
.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/example_brute.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        Click :ref:`here <sphx_glr_download_examples_example_brute.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_example_brute.py:


Global minimization using the ``brute`` method (a.k.a. grid search)
===================================================================

.. GENERATED FROM PYTHON SOURCE LINES 7-15

This notebook shows a simple example of using ``lmfit.minimize.brute`` that
uses the method with the same name from ``scipy.optimize``.

The method computes the function’s value at each point of a multidimensional
grid of points, to find the global minimum of the function. It behaves
identically to ``scipy.optimize.brute`` in case finite bounds are given on
all varying parameters, but will also deal with non-bounded parameters
(see below).

.. GENERATED FROM PYTHON SOURCE LINES 15-23

.. code-block:: default

    import copy

    from matplotlib.colors import LogNorm
    import matplotlib.pyplot as plt
    import numpy as np

    from lmfit import Minimizer, Parameters, fit_report








.. GENERATED FROM PYTHON SOURCE LINES 24-35

Let's start with the example given in the documentation of SciPy:

"We illustrate the use of brute to seek the global minimum of a function of
two variables that is given as the sum of a positive-definite quadratic and
two deep “Gaussian-shaped” craters. Specifically, define the objective
function ``f`` as the sum of three other functions, ``f = f1 + f2 + f3``. We
suppose each of these has a signature ``(z, *params), where z = (x, y)``,
and params and the functions are as defined below."

First, we create a set of Parameters where all variables except ``x`` and
``y`` are given fixed values.

.. GENERATED FROM PYTHON SOURCE LINES 35-53

.. code-block:: default

    params = Parameters()
    params.add_many(
            ('a', 2, False),
            ('b', 3, False),
            ('c', 7, False),
            ('d', 8, False),
            ('e', 9, False),
            ('f', 10, False),
            ('g', 44, False),
            ('h', -1, False),
            ('i', 2, False),
            ('j', 26, False),
            ('k', 1, False),
            ('l', -2, False),
            ('scale', 0.5, False),
            ('x', 0.0, True),
            ('y', 0.0, True))








.. GENERATED FROM PYTHON SOURCE LINES 54-55

Second, create the three functions and the objective function:

.. GENERATED FROM PYTHON SOURCE LINES 55-80

.. code-block:: default



    def f1(p):
        par = p.valuesdict()
        return (par['a'] * par['x']**2 + par['b'] * par['x'] * par['y'] +
                par['c'] * par['y']**2 + par['d']*par['x'] + par['e']*par['y'] +
                par['f'])


    def f2(p):
        par = p.valuesdict()
        return (-1.0*par['g']*np.exp(-((par['x']-par['h'])**2 +
                                       (par['y']-par['i'])**2) / par['scale']))


    def f3(p):
        par = p.valuesdict()
        return (-1.0*par['j']*np.exp(-((par['x']-par['k'])**2 +
                                       (par['y']-par['l'])**2) / par['scale']))


    def f(params):
        return f1(params) + f2(params) + f3(params)









.. GENERATED FROM PYTHON SOURCE LINES 81-85

Just as in the documentation we will do a grid search between ``-4`` and
``4`` and use a stepsize of ``0.25``. The bounds can be set as usual with
the ``min`` and ``max`` attributes, and the stepsize is set using
``brute_step``.

.. GENERATED FROM PYTHON SOURCE LINES 85-88

.. code-block:: default

    params['x'].set(min=-4, max=4, brute_step=0.25)
    params['y'].set(min=-4, max=4, brute_step=0.25)








.. GENERATED FROM PYTHON SOURCE LINES 89-90

Performing the actual grid search is done with:

.. GENERATED FROM PYTHON SOURCE LINES 90-93

.. code-block:: default

    fitter = Minimizer(f, params)
    result = fitter.minimize(method='brute')








.. GENERATED FROM PYTHON SOURCE LINES 94-96

, which will increment ``x`` and ``y`` between ``-4`` in increments of
``0.25`` until ``4`` (not inclusive).

