Actual source code: ex40.c
slepc-3.18.3 2023-03-24
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: static char help[] = "Checking the definite property in quadratic symmetric eigenproblem.\n\n"
12: "The command line options are:\n"
13: " -n <n> ... dimension of the matrices.\n"
14: " -transform... whether to transform to a hyperbolic problem or not.\n"
15: " -nonhyperbolic... to test with a modified (definite) problem that is not hyperbolic.\n\n";
17: #include <slepcpep.h>
19: /*
20: This example is based on spring.c, for fixed values mu=1,tau=10,kappa=5
22: The transformations are based on the method proposed in [Niendorf and Voss, LAA 2010].
23: */
25: PetscErrorCode QEPDefiniteTransformGetMatrices(PEP,PetscBool,PetscReal,PetscReal,Mat[3]);
26: PetscErrorCode QEPDefiniteTransformMap(PetscBool,PetscReal,PetscReal,PetscInt,PetscScalar*,PetscBool);
27: PetscErrorCode QEPDefiniteCheckError(Mat*,PEP,PetscBool,PetscReal,PetscReal);
28: PetscErrorCode TransformMatricesMoebius(Mat[3],MatStructure,PetscReal,PetscReal,PetscReal,PetscReal,Mat[3]);
30: int main(int argc,char **argv)
31: {
32: Mat M,C,K,*Op,A[3],At[3],B[3]; /* problem matrices */
33: PEP pep; /* polynomial eigenproblem solver context */
34: ST st; /* spectral transformation context */
35: KSP ksp;
36: PC pc;
37: PEPProblemType type;
38: PetscBool terse,transform=PETSC_FALSE,nohyp=PETSC_FALSE;
39: PetscInt n=100,Istart,Iend,i,def=0,hyp;
40: PetscReal muu=1,tau=10,kappa=5,inta,intb;
41: PetscReal alpha,beta,xi,mu,at[2]={0.0,0.0},c=.857,s;
42: PetscScalar target,targett,ats[2];
45: SlepcInitialize(&argc,&argv,(char*)0,help);
47: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
48: PetscPrintf(PETSC_COMM_WORLD,"\nPEP example that checks definite property, n=%" PetscInt_FMT "\n\n",n);
50: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
51: Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
52: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
54: /* K is a tridiagonal */
55: MatCreate(PETSC_COMM_WORLD,&K);
56: MatSetSizes(K,PETSC_DECIDE,PETSC_DECIDE,n,n);
57: MatSetFromOptions(K);
58: MatSetUp(K);
60: MatGetOwnershipRange(K,&Istart,&Iend);
61: for (i=Istart;i<Iend;i++) {
62: if (i>0) MatSetValue(K,i,i-1,-kappa,INSERT_VALUES);
63: MatSetValue(K,i,i,kappa*3.0,INSERT_VALUES);
64: if (i<n-1) MatSetValue(K,i,i+1,-kappa,INSERT_VALUES);
65: }
67: MatAssemblyBegin(K,MAT_FINAL_ASSEMBLY);
68: MatAssemblyEnd(K,MAT_FINAL_ASSEMBLY);
70: /* C is a tridiagonal */
71: MatCreate(PETSC_COMM_WORLD,&C);
72: MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,n,n);
73: MatSetFromOptions(C);
74: MatSetUp(C);
76: MatGetOwnershipRange(C,&Istart,&Iend);
77: for (i=Istart;i<Iend;i++) {
78: if (i>0) MatSetValue(C,i,i-1,-tau,INSERT_VALUES);
79: MatSetValue(C,i,i,tau*3.0,INSERT_VALUES);
80: if (i<n-1) MatSetValue(C,i,i+1,-tau,INSERT_VALUES);
81: }
83: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
84: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
86: /* M is a diagonal matrix */
87: MatCreate(PETSC_COMM_WORLD,&M);
88: MatSetSizes(M,PETSC_DECIDE,PETSC_DECIDE,n,n);
89: MatSetFromOptions(M);
90: MatSetUp(M);
91: MatGetOwnershipRange(M,&Istart,&Iend);
92: for (i=Istart;i<Iend;i++) MatSetValue(M,i,i,muu,INSERT_VALUES);
93: MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);
94: MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);
96: PetscOptionsGetBool(NULL,NULL,"-nonhyperbolic",&nohyp,NULL);
97: A[0] = K; A[1] = C; A[2] = M;
98: if (nohyp) {
99: s = c*.6;
100: TransformMatricesMoebius(A,UNKNOWN_NONZERO_PATTERN,c,s,-s,c,At);
101: for (i=0;i<3;i++) MatDestroy(&A[i]);
102: Op = At;
103: } else Op = A;
105: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
106: Create the eigensolver and solve the problem
107: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
109: /*
110: Create eigensolver context
111: */
112: PEPCreate(PETSC_COMM_WORLD,&pep);
113: PEPSetProblemType(pep,PEP_HERMITIAN);
114: PEPSetType(pep,PEPSTOAR);
115: /*
116: Set operators and set problem type
117: */
118: PEPSetOperators(pep,3,Op);
120: /*
121: Set shift-and-invert with Cholesky; select MUMPS if available
122: */
123: PEPGetST(pep,&st);
124: STGetKSP(st,&ksp);
125: KSPSetType(ksp,KSPPREONLY);
126: KSPGetPC(ksp,&pc);
127: PCSetType(pc,PCCHOLESKY);
129: /*
130: Use MUMPS if available.
