octave-nkf: libcruft/arpack/src/dsaup2.f comparison

comparison libcruft/arpack/src/dsaup2.f @ 12274:9f5d2ef078e8 release-3-4-x

import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1

author	John W. Eaton <jwe@octave.org>
date	Fri, 28 Jan 2011 14:04:33 -0500
parents
children

comparison

equal deleted inserted replaced

-:83133b5bf392
+:9f5d2ef078e8
+c-----------------------------------------------------------------------
+c\BeginDoc
+c
+c\Name: dsaup2
+c
+c\Description:
+c  Intermediate level interface called by dsaupd.
+c
+c\Usage:
+c  call dsaup2
+c     ( IDO, BMAT, N, WHICH, NEV, NP, TOL, RESID, MODE, IUPD,
+c       ISHIFT, MXITER, V, LDV, H, LDH, RITZ, BOUNDS, Q, LDQ, WORKL,
+c       IPNTR, WORKD, INFO )
+c
+c\Arguments
+c
+c  IDO, BMAT, N, WHICH, NEV, TOL, RESID: same as defined in dsaupd.
+c  MODE, ISHIFT, MXITER: see the definition of IPARAM in dsaupd.
+c
+c  NP      Integer.  (INPUT/OUTPUT)
+c          Contains the number of implicit shifts to apply during
+c          each Arnoldi/Lanczos iteration.
+c          If ISHIFT=1, NP is adjusted dynamically at each iteration
+c          to accelerate convergence and prevent stagnation.
+c          This is also roughly equal to the number of matrix-vector
+c          products (involving the operator OP) per Arnoldi iteration.
+c          The logic for adjusting is contained within the current
+c          subroutine.
+c          If ISHIFT=0, NP is the number of shifts the user needs
+c          to provide via reverse comunication. 0 < NP < NCV-NEV.
+c          NP may be less than NCV-NEV since a leading block of the current
+c          upper Tridiagonal matrix has split off and contains "unwanted"
+c          Ritz values.
+c          Upon termination of the IRA iteration, NP contains the number
+c          of "converged" wanted Ritz values.
+c
+c  IUPD    Integer.  (INPUT)
+c          IUPD .EQ. 0: use explicit restart instead implicit update.
+c          IUPD .NE. 0: use implicit update.
+c
+c  V       Double precision N by (NEV+NP) array.  (INPUT/OUTPUT)
+c          The Lanczos basis vectors.
+c
+c  LDV     Integer.  (INPUT)
+c          Leading dimension of V exactly as declared in the calling
+c          program.
+c
+c  H       Double precision (NEV+NP) by 2 array.  (OUTPUT)
+c          H is used to store the generated symmetric tridiagonal matrix
+c          The subdiagonal is stored in the first column of H starting
+c          at H(2,1).  The main diagonal is stored in the arscnd column
+c          of H starting at H(1,2). If dsaup2 converges store the
+c          B-norm of the final residual vector in H(1,1).
+c
+c  LDH     Integer.  (INPUT)
+c          Leading dimension of H exactly as declared in the calling
+c          program.
+c
+c  RITZ    Double precision array of length NEV+NP.  (OUTPUT)
+c          RITZ(1:NEV) contains the computed Ritz values of OP.
+c
+c  BOUNDS  Double precision array of length NEV+NP.  (OUTPUT)
+c          BOUNDS(1:NEV) contain the error bounds corresponding to RITZ.
+c
+c  Q       Double precision (NEV+NP) by (NEV+NP) array.  (WORKSPACE)
+c          Private (replicated) work array used to accumulate the
+c          rotation in the shift application step.
+c
+c  LDQ     Integer.  (INPUT)
+c          Leading dimension of Q exactly as declared in the calling
+c          program.
+c
+c  WORKL   Double precision array of length at least 3*(NEV+NP).  (INPUT/WORKSPACE)
+c          Private (replicated) array on each PE or array allocated on
+c          the front end.  It is used in the computation of the
+c          tridiagonal eigenvalue problem, the calculation and
+c          application of the shifts and convergence checking.
+c          If ISHIFT .EQ. O and IDO .EQ. 3, the first NP locations
+c          of WORKL are used in reverse communication to hold the user
+c          supplied shifts.
