tKgs=ddlmZmZmZmZmZmZmZmZm Z m Z m Z m Z m Z mZmZmZmZddlmZmZddlmZmZmZddlmZgdZddZiZdZd Zd Z d Z!d Z"d Z#dZ$dZ%dZ&ddZ'ddZ(ddZ)ddZ*y))asarraypi zeros_likearrayarctan2tanonesarangefloorr_ atleast_1dsqrtexpgreatercosaddsin) cspline2dsepfir2d)lfiltersosfiltlfiltic)BSpline) spline_filter gauss_spline cspline1d qspline1dcspline1d_evalqspline1d_evalc|jj}tgdddz }|dvrp|jd}t |j |}t |j |}t|||}t|||}|d|zzj|}|S|dvr,t ||}t|||}|j|}|Std) a4Smoothing spline (cubic) filtering of a rank-2 array. Filter an input data set, `Iin`, using a (cubic) smoothing spline of fall-off `lmbda`. Parameters ---------- Iin : array_like input data set lmbda : float, optional spline smooghing fall-off value, default is `5.0`. Returns ------- res : ndarray filtered input data Examples -------- We can filter an multi dimensional signal (ex: 2D image) using cubic B-spline filter: >>> import numpy as np >>> from scipy.signal import spline_filter >>> import matplotlib.pyplot as plt >>> orig_img = np.eye(20) # create an image >>> orig_img[10, :] = 1.0 >>> sp_filter = spline_filter(orig_img, lmbda=0.1) >>> f, ax = plt.subplots(1, 2, sharex=True) >>> for ind, data in enumerate([[orig_img, "original image"], ... [sp_filter, "spline filter"]]): ... ax[ind].imshow(data[0], cmap='gray_r') ... ax[ind].set_title(data[1]) >>> plt.tight_layout() >>> plt.show() )?g@r"f@)FDr%y?)r#dzInvalid data type for Iin) dtypecharrastyperrealimagr TypeError) Iinlmbdaintypehcolckrckioutroutiouts Z/home/alanp/www/video.onchill/myenv/lib/python3.12/site-packages/scipy/signal/_bsplines.pyrrsLYY^^F # & ,D jjo%(%(T4(T4(b4i''/ J : U#sD$'jj  J344ct|}|dzdz }dtdtz|zz t|dz dz |z zS)aGaussian approximation to B-spline basis function of order n. Parameters ---------- x : array_like a knot vector n : int The order of the spline. Must be non-negative, i.e., n >= 0 Returns ------- res : ndarray B-spline basis function values approximated by a zero-mean Gaussian function. Notes ----- The B-spline basis function can be approximated well by a zero-mean Gaussian function with standard-deviation equal to :math:`\sigma=(n+1)/12` for large `n` : .. math:: \frac{1}{\sqrt {2\pi\sigma^2}}exp(-\frac{x^2}{2\sigma}) References ---------- .. [1] Bouma H., Vilanova A., Bescos J.O., ter Haar Romeny B.M., Gerritsen F.A. (2007) Fast and Accurate Gaussian Derivatives Based on B-Splines. In: Sgallari F., Murli A., Paragios N. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2007. Lecture Notes in Computer Science, vol 4485. Springer, Berlin, Heidelberg .. [2] http://folk.uio.no/inf3330/scripting/doc/python/SciPy/tutorial/old/node24.html Examples -------- We can calculate B-Spline basis functions approximated by a gaussian distribution: >>> import numpy as np >>> from scipy.signal import gauss_spline >>> knots = np.array([-1.0, 0.0, -1.0]) >>> gauss_spline(knots, 3) array([0.15418033, 0.6909883, 0.15418033]) # may vary rg(@)rrrr)xnsignsqs r7rrJsLZ  A!et^F tAFVO$ $sAF7Q;+?'