131: Note that in complex scalars we cannot use MUMPS for spectrum slicing,
132: because MatGetInertia() is not available in that case.
133: */
134: #if defined(PETSC_HAVE_MUMPS) && !defined(PETSC_USE_COMPLEX)
135: PCFactorSetMatSolverType(pc,MATSOLVERMUMPS);
136: /*
137: Add several MUMPS options (see ex43.c for a better way of setting them in program):
138: '-st_mat_mumps_icntl_13 1': turn off ScaLAPACK for matrix inertia
139: */
140: PetscOptionsInsertString(NULL,"-st_mat_mumps_icntl_13 1 -st_mat_mumps_icntl_24 1 -st_mat_mumps_cntl_3 1e-12");
141: #endif
143: /*
144: Set solver parameters at runtime
145: */
146: PEPSetFromOptions(pep);
148: PetscOptionsGetBool(NULL,NULL,"-transform",&transform,NULL);
149: if (transform) {
150: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
151: Check if the problem is definite
152: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
153: PEPCheckDefiniteQEP(pep,&xi,&mu,&def,&hyp);
154: switch (def) {
155: case 1:
156: if (hyp==1) PetscPrintf(PETSC_COMM_WORLD,"Hyperbolic Problem xi=%g\n",(double)xi);
157: else PetscPrintf(PETSC_COMM_WORLD,"Definite Problem xi=%g mu=%g\n",(double)xi,(double)mu);
158: break;
159: case -1:
160: PetscPrintf(PETSC_COMM_WORLD,"Not Definite Problem\n");
161: break;
162: default:
163: PetscPrintf(PETSC_COMM_WORLD,"Cannot determine definiteness\n");
164: break;
165: }
167: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
168: Transform the QEP to have a definite inner product in the linearization
169: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
170: if (def==1) {
171: QEPDefiniteTransformGetMatrices(pep,hyp==1?PETSC_TRUE:PETSC_FALSE,xi,mu,B);
172: PEPSetOperators(pep,3,B);
173: PEPGetTarget(pep,&target);
174: targett = target;
175: QEPDefiniteTransformMap(hyp==1?PETSC_TRUE:PETSC_FALSE,xi,mu,1,&targett,PETSC_FALSE);
176: PEPSetTarget(pep,targett);
177: PEPGetProblemType(pep,&type);
178: PEPSetProblemType(pep,PEP_HYPERBOLIC);
179: PEPSTOARGetLinearization(pep,&alpha,&beta);
180: PEPSTOARSetLinearization(pep,1.0,0.0);
181: PEPGetInterval(pep,&inta,&intb);
182: if (inta!=intb) {
183: ats[0] = inta; ats[1] = intb;
184: QEPDefiniteTransformMap(hyp==1?PETSC_TRUE:PETSC_FALSE,xi,mu,2,ats,PETSC_FALSE);
185: at[0] = PetscRealPart(ats[0]); at[1] = PetscRealPart(ats[1]);
186: if (at[0]<at[1]) PEPSetInterval(pep,at[0],at[1]);
187: else PEPSetInterval(pep,PETSC_MIN_REAL,at[1]);
188: }
189: }
190: }
192: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
193: Solve the eigensystem
194: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
195: PEPSolve(pep);
197: /* show detailed info unless -terse option is given by user */
198: if (def!=1) {
199: PetscOptionsHasName(NULL,NULL,"-terse",&terse);
200: if (terse) PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL);
201: else {
202: PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
203: PEPConvergedReasonView(pep,PETSC_VIEWER_STDOUT_WORLD);
204: PEPErrorView(pep,PEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
