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subroutine wgesl(ar,ai,lda,n,ipvt,br,bi,job)
c Copyright INRIA
integer lda,n,ipvt(*),job
double precision ar(lda,*),ai(lda,*),br(*),bi(*)
c!purpose
c
c wgesl solves the double-complex system
c a * x = b or ctrans(a) * x = b
c using the factors computed by wgeco or wgefa.
c
c!calling sequence
c
c subroutine wgesl(ar,ai,lda,n,ipvt,br,bi,job)
c on entry
c
c a double-complex(lda, n)
c the output from wgeco or wgefa.
c
c lda integer
c the leading dimension of the array a .
c
c n integer
c the order of the matrix a .
c
c ipvt integer(n)
c the pivot vector from wgeco or wgefa.
c
c b double-complex(n)
c the right hand side vector.
c
c job integer
c = 0 to solve a*x = b ,
c = nonzero to solve ctrans(a)*x = b where
c ctrans(a) is the conjugate transpose.
c
c on return
c
c b the solution vector x .
c
c error condition
c
c a division by zero will occur if the input factor contains a
c zero on the diagonal. technically this indicates singularity
c but it is often caused by improper arguments or improper
c setting of lda . it will not occur if the subroutines are
c called correctly and if wgeco has set rcond .gt. 0.0
c or wgefa has set info .eq. 0 .
c
c to compute inverse(a) * c where c is a matrix
c with p columns
c call wgeco(a,lda,n,ipvt,rcond,z)
c if (rcond is too small) go to ...
c do 10 j = 1, p
c call wgesl(a,lda,n,ipvt,c(1,j),0)
c 10 continue
c
c!originator
c linpack. this version dated 07/01/79 .
c cleve moler, university of new mexico, argonne national lab.
c
c!auxiliary routines
c
c blas waxpy,wdotc
c
c!
c internal variables
c
double precision wdotcr,wdotci,tr,ti
integer k,kb,l,nm1
c
nm1 = n - 1
if (job .ne. 0) go to 50
c
c job = 0 , solve a * x = b
c first solve l*y = b
c
if (nm1 .lt. 1) go to 30
do 20 k = 1, nm1
l = ipvt(k)
tr = br(l)
ti = bi(l)
if (l .eq. k) go to 10
br(l) = br(k)
bi(l) = bi(k)
br(k) = tr
bi(k) = ti
10 continue
call waxpy(n-k,tr,ti,ar(k+1,k),ai(k+1,k),1,br(k+1),bi(k+1),
* 1)
20 continue
30 continue
c
c now solve u*x = y
c
do 40 kb = 1, n
k = n + 1 - kb
call wdiv(br(k),bi(k),ar(k,k),ai(k,k),br(k),bi(k))
tr = -br(k)
ti = -bi(k)
call waxpy(k-1,tr,ti,ar(1,k),ai(1,k),1,br(1),bi(1),1)
40 continue
go to 100
50 continue
c
c job = nonzero, solve ctrans(a) * x = b
c first solve ctrans(u)*y = b
c
do 60 k = 1, n
tr = br(k) - wdotcr(k-1,ar(1,k),ai(1,k),1,br(1),bi(1),1)
ti = bi(k) - wdotci(k-1,ar(1,k),ai(1,k),1,br(1),bi(1),1)
call wdiv(tr,ti,ar(k,k),-ai(k,k),br(k),bi(k))
60 continue
c
c now solve ctrans(l)*x = y
c
if (nm1 .lt. 1) go to 90
do 80 kb = 1, nm1
k = n - kb
br(k) = br(k)
* + wdotcr(n-k,ar(k+1,k),ai(k+1,k),1,br(k+1),bi(k+1),1)
bi(k) = bi(k)
* + wdotci(n-k,ar(k+1,k),ai(k+1,k),1,br(k+1),bi(k+1),1)
l = ipvt(k)
if (l .eq. k) go to 70
tr = br(l)
ti = bi(l)
br(l) = br(k)
bi(l) = bi(k)
br(k) = tr
bi(k) = ti
70 continue
80 continue
90 continue
100 continue
return
end
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