+c
+c  IPNTR   Integer array of length 3.  (OUTPUT)
+c          Pointer to mark the starting locations in the WORKD for
+c          vectors used by the Lanczos iteration.
+c          -------------------------------------------------------------
+c          IPNTR(1): pointer to the current operand vector X.
+c          IPNTR(2): pointer to the current result vector Y.
+c          IPNTR(3): pointer to the vector B * X when used in one of
+c                    the spectral transformation modes.  X is the current
+c                    operand.
+c          -------------------------------------------------------------
+c
+c  WORKD   Double precision work array of length 3*N.  (REVERSE COMMUNICATION)
+c          Distributed array to be used in the basic Lanczos iteration
+c          for reverse communication.  The user should not use WORKD
+c          as temporary workspace during the iteration !!!!!!!!!!
+c          See Data Distribution Note in dsaupd.
+c
+c  INFO    Integer.  (INPUT/OUTPUT)
+c          If INFO .EQ. 0, a randomly initial residual vector is used.
+c          If INFO .NE. 0, RESID contains the initial residual vector,
+c                          possibly from a previous run.
+c          Error flag on output.
+c          =     0: Normal return.
+c          =     1: All possible eigenvalues of OP has been found.
+c                   NP returns the size of the invariant subspace
+c                   spanning the operator OP.
+c          =     2: No shifts could be applied.
+c          =    -8: Error return from trid. eigenvalue calculation;
+c                   This should never happen.
+c          =    -9: Starting vector is zero.
+c          = -9999: Could not build an Lanczos factorization.
+c                   Size that was built in returned in NP.
+c
+c\EndDoc
+c
+c-----------------------------------------------------------------------
+c
+c\BeginLib
+c
+c\References:
+c  1. D.C. Sorensen, "Implicit Application of Polynomial Filters in
+c     a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992),
+c     pp 357-385.
+c  2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly
+c     Restarted Arnoldi Iteration", Rice University Technical Report
+c     TR95-13, Department of Computational and Applied Mathematics.
+c  3. B.N. Parlett, "The Symmetric Eigenvalue Problem". Prentice-Hall,
+c     1980.
+c  4. B.N. Parlett, B. Nour-Omid, "Towards a Black Box Lanczos Program",
+c     Computer Physics Communications, 53 (1989), pp 169-179.
+c  5. B. Nour-Omid, B.N. Parlett, T. Ericson, P.S. Jensen, "How to
+c     Implement the Spectral Transformation", Math. Comp., 48 (1987),
+c     pp 663-673.
+c  6. R.G. Grimes, J.G. Lewis and H.D. Simon, "A Shifted Block Lanczos
+c     Algorithm for Solving Sparse Symmetric Generalized Eigenproblems",
+c     SIAM J. Matr. Anal. Apps.,  January (1993).
+c  7. L. Reichel, W.B. Gragg, "Algorithm 686: FORTRAN Subroutines
+c     for Updating the QR decomposition", ACM TOMS, December 1990,
+c     Volume 16 Number 4, pp 369-377.
+c
+c\Routines called:
+c     dgetv0  ARPACK initial vector generation routine.
+c     dsaitr  ARPACK Lanczos factorization routine.
+c     dsapps  ARPACK application of implicit shifts routine.
+c     dsconv  ARPACK convergence of Ritz values routine.
+c     dseigt  ARPACK compute Ritz values and error bounds routine.
+c     dsgets  ARPACK reorder Ritz values and error bounds routine.
+c     dsortr  ARPACK sorting routine.
+c     ivout   ARPACK utility routine that prints integers.
+c     arscnd  ARPACK utility routine for timing.
+c     dvout   ARPACK utility routine that prints vectors.
+c     dlamch  LAPACK routine that determines machine constants.
+c     dcopy   Level 1 BLAS that copies one vector to another.
+c     ddot    Level 1 BLAS that computes the scalar product of two vectors.
+c     dnrm2   Level 1 BLAS that computes the norm of a vector.
+c     dscal   Level 1 BLAS that scales a vector.
+c     dswap   Level 1 BLAS that swaps two vectors.
