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Edit File: mlab.cpython-38.pyc
U ��]G� � @ s� d Z ddlZddlZddlZddlmZ ddlmZ dd� Z dd� Z d@dd �Z dAd d �Z ej d d d�dBdd��ZdCdd �ZdDdd�Zdd� ZdEdd�ZdFdd�ZdGdd�ZdHd d �Zejje�d �d � ejje�d �d!� ejje�d"�d#� ejdId$d%��ZejdJd&d'��ZejdKd(d)��Z ejdLd*d+��Z ejdMd,d-��Z ejdNd.d/��Z ejdOd0d1��Z d2Z!ejd3d4ee ddd5dfd6d7��Z"dPd<d=�Z#G d>d?� d?e$�Z%dS )Qa Numerical python functions written for compatibility with MATLAB commands with the same names. Most numerical python functions can be found in the `numpy` and `scipy` libraries. What remains here is code for performing spectral computations. Spectral functions ------------------- `cohere` Coherence (normalized cross spectral density) `csd` Cross spectral density using Welch's average periodogram `detrend` Remove the mean or best fit line from an array `psd` Power spectral density using Welch's average periodogram `specgram` Spectrogram (spectrum over segments of time) `complex_spectrum` Return the complex-valued frequency spectrum of a signal `magnitude_spectrum` Return the magnitude of the frequency spectrum of a signal `angle_spectrum` Return the angle (wrapped phase) of the frequency spectrum of a signal `phase_spectrum` Return the phase (unwrapped angle) of the frequency spectrum of a signal `detrend_mean` Remove the mean from a line. `detrend_linear` Remove the best fit line from a line. `detrend_none` Return the original line. `stride_windows` Get all windows in an array in a memory-efficient manner `stride_repeat` Repeat an array in a memory-efficient manner `apply_window` Apply a window along a given axis � N)� docstringc C s t �t| ��| S )z} Return x times the hanning window of len(x). See Also -------- window_none : Another window algorithm. )�npZhanning�len��x� r �1/usr/lib/python3/dist-packages/matplotlib/mlab.py�window_hanningA s r c C s | S )zx No window function; simply return x. See Also -------- window_hanning : Another window algorithm. r r r r r � window_noneL s r c C s� t �| �} | jdk s | jdkr&td��|d | jkr@td| ��t| j�}|�|�}t �|�rxt|�|krrtd��|}n|t j || j d��}| jdkr�|r�|| |fS || S |�� }|d d }t |||d�} |r�| | |fS | | S dS ) a Apply the given window to the given 1D or 2D array along the given axis. Parameters ---------- x : 1D or 2D array or sequence Array or sequence containing the data. window : function or array. Either a function to generate a window or an array with length *x*.shape[*axis*] axis : integer The axis over which to do the repetition. Must be 0 or 1. The default is 0 return_window : bool If true, also return the 1D values of the window that was applied � � z only 1D or 2D arrays can be used�axis(=%s) out of boundszFThe len(window) must be the same as the shape of x for the chosen axis��dtype��axisN) r �asarray�ndim� ValueError�list�shape�pop�iterabler Zonesr � stride_repeat) r �windowr � return_windowZxshapeZ xshapetarg� windowValsZ xshapeotherZ otheraxisZ windowValsRepr r r � apply_windowW s, r c C s |dks|dkr t | t|d�S |dkr4t | t|d�S |dkrJt | t|d�S t|t�r`td| ��t|�sttd| ��t� | �} |dk r�|d | j kr�td| ��|dkr�| j d ks�|s�| j dkr�|| �S z|| |d �W S t k � r� tj ||| d � Y S X dS ) a� Return x with its trend removed. Parameters ---------- x : array or sequence Array or sequence containing the data. key : [ 'default' | 'constant' | 'mean' | 'linear' | 'none'] or function Specifies the detrend algorithm to use. 'default' is 'mean', which is the same as `detrend_mean`. 'constant' is the same. 'linear' is the same as `detrend_linear`. 