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Copied over to Python files and loaded into notebook.
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‎fdm-devito-notebooks/03_diffu/diffu_rw.ipynb‎

Lines changed: 52 additions & 33 deletions
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@@ -243,26 +243,37 @@
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},
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{
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"cell_type": "code",
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"execution_count": 303,
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"import random, numpy as np\n",
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"\n",
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"import random, numpy as np"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 21,
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"metadata": {},
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"outputs": [],
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"source": [
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"# %load -s random_walk1D, src-diffu/random_walk.py\n",
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"def random_walk1D(x0, N, p, random=random):\n",
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" \"\"\"1D random walk with 1 particle.\"\"\"\n",
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" \"\"\"1D random walk with 1 particle and N moves.\"\"\"\n",
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" # random is argument so we can use np.random instead\n",
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" # and use it for testing\n",
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"\n",
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" # Store position in step k in position[k]\n",
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" position = np.zeros(N)\n",
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" position = np.zeros(N+1)\n",
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" position[0] = x0\n",
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" current_pos = x0\n",
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" for k in range(N-1):\n",
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" for k in range(N):\n",
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" r = random.uniform(0, 1)\n",
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" if r <= p:\n",
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" current_pos -= 1\n",
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" else:\n",
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" current_pos += 1\n",
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" position[k+1] = current_pos\n",
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" return position"
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" return position\n"
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]
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},
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{
@@ -287,7 +298,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 295,
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"execution_count": 22,
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"metadata": {},
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"outputs": [],
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"source": [
@@ -306,7 +317,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 296,
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"execution_count": 23,
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"metadata": {},
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"outputs": [],
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"source": [
@@ -315,12 +326,13 @@
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},
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{
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"cell_type": "code",
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"execution_count": 304,
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"execution_count": 24,
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"metadata": {},
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"outputs": [],
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"source": [
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"# %load -s random_walk1D_vec, src-diffu/random_walk.py\n",
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"def random_walk1D_vec(x0, N, p, random=random):\n",
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" \"\"\"1D random walk with 1 particle.\"\"\"\n",
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" \"\"\"Vectorized version of random_walk1D.\"\"\"\n",
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" # Create and initialise r with dimension x_d\n",
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" x_d = Dimension(name='x_d', spacing=Constant('h_x'))\n",
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" r = TimeFunction(name='r', dimensions=(x_d,), shape=(N+1,))\n",
@@ -334,7 +346,7 @@
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" eq = Eq(r.forward, r + steps)\n",
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" op = Operator(eq)\n",
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" op.apply()\n",
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" return r.data"
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" return r.data\n"
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]
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},
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{
@@ -671,15 +683,14 @@
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},
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{
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"cell_type": "code",
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"execution_count": 283,
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"execution_count": 25,
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"metadata": {},
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"outputs": [],
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"source": [
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"from devito import Grid\n",
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"\n",
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"def random_walks1D(x0, N, p, num_walks=1, num_times=1, random=random):\n",
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"# %load -s random_walks1D_vec, src-diffu/random_walk.py\n",
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"def random_walks1D_vec(x0, N, p, num_walks=1, num_times=1, random=random):\n",
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" \"\"\"Vectorized version of random_walks1D.\"\"\"\n",
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" position = np.zeros(N+1) # Accumulated positions\n",
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" position = np.zeros(N+1) # Accumulated positions\n",
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" position2 = np.zeros(N+1) # Accumulated positions**2\n",
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" # Histogram at num_times selected time points\n",
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" pos_hist = np.zeros((num_walks, num_times))\n",
@@ -711,7 +722,7 @@
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" \n",
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" pos_hist[:,:] = np.transpose(r.data[pos_hist_times,:])\n",
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" \n",
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" return position, position2, pos_hist, np.array(pos_hist_times)"
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" return position, position2, pos_hist, np.array(pos_hist_times)\n"
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]
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},
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{
@@ -754,7 +765,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 297,
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"execution_count": 26,
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"metadata": {},
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"outputs": [],
