commit 98ed13132b478e0ae6bd9ccd6c671e2876e3696e
Author: fruchti <fruchti@gvfr.de>
Date:   Sun Dec 11 12:58:10 2022 +0100

    Add plotting library, simple ODE plot

diff --git a/.envrc b/.envrc
new file mode 100644
index 0000000..65326bb
--- /dev/null
+++ b/.envrc
@@ -0,0 +1 @@
+use nix
\ No newline at end of file
diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..bfa43b8
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,4 @@
+__pycache__
+
+plots/*
+!.gitkeep
\ No newline at end of file
diff --git a/lib/plot.py b/lib/plot.py
new file mode 100644
index 0000000..6fddd06
--- /dev/null
+++ b/lib/plot.py
@@ -0,0 +1,288 @@
+#!/usr/bin/env python
+
+import cairo
+import numpy as np
+
+
+class Paper:
+    def __init__(self, width, height, margins=None):
+        self.width = width
+        self.height = height
+        self.margins = {
+            'top': 0,
+            'right': 0,
+            'bottom': 0,
+            'left': 0
+        }
+        if isinstance(margins, int) or isinstance(margins, float):
+            self.margins['top'] = margins
+            self.margins['right'] = margins
+            self.margins['bottom'] = margins
+            self.margins['left'] = margins
+        elif isinstance(margins, list) and (isinstance(margins[0], int)
+                                            or isinstance(margins[0], float)):
+            if len(margins) == 2:
+                self.margins['top'] = margins[0]
+                self.margins['bottom'] = margins[0]
+                self.margins['left'] = margins[1]
+                self.margins['right'] = margins[1]
+            elif len(margins) == 3:
+                self.margins['top'] = margins[0]
+                self.margins['left'] = margins[1]
+                self.margins['right'] = margins[1]
+                self.margins['bottom'] = margins[2]
+            elif len(margins) == 4:
+                self.margins['top'] = margins[0]
+                self.margins['right'] = margins[1]
+                self.margins['bottom'] = margins[2]
+                self.margins['left'] = margins[3]
+        else:
+            self.margins = margins
+
+    @property
+    def content_width(self):
+        return self.width - self.margins['left'] - self.margins['right']
+
+    @property
+    def content_height(self):
+        return self.height - self.margins['top'] - self.margins['bottom']
+
+    def size(self, honour_margins=True):
+        if honour_margins:
+            return np.array([self.content_width, self.content_height])
+        else:
+            return np.array([self.width, self.height])
+
+    def is_within(self, point, honour_margins=True):
+        return ((self.left(honour_margins) < point[0])
+                and (point[0] < self.right(honour_margins))
+                and (self.top(honour_margins) < point[1])
+                and (point[1] < self.bottom(honour_margins)))
+
+    def top_left(self, honour_margins=True):
+        if honour_margins:
+            return np.array([self.margins['left'],
+                             self.height - self.margins['top']])
+        else:
+            return np.array([0, self.height])
+
+    def bottom_left(self, honour_margins=True):
+        if honour_margins:
+            return np.array([self.margins['left'],
+                             self.margins['bottom']])
+        else:
+            return np.array([0, 0])
+
+    def top_right(self, honour_margins=True):
+        if honour_margins:
+            return np.array([self.width - self.margins['right'],
+                             self.height - self.margins['top']])
+        else:
+            return np.array([self.width, self.height])
+
+    def bottom_right(self, honour_margins=True):
+        if honour_margins:
+            return np.array([self.width - self.margins['right'],
+                             self.margins['bottom']])
+        else:
+            return np.array([self.width, 0])
+
+    def centre(self, honour_margins=True):
+        return (self.bottom_left(honour_margins)
+                + self.top_right(honour_margins)) / 2
+
+    def top(self, honour_margins=True):
+        if honour_margins:
+            return self.margins['top']
+        else:
+            return 0
+
+    def left(self, honour_margins=True):
+        if honour_margins:
