Actual source code: ks-harm.c
1: /*
3: SLEPc eigensolver: "krylovschur"
5: Method: Krylov-Schur
7: Algorithm:
9: Single-vector Krylov-Schur method for both symmetric and non-symmetric
10: problems.
12: References:
14: [1] "Krylov-Schur Methods in SLEPc", SLEPc Technical Report STR-7,
15: available at http://www.grycap.upv.es/slepc.
17: [2] G.W. Stewart, "A Krylov-Schur Algorithm for Large Eigenproblems",
18: SIAM J. Matrix Analysis and App., 23(3), pp. 601-614, 2001.
20: Last update: Feb 2009
22: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
23: SLEPc - Scalable Library for Eigenvalue Problem Computations
24: Copyright (c) 2002-2010, Universidad Politecnica de Valencia, Spain
26: This file is part of SLEPc.
27:
28: SLEPc is free software: you can redistribute it and/or modify it under the
29: terms of version 3 of the GNU Lesser General Public License as published by
30: the Free Software Foundation.
32: SLEPc is distributed in the hope that it will be useful, but WITHOUT ANY
33: WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
34: FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for
35: more details.
37: You should have received a copy of the GNU Lesser General Public License
38: along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
39: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
40: */
42: #include private/epsimpl.h
43: #include slepcblaslapack.h
47: /*
48: EPSTranslateHarmonic - Computes a translation of the Krylov decomposition
49: in order to perform a harmonic extraction.
51: On input:
52: S is the Rayleigh quotient (order m, leading dimension is lds)
53: tau is the translation amount
54: b is assumed to be beta*e_m^T
56: On output:
57: g = (B-sigma*eye(m))'\b
58: S is updated as S + g*b'
60: Workspace:
61: work is workspace to store a working copy of S and the pivots (int
62: of length m)
63: */
64: PetscErrorCode EPSTranslateHarmonic(PetscInt m_,PetscScalar *S,PetscInt lds,PetscScalar tau,PetscScalar beta,PetscScalar *g,PetscScalar *work)
65: {
66: #if defined(PETSC_MISSING_LAPACK_GETRF) || defined(PETSC_MISSING_LAPACK_GETRS)
68: SETERRQ(PETSC_ERR_SUP,"GETRF,GETRS - Lapack routines are unavailable.");
69: #else
71: PetscInt i,j;
72: PetscBLASInt info,m,one = 1;
73: PetscScalar *B = work;
74: PetscBLASInt *ipiv = (PetscBLASInt*)(work+m_*m_);
77: m = PetscBLASIntCast(m_);
78: /* Copy S to workspace B */
79: for (i=0;i<m;i++)
80: for (j=0;j<m;j++)
81: B[i+j*m] = S[i+j*lds];
82: /* Vector g initialy stores b */
83: PetscMemzero(g,m*sizeof(PetscScalar));
84: g[m-1] = beta;
85:
86: /* g = (B-sigma*eye(m))'\b */
87: for (i=0;i<m;i++)
88: B[i+i*m] -= tau;
89: LAPACKgetrf_(&m,&m,B,&m,ipiv,&info);
90: if (info<0) SETERRQ(PETSC_ERR_LIB,"Bad argument to LU factorization");
91: if (info>0) SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,"Bad LU factorization");
92: PetscLogFlops(2.0*m*m*m/3.0);
93: LAPACKgetrs_("C",&m,&one,B,&m,ipiv,g,&m,&info);
94: if (info) SETERRQ(PETSC_ERR_LIB,"GETRS - Bad solve");
95: PetscLogFlops(2.0*m*m-m);
97: /* S = S + g*b' */
98: for (i=0;i<m;i++)
99: S[i+(m-1)*lds] = S[i+(m-1)*lds] + g[i]*beta;
101: return(0);
102: #endif
103: }
107: /*
108: EPSRecoverHarmonic - Computes a translation of the truncated Krylov
109: decomposition in order to recover the original non-translated state
111: On input:
112: S is the truncated Rayleigh quotient (size n, leading dimension m)
113: k and l indicate the active columns of S
114: [U, u] is the basis of the Krylov subspace
115: g is the vector computed in the original translation
116: Q is the similarity transformation used to reduce to sorted Schur form
118: On output:
119: S is updated as S + g*b'
120: u is re-orthonormalized with respect to U
121: b is re-scaled
122: g is destroyed
124: Workspace:
125: ghat is workspace to store a vector of length n
126: */