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"source": [
@@ -779,7 +790,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 298,
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"execution_count": 27,
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"metadata": {},
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"outputs": [
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{
@@ -814,6 +825,8 @@
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"run, and it can be very difficult to spot bugs through averaged statistical\n",
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"quantities.\n",
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"\n",
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"A full test suite for this notebook, along with the rest of the functions for random walks, can be found in [`random_walk.py`](src-diffu/random_walk.py).\n",
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"\n",
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"## Demonstration of multiple walks\n",
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"\n",
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"Assuming now that the code works, we can just scale up the number of\n",
@@ -1084,16 +1097,17 @@
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},
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{
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"cell_type": "code",
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"execution_count": 299,
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# %load -s random_walk2D, src-diffu/random_walk.py\n",
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"def random_walk2D(x0, N, p, random=random):\n",
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" \"\"\"2D random walk with 1 particle and N moves: N, E, W, S.\"\"\"\n",
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" # Store position in step k in position[k]\n",
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" d = len(x0)\n",
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" position = np.zeros((N+1, d))\n",
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" position[0,:] = x0\n",
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" position[0, :] = x0\n",
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" current_pos = np.array(x0, dtype=float)\n",
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" for k in range(N):\n",
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" r = random.uniform(0, 1)\n",
@@ -1105,8 +1119,8 @@
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" current_pos += np.array([0, -1]) # Move south\n",
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" else:\n",
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" current_pos += np.array([-1, 0]) # Move west\n",
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" position[k+1,:] = current_pos\n",
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" return position"
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" position[k+1, :] = current_pos\n",
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" return position\n"
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]
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},
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{
@@ -1144,16 +1158,17 @@
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},
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{
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"cell_type": "code",
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"execution_count": 301,
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# %load -s random_walkdD, src-diffu/random_walk.py\n",
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"def random_walkdD(x0, N, p, random=random):\n",
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" \"\"\"Any-D (diagonal) random walk with 1 particle and N moves.\"\"\"\n",
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" # Store position in step k in position[k]\n",
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" d = len(x0)\n",
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" position = np.zeros((N+1, d))\n",
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" position[0,:] = x0\n",
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" position[0, :] = x0\n",
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" current_pos = np.array(x0, dtype=float)\n",
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" for k in range(N):\n",
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" for i in range(d):\n",
@@ -1162,8 +1177,8 @@
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" current_pos[i] -= 1\n",
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" else:\n",
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" current_pos[i] += 1\n",
1165-
" position[k+1,:] = current_pos\n",
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" return position"
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" position[k+1, :] = current_pos\n",
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" return position\n"
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]
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},
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{
@@ -1175,11 +1190,14 @@
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},
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{
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"cell_type": "code",
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"execution_count": 305,
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# %load -s random_walkdD_vec, src-diffu/random_walk.py\n",
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"def random_walkdD_vec(x0, N, p, random=random):\n",
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" \"\"\"Vectorized version of random_walkdD.\"\"\"\n",
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"\n",
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" # Here, x0 is an array of initial values in each spatial dimension\n",
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" d = len(x0)\n",
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" \n",
@@ -1197,7 +1215,7 @@
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" eq = Eq(r.forward, r + steps)\n",
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" op = Operator(eq)\n",
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" op.apply()\n",
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" return r.data"
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" return r.data\n"
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]
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},
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{
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},
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{
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"cell_type": "code",
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"execution_count": 225,
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"def random_walksdD_vec(x0, N, p, num_walks=1, num_times=1, random=random):\n",
1246+
"# %load -s random_walksdD_vec, src-diffu/random_walk.py\n",
1247+
"def random_walksdD_vec(x0, N, p, num_walks=1, num_times=1, random=np.random):\n",
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" \"\"\"Vectorized version of random_walksdD.\"\"\"\n",
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" d = len(x0)\n",
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" position = np.zeros((N+1, d)) # Accumulated positions\n",
@@ -1261,7 +1280,7 @@
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" for k in range(num_walks):\n",
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" pos_hist[k,:] = r.data[pos_hist_times,k]\n",
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" \n",
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" return position, position2, pos_hist, np.array(pos_hist_times)"
1283+
" return position, position2, pos_hist, np.array(pos_hist_times)\n"
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]
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},
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{

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