+            return self.margins['left']
+        else:
+            return 0
+
+    def right(self, honour_margins=True):
+        if honour_margins:
+            return self.width - self.margins['right']
+        else:
+            return self.width
+
+    def bottom(self, honour_margins=True):
+        if honour_margins:
+            return self.height - self.margins['bottom']
+        else:
+            return self.height
+
+
+A4_PORTRAIT = Paper(210, 297, 20)
+A6_PORTRAIT = Paper(105, 148, 8)
+
+
+class MultiPlotter:
+    def __init__(self):
+        self.plotters = []
+
+    def move_to(self, point):
+        for plotter in self.plotters:
+            plotter.move_to(point)
+
+    def line_to(self, point):
+        for plotter in self.plotters:
+            plotter.line_to(point)
+
+    def add_layer(self, *args, **kwargs):
+        for plotter in self.plotters:
+            plotter.add_layer(*args, **kwargs)
+
+    def finalise(self):
+        for plotter in self.plotters:
+            plotter.finalise()
+
+    def register_plotter(self, plotter):
+        self.plotters.append(plotter)
+
+
+class Plotter:
+
+    def __init__(self, paper, line_width=0, colour=[0, 0, 0, 1]):
+        self.paper = paper
+        self.pen_down = False
+        self.position = np.array([0, 0])
+
+        self.layers = []
+        self.add_layer(colour, line_width)
+
+    def add_layer(self, colour=[0, 0, 0, 1], line_width=0.5, name='',
+                  switch=True):
+        self.layers.append({
+            'line_width': line_width,
+            'colour': colour,
+            'name': name
+        })
+        if switch:
+            self.switch_layer(len(self.layers) - 1)
+        return len(self.layers) - 1
+
+    def switch_layer(self, layer):
+        self.current_layer = layer
+
+    def move_to(self, point):
+        self.pen_down = False
+        self.position = point
+
+    def line_to(self, point):
+        self.pen_down = True
+        self.position = point
+
+
+class SVGPlotter(Plotter):
+
+    def __init__(self, file_name, paper, line_width=0.5, colour=[0, 0, 0, 1]):
+        dpi = 72
+        self.file_name = file_name
+        self.surface = cairo.SVGSurface(file_name,
+                                        paper.width / 25.4 * dpi,
+                                        paper.height / 25.4 * dpi)
+        self.context = cairo.Context(self.surface)
+        self.context.scale(dpi / 25.4, dpi / 25.4)
+        self.context.set_line_cap(cairo.LINE_CAP_ROUND)
+
+        super().__init__(paper, line_width, colour)
+
+    def move_to(self, point):
+        if self.pen_down:
+            self.context.stroke()
+        self.context.move_to(point[0], point[1])
+        super().move_to(point)
+
+    def line_to(self, point):
+        self.context.line_to(point[0], point[1])
+        super().line_to(point)
+
+    def finalise(self):
+        if self.pen_down:
+            self.context.stroke()
+            self.pen_down = False
+        self.surface.finish()
+
+    def switch_layer(self, layer):
+        if self.pen_down:
+            self.context.stroke()
+
+        super().switch_layer(layer)
+        self.context.set_source_rgba(
+            *self.layers[self.current_layer]['colour'])
+        self.context.set_line_width(
+            self.layers[self.current_layer]['line_width'])
+
+        return len(self.layers) - 1
+
+
+class HPGLPlotter(Plotter):
+
+    def __init__(self, paper, file_name_pattern):
+        self.file_name_pattern = file_name_pattern
+        self.resolution = (4000 / 81.5, 4000 / 80.5)
+        self.file = None
+        super().__init__(paper)
+
+    def _layer_file_name(self, index):
+        return self.file_name_pattern.format(
+            index=index,
+            name=self.layers[index]['name'],
+            colour=self.layers[index]['colour']
+        )
+
+    def _mm_to_plotter(self, mm):
+        p = (mm[0] * self.resolution[0],
+             (self.paper.height - mm[1]) * self.resolution[1])
+        return f'{p[0]:.0f},{p[1]:.0f}'
+
+    def move_to(self, point):
+        if self.pen_down:
+            self.file.write(';PU')
+        else:
+            self.file.write(',')
+        self.file.write(self._mm_to_plotter(point))
+        return super().move_to(point)
+
+    def line_to(self, point):