+c
+c\Author
+c     Danny Sorensen               Phuong Vu
+c     Richard Lehoucq              CRPC / Rice University
+c     Dept. of Computational &     Houston, Texas
+c     Applied Mathematics
+c     Rice University
+c     Houston, Texas
+c
+c\Revision history:
+c     12/15/93: Version ' 2.4'
+c     xx/xx/95: Version ' 2.4'.  (R.B. Lehoucq)
+c
+c\SCCS Information: @(#)
+c FILE: saup2.F   SID: 2.7   DATE OF SID: 5/19/98   RELEASE: 2
+c
+c\EndLib
+c
+c-----------------------------------------------------------------------
+c
+subroutine 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 )
+c
+c     %----------------------------------------------------%
+c     | Include files for debugging and timing information |
+c     %----------------------------------------------------%
+c
+include   'debug.h'
+include   'stat.h'
+c
+c     %------------------%
+c     | Scalar Arguments |
+c     %------------------%
+c
+character  bmat*1, which*2
+integer    ido, info, ishift, iupd, ldh, ldq, ldv, mxiter,
+&           n, mode, nev, np
+Double precision
+&           tol
+c
+c     %-----------------%
+c     | Array Arguments |
+c     %-----------------%
+c
+integer    ipntr(3)
+Double precision
+&           bounds(nev+np), h(ldh,2), q(ldq,nev+np), resid(n),
+&           ritz(nev+np), v(ldv,nev+np), workd(3*n),
+&           workl(3*(nev+np))
+c
+c     %------------%
+c     | Parameters |
+c     %------------%
+c
+Double precision
+&           one, zero
+parameter (one = 1.0D+0, zero = 0.0D+0)
+c
+c     %---------------%
+c     | Local Scalars |
+c     %---------------%
+c
+character  wprime*2
+logical    cnorm, getv0, initv, update, ushift
+integer    ierr, iter, j, kplusp, msglvl, nconv, nevbef, nev0,
+&           np0, nptemp, nevd2, nevm2, kp(3)
+Double precision
+&           rnorm, temp, eps23
+save       cnorm, getv0, initv, update, ushift,
+&           iter, kplusp, msglvl, nconv, nev0, np0,
+&           rnorm, eps23
+c
+c     %----------------------%
+c     | External Subroutines |
+c     %----------------------%
+c
+external   dcopy, dgetv0, dsaitr, dscal, dsconv, dseigt, dsgets,
+&           dsapps, dsortr, dvout, ivout, arscnd, dswap
+c
+c     %--------------------%
+c     | External Functions |
+c     %--------------------%
+c
+Double precision
+&           ddot, dnrm2, dlamch
+external   ddot, dnrm2, dlamch
+c
+c     %---------------------%
+c     | Intrinsic Functions |
+c     %---------------------%
+c
+intrinsic    min
+c
+c     %-----------------------%
+c     | Executable Statements |
+c     %-----------------------%
+c
+if (ido .eq. 0) then
+c
+c        %-------------------------------%
+c        | Initialize timing statistics  |
+c        | & message level for debugging |
+c        %-------------------------------%
+c
+call arscnd (t0)
+msglvl = msaup2
+c
+c        %---------------------------------%
+c        | Set machine dependent constant. |
+c        %---------------------------------%
+c
+eps23 = dlamch('Epsilon-Machine')
+eps23 = eps23**(2.0D+0/3.0D+0)
+c
+c        %-------------------------------------%
+c        | nev0 and np0 are integer variables  |
+c        | hold the initial values of NEV & NP |
+c        %-------------------------------------%
+c
+nev0   = nev
+np0    = np
+c
+c        %-------------------------------------%
+c        | kplusp is the bound on the largest  |
+c        |        Lanczos factorization built. |
+c        | nconv is the current number of      |
+c        |        "converged" eigenvlues.      |
+c        | iter is the counter on the current  |
+c        |      iteration step.                |
+c        %-------------------------------------%
+c
+kplusp = nev0 + np0
+nconv  = 0
+iter   = 0
+c
+c        %--------------------------------------------%
+c        | Set flags for computing the first NEV steps |
+c        | of the Lanczos factorization.              |
+c        %--------------------------------------------%
+c
+getv0    = .true.
+update   = .false.
+ushift   = .false.
+cnorm    = .false.
+c
+if (info .ne. 0) then
+c
+c        %--------------------------------------------%
+c        | User provides the initial residual vector. |
+c        %--------------------------------------------%
+c
+initv = .true.
