B dF1@sjdZddlZddlmZddddd gZdd d Zdd dZdddZdddZ dddZ GdddZ dS)zn Methods for selecting the bin width of histograms Ported from the astroML project: https://www.astroml.org/ N)bayesian_blocks histogramscott_bin_widthfreedman_bin_widthknuth_bin_widthcalculate_bin_edges cCs|dk r$|||dk||dk@}t|trt|}|dk rLtd|dkr^t|}nX|dkrvt|d\}}n@|dkrt|d\}}n(|d krt |d\}}nt d |d |r|d|dkr|d|d<|d |dkr|d|d <n"t |dkrtj ||||d }|S)aX Calculate histogram bin edges like ``numpy.histogram_bin_edges``. Parameters ---------- a : array-like Input data. The bin edges are calculated over the flattened array. bins : int, list, or str, optional If ``bins`` is an int, it is the number of bins. If it is a list it is taken to be the bin edges. If it is a string, it must be one of 'blocks', 'knuth', 'scott' or 'freedman'. See `~astropy.stats.histogram` for a description of each method. range : tuple or None, optional The minimum and maximum range for the histogram. If not specified, it will be (a.min(), a.max()). However, if bins is a list it is returned unmodified regardless of the range argument. weights : array-like, optional An array the same shape as ``a``. If given, the histogram accumulates the value of the weight corresponding to ``a`` instead of returning the count of values. This argument does not affect determination of bin edges, though they may be used in the future as new methods are added. Nrrz8weights are not yet supported for the enhanced histogramblocksZknuthTZscottZfreedmanzunrecognized bin code: '')rangeweights) isinstancestrnpasarrayZravelNotImplementedErrorrrrr ValueErrorndimZhistogram_bin_edges)abinsr rdard/work/yifan.wang/ringdown/master-ringdown-env/lib/python3.7/site-packages/astropy/stats/histogram.pyrs.   cKs*t||||d}tj|f|||d|S)aEnhanced histogram function, providing adaptive binnings This is a histogram function that enables the use of more sophisticated algorithms for determining bins. Aside from the ``bins`` argument allowing a string specified how bins are computed, the parameters are the same as ``numpy.histogram()``. Parameters ---------- a : array-like array of data to be histogrammed bins : int, list, or str, optional If bins is a string, then it must be one of: - 'blocks' : use bayesian blocks for dynamic bin widths - 'knuth' : use Knuth's rule to determine bins - 'scott' : use Scott's rule to determine bins - 'freedman' : use the Freedman-Diaconis rule to determine bins range : tuple or None, optional the minimum and maximum range for the histogram. If not specified, it will be (x.min(), x.max()) weights : array-like, optional An array the same shape as ``a``. If given, the histogram accumulates the value of the weight corresponding to ``a`` instead of returning the count of values. This argument does not affect determination of bin edges. other keyword arguments are described in numpy.histogram(). Returns ------- hist : array The values of the histogram. See ``density`` and ``weights`` for a description of the possible semantics. bin_edges : array of dtype float Return the bin edges ``(length(hist)+1)``. See Also -------- numpy.histogram )rr r)rrr)rrr rkwargsrrrrVs1FcCst|}|jdkrtd|j}t|}d||d}|rt|||}td|}||t |d}||fS|SdS)a&Return the optimal histogram bin width using Scott's rule Scott's rule is a normal reference rule: it minimizes the integrated mean squared error in the bin approximation under the assumption that the data is approximately Gaussian. Parameters ---------- data : array-like, ndim=1 observed (one-dimensional) data return_bins : bool, optional if True, then return the bin edges Returns ------- width : float optimal bin width using Scott's rule bins : ndarray bin edges: returned if ``return_bins`` is True Notes ----- The optimal bin width is .. math:: \Delta_b = \frac{3.5\sigma}{n^{1/3}} where :math:`\sigma` is the standard deviation of the data, and :math:`n` is the number of data points [1]_. References ---------- .. [1] Scott, David W. (1979). "On optimal and data-based histograms". Biometricka 66 (3): 605-610 See Also -------- knuth_bin_width freedman_bin_width bayesian_blocks histogram rzdata should