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Module pyqt_fit.plot_fit

Author:Pierre Barbier de Reuille <pierre.barbierdereuille@gmail.com>

This modules implement functions to test and plot parametric regression.

Analyses of the residuals

pyqt_fit.plot_fit.fit_evaluation(fit, xdata, ydata, eval_points=None, CI=(), CIresults=None, xname='X', yname='Y', fct_desc=None, param_names=(), residuals=None, res_name='Standard')

This function takes the output of a curve fitting experiment and store all the relevant information for evaluating its success in the result.

Parameters:

• fit (fitting object) – object configured for the fitting
• xdata (ndarray of shape (N,) or (k,N) for function with k prefictors) – The independent variable where the data is measured
• ydata (ndarray) – The dependant data
• eval_points (ndarray or None) – Contain the list of points on which the result must be expressed. It is used both for plotting and for the bootstrapping.
• CI (tuple of int) – List of confidence intervals to calculate. If empty, none are calculated.
• xname (string) – Name of the X axis
• yname (string) – Name of the Y axis
• fct_desc (string) – Formula of the function
• param_names (tuple of strings) – Name of the various parameters
• residuals (callable) – Residual function
• res_desc (string) – Description of the residuals

Return type:

ResultStruct

Returns:

Data structure summarising the fitting and its evaluation

pyqt_fit.plot_fit.residual_measures(res)

Compute quantities needed to evaluate the quality of the estimation, based solely on the residuals.

Return type:ResidualMeasures Returns:the scaled residuals, their ordering, the theoretical quantile for each residuals, and the expected value for each quantile.

Plotting the residuals

pyqt_fit.plot_fit.plot_dist_residuals(res)

Plot the distribution of the residuals.

Returns:the handle toward the histogram and the plot of the fitted normal distribution

pyqt_fit.plot_fit.plot_residuals(xname, xdata, res_desc, res)

Plot the residuals against the X axis

Parameters:

• xname (str) – Name of the X axis
• xdata (ndarray) – 1D array with the X data
• res_desc (str) – Name of the Y axis
• res (ndarray) – 1D array with the residuals

The shapes of xdata and res must be the same

Returns:The handles of the the plots of the residuals and of the smoothed residuals.

pyqt_fit.plot_fit.scaled_location_plot(yname, yopt, scaled_res)

Plot the scaled location, given the dependant values and scaled residuals.

Parameters:

• yname (str) – Name of the Y axis
• yopt (ndarray) – Estimated values
• scaled_res (ndarray) – Scaled residuals

Returns:

the handles for the data and the smoothed curve

pyqt_fit.plot_fit.qqplot(scaled_res, normq)

Draw a Q-Q Plot from the sorted, scaled residuals (i.e. residuals sorted and normalized by their standard deviation)

Parameters:

• scaled_res (ndarray) – Scaled residuals
• normq (ndarray) – Expected value for each scaled residual, based on its quantile.

Returns:

handle to the data plot

pyqt_fit.plot_fit.plot_residual_tests(xdata, yopts, res, fct_name, xname='X', yname='Y', res_name='residuals', sorted_yopts=None, scaled_res=None, normq=None, fig=None)

Plot, in a single figure, all four residuals evaluation plots: plot_residuals(), plot_dist_residuals(), scaled_location_plot() and qqplot().

Parameters:

• xdata (ndarray) – Explaining variables
• yopt (ndarray) – Optimized explained variables
• fct_name (str) – Name of the fitted function
• xname (str) – Name of the explaining variables
• yname (str) – Name of the dependant variables
• res_name (str) – Name of the residuals
• sorted_yopts (ndarray) – yopt, sorted to match the scaled residuals
• scaled_res (ndarray) – Scaled residuals
• normq (ndarray) – Estimated value of the quantiles for a normal distribution
• fig (handle or None) – Handle of the figure to put the plots in, or None to create a new figure

Return type:

ResTestResult

Returns:

The handles to all the plots

General plotting

pyqt_fit.plot_fit.plot1d(result, loc=0, fig=None, res_fig=None)

Use matplotlib to display the result of a fit, and return the list of plots used

Return type:Plot1dResult Returns:hangles to the various figures and plots

Output to a file

pyqt_fit.plot_fit.write1d(outfile, result, res_desc, CImethod)

Write the result of a fitting and its evaluation to a CSV file.

Parameters:

• outfile (str) – Name of the file to write to
• result (ResultStruct) – Result of the fitting evaluation (e.g. output of fit_evaluation())
• res_desc (str) – Description of the residuals (in more details than just the name of the residuals)
• CImethod (str) – Description of the confidence interval estimation method

Return types

Most function return a tuple. For easier access, there are named tuple, i.e. tuples that can be accessed by name.

class pyqt_fit.plot_fit.ResultStruct(...)

Note

This is a class created with pyqt_fit.utils.namedtuple().

fct

Fitted function (i.e. result of the fitted function)

fct_desc

Description of the function being fitted

param_names

Name of the parameters fitted

xdata

Explaining variables used for fitting

ydata

Dependent variables observed during experiment

xname

Name of the explaining variables

yname

Name of the dependent variabled

res_name

Name of the residuals

residuals

Function used to compute the residuals

popt

Optimal parameters

res

Residuals computed with the parameters popt

yopts

Evaluation of the optimized function on the observed points

eval_points

Points on which the function has been interpolated (may be equal to xdata)

interpolation

Interpolated function on eval_points (may be equal to yopt)

sorted_yopts

Evaluated function for each data points, sorted in increasing residual order

scaled_res

Scaled residuals, ordered by increasing residuals

normq

Expected values for the residuals, based on their quantile

CI

List of confidence intervals evaluated (in percent)

CIs

List of arrays giving the confidence intervals for the dependent variables and for the parameters.

CIresults

Object returned by the confidence interval method

class pyqt_fit.plot_fit.ResidualMeasures(scaled_res, res_IX, prob, normq)

Note

This is a class created with pyqt_fit.utils.namedtuple().

scaled_res

Scaled residuals, sorted

res_IX

Sorting indices for the residuals

prob

Quantiles of the scaled residuals

normq

Expected values of the quantiles for a normal distribution

class pyqt_fit.plot_fit.ResTestResult(res_figure, residuals, scaled_residuals, qqplot, dist_residuals)

Note

This is a class created with pyqt_fit.utils.namedtuple().

res_figure

Handle to the figure

residuals

Handles created by plot_residuals()

scaled_residuals

Handles created by scaled_location_plot()

qqplot

Handles created by qqplot()

dist_residuals

Handles created by plot_dist_residuals()

class pyqt_fit.plot_fit.Plot1dResult(figure, estimate, data, CIs, *ResTestResult)

Note

This is a class create with pyqt_fit.utils.namedtuple(). Also, it contains all the first of ResTestResult at the end of the tuple.

figure

Handle to the figure with the data and fitted curve

estimate

Handle to the fitted curve

data

Handle to the data

CIs

Handles to the confidence interval curves