'none' is the same as `detrend_none`. The default is 'mean'. See the corresponding functions for more details regarding the algorithms. Can also be a function that carries out the detrend operation. axis : integer The axis along which to do the detrending. See Also -------- detrend_mean : Implementation of the 'mean' algorithm. detrend_linear : Implementation of the 'linear' algorithm. detrend_none : Implementation of the 'none' algorithm. N)Zconstant�mean�default)�keyr ZlinearZnonez`Unknown value for key %s, must be one of: 'default', 'constant', 'mean', 'linear', or a functionr r r r )r Zarr) �detrend� detrend_mean�detrend_linear� detrend_none� isinstance�strr �callabler r r � TypeErrorZapply_along_axis)r r r r r r r! � s. �� r! z3.1r" )Z alternativec C s t | |d�S )a� Return x minus its mean along the specified axis. Parameters ---------- x : array or sequence Array or sequence containing the data Can have any dimensionality axis : integer The axis along which to take the mean. See numpy.mean for a description of this argument. See Also -------- detrend_mean : Same as `demean` except for the default *axis*. r )r" �r r r r r �demean� s r* c C s> t �| �} |dk r,|d | jkr,td| ��| | j|dd� S )a� Return x minus the mean(x). Parameters ---------- x : array or sequence Array or sequence containing the data Can have any dimensionality axis : integer The axis along which to take the mean. See numpy.mean for a description of this argument. See Also -------- detrend_linear : Another detrend algorithm. detrend_none : Another detrend algorithm. detrend : A wrapper around all the detrend algorithms. Nr r T)Zkeepdims)r r r r r r) r r r r" � s c C s | S )a� Return x: no detrending. Parameters ---------- x : any object An object containing the data axis : integer This parameter is ignored. It is included for compatibility with detrend_mean See Also -------- detrend_mean : Another detrend algorithm. detrend_linear : Another detrend algorithm. detrend : A wrapper around all the detrend algorithms. r r) r r r r$ � s r$ c C s� t �| �} | jdkr td��| js2t jd| jd�S t j| jtd�}t j || dd�}|d |d }| � � ||� � }| || | S )a� Return x minus best fit line; 'linear' detrending. Parameters ---------- y : 0-D or 1-D array or sequence Array or sequence containing the data axis : integer The axis along which to take the mean. See numpy.mean for a description of this argument. See Also -------- detrend_mean : Another detrend algorithm. detrend_none : Another detrend algorithm. detrend : A wrapper around all the detrend algorithms. r zy cannot have ndim > 1g r )�bias�r r )r r ) r r r r �arrayr �arange�size�float�covr )�yr �C�b�ar r r r# s r# c C s |dkr d}||kr t d��|dk r,t d��t�| �} | jdkrHt d��|dkrx|dkrx|dkrj| tj S | tj �� S || jkr�t d��t|�}t|�}|| }|dkr�|| jd | | f}| j d || j d f}n.| jd | | |f}|| j d | j d f}tj j j | ||d �S ) a~ Get all windows of x with length n as a single array, using strides to avoid data duplication. .. warning:: It is not safe to write to the output array. Multiple elements may point to the same piece of memory, so modifying one value may change others. Parameters ---------- x : 1D array or sequence Array or sequence containing the data. n : integer The number of data points in each window. noverlap : integer The overlap between adjacent windows. Default is 0 (no overlap) axis : integer The axis along which the windows will run. References ---------- `stackoverflow: Rolling window for 1D arrays in Numpy? <http://stackoverflow.com/a/6811241>`_ `stackoverflow: Using strides for an efficient moving average filter <http://stackoverflow.com/a/4947453>`_ Nr z noverlap must be less than nr �n cannot be less than 1�%only 1-dimensional arrays can be usedz(n cannot be greater than the length of x����r �strides) r r r r �newaxisZ transposer/ �intr r: �lib� stride_tricks� as_strided)r �n�noverlapr �stepr r: r r r �stride_windows7 s0 ! rC c C s� |dkrt d��t�| �} | jdkr,t d��|dkrR|dkrFt�| �S t�| �jS |dk rbt d��t|�}|dkr�|| jf}d| jd f}n| j|f}| jd df}tj j j | ||d�S )a� Repeat the values in an array in a memory-efficient manner. Array x is stacked vertically n times. .. warning:: It is not safe to write to the output array. Multiple elements may point to the same piece of memory, so modifying one value may change others. Parameters ---------- x : 1D array or sequence Array or sequence containing the data. n : integer The number of time to repeat the array. axis : integer The axis along which the data will run. References ---------- `stackoverflow: Repeat NumPy array without replicating data? <http://stackoverflow.com/a/5568169>`_ r, zaxis must be 0 or 1r r7 r r6 r9 ) r r r r � atleast_2d�Tr< r/ r: r= r> r? )r r@ r r r: r r r r { s$ r c C s\ |dkrd} n|| k} |dkr"d}|dkr.d}|dkr:t }|dkrFt}|dkrRd}| dksb| dkrhd} n| dkr|td | ��| s�| dkr�td ��t�| �} | s�t�|�}|dks�|dkr�t�| �r�d }q�d }n|d kr�td| ��t| �|k �rt| �} t�| |�} d| | d�< | �sDt|�|k �rDt|�} t�||�}d|| d�< |dk�rR|}| dk�rbd} n| dk�rpd} |d k�r�|} |d �r�|d d d }n|d }d}n2|d k�r�|d �r�|d d } n |d d } d}t| ||dd�}t ||dd�}t ||ddd�\}}tj j ||dd�d| �dd�f }tj � |d| �d| � }| �s�t|||�}t ||dd�}t ||dd�}tj j ||dd�d| �dd�f }t� |�| }nz| dk�r�t� |�| }n`| dk�r�t�|�t�|��� }n<| dk�s�| dk�rt�|�}n | dk�r"|t�|��� }| dk�r�|d �sDtddd�}n tddd�}|| |9 < | �r�|| }|t�|�d �� }n|t�|��� d }t�|d t| �|d d || �| }|d k�r t�||d� |d|� f�}t�||d�dd�f |d|�dd�f fd�}n|d �s:|d d9 < | dk�rRtj|dd�}|||fS )z� This is a helper function that implements the commonality between the psd, csd, spectrogram and complex, magnitude, angle, and phase spectrums. It is *NOT* meant to be used outside of mlab and may change at any time. NTr r � r �psd)rG �complex� magnitude�angle�phasezeUnknown value for mode %s, must be one of: 'default', 'psd', 'complex', 'magnitude', 'angle', 'phase'z*x and y must be equal if mode is not 'psd'�twosided�onesided)rM rL zPUnknown value for sides %s, must be one of: 'default', 'onesided', or 'twosided'Fr g �?� @r )r r )r@ r rI rJ rK rH r8 )r$ r r r r Z iscomplexobjr ZresizerC r! r ZfftZfftfreqZconj�abs�sumrJ �slicer. Z concatenateZunwrap)r r2 �NFFT�Fs� detrend_funcr rA �pad_to�sides� scale_by_freq�modeZ same_datar@ ZnumFreqsZ freqcenterZscaling_factor�resultr �freqsZresultYZslc�tr r r �_spectral_helper� s� � � � " " * �� r\ c C s� |dks|dks|dkr$t d| ��|dkr4t| �}t| dt| �|t|d||d|d� \}}}|dkrj|j}|jd kr�|jd d kr�|dd�df }||fS ) z� This is a helper function that implements the commonality between the complex, magnitude, angle, and phase spectrums. It is *NOT* meant to be used outside of mlab and may change at any time. NrG r z2_single_spectrum_helper does not work with %s moder F� r r2 rR rS rT r rA rU rV rW rX rH r r )r r r\ r$ �realr r ) r rX rS r rU rV �specrZ �_r r r �_single_spectrum_helperP s( � � ra a� Fs : scalar The sampling frequency (samples per time unit). It is used to calculate the Fourier frequencies, freqs, in cycles per time unit. The default value is 2. window : callable or ndarray A function or a vector of length *NFFT*. To create window vectors see `window_hanning`, `window_none`, `numpy.blackman`, `numpy.hamming`, `numpy.bartlett`, `scipy.signal`, `scipy.signal.get_window`, etc. The default is `window_hanning`. If a function is passed as the argument, it must take a data segment as an argument and return the windowed version of the segment. sides : {'default', 'onesided', 'twosided'} Specifies which sides of the spectrum to return. Default gives the default behavior, which returns one-sided for real data and both for complex data. 