.. GENERATED FROM PYTHON SOURCE LINES 96-99

.. code-block:: default

    grid_x, grid_y = (np.unique(par.ravel()) for par in result.brute_grid)
    print(grid_x)





.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    [-4.   -3.75 -3.5  -3.25 -3.   -2.75 -2.5  -2.25 -2.   -1.75 -1.5  -1.25
     -1.   -0.75 -0.5  -0.25  0.    0.25  0.5   0.75  1.    1.25  1.5   1.75
      2.    2.25  2.5   2.75  3.    3.25  3.5   3.75]




.. GENERATED FROM PYTHON SOURCE LINES 100-106

The objective function is evaluated on this grid, and the raw output from
``scipy.optimize.brute`` is stored in the MinimizerResult as
``brute_<parname>`` attributes. These attributes are:

``result.brute_x0`` -- A 1-D array containing the coordinates of a point at
which the objective function had its minimum value.

.. GENERATED FROM PYTHON SOURCE LINES 106-108

.. code-block:: default

    print(result.brute_x0)





.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    [-1.    1.75]




.. GENERATED FROM PYTHON SOURCE LINES 109-110

``result.brute_fval`` -- Function value at the point ``x0``.

.. GENERATED FROM PYTHON SOURCE LINES 110-112

.. code-block:: default

    print(result.brute_fval)





.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    -2.8923637137222027




.. GENERATED FROM PYTHON SOURCE LINES 113-115

``result.brute_grid`` -- Representation of the evaluation grid. It has the
same length as ``x0``.

.. GENERATED FROM PYTHON SOURCE LINES 115-117

.. code-block:: default

    print(result.brute_grid)





.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    [[[-4.   -4.   -4.   ... -4.   -4.   -4.  ]
      [-3.75 -3.75 -3.75 ... -3.75 -3.75 -3.75]
      [-3.5  -3.5  -3.5  ... -3.5  -3.5  -3.5 ]
      ...
      [ 3.25  3.25  3.25 ...  3.25  3.25  3.25]
      [ 3.5   3.5   3.5  ...  3.5   3.5   3.5 ]
      [ 3.75  3.75  3.75 ...  3.75  3.75  3.75]]

     [[-4.   -3.75 -3.5  ...  3.25  3.5   3.75]
      [-4.   -3.75 -3.5  ...  3.25  3.5   3.75]
      [-4.   -3.75 -3.5  ...  3.25  3.5   3.75]
      ...
      [-4.   -3.75 -3.5  ...  3.25  3.5   3.75]
      [-4.   -3.75 -3.5  ...  3.25  3.5   3.75]
      [-4.   -3.75 -3.5  ...  3.25  3.5   3.75]]]




.. GENERATED FROM PYTHON SOURCE LINES 118-120

``result.brute_Jout`` -- Function values at each point of the evaluation
grid, i.e., ``Jout = func(*grid)``.

.. GENERATED FROM PYTHON SOURCE LINES 120-122

.. code-block:: default

    print(result.brute_Jout)





.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    [[134.         119.6875     106.25       ...  74.18749997  85.24999999
       97.1875    ]
     [129.125      115.         101.75       ...  74.74999948  85.99999987
       98.12499997]
     [124.5        110.5625      97.5        ...  75.5624928   86.99999818
       99.31249964]
     ...
     [ 94.12499965  85.24999772  77.24998843 ... 192.         208.5
      225.875     ]
     [ 96.49999997  87.81249979  79.99999892 ... 199.8125     216.5
      234.0625    ]
     [ 99.125       90.62499998  82.99999992 ... 207.875      224.75
      242.5       ]]




.. GENERATED FROM PYTHON SOURCE LINES 123-125

**Reassuringly, the obtained results are identical to using the method in
SciPy directly!**

.. GENERATED FROM PYTHON SOURCE LINES 127-133

Example 2: fit of a decaying sine wave

In this example, we will explain some of the options of the algorithm.

