWork_Private(ds,lwork+3*ds->n,0,0));
193: alpha = ds->work;
194: beta = ds->work + ds->n;
195: alphai = ds->work + 2*ds->n;
196: work = ds->work + 3*ds->n;
197: #endif
199: sigma = 0.0;
200: if (ds->sc->comparison==SlepcCompareTargetMagnitude || ds->sc->comparison==SlepcCompareTargetReal) sigma = *(PetscScalar*)ds->sc->comparisonctx;
201: lambda = sigma;
202: tol = n*PETSC_MACHINE_EPSILON/PetscSqrtReal(PETSC_SQRT_MACHINE_EPSILON);
204: for (it=0;it<maxit;it++) {
206: /* evaluate T and T' */
207: PetscCall(DSNEPComputeMatrix(ds,lambda,PETSC_FALSE,DS_MAT_A));
208: if (it) {
209: PetscCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&sone,A,&ld,X,&one,&szero,X+ld,&one));
210: norm = BLASnrm2_(&n,X+ld,&one);
211: if (norm/PetscAbsScalar(lambda)<=tol) break;
212: }
213: PetscCall(DSNEPComputeMatrix(ds,lambda,PETSC_TRUE,DS_MAT_B));
215: /* compute eigenvalue correction mu and eigenvector u */
216: #if PetscDefined(USE_COMPLEX)
217: PetscCallLAPACKInfo("LAPACK" LAPGEEV,LAPACKggevalt_("N","V",&n,A,&ld,B,&ld,alpha,beta,NULL,&ld,W,&ld,work,&lwork,ds->rwork,&info));
218: #else
219: PetscCallLAPACKInfo("LAPACK" LAPGEEV,LAPACKggevalt_("N","V",&n,A,&ld,B,&ld,alpha,alphai,beta,NULL,&ld,W,&ld,work,&lwork,&info));
220: #endif
222: /* find smallest eigenvalue */
223: j = 0;
224: if (beta[j]==0.0) re = (PetscRealPart(alpha[j])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
225: else re = alpha[j]/beta[j];
226: #if !PetscDefined(USE_COMPLEX)
227: if (beta[j]==0.0) im = (alphai[j]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
228: else im = alphai[j]/beta[j];
229: #endif
230: pos = 0;
231: for (j=1;j<n;j++) {
232: if (beta[j]==0.0) re2 = (PetscRealPart(alpha[j])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
233: else re2 = alpha[j]/beta[j];
234: #if !PetscDefined(USE_COMPLEX)
235: if (beta[j]==0.0) im2 = (alphai[j]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
236: else im2 = alphai[j]/beta[j];
237: PetscCall(SlepcCompareSmallestMagnitude(re,im,re2,im2,&result,NULL));
238: #else
239: PetscCall(SlepcCompareSmallestMagnitude(re,0.0,re2,0.0,&result,NULL));
240: #endif
241: if (result > 0) {
242: re = re2;
243: #if !PetscDefined(USE_COMPLEX)
244: im = im2;
245: #endif
246: pos = j;
247: }
248: }
250: #if !PetscDefined(USE_COMPLEX)
251: PetscCheck(im==0.0,PETSC_COMM_SELF,PETSC_ERR_SUP,"DSNEP found a complex eigenvalue; try rerunning with complex scalars");
252: #endif
253: mu = alpha[pos]/beta[pos];
254: PetscCall(PetscArraycpy(X,W+pos*ld,n));
255: norm = BLASnrm2_(&n,X,&one);
256: PetscCallLAPACKInfo("LAPACKlascl",LAPACKlascl_("G",&zero,&zero,&norm,&done,&n,&one,X,&n,&info));
258: /* correct eigenvalue approximation */
259: lambda = lambda - mu;
260: }
261: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
262: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_B],&B));
263: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_W],&W));
264: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_X],&X));
266: PetscCheck(it<maxit,PETSC_COMM_SELF,PETSC_ERR_CONV_FAILED,"DSNEP did not converge");
267: ds->t = 1;
268: wr[0] = lambda;
269: if (wi) wi[0] = 0.0;
270: PetscFunctionReturn(PETSC_SUCCESS);
271: }
273: #if PetscDefined(USE_COMPLEX)
274: /*
275: Newton refinement for eigenpairs computed with contour integral.
276: k - number of eigenpairs to refine
277: wr - eigenvalues (eigenvectors are stored in DS_MAT_X)
278: */
279: static PetscErrorCode DSNEPNewtonRefine(DS ds,PetscInt k,PetscScalar *wr)
280: {
281: DS_NEP *ctx = (DS_NEP*)ds->data;
282: PetscScalar *X,*W,*U,*R,sone=1.0,szero=0.0;
283: PetscReal norm;
284: PetscInt i,j,ii,nwu=0,*p,jstart=0,jend=k;
285: const PetscInt *range;
286: PetscBLASInt n,*perm,ld,one=1,n1;
287: PetscMPIInt len,size,root;
288: PetscLayout map;
290: PetscFunctionBegin;
291: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_X],&X));
292: PetscCall(PetscBLASIntCast(ds->n,&n));
293: PetscCall(PetscBLASIntCast(ds->ld,&ld));
294: n1 = n+1;
295: p = ds->perm;
296: PetscCall(PetscArrayzero(p,k));
297: PetscCall(DSAllocateWork_Private(ds,(n+2)*(n+1),0,n+1));
298: U = ds->work+nwu; nwu += (n+1)*(n+1);
299: R = ds->work+nwu; /*nwu += n+1;*/
300: perm = ds->iwork;
301: if (ds->pmode==DS_PARALLEL_DISTRIBUTED) {
302: PetscCall(PetscLayoutCreateFromSizes(PetscObjectComm((PetscObject)ds),PETSC_DECIDE,k,1,&map));
303: PetscCall(PetscLayoutGetRange(map,&jstart,&jend));
304: }
305: for (ii=0;ii<ctx->Nit;ii++) {
306: for (j=jstart;j<jend;j++) {
307: if (p[j]<2) {
308: PetscCall(DSNEPComputeMatrix(ds,wr[j],PETSC_FALSE,DS_MAT_W));
309: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_W],&W));
310: PetscCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&sone,W,&ld,X+ld*j,&one,&szero,R,&one));
311: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_W],&W));
312: norm = BLASnrm2_(&n,R,&one);
313: if (norm/PetscAbsScalar(wr[j]) > ctx->rtol) {
314: PetscCall(PetscInfo(NULL,"Refining eigenpair %" PetscInt_FMT ", residual=%g\n",j,(double)(norm/PetscAbsScalar(wr[j]))));
315: p[j] = 1;
316: R[n] = 0.0;
317: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_W],&W));
318: for (i=0;i<n;i++) {
319: PetscCall(PetscArraycpy(U+i*n1,W+i*ld,n));
320: U[n+i*n1] = PetscConj(X[j*ld+i]);
