Actual source code: dmerg2.c

slepc-3.11.2 2019-07-30
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2019, 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: */
 10: /*
 11:    BDC - Block-divide and conquer (see description in README file)
 12: */

 14: #include <slepc/private/dsimpl.h>
 15: #include <slepcblaslapack.h>

 17: PetscErrorCode BDC_dmerg2_(const char *jobz,PetscBLASInt rkct,PetscBLASInt n,
 18:         PetscReal *ev,PetscReal *q,PetscBLASInt ldq,PetscBLASInt *indxq,
 19:         PetscReal *rho,PetscReal *u,PetscBLASInt sbrkp1,PetscReal *v,
 20:         PetscBLASInt sbrk,PetscBLASInt cutpnt,PetscReal *work,PetscBLASInt lwork,
 21:         PetscBLASInt *iwork,PetscReal tol,PetscBLASInt *info,PetscBLASInt jobz_len)
 22: {
 23: /*  -- Routine written in LAPACK Version 3.0 style -- */
 24: /* *************************************************** */
 25: /*     Written by */
 26: /*     Michael Moldaschl and Wilfried Gansterer */
 27: /*     University of Vienna */
 28: /*     last modification: March 16, 2014 */

 30: /*     Small adaptations of original code written by */
 31: /*     Wilfried Gansterer and Bob Ward, */
 32: /*     Department of Computer Science, University of Tennessee */
 33: /*     see https://doi.org/10.1137/S1064827501399432 */
 34: /* *************************************************** */

 36: /*  Purpose */
 37: /*  ======= */

 39: /*  DMERG2 computes the updated eigensystem of a diagonal matrix after */
 40: /*  modification by a rank-one symmetric matrix.  The diagonal matrix */
 41: /*  consists of two diagonal submatrices, and the vectors defining the */
 42: /*  rank-1 matrix similarly have two underlying subvectors each. */
 43: /*  The dimension of the first subproblem is CUTPNT, the dimension of */
 44: /*  the second subproblem is N-CUTPNT. */

 46: /*  T = Q(in) ( EV(in) + RHO * Z*Z' ) Q'(in) = Q(out) * EV(out) * Q'(out) */

 48: /*     where Z = Q'[V U']', where V is a row vector and U is a column */
 49: /*     vector with dimensions corresponding to the two underlying */
 50: /*     subproblems. */

 52: /*     The eigenvectors of the original matrix are stored in Q, and the */
 53: /*     eigenvalues in EV.  The algorithm consists of three stages: */

 55: /*        The first stage consists of deflating the size of the problem */
 56: /*        when there are multiple eigenvalues or if there is a zero in */
 57: /*        the Z vector.  For each such occurrence the dimension of the */
 58: /*        secular equation problem is reduced by one.  This stage is */
 59: /*        performed by the routine DSRTDF. */

 61: /*        The second stage consists of calculating the updated */
 62: /*        eigenvalues. This is done by finding the roots of the secular */
 63: /*        equation via the routine DLAED4 (as called by DLAED3M). */
 64: /*        This routine also calculates the eigenvectors of the current */
 65: /*        problem. */

 67: /*        If( JOBZ.EQ.'D' ) then the final stage consists */
 68: /*        of computing the updated eigenvectors directly using the updated */
 69: /*        eigenvalues. The eigenvectors for the current problem are multiplied */
 70: /*        with the eigenvectors from the overall problem. */

 72: /*  Arguments */
 73: /*  ========= */

 75: /*  JOBZ   (input) CHARACTER*1 */
 76: /*          = 'N': Compute eigenvalues only (not implemented); */
 77: /*          = 'D': Compute eigenvalues and eigenvectors. */
 78: /*                 Eigenvectors are accumulated in the divide-and-conquer */
 79: /*                 process. */

 81: /*  RKCT   (input) INTEGER */
 82: /*         The number of the rank modification which is accounted for */
 83: /*         (RKCT >= 1). Required parameter, because the update operation of the */
 84: /*         modification vector can be performed much more efficiently */
 85: /*         if RKCT.EQ.1. In that case, the eigenvector matrix is still */
 86: /*         block-diagonal. For RKCT.GE.2 the eigenvector matrix for the update */
 87: /*         operation has filled up and is a full matrix. */

