836 lines
31 KiB
Fortran
836 lines
31 KiB
Fortran
c\BeginDoc
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c
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c\Name: snaup2
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c
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c\Description:
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c Intermediate level interface called by snaupd.
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c
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c\Usage:
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c call snaup2
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c ( IDO, BMAT, N, WHICH, NEV, NP, TOL, RESID, MODE, IUPD,
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c ISHIFT, MXITER, V, LDV, H, LDH, RITZR, RITZI, BOUNDS,
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c Q, LDQ, WORKL, IPNTR, WORKD, INFO )
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c
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c\Arguments
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c
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c IDO, BMAT, N, WHICH, NEV, TOL, RESID: same as defined in snaupd.
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c MODE, ISHIFT, MXITER: see the definition of IPARAM in snaupd.
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c
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c NP Integer. (INPUT/OUTPUT)
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c Contains the number of implicit shifts to apply during
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c each Arnoldi iteration.
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c If ISHIFT=1, NP is adjusted dynamically at each iteration
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c to accelerate convergence and prevent stagnation.
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c This is also roughly equal to the number of matrix-vector
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c products (involving the operator OP) per Arnoldi iteration.
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c The logic for adjusting is contained within the current
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c subroutine.
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c If ISHIFT=0, NP is the number of shifts the user needs
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c to provide via reverse comunication. 0 < NP < NCV-NEV.
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c NP may be less than NCV-NEV for two reasons. The first, is
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c to keep complex conjugate pairs of "wanted" Ritz values
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c together. The second, is that a leading block of the current
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c upper Hessenberg matrix has split off and contains "unwanted"
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c Ritz values.
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c Upon termination of the IRA iteration, NP contains the number
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c of "converged" wanted Ritz values.
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c
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c IUPD Integer. (INPUT)
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c IUPD .EQ. 0: use explicit restart instead implicit update.
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c IUPD .NE. 0: use implicit update.
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c
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c V Real N by (NEV+NP) array. (INPUT/OUTPUT)
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c The Arnoldi basis vectors are returned in the first NEV
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c columns of V.
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c
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c LDV Integer. (INPUT)
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c Leading dimension of V exactly as declared in the calling
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c program.
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c
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c H Real (NEV+NP) by (NEV+NP) array. (OUTPUT)
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c H is used to store the generated upper Hessenberg matrix
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c
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c LDH Integer. (INPUT)
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c Leading dimension of H exactly as declared in the calling
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c program.
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c
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c RITZR, Real arrays of length NEV+NP. (OUTPUT)
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c RITZI RITZR(1:NEV) (resp. RITZI(1:NEV)) contains the real (resp.
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c imaginary) part of the computed Ritz values of OP.
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c
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c BOUNDS Real array of length NEV+NP. (OUTPUT)
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c BOUNDS(1:NEV) contain the error bounds corresponding to
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c the computed Ritz values.
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c
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c Q Real (NEV+NP) by (NEV+NP) array. (WORKSPACE)
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c Private (replicated) work array used to accumulate the
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c rotation in the shift application step.
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c
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c LDQ Integer. (INPUT)
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c Leading dimension of Q exactly as declared in the calling
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c program.
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c
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c WORKL Real work array of length at least
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c (NEV+NP)**2 + 3*(NEV+NP). (INPUT/WORKSPACE)
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c Private (replicated) array on each PE or array allocated on
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c the front end. It is used in shifts calculation, shifts
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c application and convergence checking.
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c
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c On exit, the last 3*(NEV+NP) locations of WORKL contain
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c the Ritz values (real,imaginary) and associated Ritz
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c estimates of the current Hessenberg matrix. They are
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c listed in the same order as returned from sneigh.
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c
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c If ISHIFT .EQ. O and IDO .EQ. 3, the first 2*NP locations
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c of WORKL are used in reverse communication to hold the user
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c supplied shifts.
