Actual source code: ks-symm.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) 2002-2009, 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: ArrowTridFlip - Solves the arrowhead-tridiagonal eigenproblem by flipping
49: the matrix and tridiagonalizing the bottom part.
51: On input:
52: l is the size of diagonal part
53: d contains diagonal elements (length n)
54: e contains offdiagonal elements (length n-1)
56: On output:
57: d contains the eigenvalues in ascending order
58: Q is the eigenvector matrix (order n)
60: Workspace:
61: S is workspace to store a copy of the full matrix (nxn reals)
62: */
63: PetscErrorCode ArrowTridFlip(PetscInt n_,PetscInt l,PetscReal *d,PetscReal *e,PetscReal *Q,PetscReal *S)
64: {
65: #if defined(SLEPC_MISSING_LAPACK_SYTRD) || defined(SLEPC_MISSING_LAPACK_ORGTR) || defined(SLEPC_MISSING_LAPACK_STEQR)
67: SETERRQ(PETSC_ERR_SUP,"SYTRD/ORGTR/STEQR - Lapack routine is unavailable.");
68: #else
70: PetscInt i,j;
71: PetscBLASInt n,n1,n2,lwork,info;
75: n = PetscBLASIntCast(n_);
76: n1 = PetscBLASIntCast(l+1); /* size of leading block, including residuals */
77: n2 = PetscBLASIntCast(n-l-1); /* size of trailing block */
78: PetscMemzero(S,n*n*sizeof(PetscReal));
80: /* Flip matrix S, copying the values saved in Q */
81: for (i=0;i<n;i++)
82: S[(n-1-i)+(n-1-i)*n] = d[i];
83: for (i=0;i<l;i++)
84: S[(n-1-i)+(n-1-l)*n] = e[i];
85: for (i=l;i<n-1;i++)
86: S[(n-1-i)+(n-1-i-1)*n] = e[i];
88: /* Reduce (2,2)-block of flipped S to tridiagonal form */
89: lwork = PetscBLASIntCast(n_*n_-n_);
90: LAPACKsytrd_("L",&n1,S+n2*(n+1),&n,d,e,Q,Q+n,&lwork,&info);
91: if (info) SETERRQ1(PETSC_ERR_LIB,"Error in Lapack xSYTRD %d",info);
93: /* Flip back diag and subdiag, put them in d and e */
94: for (i=0;i<n-1;i++) {
95: d[n-i-1] = S[i+i*n];
96: e[n-i-2] = S[i+1+i*n];
97: }
98: d[0] = S[n-1+(n-1)*n];
100: /* Compute the orthogonal matrix used for tridiagonalization */
101: LAPACKorgtr_("L",&n1,S+n2*(n+1),&n,Q,Q+n,&lwork,&info);
102: if (info) SETERRQ1(PETSC_ERR_LIB,"Error in Lapack xORGTR %d",info);
104: /* Create full-size Q, flipped back to original order */
105: for (i=0;i<n;i++)
106: for (j=0;j<n;j++)
107: Q[i+j*n] = 0.0;
108: for (i=n1;i<n;i++)
109: Q[i+i*n] = 1.0;
110: for (i=0;i<n1;i++)
111: for (j=0;j<n1;j++)
112: Q[i+j*n] = S[n-i-1+(n-j-1)*n];
114: /* Solve the tridiagonal eigenproblem */
115: LAPACKsteqr_("V",&n,d,e,Q,&n,S,&info);
116: if (info) SETERRQ1(PETSC_ERR_LIB,"Error in Lapack xSTEQR %d",info);
118: return(0);
119: #endif
120: }
124: /*
125: EPSProjectedKSSym - Solves the projected eigenproblem in the Krylov-Schur
126: method (symmetric case).
