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it_rfn.f
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it_rfn.f
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CM
C->>> --------------------------------------------------> ems_it_rfn <<<
c Perform iterative refinement of the solution given by the INVERT
c of Ax=b or A^Tx=b, that is -A^{-1}b or -A^{-T}b.
c
c Use x+dx = -A^{-1}b or x+dx = -A^{-T}b
c => -A(x+dx) = b -A^T(x+dx) = b
c => -Adx = b+Ax -A^Tdx = b+A^Tx
c => dx = -A^{-1}(b+Ax) dx = -A^{-T}(b+A^Tx)
c
subroutine ems_it_rfn(
& ems_rt_cod, is, ds, rp_lvl,
& trans,
& vr_in_r,
& mtx_r_v, mtx_r_ix, mtx_c_sa,
& sol_v, sol_ix,
& rhs_v, rhs_ix,
& rsdu_v,
& mx_n_rfn_it, tl_it_rfn_norm_rsdu, it_rfn_tran_ze,
& msg)
implicit none
include 'EMSV.INC'
include 'EMSPM.INC'
include 'EMSMMGR.INC'
include 'EMSMEM.INC'
include 'EMSP.INC'
include 'ICTVR.INC'
include 'RLCTVR.INC'
include 'EMSMSG.INC'
include 'EMSRTCOD.INC'
integer ems_rt_cod, rp_lvl
logical trans
integer vr_in_r(0:n_r)
integer mtx_r_ix(0:n_a_el)
integer mtx_c_sa(0:n_c+1)
integer sol_ix(0:n_r)
integer rhs_ix(0:n_r)
integer is(0:is_n_en_m1)
double precision mtx_r_v(0:n_a_el)
double precision sol_v(0:n_r)
double precision rhs_v(0:n_r)
double precision rsdu_v(0:n_r)
double precision ds(0:ds_n_en_m1)
character*(*) msg
integer mx_n_rfn_it
double precision tl_it_rfn_norm_rsdu
double precision it_rfn_tran_ze
double precision tl_it_rfn_norm_dl
integer r_n, vr_n, c_n, el_n, og_r_n, nw_r_n
double precision sol_r_v, dl
logical perm_inv
logical alw_f7_wr
character*6 ch6_sys
integer sys_l_ch
character*12 ch12_norm_rsdu
integer norm_rsdu_f_ch
double precision sv_tran_ze
integer rfn_it_n
double precision it_rfn_iz_norm_rsdu
double precision it_rfn_norm_rsdu
double precision it_rfn_norm_dl
c integer wg_r_n
c print*, ' Enter component of solution to corrupt '
c read*, wg_r_n
c if (wg_r_n .ge. 1 .and. wg_r_n .le. n_r) then
c print*, ' Enter alternative for ', sol_v(wg_r_n)
c read*, sol_v(wg_r_n)
c endif
ems_rt_cod = ems_rt_cod_ok
perm_inv = iand(inv_alg_msk, inv_alg_perm) .ne. 0
alw_f7_wr = ems_msg_no_prt_fm .ge. 1
tl_it_rfn_norm_dl = zero
if (trans) then
c
c The solution to be refined is that of A^Tx=b
c
ch6_sys = 'A^Tx=b'
sys_l_ch = 6
ch12_norm_rsdu = '||A^Tx-b||_2'
norm_rsdu_f_ch = 1
else
ch6_sys = 'Ax=b '
sys_l_ch = 4
ch12_norm_rsdu = ' ||Ax-b||_2'
norm_rsdu_f_ch = 3
endif
CM IF (emsol_dev .EQ. 1) THEN
C? if (rp_lvl .ge. 1) then
C? if (alw_f7_wr) write(ems_li, 9100, err=8990)
C? & ch6_sys(1:sys_l_ch), msg
C? call ems_msg_wr_li(info_msg_n)
C? if (rp_lvl .ge. 2) then
C? if (alw_f7_wr) write(ems_li, 9200, err=8990)