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c
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c IPNTR Integer array of length 3. (OUTPUT)
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c Pointer to mark the starting locations in the WORKD for
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c vectors used by the Arnoldi iteration.
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c -------------------------------------------------------------
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c IPNTR(1): pointer to the current operand vector X.
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c IPNTR(2): pointer to the current result vector Y.
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c IPNTR(3): pointer to the vector B * X when used in the
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c shift-and-invert mode. X is the current operand.
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c -------------------------------------------------------------
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c
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c WORKD Real work array of length 3*N. (WORKSPACE)
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c Distributed array to be used in the basic Arnoldi iteration
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c for reverse communication. The user should not use WORKD
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c as temporary workspace during the iteration !!!!!!!!!!
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c See Data Distribution Note in DNAUPD.
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c
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c INFO Integer. (INPUT/OUTPUT)
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c If INFO .EQ. 0, a randomly initial residual vector is used.
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c If INFO .NE. 0, RESID contains the initial residual vector,
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c possibly from a previous run.
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c Error flag on output.
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c = 0: Normal return.
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c = 1: Maximum number of iterations taken.
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c All possible eigenvalues of OP has been found.
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c NP returns the number of converged Ritz values.
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c = 2: No shifts could be applied.
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c = -8: Error return from LAPACK eigenvalue calculation;
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c This should never happen.
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c = -9: Starting vector is zero.
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c = -9999: Could not build an Arnoldi factorization.
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c Size that was built in returned in NP.
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c
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c\EndDoc
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c
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c-----------------------------------------------------------------------
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c
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c\BeginLib
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c
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c\Local variables:
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c xxxxxx real
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c
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c\References:
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c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in
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c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992),
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c pp 357-385.
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c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly
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c Restarted Arnoldi Iteration", Rice University Technical Report
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c TR95-13, Department of Computational and Applied Mathematics.
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c
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c\Routines called:
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c sgetv0 ARPACK initial vector generation routine.
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c snaitr ARPACK Arnoldi factorization routine.
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c snapps ARPACK application of implicit shifts routine.
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c snconv ARPACK convergence of Ritz values routine.
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c sneigh ARPACK compute Ritz values and error bounds routine.
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c sngets ARPACK reorder Ritz values and error bounds routine.
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c ssortc ARPACK sorting routine.
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c ivout ARPACK utility routine that prints integers.
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c second ARPACK utility routine for timing.
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c smout ARPACK utility routine that prints matrices
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c svout ARPACK utility routine that prints vectors.
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c slamch LAPACK routine that determines machine constants.
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c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully.
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c scopy Level 1 BLAS that copies one vector to another .
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c sdot Level 1 BLAS that computes the scalar product of two vectors.
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c snrm2 Level 1 BLAS that computes the norm of a vector.
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c sswap Level 1 BLAS that swaps two vectors.
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c
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c\Author
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c Danny Sorensen Phuong Vu
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c Richard Lehoucq CRPC / Rice University
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c Dept. of Computational & Houston, Texas
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c Applied Mathematics
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c Rice University
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c Houston, Texas
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c
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c\SCCS Information: @(#)
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c FILE: naup2.F SID: 2.8 DATE OF SID: 10/17/00 RELEASE: 2
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c
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c\Remarks
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c 1. None
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c
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c\EndLib
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c
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c-----------------------------------------------------------------------
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c
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subroutine snaup2
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& ( ido, bmat, n, which, nev, np, tol, resid, mode, iupd,
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& ishift, mxiter, v, ldv, h, ldh, ritzr, ritzi, bounds,
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& q, ldq, workl, ipntr, workd, info )
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c
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c %----------------------------------------------------%
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c | Include files for debugging and timing information |
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c %----------------------------------------------------%
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c
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include 'debug.h'
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include 'stat.h'
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c
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c %------------------%
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c | Scalar Arguments |
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c %------------------%
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c
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character bmat*1, which*2
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integer ido, info, ishift, iupd, mode, ldh, ldq, ldv, mxiter,
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& n, nev, np
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Real
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& tol
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c
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c %-----------------%
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c | Array Arguments |
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c %-----------------%
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c
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integer ipntr(13)
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Real
