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|
/* arpack/dsaup2.f -- translated by f2c (version 20090411).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#ifdef __cplusplus
extern "C" {
#endif
#include "v3p_netlib.h"
/* Common Block Declarations */
/*Extern struct { */
/* integer logfil, ndigit, mgetv0, msaupd, msaup2, msaitr, mseigt, msapps, */
/* msgets, mseupd, mnaupd, mnaup2, mnaitr, mneigh, mnapps, mngets, */
/* mneupd, mcaupd, mcaup2, mcaitr, mceigh, mcapps, mcgets, mceupd; */
/*} debug_; */
/*#define debug_1 debug_ */
/*Extern struct { */
/* integer nopx, nbx, nrorth, nitref, nrstrt; */
/* real tsaupd, tsaup2, tsaitr, tseigt, tsgets, tsapps, tsconv, tnaupd, */
/* tnaup2, tnaitr, tneigh, tngets, tnapps, tnconv, tcaupd, tcaup2, */
/* tcaitr, tceigh, tcgets, tcapps, tcconv, tmvopx, tmvbx, tgetv0, */
/* titref, trvec; */
/*} timing_; */
/*#define timing_1 timing_ */
/* Table of constant values */
static doublereal c_b3 = .66666666666666663;
static integer c__1 = 1;
static integer c__0 = 0;
static logical c_true = TRUE_;
/* ----------------------------------------------------------------------- */
/* \BeginDoc */
/* \Name: dsaup2 */
/* \Description: */
/* Intermediate level interface called by dsaupd. */
/* \Usage: */
/* call dsaup2 */
/* ( IDO, BMAT, N, WHICH, NEV, NP, TOL, RESID, MODE, IUPD, */
/* ISHIFT, MXITER, V, LDV, H, LDH, RITZ, BOUNDS, Q, LDQ, WORKL, */
/* IPNTR, WORKD, INFO ) */
/* \Arguments */
/* IDO, BMAT, N, WHICH, NEV, TOL, RESID: same as defined in dsaupd. */
/* MODE, ISHIFT, MXITER: see the definition of IPARAM in dsaupd. */
/* NP Integer. (INPUT/OUTPUT) */
/* Contains the number of implicit shifts to apply during */
/* each Arnoldi/Lanczos iteration. */
/* If ISHIFT=1, NP is adjusted dynamically at each iteration */
/* to accelerate convergence and prevent stagnation. */
/* This is also roughly equal to the number of matrix-vector */
/* products (involving the operator OP) per Arnoldi iteration. */
/* The logic for adjusting is contained within the current */
/* subroutine. */
/* If ISHIFT=0, NP is the number of shifts the user needs */
/* to provide via reverse comunication. 0 < NP < NCV-NEV. */
/* NP may be less than NCV-NEV since a leading block of the current */
/* upper Tridiagonal matrix has split off and contains "unwanted" */
/* Ritz values. */
/* Upon termination of the IRA iteration, NP contains the number */
/* of "converged" wanted Ritz values. */
/* IUPD Integer. (INPUT) */
/* IUPD .EQ. 0: use explicit restart instead implicit update. */
/* IUPD .NE. 0: use implicit update. */
/* V Double precision N by (NEV+NP) array. (INPUT/OUTPUT) */
/* The Lanczos basis vectors. */
/* LDV Integer. (INPUT) */
/* Leading dimension of V exactly as declared in the calling */
/* program. */
/* H Double precision (NEV+NP) by 2 array. (OUTPUT) */
/* H is used to store the generated symmetric tridiagonal matrix */
/* The subdiagonal is stored in the first column of H starting */
/* at H(2,1). The main diagonal is stored in the second column */
/* of H starting at H(1,2). If dsaup2 converges store the */
/* B-norm of the final residual vector in H(1,1). */
/* LDH Integer. (INPUT) */
/* Leading dimension of H exactly as declared in the calling */
/* program. */
/* RITZ Double precision array of length NEV+NP. (OUTPUT) */
/* RITZ(1:NEV) contains the computed Ritz values of OP. */
/* BOUNDS Double precision array of length NEV+NP. (OUTPUT) */
/* BOUNDS(1:NEV) contain the error bounds corresponding to RITZ. */
/* Q Double precision (NEV+NP) by (NEV+NP) array. (WORKSPACE) */
/* Private (replicated) work array used to accumulate the */
/* rotation in the shift application step. */
/* LDQ Integer. (INPUT) */
/* Leading dimension of Q exactly as declared in the calling */
/* program. */
/* WORKL Double precision array of length at least 3*(NEV+NP). (INPUT/WORKSPACE) */
/* Private (replicated) array on each PE or array allocated on */
/* the front end. It is used in the computation of the */
/* tridiagonal eigenvalue problem, the calculation and */
/* application of the shifts and convergence checking. */
/* If ISHIFT .EQ. O and IDO .EQ. 3, the first NP locations */
/* of WORKL are used in reverse communication to hold the user */
/* supplied shifts. */
/* IPNTR Integer array of length 3. (OUTPUT) */
/* Pointer to mark the starting locations in the WORKD for */
/* vectors used by the Lanczos iteration. */
/* ------------------------------------------------------------- */
/* IPNTR(1): pointer to the current operand vector X. */
