(ph4jSSKrSSKJr SSKJr SSKJr SSKJ r S Sjr Sr S r S r S S jrg)N)lstsq)float_factorial) convolve1d) axis_slicecX:a [S5e[US5upgUcUS:XaUS- nOUnSUs=::aU:d O [S5eUS;a [S5eX!:a[R"U5nU$[R"U*X- [ S 9n US :XaU SSS 2n [R"US -5R S S 5n X-n [R"US -5n [U5X2-- X'[X5un n U$) a Compute the coefficients for a 1-D Savitzky-Golay FIR filter. Parameters ---------- window_length : int The length of the filter window (i.e., the number of coefficients). polyorder : int The order of the polynomial used to fit the samples. `polyorder` must be less than `window_length`. deriv : int, optional The order of the derivative to compute. This must be a nonnegative integer. The default is 0, which means to filter the data without differentiating. delta : float, optional The spacing of the samples to which the filter will be applied. This is only used if deriv > 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. See Also -------- savgol_filter Notes ----- .. versionadded:: 0.14.0 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. Jianwen Luo, Kui Ying, and Jing Bai. 2005. Savitzky-Golay smoothing and differentiation filter for even number data. Signal Process. 85, 7 (July 2005), 1429-1434. Examples -------- >>> import numpy as np >>> 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, 2.07548111e-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]) >>> savgol_coeffs(4, 2, pos=3, deriv=1, use='dot') array([0.45, -0.85, -0.65, 1.05]) `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) 6.0 z*polyorder must be less than window_length.Nrg?z4pos must be nonnegative and less than window_length.)convdotz`use` must be 'conv' or 'dot')dtyper r) ValueErrordivmodnpzerosarangefloatreshaperr) window_length polyorderderivdeltaposusehalflenremcoeffsxorderAy_s O/var/www/html/venv/lib/python3.13/site-packages/scipy/signal/_savitzky_golay.py savgol_coeffsr$s!x!EFF-+LG { !8C-CC  $} $*+ + /!899 -( 3$ +59A f} ddG IIi!m $ , ,R 3E A QAu%8AHAkOFAq! Mc^US:XaUnU$[U5nX1::a[R"USS2S45nU$USU*R5n[ U5HNn[R "X5- S- X- S- S5nXFR X1- 4SURS- --5-nMP UnU$)a4Differentiate polynomials represented with coefficients. p must be a 1-D or 2-D array. In the 2-D case, each column gives the coefficients of a polynomial; the first row holds the coefficients associated with the highest power. m must be a nonnegative integer. (numpy.polyder doesn't handle the 2-D case.) rNr.r )r)lenr zeros_likecopyrangerrndim)pmresultndpkrngs r#_polyderr3s Av M F 6]]1RaRW:.F M 3QBB1Xii 1519b9kk15(TQVVaZ-@"@AAF Mr%c [XX%S9n US:XdXPR*:XaU n Sn OU RUS5n Sn U RU RSS5n [ R "[ R"SX!- 5X5n US:a [X5n [ R"X1- XA- 5n[ R"XRSS55X-- n[U R5nUUUSsUS'UU'UR"XC- /USSQ76nU (aURSU5n[XXES9nUUS'g) a- Given an N-d array `x` and the specification of a slice of `x` from `window_start` to `window_stop` along `axis`, create an interpolating polynomial of each 1-D slice, and evaluate that polynomial in the slice from `interp_start` to `interp_stop`. Put the result into the corresponding slice of `y`. )startstopaxisrFTr rN.) rr+swapaxesrshaperpolyfitrr3polyvallist)r window_start window_stop interp_start interp_stopr7rrrr!x_edgexx_edgeswapped poly_coeffsivaluesshpy_edges r# _fit_edgerIs6K KF qyDVVGO//$*oogmmA.3G**RYYq+*DE$1K qy{2  ,-{/IJA ZZ YYr1%5 6%. IF qww-CD 3q6CFCI ^^K6 AQR AFD) K KFF3Kr%c xUS-n[USUSXuX#XF5 URUn[XU- XU- XX#XF5 g)z Use polynomial interpolation of x at the low and high ends of the axis to fill in the halflen values in y. This function just calls _fit_edge twice, once for each end of the axis. r rN)rIr9) rrrrrr7r!rr/s r#_fit_edges_polyfitrKsNq G aM1g*  A a]"A7{A*r%c US;a [S5e[R"U5nUR[R:wa=UR[R :waUR [R5n[XX4S9nUS:Xa8XRU:a [S5e[XUSS9n [XX#XEU 5 U $[XXVUS9n U $) a9Apply a Savitzky-Golay filter to an array. This is a 1-D filter. If `x` has dimension greater than 1, `axis` determines the axis along which the filter is applied. Parameters ---------- x : array_like The data to be filtered. If `x` is not a single or double precision floating point array, it will be converted to type ``numpy.float64`` before filtering. window_length : int The length of the filter window (i.e., the number of coefficients). If `mode` is 'interp', `window_length` must be less than or equal to the size of `x`. polyorder : int The order of the polynomial used to fit the samples. `polyorder` must be less than `window_length`. deriv : int, optional The order of the derivative to compute. This must be a nonnegative integer. The default is 0, which means to filter the data without differentiating. delta : float, optional The spacing of the samples to which the filter will be applied. This is only used if deriv > 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 -------- >>> import numpy as np >>> 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]) )mirrorconstantnearestinterpwrapz@mode must be 'mirror', 'constant', 'nearest' 'wrap' or 'interp'.)rrrPzOIf mode is 'interp', window_length must be less than or equal to the size of x.rN)r7mode)r7rRcval) rrasarrayr float64float32astyper$r9rrK) rrrrrr7rRrSrr!s r# savgol_filterrXsL FF/0 0 1 Aww"**BJJ!6 HHRZZ  =5 NF x 774= (?@ @ qt* =1YuAN H qtT B Hr%)r?Nr )rrYr rPg)numpyr scipy.linalgrscipy._lib._utilr scipy.ndimager _arraytoolsrr$r3rIrKrXr%r#r`sD,$#EIHV0)X *?B/2 r%