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& bounds(nev+np), h(ldh,nev+np), q(ldq,nev+np), resid(n),
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& ritzi(nev+np), ritzr(nev+np), v(ldv,nev+np),
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& workd(3*n), workl( (nev+np)*(nev+np+3) )
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c
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c %------------%
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c | Parameters |
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c %------------%
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c
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Real
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& one, zero
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parameter (one = 1.0E+0, zero = 0.0E+0)
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c
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c %---------------%
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c | Local Scalars |
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c %---------------%
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c
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character wprime*2
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logical cnorm , getv0, initv, update, ushift
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integer ierr , iter , j , kplusp, msglvl, nconv,
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& nevbef, nev0 , np0 , nptemp, numcnv
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Real
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& rnorm , temp , eps23
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save cnorm , getv0, initv, update, ushift,
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& rnorm , iter , eps23, kplusp, msglvl, nconv ,
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& nevbef, nev0 , np0 , numcnv
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c
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c %-----------------------%
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c | Local array arguments |
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c %-----------------------%
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c
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integer kp(4)
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c
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c %----------------------%
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c | External Subroutines |
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c %----------------------%
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c
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external scopy , sgetv0, snaitr, snconv, sneigh,
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& sngets, snapps, svout , ivout , second
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c
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c %--------------------%
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c | External Functions |
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c %--------------------%
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c
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Real
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& sdot, snrm2, slapy2, slamch
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external sdot, snrm2, slapy2, slamch
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c
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c %---------------------%
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c | Intrinsic Functions |
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c %---------------------%
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c
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intrinsic min, max, abs, sqrt
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c
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c %-----------------------%
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c | Executable Statements |
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c %-----------------------%
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c
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if (ido .eq. 0) then
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c
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call second (t0)
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c
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msglvl = mnaup2
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c
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c %-------------------------------------%
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c | Get the machine dependent constant. |
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c %-------------------------------------%
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c
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eps23 = slamch('Epsilon-Machine')
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eps23 = eps23**(2.0E+0 / 3.0E+0)
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c
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nev0 = nev
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np0 = np
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c
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c %-------------------------------------%
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c | kplusp is the bound on the largest |
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c | Lanczos factorization built. |
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c | nconv is the current number of |
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c | "converged" eigenvlues. |
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c | iter is the counter on the current |
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c | iteration step. |
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c %-------------------------------------%
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c
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kplusp = nev + np
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nconv = 0
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iter = 0
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c
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c %---------------------------------------%
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c | Set flags for computing the first NEV |
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c | steps of the Arnoldi factorization. |
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c %---------------------------------------%
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c
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getv0 = .true.
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update = .false.
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ushift = .false.
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cnorm = .false.
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c
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if (info .ne. 0) then
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c
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c %--------------------------------------------%
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c | User provides the initial residual vector. |
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c %--------------------------------------------%
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c
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initv = .true.
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info = 0
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else
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initv = .false.
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end if
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end if
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c
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c %---------------------------------------------%
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c | Get a possibly random starting vector and |
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c | force it into the range of the operator OP. |
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c %---------------------------------------------%
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c
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10 continue
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c
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if (getv0) then
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call sgetv0 (ido, bmat, 1, initv, n, 1, v, ldv, resid, rnorm,
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& ipntr, workd, info)
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c
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if (ido .ne. 99) go to 9000
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c
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if (rnorm .eq. zero) then
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c
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c %-----------------------------------------%
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c | The initial vector is zero. Error exit. |
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c %-----------------------------------------%
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c
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info = -9
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go to 1100
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end if
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getv0 = .false.
