Module: Newton
Relationships & Source Files | |
Super Chains via Extension / Inclusion / Inheritance | |
Instance Chain:
self,
::Jacobian,
::LUSolve
|
|
Defined in: | ext/bigdecimal/lib/bigdecimal/newton.rb |
Overview
newton.rb
Solves the nonlinear algebraic equation system f = 0 by Newton's method. This program is not dependent on ::BigDecimal.
To call:
n = nlsolve(f,x)
where n is the number of iterations required,
x is the initial value vector
f is an Object which is used to compute the values of the equations to be solved.
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.
On exit, x is the solution vector.
Class Method Summary
-
.nlsolve(f, x)
mod_func
See also
Newton
.
Instance Method Summary
::Jacobian - Included
#dfdxi | |
#isEqual | Determines the equality of two numbers by comparing to zero, or using the epsilon value. |
#jacobian | Computes the ::Jacobian of f at x. |
::LUSolve - Included
Class Method Details
.nlsolve(f, x) (mod_func)
See also Newton
# File 'ext/bigdecimal/lib/bigdecimal/newton.rb', line 44
def nlsolve(f,x) nRetry = 0 n = x.size f0 = f.values(x) zero = f.zero one = f.one two = f.two p5 = one/two d = norm(f0,zero) minfact = f.ten*f.ten*f.ten minfact = one/minfact e = f.eps while d >= e do nRetry += 1 # Not yet converged. => Compute Jacobian matrix dfdx = jacobian(f,f0,x) # Solve dfdx*dx = -f0 to estimate dx dx = lusolve(dfdx,f0,ludecomp(dfdx,n,zero,one),zero) fact = two xs = x.dup begin fact *= p5 if fact < minfact then raise "Failed to reduce function values." end for i in 0...n do x[i] = xs[i] - dx[i]*fact end f0 = f.values(x) dn = norm(f0,zero) end while(dn>=d) d = dn end nRetry end