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subroutine tql2(nm,n,d,e,z,job,ierr)
c
integer i,j,k,l,m,n,ii,l1,l2,nm,mml,job,ierr
double precision d(n),e(n),z(nm,n)
double precision c,c2,c3,dl1,el1,f,g,h,p,r,s,s2,tst1,tst2,pythag
c
c this subroutine is a translation of the algol procedure tql2,
c num. math. 11, 293-306(1968) by bowdler, martin, reinsch, and
c wilkinson.
c handbook for auto. comp., vol.ii-linear algebra, 227-240(1971).
c
c this subroutine finds the eigenvalues and eigenvectors
c of a symmetric tridiagonal matrix by the ql method.
c the eigenvectors of a full symmetric matrix can also
c be found if tred2 has been used to reduce this
c full matrix to tridiagonal form.
c
c!calling sequence
c
c subroutine tql2(nm,n,d,e,z,job,ierr)
c
c on input
c
c nm must be set to the row dimension of two-dimensional
c array parameters as declared in the calling program
c dimension statement.
c
c n is the order of the matrix.
c
c d contains the diagonal elements of the input matrix.
c
c e contains the subdiagonal elements of the input matrix
c in its last n-1 positions. e(1) is arbitrary.
c
c z contains (for job=1) the transformation matrix produced
c in the reduction by tred2, if performed. if the eigenvectors
c of the tridiagonal matrix are desired, z must contain
c the identity matrix. If job=0 z is not referenced
c
c on output
c
c d contains the eigenvalues in ascending order. if an
c error exit is made, the eigenvalues are correct but
c unordered for indices 1,2,...,ierr-1.
c
c e has been destroyed.
c
c z contains orthonormal eigenvectors of the symmetric
c tridiagonal (or full) matrix (for job=1). if an error
c exit is made,z contains the eigenvectors associated with the stored
c eigenvalues. If job=0 z is not referenced
c
c ierr is set to
c zero for normal return,
c j if the j-th eigenvalue has not been
c determined after 30*n iterations.
c
c calls pythag for dsqrt(a*a + b*b) .
c
c questions and comments should be directed to burton s. garbow,
c mathematics and computer science div, argonne national laboratory
c
c this version dated august 1983.
c
c ------------------------------------------------------------------
c
ierr = 0
if (n .eq. 1) go to 1001
c
do 100 i = 2, n
100 e(i-1) = e(i)
c
f = 0.0d0
tst1 = 0.0d0
e(n) = 0.0d0
c
do 240 l = 1, n
j = 0
h = abs(d(l)) + abs(e(l))
if (tst1 .lt. h) tst1 = h
c .......... look for small sub-diagonal element ..........
do 110 m = l, n
tst2 = tst1 + abs(e(m))
if (tst2 .eq. tst1) go to 120
c .......... e(n) is always zero, so there is no exit
c through the bottom of the loop ..........
110 continue
c
120 if (m .eq. l) go to 220
130 if (j .eq. 30*n) go to 1000
j = j + 1
c .......... form shift ..........
l1 = l + 1
l2 = l1 + 1
g = d(l)
p = (d(l1) - g) / (2.0d0 * e(l))
r = pythag(p,1.0d0)
d(l) = e(l) / (p + sign(r,p))
d(l1) = e(l) * (p + sign(r,p))
dl1 = d(l1)
h = g - d(l)
if (l2 .gt. n) go to 145
c
do 140 i = l2, n
140 d(i) = d(i) - h
c
145 f = f + h
c .......... ql transformation ..........
p = d(m)
c = 1.0d0
c2 = c
el1 = e(l1)
s = 0.0d0
mml = m - l
c .......... for i=m-1 step -1 until l do -- ..........
do 200 ii = 1, mml
c3 = c2
c2 = c
s2 = s
i = m - ii
g = c * e(i)
h = c * p
r = pythag(p,e(i))
e(i+1) = s * r
s = e(i) / r
c = p / r
p = c * d(i) - s * g
d(i+1) = h + s * (c * g + s * d(i))
cSS96 test on job added to inhibit z computation
if(job.eq.1) then
c .......... form vector ..........
do 180 k = 1, n
h = z(k,i+1)
z(k,i+1) = s * z(k,i) + c * h
z(k,i) = c * z(k,i) - s * h
180 continue
endif
c
200 continue
c
p = -s * s2 * c3 * el1 * e(l) / dl1
e(l) = s * p
d(l) = c * p
tst2 = tst1 + abs(e(l))
if (tst2 .gt. tst1) go to 130
220 d(l) = d(l) + f
240 continue
c .......... order eigenvalues and eigenvectors ..........
do 300 ii = 2, n
i = ii - 1
k = i
p = d(i)
c
do 260 j = ii, n
if (d(j) .ge. p) go to 260
k = j
p = d(j)
260 continue
c
if (k .eq. i) go to 300
d(k) = d(i)
d(i) = p
c
cSS96 test on job added to inhibit z computation
if(job.eq.1) then
do 280 j = 1, n
p = z(j,i)
z(j,i) = z(j,k)
z(j,k) = p
280 continue
endif
c
300 continue
c
go to 1001
c .......... set error -- no convergence to an
c eigenvalue after 30*n iterations ..........
1000 ierr = l
1001 return
end
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