321: }
322: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_W],&W));
323: U[n+n*n1] = 0.0;
324: PetscCall(DSNEPComputeMatrix(ds,wr[j],PETSC_TRUE,DS_MAT_W));
325: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_W],&W));
326: PetscCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&sone,W,&ld,X+ld*j,&one,&szero,U+n*(n+1),&one));
327: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_W],&W));
328: /* solve system */
329: PetscCallLAPACKInfo("LAPACKgetrf",LAPACKgetrf_(&n1,&n1,U,&n1,perm,&info));
330: PetscCallLAPACKInfo("LAPACKgetrs",LAPACKgetrs_("N",&n1,&one,U,&n1,perm,R,&n1,&info));
331: wr[j] -= R[n];
332: for (i=0;i<n;i++) X[j*ld+i] -= R[i];
333: /* normalization */
334: norm = BLASnrm2_(&n,X+ld*j,&one);
335: for (i=0;i<n;i++) X[ld*j+i] /= norm;
336: } else p[j] = 2;
337: }
338: }
339: }
340: if (ds->pmode==DS_PARALLEL_DISTRIBUTED) { /* communicate results */
341: PetscCall(PetscMPIIntCast(k,&len));
342: PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE,p,len,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)ds)));
343: PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)ds),&size));
344: PetscCall(PetscLayoutGetRanges(map,&range));
345: for (j=0;j<k;j++) {
346: if (p[j]) { /* j-th eigenpair has been refined */
347: for (root=0;root<size;root++) if (range[root+1]>j) break;
348: PetscCall(PetscMPIIntCast(1,&len));
349: PetscCallMPI(MPI_Bcast(wr+j,len,MPIU_SCALAR,root,PetscObjectComm((PetscObject)ds)));
350: PetscCall(PetscMPIIntCast(n,&len));
351: PetscCallMPI(MPI_Bcast(X+ld*j,len,MPIU_SCALAR,root,PetscObjectComm((PetscObject)ds)));
352: }
353: }
354: PetscCall(PetscLayoutDestroy(&map));
355: }
356: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_X],&X));
357: PetscFunctionReturn(PETSC_SUCCESS);
358: }
360: PetscErrorCode DSSolve_NEP_Contour(DS ds,PetscScalar *wr,PetscScalar *wi)
361: {
362: DS_NEP *ctx = (DS_NEP*)ds->data;
363: PetscScalar *alpha,*beta,*Q,*Z,*X,*U,*V,*W,*work,*Rc,*R,*w,*z,*zn,*S;
364: PetscScalar sone=1.0,szero=0.0,center,a;
365: PetscReal *rwork,norm,radius,vscale,rgscale,*sigma;
366: PetscBLASInt n,*perm,p,pp,ld,lwork,k_,rk_,colA,rowA,one=1;
367: PetscInt mid,lds,nnod=ctx->nnod,k,i,ii,jj,j,s,off,rk,nwu=0,nw,lrwork,*inside,kstart=0,kend=nnod;
368: PetscMPIInt len;
369: PetscBool isellipse;
370: PetscRandom rand;
372: PetscFunctionBegin;
373: PetscCheck(ctx->rg,PetscObjectComm((PetscObject)ds),PETSC_ERR_ORDER,"The contour solver requires a region passed with DSNEPSetRG()");
374: /* Contour parameters */
375: PetscCall(PetscObjectTypeCompare((PetscObject)ctx->rg,RGELLIPSE,&isellipse));
376: PetscCheck(isellipse,PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Region must be Ellipse");
377: PetscCall(RGEllipseGetParameters(ctx->rg,¢er,&radius,&vscale));
378: PetscCall(RGGetScale(ctx->rg,&rgscale));
379: if (ds->pmode==DS_PARALLEL_DISTRIBUTED) {
380: if (!ctx->map) PetscCall(PetscLayoutCreateFromSizes(PetscObjectComm((PetscObject)ds),PETSC_DECIDE,ctx->nnod,1,&ctx->map));
381: PetscCall(PetscLayoutGetRange(ctx->map,&kstart,&kend));
382: }
384: PetscCall(DSAllocateMat_Private(ds,DS_MAT_W)); /* size n */
385: PetscCall(DSAllocateMat_Private(ds,DS_MAT_Q)); /* size mid*n */
386: PetscCall(DSAllocateMat_Private(ds,DS_MAT_Z)); /* size mid*n */
387: PetscCall(DSAllocateMat_Private(ds,DS_MAT_U)); /* size mid*n */
388: PetscCall(DSAllocateMat_Private(ds,DS_MAT_V)); /* size mid*n */
389: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q));
390: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Z],&Z));
391: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_U],&U));
392: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_V],&V));
393: mid = ctx->max_mid;
394: PetscCall(PetscBLASIntCast(ds->n,&n));
395: p = n; /* maximum number of columns for the probing matrix */
396: PetscCall(PetscBLASIntCast(ds->ld,&ld));
397: PetscCall(PetscBLASIntCast(mid*n,&rowA));
398: nw = 2*n*(p+mid)+3*nnod+2*mid*n*p;
399: lrwork = 9*mid*n;
401: /* workspace query and memory allocation */
402: lwork = -1;
403: PetscCallLAPACKInfo("LAPACK" LAPGEEV,LAPACKggevalt_("N","V",&rowA,Q,&rowA,Z,&rowA,NULL,NULL,NULL,&ld,V,&rowA,&a,&lwork,NULL,&info));
404: PetscCall(PetscBLASIntCast((PetscInt)PetscRealPart(a),&lwork));
405: PetscCall(DSAllocateWork_Private(ds,lwork+nw,lrwork,n+1));
407: sigma = ds->rwork;
408: rwork = ds->rwork+mid*n;
409: perm = ds->iwork;
410: z = ds->work+nwu; nwu += nnod; /* quadrature points */
411: zn = ds->work+nwu; nwu += nnod; /* normalized quadrature points */
412: w = ds->work+nwu; nwu += nnod; /* quadrature weights */
413: Rc = ds->work+nwu; nwu += n*p;
414: R = ds->work+nwu; nwu += n*p;
415: alpha = ds->work+nwu; nwu += mid*n;
416: beta = ds->work+nwu; nwu += mid*n;
417: S = ds->work+nwu; nwu += 2*mid*n*p;
418: work = ds->work+nwu;
420: /* Compute quadrature parameters */
421: PetscCall(RGComputeQuadrature(ctx->rg,RG_QUADRULE_TRAPEZOIDAL,nnod,z,zn,w));
423: /* Set random matrix */
424: PetscCall(PetscRandomCreate(PetscObjectComm((PetscObject)ds),&rand));
425: PetscCall(PetscRandomSetSeed(rand,0x12345678));
426: PetscCall(PetscRandomSeed(rand));
427: for (j=0;j<p;j++)
428: for (i=0;i<n;i++) PetscCall(PetscRandomGetValue(rand,Rc+i+j*n));