'onesided' forces the return of a one-sided spectrum, while 'twosided' forces two-sided. )ZSpectrala� pad_to : int The number of points to which the data segment is padded when performing the FFT. While not increasing the actual resolution of the spectrum (the minimum distance between resolvable peaks), this can give more points in the plot, allowing for more detail. This corresponds to the *n* parameter in the call to fft(). The default is None, which sets *pad_to* equal to the length of the input signal (i.e. no padding). )ZSingle_Spectruma� pad_to : int The number of points to which the data segment is padded when performing the FFT. This can be different from *NFFT*, which specifies the number of data points used. While not increasing the actual resolution of the spectrum (the minimum distance between resolvable peaks), this can give more points in the plot, allowing for more detail. This corresponds to the *n* parameter in the call to fft(). The default is None, which sets *pad_to* equal to *NFFT* NFFT : int The number of data points used in each block for the FFT. A power 2 is most efficient. The default value is 256. This should *NOT* be used to get zero padding, or the scaling of the result will be incorrect. Use *pad_to* for this instead. detrend : {'none', 'mean', 'linear'} or callable, default 'none' The function applied to each segment before fft-ing, designed to remove the mean or linear trend. Unlike in MATLAB, where the *detrend* parameter is a vector, in Matplotlib is it a function. The :mod:`~matplotlib.mlab` module defines `.detrend_none`, `.detrend_mean`, and `.detrend_linear`, but you can use a custom function as well. You can also use a string to choose one of the functions: 'none' calls `.detrend_none`. 'mean' calls `.detrend_mean`. 'linear' calls `.detrend_linear`. scale_by_freq : bool, optional Specifies whether the resulting density values should be scaled by the scaling frequency, which gives density in units of Hz^-1. This allows for integration over the returned frequency values. The default is True for MATLAB compatibility. )ZPSDc C s* t | d||||||||d� \} } | j| fS )a� Compute the power spectral density. The power spectral density :math:`P_{xx}` by Welch's average periodogram method. The vector *x* is divided into *NFFT* length segments. Each segment is detrended by function *detrend* and windowed by function *window*. *noverlap* gives the length of the overlap between segments. The :math:`|\mathrm{fft}(i)|^2` of each segment :math:`i` are averaged to compute :math:`P_{xx}`. If len(*x*) < *NFFT*, it will be zero padded to *NFFT*. Parameters ---------- x : 1-D array or sequence Array or sequence containing the data %(Spectral)s %(PSD)s noverlap : integer The number of points of overlap between segments. The default value is 0 (no overlap). Returns ------- Pxx : 1-D array The values for the power spectrum `P_{xx}` (real valued) freqs : 1-D array The frequencies corresponding to the elements in *Pxx* References ---------- Bendat & Piersol -- Random Data: Analysis and Measurement Procedures, John Wiley & Sons (1986) See Also -------- specgram `specgram` differs in the