/* IPNTR(2): pointer to the current result vector Y. */
/* IPNTR(3): pointer to the vector B * X when used in one of */
/* the spectral transformation modes. X is the current */
/* operand. */
/* ------------------------------------------------------------- */
/* WORKD Double precision work array of length 3*N. (REVERSE COMMUNICATION) */
/* Distributed array to be used in the basic Lanczos iteration */
/* for reverse communication. The user should not use WORKD */
/* as temporary workspace during the iteration !!!!!!!!!! */
/* See Data Distribution Note in dsaupd. */
/* INFO Integer. (INPUT/OUTPUT) */
/* If INFO .EQ. 0, a randomly initial residual vector is used. */
/* If INFO .NE. 0, RESID contains the initial residual vector, */
/* possibly from a previous run. */
/* Error flag on output. */
/* = 0: Normal return. */
/* = 1: All possible eigenvalues of OP has been found. */
/* NP returns the size of the invariant subspace */
/* spanning the operator OP. */
/* = 2: No shifts could be applied. */
/* = -8: Error return from trid. eigenvalue calculation; */
/* This should never happen. */
/* = -9: Starting vector is zero. */
/* = -9999: Could not build an Lanczos factorization. */
/* Size that was built in returned in NP. */
/* \EndDoc */
/* ----------------------------------------------------------------------- */
/* \BeginLib */
/* \References: */
/* 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in */
/* a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), */
/* pp 357-385. */
/* 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly */
/* Restarted Arnoldi Iteration", Rice University Technical Report */
/* TR95-13, Department of Computational and Applied Mathematics. */
/* 3. B.N. Parlett, "The Symmetric Eigenvalue Problem". Prentice-Hall, */
/* 1980. */
/* 4. B.N. Parlett, B. Nour-Omid, "Towards a Black Box Lanczos Program", */
/* Computer Physics Communications, 53 (1989), pp 169-179. */
/* 5. B. Nour-Omid, B.N. Parlett, T. Ericson, P.S. Jensen, "How to */
/* Implement the Spectral Transformation", Math. Comp., 48 (1987), */
/* pp 663-673. */
/* 6. R.G. Grimes, J.G. Lewis and H.D. Simon, "A Shifted Block Lanczos */
/* Algorithm for Solving Sparse Symmetric Generalized Eigenproblems", */
/* SIAM J. Matr. Anal. Apps., January (1993). */
/* 7. L. Reichel, W.B. Gragg, "Algorithm 686: FORTRAN Subroutines */
/* for Updating the QR decomposition", ACM TOMS, December 1990, */
/* Volume 16 Number 4, pp 369-377. */
/* \Routines called: */
/* dgetv0 ARPACK initial vector generation routine. */
/* dsaitr ARPACK Lanczos factorization routine. */
/* dsapps ARPACK application of implicit shifts routine. */
/* dsconv ARPACK convergence of Ritz values routine. */
/* dseigt ARPACK compute Ritz values and error bounds routine. */
/* dsgets ARPACK reorder Ritz values and error bounds routine. */
/* dsortr ARPACK sorting routine. */
/* second ARPACK utility routine for timing. */
/* dlamch LAPACK routine that determines machine constants. */
/* dcopy Level 1 BLAS that copies one vector to another. */
/* ddot Level 1 BLAS that computes the scalar product of two vectors. */
/* dnrm2 Level 1 BLAS that computes the norm of a vector. */
/* dscal Level 1 BLAS that scales a vector. */
/* dswap Level 1 BLAS that swaps two vectors. */
/* \Author */
/* Danny Sorensen Phuong Vu */
/* Richard Lehoucq CRPC / Rice University */
/* Dept. of Computational & Houston, Texas */
/* Applied Mathematics */
/* Rice University */
/* Houston, Texas */
/* \Revision history: */
/* 12/15/93: Version ' 2.4' */
/* xx/xx/95: Version ' 2.4'. (R.B. Lehoucq) */
/* \SCCS Information: @(#) */
/* FILE: saup2.F SID: 2.6 DATE OF SID: 8/16/96 RELEASE: 2 */
/* \EndLib */
/* ----------------------------------------------------------------------- */
/*< >*/
/* Subroutine */ int dsaup2_(integer *ido, char *bmat, integer *n, char *
which, integer *nev, integer *np, doublereal *tol, doublereal *resid,
integer *mode, integer *iupd, integer *ishift, integer *mxiter,
doublereal *v, integer *ldv, doublereal *h__, integer *ldh,
doublereal *ritz, doublereal *bounds, doublereal *q, integer *ldq,
doublereal *workl, integer *ipntr, doublereal *workd, integer *info,
ftnlen bmat_len, ftnlen which_len)
{
/* System generated locals */
integer h_dim1, h_offset, q_dim1, q_offset, v_dim1, v_offset, i__1, i__2,
i__3;
doublereal d__1, d__2, d__3;
/* Builtin functions */
double pow_dd(doublereal *, doublereal *);
integer s_cmp(char *, char *, ftnlen, ftnlen);
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
double sqrt(doublereal);
/* Local variables */