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ido = 0
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end if
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c
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c %-----------------------------------%
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c | Back from reverse communication : |
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c | continue with update step |
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c %-----------------------------------%
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c
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if (update) go to 20
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c
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c %-------------------------------------------%
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c | Back from computing user specified shifts |
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c %-------------------------------------------%
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c
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if (ushift) go to 50
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c
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c %-------------------------------------%
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c | Back from computing residual norm |
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c | at the end of the current iteration |
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c %-------------------------------------%
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c
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if (cnorm) go to 100
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c
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c %----------------------------------------------------------%
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c | Compute the first NEV steps of the Arnoldi factorization |
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c %----------------------------------------------------------%
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c
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call snaitr (ido, bmat, n, 0, nev, mode, resid, rnorm, v, ldv,
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& h, ldh, ipntr, workd, info)
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c
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c %---------------------------------------------------%
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c | ido .ne. 99 implies use of reverse communication |
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c | to compute operations involving OP and possibly B |
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c %---------------------------------------------------%
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c
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if (ido .ne. 99) go to 9000
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c
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if (info .gt. 0) then
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np = info
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mxiter = iter
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info = -9999
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go to 1200
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end if
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c
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c %--------------------------------------------------------------%
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c | |
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c | M A I N ARNOLDI I T E R A T I O N L O O P |
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c | Each iteration implicitly restarts the Arnoldi |
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c | factorization in place. |
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c | |
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c %--------------------------------------------------------------%
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c
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1000 continue
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c
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iter = iter + 1
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c
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if (msglvl .gt. 0) then
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call ivout (logfil, 1, iter, ndigit,
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& '_naup2: **** Start of major iteration number ****')
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end if
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c
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c %-----------------------------------------------------------%
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c | Compute NP additional steps of the Arnoldi factorization. |
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c | Adjust NP since NEV might have been updated by last call |
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c | to the shift application routine snapps. |
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c %-----------------------------------------------------------%
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c
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np = kplusp - nev
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c
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if (msglvl .gt. 1) then
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call ivout (logfil, 1, nev, ndigit,
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& '_naup2: The length of the current Arnoldi factorization')
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call ivout (logfil, 1, np, ndigit,
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& '_naup2: Extend the Arnoldi factorization by')
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end if
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c
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c %-----------------------------------------------------------%
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c | Compute NP additional steps of the Arnoldi factorization. |
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c %-----------------------------------------------------------%
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c
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ido = 0
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20 continue
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update = .true.
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c
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call snaitr (ido , bmat, n , nev, np , mode , resid,
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& rnorm, v , ldv, h , ldh, ipntr, workd,
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& info)
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c
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c %---------------------------------------------------%
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c | ido .ne. 99 implies use of reverse communication |
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c | to compute operations involving OP and possibly B |
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c %---------------------------------------------------%
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c
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if (ido .ne. 99) go to 9000
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c
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if (info .gt. 0) then
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np = info
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mxiter = iter
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info = -9999
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go to 1200
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end if
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update = .false.