We start off by generating some synthetic data with noise for a decaying sine
wave, define an objective function, and create/initialize a Parameter set.

.. GENERATED FROM PYTHON SOURCE LINES 133-158

.. code-block:: default

    x = np.linspace(0, 15, 301)
    np.random.seed(7)
    noise = np.random.normal(size=x.size, scale=0.2)
    data = (5. * np.sin(2*x - 0.1) * np.exp(-x*x*0.025) + noise)
    plt.plot(x, data, 'o')
    plt.show()


    def fcn2min(params, x, data):
        """Model decaying sine wave, subtract data."""
        amp = params['amp']
        shift = params['shift']
        omega = params['omega']
        decay = params['decay']
        model = amp * np.sin(x*omega + shift) * np.exp(-x*x*decay)
        return model - data


    # create a set of Parameters
    params = Parameters()
    params.add('amp', value=7, min=2.5)
    params.add('decay', value=0.05)
    params.add('shift', value=0.0, min=-np.pi/2., max=np.pi/2)
    params.add('omega', value=3, max=5)




.. image-sg:: /examples/images/sphx_glr_example_brute_001.png
   :alt: example brute
   :srcset: /examples/images/sphx_glr_example_brute_001.png, /examples/images/sphx_glr_example_brute_001_3_0x.png 3.0x
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 159-163

In contrast to the implementation in SciPy (as shown in the first example),
varying parameters do not need to have finite bounds in lmfit. However, in
that case they **do** need the ``brute_step`` attribute specified, so let's
do that:

.. GENERATED FROM PYTHON SOURCE LINES 163-167

.. code-block:: default

    params['amp'].set(brute_step=0.25)
    params['decay'].set(brute_step=0.005)
    params['omega'].set(brute_step=0.25)








.. GENERATED FROM PYTHON SOURCE LINES 168-170

Our initial parameter set is now defined as shown below and this will
determine how the grid is set-up.

.. GENERATED FROM PYTHON SOURCE LINES 170-172

.. code-block:: default

    params.pretty_print()





.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    Name      Value      Min      Max   Stderr     Vary     Expr Brute_Step
    amp           7      2.5      inf     None     True     None     0.25
    decay      0.05     -inf      inf     None     True     None    0.005
    omega         3     -inf        5     None     True     None     0.25
    shift         0   -1.571    1.571     None     True     None     None




.. GENERATED FROM PYTHON SOURCE LINES 173-174

First, we initialize a ``Minimizer`` and perform the grid search:

.. GENERATED FROM PYTHON SOURCE LINES 174-177

.. code-block:: default

    fitter = Minimizer(fcn2min, params, fcn_args=(x, data))
    result_brute = fitter.minimize(method='brute', Ns=25, keep=25)








.. GENERATED FROM PYTHON SOURCE LINES 178-187

We used two new parameters here: ``Ns`` and ``keep``. The parameter ``Ns``
determines the \'number of grid points along the axes\' similarly to its usage
in SciPy. Together with ``brute_step``, ``min`` and ``max`` for a Parameter
it will dictate how the grid is set-up:

**(1)** finite bounds are specified ("SciPy implementation"): uses
``brute_step`` if present (in the example above) or uses ``Ns`` to generate
the grid. The latter scenario that interpolates ``Ns`` points from ``min``
to ``max`` (inclusive), is here shown for the parameter ``shift``:

.. GENERATED FROM PYTHON SOURCE LINES 187-192

.. code-block:: default

    par_name = 'shift'
    indx_shift = result_brute.var_names.index(par_name)
    grid_shift = np.unique(result_brute.brute_grid[indx_shift].ravel())
    print(f"parameter = {par_name}\nnumber of steps = {len(grid_shift)}\ngrid = {grid_shift}")





