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#
# jacobian.rb
#
# Computes Jacobian matrix of f at x
#
module Jacobian
def isEqual(a,b,zero=0.0,e=1.0e-8)
aa = a.abs
bb = b.abs
if aa == zero && bb == zero then
true
else
if ((a-b)/(aa+bb)).abs < e then
true
else
false
end
end
end
def dfdxi(f,fx,x,i)
nRetry = 0
n = x.size
xSave = x[i]
ok = 0
ratio = f.ten*f.ten*f.ten
dx = x[i].abs/ratio
dx = fx[i].abs/ratio if isEqual(dx,f.zero,f.zero,f.eps)
dx = f.one/f.ten if isEqual(dx,f.zero,f.zero,f.eps)
until ok>0 do
s = f.zero
deriv = []
if(nRetry>100) then
raize "Singular Jacobian matrix. No change at x[" + i.to_s + "]"
end
dx = dx*f.two
x[i] += dx
fxNew = f.values(x)
for j in 0...n do
if !isEqual(fxNew[j],fx[j],f.zero,f.eps) then
ok += 1
deriv <<= (fxNew[j]-fx[j])/dx
else
deriv <<= f.zero
end
end
x[i] = xSave
end
deriv
end
def jacobian(f,fx,x)
n = x.size
dfdx = Array::new(n*n)
for i in 0...n do
df = dfdxi(f,fx,x,i)
for j in 0...n do
dfdx[j*n+i] = df[j]
end
end
dfdx
end
end
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