
.. 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

        :ref:`Go to the end <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:: Python

    import copy

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

    from lmfit import Minimizer, create_params, fit_report








.. GENERATED FROM PYTHON SOURCE LINES 24-39

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.
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 39-56

.. code-block:: Python


    params = create_params(a=dict(value=2, vary=False),
                           b=dict(value=3, vary=False),
                           c=dict(value=7, vary=False),
                           d=dict(value=8, vary=False),
                           e=dict(value=9, vary=False),
                           f=dict(value=10, vary=False),
                           g=dict(value=44, vary=False),
                           h=dict(value=-1, vary=False),
                           i=dict(value=2, vary=False),
                           j=dict(value=26, vary=False),
                           k=dict(value=1, vary=False),
                           l=dict(value=-2, vary=False),
                           scale=dict(value=0.5, vary=False),
                           x=dict(value=0.0, vary=True, min=-4, max=4, brute_step=0.25),
                           y=dict(value=0.0, vary=True, min=-4, max=4, brute_step=0.25))








.. GENERATED FROM PYTHON SOURCE LINES 57-58

Second, create the three functions and the objective function:

.. GENERATED FROM PYTHON SOURCE LINES 58-83

.. code-block:: Python



    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 84-85

Performing the actual grid search is done with:

.. GENERATED FROM PYTHON SOURCE LINES 85-88

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 89-91

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

.. GENERATED FROM PYTHON SOURCE LINES 91-94

.. code-block:: Python

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





.. rst-class:: sphx-glr-script-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 95-101

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 101-103

.. code-block:: Python

    print(result.brute_x0)





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

 .. code-block:: none

    [-1.    1.75]




.. GENERATED FROM PYTHON SOURCE LINES 104-105

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

.. GENERATED FROM PYTHON SOURCE LINES 105-107

.. code-block:: Python

    print(result.brute_fval)





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

 .. code-block:: none

    -2.8923637137222027




.. GENERATED FROM PYTHON SOURCE LINES 108-110

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

.. GENERATED FROM PYTHON SOURCE LINES 110-112

.. code-block:: Python

    print(result.brute_grid)





.. rst-class:: sphx-glr-script-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 113-115

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

.. GENERATED FROM PYTHON SOURCE LINES 115-117

.. code-block:: Python

    print(result.brute_Jout)





.. rst-class:: sphx-glr-script-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 118-120

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

.. GENERATED FROM PYTHON SOURCE LINES 122-128

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 128-146

.. code-block:: Python

    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





.. 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_00x.png 3.00x
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 147-151

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, if a
parameter does not have finite bounds, then it does need a ``brute_step``
attribute specified:

.. GENERATED FROM PYTHON SOURCE LINES 151-156

.. code-block:: Python

    params = create_params(amp=dict(value=7, min=2.5, brute_step=0.25),
                           decay=dict(value=0.05, brute_step=0.005),
                           shift=dict(value=0.0, min=-np.pi/2., max=np.pi/2),
                           omega=dict(value=3, max=5, brute_step=0.25))








.. GENERATED FROM PYTHON SOURCE LINES 157-159

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 159-161

.. code-block:: Python

    params.pretty_print()





.. rst-class:: sphx-glr-script-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 162-163

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

.. GENERATED FROM PYTHON SOURCE LINES 163-168

.. code-block:: Python

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

    print(fit_report(result_brute))





.. rst-class:: sphx-glr-script-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 169-178

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 178-183

.. code-block:: Python

    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

 .. 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 184-189

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 189-194

.. code-block:: Python

    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

 .. 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 195-197

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

.. GENERATED FROM PYTHON SOURCE LINES 197-202

.. code-block:: Python

    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

 .. 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 203-205

**(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 205-210

.. code-block:: Python

    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

 .. 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 211-214

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 214-216

.. code-block:: Python

    print(fit_report(result_brute))





.. rst-class:: sphx-glr-script-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 217-221

.. code-block:: Python

    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_00x.png 3.00x
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 222-244

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 244-246

.. code-block:: Python

    result_brute.show_candidates(1)





.. rst-class:: sphx-glr-script-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 247-249

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

.. GENERATED FROM PYTHON SOURCE LINES 249-251

.. code-block:: Python

    result_brute.show_candidates(2)





.. rst-class:: sphx-glr-script-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 252-258

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 258-265

.. code-block:: Python

    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 266-268

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

.. GENERATED FROM PYTHON SOURCE LINES 268-270

.. code-block:: Python

    print(fit_report(best_result))





.. rst-class:: sphx-glr-script-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:    5.00323085 +/- 0.03805940 (0.76%) (init = 5)
        decay:  0.02563850 +/- 4.4572e-04 (1.74%) (init = 0.03)
        shift: -0.09162987 +/- 0.00978382 (10.68%) (init = 0)
        omega:  1.99611629 +/- 0.00316225 (0.16%) (init = 2)
    [[Correlations]] (unreported correlations are < 0.100)
        C(shift, omega) = -0.7855
        C(amp, decay)   = +0.5838
        C(amp, shift)   = -0.1208




.. GENERATED FROM PYTHON SOURCE LINES 271-274

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 274-282

.. code-block:: Python

    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_00x.png 3.00x
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 283-286

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 286-389

.. code-block:: Python

    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 390-391

and finally, to generated the figure:

.. GENERATED FROM PYTHON SOURCE LINES 391-393

.. code-block:: Python

    plot_results_brute(result_brute, best_vals=True, varlabels=None)
    plt.show()



.. 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_00x.png 3.00x
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 16.852 seconds)


.. _sphx_glr_download_examples_example_brute.py:

.. only:: html

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

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

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

    .. 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-zip

      :download:`Download zipped: example_brute.zip <example_brute.zip>`


.. only:: html

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

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