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More pathes from Tadasi Saito.

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As discussed in ruby-dev ML:
  E,PI, etc are disabled.
  BigDecimal op String disabled.
  to_f changed.
  lib directory moved.


git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@4092 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
This commit is contained in:
shigek 2003-07-18 15:24:25 +00:00
parent b10272dc37
commit e242cf9def
4 changed files with 0 additions and 243 deletions
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30
ext/bigdecimal/lib/bigdecimal-rational.rb
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#
# BigDecimal <-> Rational
#
class BigDecimal < Numeric
# Convert BigDecimal to Rational
def to_r
sign,digits,base,power = self.split
numerator = sign*digits.to_i
denomi_power = power - digits.size # base is always 10
if denomi_power < 0
denominator = base ** (-denomi_power)
else
denominator = base ** denomi_power
end
Rational(numerator,denominator)
end
end
class Rational < Numeric
# Convert Rational to BigDecimal
# to_d returns an array [quotient,residue]
def to_d(nFig=0)
num = self.numerator.to_s
if nFig<=0
nFig = BigDecimal.double_fig*2+1
end
BigDecimal.new(num).div(self.denominator,nFig)
end
end

63
ext/bigdecimal/lib/jacobian.rb
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#
# jacobian.rb
#
# Computes Jacobian matrix of f at x
#
module Jacobian
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
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
s = f.zero
deriv = []
if(nRetry>100) then
raize "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
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
end

75
ext/bigdecimal/lib/ludcmp.rb
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#
# ludcmp.rb
#
module LUSolve
def ludecomp(a,n,zero=0.0,one=1.0)
ps = []
scales = []
for i in 0...n do # pick up largest(abs. val.) element in each row.
ps <<= i
nrmrow = zero
ixn = i*n
for j in 0...n do
biggst = a[ixn+j].abs
nrmrow = biggst if biggst>nrmrow
end
if nrmrow>zero then
scales <<= one/nrmrow
else
raise "Singular matrix"
end
end
n1 = n - 1
for k in 0...n1 do # Gaussian elimination with partial pivoting.
biggst = zero;
for i in k...n do
size = a[ps[i]*n+k].abs*scales[ps[i]]
if size>biggst then
biggst = size
pividx = i
end
end
raise "Singular matrix" if biggst<=zero
if pividx!=k then
j = ps[k]
ps[k] = ps[pividx]
ps[pividx] = j
end
pivot = a[ps[k]*n+k]
for i in (k+1)...n do
psin = ps[i]*n
a[psin+k] = mult = a[psin+k]/pivot
if mult!=zero then
pskn = ps[k]*n
for j in (k+1)...n do
a[psin+j] -= mult*a[pskn+j]
end
end
end
end
raise "Singular matrix" if a[ps[n1]*n+n1] == zero
ps
end
def lusolve(a,b,ps,zero=0.0)
n = ps.size
x = []
for i in 0...n do
dot = zero
psin = ps[i]*n
for j in 0...i do
dot = a[psin+j]*x[j] + dot
end
x <<= b[ps[i]] - dot
end
(n-1).downto(0) do |i|
dot = zero
psin = ps[i]*n
for j in (i+1)...n do
dot = a[psin+j]*x[j] + dot
end
x[i] = (x[i]-dot)/a[psin+i]
end
x
end
end

75
ext/bigdecimal/lib/newton.rb
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#
# 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 "ludcmp"
require "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
raize "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