Actual source code: eige.c
2: #include <petsc/private/kspimpl.h>
3: #include <petscdm.h>
4: #include <petscblaslapack.h>
6: typedef struct {
7: KSP ksp;
8: Vec work;
9: } Mat_KSP;
11: static PetscErrorCode MatCreateVecs_KSP(Mat A,Vec *X,Vec *Y)
12: {
13: Mat_KSP *ctx;
14: Mat M;
18: MatShellGetContext(A,&ctx);
19: KSPGetOperators(ctx->ksp,&M,NULL);
20: MatCreateVecs(M,X,Y);
21: return(0);
22: }
24: static PetscErrorCode MatMult_KSP(Mat A,Vec X,Vec Y)
25: {
26: Mat_KSP *ctx;
30: MatShellGetContext(A,&ctx);
31: KSP_PCApplyBAorAB(ctx->ksp,X,Y,ctx->work);
32: return(0);
33: }
35: /*@
36: KSPComputeOperator - Computes the explicit preconditioned operator, including diagonal scaling and null
37: space removal if applicable.
39: Collective on ksp
41: Input Parameters:
42: + ksp - the Krylov subspace context
43: - mattype - the matrix type to be used
45: Output Parameter:
46: . mat - the explicit preconditioned operator
48: Notes:
49: This computation is done by applying the operators to columns of the
50: identity matrix.
52: Currently, this routine uses a dense matrix format for the output operator if mattype == NULL.
53: This routine is costly in general, and is recommended for use only with relatively small systems.
55: Level: advanced
57: .seealso: KSPComputeEigenvaluesExplicitly(), PCComputeOperator(), KSPSetDiagonalScale(), KSPSetNullSpace(), MatType
58: @*/
59: PetscErrorCode KSPComputeOperator(KSP ksp, MatType mattype, Mat *mat)
60: {
62: PetscInt N,M,m,n;
63: Mat_KSP ctx;
64: Mat A,Aksp;
69: KSPGetOperators(ksp,&A,NULL);
70: MatGetLocalSize(A,&m,&n);
71: MatGetSize(A,&M,&N);
72: MatCreateShell(PetscObjectComm((PetscObject)ksp),m,n,M,N,&ctx,&Aksp);
73: MatShellSetOperation(Aksp,MATOP_MULT,(void (*)(void))MatMult_KSP);
74: MatShellSetOperation(Aksp,MATOP_CREATE_VECS,(void (*)(void))MatCreateVecs_KSP);
75: ctx.ksp = ksp;
76: MatCreateVecs(A,&ctx.work,NULL);
77: MatComputeOperator(Aksp,mattype,mat);
78: VecDestroy(&ctx.work);
79: MatDestroy(&Aksp);
80: return(0);
81: }
83: /*@
84: KSPComputeEigenvaluesExplicitly - Computes all of the eigenvalues of the
85: preconditioned operator using LAPACK.
87: Collective on ksp
89: Input Parameters:
90: + ksp - iterative context obtained from KSPCreate()
91: - n - size of arrays r and c
93: Output Parameters:
94: + r - real part of computed eigenvalues, provided by user with a dimension at least of n
95: - c - complex part of computed eigenvalues, provided by user with a dimension at least of n
97: Notes:
98: This approach is very slow but will generally provide accurate eigenvalue
99: estimates. This routine explicitly forms a dense matrix representing
100: the preconditioned operator, and thus will run only for relatively small
101: problems, say n < 500.
103: Many users may just want to use the monitoring routine
104: KSPMonitorSingularValue() (which can be set with option -ksp_monitor_singular_value)
105: to print the singular values at each iteration of the linear solve.