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c
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if (msglvl .gt. 1) then
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call svout (logfil, 1, rnorm, ndigit,
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& '_naup2: Corresponding B-norm of the residual')
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end if
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c
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c %--------------------------------------------------------%
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c | Compute the eigenvalues and corresponding error bounds |
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c | of the current upper Hessenberg matrix. |
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c %--------------------------------------------------------%
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c
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call sneigh (rnorm, kplusp, h, ldh, ritzr, ritzi, bounds,
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& q, ldq, workl, ierr)
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c
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if (ierr .ne. 0) then
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info = -8
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go to 1200
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end if
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c
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c %----------------------------------------------------%
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c | Make a copy of eigenvalues and corresponding error |
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c | bounds obtained from sneigh. |
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c %----------------------------------------------------%
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c
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call scopy(kplusp, ritzr, 1, workl(kplusp**2+1), 1)
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call scopy(kplusp, ritzi, 1, workl(kplusp**2+kplusp+1), 1)
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call scopy(kplusp, bounds, 1, workl(kplusp**2+2*kplusp+1), 1)
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c
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c %---------------------------------------------------%
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c | Select the wanted Ritz values and their bounds |
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c | to be used in the convergence test. |
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c | The wanted part of the spectrum and corresponding |
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c | error bounds are in the last NEV loc. of RITZR, |
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c | RITZI and BOUNDS respectively. The variables NEV |
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c | and NP may be updated if the NEV-th wanted Ritz |
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c | value has a non zero imaginary part. In this case |
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c | NEV is increased by one and NP decreased by one. |
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c | NOTE: The last two arguments of sngets are no |
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c | longer used as of version 2.1. |
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c %---------------------------------------------------%
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c
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nev = nev0
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np = np0
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numcnv = nev
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call sngets (ishift, which, nev, np, ritzr, ritzi,
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& bounds, workl, workl(np+1))
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if (nev .eq. nev0+1) numcnv = nev0+1
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c
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c %-------------------%
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c | Convergence test. |
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c %-------------------%
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c
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call scopy (nev, bounds(np+1), 1, workl(2*np+1), 1)
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call snconv (nev, ritzr(np+1), ritzi(np+1), workl(2*np+1),
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& tol, nconv)
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c
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if (msglvl .gt. 2) then
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kp(1) = nev
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kp(2) = np
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kp(3) = numcnv
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kp(4) = nconv
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call ivout (logfil, 4, kp, ndigit,
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& '_naup2: NEV, NP, NUMCNV, NCONV are')
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call svout (logfil, kplusp, ritzr, ndigit,
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& '_naup2: Real part of the eigenvalues of H')