C? & ch12_norm_rsdu
C? call ems_msg_wr_li(info_msg_n)
C? endif
C? endif
CM ENDIF
c
c Make sure that the vector used to store the residual is zeroed
c
do 1, r_n = 1, n_r
rsdu_v(r_n) = zero
1 continue
rfn_it_n = 0
it_rfn_norm_dl = inf
10 continue
c
c Form y = b
c
if (rhs_ix(0) .lt. 0) then
c
c It is assumed that, for vr_n = -rhs_ix(0), the RHS is
c rhs_v(0)*a_{vr_n}, where a_{vr_n} is the corresponding column of
c [A:-I]
c
vr_n = -rhs_ix(0)
if (vr_n .le. n_c) then
do 20, el_n = mtx_c_sa(vr_n), mtx_c_sa(vr_n+1)-1
r_n = mtx_r_ix(el_n)
rsdu_v(r_n) = rhs_v(0)*mtx_r_v(el_n)
20 continue
else
r_n = vr_n - mx_n_c
rsdu_v(r_n) = -rhs_v(0)
endif
else
do 110, r_n = 1, n_r
rsdu_v(r_n) = rhs_v(r_n)
110 continue
endif
c do r_n = 1, n_r
c write(*, 9300)r_n,
c & ' sol_v(r_n) = ', sol_v(r_n),
c & ' rhs_v(r_n) = ', rsdu_v(r_n)
c enddo
if (trans) then
c
c Form y := y + A^Tx
c
do 130, r_n = 1, n_r
vr_n = vr_in_r(r_n)
if (vr_n .le. n_c) then
do 120, el_n = mtx_c_sa(vr_n), mtx_c_sa(vr_n+1)-1
c_n = mtx_r_ix(el_n)
rsdu_v(r_n) = rsdu_v(r_n) + mtx_r_v(el_n)*sol_v(c_n)
120 continue
else
c_n = vr_n - mx_n_c
rsdu_v(r_n) = rsdu_v(r_n) - sol_v(c_n)
endif
130 continue
else
c
c Form y := y + Ax
c
do 150, c_n = 1, n_r
sol_r_v = sol_v(c_n)
if (sol_r_v .eq. zero) goto 150
vr_n = vr_in_r(c_n)
if (vr_n .le. n_c) then
do 140, el_n = mtx_c_sa(vr_n), mtx_c_sa(vr_n+1)-1
r_n = mtx_r_ix(el_n)
rsdu_v(r_n) = rsdu_v(r_n) + mtx_r_v(el_n)*sol_r_v
140 continue
else
r_n = vr_n - mx_n_c
rsdu_v(r_n) = rsdu_v(r_n) - sol_r_v
endif
150 continue
endif
c do r_n = 1, n_r
c write(*, 9300)r_n,
c & ' rsdu_v(r_n) = ', rsdu_v(r_n)
c enddo
it_rfn_norm_rsdu = zero
do 160, r_n = 1, n_r
c write(*, 9300)r_n, ' rsdu_v(r_n) = ', rsdu_v(r_n)
it_rfn_norm_rsdu =
& it_rfn_norm_rsdu + rsdu_v(r_n)*rsdu_v(r_n)
160 continue
it_rfn_norm_rsdu = sqrt(it_rfn_norm_rsdu)
if (rfn_it_n .eq. 0) it_rfn_iz_norm_rsdu = it_rfn_norm_rsdu
if (rfn_it_n .ge. mx_n_rfn_it .or.
& it_rfn_norm_dl .le. tl_it_rfn_norm_dl .or.
& it_rfn_norm_rsdu .le. tl_it_rfn_norm_rsdu) then
c
c One of the termination criteria is satisfied.
c
do 170, r_n = 1, n_r
rsdu_v(r_n) = zero
170 continue
CM IF (emsol_dev .EQ. 1) THEN
C? if (rp_lvl .ge. 2) then
C? if (alw_f7_wr) write(ems_li, 9202, err=8990)
C? & rfn_it_n+1, it_rfn_norm_rsdu
C? call ems_msg_wr_li(info_msg_n)
C? else if (rp_lvl .ge. 1) then
C? if (alw_f7_wr) write(ems_li, 9201, err=8990)
C? & rfn_it_n, ch12_norm_rsdu(norm_rsdu_f_ch:12),
C? & it_rfn_iz_norm_rsdu, it_rfn_norm_rsdu
C? call ems_msg_wr_li(info_msg_n)
C? endif
CM ENDIF
goto 7000
endif
c
c Perform an iteration of refinement.
