ó šßÈ[c@`s¹dZddlmZmZmZmZddlmZddlZ ddl m Z dd d d gZ d ddd „Zed„Zed„Zeed„Zdefd„ƒYZdS(ui Methods for selecting the bin width of histograms Ported from the astroML project: http://astroML.org/ i(tabsolute_importtdivisiontprint_functiontunicode_literalsi(tsixNi(tbayesian_blocksu histogramuscott_bin_widthufreedman_bin_widthuknuth_bin_widthi c K`s4t|tjƒrtj|ƒjƒ}|d k rBtdƒ‚n|d k rs|||dk||dk@}n|dkrŽt|ƒ}q|dkr²t |t ƒ\}}q|dkrÖt |t ƒ\}}q|dkrút |t ƒ\}}qt dj|ƒƒ‚ntj|d |d |d ||S( u6Enhanced 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 or 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 Not Implemented 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 u8weights are not yet supported for the enhanced histogramiiublocksuknuthuscottufreedmanuunrecognized bin code: '{}'tbinstrangetweightsN(t isinstanceRt string_typestnptasarraytraveltNonetNotImplementedErrorRtknuth_bin_widthtTruetscott_bin_widthtfreedman_bin_widtht ValueErrortformatt histogram(taRRRtkwargstda((s6lib/python2.7/site-packages/astropy/stats/histogram.pyRs .  %    cC`sÂtj|ƒ}|jdkr-tdƒ‚n|j}tj|ƒ}d||d}|rºtj|jƒ|jƒ|ƒ}td|ƒ}|jƒ|tj |dƒ}||fS|SdS(u'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 iudata should be one-dimensionalg @iNgUUUUUUÕ?( R R tndimRtsizetstdtceiltmaxtmintarange(tdatat return_binstntsigmatdxtNbinsR((s6lib/python2.7/site-packages/astropy/stats/histogram.pyR`s+ #! c C`s<tj|ƒ}|jdkr-tdƒ‚n|j}|dkrQtdƒ‚ntj|ddgƒ\}}d|||d }|r4|jƒ|jƒ}}tdtj|||ƒƒ}y||tj |dƒ} WnDtk r)} d t | ƒkr#td j |dƒƒ‚q*‚nX|| fS|Sd S( uReturn 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 iudata should be one-dimensionaliu(data should have more than three entriesiiKiiuMaximum allowed size exceededu’The inter-quartile range of the data is too small: failed to construct histogram with {} bins. Please use another bin method, such as bins="scott"NgUUUUUUÕ?( R R RRRt percentileRRRR tstrR( R!R"R#tv25tv75R%tdmintdmaxR&Rte((s6lib/python2.7/site-packages/astropy/stats/histogram.pyRs*,    c C`sddlm}t|ƒ}t|tƒ\}}|j|t|ƒd| ƒd}|j|ƒ}|d|d} |r…| |fS| SdS(u1Return 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 i(toptimizetdispiN(tscipyR.t_KnuthFRRtfmintlenR( R!R"tquietR.tknuthFtdx0tbins0tMRR%((s6lib/python2.7/site-packages/astropy/stats/histogram.pyRçs1 # R1cB`s2eZdZd„Zd„Zd„Zd„ZRS(ugClass 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 cC`sutj|dtƒ|_|jjdkr9tdƒ‚n|jjƒ|jj|_ddl m }|j |_ dS(Ntcopyiudata should be 1-dimensionali(tspecial( R tarrayRR!RRtsortRR#R0R:tgammaln(tselfR!R:((s6lib/python2.7/site-packages/astropy/stats/histogram.pyt__init__?s cC`s+tj|jd|jdt|ƒdƒS(u%Return the bin edges given a width dxiiÿÿÿÿi(R tlinspaceR!tint(R>R8((s6lib/python2.7/site-packages/astropy/stats/histogram.pyRNscC`s |j|ƒS(N(teval(R>R8((s6lib/python2.7/site-packages/astropy/stats/histogram.pyt__call__RscC`s²t|ƒ}|dkrtjS|j|ƒ}tj|j|ƒ\}}|jtj|ƒ|jd|ƒ||jdƒ|j|jd|ƒtj |j|dƒƒ S(uEvaluate 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. igà?( RAR tinfRRR!R#tlogR=tsum(R>R8Rtnk((s6lib/python2.7/site-packages/astropy/stats/histogram.pyRBUs  M(t__name__t __module__t__doc__R?RRCRB(((s6lib/python2.7/site-packages/astropy/stats/histogram.pyR1&s    (RJt __future__RRRRtexternRtnumpyR tRt__all__RRtFalseRRRRtobjectR1(((s6lib/python2.7/site-packages/astropy/stats/histogram.pyts"   K = J?