integer j;
/* static real t0, t1, t2, t3; */
/* integer kp[3]; */
static integer np0, nev0;
extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *,
integer *);
static doublereal eps23;
integer ierr;
static integer iter;
doublereal temp;
integer nevd2;
extern doublereal dnrm2_(integer *, doublereal *, integer *);
static logical getv0;
integer nevm2;
static logical cnorm;
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *), dswap_(integer *, doublereal *, integer
*, doublereal *, integer *);
static integer nconv;
static logical initv;
static doublereal rnorm;
extern /* Subroutine */ int dgetv0_(integer *, char *, integer *, logical
*, integer *, integer *, doublereal *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *, ftnlen);
extern doublereal dlamch_(char *, ftnlen);
integer nevbef;
extern /* Subroutine */ int second_(real *);
static logical update;
char wprime[2];
static logical ushift;
static integer kplusp /*, msglvl */;
integer nptemp;
extern /* Subroutine */ int dsaitr_(integer *, char *, integer *, integer
*, integer *, integer *, doublereal *, doublereal *, doublereal *,
integer *, doublereal *, integer *, integer *, doublereal *,
integer *, ftnlen), dsconv_(integer *, doublereal *, doublereal *,
doublereal *, integer *), dseigt_(doublereal *, integer *,
doublereal *, integer *, doublereal *, doublereal *, doublereal *,
integer *), dsgets_(integer *, char *, integer *, integer *,
doublereal *, doublereal *, doublereal *, ftnlen), dsapps_(
integer *, integer *, integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
integer *, doublereal *), dsortr_(char *, logical *, integer *,
doublereal *, doublereal *, ftnlen);
/* %----------------------------------------------------% */
/* | Include files for debugging and timing information | */
/* %----------------------------------------------------% */
/*< include 'debug.h' >*/
/*< include 'stat.h' >*/
/* \SCCS Information: @(#) */
/* FILE: debug.h SID: 2.3 DATE OF SID: 11/16/95 RELEASE: 2 */
/* %---------------------------------% */
/* | See debug.doc for documentation | */
/* %---------------------------------% */
/*< >*/
/*< character bmat*1, which*2 >*/
/* %------------------% */
/* | Scalar Arguments | */
/* %------------------% */
/* %--------------------------------% */
/* | See stat.doc for documentation | */
/* %--------------------------------% */
/* \SCCS Information: @(#) */
/* FILE: stat.h SID: 2.2 DATE OF SID: 11/16/95 RELEASE: 2 */
/*< save t0, t1, t2, t3, t4, t5 >*/
/*< integer nopx, nbx, nrorth, nitref, nrstrt >*/
/*< >*/
/*< >*/
/*< >*/
/*< >*/
/* %-----------------% */
/* | Array Arguments | */
/* %-----------------% */
/*< integer ipntr(3) >*/
/*< >*/
/* %------------% */
/* | Parameters | */
/* %------------% */
/*< >*/
/*< parameter (one = 1.0D+0, zero = 0.0D+0) >*/
/* %---------------% */
/* | Local Scalars | */
/* %---------------% */
/*< character wprime*2 >*/
/*< logical cnorm, getv0, initv, update, ushift >*/
/*< >*/
/*< >*/
/*< >*/
/* %----------------------% */
/* | External Subroutines | */
/* %----------------------% */
/*< >*/
/* %--------------------% */
/* | External Functions | */
/* %--------------------% */
/*< >*/
/*< external ddot, dnrm2, dlamch >*/
/* %---------------------% */
/* | Intrinsic Functions | */
/* %---------------------% */
/*< intrinsic min >*/
/* %-----------------------% */
/* | Executable Statements | */
/* %-----------------------% */
/*< if (ido .eq. 0) then >*/
/* Parameter adjustments */
--workd;
--resid;
--workl;
--bounds;
--ritz;
v_dim1 = *ldv;
v_offset = 1 + v_dim1;
v -= v_offset;
h_dim1 = *ldh;
h_offset = 1 + h_dim1;
h__ -= h_offset;
q_dim1 = *ldq;
q_offset = 1 + q_dim1;
q -= q_offset;
--ipntr;
/* Function Body */
if (*ido == 0) {
/* %-------------------------------% */
/* | Initialize timing statistics | */
/* | & message level for debugging | */
/* %-------------------------------% */
/*< call second (t0) >*/
/* second_(&t0); */
/*< msglvl = msaup2 >*/
/* msglvl = debug_1.msaup2; */
/* %---------------------------------% */
/* | Set machine dependent constant. | */
/* %---------------------------------% */
/*< eps23 = dlamch('Epsilon-Machine') >*/
eps23 = dlamch_("Epsilon-Machine", (ftnlen)15);
/*< eps23 = eps23**(2.0D+0/3.0D+0) >*/
eps23 = pow_dd(&eps23, &c_b3);
/* %-------------------------------------% */
/* | nev0 and np0 are integer variables | */
/* | hold the initial values of NEV & NP | */
/* %-------------------------------------% */
/*< nev0 = nev >*/
nev0 = *nev;
/*< np0 = np >*/
np0 = *np;
/* %-------------------------------------% */
