Deploying to gh-pages from @ a175229 🚀

Author: boisgera

.pixi/config.toml

@@ -0,0 +1 @@
+run-post-link-scripts = "insecure"

.tmp.py

@@ -1,9 +1,7 @@
 from numpy import *
 from numpy.linalg import *
-from scipy.linalg import *
-from matplotlib.pyplot import *
-from mpl_toolkits.mplot3d import *
 from scipy.integrate import solve_ivp
+from matplotlib.pyplot import *
 # Python 3.x Standard Library
 import gc
 import os
@@ -63,206 +61,110 @@ def set_ratio(ratio=1.0, bottom=0.1, top=0.1, left=0.1, right=0.1):
     height_in = (1.0 - left - right)/(1.0 - bottom - top) * width_in / ratio
     pp.gcf().set_size_inches((width_in, height_in))
     pp.gcf().subplots_adjust(bottom=bottom, top=1.0-top, left=left, right=1.0-right)
+
+width
 def Q(f, xs, ys):
     X, Y = meshgrid(xs, ys)
-    v = vectorize
-    fx = v(lambda x, y: f([x, y])[0])
-    fy = v(lambda x, y: f([x, y])[1])
+    fx = vectorize(lambda x, y: f([x, y])[0])
+    fy = vectorize(lambda x, y: f([x, y])[1])
     return X, Y, fx(X, Y), fy(X, Y)
-a = 2.0; x0 = 1.0
-figure()
-t = linspace(0.0, 3.0, 1000)
-plot(t, exp(a*t)*x0, "k")
-xlabel("$t$"); ylabel("$x(t)$"); title(f"$a={a}$")
-grid(); axis([0.0, 2.0, 0.0, 10.0])
-tight_layout()
-save("images/scalar-LTI-2")
-figure()
-plot(real(a), imag(a), "x", color="k")
-gca().set_aspect(1.0)
-xlim(-3,3); ylim(-3,3); 
-plot([-3,3], [0,0], "k")
-plot([0, 0], [-3, 3], "k")
-xticks([-2,-1,0,1,2]); yticks([-2,-1,0,1,2])
-title(f"$a={a}$"); grid(True)
-tight_layout() 
-save("images/scalar-LTI-2-poles")
-a = 1.0; x0 = 1.0
-figure()
-t = linspace(0.0, 3.0, 1000)
-plot(t, exp(a*t)*x0, "k")
-xlabel("$t$"); ylabel("$x(t)$"); title(f"$a={a}$")
-grid(); axis([0.0, 2.0, 0.0, 10.0])
-tight_layout()
-save("images/scalar-LTI-1")
-figure()
-plot(real(a), imag(a), "x", color="k")
-gca().set_aspect(1.0)
-xlim(-3,3); ylim(-3,3); 
-plot([-3,3], [0,0], "k")
-plot([0, 0], [-3, 3], "k")
-xticks([-2,-1,0,1,2]); yticks([-2,-1,0,1,2])
-title(f"$a={a}$"); grid(True)
-tight_layout()
-save("images/scalar-LTI-1-poles")
-a = 0.0; x0 = 1.0
-figure()
-t = linspace(0.0, 3.0, 1000)
-plot(t, exp(a*t)*x0, "k")
-xlabel("$t$"); ylabel("$x(t)$"); title(f"$a={a}$")
-grid(); axis([0.0, 2.0, 0.0, 10.0])
-tight_layout()
-save("images/scalar-LTI-0")
-figure()
-plot(real(a), imag(a), "x", color="k")
-gca().set_aspect(1.0)
-xlim(-3,3); ylim(-3,3); 
-plot([-3,3], [0,0], "k")
-plot([0, 0], [-3, 3], "k")
-xticks([-2,-1,0,1,2]); yticks([-2,-1,0,1,2])
-title(f"$a={a}$"); grid(True)
-tight_layout()
-save("images/scalar-LTI-0-poles")
-a = -1.0; x0 = 1.0
-figure()
-t = linspace(0.0, 3.0, 1000)
-plot(t, exp(a*t)*x0, "k")
-xlabel("$t$"); ylabel("$x(t)$"); title(f"$a={a}$")
-grid(); axis([0.0, 2.0, 0.0, 10.0])
-tight_layout()
-save("images/scalar-LTI-m1")
-figure()
-plot(real(a), imag(a), "x", color="k")
-gca().set_aspect(1.0)
-xlim(-3,3); ylim(-3,3); 
-plot([-3,3], [0,0], "k")
-plot([0, 0], [-3, 3], "k")
-xticks([-2,-1,0,1,2]); yticks([-2,-1,0,1,2])
-title(f"$a={a}$"); grid(True)
-tight_layout()
-save("images/scalar-LTI-m1-poles")
-a = -2.0; x0 = 1.0
-figure()
-t = linspace(0.0, 3.0, 1000)
