415 lines
13 KiB
Fortran
415 lines
13 KiB
Fortran
c\BeginDoc
|
|
c
|
|
c\Name: cgetv0
|
|
c
|
|
c\Description:
|
|
c Generate a random initial residual vector for the Arnoldi process.
|
|
c Force the residual vector to be in the range of the operator OP.
|
|
c
|
|
c\Usage:
|
|
c call cgetv0
|
|
c ( IDO, BMAT, ITRY, INITV, N, J, V, LDV, RESID, RNORM,
|
|
c IPNTR, WORKD, IERR )
|
|
c
|
|
c\Arguments
|
|
c IDO Integer. (INPUT/OUTPUT)
|
|
c Reverse communication flag. IDO must be zero on the first
|
|
c call to cgetv0.
|
|
c -------------------------------------------------------------
|
|
c IDO = 0: first call to the reverse communication interface
|
|
c IDO = -1: compute Y = OP * X where
|
|
c IPNTR(1) is the pointer into WORKD for X,
|
|
c IPNTR(2) is the pointer into WORKD for Y.
|
|
c This is for the initialization phase to force the
|
|
c starting vector into the range of OP.
|
|
c IDO = 2: compute Y = B * X where
|
|
c IPNTR(1) is the pointer into WORKD for X,
|
|
c IPNTR(2) is the pointer into WORKD for Y.
|
|
c IDO = 99: done
|
|
c -------------------------------------------------------------
|
|
c
|
|
c BMAT Character*1. (INPUT)
|
|
c BMAT specifies the type of the matrix B in the (generalized)
|
|
c eigenvalue problem A*x = lambda*B*x.
|
|
c B = 'I' -> standard eigenvalue problem A*x = lambda*x
|
|
c B = 'G' -> generalized eigenvalue problem A*x = lambda*B*x
|
|
c
|
|
c ITRY Integer. (INPUT)
|
|
c ITRY counts the number of times that cgetv0 is called.
|
|
c It should be set to 1 on the initial call to cgetv0.
|
|
c
|
|
c INITV Logical variable. (INPUT)
|
|
c .TRUE. => the initial residual vector is given in RESID.
|
|
c .FALSE. => generate a random initial residual vector.
|
|
c
|
|
c N Integer. (INPUT)
|
|
c Dimension of the problem.
|
|
c
|
|
c J Integer. (INPUT)
|
|
c Index of the residual vector to be generated, with respect to
|
|
c the Arnoldi process. J > 1 in case of a "restart".
|
|
c
|
|
c V Complex N by J array. (INPUT)
|
|
c The first J-1 columns of V contain the current Arnoldi basis
|
|
c if this is a "restart".
|
|
c
|
|
c LDV Integer. (INPUT)
|
|
c Leading dimension of V exactly as declared in the calling
|
|
c program.
|
|
c
|
|
c RESID Complex array of length N. (INPUT/OUTPUT)
|
|
c Initial residual vector to be generated. If RESID is
|
|
c provided, force RESID into the range of the operator OP.
|
|
c
|
|
c RNORM Real scalar. (OUTPUT)
|
|
c B-norm of the generated residual.
|
|
c
|
|
c IPNTR Integer array of length 3. (OUTPUT)
|
|
c
|
|
c WORKD Complex work array of length 2*N. (REVERSE COMMUNICATION).
|
|
c On exit, WORK(1:N) = B*RESID to be used in SSAITR.
|
|
c
|
|
c IERR Integer. (OUTPUT)
|
|
c = 0: Normal exit.
|
|
c = -1: Cannot generate a nontrivial restarted residual vector
|
|
c in the range of the operator OP.
|
|
c
|
|
c\EndDoc
|
|
c
|
|
c-----------------------------------------------------------------------
|
|
c
|
|
c\BeginLib
|
|
c
|
|
c\Local variables:
|
|
c xxxxxx Complex
|
|
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
|
|
c\Routines called:
|
|
c second ARPACK utility routine for timing.
|
|
c cvout ARPACK utility routine that prints vectors.
|
|
c clarnv LAPACK routine for generating a random vector.
|
|
c cgemv Level 2 BLAS routine for matrix vector multiplication.
|
|
c ccopy Level 1 BLAS that copies one vector to another.
|
|
c cdotc Level 1 BLAS that computes the scalar product of two vectors.
|
|
c scnrm2 Level 1 BLAS that computes the norm of a vector.