 89: /*  N      (input) INTEGER */
 90: /*         The dimension of the symmetric block tridiagonal matrix. */
 91: /*         N >= 0. */

 93: /*  EV     (input/output) DOUBLE PRECISION array, dimension (N) */
 94: /*         On entry, the eigenvalues (=diagonal values) of the */
 95: /*         rank-1-perturbed matrix. */
 96: /*         On exit, the eigenvalues of the repaired matrix. */

 98: /*  Q      (input/output) DOUBLE PRECISION array, dimension (LDQ,N) */
 99: /*         On entry, the eigenvectors of the rank-1-perturbed matrix. */
100: /*         On exit, the eigenvectors of the repaired tridiagonal matrix. */

102: /*  LDQ    (input) INTEGER */
103: /*         The leading dimension of the array Q.  LDQ >= max(1,N). */

105: /*  INDXQ  (input/output) INTEGER array, dimension (N) */
106: /*         On entry, the permutation which separately sorts the two */
107: /*         subproblems in EV into ascending order. */
108: /*         On exit, the permutation which will reintegrate the */
109: /*         subproblems back into sorted order, */
110: /*         i.e. EV( INDXQ( I = 1, N ) ) will be in ascending order. */

112: /*  RHO    (input/output) DOUBLE PRECISION */
113: /*         The scalar in the rank-1 perturbation. Modified (multiplied */
114: /*         by 2) in DSRTDF. */

116: /*  U      (input) DOUBLE PRECISION array; dimension (SBRKP1), where SBRKP1 */
117: /*         is the size of the first (original) block after CUTPNT. */
118: /*         The column vector of the rank-1 subdiagonal connecting the */
119: /*         two diagonal subproblems. */
120: /*         Theoretically, zero entries might have to be appended after U */
121: /*         in order to make it have dimension (N-CUTPNT). However, this */
122: /*         is not required because it can be accounted for in the */
123: /*         matrix-vector product using the argument SBRKP1. */

125: /*  SBRKP1 (input) INTEGER */
126: /*         Dimension of the relevant (non-zero) part of the vector U. */
127: /*         Equal to the size of the first original block after the */
128: /*         breakpoint. */

130: /*  V      (input) DOUBLE PRECISION array; dimension (SBRK), where SBRK */
131: /*         is the size of the last (original) block before CUTPNT. */
132: /*         The row vector of the rank-1 subdiagonal connecting the two */
133: /*         diagonal subproblems. */
134: /*         Theoretically, zero entries might have to be inserted in front */
135: /*         of V in order to make it have dimension (CUTPNT). However, this */
136: /*         is not required because it can be accounted for in the */
137: /*         matrix-vector product using the argument SBRK. */

139: /*  SBRK   (input) INTEGER */
140: /*         Dimension of the relevant (non-zero) part of the vector V. */
141: /*         Equal to the size of the last original block before the */
142: /*         breakpoint. */

144: /*  CUTPNT (input) INTEGER */
145: /*         The location of the last eigenvalue of the leading diagonal */
146: /*         block.  min(1,N) <= CUTPNT <= max(1,N). */

148: /*  WORK   (workspace) DOUBLE PRECISION array, dimension (LWORK) */

150: /*  LWORK  (input) INTEGER */
151: /*         The dimension of the array WORK. */
152: /*         In order to guarantee correct results in all cases, */
153: /*         LWORK must be at least ( 2*N**2 + 3*N  ). In many cases, */
154: /*         less workspace is required. The absolute minimum required is */
155: /*         ( N**2 + 3*N ). */
156: /*         If the workspace provided is not sufficient, the routine will */
157: /*         return a corresponding error code and report how much workspace */
158: /*         was missing (see INFO). */
159: /*         NOTE: This parameter is needed for determining whether enough */
160: /*               workspace is provided, and, if not, for computing how */
161: /*               much workspace is needed. */

163: /*  IWORK  (workspace) INTEGER array, dimension ( 4*N ) */

165: /*  TOL    (input) DOUBLE PRECISION */
166: /*         User specified deflation tolerance for the routine DSRTDF. */