429: PetscCall(PetscArrayzero(S,2*mid*n*p));
430: /* Loop of integration points */
431: for (k=kstart;k<kend;k++) {
432: PetscCall(PetscInfo(NULL,"Solving integration point %" PetscInt_FMT "\n",k));
433: PetscCall(PetscArraycpy(R,Rc,p*n));
434: PetscCall(DSNEPComputeMatrix(ds,z[k],PETSC_FALSE,DS_MAT_W));
436: /* LU factorization */
437: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_W],&W));
438: PetscCallLAPACKInfo("LAPACKgetrf",LAPACKgetrf_(&n,&n,W,&ld,perm,&info));
439: PetscCallLAPACKInfo("LAPACKgetrs",LAPACKgetrs_("N",&n,&p,W,&ld,perm,R,&n,&info));
440: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_W],&W));
442: /* Moments computation */
443: for (s=0;s<2*ctx->max_mid;s++) {
444: off = s*n*p;
445: for (j=0;j<p;j++)
446: for (i=0;i<n;i++) S[off+i+j*n] += w[k]*R[j*n+i];
447: w[k] *= zn[k];
448: }
449: }
451: if (ds->pmode==DS_PARALLEL_DISTRIBUTED) { /* compute final S via reduction */
452: PetscCall(PetscMPIIntCast(2*mid*n*p,&len));
453: PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE,S,len,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)ds)));
454: }
455: PetscCall(PetscBLASIntCast(ctx->spls?PetscMin(ctx->spls,n):n,&p));
456: pp = p;
457: do {
458: p = pp;
459: PetscCall(PetscBLASIntCast(mid*p,&colA));
461: PetscCall(PetscInfo(ds,"Computing SVD of size %" PetscBLASInt_FMT "x%" PetscBLASInt_FMT "\n",rowA,colA));
462: for (jj=0;jj<mid;jj++) {
463: for (ii=0;ii<mid;ii++) {
464: off = jj*p*rowA+ii*n;
465: for (j=0;j<p;j++)
466: for (i=0;i<n;i++) Q[off+j*rowA+i] = S[((jj+ii)*n+j)*n+i];
467: }
468: }
469: PetscCallLAPACKInfo("LAPACKgesvd",LAPACKgesvd_("S","S",&rowA,&colA,Q,&rowA,sigma,U,&rowA,V,&colA,work,&lwork,rwork,&info));
471: rk = colA;
472: for (i=1;i<colA;i++) if (sigma[i]/sigma[0]<PETSC_MACHINE_EPSILON*1e4) {rk = i; break;}
473: if (rk<colA || p==n) break;
474: pp *= 2;
475: } while (pp<=n);
476: PetscCall(PetscInfo(ds,"Solving generalized eigenproblem of size %" PetscInt_FMT "\n",rk));
477: for (jj=0;jj<mid;jj++) {
478: for (ii=0;ii<mid;ii++) {
479: off = jj*p*rowA+ii*n;
480: for (j=0;j<p;j++)
481: for (i=0;i<n;i++) Q[off+j*rowA+i] = S[((jj+ii+1)*n+j)*n+i];
482: }
483: }
484: PetscCall(PetscBLASIntCast(rk,&rk_));
485: PetscCallBLAS("BLASgemm",BLASgemm_("N","C",&rowA,&rk_,&colA,&sone,Q,&rowA,V,&colA,&szero,Z,&rowA));
486: PetscCallBLAS("BLASgemm",BLASgemm_("C","N",&rk_,&rk_,&rowA,&sone,U,&rowA,Z,&rowA,&szero,Q,&rk_));
487: PetscCall(PetscArrayzero(Z,n*mid*n*mid));
488: for (j=0;j<rk;j++) Z[j+j*rk_] = sigma[j];
489: PetscCallLAPACKInfo("LAPACK" LAPGEEV,LAPACKggevalt_("N","V",&rk_,Q,&rk_,Z,&rk_,alpha,beta,NULL,&ld,V,&rk_,work,&lwork,rwork,&info));
490: for (i=0;i<rk;i++) wr[i] = (center+alpha[i]*radius/beta[i])*rgscale;
491: PetscCall(PetscMalloc1(rk,&inside));
492: PetscCall(RGCheckInside(ctx->rg,rk,wr,wi,inside));
493: k=0;
494: for (i=0;i<rk;i++)
495: if (inside[i]==1) inside[k++] = i;
496: /* Discard values outside region */
497: lds = ld*mid;
498: PetscCall(PetscArrayzero(Q,lds*lds));
499: PetscCall(PetscArrayzero(Z,lds*lds));
500: for (i=0;i<k;i++) Q[i+i*lds] = (center*beta[inside[i]]+radius*alpha[inside[i]])*rgscale;
501: for (i=0;i<k;i++) Z[i+i*lds] = beta[inside[i]];
502: for (i=0;i<k;i++) wr[i] = Q[i+i*lds]/Z[i+i*lds];
503: for (j=0;j<k;j++) for (i=0;i<rk;i++) V[j*rk+i] = sigma[i]*V[inside[j]*rk+i];
504: PetscCall(PetscBLASIntCast(k,&k_));
505: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_X],&X));
506: PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&k_,&rk_,&sone,U,&rowA,V,&rk_,&szero,X,&ld));
507: /* Normalize */
508: for (j=0;j<k;j++) {
509: norm = BLASnrm2_(&n,X+ld*j,&one);
510: for (i=0;i<n;i++) X[ld*j+i] /= norm;
511: }
512: PetscCall(PetscFree(inside));
513: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_X],&X));
514: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q));
515: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Z],&Z));
516: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_U],&U));
517: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_V],&V));
519: /* Newton refinement */
520: if (ctx->Nit) PetscCall(DSNEPNewtonRefine(ds,k,wr));
521: ds->t = k;
522: PetscCall(PetscRandomDestroy(&rand));
523: PetscFunctionReturn(PETSC_SUCCESS);
524: }
525: #endif
527: #if !PetscDefined(HAVE_MPIUNI)
528: static PetscErrorCode DSSynchronize_NEP(DS ds,PetscScalar eigr[],PetscScalar eigi[])
529: {
530: DS_NEP *ctx = (DS_NEP*)ds->data;
531: PetscInt ld=ds->ld,k=0;
532: PetscMPIInt n,n2,rank,size,off=0;
533: PetscScalar *X;
535: PetscFunctionBegin;
536: if (!ds->method) { /* SLP */
537: if (ds->state>=DS_STATE_CONDENSED) k += ds->n;
538: if (eigr) k += 1;
539: if (eigi) k += 1;
540: PetscCall(PetscMPIIntCast(1,&n));
541: PetscCall(PetscMPIIntCast(ds->n,&n2));
542: } else { /* Contour */
543: if (ds->state>=DS_STATE_CONDENSED) k += ctx->max_mid*ds->n*ld;
544: if (eigr) k += ctx->max_mid*ds->n;
545: if (eigi) k += ctx->max_mid*ds->n;
546: PetscCall(PetscMPIIntCast(ctx->max_mid*ds->n,&n));
547: PetscCall(PetscMPIIntCast(ctx->max_mid*ds->n*ld,&n2));
548: }
549: PetscCall(DSAllocateWork_Private(ds,k,0,0));
550: PetscCall(PetscMPIIntCast(k*sizeof(PetscScalar),&size));
551: if (ds->state>=DS_STATE_CONDENSED) PetscCall(MatDenseGetArray(ds->omat[DS_MAT_X],&X));
