Add bin and edit workflow

bin/gems/bigdecimal-3.1.9/lib/bigdecimal/newton.rb

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+# frozen_string_literal: false
+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