default overlap; in not returning the mean of the segment periodograms; and in returning the times of the segments. magnitude_spectrum : returns the magnitude spectrum. csd : returns the spectral density between two signals. N) r r2 rR rS r! r rA rU rV rW )�csdr^ ) r rR rS r! r rA rU rV rW �PxxrZ r r r rG � s 3 � rG c C sn |dkr d}t | ||||||||| dd� \} } } | jdkrf| jd dkrV| jdd�} n| dd�df } | | fS ) a Compute the cross-spectral density. The cross spectral density :math:`P_{xy}` by Welch's average periodogram method. The vectors *x* and *y* are divided into *NFFT* length segments. Each segment is detrended by function *detrend* and windowed by function *window*. *noverlap* gives the length of the overlap between segments. The product of the direct FFTs of *x* and *y* are averaged over each segment to compute :math:`P_{xy}`, with a scaling to correct for power loss due to windowing. If len(*x*) < *NFFT* or len(*y*) < *NFFT*, they will be zero padded to *NFFT*. Parameters ---------- x, y : 1-D arrays or sequences Arrays or sequences containing the data %(Spectral)s %(PSD)s noverlap : integer The number of points of overlap between segments. The default value is 0 (no overlap). Returns ------- Pxy : 1-D array The values for the cross spectrum `P_{xy}` before scaling (real valued) freqs : 1-D array The frequencies corresponding to the elements in *Pxy* References ---------- Bendat & Piersol -- Random Data: Analysis and Measurement Procedures, John Wiley & Sons (1986) See Also -------- psd : equivalent to setting ``y = x``. NrF rG r] r r r r )r\ r r r ) r r2 rR rS r! r rA rU rV rW �PxyrZ r` r r r rb � s 0 � rb c C s t | ||||dd�S )aX Compute the complex-valued frequency spectrum of *x*. Data is padded to a length of *pad_to* and the windowing function *window* is applied to the signal. Parameters ---------- x : 1-D array or sequence Array or sequence containing the data %(Spectral)s %(Single_Spectrum)s Returns ------- spectrum : 1-D array The values for the complex spectrum (complex valued) freqs : 1-D array The frequencies corresponding to the elements in *spectrum* See Also -------- magnitude_spectrum Returns the absolute value of this function. angle_spectrum Returns the angle of this function. phase_spectrum Returns the phase (unwrapped angle) of this function. specgram Can return the complex spectrum of segments within the signal. rH �r rS r rU rV rX �ra �r rS r rU rV r r r �complex_spectrum, s $ �rh c C s t | ||||dd�S )a� Compute the magnitude (absolute value) of the frequency spectrum of *x*. Data is padded to a length of *pad_to* and the windowing function *window* is applied to the signal. Parameters ---------- x : 1-D array or sequence Array or sequence containing the data %(Spectral)s %(Single_Spectrum)s Returns ------- spectrum : 1-D array The values for the magnitude spectrum (real valued) freqs : 1-D array The frequencies corresponding to the elements in *spectrum* See Also -------- psd Returns the power spectral density. complex_spectrum This function returns the absolute value of `complex_spectrum`. angle_spectrum Returns the angles of the corresponding frequencies. phase_spectrum Returns the phase (unwrapped angle) of the corresponding frequencies. specgram Can return the complex spectrum of segments within the signal. rI re rf rg r r r �magnitude_spectrumT s & �ri c C s t | ||||dd�S )a� Compute the angle of the frequency spectrum (wrapped phase spectrum) of *x*. Data is padded to a length of *pad_to* and the windowing function *window* is applied to the