From 77443517086c68cb51f26f68f5d25279f1be7daf Mon Sep 17 00:00:00 2001
From: shigek <shigek@b2dd03c8-39d4-4d8f-98ff-823fe69b080e>
Date: Fri, 28 Mar 2003 05:00:21 +0000
Subject: Copied from rough/bigdecimal,documents & some sample programs added.

git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@3625 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
---
 ext/bigdecimal/lib/newton.rb | 75 ++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 75 insertions(+)
 create mode 100644 ext/bigdecimal/lib/newton.rb

(limited to 'ext/bigdecimal/lib/newton.rb')

diff --git a/ext/bigdecimal/lib/newton.rb b/ext/bigdecimal/lib/newton.rb
new file mode 100644
index 0000000000..67a92474ac
--- /dev/null
+++ b/ext/bigdecimal/lib/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
-- 
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