Up-to-date version at Kantox

README.md

@@ -9,7 +9,7 @@ by adding `expline` to your list of dependencies in `mix.exs`:
 
 ```elixir
 def deps do
-  [{:expline, "~> 0.1.0"}]
+  [{:expline, "~> 0.2"}]
 end
 ```
 

lib/expline/matrix.ex

@@ -114,7 +114,8 @@ defmodule Expline.Matrix do
       at(matrix, i, j)
     end
     |> Enum.all?(fn
-      0.0 -> true
+      +0.0 -> true
+      -0.0 -> true
       _ -> false
     end)
   end
@@ -125,7 +126,8 @@ defmodule Expline.Matrix do
       at(matrix, i, j)
     end
     |> Enum.all?(fn
-      0.0 -> true
+      +0.0 -> true
+      -0.0 -> true
       _ -> false
     end)
   end

lib/expline/spline.ex

@@ -334,6 +334,68 @@ defmodule Expline.Spline do
     end
   end
 
+  @doc """
+  Interpolate a curvature from the spline.
+
+  ## Examples
+
+      iex> with {:ok, spline} <- Expline.Spline.from_points([{0.0, 0.0}, {1.0, 1.0}, {2.0, 2.0}]),
+      ...> do: Expline.Spline.interpolate_curvature(spline, 0.5)
+      {:ok, 1.0}
+  """
+  @spec interpolate_curvature(t(), independent_value()) ::
+          {:ok, curvature()}
+          | {:error, interpolation_error()}
+          | {:error, :corrupt_spline}
+  def interpolate_curvature(%__MODULE__{} = spline, x) when is_float(x) do
+    with :error <- Map.fetch(spline.derivatives, x) do
+      case :ordsets.filter(fn {x1, x2} -> x1 < x and x < x2 end, spline.ranges) do
+        [{_x1, _x2} = range] ->
+          do_interpolate_curvature(spline, range, x)
+
+        [] ->
+          extrapolate_curvature(spline, x)
+
+        _ranges ->
+          {:error, :corrupt_spline}
+      end
+    end
+  end
+
+  @spec do_interpolate_curvature(t(), range(), independent_value()) :: {:ok, dependent_value()}
+  defp do_interpolate_curvature(%__MODULE__{} = spline, {x1, x2}, x) do
+    y1 = Map.get(spline.points, x1)
+    y2 = Map.get(spline.points, x2)
+
+    k1 = Map.get(spline.derivatives, x1)
+    k2 = Map.get(spline.derivatives, x2)
+
+    # Described by equations (1), (2), (3), and (4) on
+    # https://en.wikipedia.org/wiki/Spline_interpolation
+    t = (x - x1) / (x2 - x1)
+    a = k1 * (x2 - x1) - (y2 - y1)
+    b = -k2 * (x2 - x1) + (y2 - y1)
+
+    dy = (y2 - y1 + (1 - 2 * t) * (a * (1 - t) + b * t) + t * (1 - t) * (b - a)) / (x2 - x1)
+    {:ok, dy}
+  end
+
+  @spec extrapolate_curvature(t(), independent_value()) ::
+          {:ok, dependent_value()}
+          | {:error, :corrupt_extrema}
+  defp extrapolate_curvature(spline, x) do
+    cond do
+      spline.min > x ->
+        {:ok, Map.get(spline.derivatives, spline.min)}
+
+      spline.max < x ->
+        {:ok, Map.get(spline.derivatives, spline.max)}
+
+      true ->
+        {:error, :corrupt_extrema}
+    end
+  end
+
   @spec make_derivatives(%{required(independent_value()) => dependent_value()}) :: %{
           required(independent_value()) => curvature()
         }
@@ -357,38 +419,38 @@ defmodule Expline.Spline do
       Expline.Matrix.construct(n + 1, n + 2, fn
         # first row
         0, 0 ->
-          2 / (x1 - x0)
+          2 / subtract(x1, x0)
 