552: PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank));
553: if (!rank) {
554: if (ds->state>=DS_STATE_CONDENSED) PetscCallMPI(MPI_Pack(X,n2,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
555: if (eigr) PetscCallMPI(MPI_Pack(eigr,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
556: #if !PetscDefined(USE_COMPLEX)
557: if (eigi) PetscCallMPI(MPI_Pack(eigi,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
558: #endif
559: }
560: PetscCallMPI(MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds)));
561: if (rank) {
562: if (ds->state>=DS_STATE_CONDENSED) PetscCallMPI(MPI_Unpack(ds->work,size,&off,X,n2,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
563: if (eigr) PetscCallMPI(MPI_Unpack(ds->work,size,&off,eigr,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
564: #if !PetscDefined(USE_COMPLEX)
565: if (eigi) PetscCallMPI(MPI_Unpack(ds->work,size,&off,eigi,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
566: #endif
567: }
568: if (ds->state>=DS_STATE_CONDENSED) PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_X],&X));
569: PetscFunctionReturn(PETSC_SUCCESS);
570: }
571: #endif
573: static PetscErrorCode DSNEPSetFN_NEP(DS ds,PetscInt n,FN fn[])
574: {
575: DS_NEP *ctx = (DS_NEP*)ds->data;
576: PetscInt i;
578: PetscFunctionBegin;
579: PetscCheck(n>0,PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Must have one or more functions, you have %" PetscInt_FMT,n);
580: PetscCheck(n<=DS_NUM_EXTRA,PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Too many functions, you specified %" PetscInt_FMT " but the limit is %d",n,DS_NUM_EXTRA);
581: if (ds->ld) PetscCall(PetscInfo(ds,"DSNEPSetFN() called after DSAllocate()\n"));
582: for (i=0;i<n;i++) PetscCall(PetscObjectReference((PetscObject)fn[i]));
583: for (i=0;i<ctx->nf;i++) PetscCall(FNDestroy(&ctx->f[i]));
584: for (i=0;i<n;i++) ctx->f[i] = fn[i];
585: ctx->nf = n;
586: PetscFunctionReturn(PETSC_SUCCESS);
587: }
589: /*@
590: DSNEPSetFN - Sets a number of functions that define the nonlinear
591: eigenproblem.
593: Collective
595: Input Parameters:
596: + ds - the direct solver context
597: . n - number of functions
598: - fn - array of functions
600: Notes:
601: The nonlinear eigenproblem is defined in terms of the split nonlinear
602: operator $T(\lambda) = \sum_i E_i f_i(\lambda)$.
604: This function must be called before `DSAllocate()`. Then `DSAllocate()`
605: will allocate an extra matrix $E_i$ per each function, that can be
606: filled in the usual way.
608: Level: advanced
610: .seealso: [](sec:ds), `DSNEP`, `DSNEPGetFN()`, `DSAllocate()`
611: @*/
612: PetscErrorCode DSNEPSetFN(DS ds,PetscInt n,FN fn[])
613: {
614: PetscInt i;
616: PetscFunctionBegin;
619: PetscAssertPointer(fn,3);
620: for (i=0;i<n;i++) {
622: PetscCheckSameComm(ds,1,fn[i],3);
623: }
624: PetscTryMethod(ds,"DSNEPSetFN_C",(DS,PetscInt,FN[]),(ds,n,fn));
625: PetscFunctionReturn(PETSC_SUCCESS);
626: }
628: static PetscErrorCode DSNEPGetFN_NEP(DS ds,PetscInt k,FN *fn)
629: {
630: DS_NEP *ctx = (DS_NEP*)ds->data;
632: PetscFunctionBegin;
633: PetscCheck(k>=0 && k<ctx->nf,PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"k must be between 0 and %" PetscInt_FMT,ctx->nf-1);
634: *fn = ctx->f[k];
635: PetscFunctionReturn(PETSC_SUCCESS);
636: }
638: /*@
639: DSNEPGetFN - Gets the functions associated with the nonlinear `DS`.
641: Not Collective
643: Input Parameters:
644: + ds - the direct solver context
645: - k - the index of the requested function (starting in 0)
647: Output Parameter:
648: . fn - the function
650: Level: advanced
652: .seealso: [](sec:ds), `DSNEP`, `DSNEPSetFN()`
653: @*/
654: PetscErrorCode DSNEPGetFN(DS ds,PetscInt k,FN *fn)
655: {
656: PetscFunctionBegin;
658: PetscAssertPointer(fn,3);
659: PetscUseMethod(ds,"DSNEPGetFN_C",(DS,PetscInt,FN*),(ds,k,fn));
660: PetscFunctionReturn(PETSC_SUCCESS);
661: }
663: static PetscErrorCode DSNEPGetNumFN_NEP(DS ds,PetscInt *n)
664: {
665: DS_NEP *ctx = (DS_NEP*)ds->data;
667: PetscFunctionBegin;
668: *n = ctx->nf;
669: PetscFunctionReturn(PETSC_SUCCESS);
670: }
672: /*@
673: DSNEPGetNumFN - Returns the number of functions stored internally by
674: the `DS`.
676: Not Collective
678: Input Parameter:
679: . ds - the direct solver context
681: Output Parameter:
682: . n - the number of functions passed in `DSNEPSetFN()`
684: Level: advanced
686: .seealso: [](sec:ds), `DSNEP`, `DSNEPSetFN()`
687: @*/
688: PetscErrorCode DSNEPGetNumFN(DS ds,PetscInt *n)
689: {
690: PetscFunctionBegin;
692: PetscAssertPointer(n,2);
693: PetscUseMethod(ds,"DSNEPGetNumFN_C",(DS,PetscInt*),(ds,n));
694: PetscFunctionReturn(PETSC_SUCCESS);
695: }
697: static PetscErrorCode DSNEPSetMinimality_NEP(DS ds,PetscInt n)
698: {
699: DS_NEP *ctx = (DS_NEP*)ds->data;
701: PetscFunctionBegin;
702: if (n == PETSC_DECIDE || n == PETSC_DEFAULT) ctx->max_mid = 4;
703: else {
704: PetscCheck(n>0,PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"The minimality value must be > 0");
705: ctx->max_mid = n;
706: }
707: PetscFunctionReturn(PETSC_SUCCESS);
708: }
710: /*@
711: DSNEPSetMinimality - Sets the maximum minimality index used internally by
712: the `DSNEP`.
