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C Copyright (c) 2003-2010 University of Florida
C
C This program is free software; you can redistribute it and/or modify
C it under the terms of the GNU General Public License as published by
C the Free Software Foundation; either version 2 of the License, or
C (at your option) any later version.
C This program is distributed in the hope that it will be useful,
C but WITHOUT ANY WARRANTY; without even the implied warranty of
C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
C GNU General Public License for more details.
C The GNU General Public License is included in this distribution
C in the file COPYRIGHT.
subroutine flowqsdmin(scratch, grad, ehess, eigvh, dmr1, dmr2,
& stp, eps, nx, ndim, ncycle)
c
c This subroutine implements the quadratic gradient descent
c algorithm of J.-Q. Sun and K.Ruedenberg in JCP 99, 5257 (1993).
c
implicit double precision(a-h, o-z)
#include "fnamelen.par"
character*(fnamelen) fname
logical yesno, update, nwtonrpson, negeval, genstpsz
c
dimension scratch(nx*nx), grad(ndim), ehess(ndim, ndim),
& eigvh(ndim, ndim), dmr1(ndim, ndim), dmr2(ndim,ndim)
c
c find the eigenvalues and eigenvectors of the hessian to build the
c solution to eqn. 11 in Sun & Ruedenberg.
c
call eig(ehess, eigvh, ndim, ndim, 1)
c
c Find the tangential vector, the scalar curvature, and define some
c ad hoc factors from Sun & Ruedenburg.
c
update = .false.
nwtonrpson = .false.
negeval = .false.
genstpsz = .true.
unew = 0.0d0
u_upper = 0.0d0
u_lower = 0.0d0
hvalue = 0.0d0
anu = 5.0d0/6.0d0
c
call qsdline(scratch, ehess, eigvh, dmr1, dmr2, unew, u_upper,
& u_lower, hvalue, curvtre, ndim, nx, update,
& nwtonrpson, negeval, genstpsz)
c
c construct the curvature dependent step size (eqn. 20b)
c
crvdstsz = 0.25d0 + (0.75d0)/(1.d0 + 3.0d0*curvtre**anu)
Write(6, *) "The value of curv =", curvtre
eh = 0.3d0*crvdstsz
Write(6, *) "The value of stpsize = ", eh
c
c
c if (ncycle .eq. 1) then
c
c P_0=Q_0=R_0 at the initial point. Calculate P* and Q_1 and
c Save P*
c
c call xdcopy(ndim, scratch(1), 1, scratch(1 + 2*ndim), 1)
c call getptspqr(scratch, ehess, eigvh, dmr1, dmr2,
c & (eh/2)**2, eps, nx, ndim)
c
c open(unit = 99, file = "QSDPINTS", form = "formatted")
c write(99, 999) eh
c write(99, 9999) (scratch(i + 2*ndim), i = 1, ndim)
c
c Get the Q_1 based on P*
c
call getptspqr(scratch, ehess, eigvh, dmr1, dmr2,
& (eh/2.0d0), eps, nx, ndim)
c call vadd(scratch(1 + 2*ndim), scratch(1 + 2*ndim),
c & scratch(1), ndim, -1.0d0)
c
c call xdcopy(ndim, scratch(1 + 2*ndim), 1, scratch(1 + ndim),
c & 1)
c
c else if (ncycle .eq. 2) then
c
c Calculate R_1 based on P*
c
c call gfname('QSDPINTS', fname, ilength)
c inquire(file=fname(1:ilength), exist=yesno)
c if (yesno) open(unit = 99, file = "QSDPINTS",
c & form = "formatted", status ="old")
c
c read(99, 999) ehp
c read(99, 9999) (scratch(i + 2*ndim), i = 1, ndim)
c call getptspqr(scratch, ehess, eigvh, dmr1, dmr2,
c & (ehp/4.0d0)**2, eps, nx, ndim)
c
c Calculate P_1 based on Q_1
c
c call xdcopy(ndim, scratch(1), 1, scratch(1 + 2*ndim), 1)
c call getptspqr(scratch, ehess, eigvh, dmr1, dmr2,
c & (ehp/2.0d0)**2, eps, nx, ndim)
c rewind(99)
c write(99, 999) eh
c write(99, 9999) (scratch(i + 2*ndim), i = 1, ndim)
c
c Calculate Q_2 based on P_1
c
c call getptspqr(scratch, ehess, eigvh, dmr1, dmr2,
c & (eh/2.0d0)**2, eps, nx, ndim)
c
c call vadd(scratch(1 + 2*ndim), scratch(1 + 2*ndim),
c & scratch(1), ndim, -1.0d0)
c
c call xdcopy(ndim, scratch(1 + 2*ndim), 1, scratch(1 + ndim),
c & 1)
c
c else
c
c Calculate R_n based on P_n-1
c
c call gfname('QSDPINTS', fname, ilength)
c inquire(file=fname(1:ilength), exist=yesno)
c if (yesno) open(unit = 99, file = "QSDPINTS",
c & form = "formatted", status="old")
c
c read(99, 999) ehp
c read(99, 9999) (scratch(i + 2*ndim), i = 1, ndim)
c call getptspqr(scratch, ehess, eigvh, dmr1, dmr2,
c & (ehp/2.0d0)**2, eps, nx, ndim)
c
c Calculate P_n based on Q_n
c
c call xdcopy(ndim, scratch(1), 1, scratch(1 + 2*ndim), 1)
c call getptspqr(scratch, ehess, eigvh, dmr1, dmr2,
c & (eh/2.0d0)**2, eps, nx, ndim)
c rewind(99)
c write(99, 999) eh
c write(99, 9999) (scratch(i + 2*ndim), i = 1, ndim)
c
c Calculate Q_n+1 based on P_n
c
c call getptspqr(scratch, ehess, eigvh, dmr1, dmr2,
c & (eh/2.0d0)**2, eps, nx, ndim)
c
c call vadd(scratch(1 + 2*ndim), scratch(1 + 2*ndim),
c & scratch(1), ndim, -1.0d0)
c
c call xdcopy(ndim, scratch(1 + 2*ndim), 1,
c & scratch(1 + ndim), 1)
c
c
c endif
c
999 format(1x, f15.8)
9999 format(1x, 3(f15.8, 1x))
c
return
end
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