.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    parameter = shift
    number of steps = 25
    grid = [-1.57079633 -1.43989663 -1.30899694 -1.17809725 -1.04719755 -0.91629786
     -0.78539816 -0.65449847 -0.52359878 -0.39269908 -0.26179939 -0.13089969
      0.          0.13089969  0.26179939  0.39269908  0.52359878  0.65449847
      0.78539816  0.91629786  1.04719755  1.17809725  1.30899694  1.43989663
      1.57079633]




.. GENERATED FROM PYTHON SOURCE LINES 193-198

If finite bounds are not set for a certain parameter then the user **must**
specify ``brute_step`` - three more scenarios are considered here:

**(2)** lower bound ``(min``) and ``brute_step`` are specified:
``range = (min, min + Ns * brute_step, brute_step)``

.. GENERATED FROM PYTHON SOURCE LINES 198-203

.. code-block:: default

    par_name = 'amp'
    indx_shift = result_brute.var_names.index(par_name)
    grid_shift = np.unique(result_brute.brute_grid[indx_shift].ravel())
    print(f"parameter = {par_name}\nnumber of steps = {len(grid_shift)}\ngrid = {grid_shift}")





.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    parameter = amp
    number of steps = 25
    grid = [2.5  2.75 3.   3.25 3.5  3.75 4.   4.25 4.5  4.75 5.   5.25 5.5  5.75
     6.   6.25 6.5  6.75 7.   7.25 7.5  7.75 8.   8.25 8.5 ]




.. GENERATED FROM PYTHON SOURCE LINES 204-206

**(3)** upper bound (``max``) and ``brute_step`` are specified:
``range = (max - Ns * brute_step, max, brute_step)``

.. GENERATED FROM PYTHON SOURCE LINES 206-211

.. code-block:: default

    par_name = 'omega'
    indx_shift = result_brute.var_names.index(par_name)
    grid_shift = np.unique(result_brute.brute_grid[indx_shift].ravel())
    print(f"parameter = {par_name}\nnumber of steps = {len(grid_shift)}\ngrid = {grid_shift}")





.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    parameter = omega
    number of steps = 25
    grid = [-1.25 -1.   -0.75 -0.5  -0.25  0.    0.25  0.5   0.75  1.    1.25  1.5
      1.75  2.    2.25  2.5   2.75  3.    3.25  3.5   3.75  4.    4.25  4.5
      4.75]




.. GENERATED FROM PYTHON SOURCE LINES 212-214

**(4)** numerical value (``value``) and ``brute_step`` are specified:
``range = (value - (Ns//2) * brute_step, value + (Ns//2) * brute_step, brute_step)``

.. GENERATED FROM PYTHON SOURCE LINES 214-219

.. code-block:: default

    par_name = 'decay'
    indx_shift = result_brute.var_names.index(par_name)
    grid_shift = np.unique(result_brute.brute_grid[indx_shift].ravel())
    print(f"parameter = {par_name}\nnumber of steps = {len(grid_shift)}\ngrid = {grid_shift}")





.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    parameter = decay
    number of steps = 24
    grid = [-1.00000000e-02 -5.00000000e-03  5.20417043e-18  5.00000000e-03
      1.00000000e-02  1.50000000e-02  2.00000000e-02  2.50000000e-02
      3.00000000e-02  3.50000000e-02  4.00000000e-02  4.50000000e-02
      5.00000000e-02  5.50000000e-02  6.00000000e-02  6.50000000e-02
      7.00000000e-02  7.50000000e-02  8.00000000e-02  8.50000000e-02
      9.00000000e-02  9.50000000e-02  1.00000000e-01  1.05000000e-01]




.. GENERATED FROM PYTHON SOURCE LINES 220-223

The ``MinimizerResult`` contains all the usual best-fit parameters and
fitting statistics. For example, the optimal solution from the grid search
is given below together with a plot:

.. GENERATED FROM PYTHON SOURCE LINES 223-225

.. code-block:: default

    print(fit_report(result_brute))