168: /*  INFO   (output) INTEGER */
169: /*          = 0:  successful exit. */
170: /*          < -200: not enough workspace */
171: /*                ABS(INFO + 200) numbers have to be stored in addition */
172: /*                to the workspace provided, otherwise some eigenvectors */
173: /*                will be incorrect. */
174: /*          < 0, > -99:  if INFO.EQ.-i, the i-th argument had an */
175: /*                       illegal value. */
176: /*          > 0:  if INFO.EQ.1, an eigenvalue did not converge */
177: /*                if INFO.EQ.2, the deflation counters DZ and DE do not sum */
178: /*                              up to the total number N-K of components */
179: /*                              deflated */

181: /*  Further Details */
182: /*  =============== */

184: /*  Based on code written by */
185: /*     Wilfried Gansterer and Bob Ward, */
186: /*     Department of Computer Science, University of Tennessee */

188: /*  Based on the design of the LAPACK code Dlaed1.f written by Jeff */
189: /*  Rutter, Computer Science Division, University of California at */
190: /*  Berkeley, and modified by Francoise Tisseur, University of Tennessee. */

192: /*  ===================================================================== */

194: #if defined(SLEPC_MISSING_LAPACK_LAMRG)
196:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"LAMRG - Lapack routine is unavailable");
197: #else
198:   PetscBLASInt   i, k, n1, n2, de, is, dz, iw, iz, iq2, nmc, cpp1;
199:   PetscBLASInt   indx, indxc, indxp, lwmin, idlmda;
200:   PetscBLASInt   spneed, coltyp, tmpcut, i__1, i__2, one=1, mone=-1;
201:   char           defl[1];
202:   PetscReal      done = 1.0, dzero = 0.0;

206:   *info = 0;
207:   lwmin = n*n + n * 3;

209:   if (n < 0) {
210:     *info = -3;
211:   } else if (ldq < PetscMax(1,n)) {
212:     *info = -6;
213:   } else if (cutpnt < PetscMin(1,n) || cutpnt > PetscMax(1,n)) {
214:     *info = -13;
215:   } else if (lwork < lwmin) {
216:     *info = -15;
217:   }
218:   if (*info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Wrong argument %d in DMERG2",-(*info));

220: /* **************************************************************************** */

222:   /* Quick return if possible */

224:   if (n == 0) return(0);

226: /* **************************************************************************** */

228:   /* The following values are integer pointers which indicate */
229:   /* the portion of the workspace used by a particular array in DSRTDF */
230:   /* and DLAED3M. */

232:   iz = 0;
233:   idlmda = iz + n;
234:   iw = idlmda + n;
235:   iq2 = iw + n;
236:   is = iq2 + n * n;

238:   /* After the pointer IS the matrix S is stored and read in WORK */
239:   /* in the routine DLAED3M. */

241:   indx = 0;
242:   indxc = indx + n;
243:   coltyp = indxc + n;
244:   indxp = coltyp + n;

246:   /* If eigenvectors are to be accumulated in the divide-and-conquer */
247:   /* process ( JOBZ.EQ.'D' ) form the z-vector which consists of */
248:   /* Q_1^T * V and Q_2^T * U. */

250:   cpp1 = cutpnt + 1;
251:   if (rkct == 1) {

253:     /* for the first rank modification the eigenvector matrix has */
254:     /* special block-diagonal structure and therefore Q_1^T * V and */
255:     /* Q_2^T * U can be formed separately. */

257:     PetscStackCallBLAS("BLASgemv",BLASgemv_("T", &sbrk, &cutpnt, &done,
258:               &q[cutpnt - sbrk], &ldq, v, &one, &dzero, &work[iz], &one));
259:     nmc = n - cutpnt;
260:     PetscStackCallBLAS("BLASgemv",BLASgemv_("T", &sbrkp1, &nmc, &done,
261:               &q[cpp1-1 + (cpp1-1)*ldq], &ldq, u,
262:               &one, &dzero, &work[iz + cutpnt], &one));

264:   } else {

266:     /* for the higher rank modifications, the vectors V and U */
267:     /* have to be multiplied with the full eigenvector matrix */

