.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/sensitivity_analysis.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code or to run this example in your browser via Binder .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_sensitivity_analysis.py: Sensitivity Analysis in Python ============================== This guide is organized in the following sections: - `Sensitivity Analysis Theory <#What-is-Sensitivity-Analysis%3F>`__ - `The Hard Way <#How-to-Do-Sensitivity-Analysis-in-Python%3F>`__ - `The Easy Way (use ``sensitivity``) <#Using-The-Sensitivity-Library>`__ What is Sensitivity Analysis? ----------------------------- Sensitivity Analysis is the process of passing different inputs to a model to see how the outputs change. It differs from Monte Carlo Simulation in that no probability distributions are assigned to the inputs, and typically larger ranges of the inputs are chosen. The purpose of Sensitivity Analysis is to understand how the outputs change over the full range of possible inputs. Sensitivity Analysis does not derive any expected outcome or a probability distribution of outcomes, instead returning a range of possible output values associated with each set of inputs. The general process for Sensitivity Analysis is as follows: For the model given by: .. math:: y = f(X) .. math:: X = [x_1, x_2, ..., x_n] Where: - :math:`y`: Model output - :math:`X`: Model input matrix - :math:`x_i` Value if :math:`i`\ th :math:`x` variable Follow the following steps: - Choose a set of values for each :math:`x_i` - Take the cartesian product of these values as :math:`[X_1, X_2, ..., X_m]` - For each :math:`X_i`, calculate :math:`y_i = f(X_i)` - Store the values of :math:`X_i` mapped to :math:`y_i` - Visualize :math:`y_i` versus :math:`X_i` How to Do Sensitivity Analysis in Python? ----------------------------------------- Abstract algorithms are great, but let’s see the code that can make this happen. First we’ll import pandas to use later and define a function which represents the model: .. GENERATED FROM PYTHON SOURCE LINES 56-66 .. code-block:: default import pandas as pd def my_model(x_1, x_2): """ Represents f from above """ return x_1 ** x_2 .. GENERATED FROM PYTHON SOURCE LINES 67-69 We can run this model once to get a single result: .. GENERATED FROM PYTHON SOURCE LINES 69-74 .. code-block:: default y = my_model(2, 4) y .. rst-class:: sphx-glr-script-out .. code-block:: none 16 .. GENERATED FROM PYTHON SOURCE LINES 75-78 Now let’s go step by step through the above algorithm. First let’s choose a set of values for each :math:`x_i`: .. GENERATED FROM PYTHON SOURCE LINES 78-83 .. code-block:: default x1_values = [10, 20, 30] x2_values = [1, 2, 3] .. GENERATED FROM PYTHON SOURCE LINES 84-89 While we can use ``itertools.product`` to take a cartesian product of an arbitrary number of inputs, a more straightforward approach is to use nested for loops. A for loop within a for loop will run with each combination of the inputs. .. GENERATED FROM PYTHON SOURCE LINES 89-95 .. code-block:: default for x1 in x1_values: for x2 in x2_values: print(x1, x2) .. rst-class:: sphx-glr-script-out .. code-block:: none 10 1 10 2 10 3 20 1 20 2 20 3 30 1 30 2 30 3 .. GENERATED FROM PYTHON SOURCE LINES 96-98 Now we have each :math:`X_i`, we need to calculate :math:`y_i = f(X_i)`: .. GENERATED FROM PYTHON SOURCE LINES 98-105 .. code-block:: default for x1 in x1_values: for x2 in x2_values: y_i = my_model(x1, x2) print(y_i) .. rst-class:: sphx-glr-script-out .. code-block:: none 10 100 1000 20 400 8000 30 900 27000 .. GENERATED FROM PYTHON SOURCE LINES 106-108 Now store the values of :math:`X_i` mapped to :math:`y_i`: .. GENERATED FROM PYTHON SOURCE LINES 108-117 .. code-block:: default outputs = [] for x1 in x1_values: for x2 in x2_values: y_i = my_model(x1, x2) outputs.append((x1, x2, y_i)) outputs .. rst-class:: sphx-glr-script-out .. code-block:: none [(10, 1, 10), (10, 2, 100), (10, 3, 1000), (20, 1, 20), (20, 2, 400), (20, 3, 8000), (30, 1, 30), (30, 2, 900), (30, 3, 27000)] .. GENERATED FROM PYTHON SOURCE LINES 118-121 Now the last is to visualize the result. We can do this with a table format through a ``DataFrame``: .. GENERATED FROM PYTHON SOURCE LINES 121-126 .. code-block:: default df = pd.DataFrame(outputs, columns=['x_1', 'x_2', 'y']) df .. raw:: html
x_1 x_2 y
0 10 1 10
1 10 2 100
2 10 3 1000
3 20 1 20
4 20 2 400
5 20 3 8000
6 30 1 30
7 30 2 900
8 30 3 27000


.. GENERATED FROM PYTHON SOURCE LINES 127-130 We can add some styling to the DataFrame to highlight the high and low values: .. GENERATED FROM PYTHON SOURCE LINES 130-134 .. code-block:: default df.style.background_gradient(subset='y', cmap='RdYlGn') .. raw:: html
  x_1 x_2 y
0 10 1 10
1 10 2 100
2 10 3 1000
3 20 1 20
4 20 2 400
5 20 3 8000
6 30 1 30
7 30 2 900
8 30 3 27000