/* | kplusp is the bound on the largest | */
/* | Lanczos factorization built. | */
/* | nconv is the current number of | */
/* | "converged" eigenvlues. | */
/* | iter is the counter on the current | */
/* | iteration step. | */
/* %-------------------------------------% */
/*< kplusp = nev0 + np0 >*/
kplusp = nev0 + np0;
/*< nconv = 0 >*/
nconv = 0;
/*< iter = 0 >*/
iter = 0;
/* %--------------------------------------------% */
/* | Set flags for computing the first NEV steps | */
/* | of the Lanczos factorization. | */
/* %--------------------------------------------% */
/*< getv0 = .true. >*/
getv0 = TRUE_;
/*< update = .false. >*/
update = FALSE_;
/*< ushift = .false. >*/
ushift = FALSE_;
/*< cnorm = .false. >*/
cnorm = FALSE_;
/*< if (info .ne. 0) then >*/
if (*info != 0) {
/* %--------------------------------------------% */
/* | User provides the initial residual vector. | */
/* %--------------------------------------------% */
/*< initv = .true. >*/
initv = TRUE_;
/*< info = 0 >*/
*info = 0;
/*< else >*/
} else {
/*< initv = .false. >*/
initv = FALSE_;
/*< end if >*/
}
/*< end if >*/
}
/* %---------------------------------------------% */
/* | Get a possibly random starting vector and | */
/* | force it into the range of the operator OP. | */
/* %---------------------------------------------% */
/*< 10 continue >*/
/* L10: */
/*< if (getv0) then >*/
if (getv0) {
/*< >*/
dgetv0_(ido, bmat, &c__1, &initv, n, &c__1, &v[v_offset], ldv, &resid[
1], &rnorm, &ipntr[1], &workd[1], info, (ftnlen)1);
/*< if (ido .ne. 99) go to 9000 >*/
if (*ido != 99) {
goto L9000;
}
/*< if (rnorm .eq. zero) then >*/
if (rnorm == 0.) {
/* %-----------------------------------------% */
/* | The initial vector is zero. Error exit. | */
/* %-----------------------------------------% */
/*< info = -9 >*/
*info = -9;
/*< go to 1200 >*/
goto L1200;
/*< end if >*/
}
/*< getv0 = .false. >*/
getv0 = FALSE_;
/*< ido = 0 >*/
*ido = 0;
/*< end if >*/
}
/* %------------------------------------------------------------% */
/* | Back from reverse communication: continue with update step | */
/* %------------------------------------------------------------% */
/*< if (update) go to 20 >*/
if (update) {
goto L20;
}
/* %-------------------------------------------% */
/* | Back from computing user specified shifts | */
/* %-------------------------------------------% */
/*< if (ushift) go to 50 >*/
if (ushift) {
goto L50;
}
/* %-------------------------------------% */
/* | Back from computing residual norm | */
/* | at the end of the current iteration | */
/* %-------------------------------------% */
/*< if (cnorm) go to 100 >*/
if (cnorm) {
goto L100;
}
/* %----------------------------------------------------------% */
/* | Compute the first NEV steps of the Lanczos factorization | */
/* %----------------------------------------------------------% */
/*< >*/
dsaitr_(ido, bmat, n, &c__0, &nev0, mode, &resid[1], &rnorm, &v[v_offset],
ldv, &h__[h_offset], ldh, &ipntr[1], &workd[1], info, (ftnlen)1);
/* %---------------------------------------------------% */
/* | ido .ne. 99 implies use of reverse communication | */
/* | to compute operations involving OP and possibly B | */
/* %---------------------------------------------------% */
/*< if (ido .ne. 99) go to 9000 >*/
if (*ido != 99) {
goto L9000;
}
/*< if (info .gt. 0) then >*/
if (*info > 0) {
/* %-----------------------------------------------------% */
/* | dsaitr was unable to build an Lanczos factorization | */
/* | of length NEV0. INFO is returned with the size of | */
/* | the factorization built. Exit main loop. | */
/* %-----------------------------------------------------% */
/*< np = info >*/
*np = *info;
/*< mxiter = iter >*/
*mxiter = iter;
/*< info = -9999 >*/
*info = -9999;
/*< go to 1200 >*/
goto L1200;
/*< end if >*/
}
/* %--------------------------------------------------------------% */
/* | | */
/* | M A I N LANCZOS I T E R A T I O N L O O P | */
/* | Each iteration implicitly restarts the Lanczos | */
/* | factorization in place. | */
/* | | */
/* %--------------------------------------------------------------% */
/*< 1000 continue >*/
L1000:
/*< iter = iter + 1 >*/
++iter;
/* if (msglvl .gt. 0) then */
/* call ivout (logfil, 1, iter, ndigit, */
/* & '_saup2: **** Start of major iteration number ****') */
/* end if */
/* if (msglvl .gt. 1) then */
/* call ivout (logfil, 1, nev, ndigit, */
/* & '_saup2: The length of the current Lanczos factorization') */
/* call ivout (logfil, 1, np, ndigit, */