signal. Parameters ---------- x : 1-D array or sequence Array or sequence containing the data %(Spectral)s %(Single_Spectrum)s Returns ------- spectrum : 1-D array The values for the angle spectrum in radians (real valued) freqs : 1-D array The frequencies corresponding to the elements in *spectrum* See Also -------- complex_spectrum This function returns the angle value of `complex_spectrum`. magnitude_spectrum Returns the magnitudes of the corresponding frequencies. phase_spectrum Returns the phase (unwrapped angle) of the corresponding frequencies. specgram Can return the complex spectrum of segments within the signal. rJ re rf rg r r r �angle_spectrum~ s $ �rj c C s t | ||||dd�S )a� Compute the phase of the frequency spectrum (unwrapped angle spectrum) of *x*. Data is padded to a length of *pad_to* and the windowing function *window* is applied to the signal. Parameters ---------- x : 1-D array or sequence Array or sequence containing the data %(Spectral)s %(Single_Spectrum)s Returns ------- spectrum : 1-D array The values for the phase spectrum in radians (real valued) freqs : 1-D array The frequencies corresponding to the elements in *spectrum* See Also -------- complex_spectrum This function returns the phase value of `complex_spectrum`. magnitude_spectrum Returns the magnitudes of the corresponding frequencies. angle_spectrum Returns the angle (wrapped phase) of the corresponding frequencies. specgram Can return the complex spectrum of segments within the signal. rK re rf rg r r r �phase_spectrum� s $ �rk c C sv |dkr d}|dkrd}t | �|kr:t�d|t | �f � t| d||||||||| d� \} } } | dkrl| j} | | | fS )a& Compute a spectrogram. Compute and plot a spectrogram of data in x. Data are split into NFFT length segments and the spectrum of each section is computed. The windowing function window is applied to each segment, and the amount of overlap of each segment is specified with noverlap. Parameters ---------- x : array_like 1-D array or sequence. %(Spectral)s %(PSD)s noverlap : int, optional The number of points of overlap between blocks. The default value is 128. mode : str, optional What sort of spectrum to use, default is 'psd'. 'psd' Returns the power spectral density. 'complex' Returns the complex-valued frequency spectrum. 'magnitude' Returns the magnitude spectrum. 'angle' Returns the phase spectrum without unwrapping. 'phase' Returns the phase spectrum with unwrapping. Returns ------- spectrum : array_like 2-D array, columns are the periodograms of successive segments. freqs : array_like 1-D array, frequencies corresponding to the rows in *spectrum*. t : array_like 1-D array, the times corresponding to midpoints of segments (i.e the columns in *spectrum*). See Also -------- psd : differs in the overlap and in the return values. complex_spectrum : similar, but with complex valued frequencies. magnitude_spectrum : similar single segment when mode is 'magnitude'. angle_spectrum : similar to single segment when mode is 'angle'. phase_spectrum : similar to single segment when mode is 'phase'. Notes ----- detrend and scale_by_freq only apply when *mode* is set to 'psd'. N� rF zQOnly one segment is calculated since parameter NFFT (=%d) >= signal length (=%d).r] rH )r �cbookZ_warn_externalr\ r^ ) r rR rS r! r rA rU rV rW rX r_ rZ r[ r r r �specgram� s( C � � rn zwCoherence is calculated by averaging over *NFFT* length segments. Your signal is too short for your choice of *NFFT*. rF r r c C s� t | �d| k rtt��t| |||||||| � \} } t||||||||| � \} } t| ||||||||| � \} } t�| �d | | }|| fS )aH The coherence between *x* and *y*. Coherence is the normalized cross spectral density: .. math:: C_{xy} = \frac{|P_{xy}|^2}{P_{xx}P_{yy}} Parameters ---------- x, y Array or sequence containing the data %(Spectral)s %(PSD)s noverlap : integer The number of points of overlap between blocks. The default value is 0 (no overlap). Returns ------- The return value is the tuple (*Cxy*, *f*), where *f* are the frequencies of the coherence vector. For cohere, scaling the individual densities by the sampling frequency has no effect, since the factors cancel out. See Also -------- :func:`psd`, :func:`csd` : For information about the methods used to compute :math:`P_{xy}`, :math:`P_{xx}` and :math:`P_{yy}`. r )r r � _coh_errorrG rb r rO )r r2 rR rS r! r rA rU rV rW rc �fZPyyrd ZCxyr r r �cohere, s &���rq �#�,� Fc s� �dkrt � �� dkri � ddl} ddl} t�| ��t|�}G dd� d�}|dkrZ|���tj�|d�}��fdd�}||� �� fd d ���fd d ��d d� � | jj ����fdd�� �� | �ddd��� �t t j �� �t d���td���� d�� ���fdd�� �� | �ddd��� � � � � ��fdd��dddd�}� ��� ��fd d �}�dk}|�rZ|D ]8}t|��r�|dk �r�|d �|��r��qd|} �q��qdtd ����d � g �t � }t|�D ]�\}}|�� �� �dd �}d��fd!d"�|D ��}t|��sd#| }|�||�}|�|d�}|dk�r>��|d$| � n ��|� |d ||< �q�n t�t��rzd%d"� ��d&�D ��|||�}|dk�r�t d'���� d� tj�|d�}||� |�r�t |�}t|��r�|dk �r�|d �|��r�q��q�q�g }g } t|�D ]�\}}t|��s�q|dk �r8|d �|��r8�q|� dgt|�t|� � |�d(d"� t |�|�D �� | ��fd)d"�t �|�D �� �q��!� t|��s�dS | �r�t �"| ��r�t j#j$j%|�| d*�} nt j&j%|�d+�} | S ),a. Load data from comma/space/tab delimited file in *fname* into a numpy record array and return the record array. If *names* is *None*, a header row is required to automatically assign the recarray names. The headers will be lower cased, spaces will be converted to underscores, and illegal attribute name characters removed. If *names* is not *None*, it is a sequence of names to use for the column names. In this case, it is assumed there is no header row. - *fname*: can be a filename or a file handle. Support for gzipped files is automatic, if the filename ends in '.gz' - *comments*: the character used to indicate the start of a comment in the file, or *None* to switch off the removal of comments - *skiprows*: is the number of rows from the top to skip - *checkrows*: is the number of rows to check to validate the column data type. When set to zero all rows are validated. - *converterd*: if not *None*, is a dictionary mapping column number or munged column name to a converter function. - *names*: if not None, is a list of header names. In this case, no header will be read from the file - *missingd* is a dictionary mapping munged column names to field values which signify that the field does not contain actual data and should be masked, e.g., '0000-00-00' or 'unused' - *missing*: a string whose value signals a missing field regardless of the column it appears in - *use_mrecords*: if True, return an mrecords.fromrecords record array if any of the data are missing - *dayfirst*: default is False so that MM-DD-YY has precedence over DD-MM-YY. See http://labix.org/python-dateutil#head-b95ce2094d189a89f80f5ae52a05b4ab7b41af47 for further information. - *yearfirst*: default is False so that MM-DD-YY has precedence over YY-MM-DD. See http://labix.org/python-dateutil#head-b95ce2094d189a89f80f5ae52a05b4ab7b41af47 for further information. If no rows are found, *None* is returned Nr c @ s@ e Zd ZdZdd� Zdd� Zdd� Zdd � Zd d � Zd d � Z dS )z_csv2rec.