-plot(t, exp(a*t)*x0, "k")
-xlabel("$t$"); ylabel("$x(t)$"); title(f"$a={a}$")
-grid(); axis([0.0, 2.0, 0.0, 10.0])
-tight_layout()
-save("images/scalar-LTI-m2")
-figure()
-plot(real(a), imag(a), "x", color="k")
+def fun(t, y):
+    return y * y
+t0, tf, y0 = 0.0, 3.0, array([1.0])
+result = solve_ivp(fun, t_span=[t0, tf], y0=y0)
+figure()
+plot(result["t"], result["y"][0], "k")
+xlim(t0, tf); xlabel("$t$"); ylabel("$x(t)$")
+tight_layout()
+save("images/finite-time-blowup")
+tf = 1.0
+r = solve_ivp(fun, [t0, tf], y0,
+              dense_output=True)
+figure()
+t = linspace(t0, tf, 1000)
+plot(t, r["sol"](t)[0], "k")
+ylim(0.0, 10.0); grid();
+xlabel("$t$"); ylabel("$x(t)$")
+tight_layout()
+save("images/finite-time-blowup-2")
+def f(x1x2):
+    x1, x2 = x1x2
+    dx1 = 1.0 if x1 < 0.0 else -1.0
+    return array([dx1, 0.0])
+figure()
+x1 = x2 = linspace(-1.0, 1.0, 20)
 gca().set_aspect(1.0)
-xlim(-3,3); ylim(-3,3); 
-plot([-3,3], [0,0], "k")
-plot([0, 0], [-3, 3], "k")
-xticks([-2,-1,0,1,2]); yticks([-2,-1,0,1,2])
-title(f"$a={a}$"); grid(True)
+quiver(*Q(f, x1, x2), color="k")
 tight_layout()
-save("images/scalar-LTI-m2-poles")
-a1 = -1.0; a2 = 2.0; x10 = x20 = 1.0
+save("images/discont")
+def sigma(x):
+  return 1 / (1 + exp(-x))
 figure()
-t = linspace(0.0, 3.0, 1000)
-x1 = exp(a1*t)*x10; x2 = exp(a2*t)*x20
-xn = sqrt(x1**2 + x2**2)
-plot(t, xn , "k")
-plot(t, x1, "k--")
-plot(t, x2 , "k--")
-xlabel("$t$"); ylabel("$\|x(t)\|$"); title(f"$a_1={a1}, \; a_2={a2}$")
-grid(); axis([0.0, 2.0, 0.0, 10.0])
-tight_layout()
-save("images/scalar-LTI-m1p2")
-figure()
-plot(real(a1), imag(a1), "x", color="k")
-plot(real(a2), imag(a2), "x", color="k")
-gca().set_aspect(1.0)
-xlim(-3,3); ylim(-3,3); 
-plot([-3,3], [0,0], "k")
-plot([0, 0], [-3, 3], "k")
-xticks([-2,-1,0,1,2]); yticks([-2,-1,0,1,2])
-title(f"$a_1={a1}, \; a_2={a2}$")
-grid(True)
-tight_layout()
-save("images/scalar-LTI-m1p2-poles")
-a1 = -1.0; a2 = -2.0; x10 = x20 = 1.0
-figure()
-t = linspace(0.0, 3.0, 1000)
-x1 = exp(a1*t)*x10; x2 = exp(a2*t)*x20
-xn = sqrt(x1**2 + x2**2)
-plot(t, xn , "k")
-plot(t, x1, "k--")
-plot(t, x2 , "k--")
-xlabel("$t$"); ylabel("$\|x(t)\|$"); title(f"$a_1={a1}, \; a_2={a2}$")
-grid(); axis([0.0, 2.0, 0.0, 10.0])
-tight_layout()
-save("images/scalar-LTI-m1m2")
-figure()
-plot(real(a1), imag(a1), "x", color="k")
-plot(real(a2), imag(a2), "x", color="k")
-gca().set_aspect(1.0)
-xlim(-3,3); ylim(-3,3); 
-plot([-3,3], [0,0], "k")
-plot([0, 0], [-3, 3], "k")
-xticks([-2,-1,0,1,2]); yticks([-2,-1,0,1,2])
-title(f"$a_1={a1}, \; a_2={a2}$")
-grid(True)
-tight_layout()
-save("images/scalar-LTI-m1m2-poles")
-a = 1.0j; x0=1.0
-figure()
-t = linspace(0.0, 20.0, 1000)
-plot(t, real(exp(a*t)*x0), label="$\Re(x(t))$")
-plot(t, imag(exp(a*t)*x0), label="$\mathrm{Im}(x(t))$")
-xlabel("$t$")
-legend(); grid()
-tight_layout()
-save("images/scalar-LTI-alt-1")
-fig = figure()
-ax = fig.add_subplot(111, projection="3d")
-zticks = ax.set_zticks
-ax.plot(t, real(exp(a*t)*x0), imag(exp(a*t)*x0))
-xticks([0.0, 20.0]); yticks([]); zticks([])
-ax.set_xlabel("$t$")