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call svout (logfil, kplusp, ritzi, ndigit,
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& '_naup2: Imaginary part of the eigenvalues of H')
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call svout (logfil, kplusp, bounds, ndigit,
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& '_naup2: Ritz estimates of the current NCV Ritz values')
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end if
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c
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c %---------------------------------------------------------%
|
|
c | Count the number of unwanted Ritz values that have zero |
|
|
c | Ritz estimates. If any Ritz estimates are equal to zero |
|
|
c | then a leading block of H of order equal to at least |
|
|
c | the number of Ritz values with zero Ritz estimates has |
|
|
c | split off. None of these Ritz values may be removed by |
|
|
c | shifting. Decrease NP the number of shifts to apply. If |
|
|
c | no shifts may be applied, then prepare to exit |
|
|
c %---------------------------------------------------------%
|
|
c
|
|
nptemp = np
|
|
do 30 j=1, nptemp
|
|
if (bounds(j) .eq. zero) then
|
|
np = np - 1
|
|
nev = nev + 1
|
|
end if
|
|
30 continue
|
|
c
|
|
if ( (nconv .ge. numcnv) .or.
|
|
& (iter .gt. mxiter) .or.
|
|
& (np .eq. 0) ) then
|
|
c
|
|
if (msglvl .gt. 4) then
|
|
call svout(logfil, kplusp, workl(kplusp**2+1), ndigit,
|
|
& '_naup2: Real part of the eig computed by _neigh:')
|
|
call svout(logfil, kplusp, workl(kplusp**2+kplusp+1),
|
|
& ndigit,
|
|
& '_naup2: Imag part of the eig computed by _neigh:')
|
|
call svout(logfil, kplusp, workl(kplusp**2+kplusp*2+1),
|
|
& ndigit,
|
|
& '_naup2: Ritz eistmates computed by _neigh:')
|
|
end if
|
|
c
|
|
c %------------------------------------------------%
|
|
c | Prepare to exit. Put the converged Ritz values |
|
|
c | and corresponding bounds in RITZ(1:NCONV) and |
|
|
c | BOUNDS(1:NCONV) respectively. Then sort. Be |
|
|
c | careful when NCONV > NP |
|
|
c %------------------------------------------------%
|
|
c
|
|
c %------------------------------------------%
|
|
c | Use h( 3,1 ) as storage to communicate |
|
|
c | rnorm to _neupd if needed |
|
|
c %------------------------------------------%
|
|
|
|
h(3,1) = rnorm
|
|
c
|
|
c %----------------------------------------------%
|
|
c | To be consistent with sngets, we first do a |
|
|
c | pre-processing sort in order to keep complex |
|
|
c | conjugate pairs together. This is similar |
|
|
c | to the pre-processing sort used in sngets |
|
|
c | except that the sort is done in the opposite |
|
|
c | order. |
|
|
c %----------------------------------------------%
|
|
c
|
|
if (which .eq. 'LM') wprime = 'SR'
|
|
if (which .eq. 'SM') wprime = 'LR'
|
|
if (which .eq. 'LR') wprime = 'SM'
|
|
if (which .eq. 'SR') wprime = 'LM'
|
|
if (which .eq. 'LI') wprime = 'SM'
|
|
if (which .eq. 'SI') wprime = 'LM'
|
|
c
|
|
call ssortc (wprime, .true., kplusp, ritzr, ritzi, bounds)
|
|
c
|
|
c %----------------------------------------------%
|
|
c | Now sort Ritz values so that converged Ritz |
|
|
c | values appear within the first NEV locations |
|
|
c | of ritzr, ritzi and bounds, and the most |
|
|
c | desired one appears at the front. |
|
|
c %----------------------------------------------%
|
|
c
|
|
if (which .eq. 'LM') wprime = 'SM'
|
|
if (which .eq. 'SM') wprime = 'LM'
|
|
if (which .eq. 'LR') wprime = 'SR'
|
|
if (which .eq. 'SR') wprime = 'LR'
|
|
if (which .eq. 'LI') wprime = 'SI'
|
|
if (which .eq. 'SI') wprime = 'LI'
|
|
c
|
|
call ssortc(wprime, .true., kplusp, ritzr, ritzi, bounds)
|
|
c
|
|
c %--------------------------------------------------%
|
|
c | Scale the Ritz estimate of each Ritz value |
|
|
c | by 1 / max(eps23,magnitude of the Ritz value). |
|
|
c %--------------------------------------------------%
|
|
c
|
|
do 35 j = 1, numcnv
|
|
temp = max(eps23,slapy2(ritzr(j),
|
|
& ritzi(j)))
|
|
bounds(j) = bounds(j)/temp
|
|
35 continue
|
|
c
|
|
c %----------------------------------------------------%
|
|
c | Sort the Ritz values according to the scaled Ritz |
|
|
c | esitmates. This will push all the converged ones |
|
|
c | towards the front of ritzr, ritzi, bounds |
|
|
c | (in the case when NCONV < NEV.) |
|
|
c %----------------------------------------------------%
|
|
c
|
|
wprime = 'LR'
|
|
call ssortc(wprime, .true., numcnv, bounds, ritzr, ritzi)
|
|
c
|
|
c %----------------------------------------------%
|
|
c | Scale the Ritz estimate back to its original |
|
|
c | value. |
|
|
c %----------------------------------------------%
|
|
c
|
|
do 40 j = 1, numcnv
|
|
temp = max(eps23, slapy2(ritzr(j),
|
|
& ritzi(j)))
|
|
bounds(j) = bounds(j)*temp
|
|
40 continue
|
|
c
|
|
c %------------------------------------------------%
|
|
c | Sort the converged Ritz values again so that |
|
|
c | the "threshold" value appears at the front of |
|
|
c | ritzr, ritzi and bound. |
|
|
c %------------------------------------------------%
|
|
c
|
|
call ssortc(which, .true., nconv, ritzr, ritzi, bounds)
|
|
c
|
|
if (msglvl .gt. 1) then
|
|
call svout (logfil, kplusp, ritzr, ndigit,
|
|
& '_naup2: Sorted real part of the eigenvalues')
|
|
call svout (logfil, kplusp, ritzi, ndigit,
|
|
& '_naup2: Sorted imaginary part of the eigenvalues')
|
|
call svout (logfil, kplusp, bounds, ndigit,
|
|
& '_naup2: Sorted ritz estimates.')
