add test for archimedian spiral without function arguments

test/test_archimedean_spiral_noargs.py

@@ -0,0 +1,57 @@
+import matplotlib.pyplot as plt
+import numpy as np
+import pytest
+
+import contique
+
+
+def fun(x, l):
+    a = 1
+    r = a * l
+    return np.array([-x[0] + r * np.cos(l), -x[1] + r * np.sin(l)])
+
+
+def test_archimedian_spiral_noargs():
+
+    # initial solution
+    x0 = np.zeros(2)
+    lpf0 = 0.0
+
+    # numeric continuation
+    Res = contique.solve(
+        fun=fun,
+        x0=x0,
+        lpf0=lpf0,
+        dxmax=0.2,
+        dlpfmax=0.2,
+        maxsteps=500,
+        maxcycles=4,
+        maxiter=8,
+        tol=1e-10,
+        overshoot=1.05,
+    )
+
+    X = np.array([res.x for res in Res])
+
+    plt.plot(X[:, 0], X[:, 1], "-")
+    plt.xlabel("$x_1$")
+    plt.ylabel("$x_2$")
+    plt.xlim(-15, 15)
+    plt.ylim(-15, 15)
+    plt.plot([0], [0], "C0o", lw=3)
+    plt.arrow(
+        X[-2, 0],
+        X[-2, 1],
+        X[-1, 0] - X[-2, 0],
+        X[-1, 1] - X[-2, 1],
+        head_width=1,
+        head_length=2,
+        fc="C0",
+        ec="C0",
+    )
+    plt.gca().set_aspect("equal")
+    plt.savefig("test_archimedean_spiral_noargs.svg")
+
+
+if __name__ == "__main__":
+    test_archimedian_spiral_noargs()