         0, 1 ->
-          1 / (x1 - x0)
+          1 / subtract(x1, x0)
 
         # =
         0, j when j == n + 1 ->
-          3.0 * ((y1 - y0) / :math.pow(x1 - x0, 2))
+          3.0 * (subtract(y1, y0) / :math.pow(subtract(x1, x0), 2))
 
         # last row
         ^n, j when j == n - 1 ->
-          1 / (xn - xn_1)
+          1 / subtract(xn, xn_1)
 
         ^n, ^n ->
-          2 / (xn - xn_1)
+          2 / subtract(xn, xn_1)
 
         # =
         ^n, j when j == n + 1 ->
-          3.0 * ((yn - yn_1) / :math.pow(xn - xn_1, 2))
+          3.0 * (subtract(yn, yn_1) / :math.pow(subtract(xn, xn_1), 2))
 
         # middle rows
         i, j when j == i - 1 ->
           [xi_1, xi] = Enum.map(-1..0, fn offset -> Enum.at(xs, i + offset) end)
-          1.0 / (xi - xi_1)
+          1.0 / subtract(xi, xi_1)
 
         i, i ->
           [xi_1, xi, xi1] = Enum.map(-1..1, fn offset -> Enum.at(xs, i + offset) end)
-          2.0 * (1.0 / (xi - xi_1) + 1.0 / (xi1 - xi))
+          2.0 * (1.0 / subtract(xi, xi_1) + 1.0 / subtract(xi1, xi))
 
         i, j when j == i + 1 ->
           [xi, xi1] = Enum.map(0..1, fn offset -> Enum.at(xs, i + offset) end)
-          1.0 / (xi1 - xi)
+          1.0 / subtract(xi1, xi)
 
         # =
         i, j when j == n + 1 ->
@@ -399,8 +461,8 @@ defmodule Expline.Spline do
             |> Enum.map(&Map.get(points, &1))
 
           3.0 *
-            ((yi - yi_1) / :math.pow(xi - xi_1, 2) +
-               (yi1 - yi) / :math.pow(xi1 - xi, 2))
+            (subtract(yi, yi_1) / :math.pow(subtract(xi, xi_1), 2) +
+               subtract(yi1, yi) / :math.pow(subtract(xi1, xi), 2))
 
         # empty terms
         _i, _j ->
@@ -414,4 +476,9 @@ defmodule Expline.Spline do
       Enum.zip(xs, Vector.to_list(derivative_vector)) |> Map.new()
     end
   end
+
+  @spec subtract(minuend :: nil | number(), subtrahend :: nil | number()) :: number()
+  defp subtract(nil, _), do: 0.0
+  defp subtract(_, nil), do: 0.0
+  defp subtract(minuend, subtrahend), do: minuend - subtrahend
 end

mix.exs

@@ -1,8 +1,8 @@
 defmodule Expline.Mixfile do
   use Mix.Project
 
-  @app :expline
-  @version "0.2.0"
+  @app :explinex
+  @version "0.2.4"
 
   def project do
     [
@@ -22,7 +22,7 @@ defmodule Expline.Mixfile do
 
       # Generated documentation parameters
       name: "Expline",
-      source_url: "https://github.com/isaacsanders/#{@app}",
+      source_url: "https://github.com/am-kantox/#{@app}",
       docs: docs()
     ]
   end
@@ -42,34 +42,17 @@ defmodule Expline.Mixfile do
 
   def package do
     [
-      name: :expline,
+      organization: "kantox",
+      name: @app,
       files: ["lib", "mix.exs", "README*", "LICENSE*"],
       licenses: ["MIT"],
-      maintainers: ["Isaac Sanders"],
-      links: %{"GitHub" => "https://github.com/isaacsanders/#{@app}"}
+      maintainers: ["Isaac Sanders", "Aleksei Matiushkin"],
+      links: %{"GitHub" => "https://github.com/am-kantox/#{@app}"}
     ]
   end
 
