update

Source/initial_conditions.py

@@ -0,0 +1,96 @@
+import numpy as np
+import matplotlib.pyplot as plt
+POS_MIN = -1
+POS_MAX = +1
+VEL_MIN = -1
+VEL_MAX = +1
+N_PART = 1
+
+def mesh_grid(N: int = N_PART,
+              xmin: float = POS_MIN, 
+              xmax: float = POS_MAX, 
+              ymin: float = POS_MIN, 
+              ymax: float = POS_MAX) -> np.ndarray:
+    """Generates a set of regularly sampled particles with no velocity
+    :param N: number of particles
+    :parma xmin: Minimum value for position x
+    :param xmax: Maximum value for position x
+    :param ymin: Minimum value for position y
+    :param ymax: Maximum value for position y
+    :returns W: Phase-space vector
+    """
+    X = np.linspace(xmin, xmax, N)
+    Y = np.linspace(ymin, ymax, N)
+    X,Y = np.meshgrid(X,Y, indexing="ij")
+    return np.array([X,Y])
+
+def one_part(x0: float = 0, 
+             y0: float = 0, 
+             u0: float= 0, 
+             v0: float = 0) -> np.ndarray:
+    """Generates a particle at position (x0, y0) 
+    with velocities (u0,v0)
+    :param x0: Initial position x
+    :param y0: Initial position y
+    :param u0: Initial velocity u
+    :param v0: Initial velocity v
+    """
+    X = x0
+    Y = y0
+    U = u0
+    V = v0
+    return np.array([[X,Y], [U,V]])
+
+def n_energy_part(potential,
+                  N: int = N_PART,
+                  E: float = 0,
+                  xmin: float = -1,
+                  xmax: float = +1,
+                  ymin: float = -0.5,
+                  ymax: float = +1):
+    X = []
+    Y = []
+    POT = []
+    U = []
+    V = []
+    while len(X) < N:
+        x = np.random.random()*(xmax-xmin)+xmin
+        y = np.random.random()*(ymax-ymin)+ymin
+        w = np.array([x, y])
+        pot = potential(w, position_only=True)[0]
+        if pot <= E:
+            X.append(x)
+            Y.append(y)
+            POT.append(pot)
+    X = np.array(X)
+    Y = np.array(Y)
+    POT = np.array(POT)
+    U = np.zeros_like(X)
+    V = np.zeros_like(Y)
+    C = np.sqrt(2 * (E - POT))
+    THETA = np.random.random(N)*2*np.pi
+    U = C*np.cos(THETA)
+    V = C*np.sin(THETA)
+    return np.array([[X, Y], [U, V]])
+
+def n_energy_2part(potential,
+                   N: int = N_PART,
+                   E: float = 0,
+                   sep: float = 1e-7,
+                   xmin: float = -1,
+                   xmax: float = +1,
+                   ymin: float = -0.5,
+                   ymax: float = +1):
+    W_1 = n_energy_part(potential, N, E)
+    W_2 = np.zeros_like(W_1)
+    alpha = np.random.uniform(0, 2*np.pi, N)
+    W_2[0, 0] = W_1[0, 0] + sep*np.cos(alpha)
+    W_2[0, 1] = W_1[0, 1] + sep*np.sin(alpha)
+    W_2[1, 0] = W_1[1, 0]
+    W_2[1, 1] = W_1[1, 1]
+    return (W_1, W_2)
+
+
+
+
+