269:     PetscStackCallBLAS("BLASgemv",BLASgemv_("T", &sbrk, &n, &done,
270:               &q[cutpnt - sbrk], &ldq, v, &one, &dzero, &work[iz], &one));
271:     PetscStackCallBLAS("BLASgemv",BLASgemv_("T", &sbrkp1, &n, &done, &q[cpp1-1],
272:               &ldq, u, &one, &done, &work[iz], &one));

274:   }

276: /* **************************************************************************** */

278:   /* Deflate eigenvalues. */

280:   if (rkct == 1) {

282:     /* for the first rank modification we need the actual cutpoint */

284:     n1 = cutpnt;
285:     tmpcut = cutpnt;
286:   } else {

288:     /* for the later rank modifications there is no actual cutpoint any more */

290:     n1 = n;

292:     /* The original value of CUTPNT has to be preserved for the next time */
293:     /* this subroutine is called (therefore, CUTPNT is an INPUT parameter */
294:     /* and not to be changed). Thus, assign N to TMPCUT and use the local */
295:     /* variable TMPCUT from now on for the cut point. */

297:     tmpcut = n;
298:   }

300:   /* initialize the flag DEFL (indicates whether deflation occurred - */
301:   /* this information is needed later in DLAED3M) */

303:   *(unsigned char *)defl = '0';

305:   /* call DSRTDF for deflation */

307:   BDC_dsrtdf_(&k, n, n1, ev, q, ldq, indxq, rho, &work[iz],
308:           &work[idlmda], &work[iw], &work[iq2], &iwork[indx],
309:           &iwork[indxc], &iwork[indxp], &iwork[coltyp], tol, &dz, &de, info);
310:           
311:   if (*info) SETERRQ1(PETSC_COMM_SELF,1,"dmerg2: error in dsrtdf, info = %d",*info);

313:   if (k < n) {

315:    /* ....some deflation occurred in dsrtdf, set the flag DEFL */
316:    /*     (needed in DLAED3M.f, since Givens rotations need to be */
317:    /*     applied to the eigenvector matrix only if some deflation */
318:    /*     happened) */

320:     *(unsigned char *)defl = '1';
321:   }

323: /* **************************************************************************** */

325:   /* Solve the Secular Equation. */

327:   if (k != 0 || k == 0) {

329:     /* ....not everything was deflated. */

331:     /* ....check whether enough workspace is available: */

333:     /* Note that the following (upper) bound SPNEED for the workspace */
334:     /* requirements should also hold in the extreme case TMPCUT=N, */
335:     /* which happens for every rank modification after the first one. */

337:     i__1 = (iwork[coltyp] + iwork[coltyp+1]) * k;
338:     i__2 = (iwork[coltyp+1] + iwork[coltyp + 2]) * k;
339:     spneed = is + PetscMax(i__1,i__2) - 1;

341:     if (spneed > lwork) SETERRQ1(PETSC_COMM_SELF,1,"dmerg2: Workspace needed exceeds the workspace provided by %d numbers",spneed-lwork);

343:     /* calling DLAED3M for solving the secular equation. */

345:     BDC_dlaed3m_(jobz, defl, k, n, tmpcut, ev, q, ldq,
346:                 *rho, &work[idlmda], &work[iq2], &iwork[indxc], &iwork[coltyp],
347:                 &work[iw], &work[is], info, 1, 1);
348:     if (*info) SETERRQ1(PETSC_COMM_SELF,1,"dmerg2: error in dlaed3m, info = %d",*info);

350:     /* Prepare the INDXQ sorting permutation. */

352:     n1 = k;
353:     n2 = n - k;
354:     PetscStackCallBLAS("LAPACKlamrg",LAPACKlamrg_(&n1, &n2, ev, &one, &mone, indxq));
355:     if (k == 0) {
356:       for (i = 0; i < n; ++i) indxq[i] = i+1;
357:     }

359:   } else {

361:     /* ....everything was deflated (K.EQ.0) */

363:     for (i = 0; i < n; ++i) indxq[i] = i+1;
364:   }
365:   return(0);
366: #endif
367: }