714: Logically Collective
716: Input Parameters:
717: + ds - the direct solver context
718: - n - the maximum minimality index
720: Options Database Key:
721: . -ds_nep_minimality n - sets the maximum minimality index
723: Notes:
724: The maximum minimality index is used only in the contour integral method,
725: and is related to the highest moments used in the method. The default
726: value is 1, a larger value might give better accuracy in some cases, but
727: at a higher cost.
729: Level: advanced
731: .seealso: [](sec:ds), `DSNEP`, `DSNEPGetMinimality()`
732: @*/
733: PetscErrorCode DSNEPSetMinimality(DS ds,PetscInt n)
734: {
735: PetscFunctionBegin;
738: PetscTryMethod(ds,"DSNEPSetMinimality_C",(DS,PetscInt),(ds,n));
739: PetscFunctionReturn(PETSC_SUCCESS);
740: }
742: static PetscErrorCode DSNEPGetMinimality_NEP(DS ds,PetscInt *n)
743: {
744: DS_NEP *ctx = (DS_NEP*)ds->data;
746: PetscFunctionBegin;
747: *n = ctx->max_mid;
748: PetscFunctionReturn(PETSC_SUCCESS);
749: }
751: /*@
752: DSNEPGetMinimality - Returns the maximum minimality index used internally by
753: the `DSNEP`.
755: Not Collective
757: Input Parameter:
758: . ds - the direct solver context
760: Output Parameter:
761: . n - the maximum minimality index passed in `DSNEPSetMinimality()`
763: Level: advanced
765: .seealso: [](sec:ds), `DSNEP`, `DSNEPSetMinimality()`
766: @*/
767: PetscErrorCode DSNEPGetMinimality(DS ds,PetscInt *n)
768: {
769: PetscFunctionBegin;
771: PetscAssertPointer(n,2);
772: PetscUseMethod(ds,"DSNEPGetMinimality_C",(DS,PetscInt*),(ds,n));
773: PetscFunctionReturn(PETSC_SUCCESS);
774: }
776: static PetscErrorCode DSNEPSetRefine_NEP(DS ds,PetscReal tol,PetscInt its)
777: {
778: DS_NEP *ctx = (DS_NEP*)ds->data;
780: PetscFunctionBegin;
781: if (tol == (PetscReal)PETSC_DETERMINE) {
782: ctx->rtol = PETSC_MACHINE_EPSILON/PetscSqrtReal(PETSC_SQRT_MACHINE_EPSILON);
783: } else if (tol != (PetscReal)PETSC_CURRENT) {
784: PetscCheck(tol>0.0,PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"The tolerance must be > 0");
785: ctx->rtol = tol;
786: }
787: if (its == PETSC_DETERMINE) {
788: ctx->Nit = 3;
789: } else if (its != PETSC_CURRENT) {
790: PetscCheck(its>=0,PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"The number of iterations must be >= 0");
791: ctx->Nit = its;
792: }
793: PetscFunctionReturn(PETSC_SUCCESS);
794: }
796: /*@
797: DSNEPSetRefine - Sets the tolerance and the number of iterations of Newton iterative
798: refinement for eigenpairs when solving a `DSNEP`.
800: Logically Collective
802: Input Parameters:
803: + ds - the direct solver context
804: . tol - the tolerance
805: - its - the number of iterations
807: Options Database Keys:
808: + -ds_nep_refine_tol tol - sets the tolerance
809: - -ds_nep_refine_its its - sets the number of Newton iterations
811: Notes:
812: Iterative refinement of eigenpairs is currently used only in the contour
813: integral method.
815: Use `PETSC_CURRENT` to retain the current value of any of the parameters.
816: Use `PETSC_DETERMINE` for either argument to assign a default value computed
817: internally.
819: Level: advanced
821: .seealso: [](sec:ds), `DSNEP`, `DSNEPGetRefine()`
822: @*/
823: PetscErrorCode DSNEPSetRefine(DS ds,PetscReal tol,PetscInt its)
824: {
825: PetscFunctionBegin;
829: PetscTryMethod(ds,"DSNEPSetRefine_C",(DS,PetscReal,PetscInt),(ds,tol,its));
830: PetscFunctionReturn(PETSC_SUCCESS);
831: }
833: static PetscErrorCode DSNEPGetRefine_NEP(DS ds,PetscReal *tol,PetscInt *its)
834: {
835: DS_NEP *ctx = (DS_NEP*)ds->data;
837: PetscFunctionBegin;
838: if (tol) *tol = ctx->rtol;
839: if (its) *its = ctx->Nit;
840: PetscFunctionReturn(PETSC_SUCCESS);
841: }
843: /*@
844: DSNEPGetRefine - Returns the tolerance and the number of iterations of Newton iterative
845: refinement for eigenpairs.
847: Not Collective
849: Input Parameter:
850: . ds - the direct solver context
852: Output Parameters:
853: + tol - the tolerance
854: - its - the number of iterations
856: Level: advanced
858: .seealso: [](sec:ds), `DSNEP`, `DSNEPSetRefine()`
859: @*/
860: PetscErrorCode DSNEPGetRefine(DS ds,PetscReal *tol,PetscInt *its)
861: {
862: PetscFunctionBegin;
864: PetscUseMethod(ds,"DSNEPGetRefine_C",(DS,PetscReal*,PetscInt*),(ds,tol,its));
865: PetscFunctionReturn(PETSC_SUCCESS);
866: }
868: static PetscErrorCode DSNEPSetIntegrationPoints_NEP(DS ds,PetscInt ip)
869: {
870: DS_NEP *ctx = (DS_NEP*)ds->data;
872: PetscFunctionBegin;
873: if (ip == PETSC_DECIDE || ip == PETSC_DEFAULT) ctx->nnod = 64;
874: else {
875: PetscCheck(ip>0,PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"The number of integration points must be > 0");
876: ctx->nnod = ip;
877: }
878: PetscCall(PetscLayoutDestroy(&ctx->map)); /* need to redistribute at next solve */
879: PetscFunctionReturn(PETSC_SUCCESS);
880: }
882: /*@
883: DSNEPSetIntegrationPoints - Sets the number of integration points to be
884: used in the contour integral method when solving a `DSNEP`.
886: Logically Collective
888: Input Parameters:
889: + ds - the direct solver context
890: - ip - the number of integration points
892: Options Database Key:
893: . -ds_nep_integration_points ip - sets the number of integration points
895: Notes:
896: This parameter is relevant only in the contour integral method.
