Add bin and edit workflow

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

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+# frozen_string_literal: false
+
+require 'bigdecimal'
+
+# require 'bigdecimal/jacobian'
+#
+# Provides methods to compute the Jacobian matrix of a set of equations at a
+# point x. In the methods below:
+#
+# f is an Object which is used to compute the Jacobian matrix of the equations.
+# 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.
+#
+# x is the point at which to compute the Jacobian.
+#
+# fx is f.values(x).
+#
+module Jacobian
+  module_function
+
+  # Determines the equality of two numbers by comparing to zero, or using the epsilon value
+  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
+
+
+  # Computes the derivative of +f[i]+ at +x[i]+.
+  # +fx+ is the value of +f+ at +x+.
+  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
+      deriv = []
+      nRetry += 1
+      if nRetry > 100
+        raise "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
+
+  # Computes the Jacobian of +f+ at +x+. +fx+ is the value of +f+ at +x+.
+  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