3 h5 @s0ddlmZmZmZmZmZmZmZmZm Z m Z m Z ddl m Z mZmZmZmZmZmZmZmZddlmZmZddlmZddlmZddd d d d d ddg Zd+ddZiZddZ ddZ!dd Z"dd Z#dd Z$ddZ%ddZ&ddZ'ddZ(d d!Z)d"d#Z*d,d%d Z+d-d&d Z,d.d(dZ-d/d)dZ.d*S)0) logical_andasarraypi zeros_like piecewisearrayarctan2tanzerosarangefloor) sqrtexpgreaterlesscosaddsin less_equal greater_equal) cspline2dsepfir2d)comb)float_factorial spline_filterbspline gauss_splinecubic quadratic cspline1d qspline1dcspline1d_evalqspline1d_eval@c Cs|jj}tdddgdd}|d krr|jd}t|j|}t|j|}t|||}t|||}|d|j|}n2|d krt||}t|||}|j|}ntd |S) zSmoothing spline (cubic) filtering of a rank-2 array. Filter an input data set, `Iin`, using a (cubic) smoothing spline of fall-off `lmbda`. g?g@fg@FDy?dzInvalid data type for Iin)r&r')r%r() dtypecharrastyperrealimagr TypeError) ZIinZlmbdaZintypeZhcolZckrZckiZoutrZoutioutr06/tmp/pip-build-riy7u7_k/scipy/scipy/signal/bsplines.pyrs        csytStk rYnXdd}dd}dr@d }nd}|dd|g}|x4td|dD]"}|j|dddqfW|j|ddd dtfd d fd d t|D}||ft<||fS)aReturns the function defined over the left-side pieces for a bspline of a given order. The 0th piece is the first one less than 0. The last piece is a function identical to 0 (returned as the constant 0). (There are order//2 + 2 total pieces). Also returns the condition functions that when evaluated return boolean arrays for use with `numpy.piecewise`. cs<|dkrfddS|dkr*fddSfddSdS)Nrcstt|t|S)N)rrr)x)val1val2r0r1=s z>_bspline_piecefunctions..condfuncgen..cs t|S)N)r)r2)r4r0r1r5@scstt|t|S)N)rrr)r2)r3r4r0r1r5Bs r0)numr3r4r0)r3r4r1 condfuncgen;s  z,_bspline_piecefunctions..condfuncgenr6g?g?rrg@csdd|dkrdSfddtdDfddtdDfdd}|S) Nr6rc s6g|].}dd|dttd|ddqS)rr6)exact)floatr).0k)fvalorderr0r1 ]szA_bspline_piecefunctions..piecefuncgen..rcsg|]} |qSr0r0)r;r<)boundr0r1r?_scs:d}x0tdD] }||||7}qW|S)Ngr)range)r2resr<)Mkcoeffsr>shiftsr0r1thefuncas z>_bspline_piecefunctions..piecefuncgen..thefunc)rA)r7rF)r@r=r>)rCrDrEr1 piecefuncgenYs  z-_bspline_piecefunctions..piecefuncgencsg|] }|qSr0r0)r;r<)rGr0r1r?hsz+_bspline_piecefunctions..gg)_splinefunc_cacheKeyErrorrAappendr)r>r8lastZ startbound condfuncsr7funclistr0)r@r=r>rGr1_bspline_piecefunctions+s(    rNcs8tt| t|\}}fdd|D}t||S)zyB-spline basis function of order n. Notes ----- Uses numpy.piecewise and automatic function-generator. csg|] }|qSr0r0)r;func)axr0r1r?zszbspline..)absrrNr)r2nrMrLZcondlistr0)rPr1ros cCs6|dd}dtdt|t|d d|S)a:Gaussian approximation to B-spline basis function of order n. Parameters ---------- n : int The order of the spline. Must be nonnegative, i.e., n >= 0 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 rg(@r6)r rr)r2rRZsignsqr0r0r1r~s cCstt|}t|}t|d}|jrJ||}dd|dd|||<|t|d@}|jr~||}d d|d||<|S) zeA cubic B-spline. This is a special case of `bspline`, and equivalent to ``bspline(x, 3)``. rg@g?r6gUUUUUU?g?gUUUUUU?)rQrrrany)r2rPrBcond1ax1cond2ax2r0r0r1rs  cCsvtt|}t|}t|d}|jr>||}d|d||<|t|d@}|jrr||}|ddd||<|S)ziA quadratic B-spline. This is a special case of `bspline`, and equivalent to ``bspline(x, 2)``. g?g?r6g?g@)rQrrrrU)r2rPrBrVrWrXrYr0r0r1rs  cCsdd|d|tdd|}ttd|dt|}d|dt|d|}|td|d|tdd||}||fS)Nr`rS0)r r)ZlamxiZomegrhor0r0r1 _coeff_smooths $,r`cCs.