898: Level: advanced
900: .seealso: [](sec:ds), `DSNEP`, `DSNEPGetIntegrationPoints()`
901: @*/
902: PetscErrorCode DSNEPSetIntegrationPoints(DS ds,PetscInt ip)
903: {
904: PetscFunctionBegin;
907: PetscTryMethod(ds,"DSNEPSetIntegrationPoints_C",(DS,PetscInt),(ds,ip));
908: PetscFunctionReturn(PETSC_SUCCESS);
909: }
911: static PetscErrorCode DSNEPGetIntegrationPoints_NEP(DS ds,PetscInt *ip)
912: {
913: DS_NEP *ctx = (DS_NEP*)ds->data;
915: PetscFunctionBegin;
916: *ip = ctx->nnod;
917: PetscFunctionReturn(PETSC_SUCCESS);
918: }
920: /*@
921: DSNEPGetIntegrationPoints - Returns the number of integration points used
922: in the contour integral method.
924: Not Collective
926: Input Parameter:
927: . ds - the direct solver context
929: Output Parameter:
930: . ip - the number of integration points
932: Level: advanced
934: .seealso: [](sec:ds), `DSNEP`, `DSNEPSetIntegrationPoints()`
935: @*/
936: PetscErrorCode DSNEPGetIntegrationPoints(DS ds,PetscInt *ip)
937: {
938: PetscFunctionBegin;
940: PetscAssertPointer(ip,2);
941: PetscUseMethod(ds,"DSNEPGetIntegrationPoints_C",(DS,PetscInt*),(ds,ip));
942: PetscFunctionReturn(PETSC_SUCCESS);
943: }
945: static PetscErrorCode DSNEPSetSamplingSize_NEP(DS ds,PetscInt p)
946: {
947: DS_NEP *ctx = (DS_NEP*)ds->data;
949: PetscFunctionBegin;
950: if (p == PETSC_DECIDE || p == PETSC_DEFAULT) ctx->spls = 0;
951: else {
952: PetscCheck(p>0,PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"The sample size must be > 0");
953: PetscCheck(p>=20,PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"The sample size cannot be smaller than 20");
954: ctx->spls = p;
955: }
956: PetscFunctionReturn(PETSC_SUCCESS);
957: }
959: /*@
960: DSNEPSetSamplingSize - Sets the number of sampling columns to be
961: used in the contour integral method when solving a `DSNEP`.
963: Logically Collective
965: Input Parameters:
966: + ds - the direct solver context
967: - p - the number of columns for the sampling matrix
969: Options Database Key:
970: . -ds_nep_sampling_size p - set the number of sampling columns
972: Note:
973: This parameter is relevant only in the contour integral method.
975: Level: advanced
977: .seealso: [](sec:ds), `DSNEP`, `DSNEPGetSamplingSize()`
978: @*/
979: PetscErrorCode DSNEPSetSamplingSize(DS ds,PetscInt p)
980: {
981: PetscFunctionBegin;
984: PetscTryMethod(ds,"DSNEPSetSamplingSize_C",(DS,PetscInt),(ds,p));
985: PetscFunctionReturn(PETSC_SUCCESS);
986: }
988: static PetscErrorCode DSNEPGetSamplingSize_NEP(DS ds,PetscInt *p)
989: {
990: DS_NEP *ctx = (DS_NEP*)ds->data;
992: PetscFunctionBegin;
993: *p = ctx->spls;
994: PetscFunctionReturn(PETSC_SUCCESS);
995: }
997: /*@
998: DSNEPGetSamplingSize - Returns the number of sampling columns used
999: in the contour integral method.
1001: Not Collective
1003: Input Parameter:
1004: . ds - the direct solver context
1006: Output Parameter:
1007: . p - the number of columns for the sampling matrix
1009: Level: advanced
1011: .seealso: [](sec:ds), `DSNEP`, `DSNEPSetSamplingSize()`
1012: @*/
1013: PetscErrorCode DSNEPGetSamplingSize(DS ds,PetscInt *p)
1014: {
1015: PetscFunctionBegin;
1017: PetscAssertPointer(p,2);
1018: PetscUseMethod(ds,"DSNEPGetSamplingSize_C",(DS,PetscInt*),(ds,p));
1019: PetscFunctionReturn(PETSC_SUCCESS);
1020: }
1022: static PetscErrorCode DSNEPSetComputeMatrixFunction_NEP(DS ds,DSNEPMatrixFunctionFn *fun,PetscCtx ctx,PetscCtxDestroyFn *destroy)
1023: {
1024: DS_NEP *dsctx = (DS_NEP*)ds->data;
1026: PetscFunctionBegin;
1027: if (dsctx->computematrixdestroy) PetscCall((*dsctx->computematrixdestroy)(&dsctx->computematrixctx));
1028: dsctx->computematrix = fun;
1029: dsctx->computematrixctx = ctx;
1030: dsctx->computematrixdestroy = destroy;
1031: PetscFunctionReturn(PETSC_SUCCESS);
1032: }
1034: /*@
1035: DSNEPSetComputeMatrixFunction - Sets a user-provided subroutine to compute
1036: the matrices $T(\lambda)$ or $T'(\lambda)$.
1038: Logically Collective
1040: Input Parameters:
1041: + ds - the direct solver context
1042: . fun - matrix function evaluation routine, see `DSNEPMatrixFunctionFn` for the calling sequence
1043: . ctx - a context pointer (the last parameter to the user function)
1044: - destroy - a routine for destroying the context (may be `NULL`), see `PetscCtxDestroyFn`
1045: for the calling sequence
1047: Note:
1048: The result is computed as $T(\lambda) = \sum_i E_i f_i(\lambda)$, and similarly
1049: for the derivative, where $E_i$ are the extra matrices, see `DSMatType`.
1051: Level: developer
1053: .seealso: [](sec:ds), `DSNEP`, `DSNEPGetComputeMatrixFunction()`
1054: @*/
1055: PetscErrorCode DSNEPSetComputeMatrixFunction(DS ds,DSNEPMatrixFunctionFn *fun,PetscCtx ctx,PetscCtxDestroyFn *destroy)
1056: {
1057: PetscFunctionBegin;
1059: PetscTryMethod(ds,"DSNEPSetComputeMatrixFunction_C",(DS,DSNEPMatrixFunctionFn*,PetscCtx,PetscCtxDestroyFn*),(ds,fun,ctx,destroy));
1060: PetscFunctionReturn(PETSC_SUCCESS);
1061: }
1063: static PetscErrorCode DSNEPGetComputeMatrixFunction_NEP(DS ds,DSNEPMatrixFunctionFn **fun,PetscCtxRt ctx,PetscCtxDestroyFn **destroy)
1064: {
1065: DS_NEP *dsctx = (DS_NEP*)ds->data;
1067: PetscFunctionBegin;
1068: if (fun) *fun = dsctx->computematrix;
1069: if (ctx) *(void**)ctx = dsctx->computematrixctx;
1070: if (destroy) *destroy = dsctx->computematrixdestroy;
1071: PetscFunctionReturn(PETSC_SUCCESS);
1072: }
1074: /*@
1075: DSNEPGetComputeMatrixFunction - Returns the user-provided callback function
1076: set in `DSNEPSetComputeMatrixFunction()`.
