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c4fdfabcc8
g -L frozen_string_literal ext/**/*.rb|xargs ruby -Ka -e'ARGV.each{|fn|puts
fn;open(fn,"r+"){|f|s=f.read.sub(/\A(#!.*\n)?(#.*coding.*\n)?/,"\\&#
frozen_string_literal: false\n");f.rewind;f.write s}}'
git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@53143 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
88 lines
2.1 KiB
Ruby
88 lines
2.1 KiB
Ruby
# frozen_string_literal: false
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#
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# require 'bigdecimal/jacobian'
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#
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# Provides methods to compute the Jacobian matrix of a set of equations at a
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# point x. In the methods below:
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#
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# f is an Object which is used to compute the Jacobian matrix of the equations.
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# It must provide the following methods:
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#
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# f.values(x):: returns the values of all functions at x
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#
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# f.zero:: returns 0.0
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# f.one:: returns 1.0
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# f.two:: returns 2.0
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# f.ten:: returns 10.0
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#
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# 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.
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#
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# x is the point at which to compute the Jacobian.
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#
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# fx is f.values(x).
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#
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module Jacobian
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module_function
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# Determines the equality of two numbers by comparing to zero, or using the epsilon value
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def isEqual(a,b,zero=0.0,e=1.0e-8)
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aa = a.abs
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bb = b.abs
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if aa == zero && bb == zero then
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true
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else
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if ((a-b)/(aa+bb)).abs < e then
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true
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else
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false
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end
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end
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end
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# Computes the derivative of f[i] at x[i].
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# fx is the value of f at x.
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def dfdxi(f,fx,x,i)
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nRetry = 0
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n = x.size
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xSave = x[i]
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ok = 0
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ratio = f.ten*f.ten*f.ten
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dx = x[i].abs/ratio
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dx = fx[i].abs/ratio if isEqual(dx,f.zero,f.zero,f.eps)
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dx = f.one/f.ten if isEqual(dx,f.zero,f.zero,f.eps)
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until ok>0 do
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deriv = []
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nRetry += 1
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if nRetry > 100
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raise "Singular Jacobian matrix. No change at x[" + i.to_s + "]"
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end
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dx = dx*f.two
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x[i] += dx
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fxNew = f.values(x)
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for j in 0...n do
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if !isEqual(fxNew[j],fx[j],f.zero,f.eps) then
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ok += 1
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deriv <<= (fxNew[j]-fx[j])/dx
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else
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deriv <<= f.zero
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end
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end
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x[i] = xSave
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end
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deriv
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end
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# Computes the Jacobian of f at x. fx is the value of f at x.
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def jacobian(f,fx,x)
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n = x.size
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dfdx = Array.new(n*n)
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for i in 0...n do
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df = dfdxi(f,fx,x,i)
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for j in 0...n do
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dfdx[j*n+i] = df[j]
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end
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end
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dfdx
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end
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end
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