/* & '_saup2: Extend the Lanczos factorization by') */
/* end if */
/* %------------------------------------------------------------% */
/* | Compute NP additional steps of the Lanczos factorization. | */
/* %------------------------------------------------------------% */
/*< ido = 0 >*/
*ido = 0;
/*< 20 continue >*/
L20:
/*< update = .true. >*/
update = TRUE_;
/*< >*/
dsaitr_(ido, bmat, n, nev, np, mode, &resid[1], &rnorm, &v[v_offset], ldv,
&h__[h_offset], ldh, &ipntr[1], &workd[1], info, (ftnlen)1);
/* %---------------------------------------------------% */
/* | ido .ne. 99 implies use of reverse communication | */
/* | to compute operations involving OP and possibly B | */
/* %---------------------------------------------------% */
/*< if (ido .ne. 99) go to 9000 >*/
if (*ido != 99) {
goto L9000;
}
/*< if (info .gt. 0) then >*/
if (*info > 0) {
/* %-----------------------------------------------------% */
/* | dsaitr was unable to build an Lanczos factorization | */
/* | of length NEV0+NP0. INFO is returned with the size | */
/* | of the factorization built. Exit main loop. | */
/* %-----------------------------------------------------% */
/*< np = info >*/
*np = *info;
/*< mxiter = iter >*/
*mxiter = iter;
/*< info = -9999 >*/
*info = -9999;
/*< go to 1200 >*/
goto L1200;
/*< end if >*/
}
/*< update = .false. >*/
update = FALSE_;
/* if (msglvl .gt. 1) then */
/* call dvout (logfil, 1, rnorm, ndigit, */
/* & '_saup2: Current B-norm of residual for factorization') */
/* end if */
/* %--------------------------------------------------------% */
/* | Compute the eigenvalues and corresponding error bounds | */
/* | of the current symmetric tridiagonal matrix. | */
/* %--------------------------------------------------------% */
/*< call dseigt (rnorm, kplusp, h, ldh, ritz, bounds, workl, ierr) >*/
dseigt_(&rnorm, &kplusp, &h__[h_offset], ldh, &ritz[1], &bounds[1], &
workl[1], &ierr);
/*< if (ierr .ne. 0) then >*/
if (ierr != 0) {
/*< info = -8 >*/
*info = -8;
/*< go to 1200 >*/
goto L1200;
/*< end if >*/
}
/* %----------------------------------------------------% */
/* | Make a copy of eigenvalues and corresponding error | */
/* | bounds obtained from _seigt. | */
/* %----------------------------------------------------% */
/*< call dcopy(kplusp, ritz, 1, workl(kplusp+1), 1) >*/
dcopy_(&kplusp, &ritz[1], &c__1, &workl[kplusp + 1], &c__1);
/*< call dcopy(kplusp, bounds, 1, workl(2*kplusp+1), 1) >*/
dcopy_(&kplusp, &bounds[1], &c__1, &workl[(kplusp << 1) + 1], &c__1);
/* %---------------------------------------------------% */
/* | Select the wanted Ritz values and their bounds | */
/* | to be used in the convergence test. | */
/* | The selection is based on the requested number of | */
/* | eigenvalues instead of the current NEV and NP to | */
/* | prevent possible misconvergence. | */
/* | * Wanted Ritz values := RITZ(NP+1:NEV+NP) | */
/* | * Shifts := RITZ(1:NP) := WORKL(1:NP) | */
/* %---------------------------------------------------% */
/*< nev = nev0 >*/
*nev = nev0;
/*< np = np0 >*/
*np = np0;
/*< call dsgets (ishift, which, nev, np, ritz, bounds, workl) >*/
dsgets_(ishift, which, nev, np, &ritz[1], &bounds[1], &workl[1], (ftnlen)
2);
/* %-------------------% */
/* | Convergence test. | */
/* %-------------------% */
/*< call dcopy (nev, bounds(np+1), 1, workl(np+1), 1) >*/
dcopy_(nev, &bounds[*np + 1], &c__1, &workl[*np + 1], &c__1);
/*< call dsconv (nev, ritz(np+1), workl(np+1), tol, nconv) >*/
dsconv_(nev, &ritz[*np + 1], &workl[*np + 1], tol, &nconv);
/*< if (msglvl .gt. 2) then >*/
/* if (msglvl > 2) { */
/*< kp(1) = nev >*/
/* kp[0] = *nev; */
/*< kp(2) = np >*/
/* kp[1] = *np; */
/*< kp(3) = nconv >*/
/* kp[2] = nconv; */
/* call ivout (logfil, 3, kp, ndigit, */
/* & '_saup2: NEV, NP, NCONV are') */
/* call dvout (logfil, kplusp, ritz, ndigit, */
/* & '_saup2: The eigenvalues of H') */
/* call dvout (logfil, kplusp, bounds, ndigit, */
/* & '_saup2: Ritz estimates of the current NCV Ritz values') */
/*< end if >*/
/* } */
/* %---------------------------------------------------------% */
/* | Count the number of unwanted Ritz values that have zero | */
/* | Ritz estimates. If any Ritz estimates are equal to zero | */
/* | then a leading block of H of order equal to at least | */
/* | the number of Ritz values with zero Ritz estimates has | */
/* | split off. None of these Ritz values may be removed by | */
/* | shifting. Decrease NP the number of shifts to apply. If | */
/* | no shifts may be applied, then prepare to exit | */
/* %---------------------------------------------------------% */