205: PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
206: }
207: } else {
208: /* Map the solution */
209: PEPConvergedReasonView(pep,PETSC_VIEWER_STDOUT_WORLD);
210: QEPDefiniteCheckError(Op,pep,hyp==1?PETSC_TRUE:PETSC_FALSE,xi,mu);
211: for (i=0;i<3;i++) MatDestroy(B+i);
212: }
213: if (at[0]>at[1]) {
214: PEPSetInterval(pep,at[0],PETSC_MAX_REAL);
215: PEPSolve(pep);
216: PEPConvergedReasonView(pep,PETSC_VIEWER_STDOUT_WORLD);
217: /* Map the solution */
218: QEPDefiniteCheckError(Op,pep,hyp==1?PETSC_TRUE:PETSC_FALSE,xi,mu);
219: }
220: if (def==1) {
221: PEPSetTarget(pep,target);
222: PEPSetProblemType(pep,type);
223: PEPSTOARSetLinearization(pep,alpha,beta);
224: if (inta!=intb) PEPSetInterval(pep,inta,intb);
225: }
227: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
228: Clean up
229: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
230: PEPDestroy(&pep);
231: for (i=0;i<3;i++) MatDestroy(Op+i);
232: SlepcFinalize();
233: return 0;
234: }
236: /* ------------------------------------------------------------------- */
237: /*
238: QEPDefiniteTransformMap_Initial - map a scalar value with a certain Moebius transform
240: a theta + b
241: lambda = --------------
242: c theta + d
244: Input:
245: xi,mu: real values such that Q(xi)<0 and Q(mu)>0
246: hyperbolic: if true the problem is assumed hyperbolic (mu is not used)
247: Input/Output:
248: val (array of length n)
249: if backtransform=true returns lambda from theta, else returns theta from lambda
250: */
251: static PetscErrorCode QEPDefiniteTransformMap_Initial(PetscBool hyperbolic,PetscReal xi,PetscReal mu,PetscInt n,PetscScalar *val,PetscBool backtransform)
252: {
253: PetscInt i;
254: PetscReal a,b,c,d,s;
256: if (hyperbolic) { a = 1.0; b = xi; c =0.0; d = 1.0; }
257: else { a = mu; b = mu*xi-1; c = 1.0; d = xi+mu; }
258: if (!backtransform) { s = a; a = -d; d = -s; }
259: for (i=0;i<n;i++) {
260: if (PetscRealPart(val[i]) >= PETSC_MAX_REAL || PetscRealPart(val[i]) <= PETSC_MIN_REAL) val[i] = a/c;
261: else if (val[i] == -d/c) val[i] = PETSC_MAX_REAL;
262: else val[i] = (a*val[i]+b)/(c*val[i]+d);
263: }
264: return 0;
265: }
267: /* ------------------------------------------------------------------- */
268: /*
269: QEPDefiniteTransformMap - perform the mapping if the problem is hyperbolic, otherwise
270: modify the value of xi in advance
271: */
272: PetscErrorCode QEPDefiniteTransformMap(PetscBool hyperbolic,PetscReal xi,PetscReal mu,PetscInt n,PetscScalar *val,PetscBool backtransform)
273: {
274: PetscReal xit;
275: PetscScalar alpha;
277: xit = xi;
278: if (!hyperbolic) {
279: alpha = xi;
280: QEPDefiniteTransformMap_Initial(PETSC_FALSE,0.0,mu,1,&alpha,PETSC_FALSE);
281: xit = PetscRealPart(alpha);
282: }
283: QEPDefiniteTransformMap_Initial(hyperbolic,xit,mu,n,val,backtransform);
284: return 0;
285: }
287: /* ------------------------------------------------------------------- */
288: /*
289: TransformMatricesMoebius - transform the coefficient matrices of a QEP
