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ho.f
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ho.f
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program ho
parameter(n=101)
real a(n,n),h(n,n),x(n),d(n),e(n),sum,int
call hmg(h,x,d,e,n,dx)
a = 0.
do 13 i=1,n
a(i,i)=1.
13 continue
call tql2(n,n,d,e,a,ierr)
do 16 i=1,n
write(*,*) "Eigenvalue", i, " =", d(i)
16 continue
sum = 0
do i=2,n-1
sum = sum + 2*a(i,1)**2
enddo
int = dx/2. * (a(1,1)**2 + sum + a(n,1)**2)
cons = sqrt(1.0/int)
a = cons * a
write(*,*) "Normalization Constant =", cons
open(11,file='ho.txt')
do 18 i=1,n
write(11,*) x(i), a(i,1)+d(1), 0.5*x(i)**2
18 continue
open(12,file='hoa.txt')
do 19 i=1,n
write(12,*) x(i), 0.75*a(i,1)+d(1), 0.75*a(i,2)+d(2),
& 0.5*x(i)**2
19 continue
end
subroutine hmg(h,x,d,e,n,a)
real L,h(n,n),d(n),e(n),v(n),x(n),a
x0 = -5.
L = 10.
a = L/(n - 1)
pi = 4.*atan(1.)
do 11 i = 1,n
x(i) = x0+(i-1)*a
v(i) = 0.5*1.*(x0+(i-1)*a)**2
d(i) = v(i) + 1./a**2
e(i) = - 1./(2*a**2)
11 continue
h = 0.
do 12 i = 1,n
do 13 j = 1,n
if (i.eq.j) then
h(i,j) = d(i)
if (j.gt.1) then
h(i,j-1) = e(i)
end if
if (j.lt.n) then
h(i,j+1) = e(i)
end if
end if
13 continue
12 continue
end
c finds the eigenvalues and eigenvectors of a tridiagonal matrix
subroutine tql2(nm,n,d,e,z,ierr)
real d(n),e(n),z(nm,n)
ierr = 0
if (n .eq. 1) go to 1001
do 100 i = 2, n
100 e(i-1) = e(i)
f = 0.0e0
tst1 = 0.0e0
e(n) = 0.0e0
do 240 l = 1, n
j = 0
h = abs(d(l)) + abs(e(l))
if (tst1 .lt. h) tst1 = h
do 110 m = l, n
tst2 = tst1 + abs(e(m))
if (tst2 .eq. tst1) go to 120
110 continue
120 if (m .eq. l) go to 220
130 if (j .eq. 30) go to 1000
j = j + 1
l1 = l + 1
l2 = l1 + 1
g = d(l)
p = (d(l1) - g) / (2.0e0 * e(l))
r = pythag(p,1.0e0)
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
do 140 i = l2, n
140 d(i) = d(i) - h
145 f = f + h
p = d(m)
c = 1.0e0
c2 = c
el1 = e(l1)
s = 0.0e0
mml = m - l
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))
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
200 continue
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
do 300 ii = 2, n
i = ii - 1
k = i
p = d(i)
do 260 j = ii, n
if (d(j) .ge. p) go to 260
k = j
p = d(j)
260 continue
if (k .eq. i) go to 300
d(k) = d(i)
d(i) = p
do 280 j = 1, n
p = z(j,i)
z(j,i) = z(j,k)
z(j,k) = p
280 continue
300 continue
go to 1001
1000 ierr = l
1001 return
end
c finds sqrt(a**2+b**2)
real function pythag(a,b)
p = amax1(abs(a),abs(b))
if (p .eq. 0.0e0) go to 20
r = (amin1(abs(a),abs(b))/p)**2
10 continue
t = 4.0e0 + r
if (t .eq. 4.0e0) go to 20
s = r/t
u = 1.0e0 + 2.0e0*s
p = u*p
r = (s/u)**2 * r
go to 10
20 pythag = p
return
end