subroutine ctrco(t,ldt,n,rcond,z,job)
integer ldt,n,job
complex t(ldt,1),z(1)
real rcond
c
c ctrco estimates the condition of a complex triangular matrix.
c
c on entry
c
c t complex(ldt,n)
c t contains the triangular matrix. the zero
c elements of the matrix are not referenced, and
c the corresponding elements of the array can be
c used to store other information.
c
c ldt integer
c ldt is the leading dimension of the array t.
c
c n integer
c n is the order of the system.
c
c job integer
c = 0 t is lower triangular.
c = nonzero t is upper triangular.
c
c on return
c
c rcond real
c an estimate of the reciprocal condition of t .
c for the system t*x = b , relative perturbations
c in t and b of size epsilon may cause
c relative perturbations in x of size epsilon/rcond .
c if rcond is so small that the logical expression
c 1.0 + rcond .eq. 1.0
c is true, then t may be singular to working
c precision. in particular, rcond is zero if
c exact singularity is detected or the estimate
c underflows.
c
c z complex(n)
c a work vector whose contents are usually unimportant.
c if t is close to a singular matrix, then z is
c an approximate null vector in the sense that
c norm(a*z) = rcond*norm(a)*norm(z) .
c
c linpack. this version dated 08/14/78 .
c cleve moler, university of new mexico, argonne national lab.
c
c subroutines and functions
c
c blas caxpy,csscal,scasum
c fortran abs,aimag,amax1,cmplx,conjg,real
c
c internal variables
c
complex w,wk,wkm,ek
real tnorm,ynorm,s,sm,scasum
integer i1,j,j1,j2,k,kk,l
logical lower
complex zdum,zdum1,zdum2,csign1
real cabs1
cabs1(zdum) = abs(real(zdum)) + abs(aimag(zdum))
csign1(zdum1,zdum2) = cabs1(zdum1)*(zdum2/cabs1(zdum2))
c
lower = job .eq. 0
c
c compute 1-norm of t
c
tnorm = 0.0e0
do 10 j = 1, n
l = j
if (lower) l = n + 1 - j
i1 = 1
if (lower) i1 = j
tnorm = amax1(tnorm,scasum(l,t(i1,j),1))
10 continue
c
c rcond = 1/(norm(t)*(estimate of norm(inverse(t)))) .
c estimate = norm(z)/norm(y) where t*z = y and ctrans(t)*y = e .
c ctrans(t) is the conjugate transpose of t .
c the components of e are chosen to cause maximum local
c growth in the elements of y .
c the vectors are frequently rescaled to avoid overflow.
c
c solve ctrans(t)*y = e
c
ek = (1.0e0,0.0e0)
do 20 j = 1, n
z(j) = (0.0e0,0.0e0)
20 continue
do 100 kk = 1, n
k = kk
if (lower) k = n + 1 - kk
if (cabs1(z(k)) .ne. 0.0e0) ek = csign1(ek,-z(k))
if (cabs1(ek-z(k)) .le. cabs1(t(k,k))) go to 30
s = cabs1(t(k,k))/cabs1(ek-z(k))
call csscal(n,s,z,1)
ek = cmplx(s,0.0e0)*ek
30 continue
wk = ek - z(k)
wkm = -ek - z(k)
s = cabs1(wk)
sm = cabs1(wkm)
if (cabs1(t(k,k)) .eq. 0.0e0) go to 40
wk = wk/conjg(t(k,k))
wkm = wkm/conjg(t(k,k))
go to 50
40 continue
wk = (1.0e0,0.0e0)
wkm = (1.0e0,0.0e0)
50 continue
if (kk .eq. n) go to 90
j1 = k + 1
if (lower) j1 = 1
j2 = n
if (lower) j2 = k - 1
do 60 j = j1, j2
sm = sm + cabs1(z(j)+wkm*conjg(t(k,j)))
z(j) = z(j) + wk*conjg(t(k,j))
s = s + cabs1(z(j))
60 continue
if (s .ge. sm) go to 80
w = wkm - wk
wk = wkm
do 70 j = j1, j2
z(j) = z(j) + w*conjg(t(k,j))
70 continue
80 continue
90 continue
z(k) = wk
100 continue
s = 1.0e0/scasum(n,z,1)
call csscal(n,s,z,1)
c
ynorm = 1.0e0
c
c solve t*z = y
c
do 130 kk = 1, n
k = n + 1 - kk
if (lower) k = kk
if (cabs1(z(k)) .le. cabs1(t(k,k))) go to 110
s = cabs1(t(k,k))/cabs1(z(k))
call csscal(n,s,z,1)
ynorm = s*ynorm
110 continue
if (cabs1(t(k,k)) .ne. 0.0e0) z(k) = z(k)/t(k,k)
if (cabs1(t(k,k)) .eq. 0.0e0) z(k) = (1.0e0,0.0e0)
i1 = 1
if (lower) i1 = k + 1
if (kk .ge. n) go to 120
w = -z(k)
call caxpy(n-kk,w,t(i1,k),1,z(i1),1)
120 continue
130 continue
c make znorm = 1.0
s = 1.0e0/scasum(n,z,1)
call csscal(n,s,z,1)
ynorm = s*ynorm
c
if (tnorm .ne. 0.0e0) rcond = ynorm/tnorm
if (tnorm .eq. 0.0e0) rcond = 0.0e0
return
end