+info  = 0
+else
+initv = .false.
+end if
+end if
+c
+c     %---------------------------------------------%
+c     | Get a possibly random starting vector and   |
+c     | force it into the range of the operator OP. |
+c     %---------------------------------------------%
+c
+10 continue
+c
+if (getv0) then
+call dgetv0 (ido, bmat, 1, initv, n, 1, v, ldv, resid, rnorm,
+&                ipntr, workd, info)
+c
+if (ido .ne. 99) go to 9000
+c
+if (rnorm .eq. zero) then
+c
+c           %-----------------------------------------%
+c           | The initial vector is zero. Error exit. |
+c           %-----------------------------------------%
+c
+info = -9
+go to 1200
+end if
+getv0 = .false.
+ido  = 0
+end if
+c
+c     %------------------------------------------------------------%
+c     | Back from reverse communication: continue with update step |
+c     %------------------------------------------------------------%
+c
+if (update) go to 20
+c
+c     %-------------------------------------------%
+c     | Back from computing user specified shifts |
+c     %-------------------------------------------%
+c
+if (ushift) go to 50
+c
+c     %-------------------------------------%
+c     | Back from computing residual norm   |
+c     | at the end of the current iteration |
+c     %-------------------------------------%
+c
+if (cnorm)  go to 100
+c
+c     %----------------------------------------------------------%
+c     | Compute the first NEV steps of the Lanczos factorization |
+c     %----------------------------------------------------------%
+c
+call dsaitr (ido, bmat, n, 0, nev0, mode, resid, rnorm, v, ldv,
+&             h, ldh, ipntr, workd, info)
+c
+c     %---------------------------------------------------%
+c     | ido .ne. 99 implies use of reverse communication  |
+c     | to compute operations involving OP and possibly B |
+c     %---------------------------------------------------%
+c
+if (ido .ne. 99) go to 9000
+c
+if (info .gt. 0) then
+c
+c        %-----------------------------------------------------%
+c        | dsaitr was unable to build an Lanczos factorization |
+c        | of length NEV0. INFO is returned with the size of   |
+c        | the factorization built. Exit main loop.            |
+c        %-----------------------------------------------------%
+c
+np   = info
+mxiter = iter
+info = -9999
+go to 1200
+end if
+c
+c     %--------------------------------------------------------------%
+c     |                                                              |
+c     |           M A I N  LANCZOS  I T E R A T I O N  L O O P       |
+c     |           Each iteration implicitly restarts the Lanczos     |
+c     |           factorization in place.                            |
+c     |                                                              |
+c     %--------------------------------------------------------------%
+c
+1000 continue
+c
+iter = iter + 1
+c
+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
+c
+c        %------------------------------------------------------------%
+c        | Compute NP additional steps of the Lanczos factorization. |
+c        %------------------------------------------------------------%
+c
+ido = 0
+20    continue
+update = .true.
+c
+call dsaitr (ido, bmat, n, nev, np, mode, resid, rnorm, v,
+&                ldv, h, ldh, ipntr, workd, info)
+c
+c        %---------------------------------------------------%
+c        | ido .ne. 99 implies use of reverse communication  |
+c        | to compute operations involving OP and possibly B |
+c        %---------------------------------------------------%
+c
+if (ido .ne. 99) go to 9000
+c
+if (info .gt. 0) then
+c
+c           %-----------------------------------------------------%
+c           | dsaitr was unable to build an Lanczos factorization |
+c           | of length NEV0+NP0. INFO is returned with the size  |
+c           | of the factorization built. Exit main loop.         |
+c           %-----------------------------------------------------%
+c
+np = info
+mxiter = iter
+info = -9999
+go to 1200
+end if
+update = .false.