1078: Not Collective
1080: Input Parameter:
1081: . ds - the direct solver context
1083: Output Parameters:
1084: + fun - the pointer to the user function
1085: . ctx - the context pointer
1086: - destroy - a routine for destroying the context (may be `NULL`)
1088: Level: developer
1090: .seealso: [](sec:ds), `DSNEP`, `DSNEPSetComputeMatrixFunction()`
1091: @*/
1092: PetscErrorCode DSNEPGetComputeMatrixFunction(DS ds,DSNEPMatrixFunctionFn **fun,PetscCtxRt ctx,PetscCtxDestroyFn **destroy)
1093: {
1094: PetscFunctionBegin;
1096: PetscUseMethod(ds,"DSNEPGetComputeMatrixFunction_C",(DS,DSNEPMatrixFunctionFn**,PetscCtxRt,PetscCtxDestroyFn**),(ds,fun,ctx,destroy));
1097: PetscFunctionReturn(PETSC_SUCCESS);
1098: }
1100: static PetscErrorCode DSNEPSetRG_NEP(DS ds,RG rg)
1101: {
1102: DS_NEP *dsctx = (DS_NEP*)ds->data;
1104: PetscFunctionBegin;
1105: PetscCall(PetscObjectReference((PetscObject)rg));
1106: PetscCall(RGDestroy(&dsctx->rg));
1107: dsctx->rg = rg;
1108: PetscFunctionReturn(PETSC_SUCCESS);
1109: }
1111: /*@
1112: DSNEPSetRG - Associates a region object to the `DSNEP` solver.
1114: Collective
1116: Input Parameters:
1117: + ds - the direct solver context
1118: - rg - the region context
1120: Notes:
1121: The region is used only in the contour integral method, and
1122: should enclose the wanted eigenvalues.
1124: Level: developer
1126: .seealso: [](sec:ds), `DSNEP`, `DSNEPGetRG()`
1127: @*/
1128: PetscErrorCode DSNEPSetRG(DS ds,RG rg)
1129: {
1130: PetscFunctionBegin;
1132: if (rg) {
1134: PetscCheckSameComm(ds,1,rg,2);
1135: }
1136: PetscTryMethod(ds,"DSNEPSetRG_C",(DS,RG),(ds,rg));
1137: PetscFunctionReturn(PETSC_SUCCESS);
1138: }
1140: static PetscErrorCode DSNEPGetRG_NEP(DS ds,RG *rg)
1141: {
1142: DS_NEP *ctx = (DS_NEP*)ds->data;
1144: PetscFunctionBegin;
1145: if (!ctx->rg) {
1146: PetscCall(RGCreate(PetscObjectComm((PetscObject)ds),&ctx->rg));
1147: PetscCall(PetscObjectIncrementTabLevel((PetscObject)ctx->rg,(PetscObject)ds,1));
1148: PetscCall(RGSetOptionsPrefix(ctx->rg,((PetscObject)ds)->prefix));
1149: PetscCall(RGAppendOptionsPrefix(ctx->rg,"ds_nep_"));
1150: PetscCall(PetscObjectSetOptions((PetscObject)ctx->rg,((PetscObject)ds)->options));
1151: }
1152: *rg = ctx->rg;
1153: PetscFunctionReturn(PETSC_SUCCESS);
1154: }
1156: /*@
1157: DSNEPGetRG - Obtain the region object associated to the `DSNEP` solver.
1159: Collective
1161: Input Parameter:
1162: . ds - the direct solver context
1164: Output Parameter:
1165: . rg - the region context
1167: Level: developer
1169: .seealso: [](sec:ds), `DSNEP`, `DSNEPSetRG()`
1170: @*/
1171: PetscErrorCode DSNEPGetRG(DS ds,RG *rg)
1172: {
1173: PetscFunctionBegin;
1175: PetscAssertPointer(rg,2);
1176: PetscUseMethod(ds,"DSNEPGetRG_C",(DS,RG*),(ds,rg));
1177: PetscFunctionReturn(PETSC_SUCCESS);
1178: }
1180: static PetscErrorCode DSSetFromOptions_NEP(DS ds,PetscOptionItems PetscOptionsObject)
1181: {
1182: PetscInt k;
1183: PetscBool flg;
1184: #if PetscDefined(USE_COMPLEX)
1185: PetscReal r;
1186: PetscBool flg1;
1187: DS_NEP *ctx = (DS_NEP*)ds->data;
1188: #endif
1190: PetscFunctionBegin;
1191: PetscOptionsHeadBegin(PetscOptionsObject,"DS NEP Options");
1193: PetscCall(PetscOptionsInt("-ds_nep_minimality","Maximum minimality index","DSNEPSetMinimality",4,&k,&flg));
1194: if (flg) PetscCall(DSNEPSetMinimality(ds,k));
1196: PetscCall(PetscOptionsInt("-ds_nep_integration_points","Number of integration points","DSNEPSetIntegrationPoints",64,&k,&flg));
1197: if (flg) PetscCall(DSNEPSetIntegrationPoints(ds,k));
1199: PetscCall(PetscOptionsInt("-ds_nep_sampling_size","Number of sampling columns","DSNEPSetSamplingSize",0,&k,&flg));
1200: if (flg) PetscCall(DSNEPSetSamplingSize(ds,k));
1202: #if PetscDefined(USE_COMPLEX)
1203: r = ctx->rtol;
1204: PetscCall(PetscOptionsReal("-ds_nep_refine_tol","Refinement tolerance","DSNEPSetRefine",ctx->rtol,&r,&flg1));
1205: k = ctx->Nit;
1206: PetscCall(PetscOptionsInt("-ds_nep_refine_its","Number of iterative refinement iterations","DSNEPSetRefine",ctx->Nit,&k,&flg));
1207: if (flg1||flg) PetscCall(DSNEPSetRefine(ds,r,k));
1209: if (ds->method==1) {
1210: if (!ctx->rg) PetscCall(DSNEPGetRG(ds,&ctx->rg));
1211: PetscCall(RGSetFromOptions(ctx->rg));
1212: }
1213: #endif
1215: PetscOptionsHeadEnd();
1216: PetscFunctionReturn(PETSC_SUCCESS);
1217: }
1219: static PetscErrorCode DSDestroy_NEP(DS ds)
1220: {
1221: DS_NEP *ctx = (DS_NEP*)ds->data;
1222: PetscInt i;
1224: PetscFunctionBegin;
1225: for (i=0;i<ctx->nf;i++) PetscCall(FNDestroy(&ctx->f[i]));
1226: PetscCall(RGDestroy(&ctx->rg));
1227: PetscCall(PetscLayoutDestroy(&ctx->map));
1228: if (ctx->computematrixdestroy) PetscCall((*ctx->computematrixdestroy)(&ctx->computematrixctx));
1229: PetscCall(PetscFree(ds->data));
1230: PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetFN_C",NULL));
1231: PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetFN_C",NULL));
1232: PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetNumFN_C",NULL));
1233: PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetMinimality_C",NULL));
1234: PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetMinimality_C",NULL));
1235: PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetRefine_C",NULL));
