As discussed in ruby-dev ML:

  lib directory moved.
  util.rb created instead of bigdecimal-rational.rb


git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@4093 b2dd03c8-39d4-4d8f-98ff-823fe69b080e

1 files changed, 75 insertions, 0 deletions

diff --git a/ext/bigdecimal/lib/bigdecimal/newton.rb b/ext/bigdecimal/lib/bigdecimal/newton.rb
new file mode 100644
index 0000000000..67a92474ac
--- /dev/null
+++ b/ext/bigdecimal/lib/bigdecimal/newton.rb
@@ -0,0 +1,75 @@
+#
+# 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