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.gitignore: add bigdecimal (native gem)
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.gitignore
vendored
@ -71,6 +71,7 @@
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# Ignore dependencies we don't wish to vendor
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**/vendor/bundle/ruby/*/gems/ast-*/
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**/vendor/bundle/ruby/*/gems/bigdecimal-*/
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**/vendor/bundle/ruby/*/gems/bootsnap-*/
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**/vendor/bundle/ruby/*/gems/bundler-*/
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**/vendor/bundle/ruby/*/gems/byebug-*/
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@ -1,56 +0,0 @@
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Ruby is copyrighted free software by Yukihiro Matsumoto <matz@netlab.jp>.
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You can redistribute it and/or modify it under either the terms of the
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2-clause BSDL (see the file BSDL), or the conditions below:
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1. You may make and give away verbatim copies of the source form of the
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software without restriction, provided that you duplicate all of the
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original copyright notices and associated disclaimers.
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2. You may modify your copy of the software in any way, provided that
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you do at least ONE of the following:
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a) place your modifications in the Public Domain or otherwise
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make them Freely Available, such as by posting said
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modifications to Usenet or an equivalent medium, or by allowing
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the author to include your modifications in the software.
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b) use the modified software only within your corporation or
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organization.
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c) give non-standard binaries non-standard names, with
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instructions on where to get the original software distribution.
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d) make other distribution arrangements with the author.
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3. You may distribute the software in object code or binary form,
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provided that you do at least ONE of the following:
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a) distribute the binaries and library files of the software,
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together with instructions (in the manual page or equivalent)
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on where to get the original distribution.
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b) accompany the distribution with the machine-readable source of
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the software.
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c) give non-standard binaries non-standard names, with
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instructions on where to get the original software distribution.
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d) make other distribution arrangements with the author.
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4. You may modify and include the part of the software into any other
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software (possibly commercial). But some files in the distribution
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are not written by the author, so that they are not under these terms.
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For the list of those files and their copying conditions, see the
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file LEGAL.
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5. The scripts and library files supplied as input to or produced as
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output from the software do not automatically fall under the
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copyright of the software, but belong to whomever generated them,
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and may be sold commercially, and may be aggregated with this
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software.
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6. THIS SOFTWARE IS PROVIDED "AS IS" AND WITHOUT ANY EXPRESS OR
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IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
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WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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PURPOSE.
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@ -1,5 +0,0 @@
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if RUBY_ENGINE == 'jruby'
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JRuby::Util.load_ext("org.jruby.ext.bigdecimal.BigDecimalLibrary")
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else
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require 'bigdecimal.so'
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end
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@ -1,90 +0,0 @@
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# frozen_string_literal: false
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require 'bigdecimal'
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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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@ -1,89 +0,0 @@
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# frozen_string_literal: false
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require 'bigdecimal'
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#
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# Solves a*x = b for x, using LU decomposition.
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#
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module LUSolve
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module_function
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# Performs LU decomposition of the n by n matrix a.
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def ludecomp(a,n,zero=0,one=1)
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prec = BigDecimal.limit(nil)
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ps = []
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scales = []
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for i in 0...n do # pick up largest(abs. val.) element in each row.
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ps <<= i
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nrmrow = zero
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ixn = i*n
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for j in 0...n do
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biggst = a[ixn+j].abs
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nrmrow = biggst if biggst>nrmrow
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end
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if nrmrow>zero then
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scales <<= one.div(nrmrow,prec)
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else
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raise "Singular matrix"
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end
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end
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n1 = n - 1
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for k in 0...n1 do # Gaussian elimination with partial pivoting.
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biggst = zero;
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for i in k...n do
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size = a[ps[i]*n+k].abs*scales[ps[i]]
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if size>biggst then
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biggst = size
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pividx = i
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end
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end
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raise "Singular matrix" if biggst<=zero
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if pividx!=k then
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j = ps[k]
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ps[k] = ps[pividx]
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ps[pividx] = j
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end
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pivot = a[ps[k]*n+k]
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for i in (k+1)...n do
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psin = ps[i]*n
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a[psin+k] = mult = a[psin+k].div(pivot,prec)
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if mult!=zero then
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pskn = ps[k]*n
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for j in (k+1)...n do
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a[psin+j] -= mult.mult(a[pskn+j],prec)
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end
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end
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end
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end
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raise "Singular matrix" if a[ps[n1]*n+n1] == zero
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ps
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end
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# Solves a*x = b for x, using LU decomposition.
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#
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# a is a matrix, b is a constant vector, x is the solution vector.
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#
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# ps is the pivot, a vector which indicates the permutation of rows performed
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# during LU decomposition.