128: On input:
129: n is the matrix dimension
130: l is the number of vectors kept in previous restart
131: a contains diagonal elements (length n)
132: b contains offdiagonal elements (length n-1)
134: On output:
135: eig is the sorted list of eigenvalues
136: Q is the eigenvector matrix (order n, leading dimension n)
138: Workspace:
139: work is workspace to store a real square matrix of order n
140: perm is workspace to store 2n integers
141: */
142: PetscErrorCode EPSProjectedKSSym(EPS eps,PetscInt n,PetscInt l,PetscReal *a,PetscReal *b,PetscScalar *eig,PetscScalar *Q,PetscReal *work,PetscInt *perm)
143: {
145: PetscInt i,j,k,p;
146: PetscReal rtmp,*Qreal = (PetscReal*)Q;
149: /* Compute eigendecomposition of projected matrix */
150: ArrowTridFlip(n,l,a,b,Qreal,work);
152: /* Sort eigendecomposition according to eps->which */
153: EPSSortEigenvaluesReal(n,a,eps->which,n,perm,work);
154: for (i=0;i<n;i++)
155: eig[i] = a[perm[i]];
156: for (i=0;i<n;i++) {
157: p = perm[i];
158: if (p != i) {
159: j = i + 1;
160: while (perm[j] != i) j++;
161: perm[j] = p; perm[i] = i;
162: /* swap eigenvectors i and j */
163: for (k=0;k<n;k++) {
164: rtmp = Qreal[k+p*n]; Qreal[k+p*n] = Qreal[k+i*n]; Qreal[k+i*n] = rtmp;
165: }
166: }
167: }
169: #if defined(PETSC_USE_COMPLEX)
170: for (j=n-1;j>=0;j--)
171: for (i=n-1;i>=0;i--)
172: Q[i+j*n] = Qreal[i+j*n];
173: #endif
174: return(0);
175: }
179: PetscErrorCode EPSSolve_KRYLOVSCHUR_SYMM(EPS eps)
180: {
182: PetscInt i,k,l,lds,lt,nv,m;
183: Vec u=eps->work[1];
184: PetscScalar *Q;
185: PetscReal *a,*b,*work,beta;
186: PetscInt *iwork;
187: PetscTruth breakdown;
190: lds = PetscMin(eps->mpd,eps->ncv);
191: PetscMalloc(lds*lds*sizeof(PetscReal),&work);
192: PetscMalloc(lds*lds*sizeof(PetscScalar),&Q);
193: PetscMalloc(2*lds*sizeof(PetscInt),&iwork);
194: lt = PetscMin(eps->nev+eps->mpd,eps->ncv);
195: PetscMalloc(lt*sizeof(PetscReal),&a);
196: PetscMalloc(lt*sizeof(PetscReal),&b);
198: /* Get the starting Lanczos vector */
199: EPSGetStartVector(eps,0,eps->V[0],PETSC_NULL);
200: l = 0;
201:
202: /* Restart loop */
203: while (eps->reason == EPS_CONVERGED_ITERATING) {
204: eps->its++;
206: /* Compute an nv-step Lanczos factorization */
207: m = PetscMin(eps->nconv+eps->mpd,eps->ncv);
208: EPSFullLanczos(eps,a+l,b+l,eps->V,eps->nconv+l,&m,u,&breakdown);
209: nv = m - eps->nconv;
210: beta = b[nv-1];
212: /* Solve projected problem and compute residual norm estimates */
213: EPSProjectedKSSym(eps,nv,l,a,b,eps->eigr+eps->nconv,Q,work,iwork);
214: for (i=0;i<nv;i++)
215: eps->errest[i+eps->nconv] = beta*PetscAbsScalar(Q[(i+1)*nv-1]) / PetscAbsScalar(eps->eigr[i+eps->nconv]);
217: /* Check convergence */
218: k = eps->nconv;
219: while (k<eps->nconv+nv && eps->errest[k]<eps->tol) k++;
220: if (eps->its >= eps->max_it) eps->reason = EPS_DIVERGED_ITS;
221: if (k >= eps->nev) eps->reason = EPS_CONVERGED_TOL;
222:
223: /* Update l */
224: if (eps->reason != EPS_CONVERGED_ITERATING || breakdown) l = 0;
225: else l = (eps->nconv+nv-k)/2;
227: if (eps->reason == EPS_CONVERGED_ITERATING) {
228: if (breakdown) {
229: /* Start a new Lanczos factorization */
230: PetscInfo2(eps,"Breakdown in Krylov-Schur method (it=%i norm=%g)\n",eps->its,beta);
231: EPSGetStartVector(eps,k,eps->V[k],&breakdown);
232: if (breakdown) {
233: eps->reason = EPS_DIVERGED_BREAKDOWN;
234: PetscInfo(eps,"Unable to generate more start vectors\n");
235: }
236: } else {
237: /* Prepare the Rayleigh quotient for restart */
238: for (i=0;i<l;i++) {
239: a[i] = PetscRealPart(eps->eigr[i+k]);
240: b[i] = PetscRealPart(Q[nv-1+(i+k-eps->nconv)*nv]*beta);
241: }
242: }
243: }
244: /* Update the corresponding vectors V(:,idx) = V*Q(:,idx) */
245: SlepcUpdateVectors(nv,eps->V+eps->nconv,0,k+l-eps->nconv,Q,nv,PETSC_FALSE);
246: /* Normalize u and append it to V */
247: if (eps->reason == EPS_CONVERGED_ITERATING && !breakdown) {
248: VecAXPBY(eps->V[k+l],1.0/beta,0.0,u);
249: }
251: EPSMonitor(eps,eps->its,k,eps->eigr,eps->eigi,eps->errest,nv+eps->nconv);
252: eps->nconv = k;
253:
254: }
256: PetscFree(Q);
257: PetscFree(a);
258: PetscFree(b);
259: PetscFree(work);
260: PetscFree(iwork);
261: return(0);
262: }