.. GENERATED FROM PYTHON SOURCE LINES 135-137 We can plot the result as well with a hex-bin plot. .. GENERATED FROM PYTHON SOURCE LINES 137-141 .. code-block:: default df.plot.hexbin(x='x_1', y='x_2', C='y', gridsize=3, cmap='RdYlGn', sharex=False) .. image-sg:: /auto_examples/images/sphx_glr_sensitivity_analysis_001.png :alt: sensitivity analysis :srcset: /auto_examples/images/sphx_glr_sensitivity_analysis_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 142-153 Using The Sensitivity Library ----------------------------- The ``sensitivity`` package is designed around making this whole process easier. It is also able to handle more than two varying inputs with ease. The basic usage is to construct a dictionary where the keys are the names of inputs in a function and values are iterables of the values for that input. Then this dictionary is passed to ``SensitivityAnalyzer`` along with the function. The rest is handled for you. .. GENERATED FROM PYTHON SOURCE LINES 153-164 .. code-block:: default from sensitivity import SensitivityAnalyzer sensitivity_dict = { 'x_1': [10, 20, 30], 'x_2': [1, 2, 3] } sa = SensitivityAnalyzer(sensitivity_dict, my_model) .. rst-class:: sphx-glr-script-out .. code-block:: none 0%| | 0/9 [00:00
x_1 x_2 Result
0 10 1 10
1 10 2 100
2 10 3 1000
3 20 1 20
4 20 2 400
5 20 3 8000
6 30 1 30
7 30 2 900
8 30 3 27000


.. GENERATED FROM PYTHON SOURCE LINES 174-176 We can also get the hex-bin plot and styled DataFrame: .. GENERATED FROM PYTHON SOURCE LINES 176-182 .. code-block:: default plot = sa.plot() styled = sa.styled_dfs() .. image-sg:: /auto_examples/images/sphx_glr_sensitivity_analysis_002.png :alt: sensitivity analysis :srcset: /auto_examples/images/sphx_glr_sensitivity_analysis_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 183-186 When creating the ``SensitivityAnalyzer`` object, you can pass other options for formatting the outputs: .. GENERATED FROM PYTHON SOURCE LINES 186-200 .. code-block:: default labels = { 'x_1': 'First Input', 'x_2': 'Second Input' } sa = SensitivityAnalyzer( sensitivity_dict, my_model, grid_size=3, reverse_colors=True, color_map='coolwarm', labels=labels ) plot = sa.plot() styled = sa.styled_dfs() .. image-sg:: /auto_examples/images/sphx_glr_sensitivity_analysis_003.png :alt: sensitivity analysis :srcset: /auto_examples/images/sphx_glr_sensitivity_analysis_003.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none 0%| | 0/9 [00:00 .. GENERATED FROM PYTHON SOURCE LINES 201-204 This all works with more than two inputs as well. In that case we will get multiple pair-wise plots and styled ``DataFrame``\ s: .. GENERATED FROM PYTHON SOURCE LINES 204-221 .. code-block:: default def my_model_2(x_1, x_2, x_3): return x_1 * x_2 ** x_3 sensitivity_dict = { 'x_1': [1, 2, 3], 'x_2': [4, 5, 6], 'x_3': [7, 8, 9] } sa = SensitivityAnalyzer(sensitivity_dict, my_model_2, grid_size=3) plot = sa.plot() styled_dict = sa.styled_dfs() .. image-sg:: /auto_examples/images/sphx_glr_sensitivity_analysis_004.png :alt: sensitivity analysis :srcset: /auto_examples/images/sphx_glr_sensitivity_analysis_004.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none 0%| | 0/27 [00:00 .. GENERATED FROM PYTHON SOURCE LINES 222-227 The plot is still a single ``Figure`` object, but the ``styled_dfs`` produces a dictionary where there are more than two inputs. The keys of the dictionary are a tuple of the column names involved in the ``Styler``, and the values are the ``Styler``\ s. .. GENERATED FROM PYTHON SOURCE LINES 227-231 .. code-block:: default styled_dict .. rst-class:: sphx-glr-script-out .. code-block:: none {('x_1', 'x_2'): , ('x_1', 'x_3'): , ('x_2', 'x_3'): } .. GENERATED FROM PYTHON SOURCE LINES 232-242 Adding Additional Styling to Styled ``DataFrames`` ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ It could be desired to pass some number or other formatting to the styled ``DataFrames``. This can be done with the ``num_fmt`` argument, either when first creating the ``SensitivityAnalyzer`` or when calling the ``styled_dfs`` method. Just pass it the string of the number format, in the same way you would specify the number formatting string for ``df.style.format``. .. GENERATED FROM PYTHON SOURCE LINES 242-243 .. code-block:: default styled_dict = sa.styled_dfs(num_fmt='${:,.0f}') .. rst-class:: sphx-glr-script-out .. code-block:: none .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 2.521 seconds) .. _sphx_glr_download_auto_examples_sensitivity_analysis.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: binder-badge .. image:: images/binder_badge_logo.svg :target: https://mybinder.org/v2/gh/nickderobertis/sensitivity/gh-pages?urlpath=lab/tree/notebooks/auto_examples/sensitivity_analysis.ipynb :alt: Launch binder :width: 150 px .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: sensitivity_analysis.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: sensitivity_analysis.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_