be one-dimensionalg @gUUUUUU?N) rrrrsizeZstdceilmaxminarange)data return_binsnsigmadxNbinsrrrrrs+    c Cst|}|jdkrtd|j}|dkr2tdt|ddg\}}d|||d}|r||}}tdt|||}y||t |d} WnDtk r} z&d t | krtd |dnWd d } ~ XYnX|| fS|Sd S) aReturn the optimal histogram bin width using the Freedman-Diaconis rule The Freedman-Diaconis rule is a normal reference rule like Scott's rule, but uses rank-based statistics for results which are more robust to deviations from a normal distribution. Parameters ---------- data : array-like, ndim=1 observed (one-dimensional) data return_bins : bool, optional if True, then return the bin edges Returns ------- width : float optimal bin width using the Freedman-Diaconis rule bins : ndarray bin edges: returned if ``return_bins`` is True Notes ----- The optimal bin width is .. math:: \Delta_b = \frac{2(q_{75} - q_{25})}{n^{1/3}} where :math:`q_{N}` is the :math:`N` percent quartile of the data, and :math:`n` is the number of data points [1]_. References ---------- .. [1] D. Freedman & P. Diaconis (1981) "On the histogram as a density estimator: L2 theory". Probability Theory and Related Fields 57 (4): 453-476 See Also -------- knuth_bin_width scott_bin_width bayesian_blocks histogram rzdata should be one-dimensionalz(data should have more than three entriesKgUUUUUU?zMaximum allowed size exceededzThe inter-quartile range of the data is too small: failed to construct histogram with {} bins. Please use another bin method, such as bins="scott"N) rrrrrZ percentilerrrr rformat) r!r"r#Zv25Zv75r%ZdminZdmaxr&rerrrrs*,   Tc Csjddlm}t|}t|d\}}|j|t|| dd}||}|d|d} |rb| |fS| SdS)a/Return the optimal histogram bin width using Knuth's rule. Knuth's rule is a fixed-width, Bayesian approach to determining the optimal bin width of a histogram. Parameters ---------- data : array-like, ndim=1 observed (one-dimensional) data return_bins : bool, optional if True, then return the bin edges quiet : bool, optional if True (default) then suppress stdout output from scipy.optimize Returns ------- dx : float optimal bin width. Bins are measured starting at the first data point. bins : ndarray bin edges: returned if ``return_bins`` is True Notes ----- The optimal number of bins is the value M which maximizes the function .. math:: F(M|x,I) = n\log(M) + \log\Gamma(\frac{M}{2}) - M\log\Gamma(\frac{1}{2}) - \log\Gamma(\frac{2n+M}{2}) + \sum_{k=1}^M \log\Gamma(n_k + \frac{1}{2}) where :math:`\Gamma` is the Gamma function, :math:`n` is the number of data points, :math:`n_k` is the number of measurements in bin :math:`k` [1]_. References ---------- .. [1] Knuth, K.H. "Optimal Data-Based Binning for Histograms". arXiv:0605197, 2006 See Also -------- freedman_bin_width scott_bin_width bayesian_blocks histogram r)optimizeT)ZdisprN)scipyr-_KnuthFrZfminlenr) r!r"quietr-ZknuthFZdx0Zbins0Mrr%rrrrs1  c@s0eZdZdZddZddZddZdd Zd S) r/agClass which implements the function minimized by knuth_bin_width Parameters ---------- data : array-like, one dimension data to be histogrammed Notes ----- the function F is given by .. math:: F(M|x,I) = n\log(M) + \log\Gamma(\frac{M}{2}) - M\log\Gamma(\frac{1}{2}) - \log\Gamma(\frac{2n+M}{2}) + \sum_{k=1}^M \log\Gamma(n_k + \frac{1}{2}) where :math:`\Gamma` is the Gamma function, :math:`n` is the number of data points, :math:`n_k` is the number of measurements in bin :math:`k`. See Also -------- knuth_bin_width cCsPtj|dd|_|jjdkr$td|j|jj|_ddlm }|j |_ dS)NT)copyrzdata should be 1-dimensionalr)special) rarrayr!rrsortrr#r.r4gammaln)selfr!r4rrr__init__ks    z_KnuthF.__init__cCs"t|jd|jdt|dS)z%Return the bin edges given a width dxrr r)rZlinspacer!int)r8r2rrrrzsz _KnuthF.binscCs ||S)N)eval)r8r2rrr__call__~sz_KnuthF.__call__cCst|}|dkrtjS||}t|j|\}}|jt||d|||d||jd|t ||d S)aEvaluate the Knuth function Parameters ---------- dx : float Width of bins Returns ------- F : float evaluation of the negative Knuth likelihood function: smaller values indicate a better fit. rg?) r:rinfrrr!r#logr7sum)r8r2rZnkrrrr;s >z _KnuthF.evalN)__name__ __module__ __qualname____doc__r9rr<r;rrrrr/Rs r/)r NN)r NN)F)F)FT) rCnumpyrr__all__rrrrrr/rrrrs  F 6 = J ?