require ‘bigdecimal/jacobian’
Provides methods to compute the Jacobian matrix of a set of equations at a point x. In the methods below:
f is an Object which is used to compute the Jacobian matrix of the equations. It must provide the following methods:
- f.values(x)
-
returns the values of all functions at x
- f.zero
-
returns 0.0
- f.one
-
returns 1.0
- f.two
-
returns 2.0
- f.ten
-
returns 10.0
- f.eps
-
returns the convergence criterion (epsilon value) used to determine whether two values are considered equal. If |a-b| < epsilon, the two values are considered equal.
x is the point at which to compute the Jacobian.
fx is f.values(x).
# File tmp/rubies/ruby-3.3.0/ext/bigdecimal/lib/bigdecimal/jacobian.rb, line 47
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
deriv = []
nRetry += 1
if nRetry > 100
raise "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
Computes the derivative of f[i] at x[i]. fx is the value of f at x.
# File tmp/rubies/ruby-3.3.0/ext/bigdecimal/lib/bigdecimal/jacobian.rb, line 30
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
Determines the equality of two numbers by comparing to zero, or using the epsilon value
# File tmp/rubies/ruby-3.3.0/ext/bigdecimal/lib/bigdecimal/jacobian.rb, line 79
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
Computes the Jacobian of f at x. fx is the value of f at x.