c
rfn_it_n = rfn_it_n + 1
if (trans) then
c
c Form y := -A^{-T}y
c
sv_tran_ze = bwd_tran_ze
bwd_tran_ze = it_rfn_tran_ze
call ems_btran(rsdu_v, n_r+1, ds, is)
bwd_tran_ze = sv_tran_ze
else
c
c Form y := -A^{-1}y
c
if (perm_inv) then
c
c Permute the RHS in copying from rsdu to perm_rsdu.
c
do 210, og_r_n = 1, n_r
r_n = is(p_og_t_nw_perm+og_r_n)
ds(p_perm_tran_vec+r_n) = rsdu_v(og_r_n)
rsdu_v(og_r_n) = zero
210 continue
sv_tran_ze = fwd_tran_ze
fwd_tran_ze = it_rfn_tran_ze
call ems_ftran(ds(p_perm_tran_vec), n_r+1, ds, is)
fwd_tran_ze = sv_tran_ze
else
c
c If not permuting INVERT
c
sv_tran_ze = fwd_tran_ze
fwd_tran_ze = it_rfn_tran_ze
call ems_ftran(rsdu_v, n_r+1, ds, is)
fwd_tran_ze = sv_tran_ze
endif
endif
c
c Form x: = x + y and zero the vector used to compute y.
c
it_rfn_norm_dl = zero
if (perm_inv) then
c
c If permuting INVERT
c
if (trans) then
c
c If refining the solution to A^Tx=b, correction is in rsdu_v and
c have to apply permutation in updating x.
c
do 310, nw_r_n = 1, n_r
dl = rsdu_v(nw_r_n)
it_rfn_norm_dl = it_rfn_norm_dl + dl*dl
r_n = is(p_nw_t_og_perm+nw_r_n)
sol_v(r_n) = sol_v(r_n) + dl
rsdu_v(nw_r_n) = zero
310 continue
else
c
c If refining the solution to Ax=b, correction is in perm_tran_vec.
c
do 320, r_n = 1, n_r
dl = ds(p_perm_tran_vec+r_n)
it_rfn_norm_dl = it_rfn_norm_dl + dl*dl
sol_v(r_n) = sol_v(r_n) + dl
ds(p_perm_tran_vec+r_n) = zero
320 continue
endif
else
c
c If not permuting INVERT then correction is in rsdu_v
c
do 330, r_n = 1, n_r
dl = rsdu_v(r_n)
it_rfn_norm_dl = it_rfn_norm_dl + dl*dl
sol_v(r_n) = sol_v(r_n) + dl
rsdu_v(r_n) = zero
330 continue
endif
it_rfn_norm_dl = sqrt(it_rfn_norm_dl)
CM IF (emsol_dev .EQ. 1) THEN
C? if (rp_lvl .ge. 2) then
C? if (alw_f7_wr) write(ems_li, 9202, err=8990)
C? & rfn_it_n, it_rfn_norm_rsdu, it_rfn_norm_dl
C? call ems_msg_wr_li(info_msg_n)
C? endif
CM ENDIF
goto 10
7000 continue
CM IF (emsol_dev .EQ. 1) THEN
C? 7100 continue
CM ENDIF
return
CM IF (emsol_dev .EQ. 1) THEN
C? 8990 continue
C? ems_rt_cod = max(ems_rt_cod_serious_f7_wr_er,
C? & ems_rt_cod)
C? goto 7100
C? 9100 format('Performing iterative refinement on solution of ', a,
C? & ': ', a)
C? 9200 format(' It ', a12, ' ||dx||_2')
C? 9201 format('After ', i3, ' iterations, ', a,
C? & ' has changed from ', g11.4, ' to ', g11.4)
C? 9202 format(i3, 2x, 2(2x, g11.4))
CM ENDIF
c 9300 format(i5, 2(2x, a, g11.4))
end