|
|
end if
|
|
c
|
|
c %------------------------------------%
|
|
c | Max iterations have been exceeded. |
|
|
c %------------------------------------%
|
|
c
|
|
if (iter .gt. mxiter .and. nconv .lt. numcnv) info = 1
|
|
c
|
|
c %---------------------%
|
|
c | No shifts to apply. |
|
|
c %---------------------%
|
|
c
|
|
if (np .eq. 0 .and. nconv .lt. numcnv) info = 2
|
|
c
|
|
np = nconv
|
|
go to 1100
|
|
c
|
|
else if ( (nconv .lt. numcnv) .and. (ishift .eq. 1) ) then
|
|
c
|
|
c %-------------------------------------------------%
|
|
c | Do not have all the requested eigenvalues yet. |
|
|
c | To prevent possible stagnation, adjust the size |
|
|
c | of NEV. |
|
|
c %-------------------------------------------------%
|
|
c
|
|
nevbef = nev
|
|
nev = nev + min(nconv, np/2)
|
|
if (nev .eq. 1 .and. kplusp .ge. 6) then
|
|
nev = kplusp / 2
|
|
else if (nev .eq. 1 .and. kplusp .gt. 3) then
|
|
nev = 2
|
|
end if
|
|
np = kplusp - nev
|
|
c
|
|
c %---------------------------------------%
|
|
c | If the size of NEV was just increased |
|
|
c | resort the eigenvalues. |
|
|
c %---------------------------------------%
|
|
c
|
|
if (nevbef .lt. nev)
|
|
& call sngets (ishift, which, nev, np, ritzr, ritzi,
|
|
& bounds, workl, workl(np+1))
|
|
c
|
|
end if
|
|
c
|
|
if (msglvl .gt. 0) then
|
|
call ivout (logfil, 1, nconv, ndigit,
|
|
& '_naup2: no. of "converged" Ritz values at this iter.')
|
|
if (msglvl .gt. 1) then
|
|
kp(1) = nev
|
|
kp(2) = np
|
|
call ivout (logfil, 2, kp, ndigit,
|
|
& '_naup2: NEV and NP are')
|
|
call svout (logfil, nev, ritzr(np+1), ndigit,
|
|
& '_naup2: "wanted" Ritz values -- real part')
|
|
call svout (logfil, nev, ritzi(np+1), ndigit,
|
|
& '_naup2: "wanted" Ritz values -- imag part')
|
|
call svout (logfil, nev, bounds(np+1), ndigit,
|
|
& '_naup2: Ritz estimates of the "wanted" values ')
|
|
end if
|
|
end if
|
|
c
|
|
if (ishift .eq. 0) then
|
|
c
|
|
c %-------------------------------------------------------%
|
|
c | User specified shifts: reverse comminucation to |
|
|
c | compute the shifts. They are returned in the first |
|
|
c | 2*NP locations of WORKL. |
|
|
c %-------------------------------------------------------%
|
|
c
|
|
ushift = .true.
|
|
ido = 3
|
|
go to 9000
|
|
end if
|
|
c
|
|
50 continue
|
|
c
|
|
c %------------------------------------%
|
|
c | Back from reverse communication; |
|
|
c | User specified shifts are returned |
|
|
c | in WORKL(1:2*NP) |
|
|
c %------------------------------------%
|
|
c
|
|
ushift = .false.