@ @@r8ct|t}tjgdd}||}d||dk|dkDz<|S)Nr()rrr:F extrapolaterr@r:)rfloatr basis_elementr;br6s r7_cubicrH|sFA/UCA A$CCRAE Jr8ctt|t}tjgdd}||}d||dk|dkDz<|S)Nr?)gg??FrBrrJrK)absrrDrrErFs r7 _quadraticrMsK GAU #$A4%HA A$C"#CTa#g Jr8c dd|zz d|ztdd|zzzz}ttd|zdz t|}d|zdz t|z d|zz }|td|zd|ztdd|zzzz|z z}||fS)Nr`0)rr)lamxiomegrhos r7 _coeff_smoothrXs R#XS4C#I #66 6B 4c A &R 1D 8a<$r( "rCx 0C b3hcDS3Y,?!??2EF FC 9r8ch|t|z ||zzt||dzzzt|dzS)NrrA)rr)kcsrWomegas r7_hcr]s; UOsax (3uA+? ? ArN r8c||zd||zzzd||zz z dd|z|ztd|zzz |dzzz }d||zz d||zzz t|z }t|}|||zzt||z|t||zzzzS)Nrr:)rrrLr)rZr[rWr\c0gammaaks r7_hsrcs r'Qs] #q39} 5 q3w}s1u9~- -q 8 :B s]q39} -E :E QB r >S_us52:/FF GGr8c t|\}}dd|zt|zz ||zz}t|}t|}t d||||dzt j t |dz||||zz}t d||||dzt d||||dzzt j t |dz||||zz}t|tdd|zt|z||zft||f} | jdd} t|dddd|zt|z||zf} | jdd} t| |dd| \} } t||| f} t j t||||t|dz|||z|dddz}t j t|dz |||t|dz|||z|dddz}t|tdd|zt|z||zft||f} | jdd} t| | ddd| \} } t| ddd||f} | S)Nrr:rr@rAzi) rXrlenr r]rreducerr reshaperrc)signallambrWr\r[KrZzi_2zi_1rfsosyp_ys r7_cubic_smooth_coeffrtst$JC QWs5z ! !C#I -B F Aq A 2sE "VAY . JJs1q5"c51F: ; >> import numpy as np >>> import matplotlib.pyplot as plt >>> from scipy.signal import cspline1d, cspline1d_eval >>> rng = np.random.default_rng() >>> sig = np.repeat([0., 1., 0.], 100) >>> sig += rng.standard_normal(len(sig))*0.05 # add noise >>> time = np.linspace(0, len(sig)) >>> filtered = cspline1d_eval(cspline1d(sig), time) >>> plt.plot(sig, label="signal") >>> plt.plot(time, filtered, label="filtered") >>> plt.legend() >>> plt.show() )rtr~rkrls r7rrs$X s{"6400F##r8c8|dk7r tdt|S)aFCompute quadratic spline coefficients for rank-1 array. Parameters ---------- signal : ndarray A rank-1 array representing samples of a signal. lamb : float, optional Smoothing coefficient (must be zero for now). Returns ------- c : ndarray Quadratic spline coefficients. See Also -------- qspline1d_eval : Evaluate a quadratic spline at the new set of points. Notes ----- Find the quadratic spline coefficients for a 1-D signal assuming mirror-symmetric boundary conditions. To obtain the signal back from the spline representation mirror-symmetric-convolve these coefficients with a length 3 FIR window [1.0, 6.0, 1.0]/ 8.0 . Examples -------- We can filter a signal to reduce and smooth out high-frequency noise with a quadratic spline: >>> import numpy as np >>> import matplotlib.pyplot as plt >>> from scipy.signal import qspline1d, qspline1d_eval >>> rng = np.random.default_rng() >>> sig = np.repeat([0., 1., 0.], 100) >>> sig += rng.standard_normal(len(sig))*0.05 # add noise >>> time = np.linspace(0, len(sig)) >>> filtered = qspline1d_eval(qspline1d(sig), time) >>> plt.plot(sig, label="signal") >>> plt.plot(time, filtered, label="filtered") >>> plt.legend() >>> plt.show() rz.Smoothing quadratic splines not supported yet.) ValueErrorrrs r7rrAs#Z s{IJJ''r8cPt||z t|z }t||j}|jdk(r|St |}|dk}||dz kD}||z}t ||| ||<t |d|dz z||z ||<||}|jdk(r|St||j} t|dz jtdz} tdD]3} | | z} | jd|dz } | || t|| z zz } 5| ||<|S)aEvaluate a cubic spline at the new set of points. `dx` is the old sample-spacing while `x0` was the old origin. In other-words the old-sample points (knot-points) for which the `cj` represent