|
|
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\SCCS Information: @(#)
|
|
c FILE: getv0.F SID: 2.3 DATE OF SID: 08/27/96 RELEASE: 2
|
|
c
|
|
c\EndLib
|
|
c
|
|
c-----------------------------------------------------------------------
|
|
c
|
|
subroutine cgetv0
|
|
& ( ido, bmat, itry, initv, n, j, v, ldv, resid, rnorm,
|
|
& ipntr, workd, ierr )
|
|
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
|
|
logical initv
|
|
integer ido, ierr, itry, j, ldv, n
|
|
Real
|
|
& rnorm
|
|
c
|
|
c %-----------------%
|
|
c | Array Arguments |
|
|
c %-----------------%
|
|
c
|
|
integer ipntr(3)
|
|
Complex
|
|
& resid(n), v(ldv,j), workd(2*n)
|
|
c
|
|
c %------------%
|
|
c | Parameters |
|
|
c %------------%
|
|
c
|
|
Complex
|
|
& one, zero
|
|
Real
|
|
& rzero
|
|
parameter (one = (1.0E+0, 0.0E+0), zero = (0.0E+0, 0.0E+0),
|
|
& rzero = 0.0E+0)
|
|
c
|
|
c %------------------------%
|
|
c | Local Scalars & Arrays |
|
|
c %------------------------%
|
|
c
|
|
logical first, inits, orth
|
|
integer idist, iseed(4), iter, msglvl, jj
|
|
Real
|
|
& rnorm0
|
|
Complex
|
|
& cnorm
|
|
save first, iseed, inits, iter, msglvl, orth, rnorm0
|
|
c
|
|
c %----------------------%
|
|
c | External Subroutines |
|
|
c %----------------------%
|
|
c
|
|
external ccopy, cgemv, clarnv, cvout, second
|
|
c
|
|
c %--------------------%
|
|
c | External Functions |
|
|
c %--------------------%
|
|
c
|
|
Real
|
|
& scnrm2, slapy2
|
|
Complex
|
|
& cdotc
|
|
external cdotc, scnrm2, slapy2
|
|
c
|
|
c %-----------------%
|
|
c | Data Statements |
|
|
c %-----------------%
|
|
c
|
|
data inits /.true./
|
|
c
|
|
c %-----------------------%
|
|
c | Executable Statements |
|
|
c %-----------------------%
|
|
c
|
|
c
|
|
c %-----------------------------------%
|
|
c | Initialize the seed of the LAPACK |
|
|
c | random number generator |
|
|
c %-----------------------------------%
|
|
c
|
|
if (inits) then
|
|
iseed(1) = 1
|
|
iseed(2) = 3
|
|
iseed(3) = 5
|
|
iseed(4) = 7
|
|
inits = .false.
|
|
end if
|
|
c
|
|
if (ido .eq. 0) then
|
|
c
|
|
c %-------------------------------%
|
|
c | Initialize timing statistics |
|
|
c | & message level for debugging |
|
|
c %-------------------------------%
|
|
c
|
|
call second (t0)
|
|
msglvl = mgetv0
|
|
c
|
|
ierr = 0
|
|
iter = 0
|
|
first = .FALSE.
|
|
orth = .FALSE.
|
|
c
|
|
c %-----------------------------------------------------%
|
|
c | Possibly generate a random starting vector in RESID |
|
|
c | Use a LAPACK random number generator used by the |
|
|
c | matrix generation routines. |
|
|
c | idist = 1: uniform (0,1) distribution; |
|
|
c | idist = 2: uniform (-1,1) distribution; |
|
|
c | idist = 3: normal (0,1) distribution; |
|
|
c %-----------------------------------------------------%
|
|
c
|
|
if (.not.initv) then
|
|
idist = 2
|
|
call clarnv (idist, iseed, n, resid)
|
|
end if
|
|
c
|
|
c %----------------------------------------------------------%
|
|
c | Force the starting vector into the range of OP to handle |
|
|
c | the generalized problem when B is possibly (singular). |
|
|
c %----------------------------------------------------------%
|
|
c
|
|
call second (t2)
|
|
if (bmat .eq. 'G') then
|
|
nopx = nopx + 1
|
|
ipntr(1) = 1
|
|
ipntr(2) = n + 1
|
|
call ccopy (n, resid, 1, workd, 1)
|
|
ido = -1
|
|
go to 9000
|
|
end if
|
|
end if
|
|
c
|
|
c %----------------------------------------%
|
|
c | Back from computing B*(initial-vector) |
|
|
c %----------------------------------------%
|
|
c
|
|
if (first) go to 20
|
|
c
|
|
c %-----------------------------------------------%
|
|
c | Back from computing B*(orthogonalized-vector) |
|
|
c %-----------------------------------------------%
|
|
c
|
|
if (orth) go to 40
|
|
c
|
|
call second (t3)
|
|
tmvopx = tmvopx + (t3 - t2)
|
|
c
|
|
c %------------------------------------------------------%
|
|
c | Starting vector is now in the range of OP; r = OP*r; |
|
|
c | Compute B-norm of starting vector. |
|
|
c %------------------------------------------------------%
|
|
c
|
|
call second (t2)
|
|
first = .TRUE.
|
|
if (bmat .eq. 'G') then
|
|
nbx = nbx + 1
|
|
call ccopy (n, workd(n+1), 1, resid, 1)
|
|
ipntr(1) = n + 1
|
|
ipntr(2) = 1
|
|
ido = 2
|
|
go to 9000
|
|
else if (bmat .eq. 'I') then
|
|
call ccopy (n, resid, 1, workd, 1)
|
|
end if
|
|
c
|
|
20 continue
|
|
c
|
|
if (bmat .eq. 'G') then
|
|
call second (t3)
|
|
tmvbx = tmvbx + (t3 - t2)
|
|
end if
|
|
c
|
|
first = .FALSE.