291: Input:
292: A: coefficient matrices of the original QEP
293: a,b,c,d: parameters of the Moebius transform
294: str: structure flag for MatAXPY operations
295: Output:
296: B: transformed matrices
297: */
298: PetscErrorCode TransformMatricesMoebius(Mat A[3],MatStructure str,PetscReal a,PetscReal b,PetscReal c,PetscReal d,Mat B[3])
299: {
300: PetscInt i,k;
301: PetscReal cf[9];
303: for (i=0;i<3;i++) MatDuplicate(A[2],MAT_COPY_VALUES,&B[i]);
304: /* Ct = b*b*A+b*d*B+d*d*C */
305: cf[0] = d*d; cf[1] = b*d; cf[2] = b*b;
306: /* Bt = 2*a*b*A+(b*c+a*d)*B+2*c*d*C*/
307: cf[3] = 2*c*d; cf[4] = b*c+a*d; cf[5] = 2*a*b;
308: /* At = a*a*A+a*c*B+c*c*C */
309: cf[6] = c*c; cf[7] = a*c; cf[8] = a*a;
310: for (k=0;k<3;k++) {
311: MatScale(B[k],cf[k*3+2]);
312: for (i=0;i<2;i++) MatAXPY(B[k],cf[3*k+i],A[i],str);
313: }
314: return 0;
315: }
317: /* ------------------------------------------------------------------- */
318: /*
319: QEPDefiniteTransformGetMatrices - given a PEP of degree 2, transform the three
320: matrices with TransformMatricesMoebius
322: Input:
323: pep: polynomial eigenproblem to be transformed, with Q(.) being the quadratic polynomial
324: xi,mu: real values such that Q(xi)<0 and Q(mu)>0
325: hyperbolic: if true the problem is assumed hyperbolic (mu is not used)
326: Output:
327: T: coefficient matrices of the transformed polynomial
328: */
329: PetscErrorCode QEPDefiniteTransformGetMatrices(PEP pep,PetscBool hyperbolic,PetscReal xi,PetscReal mu,Mat T[3])
330: {
331: MatStructure str;
332: ST st;
333: PetscInt i;
334: PetscReal a,b,c,d;
335: PetscScalar xit;
336: Mat A[3];
338: for (i=2;i>=0;i--) PEPGetOperators(pep,i,&A[i]);
339: if (hyperbolic) { a = 1.0; b = xi; c =0.0; d = 1.0; }
340: else {
341: xit = xi;
342: QEPDefiniteTransformMap_Initial(PETSC_FALSE,0.0,mu,1,&xit,PETSC_FALSE);
343: a = mu; b = mu*PetscRealPart(xit)-1.0; c = 1.0; d = PetscRealPart(xit)+mu;
344: }
345: PEPGetST(pep,&st);
346: STGetMatStructure(st,&str);
347: TransformMatricesMoebius(A,str,a,b,c,d,T);
348: return 0;
349: }
351: /* ------------------------------------------------------------------- */
352: /*
353: Auxiliary function to compute the residual norm of an eigenpair of a QEP defined
354: by coefficient matrices A
355: */
356: static PetscErrorCode PEPResidualNorm(Mat *A,PetscScalar kr,PetscScalar ki,Vec xr,Vec xi,Vec *z,PetscReal *norm)
357: {
358: PetscInt i,nmat=3;
359: PetscScalar vals[3];
360: Vec u,w;
361: #if !defined(PETSC_USE_COMPLEX)
362: Vec ui,wi;
363: PetscReal ni;
364: PetscBool imag;
365: PetscScalar ivals[3];
366: #endif
368: u = z[0]; w = z[1];
369: VecSet(u,0.0);
370: #if !defined(PETSC_USE_COMPLEX)
371: ui = z[2]; wi = z[3];
372: #endif
373: vals[0] = 1.0;
374: vals[1] = kr;
375: vals[2] = kr*kr-ki*ki;
376: #if !defined(PETSC_USE_COMPLEX)
377: ivals[0] = 0.0;
378: ivals[1] = ki;
379: ivals[2] = 2.0*kr*ki;
380: if (ki == 0 || PetscAbsScalar(ki) < PetscAbsScalar(kr*PETSC_MACHINE_EPSILON))
381: imag = PETSC_FALSE;