spline coefficients were at equally-spaced points of: oldx = x0 + j*dx j=0...N-1, with N=len(cj) Edges are handled using mirror-symmetric boundary conditions. Parameters ---------- cj : ndarray cublic spline coefficients newx : ndarray New set of points. dx : float, optional Old sample-spacing, the default value is 1.0. x0 : int, optional Old origin, the default value is 0. Returns ------- res : ndarray Evaluated a cubic spline points. See Also -------- cspline1d : Compute cubic spline coefficients for rank-1 array. Examples -------- We can filter a signal to reduce and smooth out high-frequency noise with a cubic spline: >>> import numpy as np >>> import matplotlib.pyplot as plt >>> from scipy.signal import cspline1d, cspline1d_eval >>> rng = np.random.default_rng() >>> sig = np.repeat([0., 1., 0.], 100) >>> sig += rng.standard_normal(len(sig))*0.05 # add noise >>> time = np.linspace(0, len(sig)) >>> filtered = cspline1d_eval(cspline1d(sig), time) >>> plt.plot(sig, label="signal") >>> plt.plot(time, filtered, label="filtered") >>> plt.legend() >>> plt.show() r?rrr:r_) rrDrr(sizerhrr r*intrangecliprHcjnewxdxx0resNcond1cond2cond3resultjlowerithisjindjs r7rrts;d DMB %) +D T *C xx1}  BA 1HE AENEem ET%[L1CJAQK$u+$=>CJ ;D yyA~ BHH -F 4!8_ # #C (1 ,F 1X zz!QU#"T(VD5L111CJ Jr8ct||z |z }t|}|jdk(r|St|}|dk}||dz kD}||z}t ||| ||<t |d|dz z||z ||<||}|jdk(r|St|} t |dz j tdz} tdD]3} | | z} | jd|dz } | || t|| z zz } 5| ||<|S)aEvaluate a quadratic spline at the new set of points. Parameters ---------- cj : ndarray Quadratic spline coefficients newx : ndarray New set of points. dx : float, optional Old sample-spacing, the default value is 1.0. x0 : int, optional Old origin, the default value is 0. Returns ------- res : ndarray Evaluated a quadratic spline points. See Also -------- qspline1d : Compute quadratic spline coefficients for rank-1 array. Notes ----- `dx` is the old sample-spacing while `x0` was the old origin. In other-words the old-sample points (knot-points) for which the `cj` represent spline coefficients were at equally-spaced points of:: oldx = x0 + j*dx j=0...N-1, with N=len(cj) Edges are handled using mirror-symmetric boundary conditions. Examples -------- We can filter a signal to reduce and smooth out high-frequency noise with a quadratic spline: >>> import numpy as np >>> import matplotlib.pyplot as plt >>> from scipy.signal import qspline1d, qspline1d_eval >>> rng = np.random.default_rng() >>> sig = np.repeat([0., 1., 0.], 100) >>> sig += rng.standard_normal(len(sig))*0.05 # add noise >>> time = np.linspace(0, len(sig)) >>> filtered = qspline1d_eval(qspline1d(sig), time) >>> plt.plot(sig, label="signal") >>> plt.plot(time, filtered, label="filtered") >>> plt.legend() >>> plt.show() rrr:rKrQ) rrrrhr r r*rrrrMrs r7r r s,h DMB " $D T C xx1}  BA 1HE AENEem ET%[L1CJAQK$u+$=>CJ ;D yyA~  F 4#:  % %c *Q .F 1X zz!QU#"T(Zu 555CJ Jr8N)g@)r)r"r)+numpyrrrrrrr r r r r rrrrrr_splinerr _signaltoolsrrrscipy.interpolater__all__r_splinefunc_cacherrHrMrXr]rcrtr~rrrrr r8r7rsFFFFF )33% I5p/Ad H' TDD/$d0(fGTIr8