.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    [[Fit Statistics]]
        # fitting method   = brute
        # function evals   = 375000
        # data points      = 301
        # variables        = 4
        chi-square         = 11.9353671
        reduced chi-square = 0.04018642
        Akaike info crit   = -963.508878
        Bayesian info crit = -948.680437
    ##  Warning: uncertainties could not be estimated:
        this fitting method does not natively calculate uncertainties
        and numdifftools is not installed for lmfit to do this. Use
        `pip install numdifftools` for lmfit to estimate uncertainties
        with this fitting method.
    [[Variables]]
        amp:    5.00000000 (init = 7)
        decay:  0.02500000 (init = 0.05)
        shift: -0.13089969 (init = 0)
        omega:  2.00000000 (init = 3)




.. GENERATED FROM PYTHON SOURCE LINES 226-230

.. code-block:: default

    plt.plot(x, data, 'o')
    plt.plot(x, data + fcn2min(result_brute.params, x, data), '--')
    plt.show()




.. image-sg:: /examples/images/sphx_glr_example_brute_002.png
   :alt: example brute
   :srcset: /examples/images/sphx_glr_example_brute_002.png, /examples/images/sphx_glr_example_brute_002_3_0x.png 3.0x
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 231-253

We can see that this fit is already very good, which is what we should expect
since our ``brute`` force grid is sampled rather finely and encompasses the
"correct" values.

In a more realistic, complicated example the ``brute`` method will be used
to get reasonable values for the parameters and perform another minimization
(e.g., using ``leastsq``) using those as starting values. That is where the
``keep`` parameter comes into play: it determines the "number of best
candidates from the brute force method that are stored in the ``candidates``
attribute". In the example above we store the best-ranking 25 solutions (the
default value is ``50`` and storing all the grid points can be accomplished
by choosing ``all``). The ``candidates`` attribute contains the parameters
and ``chisqr`` from the brute force method as a ``namedtuple``,
``(‘Candidate’, [‘params’, ‘score’])``, sorted on the (lowest) ``chisqr``
value. To access the values for a particular candidate one can use
``result.candidate[#].params`` or ``result.candidate[#].score``, where a
lower # represents a better candidate. The ``show_candidates(#)`` uses the
``pretty_print()`` method to show a specific candidate-# or all candidates
when no number is specified.

The optimal fit is, as usual, stored in the ``MinimizerResult.params``
attribute and is, therefore, identical to ``result_brute.show_candidates(1)``.

.. GENERATED FROM PYTHON SOURCE LINES 253-255

.. code-block:: default

    result_brute.show_candidates(1)





.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none


    Candidate #1, chisqr = 11.935
    Name      Value      Min      Max   Stderr     Vary     Expr Brute_Step
    amp           5      2.5      inf     None     True     None     0.25
    decay     0.025     -inf      inf     None     True     None    0.005
    omega         2     -inf        5     None     True     None     0.25
    shift   -0.1309   -1.571    1.571     None     True     None     None




.. GENERATED FROM PYTHON SOURCE LINES 256-258

In this case, the next-best scoring candidate has already a ``chisqr`` that
increased quite a bit:

.. GENERATED FROM PYTHON SOURCE LINES 258-260

.. code-block:: default

    result_brute.show_candidates(2)





.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none


    Candidate #2, chisqr = 13.994
    Name      Value      Min      Max   Stderr     Vary     Expr Brute_Step
    amp        4.75      2.5      inf     None     True     None     0.25
    decay     0.025     -inf      inf     None     True     None    0.005
    omega         2     -inf        5     None     True     None     0.25
    shift   -0.1309   -1.571    1.571     None     True     None     None




.. GENERATED FROM PYTHON SOURCE LINES 261-267

and is, therefore, probably not so likely... However, as said above, in most
cases you'll want to do another minimization using the solutions from the
``brute`` method as starting values. That can be easily accomplished as
shown in the code below, where we now perform a ``leastsq`` minimization
starting from the top-25 solutions and accept the solution if the ``chisqr``
is lower than the previously 'optimal' solution:

.. GENERATED FROM PYTHON SOURCE LINES 267-274

.. code-block:: default

    best_result = copy.deepcopy(result_brute)

    for candidate in result_brute.candidates:
        trial = fitter.minimize(method='leastsq', params=candidate.params)
        if trial.chisqr < best_result.chisqr:
            best_result = trial








.. GENERATED FROM PYTHON SOURCE LINES 275-277

From the ``leastsq`` minimization we obtain the following parameters for the
most optimal result:

.. GENERATED FROM PYTHON SOURCE LINES 277-279

.. code-block:: default

    print(fit_report(best_result))





.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    [[Fit Statistics]]
        # fitting method   = leastsq
        # function evals   = 21
        # data points      = 301
        # variables        = 4
        chi-square         = 10.8653514
        reduced chi-square = 0.03658367
        Akaike info crit   = -991.780924
        Bayesian info crit = -976.952483
    [[Variables]]
        amp:    5.00323088 +/- 0.03805940 (0.76%) (init = 5.5)
        decay:  0.02563850 +/- 4.4571e-04 (1.74%) (init = 0.025)
        shift: -0.09162988 +/- 0.00978382 (10.68%) (init = -0.1308997)
        omega:  1.99611629 +/- 0.00316225 (0.16%) (init = 2)
    [[Correlations]] (unreported correlations are < 0.100)
        C(shift, omega) = -0.785
        C(amp, decay)   = 0.584
        C(amp, shift)   = -0.121




.. GENERATED FROM PYTHON SOURCE LINES 280-283

As expected the parameters have not changed significantly as they were
already very close to the "real" values, which can also be appreciated from
the plots below.

.. GENERATED FROM PYTHON SOURCE LINES 283-291

.. code-block:: default

    plt.plot(x, data, 'o')
    plt.plot(x, data + fcn2min(result_brute.params, x, data), '-',
             label='brute')
    plt.plot(x, data + fcn2min(best_result.params, x, data), '--',
             label='brute followed by leastsq')
    plt.legend()





.. image-sg:: /examples/images/sphx_glr_example_brute_003.png
   :alt: example brute
   :srcset: /examples/images/sphx_glr_example_brute_003.png, /examples/images/sphx_glr_example_brute_003_3_0x.png 3.0x
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 292-295

Finally, the results from the ``brute`` force grid-search can be visualized
using the rather lengthy Python function below (which might get incorporated
in lmfit at some point).

.. GENERATED FROM PYTHON SOURCE LINES 295-398

.. code-block:: default

    def plot_results_brute(result, best_vals=True, varlabels=None,
                           output=None):
        """Visualize the result of the brute force grid search.

        The output file will display the chi-square value per parameter and contour
        plots for all combination of two parameters.

        Inspired by the `corner` package (https://github.com/dfm/corner.py).

        Parameters
        ----------
        result : :class:`~lmfit.minimizer.MinimizerResult`
            Contains the results from the :meth:`brute` method.

        best_vals : bool, optional
            Whether to show the best values from the grid search (default is True).

        varlabels : list, optional
            If None (default), use `result.var_names` as axis labels, otherwise
            use the names specified in `varlabels`.

        output : str, optional
            Name of the output PDF file (default is 'None')
        """
        npars = len(result.var_names)
        _fig, axes = plt.subplots(npars, npars)

        if not varlabels:
            varlabels = result.var_names
        if best_vals and isinstance(best_vals, bool):
            best_vals = result.params

        for i, par1 in enumerate(result.var_names):
            for j, par2 in enumerate(result.var_names):

                # parameter vs chi2 in case of only one parameter
                if npars == 1:
                    axes.plot(result.brute_grid, result.brute_Jout, 'o', ms=3)
                    axes.set_ylabel(r'$\chi^{2}$')
                    axes.set_xlabel(varlabels[i])
                    if best_vals:
                        axes.axvline(best_vals[par1].value, ls='dashed', color='r')