   def dialyzer do
-    [
-      flags: [
-        :error_handling,
-        :no_behaviours,
-        :no_contracts,
-        :no_fail_call,
-        :no_fun_app,
-        :no_improper_lists,
-        :no_match,
-        :no_missing_calls,
-        :no_opaque,
-        :no_return,
-        :no_undefined_callbacks,
-        :no_unused,
-        :race_conditions,
-        :underspecs,
-        :unknown
-      ]
-    ]
+    []
   end
 
   def docs do

mix.lock

@@ -1,12 +1,14 @@
 %{
   "decimal": {:hex, :decimal, "1.3.1", "157b3cedb2bfcb5359372a7766dd7a41091ad34578296e951f58a946fcab49c6", [:mix], []},
-  "dialyxir": {:hex, :dialyxir, "1.0.0", "6a1fa629f7881a9f5aaf3a78f094b2a51a0357c843871b8bc98824e7342d00a5", [:mix], [{:erlex, ">= 0.2.6", [hex: :erlex, repo: "hexpm", optional: false]}], "hexpm", "aeb06588145fac14ca08d8061a142d52753dbc2cf7f0d00fc1013f53f8654654"},
+  "dialyxir": {:hex, :dialyxir, "1.3.0", "fd1672f0922b7648ff9ce7b1b26fcf0ef56dda964a459892ad15f6b4410b5284", [:mix], [{:erlex, ">= 0.2.6", [hex: :erlex, repo: "hexpm", optional: false]}], "hexpm", "00b2a4bcd6aa8db9dcb0b38c1225b7277dca9bc370b6438715667071a304696f"},
   "earmark": {:hex, :earmark, "1.4.3", "364ca2e9710f6bff494117dbbd53880d84bebb692dafc3a78eb50aa3183f2bfd", [:mix], [], "hexpm", "8cf8a291ebf1c7b9539e3cddb19e9cef066c2441b1640f13c34c1d3cfc825fec"},
+  "earmark_parser": {:hex, :earmark_parser, "1.4.32", "fa739a0ecfa34493de19426681b23f6814573faee95dfd4b4aafe15a7b5b32c6", [:mix], [], "hexpm", "b8b0dd77d60373e77a3d7e8afa598f325e49e8663a51bcc2b88ef41838cca755"},
   "erlex": {:hex, :erlex, "0.2.6", "c7987d15e899c7a2f34f5420d2a2ea0d659682c06ac607572df55a43753aa12e", [:mix], [], "hexpm", "2ed2e25711feb44d52b17d2780eabf998452f6efda104877a3881c2f8c0c0c75"},
-  "ex_doc": {:hex, :ex_doc, "0.21.3", "857ec876b35a587c5d9148a2512e952e24c24345552259464b98bfbb883c7b42", [:mix], [{:earmark, "~> 1.4", [hex: :earmark, repo: "hexpm", optional: false]}, {:makeup_elixir, "~> 0.14", [hex: :makeup_elixir, repo: "hexpm", optional: false]}], "hexpm", "0db1ee8d1547ab4877c5b5dffc6604ef9454e189928d5ba8967d4a58a801f161"},
-  "makeup": {:hex, :makeup, "1.0.1", "82f332e461dc6c79dbd82fbe2a9c10d48ed07146f0a478286e590c83c52010b5", [:mix], [{:nimble_parsec, "~> 0.5.0", [hex: :nimble_parsec, repo: "hexpm", optional: false]}], "hexpm", "49736fe5b66a08d8575bf5321d716bac5da20c8e6b97714fec2bcd6febcfa1f8"},
