&]\c@`sddlmZmZmZddlZddlmZddlm Z ddl m Z ddl m Z dddd d Zd Zd Zd ZddddddZdS(i(tdivisiontprint_functiontabsolute_importN(tlstsq(t factorial(t convolve1di(t axis_sliceg?tconvcC`sX||krtdnt|d\}}|dkrKtdn|d kr`|}nd|kow|knstdn|d krtdntj| ||d t}|dkr|d d d }ntj|d jd d } || } tj|d } t|||| | 0. pos : int or None, optional If pos is not None, it specifies evaluation position within the window. The default is the middle of the window. use : str, optional Either 'conv' or 'dot'. This argument chooses the order of the coefficients. The default is 'conv', which means that the coefficients are ordered to be used in a convolution. With use='dot', the order is reversed, so the filter is applied by dotting the coefficients with the data set. Returns ------- coeffs : 1-d ndarray The filter coefficients. References ---------- A. Savitzky, M. J. E. Golay, Smoothing and Differentiation of Data by Simplified Least Squares Procedures. Analytical Chemistry, 1964, 36 (8), pp 1627-1639. See Also -------- savgol_filter Notes ----- .. versionadded:: 0.14.0 Examples -------- >>> from scipy.signal import savgol_coeffs >>> savgol_coeffs(5, 2) array([-0.08571429, 0.34285714, 0.48571429, 0.34285714, -0.08571429]) >>> savgol_coeffs(5, 2, deriv=1) array([ 2.00000000e-01, 1.00000000e-01, 2.00607895e-16, -1.00000000e-01, -2.00000000e-01]) Note that use='dot' simply reverses the coefficients. >>> savgol_coeffs(5, 2, pos=3) array([ 0.25714286, 0.37142857, 0.34285714, 0.17142857, -0.14285714]) >>> savgol_coeffs(5, 2, pos=3, use='dot') array([-0.14285714, 0.17142857, 0.34285714, 0.37142857, 0.25714286]) `x` contains data from the parabola x = t**2, sampled at t = -1, 0, 1, 2, 3. `c` holds the coefficients that will compute the derivative at the last position. When dotted with `x` the result should be 6. >>> x = np.array([1, 0, 1, 4, 9]) >>> c = savgol_coeffs(5, 2, pos=4, deriv=1, use='dot') >>> c.dot(x) 6.0000000000000018 s*polyorder must be less than window_length.iiswindow_length must be odd.s4pos must be nonnegative and less than window_length.Rtdots`use` must be 'conv' or 'dot'tdtypeNii(RR( t ValueErrortdivmodtNonetnptarangetfloattreshapetzerosRR(t window_lengtht polyordertderivtdeltatpostusethalflentremtxtordertAtytcoeffst_((s;lib/python2.7/site-packages/scipy/signal/_savitzky_golay.pyt savgol_coeffs s(X       cC`s|dkr|}nt|}||krOtj|dddf}n||| j}xbt|D]T}tj||d||dd}||j||fd|jd9}qmW|}|S(sEDifferentiate polynomials represented with coefficients. p must be a 1D or 2D array. In the 2D case, each column gives the coefficients of a polynomial; the first row holds the coefficients associated with the highest power. m must be a nonnegative integer. (numpy.polyder doesn't handle the 2D case.) iNi.i(i(tlenR t zeros_liketcopytrangeRRtndim(tptmtresulttntdptktrng((s;lib/python2.7/site-packages/scipy/signal/_savitzky_golay.pyt_polyders    "%-c C`st|d|d|d|} |dks:||j krI| } t} n| j|d} t} | j| jdd} tjtj d||| |} |dkrt | |} ntj ||||}tj | |jdd||}t | j}|||d|d<||<|j|||d}| r^|jd|}nt| d|d|d|}||d 0. Default is 1.0. axis : int, optional The axis of the array `x` along which the filter is to be applied. Default is -1. mode : str, optional Must be 'mirror', 'constant', 'nearest', 'wrap' or 'interp'. This determines the type of extension to use for the padded signal to which the filter is applied. When `mode` is 'constant', the padding value is given by `cval`. See the Notes for more details on 'mirror', 'constant', 'wrap', and 'nearest'. When the 'interp' mode is selected (the default), no extension is used. Instead, a degree `polyorder` polynomial is fit to the last `window_length` values of the edges, and this polynomial is used to evaluate the last `window_length // 2` output values. cval : scalar, optional Value to fill past the edges of the input if `mode` is 'constant'. Default is 0.0. Returns ------- y : ndarray, same shape as `x` The filtered data. See Also -------- savgol_coeffs Notes ----- Details on the `mode` options: 'mirror': Repeats the values at the edges in reverse order. The value closest to the edge is not included. 'nearest': The extension contains the nearest input value. 'constant': The extension contains the value given by the `cval` argument. 'wrap': The extension contains the values from the other end of the array. For example, if the input is [1, 2, 3, 4, 5, 6, 7, 8], and `window_length` is 7, the following shows the extended data for the various `mode` options (assuming `cval` is 0):: mode | Ext | Input | Ext -----------+---------+------------------------+--------- 'mirror' | 4 3 2 | 1 2 3 4 5 6 7 8 | 7 6 5 'nearest' | 1 1 1 | 1 2 3 4 5 6 7 8 | 8 8 8 'constant' | 0 0 0 | 1 2 3 4 5 6 7 8 | 0 0 0 'wrap' | 6 7 8 | 1 2 3 4 5 6 7 8 | 1 2 3 .. versionadded:: 0.14.0 Examples -------- >>> from scipy.signal import savgol_filter >>> np.set_printoptions(precision=2) # For compact display. >>> x = np.array([2, 2, 5, 2, 1, 0, 1, 4, 9]) Filter with a window length of 5 and a degree 2 polynomial. Use the defaults for all other parameters. >>> savgol_filter(x, 5, 2) array([ 1.66, 3.17, 3.54, 2.86, 0.66, 0.17, 1. , 4. , 9. ]) Note that the last five values in x are samples of a parabola, so when mode='interp' (the default) is used with polyorder=2, the last three values are unchanged. Compare that to, for example, `mode='nearest'`: >>> savgol_filter(x, 5, 2, mode='nearest') array([ 1.74, 3.03, 3.54, 2.86, 0.66, 0.17, 1. , 4.6 , 7.97]) tmirrortconstanttnearestRFtwraps@mode must be 'mirror', 'constant', 'nearest' 'wrap' or 'interp'.RRsOIf mode is 'interp', window_length must be less than or equal to the size of x.R0tmodetcval(RGRHRIRFRJ( R R tasarrayR tfloat64tfloat32tastypeR tsizeRRE( RRRRRR0RKRLRR((s;lib/python2.7/site-packages/scipy/signal/_savitzky_golay.pyt savgol_filterse $ !(t __future__RRRtnumpyR t scipy.linalgRtmathRt scipy.ndimageRt _arraytoolsRR R R-RDRERR(((s;lib/python2.7/site-packages/scipy/signal/_savitzky_golay.pyts    ,