1 files changed, 57 insertions, 0 deletions
diff --git a/vendor/bundle/ruby/3.4.0/gems/bigdecimal-4.1.2/sample/nlsolve.rb b/vendor/bundle/ruby/3.4.0/gems/bigdecimal-4.1.2/sample/nlsolve.rb
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--- /dev/null
+++ b/vendor/bundle/ruby/3.4.0/gems/bigdecimal-4.1.2/sample/nlsolve.rb
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+#
+# nlsolve.rb
+# An example for solving nonlinear algebraic equation system.
+#
+
+require "bigdecimal"
+require_relative "linear"
+
+# Requires gem matrix
+require "matrix"
+
+# :stopdoc:
+
+def func((x, y)) # defines functions solved
+  [
+    x**2 + y**2 - 2,
+    (x - 1)**2 + (y + 1)**2 - 3
+  ]
+end
+
+def jacobian(x, f, delta, prec)
+  dim = x.size
+  dim.times.map do |i|
+    xplus = Array.new(dim) {|j| x[i] + (j == i ? delta : 0) }
+    xminus = Array.new(dim) {|j| x[i] - (j == i ? delta : 0) }
+    yplus = f.call(xplus)
+    yminus = f.call(xminus)
+    yplus.zip(yminus).map {|p, m| (p - m).div(2 * delta, prec) }
+  end.transpose
+end
+
+def nlsolve(initial_x, prec:, max_iteration: 100, &f)
+  initial_x = initial_x.map {|v| BigDecimal(v) }
+  x = initial_x
+  delta = BigDecimal(0.01)
+  calc_prec = prec + 10
+  max_iteration.times do |iteration|
+    # Newton step
+    jacobian = jacobian(x, f, delta, calc_prec)
+    matrix = Matrix[*jacobian.map {|row| row.map {|v| PrecisionSpecifiedValue.new(v, calc_prec) } }]
+    y = f.call(x)
+    vector = y.map {|v| PrecisionSpecifiedValue.new(v, calc_prec) }
+    dx = matrix.lup.solve(vector).map(&:value)
+    x_prev = x
+    x = x.zip(dx).map {|xi, di| xi.sub(di, prec) }
+    movement = x_prev.zip(x).map {|xn, xi| (xn - xi).abs }.max
+    delta = [movement, delta].min.mult(1, 10)
+    break if movement.zero? || movement.exponent < -prec
+  end
+  x
+end
+
+initial_value = [1, 1]
+ans = nlsolve(initial_value, prec: 100) {|x| func(x) }
+diff = func(ans).map {|v| v.mult(1, 10) }
+p(ans:)
+p(diff:)