382: else {
383: imag = PETSC_TRUE;
384: VecSet(ui,0.0);
385: }
386: #endif
387: for (i=0;i<nmat;i++) {
388: if (vals[i]!=0.0) {
389: MatMult(A[i],xr,w);
390: VecAXPY(u,vals[i],w);
391: }
392: #if !defined(PETSC_USE_COMPLEX)
393: if (imag) {
394: if (ivals[i]!=0 || vals[i]!=0) {
395: MatMult(A[i],xi,wi);
396: if (vals[i]==0) MatMult(A[i],xr,w);
397: }
398: if (ivals[i]!=0) {
399: VecAXPY(u,-ivals[i],wi);
400: VecAXPY(ui,ivals[i],w);
401: }
402: if (vals[i]!=0) VecAXPY(ui,vals[i],wi);
403: }
404: #endif
405: }
406: VecNorm(u,NORM_2,norm);
407: #if !defined(PETSC_USE_COMPLEX)
408: if (imag) {
409: VecNorm(ui,NORM_2,&ni);
410: *norm = SlepcAbsEigenvalue(*norm,ni);
411: }
412: #endif
413: return 0;
414: }
416: /* ------------------------------------------------------------------- */
417: /*
418: QEPDefiniteCheckError - check and print the residual norm of a transformed PEP
420: Input:
421: A: coefficient matrices of the original problem
422: pep: solver containing the computed solution of the transformed problem
423: xi,mu,hyperbolic: parameters used in transformation
424: */
425: PetscErrorCode QEPDefiniteCheckError(Mat *A,PEP pep,PetscBool hyperbolic,PetscReal xi,PetscReal mu)
426: {
427: PetscScalar er,ei;
428: PetscReal re,im,error;
429: Vec vr,vi,w[4];
430: PetscInt i,nconv;
431: BV bv;
432: char ex[30],sep[]=" ---------------------- --------------------\n";
434: PetscSNPrintf(ex,sizeof(ex),"||P(k)x||/||kx||");
435: PetscPrintf(PETSC_COMM_WORLD,"%s k %s\n%s",sep,ex,sep);
436: PEPGetConverged(pep,&nconv);
437: PEPGetBV(pep,&bv);
438: BVCreateVec(bv,w);
439: VecDuplicate(w[0],&vr);
440: VecDuplicate(w[0],&vi);
441: for (i=1;i<4;i++) VecDuplicate(w[0],w+i);
442: for (i=0;i<nconv;i++) {
443: PEPGetEigenpair(pep,i,&er,&ei,vr,vi);
444: QEPDefiniteTransformMap(hyperbolic,xi,mu,1,&er,PETSC_TRUE);
445: PEPResidualNorm(A,er,0.0,vr,vi,w,&error);
446: error /= SlepcAbsEigenvalue(er,0.0);
447: #if defined(PETSC_USE_COMPLEX)
448: re = PetscRealPart(er);
449: im = PetscImaginaryPart(ei);
450: #else
451: re = er;
452: im = ei;
453: #endif
454: if (im!=0.0) PetscPrintf(PETSC_COMM_WORLD," % 9f%+9fi %12g\n",(double)re,(double)im,(double)error);
455: else PetscPrintf(PETSC_COMM_WORLD," % 12f %12g\n",(double)re,(double)error);
456: }
457: PetscPrintf(PETSC_COMM_WORLD,"%s",sep);
458: for (i=0;i<4;i++) VecDestroy(w+i);
459: VecDestroy(&vi);
460: VecDestroy(&vr);
461: return 0;
462: }
464: /*TEST
466: testset:
467: requires: !single
468: args: -pep_nev 3 -nonhyperbolic -pep_target 2
469: output_file: output/ex40_1.out
470: filter: grep -v "Definite" | sed -e "s/iterations [0-9]\([0-9]*\)/iterations xx/g" | sed -e "s/[0-9]\.[0-9]*e[+-]\([0-9]*\)/removed/g"
471: test:
472: suffix: 1
473: requires: !complex
474: test:
475: suffix: 1_complex
476: requires: complex !mumps
477: test:
478: suffix: 1_transform
479: requires: !complex
480: args: -transform
481: test:
482: suffix: 1_transform_complex
483: requires: complex !mumps
484: args: -transform
486: TEST*/