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def lusolve(a,b,ps,zero=0.0)
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prec = BigDecimal.limit(nil)
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n = ps.size
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x = []
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for i in 0...n do
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dot = zero
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psin = ps[i]*n
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for j in 0...i do
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dot = a[psin+j].mult(x[j],prec) + dot
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end
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x <<= b[ps[i]] - dot
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end
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(n-1).downto(0) do |i|
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dot = zero
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psin = ps[i]*n
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for j in (i+1)...n do
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dot = a[psin+j].mult(x[j],prec) + dot
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end
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x[i] = (x[i]-dot).div(a[psin+i],prec)
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end
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x
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end
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end
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@ -1,232 +0,0 @@
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# frozen_string_literal: false
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require 'bigdecimal'
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#
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#--
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# Contents:
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# sqrt(x, prec)
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# sin (x, prec)
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# cos (x, prec)
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# atan(x, prec) Note: |x|<1, x=0.9999 may not converge.
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# PI (prec)
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# E (prec) == exp(1.0,prec)
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#
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# where:
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# x ... BigDecimal number to be computed.
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# |x| must be small enough to get convergence.
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# prec ... Number of digits to be obtained.
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#++
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#
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# Provides mathematical functions.
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#
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# Example:
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#
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# require "bigdecimal/math"
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#
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# include BigMath
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#
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# a = BigDecimal((PI(100)/2).to_s)
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# puts sin(a,100) # => 0.99999999999999999999......e0
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#
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module BigMath
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module_function
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# call-seq:
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# sqrt(decimal, numeric) -> BigDecimal
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#
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# Computes the square root of +decimal+ to the specified number of digits of
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# precision, +numeric+.
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#
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# BigMath.sqrt(BigDecimal('2'), 16).to_s
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# #=> "0.1414213562373095048801688724e1"
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#
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def sqrt(x, prec)
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x.sqrt(prec)
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end
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# call-seq:
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# sin(decimal, numeric) -> BigDecimal
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#
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# Computes the sine of +decimal+ to the specified number of digits of
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# precision, +numeric+.
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#
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# If +decimal+ is Infinity or NaN, returns NaN.
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#
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# BigMath.sin(BigMath.PI(5)/4, 5).to_s
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# #=> "0.70710678118654752440082036563292800375e0"
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#
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def sin(x, prec)
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raise ArgumentError, "Zero or negative precision for sin" if prec <= 0
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return BigDecimal("NaN") if x.infinite? || x.nan?
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n = prec + BigDecimal.double_fig
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one = BigDecimal("1")
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two = BigDecimal("2")
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x = -x if neg = x < 0
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if x > (twopi = two * BigMath.PI(prec))
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if x > 30
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x %= twopi
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else
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x -= twopi while x > twopi
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end
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end
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x1 = x
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x2 = x.mult(x,n)
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sign = 1
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y = x
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d = y
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i = one
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z = one
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while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0)
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m = BigDecimal.double_fig if m < BigDecimal.double_fig
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sign = -sign
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x1 = x2.mult(x1,n)
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i += two
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z *= (i-one) * i
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d = sign * x1.div(z,m)
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y += d
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end
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neg ? -y : y
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end
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# call-seq:
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# cos(decimal, numeric) -> BigDecimal
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#
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# Computes the cosine of +decimal+ to the specified number of digits of
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# precision, +numeric+.
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#
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# If +decimal+ is Infinity or NaN, returns NaN.
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#
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# BigMath.cos(BigMath.PI(4), 16).to_s
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# #=> "-0.999999999999999999999999999999856613163740061349e0"
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#
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def cos(x, prec)
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raise ArgumentError, "Zero or negative precision for cos" if prec <= 0
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return BigDecimal("NaN") if x.infinite? || x.nan?
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n = prec + BigDecimal.double_fig
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one = BigDecimal("1")
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two = BigDecimal("2")
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x = -x if x < 0
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if x > (twopi = two * BigMath.PI(prec))
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if x > 30
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x %= twopi
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else
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x -= twopi while x > twopi
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end
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end
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x1 = one
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x2 = x.mult(x,n)
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sign = 1
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y = one
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d = y
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i = BigDecimal("0")
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z = one
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while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0)
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m = BigDecimal.double_fig if m < BigDecimal.double_fig
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sign = -sign
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x1 = x2.mult(x1,n)
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i += two
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z *= (i-one) * i
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d = sign * x1.div(z,m)
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y += d
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end
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y
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end
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# call-seq:
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# atan(decimal, numeric) -> BigDecimal
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#
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# Computes the arctangent of +decimal+ to the specified number of digits of
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# precision, +numeric+.
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#
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# If +decimal+ is NaN, returns NaN.
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#
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# BigMath.atan(BigDecimal('-1'), 16).to_s
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# #=> "-0.785398163397448309615660845819878471907514682065e0"
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#
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def atan(x, prec)
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raise ArgumentError, "Zero or negative precision for atan" if prec <= 0
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return BigDecimal("NaN") if x.nan?