107: The preconditoner operator, rhs vector, solution vectors should be
108: set before this routine is called. i.e use KSPSetOperators(),KSPSolve() or
109: KSPSetOperators()
111: Level: advanced
113: .seealso: KSPComputeEigenvalues(), KSPMonitorSingularValue(), KSPComputeExtremeSingularValues(), KSPSetOperators(), KSPSolve()
114: @*/
115: PetscErrorCode KSPComputeEigenvaluesExplicitly(KSP ksp,PetscInt nmax,PetscReal r[],PetscReal c[])
116: {
117: Mat BA;
118: PetscErrorCode ierr;
119: PetscMPIInt size,rank;
120: MPI_Comm comm;
121: PetscScalar *array;
122: Mat A;
123: PetscInt m,row,nz,i,n,dummy;
124: const PetscInt *cols;
125: const PetscScalar *vals;
128: PetscObjectGetComm((PetscObject)ksp,&comm);
129: KSPComputeOperator(ksp,MATDENSE,&BA);
130: MPI_Comm_size(comm,&size);
131: MPI_Comm_rank(comm,&rank);
133: MatGetSize(BA,&n,&n);
134: if (size > 1) { /* assemble matrix on first processor */
135: MatCreate(PetscObjectComm((PetscObject)ksp),&A);
136: if (rank == 0) {
137: MatSetSizes(A,n,n,n,n);
138: } else {
139: MatSetSizes(A,0,0,n,n);
140: }
141: MatSetType(A,MATMPIDENSE);
142: MatMPIDenseSetPreallocation(A,NULL);
143: PetscLogObjectParent((PetscObject)BA,(PetscObject)A);
145: MatGetOwnershipRange(BA,&row,&dummy);
146: MatGetLocalSize(BA,&m,&dummy);
147: for (i=0; i<m; i++) {
148: MatGetRow(BA,row,&nz,&cols,&vals);
149: MatSetValues(A,1,&row,nz,cols,vals,INSERT_VALUES);
150: MatRestoreRow(BA,row,&nz,&cols,&vals);
151: row++;
152: }
154: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
155: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
156: MatDenseGetArray(A,&array);
157: } else {
158: MatDenseGetArray(BA,&array);
159: }
161: #if !defined(PETSC_USE_COMPLEX)
162: if (rank == 0) {
163: PetscScalar *work;
164: PetscReal *realpart,*imagpart;
165: PetscBLASInt idummy,lwork;
166: PetscInt *perm;
168: idummy = n;
169: lwork = 5*n;
170: PetscMalloc2(n,&realpart,n,&imagpart);
171: PetscMalloc1(5*n,&work);
172: {
173: PetscBLASInt lierr;
174: PetscScalar sdummy;
175: PetscBLASInt bn;
177: PetscBLASIntCast(n,&bn);
178: PetscFPTrapPush(PETSC_FP_TRAP_OFF);
179: PetscStackCallBLAS("LAPACKgeev",LAPACKgeev_("N","N",&bn,array,&bn,realpart,imagpart,&sdummy,&idummy,&sdummy,&idummy,work,&lwork,&lierr));
180: if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in LAPACK routine %d",(int)lierr);
181: PetscFPTrapPop();
182: }
183: PetscFree(work);
184: PetscMalloc1(n,&perm);
186: for (i=0; i<n; i++) perm[i] = i;
187: PetscSortRealWithPermutation(n,realpart,perm);
188: for (i=0; i<n; i++) {
189: r[i] = realpart[perm[i]];
190: c[i] = imagpart[perm[i]];
191: }
192: PetscFree(perm);
193: PetscFree2(realpart,imagpart);
194: }
195: #else
196: if (rank == 0) {
197: PetscScalar *work,*eigs;
198: PetscReal *rwork;
199: PetscBLASInt idummy,lwork;
200: PetscInt *perm;
202: idummy = n;
203: lwork = 5*n;
204: PetscMalloc1(5*n,&work);
205: PetscMalloc1(2*n,&rwork);
206: PetscMalloc1(n,&eigs);
207: {
208: PetscBLASInt lierr;
209: PetscScalar sdummy;
210: PetscBLASInt nb;
211: PetscBLASIntCast(n,&nb);
212: PetscFPTrapPush(PETSC_FP_TRAP_OFF);
213: PetscStackCallBLAS("LAPACKgeev",LAPACKgeev_("N","N",&nb,array,&nb,eigs,&sdummy,&idummy,&sdummy,&idummy,work,&lwork,rwork,&lierr));
214: if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in LAPACK routine %d",(int)lierr);