-ax.set_ylabel("$\Re(x(t))$")
-ax.set_zlabel("$\mathrm{Im}(x(t))$")
-tight_layout()
-save("images/scalar-LTI-3d")
-figure()
-plot(real(a), imag(a), "x", color="k")
-gca().set_aspect(1.0)
-xlim(-3,3); ylim(-3,3); 
-plot([-3,3], [0,0], "k")
-plot([0, 0], [-3, 3], "k")
-xticks([-2,-1,0,1,2]); yticks([-2,-1,0,1,2])
-title(f"$a={a}$"); grid(True)
-tight_layout()
-save("images/scalar-LTI-1j-poles")
-a = -0.5 + 1.0j; x0=1.0
-figure()
-t = linspace(0.0, 20.0, 1000)
-plot(t, real(exp(a*t)*x0), label="$\Re(x(t))$")
-plot(t, imag(exp(a*t)*x0), label="$\mathrm{Im}(x(t))$")
-xlabel("$t$")
-legend(); grid()
-tight_layout()
-save("images/scalar-LTI-alt-2")
-fig = figure()
-ax = fig.add_subplot(111, projection="3d")
-zticks = ax.set_zticks
-ax.plot(t, real(exp(a*t)*x0), imag(exp(a*t)*x0))
-xticks([0.0, 20.0]); yticks([]); zticks([])
-ax.set_xlabel("$t$")
-ax.set_ylabel("$\Re(x(t))$")
-ax.set_zlabel("$\mathrm{Im}(x(t))$")
-tight_layout()
-save("images/scalar-LTI-3d-2")
-figure()
-plot(real(a), imag(a), "x", color="k")
-gca().set_aspect(1.0)
-xlim(-3,3); ylim(-3,3); 
-plot([-3,3], [0,0], "k")
-plot([0, 0], [-3, 3], "k")
-xticks([-2,-1,0,1,2]); yticks([-2,-1,0,1,2])
-title(f"$a={a}$")
+x = linspace(-7.0, 7.0, 1000)
+plot(x, sigma(x), label="$y=\sigma(x)$")
 grid(True)
-tight_layout()
-save("images/scalar-LTI-m11j-poles")
+xlim(-5, 5)
+xticks([-5.0, 0.0, 5.0])
+yticks([0.0, 0.5, 1.0])
+xlabel("$x$")
+ylabel("$y$")
+legend()
+pp.gcf().subplots_adjust(bottom=0.2)
+save("images/sigmoid")
+alpha = 2 / 3; beta = 4 / 3; delta = gamma = 1.0
+
+def fun(t, y):
+    x, y = y
+    u = alpha * x - beta * x * y
+    v = delta * x * y - gamma * y
+    return array([u, v])
+tf = 3.0
+result = solve_ivp(
+  fun, 
+  t_span=(0.0, tf), 
+  y0=[1.5, 1.5], 
+  max_step=0.01)
+x, y = result["y"][0], result["y"][1]
+def display_streamplot():
+    ax = gca()
+    xr = yr = linspace(0.0, 2.0, 1000)
+    def f(y):
+        return fun(0, y)
+    streamplot(*Q(f, xr, yr), color="grey")
+def display_reference_solution():
+    for xy in zip(x, y):
+        x_, y_ = xy
+        gca().add_artist(Circle((x_, y_), 
+                         0.2, color="#d3d3d3"))
+    gca().add_artist(Circle((x[0], y[0]), 0.1, 
+                     color="#808080"))
+    plot(x, y, "k")
+def display_alternate_solution():
+    result = solve_ivp(fun, 
+                       t_span=[0.0, tf],
+                       y0=[1.5, 1.575], 
+                       max_step=0.01)
+    x, y = result["y"][0], result["y"][1]
+    plot(x, y, "k--")
+figure()
+display_streamplot()
+display_reference_solution()
+display_alternate_solution()
+axis([0,2,0,2]); axis("square")
+save("images/continuity")
+def fun(t, y):
+  x = y[0]
+  dx = sqrt(abs(y))
+  return [dx]
+tspan = [0.0, 3.0]
+t = linspace(tspan[0], tspan[1], 1000)
+figure()
+for x0 in [0.1, 0.01, 0.001, 0.0001, 0.0]:
+    r = solve_ivp(fun, tspan, [x0], 
+        dense_output=True)
+    plot(t, r["sol"](t)[0], 
+         label=f"$x_0 = {x0}$")
+xlabel("$t$"); ylabel("$x(t)$")
+legend()
+pp.gcf().subplots_adjust(bottom=0.2)
+save("images/eps")