                # parameter vs chi2 profile on top
                elif i == j and j < npars-1:
                    if i == 0:
                        axes[0, 0].axis('off')
                    ax = axes[i, j+1]
                    red_axis = tuple(a for a in range(npars) if a != i)
                    ax.plot(np.unique(result.brute_grid[i]),
                            np.minimum.reduce(result.brute_Jout, axis=red_axis),
                            'o', ms=3)
                    ax.set_ylabel(r'$\chi^{2}$')
                    ax.yaxis.set_label_position("right")
                    ax.yaxis.set_ticks_position('right')
                    ax.set_xticks([])
                    if best_vals:
                        ax.axvline(best_vals[par1].value, ls='dashed', color='r')

                # parameter vs chi2 profile on the left
                elif j == 0 and i > 0:
                    ax = axes[i, j]
                    red_axis = tuple(a for a in range(npars) if a != i)
                    ax.plot(np.minimum.reduce(result.brute_Jout, axis=red_axis),
                            np.unique(result.brute_grid[i]), 'o', ms=3)
                    ax.invert_xaxis()
                    ax.set_ylabel(varlabels[i])
                    if i != npars-1:
                        ax.set_xticks([])
                    else:
                        ax.set_xlabel(r'$\chi^{2}$')
                    if best_vals:
                        ax.axhline(best_vals[par1].value, ls='dashed', color='r')

                # contour plots for all combinations of two parameters
                elif j > i:
                    ax = axes[j, i+1]
                    red_axis = tuple(a for a in range(npars) if a not in (i, j))
                    X, Y = np.meshgrid(np.unique(result.brute_grid[i]),
                                       np.unique(result.brute_grid[j]))
                    lvls1 = np.linspace(result.brute_Jout.min(),
                                        np.median(result.brute_Jout)/2.0, 7, dtype='int')
                    lvls2 = np.linspace(np.median(result.brute_Jout)/2.0,
                                        np.median(result.brute_Jout), 3, dtype='int')
                    lvls = np.unique(np.concatenate((lvls1, lvls2)))
                    ax.contourf(X.T, Y.T, np.minimum.reduce(result.brute_Jout, axis=red_axis),
                                lvls, norm=LogNorm())
                    ax.set_yticks([])
                    if best_vals:
                        ax.axvline(best_vals[par1].value, ls='dashed', color='r')
                        ax.axhline(best_vals[par2].value, ls='dashed', color='r')
                        ax.plot(best_vals[par1].value, best_vals[par2].value, 'rs', ms=3)
                    if j != npars-1:
                        ax.set_xticks([])
                    else:
                        ax.set_xlabel(varlabels[i])
                    if j - i >= 2:
                        axes[i, j].axis('off')

        if output is not None:
            plt.savefig(output)









.. GENERATED FROM PYTHON SOURCE LINES 399-400

and finally, to generated the figure:

.. GENERATED FROM PYTHON SOURCE LINES 400-401

.. code-block:: default

    plot_results_brute(result_brute, best_vals=True, varlabels=None)



.. image-sg:: /examples/images/sphx_glr_example_brute_004.png
   :alt: example brute
   :srcset: /examples/images/sphx_glr_example_brute_004.png, /examples/images/sphx_glr_example_brute_004_3_0x.png 3.0x
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 0 minutes  24.478 seconds)


.. _sphx_glr_download_examples_example_brute.py:


.. only :: html

 .. container:: sphx-glr-footer
    :class: sphx-glr-footer-example



  .. container:: sphx-glr-download sphx-glr-download-python

     :download:`Download Python source code: example_brute.py <example_brute.py>`



  .. container:: sphx-glr-download sphx-glr-download-jupyter

     :download:`Download Jupyter notebook: example_brute.ipynb <example_brute.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_
