subroutine strco(t,ldt,n,rcond,z,job)
integer ldt,n,job
real t(ldt,1),z(1)
real rcond
c
c strco estimates the condition of a real triangular matrix.
c
c on entry
c
c t real(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 real(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 saxpy,sscal,sasum
c fortran abs,amax1,sign
c
c internal variables
c
real w,wk,wkm,ek
real tnorm,ynorm,s,sm,sasum
integer i1,j,j1,j2,k,kk,l
logical lower
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,sasum(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 trans(t)*y = e .
c trans(t) is the 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 trans(t)*y = e
c
ek = 1.0e0
do 20 j = 1, n
z(j) = 0.0e0
20 continue
do 100 kk = 1, n
k = kk
if (lower) k = n + 1 - kk
if (z(k) .ne. 0.0e0) ek = sign(ek,-z(k))
if (abs(ek-z(k)) .le. abs(t(k,k))) go to 30
s = abs(t(k,k))/abs(ek-z(k))
call sscal(n,s,z,1)
ek = s*ek
30 continue
wk = ek - z(k)
wkm = -ek - z(k)
s = abs(wk)
sm = abs(wkm)
if (t(k,k) .eq. 0.0e0) go to 40
wk = wk/t(k,k)
wkm = wkm/t(k,k)
go to 50
40 continue
wk = 1.0e0
wkm = 1.0e0
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 + abs(z(j)+wkm*t(k,j))
z(j) = z(j) + wk*t(k,j)
s = s + abs(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*t(k,j)
70 continue
80 continue
90 continue
z(k) = wk
100 continue
s = 1.0e0/sasum(n,z,1)
call sscal(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 (abs(z(k)) .le. abs(t(k,k))) go to 110
s = abs(t(k,k))/abs(z(k))
call sscal(n,s,z,1)
ynorm = s*ynorm
110 continue
if (t(k,k) .ne. 0.0e0) z(k) = z(k)/t(k,k)
if (t(k,k) .eq. 0.0e0) z(k) = 1.0e0
i1 = 1
if (lower) i1 = k + 1
if (kk .ge. n) go to 120
w = -z(k)
call saxpy(n-kk,w,t(i1,k),1,z(i1),1)
120 continue
130 continue
c make znorm = 1.0
s = 1.0e0/sasum(n,z,1)
call sscal(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