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pi = PI(prec)
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x = -x if neg = x < 0
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return pi.div(neg ? -2 : 2, prec) if x.infinite?
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return pi / (neg ? -4 : 4) if x.round(prec) == 1
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x = BigDecimal("1").div(x, prec) if inv = x > 1
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x = (-1 + sqrt(1 + x**2, prec))/x if dbl = x > 0.5
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n = prec + BigDecimal.double_fig
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y = x
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d = y
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t = x
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r = BigDecimal("3")
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x2 = x.mult(x,n)
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while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0)
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m = BigDecimal.double_fig if m < BigDecimal.double_fig
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t = -t.mult(x2,n)
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d = t.div(r,m)
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y += d
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r += 2
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end
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y *= 2 if dbl
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y = pi / 2 - y if inv
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y = -y if neg
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y
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end
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# call-seq:
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# PI(numeric) -> BigDecimal
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#
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# Computes the value of pi to the specified number of digits of precision,
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# +numeric+.
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#
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# BigMath.PI(10).to_s
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# #=> "0.3141592653589793238462643388813853786957412e1"
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#
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def PI(prec)
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raise ArgumentError, "Zero or negative precision for PI" if prec <= 0
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n = prec + BigDecimal.double_fig
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zero = BigDecimal("0")
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one = BigDecimal("1")
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two = BigDecimal("2")
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m25 = BigDecimal("-0.04")
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m57121 = BigDecimal("-57121")
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pi = zero
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d = one
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k = one
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t = BigDecimal("-80")
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while d.nonzero? && ((m = n - (pi.exponent - d.exponent).abs) > 0)
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m = BigDecimal.double_fig if m < BigDecimal.double_fig
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t = t*m25
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d = t.div(k,m)
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k = k+two
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pi = pi + d
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end
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d = one
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k = one
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t = BigDecimal("956")
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while d.nonzero? && ((m = n - (pi.exponent - d.exponent).abs) > 0)
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m = BigDecimal.double_fig if m < BigDecimal.double_fig
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t = t.div(m57121,n)
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d = t.div(k,m)
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pi = pi + d
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k = k+two
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end
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pi
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end
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# call-seq:
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# E(numeric) -> BigDecimal
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#
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# Computes e (the base of natural logarithms) to the specified number of
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# digits of precision, +numeric+.
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#
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# BigMath.E(10).to_s
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# #=> "0.271828182845904523536028752390026306410273e1"
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#
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def E(prec)
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raise ArgumentError, "Zero or negative precision for E" if prec <= 0
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BigMath.exp(1, prec)
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end
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end
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@ -1,80 +0,0 @@
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# frozen_string_literal: false
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||||
require "bigdecimal/ludcmp"
|
||||
require "bigdecimal/jacobian"
|
||||
|
||||
#
|
||||
# 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.
|
||||
#
|
||||
module Newton
|
||||
include LUSolve
|
||||
include Jacobian
|
||||
module_function
|
||||
|
||||
def norm(fv,zero=0.0) # :nodoc:
|
||||
s = zero
|
||||
n = fv.size
|
||||
for i in 0...n do
|
||||
s += fv[i]*fv[i]
|
||||
end
|
||||
s
|
||||
end
|
||||
|
||||
# See also Newton
|
||||
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
|
@ -1,185 +0,0 @@
|
||||
# frozen_string_literal: false
|
||||
#
|
||||
#--
|
||||
# bigdecimal/util extends various native classes to provide the #to_d method,
|
||||
# and provides BigDecimal#to_d and BigDecimal#to_digits.
|
||||
#++
|
||||
|
||||
require 'bigdecimal'
|
||||
|
||||
class Integer < Numeric
|
||||
# call-seq:
|
||||
# int.to_d -> bigdecimal
|
||||
#
|
||||
# Returns the value of +int+ as a BigDecimal.
|
||||
#
|
||||
# require 'bigdecimal'
|
||||
# require 'bigdecimal/util'
|
||||
#
|
||||
# 42.to_d # => 0.42e2
|
||||
#
|
||||
# See also Kernel.BigDecimal.
|
||||
#
|
||||
def to_d
|
||||
BigDecimal(self)