|
|
c
|
|
if ( ishift .eq. 0 ) then
|
|
c
|
|
c %----------------------------------%
|
|
c | Move the NP shifts from WORKL to |
|
|
c | RITZR, RITZI to free up WORKL |
|
|
c | for non-exact shift case. |
|
|
c %----------------------------------%
|
|
c
|
|
call scopy (np, workl, 1, ritzr, 1)
|
|
call scopy (np, workl(np+1), 1, ritzi, 1)
|
|
end if
|
|
c
|
|
if (msglvl .gt. 2) then
|
|
call ivout (logfil, 1, np, ndigit,
|
|
& '_naup2: The number of shifts to apply ')
|
|
call svout (logfil, np, ritzr, ndigit,
|
|
& '_naup2: Real part of the shifts')
|
|
call svout (logfil, np, ritzi, ndigit,
|
|
& '_naup2: Imaginary part of the shifts')
|
|
if ( ishift .eq. 1 )
|
|
& call svout (logfil, np, bounds, ndigit,
|
|
& '_naup2: Ritz estimates of the shifts')
|
|
end if
|
|
c
|
|
c %---------------------------------------------------------%
|
|
c | Apply the NP implicit shifts by QR bulge chasing. |
|
|
c | Each shift is applied to the whole upper Hessenberg |
|
|
c | matrix H. |
|
|
c | The first 2*N locations of WORKD are used as workspace. |
|
|
c %---------------------------------------------------------%
|
|
c
|
|
call snapps (n, nev, np, ritzr, ritzi, v, ldv,
|
|
& h, ldh, resid, q, ldq, workl, workd)
|
|
c
|
|
c %---------------------------------------------%
|
|
c | Compute the B-norm of the updated residual. |
|
|
c | Keep B*RESID in WORKD(1:N) to be used in |
|
|
c | the first step of the next call to snaitr. |
|
|
c %---------------------------------------------%
|
|
c
|
|
cnorm = .true.
|
|
call second (t2)
|
|
if (bmat .eq. 'G') then
|
|
nbx = nbx + 1
|
|
call scopy (n, resid, 1, workd(n+1), 1)
|
|
ipntr(1) = n + 1
|
|
ipntr(2) = 1
|
|
ido = 2
|
|
c
|
|
c %----------------------------------%
|
|
c | Exit in order to compute B*RESID |
|
|
c %----------------------------------%
|
|
c
|
|
go to 9000
|
|
else if (bmat .eq. 'I') then
|
|
call scopy (n, resid, 1, workd, 1)
|
|
end if
|
|
c
|
|
100 continue
|
|
c
|
|
c %----------------------------------%
|
|
c | Back from reverse communication; |
|
|
c | WORKD(1:N) := B*RESID |
|
|
c %----------------------------------%
|
|
c
|
|
if (bmat .eq. 'G') then
|
|
call second (t3)
|
|
tmvbx = tmvbx + (t3 - t2)
|
|
end if
|
|
c
|
|
if (bmat .eq. 'G') then
|
|
rnorm = sdot (n, resid, 1, workd, 1)
|
|
rnorm = sqrt(abs(rnorm))
|
|
else if (bmat .eq. 'I') then
|
|
rnorm = snrm2(n, resid, 1)
|
|
end if
|
|
cnorm = .false.
|
|
c
|
|
if (msglvl .gt. 2) then
|
|
call svout (logfil, 1, rnorm, ndigit,
|
|
& '_naup2: B-norm of residual for compressed factorization')
|
|
call smout (logfil, nev, nev, h, ldh, ndigit,
|
|
& '_naup2: Compressed upper Hessenberg matrix H')
|
|
end if
|
|
c
|
|
go to 1000
|
|
c
|
|
c %---------------------------------------------------------------%
|
|
c | |
|
|
c | E N D O F M A I N I T E R A T I O N L O O P |
|
|
c | |
|
|
c %---------------------------------------------------------------%
|
|
c
|
|
1100 continue
|
|
c
|
|
mxiter = iter
|
|
nev = numcnv
|
|
c
|
|
1200 continue
|
|
ido = 99
|
|
c
|
|
c %------------%
|
|
c | Error Exit |
|
|
c %------------%
|
|
c
|
|
call second (t1)
|
|
tnaup2 = t1 - t0
|
|
c
|
|
9000 continue
|
|
c
|
|
c %---------------%
|
|
c | End of snaup2 |
|
|
c %---------------%
|
|
c
|
|
return
|
|
end
|