1236: PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetRefine_C",NULL));
1237: PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetIntegrationPoints_C",NULL));
1238: PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetIntegrationPoints_C",NULL));
1239: PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetSamplingSize_C",NULL));
1240: PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetSamplingSize_C",NULL));
1241: PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetRG_C",NULL));
1242: PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetRG_C",NULL));
1243: PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetComputeMatrixFunction_C",NULL));
1244: PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetComputeMatrixFunction_C",NULL));
1245: PetscFunctionReturn(PETSC_SUCCESS);
1246: }
1248: static PetscErrorCode DSMatGetSize_NEP(DS ds,DSMatType t,PetscInt *rows,PetscInt *cols)
1249: {
1250: DS_NEP *ctx = (DS_NEP*)ds->data;
1252: PetscFunctionBegin;
1253: *rows = ds->n;
1254: if (t==DS_MAT_Q || t==DS_MAT_Z || t==DS_MAT_U || t==DS_MAT_V) *rows *= ctx->max_mid;
1255: *cols = ds->n;
1256: if (t==DS_MAT_Q || t==DS_MAT_Z || t==DS_MAT_U || t==DS_MAT_V || t==DS_MAT_X || t==DS_MAT_Y) *cols *= ctx->max_mid;
1257: PetscFunctionReturn(PETSC_SUCCESS);
1258: }
1260: /*MC
1261: DSNEP - Dense Nonlinear Eigenvalue Problem.
1263: Notes:
1264: The problem is expressed as $T(\lambda)x = 0$, where $T(\lambda)$ is a
1265: parameter-dependent matrix written as $T(\lambda) = \sum_i E_i f_i(\lambda)$.
1266: The eigenvalues $\lambda$ are the arguments returned by `DSSolve()`.
1268: The coefficient matrices $E_i$ are the extra matrices of the `DS`, and
1269: the scalar functions $f_i$ are passed via `DSNEPSetFN()`. Optionally, a
1270: callback function to fill the $E_i$ matrices can be set with
1271: `DSNEPSetComputeMatrixFunction()`.
1273: Used DS matrices:
1274: + `DS_MAT_E0` to `DS_MAT_E9` - coefficient matrices of the split form of $T(\lambda)$
1275: . `DS_MAT_X` - eigenvectors
1276: . `DS_MAT_A` - (workspace) $T(\lambda)$ evaluated at a given $\lambda$ (SLP only)
1277: . `DS_MAT_B` - (workspace) $T'(\lambda)$ evaluated at a given $\lambda$ (SLP only)
1278: . `DS_MAT_Q` - (workspace) left Hankel matrix (contour only)
1279: . `DS_MAT_Z` - (workspace) right Hankel matrix (contour only)
1280: . `DS_MAT_U` - (workspace) left singular vectors (contour only)
1281: . `DS_MAT_V` - (workspace) right singular vectors (contour only)
1282: - `DS_MAT_W` - (workspace) auxiliary matrix of size $n\times n$
1284: Implemented methods:
1285: + 0 - Successive Linear Problems (SLP), computes just one eigenpair
1286: - 1 - Contour integral, computes all eigenvalues inside a region
1288: Level: beginner
1290: .seealso: [](sec:ds), `DSCreate()`, `DSSetType()`, `DSType`, `DSNEPSetFN()`, `DSNEPSetComputeMatrixFunction()`
1291: M*/
1292: SLEPC_EXTERN PetscErrorCode DSCreate_NEP(DS ds)
1293: {
1294: DS_NEP *ctx;
1296: PetscFunctionBegin;
1297: PetscCall(PetscNew(&ctx));
1298: ds->data = (void*)ctx;
1299: ctx->max_mid = 4;
1300: ctx->nnod = 64;
1301: ctx->Nit = 3;
1302: ctx->rtol = PETSC_MACHINE_EPSILON/PetscSqrtReal(PETSC_SQRT_MACHINE_EPSILON);
1304: ds->ops->allocate = DSAllocate_NEP;
1305: ds->ops->setfromoptions = DSSetFromOptions_NEP;
1306: ds->ops->view = DSView_NEP;
1307: ds->ops->vectors = DSVectors_NEP;
1308: ds->ops->solve[0] = DSSolve_NEP_SLP;
1309: #if PetscDefined(USE_COMPLEX)
1310: ds->ops->solve[1] = DSSolve_NEP_Contour;
1311: #endif
1312: ds->ops->sort = DSSort_NEP;
1313: #if !PetscDefined(HAVE_MPIUNI)
1314: ds->ops->synchronize = DSSynchronize_NEP;
1315: #endif
1316: ds->ops->destroy = DSDestroy_NEP;
1317: ds->ops->matgetsize = DSMatGetSize_NEP;
1319: PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetFN_C",DSNEPSetFN_NEP));
1320: PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetFN_C",DSNEPGetFN_NEP));
1321: PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetNumFN_C",DSNEPGetNumFN_NEP));
1322: PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetMinimality_C",DSNEPGetMinimality_NEP));
1323: PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetMinimality_C",DSNEPSetMinimality_NEP));
1324: PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetRefine_C",DSNEPGetRefine_NEP));
1325: PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetRefine_C",DSNEPSetRefine_NEP));
1326: PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetIntegrationPoints_C",DSNEPGetIntegrationPoints_NEP));
1327: PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetIntegrationPoints_C",DSNEPSetIntegrationPoints_NEP));
1328: PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetSamplingSize_C",DSNEPGetSamplingSize_NEP));
1329: PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetSamplingSize_C",DSNEPSetSamplingSize_NEP));
1330: PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetRG_C",DSNEPSetRG_NEP));
1331: PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetRG_C",DSNEPGetRG_NEP));
1332: PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetComputeMatrixFunction_C",DSNEPSetComputeMatrixFunction_NEP));
1333: PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetComputeMatrixFunction_C",DSNEPGetComputeMatrixFunction_NEP));
1334: PetscFunctionReturn(PETSC_SUCCESS);
1335: }