# # newton.rb # # Solves 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 solution vector. # f is the object to be solved which must have following methods. # # f ... Object to compute Jacobian matrix of the equation systems. # [Methods required for f] # f.values(x) returns values of all functions at x. # f.zero returns 0.0 # f.one returns 1.0 # f.two returns 1.0 # f.ten returns 10.0 # f.eps convergence criterion # x ... initial values # require "bigdecimal/ludcmp" require "bigdecimal/jacobian" module Newton include LUSolve include Jacobian def norm(fv,zero=0.0) s = zero n = fv.size for i in 0...n do s += fv[i]*fv[i] end s end 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 end