<locals>.FHaC For space-delimited files, we want different behavior than comma or tab. Generally, we want multiple spaces to be treated as a single separator, whereas with comma and tab we want multiple commas to return multiple (empty) fields. 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Parameters ---------- dataset : array_like Datapoints to estimate from. In case of univariate data this is a 1-D array, otherwise a 2-D array with shape (# of dims, # of data). bw_method : str, scalar or callable, optional The method used to calculate the estimator bandwidth. This can be 'scott', 'silverman', a scalar constant or a callable. If a scalar, this will be used directly as `kde.factor`. If a callable, it should take a `GaussianKDE` instance as only parameter and return a scalar. If None (default), 'scott' is used. Attributes ---------- dataset : ndarray The dataset with which `gaussian_kde` was initialized. dim : int Number of dimensions. num_dp : int Number of datapoints. factor : float The bandwidth factor, obtained from `kde.covariance_factor`, with which the covariance matrix is multiplied. covariance : ndarray The covariance matrix of `dataset`, scaled by the calculated bandwidth (`kde.factor`). inv_cov : ndarray The inverse of `covariance`. Methods ------- kde.evaluate(points) : ndarray Evaluate the estimated pdf on a provided set of points. kde(points) : ndarray Same as kde.evaluate(points) Nc sT t �|��_t ��j�jdks&td��t ��j�j\�_�_t � t �}� d krPnv|rf� dkrf�j �_ n`|r|� dkr|�j �_ nJt �� �r�|s�d�_� fdd��_ n&t� �r�� �_�fdd��_ ntd ���� � �_t�d ��st �t j�jdd d ���_t j��j��_�j�jd �_�j�jd �_t �t j�d t j �j ���j �_ d S )Nr z.`dataset` input should have multiple elements.ZscottZ silvermanz use constantc s � S ru r r )� bw_methodr r �<lambda>� � z&GaussianKDE.__init__.<locals>.<lambda>c s � � � �S ru )� _bw_methodr rz r r r� � r� zB`bw_method` should be 'scott', 'silverman', a scalar or a callableZ _data_inv_covF)Zrowvarr+ r ) r rD �datasetr- r/ r r �dim�num_dpr% r& � scotts_factor�covariance_factor�silverman_factorZisscalarr� r' Zfactor�hasattrr1 Zdata_covarianceZlinalg�invZ data_inv_covZ covariance�inv_covZsqrtZdetZpi� norm_factor)rw r� r� ZisStringr )r� rw r rx � sJ �����zGaussianKDE.__init__c C s t �| jd| jd �S )N� �� �r Zpowerr� r� rz r r r r� � s zGaussianKDE.scotts_factorc C s& t �| j| jd d d| jd �S )NrN g @r� r� r� rz r r r r� � s �z GaussianKDE.silverman_factorc C s t �|�}t �|�j\}}|| jkr6td�|| j���t �|�}|| jkr�t | j�D ]R}| j dd�|t j f | }t � | j |�}t j|| dd�d }|t �| � }qTnft |�D ]\}| j |dd�|t j f }t � | j |�}t j|| dd�d }t jt �| �dd�||< q�|| j }|S )a Evaluate the estimated pdf on a set of points. Parameters ---------- points : (# of dimensions, # of points)-array Alternatively, a (# of dimensions,) vector can be passed in and treated as a single point. Returns ------- values : (# of points,)-array The values at each point. Raises ------ ValueError : if the dimensionality of the input points is different than the dimensionality of the KDE. z2points have dimension {}, dataset has dimension {}Nr r rN )r rD r- r r� r �formatZzerosr� �ranger� r; �dotr� rP Zexpr� ) rw Zpointsr� Znum_mrY r� ZdiffZtdiffZenergyr r r �evaluate� s* � zGaussianKDE.evaluate)N) r� r� r� r� rx r� r� r� r� �__call__r r r r r� v s 3 +0r� )r N)NN)r )N)N)Nr )r ) NNNNNNNNNN)NNNN)NNNNNNNN)NNNNNNNN)NNNN)NNNN)NNNN)NNNN) NNNNNNNNN) rr r r rs NNrt NFFF)&r� r� �inspectZnumpyr Zmatplotlib.cbookrm Z matplotlibr r r r r! Z deprecatedr* r" r$ r# rC r r\ ra Zinterpd�updateZcleandocZdedent_interpdrG rb rh ri rj rk rn ro rq r� �objectr� r r r r �<module> s� 7 8 : & D 7 � � # � 8 � ? � ' � ) � ' � ' � X � 1 