|t|||t||dt|dS)Nr)rr)r<csr_omegar0r0r1_hcs"rdcCs||d||d||dd||td||d}d||d||t|}t|}|||t|||t||S)Nrr6)rr rQr)r<rbr_rcZc0gammaZakr0r0r1_hss & rgc Cs t|\}}dd|t|||}t|}t|f|jj}t|}td||||dtj t|d|||||d<td||||dtd||||dtj t|d|||||d<xRt d|D]D}|||d|t|||d||||d||<qWt|f|jj} tj t ||||t |d||||ddd| |d<tj t |d|||t |d||||ddd| |d<xZt |dddD]F}|||d|t|| |d||| |d| |<qW| S) Nrr6rrSrararara) r`rlenr r)r*r rdrreducerArg) signallambr_rcrbKZypr<rRyr0r0r1_cubic_smooth_coeffs* "*"&,,& rncCsdtd}t|}t|f|jj}|t|}|d|tj|||d<x.td|D] }|||||d||<qZWt|f|j}||d||d||d<x4t|dddD] }|||d||||<qW|dS) Nr6rSrrg@rara) r rhr r)r*r rrirA)rjzirlypluspowersr<outputr0r0r1 _cubic_coeffs     rtcCsddtd}t|}t|f|jj}|t|}|d|tj|||d<x.td|D] }|||||d||<q^Wt|f|jj}||d||d||d<x4t|ddd D] }|||d||||<qW|dS) NrSr6g@rrg @rara) r rhr r)r*r rrirA)rjrprlrqrrr<rsr0r0r1_quadratic_coeffs    rvcCs|dkrt||St|SdS)aM Compute cubic spline coefficients for rank-1 array. Find the cubic 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, 4.0, 1.0]/ 6.0 . Parameters ---------- signal : ndarray A rank-1 array representing samples of a signal. lamb : float, optional Smoothing coefficient, default is 0.0. Returns ------- c : ndarray Cubic spline coefficients. gN)rnrt)rjrkr0r0r1r s cCs|dkrtdnt|SdS)aCompute 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 matplotlib.pyplot as plt >>> from scipy.signal import qspline1d, qspline1d_eval >>> sig = np.repeat([0., 1., 0.], 100) >>> sig += np.random.randn(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() gz.Smoothing quadratic splines not supported yet.N) ValueErrorrv)rjrkr0r0r1r!$s+ ?cCst||t|}t||jd}|jdkr0|St|}|dk}||dk}||B}t||| ||<t|d|d||||<||}|jdkr|St||jd} t|djt d} x@t dD]4} | | } | j d|d} | || t || 7} qW| ||<|S)axEvaluate a 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. )r)rrr6re) rr:rr)sizerhr"r r+intrAclipr)cjnewxdxx0rBNrVrXcond3resultjlowerithisjindjr0r0r1r"Us*     cCst|||}t|}|jdkr&|St|}|dk}||dk}||B}t||| ||<t|d|d||||<||}|jdkr|St|} t|djtd} x@tdD]4} | | } | j d|d} | || t || 7} qW| ||<|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 matplotlib.pyplot as plt >>> from scipy.signal import qspline1d, qspline1d_eval >>> sig = np.repeat([0., 1., 0.], 100) >>> sig += np.random.randn(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() rrr6g?rS) rrrzrhr#r r+r{rAr|r)r}r~rrrBrrVrXrrrrrrr0r0r1r#ys*2    N)r$)rw)rw)ryr)ryr)/Znumpyrrrrrrrr r r r Znumpy.core.umathr rrrrrrrrZsplinerrZ scipy.specialrZscipy._lib._utilr__all__rrHrNrrrrr`rdrgrnrtrvr r!r"r#r0r0r0r1s.4,     D  1 $