From fb31cc1bf87baa973dc3382f97f139264a7fdac3 Mon Sep 17 00:00:00 2001 From: Kees van Kempen Date: Mon, 3 Oct 2022 10:15:55 +0200 Subject: [PATCH] 04: Solve 1a --- Exercise sheet 4/exercise_sheet_04.ipynb | 28 ++++++++++++++---------- 1 file changed, 17 insertions(+), 11 deletions(-) diff --git a/Exercise sheet 4/exercise_sheet_04.ipynb b/Exercise sheet 4/exercise_sheet_04.ipynb index 80d1d3b..5e4508d 100644 --- a/Exercise sheet 4/exercise_sheet_04.ipynb +++ b/Exercise sheet 4/exercise_sheet_04.ipynb @@ -20,7 +20,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "id": "e39c230e", "metadata": {}, "outputs": [], @@ -62,7 +62,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "id": "6d3bb610", "metadata": { "deletable": false, @@ -131,13 +131,13 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 3, "id": "071e5617", "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ "
" ] @@ -183,7 +183,7 @@ "h = np.zeros((n, n))\n", "for x in range(n): \n", " for k in example_graph.neighbors(x):\n", - " h[x,k] = round(1/example_graph.degree(x),2) \n", + " h[x,k] = round(1/example_graph.degree(x),2)\n", "\n", "h" ] @@ -213,7 +213,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 33, "id": "449da919", "metadata": { "deletable": false, @@ -231,13 +231,15 @@ "outputs": [], "source": [ "def sample_proposal(graph,x):\n", - " # YOUR CODE HERE\n", - " raise NotImplementedError()" + " '''Pick a random node y from the neighbors of x in graph with uniform\n", + " probability.'''\n", + " y_list = np.fromiter(graph.neighbors(x), dtype=int)\n", + " return np.random.choice(y_list)" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 34, "id": "604ce3f4", "metadata": { "deletable": false, @@ -311,8 +313,12 @@ "\n", "def transition_matrix_Q(graph):\n", " '''Construct transition matrix Q from graph as two-dimensional Numpy array.'''\n", - " # YOUR CODE HERE\n", - " raise NotImplementedError()\n", + " n = example_graph.number_of_nodes()\n", + " Q = np.zeros((n, n))\n", + " for x in range(n): \n", + " for k in example_graph.neighbors(x):\n", + " Q[x,k] = round(1/example_graph.degree(x),2)\n", + " return Q\n", "\n", "# Compare histogram and stationary distribution in a plot\n", "# YOUR CODE HERE\n",