/*< nptemp = np >*/
nptemp = *np;
/*< do 30 j=1, nptemp >*/
i__1 = nptemp;
for (j = 1; j <= i__1; ++j) {
/*< if (bounds(j) .eq. zero) then >*/
if (bounds[j] == 0.) {
/*< np = np - 1 >*/
--(*np);
/*< nev = nev + 1 >*/
++(*nev);
/*< end if >*/
}
/*< 30 continue >*/
/* L30: */
}
/*< >*/
if (nconv >= nev0 || iter > *mxiter || *np == 0) {
/* %------------------------------------------------% */
/* | Prepare to exit. Put the converged Ritz values | */
/* | and corresponding bounds in RITZ(1:NCONV) and | */
/* | BOUNDS(1:NCONV) respectively. Then sort. Be | */
/* | careful when NCONV > NP since we don't want to | */
/* | swap overlapping locations. | */
/* %------------------------------------------------% */
/*< if (which .eq. 'BE') then >*/
if (s_cmp(which, "BE", (ftnlen)2, (ftnlen)2) == 0) {
/* %-----------------------------------------------------% */
/* | Both ends of the spectrum are requested. | */
/* | Sort the eigenvalues into algebraically decreasing | */
/* | order first then swap low end of the spectrum next | */
/* | to high end in appropriate locations. | */
/* | NOTE: when np < floor(nev/2) be careful not to swap | */
/* | overlapping locations. | */
/* %-----------------------------------------------------% */
/*< wprime = 'SA' >*/
s_copy(wprime, "SA", (ftnlen)2, (ftnlen)2);
/*< call dsortr (wprime, .true., kplusp, ritz, bounds) >*/
dsortr_(wprime, &c_true, &kplusp, &ritz[1], &bounds[1], (ftnlen)2)
;
/*< nevd2 = nev / 2 >*/
nevd2 = *nev / 2;
/*< nevm2 = nev - nevd2 >*/
nevm2 = *nev - nevd2;
/*< if ( nev .gt. 1 ) then >*/
if (*nev > 1) {
/*< >*/
i__1 = min(nevd2,*np);
/* Computing MAX */
i__2 = kplusp - nevd2 + 1, i__3 = kplusp - *np + 1;
dswap_(&i__1, &ritz[nevm2 + 1], &c__1, &ritz[max(i__2,i__3)],
&c__1);
/*< >*/
i__1 = min(nevd2,*np);
/* Computing MAX */
i__2 = kplusp - nevd2 + 1, i__3 = kplusp - *np;
dswap_(&i__1, &bounds[nevm2 + 1], &c__1, &bounds[max(i__2,
i__3) + 1], &c__1);
/*< end if >*/
}
/*< else >*/
} else {
/* %--------------------------------------------------% */
/* | LM, SM, LA, SA case. | */
/* | Sort the eigenvalues of H into the an order that | */
/* | is opposite to WHICH, and apply the resulting | */
/* | order to BOUNDS. The eigenvalues are sorted so | */
/* | that the wanted part are always within the first | */
/* | NEV locations. | */
/* %--------------------------------------------------% */
/*< if (which .eq. 'LM') wprime = 'SM' >*/
if (s_cmp(which, "LM", (ftnlen)2, (ftnlen)2) == 0) {
s_copy(wprime, "SM", (ftnlen)2, (ftnlen)2);
}
/*< if (which .eq. 'SM') wprime = 'LM' >*/
if (s_cmp(which, "SM", (ftnlen)2, (ftnlen)2) == 0) {
s_copy(wprime, "LM", (ftnlen)2, (ftnlen)2);
}
/*< if (which .eq. 'LA') wprime = 'SA' >*/
if (s_cmp(which, "LA", (ftnlen)2, (ftnlen)2) == 0) {
s_copy(wprime, "SA", (ftnlen)2, (ftnlen)2);
}
/*< if (which .eq. 'SA') wprime = 'LA' >*/
if (s_cmp(which, "SA", (ftnlen)2, (ftnlen)2) == 0) {
s_copy(wprime, "LA", (ftnlen)2, (ftnlen)2);
}
/*< call dsortr (wprime, .true., kplusp, ritz, bounds) >*/
dsortr_(wprime, &c_true, &kplusp, &ritz[1], &bounds[1], (ftnlen)2)
;
/*< end if >*/
}
/* %--------------------------------------------------% */
/* | Scale the Ritz estimate of each Ritz value | */
/* | by 1 / max(eps23,magnitude of the Ritz value). | */
/* %--------------------------------------------------% */
/*< do 35 j = 1, nev0 >*/
i__1 = nev0;
for (j = 1; j <= i__1; ++j) {
/*< temp = max( eps23, abs(ritz(j)) ) >*/
/* Computing MAX */
d__2 = eps23, d__3 = (d__1 = ritz[j], abs(d__1));
temp = max(d__2,d__3);
/*< bounds(j) = bounds(j)/temp >*/
bounds[j] /= temp;
/*< 35 continue >*/
/* L35: */
}
/* %----------------------------------------------------% */
/* | Sort the Ritz values according to the scaled Ritz | */
/* | esitmates. This will push all the converged ones | */
/* | towards the front of ritzr, ritzi, bounds | */
/* | (in the case when NCONV < NEV.) | */
/* %----------------------------------------------------% */
/*< wprime = 'LA' >*/
s_copy(wprime, "LA", (ftnlen)2, (ftnlen)2);
/*< call dsortr(wprime, .true., nev0, bounds, ritz) >*/
dsortr_(wprime, &c_true, &nev0, &bounds[1], &ritz[1], (ftnlen)2);
/* %----------------------------------------------% */
/* | Scale the Ritz estimate back to its original | */
/* | value. | */
/* %----------------------------------------------% */
/*< do 40 j = 1, nev0 >*/
i__1 = nev0;
for (j = 1; j <= i__1; ++j) {
/*< temp = max( eps23, abs(ritz(j)) ) >*/
/* Computing MAX */
d__2 = eps23, d__3 = (d__1 = ritz[j], abs(d__1));
temp = max(d__2,d__3);
/*< bounds(j) = bounds(j)*temp >*/