+c
+if (msglvl .gt. 1) then
+call dvout (logfil, 1, rnorm, ndigit,
+&           '_saup2: Current B-norm of residual for factorization')
+end if
+c
+c        %--------------------------------------------------------%
+c        | Compute the eigenvalues and corresponding error bounds |
+c        | of the current symmetric tridiagonal matrix.           |
+c        %--------------------------------------------------------%
+c
+call dseigt (rnorm, kplusp, h, ldh, ritz, bounds, workl, ierr)
+c
+if (ierr .ne. 0) then
+info = -8
+go to 1200
+end if
+c
+c        %----------------------------------------------------%
+c        | Make a copy of eigenvalues and corresponding error |
+c        | bounds obtained from _seigt.                       |
+c        %----------------------------------------------------%
+c
+call dcopy(kplusp, ritz, 1, workl(kplusp+1), 1)
+call dcopy(kplusp, bounds, 1, workl(2*kplusp+1), 1)
+c
+c        %---------------------------------------------------%
+c        | Select the wanted Ritz values and their bounds    |
+c        | to be used in the convergence test.               |
+c        | The selection is based on the requested number of |
+c        | eigenvalues instead of the current NEV and NP to  |
+c        | prevent possible misconvergence.                  |
+c        | * Wanted Ritz values := RITZ(NP+1:NEV+NP)         |
+c        | * Shifts := RITZ(1:NP) := WORKL(1:NP)             |
+c        %---------------------------------------------------%
+c
+nev = nev0
+np = np0
+call dsgets (ishift, which, nev, np, ritz, bounds, workl)
+c
+c        %-------------------%
+c        | Convergence test. |
+c        %-------------------%
+c
+call dcopy (nev, bounds(np+1), 1, workl(np+1), 1)
+call dsconv (nev, ritz(np+1), workl(np+1), tol, nconv)
+c
+if (msglvl .gt. 2) then
+kp(1) = nev
+kp(2) = np
+kp(3) = 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
+c
+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. nev0) .or.
+&        (iter .gt. mxiter) .or.
+&        (np .eq. 0) ) then
+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 since we don't want to |
+c           | swap overlapping locations.                    |
+c           %------------------------------------------------%
+c
+if (which .eq. 'BE') then
+c
+c              %-----------------------------------------------------%
+c              | Both ends of the spectrum are requested.            |
+c              | Sort the eigenvalues into algebraically decreasing  |
+c              | order first then swap low end of the spectrum next  |
+c              | to high end in appropriate locations.               |
+c              | NOTE: when np < floor(nev/2) be careful not to swap |
+c              | overlapping locations.                              |
+c              %-----------------------------------------------------%
+c
+wprime = 'SA'
+call dsortr (wprime, .true., kplusp, ritz, bounds)
+nevd2 = nev0 / 2
+nevm2 = nev0 - nevd2
+if ( nev .gt. 1 ) then
+call dswap ( min(nevd2,np), ritz(nevm2+1), 1,
+&                 ritz( max(kplusp-nevd2+1,kplusp-np+1) ), 1)
+call dswap ( min(nevd2,np), bounds(nevm2+1), 1,
+&                 bounds( max(kplusp-nevd2+1,kplusp-np+1)), 1)
+end if
+c
+else
+c
+c              %--------------------------------------------------%
+c              | LM, SM, LA, SA case.                             |
+c              | Sort the eigenvalues of H into the an order that |
+c              | is opposite to WHICH, and apply the resulting    |
+c              | order to BOUNDS.  The eigenvalues are sorted so  |
+c              | that the wanted part are always within the first |
+c              | NEV locations.                                   |
+c              %--------------------------------------------------%
+c
+if (which .eq. 'LM') wprime = 'SM'
+if (which .eq. 'SM') wprime = 'LM'
+if (which .eq. 'LA') wprime = 'SA'
+if (which .eq. 'SA') wprime = 'LA'
+c
+call dsortr (wprime, .true., kplusp, ritz, bounds)
+c
+end if
+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, nev0
+temp = max( eps23, abs(ritz(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 = 'LA'
+call dsortr(wprime, .true., nev0, bounds, ritz)
+c
+c           %----------------------------------------------%
+c           | Scale the Ritz estimate back to its original |
+c           | value.                                       |
+c           %----------------------------------------------%
+c
+do 40 j = 1, nev0
+temp = max( eps23, abs(ritz(j)) )
+bounds(j) = bounds(j)*temp
+40         continue
+c
+c           %--------------------------------------------------%
+c           | Sort the "converged" Ritz values again so that   |
+c           | the "threshold" values and their associated Ritz |
+c           | estimates appear at the appropriate position in  |
+c           | ritz and bound.                                  |