+        if not self.pen_down:
+            self.file.write(';PD')
+        else:
+            self.file.write(',')
+        self.file.write(self._mm_to_plotter(point))
+        return super().line_to(point)
+
+    def add_layer(self, colour='black', line_width=0.5, name='', switch=True):
+        new_index = super().add_layer(colour=colour, line_width=line_width,
+                                      name=name, switch=False)
+        layer_file = open(self._layer_file_name(new_index), 'wt')
+
+        layer_file.write('IN;PU0,0')
+
+        if switch:
+            if self.file:
+                self.file.close()
+            self.file = layer_file
+            self.current_layer = len(self.layers) - 1
+        else:
+            layer_file.close()
+
+        return len(self.layers) - 1
+
+    def switch_layer(self, layer):
+        if self.pen_down:
+            self.file.write(';PU')
+            self.pen_down = False
+        self.file.close()
+        super().switch_layer(layer)
+        self.file = open(self._layer_file_name(self.current_layer), 'at')
+
+    def finalise(self):
+        self.file.close()
+        for i in range(len(self.layers)):
+            with open(self._layer_file_name(i), 'at') as file:
+                file.write(';PU0,0;IN')
diff --git a/ode.ipynb b/ode.ipynb
new file mode 100644
index 0000000..701b6d5
--- /dev/null
+++ b/ode.ipynb
@@ -0,0 +1,108 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from lib import plot\n",
+    "import IPython\n",
+    "import numpy as np"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
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+      "text/plain": [
+       "<IPython.core.display.SVG object>"
+      ]
+     },
+     "execution_count": 18,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "a = plot.A6_PORTRAIT\n",
+    "p_svg = plot.SVGPlotter('plots/ode.svg', a)\n",
+    "p_hpgl = plot.HPGLPlotter(a, 'plots/ode_{index}.hpgl')\n",
+    "p = plot.MultiPlotter()\n",
+    "p.register_plotter(p_svg)\n",
+    "p.register_plotter(p_hpgl)\n",
+    "\n",
+    "p.move_to(a.bottom_left())\n",
+    "p.line_to(a.bottom_right())\n",
+    "p.line_to(a.top_right())\n",
+    "p.line_to(a.top_left())\n",
+    "p.line_to(a.bottom_left())\n",
+    "\n",
+    "A = np.array([[-0.4, -0.2], [0.1, -0.3]])\n",
+    "A = np.random.normal(size=(2, 2))\n",
+    "\n",
+    "def plot_ode(A):\n",
+    "    dia = np.min(a.size()) * 0.75\n",
+    "    # step_size = 0.01 / np.max(np.abs(np.linalg.eig(A)[0]))\n",
+    "\n",
+    "    states = np.linspace(0, 2 * np.pi, 24)\n",
+    "    states = np.vstack([np.cos(states), np.sin(states)])\n",
+    "    for s in states.T:\n",
+    "        p.move_to(s * dia / 2 + a.centre())\n",
+    "        for _ in range(100000):\n",
+    "            step = A @ s\n",
+    "            step *= (0.5 / dia) / np.linalg.norm(step)\n",
+    "            s = step + s\n",
+    "            n = s * dia / 2 + a.centre()\n",
+    "            if not a.is_within(n):\n",
+    "                break\n",
+    "            if np.linalg.norm(s * dia / 2) < 0.5:\n",
+    "                break\n",
+    "            p.line_to(n)\n",
+    "\n",
+    "p.add_layer([1, 0, 1, 0.5])\n",
+    "plot_ode(A)\n",
+    "p.add_layer([1, 0, 0, 0.5])\n",
+    "plot_ode(-A)\n",
+    "# A = np.linalg.inv(A)\n",
+    "# plot_ode(A)\n",
+    "# plot_ode(-A)\n",
+    "\n",
+    "p.finalise()\n",
+    "\n",
+    "IPython.display.SVG(filename=p_svg.file_name)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3.9.15 64-bit",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.15"
+  },
+  "orig_nbformat": 4,
+  "vscode": {
+   "interpreter": {
+    "hash": "1dc4d77b1edb83bef89f833b7ed5251134c6a4899ef5e2c90c44e9927b4ae63a"
+   }
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/plots/.gitkeep b/plots/.gitkeep
new file mode 100644
index 0000000..e69de29
diff --git a/shell.nix b/shell.nix
new file mode 100644
index 0000000..e8d9bce
--- /dev/null
+++ b/shell.nix
@@ -0,0 +1,15 @@
+{ pkgs ? import <nixpkgs> {} }:
+let
+    pythonWithPackages = pkgs.python3.withPackages (p: with p; [
+        pycairo
+        numpy
+        jupyter
+        ipykernel
+        matplotlib
+        scipy
+        opencv4
+        noise
+        autopep8
+    ]);
+in
+pythonWithPackages.env
\ No newline at end of file