127: PetscErrorCode EPSRecoverHarmonic(PetscScalar *S,PetscInt n_,PetscInt k,PetscInt l,PetscInt m_,PetscScalar *g,PetscScalar *Q,Vec *U,Vec u,PetscScalar *ghat)
128: {
130: PetscBLASInt one=1,ncol=k+l,n,m;
131: PetscScalar done=1.0,dmone=-1.0,dzero=0.0;
132: PetscReal gamma,gnorm;
133: PetscBLASInt i,j;
136: n = PetscBLASIntCast(n_);
137: m = PetscBLASIntCast(m_);
139: /* g^ = -Q(:,idx)'*g */
140: BLASgemv_("C",&n,&ncol,&dmone,Q,&n,g,&one,&dzero,ghat,&one);
142: /* S = S + g^*b' */
143: for (i=0;i<k+l;i++) {
144: for (j=k;j<k+l;j++) {
145: S[i+j*m] += ghat[i]*S[k+l+j*m];
146: }
147: }
149: /* g~ = (I-Q(:,idx)*Q(:,idx)')*g = g+Q(:,idx)*g^ */
150: BLASgemv_("N",&n,&ncol,&done,Q,&n,ghat,&one,&done,g,&one);
152: /* gamma u^ = u - U*g~ */
153: SlepcVecMAXPBY(u,1.0,-1.0,m,g,U);
155: /* Renormalize u */
156: gnorm = 0.0;
157: for (i=0;i<n;i++)
158: gnorm = gnorm + PetscRealPart(g[i]*PetscConj(g[i]));
159: gamma = sqrt(1.0+gnorm);
160: VecScale(u,1.0/gamma);
162: /* b = gamma*b */
163: for (i=k;i<k+l;i++) {
164: S[i*m+k+l] *= gamma;
165: }
166: return(0);
167: }
171: PetscErrorCode EPSSolve_KRYLOVSCHUR_HARMONIC(EPS eps)
172: {
174: PetscInt i,k,l,lwork,nv;
175: Vec u=eps->work[0];
176: PetscScalar *S=eps->T,*Q,*g,*work;
177: PetscReal beta,gnorm;
178: PetscTruth breakdown;
181: PetscMemzero(S,eps->ncv*eps->ncv*sizeof(PetscScalar));
182: PetscMalloc(eps->ncv*eps->ncv*sizeof(PetscScalar),&Q);
183: lwork = PetscMax((eps->ncv+1)*eps->ncv,7*eps->ncv);
184: PetscMalloc(lwork*sizeof(PetscScalar),&work);
185: PetscMalloc(eps->ncv*sizeof(PetscScalar),&g);
187: /* Get the starting Arnoldi vector */
188: EPSGetStartVector(eps,0,eps->V[0],PETSC_NULL);
189: l = 0;
190:
191: /* Restart loop */
192: while (eps->reason == EPS_CONVERGED_ITERATING) {
193: eps->its++;
195: /* Compute an nv-step Arnoldi factorization */
196: nv = PetscMin(eps->nconv+eps->mpd,eps->ncv);
197: EPSBasicArnoldi(eps,PETSC_FALSE,S,eps->ncv,eps->V,eps->nconv+l,&nv,u,&beta,&breakdown);
198: VecScale(u,1.0/beta);
200: /* Compute translation of Krylov decomposition */
201: EPSTranslateHarmonic(nv,S,eps->ncv,eps->target,(PetscScalar)beta,g,work);
202: gnorm = 0.0;
203: for (i=0;i<nv;i++)
204: gnorm = gnorm + PetscRealPart(g[i]*PetscConj(g[i]));
206: /* Solve projected problem and compute residual norm estimates */
207: EPSProjectedKSNonsym(eps,l,S,eps->ncv,Q,nv);
209: /* Check convergence */
210: EPSKrylovConvergence(eps,PETSC_FALSE,eps->nconv,nv-eps->nconv,S,eps->ncv,Q,eps->V,nv,beta,sqrt(1.0+gnorm),&k,work);
211: if (eps->its >= eps->max_it) eps->reason = EPS_DIVERGED_ITS;
212: if (k >= eps->nev) eps->reason = EPS_CONVERGED_TOL;
213:
214: /* Update l */
215: if (eps->reason != EPS_CONVERGED_ITERATING || breakdown) l = 0;
216: else {
217: l = (nv-k)/2;
218: #if !defined(PETSC_USE_COMPLEX)
219: if (S[(k+l-1)*(eps->ncv+1)+1] != 0.0) {
220: if (k+l<nv-1) l = l+1;
221: else l = l-1;
222: }
223: #endif
224: }
225:
226: if (eps->reason == EPS_CONVERGED_ITERATING) {
227: if (breakdown) {
228: /* Start a new Arnoldi factorization */
229: PetscInfo2(eps,"Breakdown in Krylov-Schur method (it=%i norm=%g)\n",eps->its,beta);
230: EPSGetStartVector(eps,k,eps->V[k],&breakdown);
231: if (breakdown) {
232: eps->reason = EPS_DIVERGED_BREAKDOWN;
233: PetscInfo(eps,"Unable to generate more start vectors\n");
234: }
235: } else {
236: /* Prepare the Rayleigh quotient for restart */
237: for (i=k;i<k+l;i++) {
238: S[i*eps->ncv+k+l] = Q[(i+1)*nv-1]*beta;
239: }
240: EPSRecoverHarmonic(S,nv,k,l,eps->ncv,g,Q,eps->V,u,work);
241: }
242: }
243: /* Update the corresponding vectors V(:,idx) = V*Q(:,idx) */
244: SlepcUpdateVectors(nv,eps->V,eps->nconv,k+l,Q,nv,PETSC_FALSE);
245:
246: if (eps->reason == EPS_CONVERGED_ITERATING && !breakdown) {
247: VecCopy(u,eps->V[k+l]);
248: }
249: eps->nconv = k;
251: EPSMonitor(eps,eps->its,eps->nconv,eps->eigr,eps->eigi,eps->errest,nv);
252:
253: }
255: PetscFree(Q);
256: PetscFree(work);
257: PetscFree(g);
258: return(0);
259: }