215: PetscFPTrapPop();
216: }
217: PetscFree(work);
218: PetscFree(rwork);
219: PetscMalloc1(n,&perm);
220: for (i=0; i<n; i++) perm[i] = i;
221: for (i=0; i<n; i++) r[i] = PetscRealPart(eigs[i]);
222: PetscSortRealWithPermutation(n,r,perm);
223: for (i=0; i<n; i++) {
224: r[i] = PetscRealPart(eigs[perm[i]]);
225: c[i] = PetscImaginaryPart(eigs[perm[i]]);
226: }
227: PetscFree(perm);
228: PetscFree(eigs);
229: }
230: #endif
231: if (size > 1) {
232: MatDenseRestoreArray(A,&array);
233: MatDestroy(&A);
234: } else {
235: MatDenseRestoreArray(BA,&array);
236: }
237: MatDestroy(&BA);
238: return(0);
239: }
241: static PetscErrorCode PolyEval(PetscInt nroots,const PetscReal *r,const PetscReal *c,PetscReal x,PetscReal y,PetscReal *px,PetscReal *py)
242: {
243: PetscInt i;
244: PetscReal rprod = 1,iprod = 0;
247: for (i=0; i<nroots; i++) {
248: PetscReal rnew = rprod*(x - r[i]) - iprod*(y - c[i]);
249: PetscReal inew = rprod*(y - c[i]) + iprod*(x - r[i]);
250: rprod = rnew;
251: iprod = inew;
252: }
253: *px = rprod;
254: *py = iprod;
255: return(0);
256: }
258: #include <petscdraw.h>
259: /* collective on ksp */
260: PetscErrorCode KSPPlotEigenContours_Private(KSP ksp,PetscInt neig,const PetscReal *r,const PetscReal *c)
261: {
263: PetscReal xmin,xmax,ymin,ymax,*xloc,*yloc,*value,px0,py0,rscale,iscale;
264: PetscInt M,N,i,j;
265: PetscMPIInt rank;
266: PetscViewer viewer;
267: PetscDraw draw;
268: PetscDrawAxis drawaxis;
271: MPI_Comm_rank(PetscObjectComm((PetscObject)ksp),&rank);
272: if (rank) return(0);
273: M = 80;
274: N = 80;
275: xmin = r[0]; xmax = r[0];
276: ymin = c[0]; ymax = c[0];
277: for (i=1; i<neig; i++) {
278: xmin = PetscMin(xmin,r[i]);
279: xmax = PetscMax(xmax,r[i]);
280: ymin = PetscMin(ymin,c[i]);
281: ymax = PetscMax(ymax,c[i]);
282: }
283: PetscMalloc3(M,&xloc,N,&yloc,M*N,&value);
284: for (i=0; i<M; i++) xloc[i] = xmin - 0.1*(xmax-xmin) + 1.2*(xmax-xmin)*i/(M-1);
285: for (i=0; i<N; i++) yloc[i] = ymin - 0.1*(ymax-ymin) + 1.2*(ymax-ymin)*i/(N-1);
286: PolyEval(neig,r,c,0,0,&px0,&py0);
287: rscale = px0/(PetscSqr(px0)+PetscSqr(py0));
288: iscale = -py0/(PetscSqr(px0)+PetscSqr(py0));
289: for (j=0; j<N; j++) {
290: for (i=0; i<M; i++) {
291: PetscReal px,py,tx,ty,tmod;
292: PolyEval(neig,r,c,xloc[i],yloc[j],&px,&py);
293: tx = px*rscale - py*iscale;
294: ty = py*rscale + px*iscale;
295: tmod = PetscSqr(tx) + PetscSqr(ty); /* modulus of the complex polynomial */
296: if (tmod > 1) tmod = 1.0;
297: if (tmod > 0.5 && tmod < 1) tmod = 0.5;
298: if (tmod > 0.2 && tmod < 0.5) tmod = 0.2;
299: if (tmod > 0.05 && tmod < 0.2) tmod = 0.05;
300: if (tmod < 1e-3) tmod = 1e-3;
301: value[i+j*M] = PetscLogReal(tmod) / PetscLogReal(10.0);
302: }
303: }
304: PetscViewerDrawOpen(PETSC_COMM_SELF,NULL,"Iteratively Computed Eigen-contours",PETSC_DECIDE,PETSC_DECIDE,450,450,&viewer);
305: PetscViewerDrawGetDraw(viewer,0,&draw);
306: PetscDrawTensorContour(draw,M,N,NULL,NULL,value);
307: if (0) {
308: PetscDrawAxisCreate(draw,&drawaxis);
309: PetscDrawAxisSetLimits(drawaxis,xmin,xmax,ymin,ymax);
310: PetscDrawAxisSetLabels(drawaxis,"Eigen-counters","real","imag");
311: PetscDrawAxisDraw(drawaxis);
312: PetscDrawAxisDestroy(&drawaxis);
313: }
314: PetscViewerDestroy(&viewer);
315: PetscFree3(xloc,yloc,value);
316: return(0);
317: }