0-1-Introduction.html

@@ -357,12 +357,15 @@ <h4 id="spacexs-starship">🚀 <a
 <section id="adas-self-driving-cars" class="slide level2"
 data-background-color="None">
 <h2 data-background-color="None">ADAS &amp; Self-Driving Cars</h2>
-<p>🏷️ <strong>ADAS:</strong> Advanced Driver-Assistance Systems</p>
-<p>📆 <strong>2025:</strong> fully autonomous cars are not there
-yet.</p>
-<p>Actors: <a href="https://www.tesla.com">Tesla</a>, <a
+<ul>
+<li><p>🏷️ <strong>ADAS:</strong> Advanced Driver-Assistance
+Systems</p></li>
+<li><p>🏢 <a href="https://www.tesla.com">Tesla</a>, <a
 href="https://www.mercedes-benz.com">Mercedes-Benz</a>, <a
-href="https://waymo.com/">Waymo</a>, etc.</p>
+href="https://waymo.com/">Waymo</a>, etc.</p></li>
+<li><p>📆 <strong>2026:</strong> fully autonomous cars are not there yet
+… but we’re coming close!</p></li>
+</ul>
 </section>
 <section id="sae-automation-levels" class="slide level2"
 data-background-color="None">

0-1-Introduction.ipynb

@@ -407,17 +407,7 @@
     {
       "cell_type": "markdown",
       "metadata": {},
-      "source": "\ud83c\udff7\ufe0f **ADAS:** Advanced Driver-Assistance Systems\n"
-    },
-    {
-      "cell_type": "markdown",
-      "metadata": {},
-      "source": "\ud83d\udcc6 **2025:** fully autonomous cars are not there yet.\n"
-    },
-    {
-      "cell_type": "markdown",
-      "metadata": {},
-      "source": "Actors: [Tesla](https://www.tesla.com),\n[Mercedes-Benz](https://www.mercedes-benz.com),\n[Waymo](https://waymo.com/), etc.\n"
+      "source": "-   \ud83c\udff7\ufe0f **ADAS:** Advanced Driver-Assistance Systems\n\n-   \ud83c\udfe2 [Tesla](https://www.tesla.com),\n    [Mercedes-Benz](https://www.mercedes-benz.com),\n    [Waymo](https://waymo.com/), etc.\n\n-   \ud83d\udcc6 **2026:** fully autonomous cars are not there yet \u2026 but we\u2019re\n    coming close!\n"
     },
     {
       "cell_type": "markdown",

0-1-Introduction.md

@@ -217,11 +217,14 @@ $\to$ 🛑 **global 737 MAX groundings.**
 
 ## ADAS & Self-Driving Cars
 
-🏷️ **ADAS:** Advanced Driver-Assistance Systems
+  - 🏷️ **ADAS:** Advanced Driver-Assistance Systems
+
+  - 🏢 [Tesla], [Mercedes-Benz], [Waymo], etc.
+
+  - 📆 **2026:** fully autonomous cars are not there yet ... 
+    but we're coming close!
 
-📆 **2025:** fully autonomous cars are not there yet.
 
-Actors: [Tesla], [Mercedes-Benz], [Waymo], etc.
 
 [Tesla]: https://www.tesla.com
 [Mercedes-Benz]: https://www.mercedes-benz.com