bounds[j] *= temp;
/*< 40 continue >*/
/* L40: */
}
/* %--------------------------------------------------% */
/* | Sort the "converged" Ritz values again so that | */
/* | the "threshold" values and their associated Ritz | */
/* | estimates appear at the appropriate position in | */
/* | ritz and bound. | */
/* %--------------------------------------------------% */
/*< if (which .eq. 'BE') then >*/
if (s_cmp(which, "BE", (ftnlen)2, (ftnlen)2) == 0) {
/* %------------------------------------------------% */
/* | Sort the "converged" Ritz values in increasing | */
/* | order. The "threshold" values are in the | */
/* | middle. | */
/* %------------------------------------------------% */
/*< wprime = 'LA' >*/
s_copy(wprime, "LA", (ftnlen)2, (ftnlen)2);
/*< call dsortr(wprime, .true., nconv, ritz, bounds) >*/
dsortr_(wprime, &c_true, &nconv, &ritz[1], &bounds[1], (ftnlen)2);
/*< else >*/
} else {
/* %----------------------------------------------% */
/* | In LM, SM, LA, SA case, sort the "converged" | */
/* | Ritz values according to WHICH so that the | */
/* | "threshold" value appears at the front of | */
/* | ritz. | */
/* %----------------------------------------------% */
/*< call dsortr(which, .true., nconv, ritz, bounds) >*/
dsortr_(which, &c_true, &nconv, &ritz[1], &bounds[1], (ftnlen)2);
/*< end if >*/
}
/* %------------------------------------------% */
/* | Use h( 1,1 ) as storage to communicate | */
/* | rnorm to _seupd if needed | */
/* %------------------------------------------% */
/*< h(1,1) = rnorm >*/
h__[h_dim1 + 1] = rnorm;
/* if (msglvl .gt. 1) then */
/* call dvout (logfil, kplusp, ritz, ndigit, */
/* & '_saup2: Sorted Ritz values.') */
/* call dvout (logfil, kplusp, bounds, ndigit, */
/* & '_saup2: Sorted ritz estimates.') */
/* end if */
/* %------------------------------------% */
/* | Max iterations have been exceeded. | */
/* %------------------------------------% */
/*< if (iter .gt. mxiter .and. nconv .lt. nev) info = 1 >*/
if (iter > *mxiter && nconv < *nev) {
*info = 1;
}
/* %---------------------% */
/* | No shifts to apply. | */
/* %---------------------% */
/*< if (np .eq. 0 .and. nconv .lt. nev0) info = 2 >*/
if (*np == 0 && nconv < nev0) {
*info = 2;
}
/*< np = nconv >*/
*np = nconv;
/*< go to 1100 >*/
goto L1100;
/*< else if (nconv .lt. nev .and. ishift .eq. 1) then >*/
} else if (nconv < *nev && *ishift == 1) {
/* %---------------------------------------------------% */
/* | Do not have all the requested eigenvalues yet. | */
/* | To prevent possible stagnation, adjust the number | */
/* | of Ritz values and the shifts. | */
/* %---------------------------------------------------% */
/*< nevbef = nev >*/
nevbef = *nev;
/*< nev = nev + min (nconv, np/2) >*/
/* Computing MIN */
i__1 = nconv, i__2 = *np / 2;
*nev += min(i__1,i__2);
/*< if (nev .eq. 1 .and. kplusp .ge. 6) then >*/
if (*nev == 1 && kplusp >= 6) {
/*< nev = kplusp / 2 >*/
*nev = kplusp / 2;
/*< else if (nev .eq. 1 .and. kplusp .gt. 2) then >*/
} else if (*nev == 1 && kplusp > 2) {
/*< nev = 2 >*/
*nev = 2;
/*< end if >*/
}
/*< np = kplusp - nev >*/
*np = kplusp - *nev;
/* %---------------------------------------% */
/* | If the size of NEV was just increased | */
/* | resort the eigenvalues. | */
/* %---------------------------------------% */
/*< >*/
if (nevbef < *nev) {
dsgets_(ishift, which, nev, np, &ritz[1], &bounds[1], &workl[1], (
ftnlen)2);
}
/*< end if >*/
}
/*< if (msglvl .gt. 0) then >*/
/* if (msglvl > 0) { */
/* call ivout (logfil, 1, nconv, ndigit, */
/* & '_saup2: no. of "converged" Ritz values at this iter.') */
/*< if (msglvl .gt. 1) then >*/
/* if (msglvl > 1) { */
/*< kp(1) = nev >*/
/* kp[0] = *nev; */
/*< kp(2) = np >*/
/* kp[1] = *np; */
/* call ivout (logfil, 2, kp, ndigit, */
/* & '_saup2: NEV and NP are') */
/* call dvout (logfil, nev, ritz(np+1), ndigit, */
/* & '_saup2: "wanted" Ritz values.') */
/* call dvout (logfil, nev, bounds(np+1), ndigit, */
/* & '_saup2: Ritz estimates of the "wanted" values ') */
/*< end if >*/
/* } */
/*< end if >*/
/* } */
/*< if (ishift .eq. 0) then >*/
if (*ishift == 0) {
/* %-----------------------------------------------------% */
/* | User specified shifts: reverse communication to | */
/* | compute the shifts. They are returned in the first | */
/* | NP locations of WORKL. | */
/* %-----------------------------------------------------% */
/*< ushift = .true. >*/
ushift = TRUE_;
/*< ido = 3 >*/
*ido = 3;
/*< go to 9000 >*/
goto L9000;
/*< end if >*/
}
/*< 50 continue >*/
L50:
/* %------------------------------------% */
/* | Back from reverse communication; | */
/* | User specified shifts are returned | */
/* | in WORKL(1:*NP) | */
/* %------------------------------------% */
/*< ushift = .false. >*/
ushift = FALSE_;
/* %---------------------------------------------------------% */
/* | Move the NP shifts to the first NP locations of RITZ to | */
/* | free up WORKL. This is for the non-exact shift case; | */
/* | in the exact shift case, dsgets already handles this. | */
/* %---------------------------------------------------------% */
/*< if (ishift .eq. 0) call dcopy (np, workl, 1, ritz, 1) >*/
if (*ishift == 0) {
dcopy_(np, &workl[1], &c__1, &ritz[1], &c__1);
}
/* if (msglvl .gt. 2) then */
/* call ivout (logfil, 1, np, ndigit, */
/* & '_saup2: The number of shifts to apply ') */
/* call dvout (logfil, np, workl, ndigit, */
/* & '_saup2: shifts selected') */
/* if (ishift .eq. 1) then */
/* call dvout (logfil, np, bounds, ndigit, */
/* & '_saup2: corresponding Ritz estimates') */
/* end if */
/* end if */
/* %---------------------------------------------------------% */
/* | Apply the NP0 implicit shifts by QR bulge chasing. | */
/* | Each shift is applied to the entire tridiagonal matrix. | */
/* | The first 2*N locations of WORKD are used as workspace. | */
/* | After dsapps is done, we have a Lanczos | */
/* | factorization of length NEV. | */
/* %---------------------------------------------------------% */
/*< >*/
dsapps_(n, nev, np, &ritz[1], &v[v_offset], ldv, &h__[h_offset], ldh, &
resid[1], &q[q_offset], ldq, &workd[1]);
/* %---------------------------------------------% */
/* | Compute the B-norm of the updated residual. | */
/* | Keep B*RESID in WORKD(1:N) to be used in | */
/* | the first step of the next call to dsaitr. | */
/* %---------------------------------------------% */
/*< cnorm = .true. >*/
cnorm = TRUE_;
/*< call second (t2) >*/
/* second_(&t2); */
/*< if (bmat .eq. 'G') then >*/
if (*(unsigned char *)bmat == 'G') {
/*< nbx = nbx + 1 >*/
/* ++timing_1.nbx; */
/*< call dcopy (n, resid, 1, workd(n+1), 1) >*/
dcopy_(n, &resid[1], &c__1, &workd[*n + 1], &c__1);
/*< ipntr(1) = n + 1 >*/
ipntr[1] = *n + 1;
/*< ipntr(2) = 1 >*/
ipntr[2] = 1;
/*< ido = 2 >*/
*ido = 2;
/* %----------------------------------% */
/* | Exit in order to compute B*RESID | */
/* %----------------------------------% */
/*< go to 9000 >*/
goto L9000;
/*< else if (bmat .eq. 'I') then >*/
} else if (*(unsigned char *)bmat == 'I') {
/*< call dcopy (n, resid, 1, workd, 1) >*/
dcopy_(n, &resid[1], &c__1, &workd[1], &c__1);
/*< end if >*/
}
/*< 100 continue >*/
L100:
/* %----------------------------------% */
/* | Back from reverse communication; | */
/* | WORKD(1:N) := B*RESID | */
/* %----------------------------------% */
/*< if (bmat .eq. 'G') then >*/
if (*(unsigned char *)bmat == 'G') {
/*< call second (t3) >*/
/* second_(&t3); */
/*< tmvbx = tmvbx + (t3 - t2) >*/
/* timing_1.tmvbx += t3 - t2; */
/*< end if >*/
}
/*< if (bmat .eq. 'G') then >*/
if (*(unsigned char *)bmat == 'G') {
/*< rnorm = ddot (n, resid, 1, workd, 1) >*/
rnorm = ddot_(n, &resid[1], &c__1, &workd[1], &c__1);
/*< rnorm = sqrt(abs(rnorm)) >*/
rnorm = sqrt((abs(rnorm)));
/*< else if (bmat .eq. 'I') then >*/
} else if (*(unsigned char *)bmat == 'I') {
/*< rnorm = dnrm2(n, resid, 1) >*/
rnorm = dnrm2_(n, &resid[1], &c__1);
/*< end if >*/
}
/*< cnorm = .false. >*/
cnorm = FALSE_;
/*< 130 continue >*/
/* L130: */
/* if (msglvl .gt. 2) then */
/* call dvout (logfil, 1, rnorm, ndigit, */
/* & '_saup2: B-norm of residual for NEV factorization') */
/* call dvout (logfil, nev, h(1,2), ndigit, */
/* & '_saup2: main diagonal of compressed H matrix') */
/* call dvout (logfil, nev-1, h(2,1), ndigit, */
/* & '_saup2: subdiagonal of compressed H matrix') */
/* end if */
/*< go to 1000 >*/
goto L1000;
/* %---------------------------------------------------------------% */
/* | | */
/* | E N D O F M A I N I T E R A T I O N L O O P | */
/* | | */
/* %---------------------------------------------------------------% */
/*< 1100 continue >*/
L1100:
/*< mxiter = iter >*/
*mxiter = iter;
/*< nev = nconv >*/
*nev = nconv;
/*< 1200 continue >*/
L1200:
/*< ido = 99 >*/
*ido = 99;
/* %------------% */
/* | Error exit | */
/* %------------% */
/*< call second (t1) >*/
/* second_(&t1); */
/*< tsaup2 = t1 - t0 >*/
/* timing_1.tsaup2 = t1 - t0; */
/*< 9000 continue >*/
L9000:
/*< return >*/
return 0;
/* %---------------% */
/* | End of dsaup2 | */
/* %---------------% */
/*< end >*/
} /* dsaup2_ */
#ifdef __cplusplus
}
#endif
|