+c           %--------------------------------------------------%
+c
+if (which .eq. 'BE') then
+c
+c              %------------------------------------------------%
+c              | Sort the "converged" Ritz values in increasing |
+c              | order.  The "threshold" values are in the      |
+c              | middle.                                        |
+c              %------------------------------------------------%
+c
+wprime = 'LA'
+call dsortr(wprime, .true., nconv, ritz, bounds)
+c
+else
+c
+c              %----------------------------------------------%
+c              | In LM, SM, LA, SA case, sort the "converged" |
+c              | Ritz values according to WHICH so that the   |
+c              | "threshold" value appears at the front of    |
+c              | ritz.                                        |
+c              %----------------------------------------------%
+call dsortr(which, .true., nconv, ritz, bounds)
+c
+end if
+c
+c           %------------------------------------------%
+c           |  Use h( 1,1 ) as storage to communicate  |
+c           |  rnorm to _seupd if needed               |
+c           %------------------------------------------%
+c
+h(1,1) = rnorm
+c
+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
+c
+c           %------------------------------------%
+c           | Max iterations have been exceeded. |
+c           %------------------------------------%
+c
+if (iter .gt. mxiter .and. nconv .lt. nev) info = 1
+c
+c           %---------------------%
+c           | No shifts to apply. |
+c           %---------------------%
+c
+if (np .eq. 0 .and. nconv .lt. nev0) info = 2
+c
+np = nconv
+go to 1100
+c
+else if (nconv .lt. nev .and. ishift .eq. 1) then
+c
+c           %---------------------------------------------------%
+c           | Do not have all the requested eigenvalues yet.    |
+c           | To prevent possible stagnation, adjust the number |
+c           | of Ritz values and the shifts.                    |
+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. 2) 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 dsgets (ishift, which, nev, np, ritz, bounds,
+&              workl)
+c
+end if
+c
+if (msglvl .gt. 0) then
+call ivout (logfil, 1, nconv, ndigit,
+&           '_saup2: 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,
+&              '_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
+c
+if (ishift .eq. 0) then
+c
+c           %-----------------------------------------------------%
+c           | User specified shifts: reverse communication to     |
+c           | compute the shifts. They are returned in the first  |
+c           | 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:*NP)                   |
+c        %------------------------------------%
+c
+ushift = .false.
+c
+c
+c        %---------------------------------------------------------%
+c        | Move the NP shifts to the first NP locations of RITZ to |
+c        | free up WORKL.  This is for the non-exact shift case;   |
+c        | in the exact shift case, dsgets already handles this.   |
+c        %---------------------------------------------------------%
+c
+if (ishift .eq. 0) call dcopy (np, workl, 1, ritz, 1)
+c
+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
+c
+c        %---------------------------------------------------------%
+c        | Apply the NP0 implicit shifts by QR bulge chasing.      |
+c        | Each shift is applied to the entire tridiagonal matrix. |
+c        | The first 2*N locations of WORKD are used as workspace. |
+c        | After dsapps is done, we have a Lanczos                 |
+c        | factorization of length NEV.                            |
+c        %---------------------------------------------------------%
+c
+call dsapps (n, nev, np, ritz, v, ldv, h, ldh, resid, q, ldq,
+&        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 dsaitr.  |
+c        %---------------------------------------------%
+c
+cnorm = .true.
+call arscnd (t2)
+if (bmat .eq. 'G') then
+nbx = nbx + 1
+call dcopy (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 dcopy (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 arscnd (t3)
+tmvbx = tmvbx + (t3 - t2)
+end if
+c
+if (bmat .eq. 'G') then
+rnorm = ddot (n, resid, 1, workd, 1)
+rnorm = sqrt(abs(rnorm))
+else if (bmat .eq. 'I') then
+rnorm = dnrm2(n, resid, 1)
+end if
+cnorm = .false.
+130    continue
+c
+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
+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 = nconv
+c
+1200 continue
+ido = 99
+c
+c     %------------%
+c     | Error exit |
+c     %------------%
+c
+call arscnd (t1)
+tsaup2 = t1 - t0
+c
+9000 continue
+return
+c
+c     %---------------%
+c     | End of dsaup2 |
+c     %---------------%
+c
+end

Mercurial > octave-nkf

comparison libcruft/arpack/src/dsaup2.f @ 12274:9f5d2ef078e8 release-3-4-x