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
class Float < Numeric
|
||||
# call-seq:
|
||||
# float.to_d -> bigdecimal
|
||||
# float.to_d(precision) -> bigdecimal
|
||||
#
|
||||
# Returns the value of +float+ as a BigDecimal.
|
||||
# The +precision+ parameter is used to determine the number of
|
||||
# significant digits for the result. When +precision+ is set to +0+,
|
||||
# the number of digits to represent the float being converted is determined
|
||||
# automatically.
|
||||
# The default +precision+ is +0+.
|
||||
#
|
||||
# require 'bigdecimal'
|
||||
# require 'bigdecimal/util'
|
||||
#
|
||||
# 0.5.to_d # => 0.5e0
|
||||
# 1.234.to_d # => 0.1234e1
|
||||
# 1.234.to_d(2) # => 0.12e1
|
||||
#
|
||||
# See also Kernel.BigDecimal.
|
||||
#
|
||||
def to_d(precision=0)
|
||||
BigDecimal(self, precision)
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
class String
|
||||
# call-seq:
|
||||
# str.to_d -> bigdecimal
|
||||
#
|
||||
# Returns the result of interpreting leading characters in +str+
|
||||
# as a BigDecimal.
|
||||
#
|
||||
# require 'bigdecimal'
|
||||
# require 'bigdecimal/util'
|
||||
#
|
||||
# "0.5".to_d # => 0.5e0
|
||||
# "123.45e1".to_d # => 0.12345e4
|
||||
# "45.67 degrees".to_d # => 0.4567e2
|
||||
#
|
||||
# See also Kernel.BigDecimal.
|
||||
#
|
||||
def to_d
|
||||
BigDecimal.interpret_loosely(self)
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
class BigDecimal < Numeric
|
||||
# call-seq:
|
||||
# a.to_digits -> string
|
||||
#
|
||||
# Converts a BigDecimal to a String of the form "nnnnnn.mmm".
|
||||
# This method is deprecated; use BigDecimal#to_s("F") instead.
|
||||
#
|
||||
# require 'bigdecimal/util'
|
||||
#
|
||||
# d = BigDecimal("3.14")
|
||||
# d.to_digits # => "3.14"
|
||||
#
|
||||
def to_digits
|
||||
if self.nan? || self.infinite? || self.zero?
|
||||
self.to_s
|
||||
else
|
||||
i = self.to_i.to_s
|
||||
_,f,_,z = self.frac.split
|
||||
i + "." + ("0"*(-z)) + f
|
||||
end
|
||||
end
|
||||
|
||||
# call-seq:
|
||||
# a.to_d -> bigdecimal
|
||||
#
|
||||
# Returns self.
|
||||
#
|
||||
# require 'bigdecimal/util'
|
||||
#
|
||||
# d = BigDecimal("3.14")
|
||||
# d.to_d # => 0.314e1
|
||||
#
|
||||
def to_d
|
||||
self
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
class Rational < Numeric
|
||||
# call-seq:
|
||||
# rat.to_d(precision) -> bigdecimal
|
||||
#
|
||||
# Returns the value as a BigDecimal.
|
||||
#
|
||||
# The required +precision+ parameter is used to determine the number of
|
||||
# significant digits for the result.
|
||||
#
|
||||
# require 'bigdecimal'
|
||||
# require 'bigdecimal/util'
|
||||
#
|
||||
# Rational(22, 7).to_d(3) # => 0.314e1
|
||||
#
|
||||
# See also Kernel.BigDecimal.
|
||||
#
|
||||
def to_d(precision)
|
||||
BigDecimal(self, precision)
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
class Complex < Numeric
|
||||
# call-seq:
|
||||
# cmp.to_d -> bigdecimal
|
||||
# cmp.to_d(precision) -> bigdecimal
|
||||
#
|
||||
# Returns the value as a BigDecimal.
|
||||
#
|
||||
# The +precision+ parameter is required for a rational complex number.
|
||||
# This parameter is used to determine the number of significant digits
|
||||
# for the result.
|
||||
#
|
||||
# require 'bigdecimal'
|
||||
# require 'bigdecimal/util'
|
||||
#
|
||||
# Complex(0.1234567, 0).to_d(4) # => 0.1235e0
|
||||
# Complex(Rational(22, 7), 0).to_d(3) # => 0.314e1
|
||||
#
|
||||
# See also Kernel.BigDecimal.
|
||||
#
|
||||
def to_d(*args)
|
||||
BigDecimal(self) unless self.imag.zero? # to raise eerror
|
||||
|
||||
if args.length == 0
|
||||
case self.real
|
||||
when Rational
|
||||
BigDecimal(self.real) # to raise error
|
||||
end
|
||||
end
|
||||
self.real.to_d(*args)
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
class NilClass
|
||||
# call-seq:
|
||||
# nil.to_d -> bigdecimal
|
||||
#
|
||||
# Returns nil represented as a BigDecimal.
|
||||
#
|
||||
# require 'bigdecimal'
|
||||
# require 'bigdecimal/util'
|
||||
#
|
||||
# nil.to_d # => 0.0
|
||||
#
|
||||
def to_d
|
||||
BigDecimal(0)
|
||||
end
|
||||
end
|
Loading…
x
Reference in New Issue
Block a user