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• bigdecimal/lib/bigdecimal/jacobian.rb

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# Jacobian

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).

### Public Instance Methods

dfdxi(f,fx,x,i) click to toggle source

Computes the derivative of f at x. fx is the value of f at x.

```
# File bigdecimal/lib/bigdecimal/jacobian.rb, line 44
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
```
isEqual(a,b,zero=0.0,e=1.0e-8) click to toggle source

Determines the equality of two numbers by comparing to zero, or using the epsilon value

```
# File bigdecimal/lib/bigdecimal/jacobian.rb, line 27
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
```
jacobian(f,fx,x) click to toggle source

Computes the Jacobian of f at x. fx is the value of f at x.

```
# File bigdecimal/lib/bigdecimal/jacobian.rb, line 76
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
```