-  "makeup_elixir": {:hex, :makeup_elixir, "0.14.0", "cf8b7c66ad1cff4c14679698d532f0b5d45a3968ffbcbfd590339cb57742f1ae", [:mix], [{:makeup, "~> 1.0", [hex: :makeup, repo: "hexpm", optional: false]}], "hexpm", "d4b316c7222a85bbaa2fd7c6e90e37e953257ad196dc229505137c5e505e9eff"},
-  "nimble_parsec": {:hex, :nimble_parsec, "0.5.3", "def21c10a9ed70ce22754fdeea0810dafd53c2db3219a0cd54cf5526377af1c6", [:mix], [], "hexpm", "589b5af56f4afca65217a1f3eb3fee7e79b09c40c742fddc1c312b3ac0b3399f"},
+  "ex_doc": {:hex, :ex_doc, "0.29.4", "6257ecbb20c7396b1fe5accd55b7b0d23f44b6aa18017b415cb4c2b91d997729", [:mix], [{:earmark_parser, "~> 1.4.31", [hex: :earmark_parser, repo: "hexpm", optional: false]}, {:makeup_elixir, "~> 0.14", [hex: :makeup_elixir, repo: "hexpm", optional: false]}, {:makeup_erlang, "~> 0.1", [hex: :makeup_erlang, repo: "hexpm", optional: false]}], "hexpm", "2c6699a737ae46cb61e4ed012af931b57b699643b24dabe2400a8168414bc4f5"},
+  "makeup": {:hex, :makeup, "1.1.0", "6b67c8bc2882a6b6a445859952a602afc1a41c2e08379ca057c0f525366fc3ca", [:mix], [{:nimble_parsec, "~> 1.2.2 or ~> 1.3", [hex: :nimble_parsec, repo: "hexpm", optional: false]}], "hexpm", "0a45ed501f4a8897f580eabf99a2e5234ea3e75a4373c8a52824f6e873be57a6"},
+  "makeup_elixir": {:hex, :makeup_elixir, "0.16.1", "cc9e3ca312f1cfeccc572b37a09980287e243648108384b97ff2b76e505c3555", [:mix], [{:makeup, "~> 1.0", [hex: :makeup, repo: "hexpm", optional: false]}, {:nimble_parsec, "~> 1.2.3 or ~> 1.3", [hex: :nimble_parsec, repo: "hexpm", optional: false]}], "hexpm", "e127a341ad1b209bd80f7bd1620a15693a9908ed780c3b763bccf7d200c767c6"},
+  "makeup_erlang": {:hex, :makeup_erlang, "0.1.1", "3fcb7f09eb9d98dc4d208f49cc955a34218fc41ff6b84df7c75b3e6e533cc65f", [:mix], [{:makeup, "~> 1.0", [hex: :makeup, repo: "hexpm", optional: false]}], "hexpm", "174d0809e98a4ef0b3309256cbf97101c6ec01c4ab0b23e926a9e17df2077cbb"},
+  "nimble_parsec": {:hex, :nimble_parsec, "1.3.1", "2c54013ecf170e249e9291ed0a62e5832f70a476c61da16f6aac6dca0189f2af", [:mix], [], "hexpm", "2682e3c0b2eb58d90c6375fc0cc30bc7be06f365bf72608804fb9cffa5e1b167"},
   "pollution": {:hex, :pollution, "0.9.2", "3f67542631071c99f807d2a8f9da799c07cd983c902f5357b9e1569c20a26e76", [:mix], [], "hexpm", "6399fd8ffd97dcc3d9d277f60542a234d644d7bcc0d48c8fda93d6be4801bac2"},
   "quixir": {:hex, :quixir, "0.9.3", "f01c37386b9e1d0526f01a8734a6d7884af294a0ec360f05c24c7171d74632bd", [:mix], [{:pollution, "~> 0.9.2", [hex: :pollution, repo: "hexpm", optional: false]}], "hexpm", "4f3a1fe7c82b767d935b3f7b94cf34b91ef78bb487ef256b303d77417fc7d589"},
 }