tempestpy/doc/source/doc/models/building_ctmcs.ipynb

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   "source": [
    "# Continuous-time Markov chains (CTMCs)"
   ]
  },
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   "source": [
    "## Background\n",
    "\n",
    "In this section, we explain how Stormpy can be used to build a simple CTMC.\n",
    "Building CTMCs works similar to building DTMCs as in [Discrete-time Markov chains (DTMCs)](building_dtmcs.ipynb), but additionally every state is equipped with an exit rate.\n",
    "\n",
    "[01-building-ctmcs.py](https://github.com/moves-rwth/stormpy/blob/master/examples/building_ctmcs/01-building-ctmcs.py)\n",
    "\n",
    "First, we import Stormpy:"
   ]
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  {
   "cell_type": "code",
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   "source": [
    ">>> import stormpy"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "## Transition Matrix\n",
    "\n",
    "In this example, we build the transition matrix using a numpy array"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
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   "source": [
    ">>> import numpy as np\n",
    ">>> transitions = np.array([\n",
    "...    [0, 1.5, 0, 0],\n",
    "...    [3, 0, 1.5, 0],\n",
    "...    [0, 3, 0, 1.5],\n",
    "...    [0, 0, 3, 0], ], dtype='float64')"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "The following function call returns a sparse matrix with default row groups:"
   ]
  },
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   "cell_type": "code",
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   "source": [
    ">>> transition_matrix = stormpy.build_sparse_matrix(transitions)\n",
    ">>> print(transition_matrix) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Labeling\n",
    "\n",
    "The state labeling is created analogously to the previous example in [building DTMCs](building_dtmcs.ipynb#labeling):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "source": [
    ">>> state_labeling = stormpy.storage.StateLabeling(4)\n",
    ">>> state_labels = {'empty', 'init', 'deadlock', 'full'}\n",
    ">>> for label in state_labels:\n",
    "...    state_labeling.add_label(label)\n",
    ">>> state_labeling.add_label_to_state('init', 0)\n",
    ">>> state_labeling.add_label_to_state('empty', 0)\n",
    ">>> state_labeling.add_label_to_state('full', 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exit Rates\n",
    "\n",
    "Lastly, we initialize a list to equip every state with an exit rate:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "hide-output": false
   },
   "outputs": [],
   "source": [
    ">>> exit_rates = [1.5, 4.5, 4.5, 3.0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Building the Model\n",
    "\n",
    "Now, we can collect all components, including the choice labeling and the exit rates.\n",
    "To let the transition values be interpreted as rates we set rate_transitions to True:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "hide-output": false
   },
   "outputs": [],
   "source": [
    ">>> components = stormpy.SparseModelComponents(transition_matrix=transition_matrix, state_labeling=state_labeling, rate_transitions=True)\n",
    ">>> components.exit_rates = exit_rates"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And finally, we can build the model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "hide-output": false
   },
   "outputs": [],
   "source": [
    ">>> ctmc = stormpy.storage.SparseCtmc(components)\n",
    ">>> print(ctmc) "
   ]
  }
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