|
|
if (bmat .eq. 'G') then
|
|
cnorm = cdotc (n, resid, 1, workd, 1)
|
|
rnorm0 = sqrt(slapy2(real(cnorm),aimag(cnorm)))
|
|
else if (bmat .eq. 'I') then
|
|
rnorm0 = scnrm2(n, resid, 1)
|
|
end if
|
|
rnorm = rnorm0
|
|
c
|
|
c %---------------------------------------------%
|
|
c | Exit if this is the very first Arnoldi step |
|
|
c %---------------------------------------------%
|
|
c
|
|
if (j .eq. 1) go to 50
|
|
c
|
|
c %----------------------------------------------------------------
|
|
c | Otherwise need to B-orthogonalize the starting vector against |
|
|
c | the current Arnoldi basis using Gram-Schmidt with iter. ref. |
|
|
c | This is the case where an invariant subspace is encountered |
|
|
c | in the middle of the Arnoldi factorization. |
|
|
c | |
|
|
c | s = V^{T}*B*r; r = r - V*s; |
|
|
c | |
|
|
c | Stopping criteria used for iter. ref. is discussed in |
|
|
c | Parlett's book, page 107 and in Gragg & Reichel TOMS paper. |
|
|
c %---------------------------------------------------------------%
|
|
c
|
|
orth = .TRUE.
|
|
30 continue
|
|
c
|
|
call cgemv ('C', n, j-1, one, v, ldv, workd, 1,
|
|
& zero, workd(n+1), 1)
|
|
call cgemv ('N', n, j-1, -one, v, ldv, workd(n+1), 1,
|
|
& one, resid, 1)
|
|
c
|
|
c %----------------------------------------------------------%
|
|
c | Compute the B-norm of the orthogonalized starting vector |
|
|
c %----------------------------------------------------------%
|
|
c
|
|
call second (t2)
|
|
if (bmat .eq. 'G') then
|
|
nbx = nbx + 1
|
|
call ccopy (n, resid, 1, workd(n+1), 1)
|
|
ipntr(1) = n + 1
|
|
ipntr(2) = 1
|
|
ido = 2
|
|
go to 9000
|
|
else if (bmat .eq. 'I') then
|
|
call ccopy (n, resid, 1, workd, 1)
|
|
end if
|
|
c
|
|
40 continue
|
|
c
|
|
if (bmat .eq. 'G') then
|
|
call second (t3)
|
|
tmvbx = tmvbx + (t3 - t2)
|
|
end if
|
|
c
|
|
if (bmat .eq. 'G') then
|
|
cnorm = cdotc (n, resid, 1, workd, 1)
|
|
rnorm = sqrt(slapy2(real(cnorm),aimag(cnorm)))
|
|
else if (bmat .eq. 'I') then
|
|
rnorm = scnrm2(n, resid, 1)
|
|
end if
|
|
c
|
|
c %--------------------------------------%
|
|
c | Check for further orthogonalization. |
|
|
c %--------------------------------------%
|
|
c
|
|
if (msglvl .gt. 2) then
|
|
call svout (logfil, 1, rnorm0, ndigit,
|
|
& '_getv0: re-orthonalization ; rnorm0 is')
|
|
call svout (logfil, 1, rnorm, ndigit,
|
|
& '_getv0: re-orthonalization ; rnorm is')
|
|
end if
|
|
c
|
|
if (rnorm .gt. 0.717*rnorm0) go to 50
|
|
c
|
|
iter = iter + 1
|
|
if (iter .le. 1) then
|
|
c
|
|
c %-----------------------------------%
|
|
c | Perform iterative refinement step |
|
|
c %-----------------------------------%
|
|
c
|
|
rnorm0 = rnorm
|
|
go to 30
|
|
else
|
|
c
|
|
c %------------------------------------%
|
|
c | Iterative refinement step "failed" |
|
|
c %------------------------------------%
|
|
c
|
|
do 45 jj = 1, n
|
|
resid(jj) = zero
|
|
45 continue
|
|
rnorm = rzero
|
|
ierr = -1
|
|
end if
|
|
c
|
|
50 continue
|
|
c
|
|
if (msglvl .gt. 0) then
|
|
call svout (logfil, 1, rnorm, ndigit,
|
|
& '_getv0: B-norm of initial / restarted starting vector')
|
|
end if
|
|
if (msglvl .gt. 2) then
|
|
call cvout (logfil, n, resid, ndigit,
|
|
& '_getv0: initial / restarted starting vector')
|
|
end if
|
|
ido = 99
|
|
c
|
|
call second (t1)
|
|
tgetv0 = tgetv0 + (t1 - t0)
|
|
c
|
|
9000 continue
|
|
return
|
|
c
|
|
c %---------------%
|
|
c | End of cgetv0 |
|
|
c %---------------%
|
|
c
|
|
end
|