B &]\#@s|dZddlmZmZmZddlmZmZmZm Z m Z m Z m Z dddddgZ dd dZdddZddZdddZddZdS)zW Functions which are common and require SciPy Base and Level 1 SciPy (special, linalg) )divisionprint_functionabsolute_import)arangenewaxishstackproductarray frombufferloadcentral_diff_weights derivativeascentfaceelectrocardiogramcCs||dkrtd|ddkr(tdddlm}|d?}t| |d}|ddtf}|d }x"td|D]}t|||g}qpWttd|ddd |||}|S) a Return weights for an Np-point central derivative. Assumes equally-spaced function points. If weights are in the vector w, then derivative is w[0] * f(x-ho*dx) + ... + w[-1] * f(x+h0*dx) Parameters ---------- Np : int Number of points for the central derivative. ndiv : int, optional Number of divisions. Default is 1. Notes ----- Can be inaccurate for large number of points. rz;Number of points must be at least the derivative order + 1.rz!The number of points must be odd.)linalgg?Ng)axis) ValueErrorZscipyrrrrangerrinv)ZNpZndivrhoxXkwr0lib/python3.7/site-packages/scipy/misc/common.pyr s   $?rc Cs||dkrtd|ddkr(td|dkr|dkrLtdddgd}nv|d krltdd dd dgd }nV|d krtdddddddgd}n2|dkrtdddddddddg d}n t|d}n|dkrd|dkrtdddg}n||d krtdddddgd }nZ|d kr.tdddd dddgd!}n4|dkrXtdd"d#d$d%d$d#d"dg d&}n t|d}n t||}d'}|d?}x8t|D],} ||| ||| ||f|7}qW|t|f|dd(S))a6 Find the n-th derivative of a function at a point. Given a function, use a central difference formula with spacing `dx` to compute the `n`-th derivative at `x0`. Parameters ---------- func : function Input function. x0 : float The point at which `n`-th derivative is found. dx : float, optional Spacing. n : int, optional Order of the derivative. Default is 1. args : tuple, optional Arguments order : int, optional Number of points to use, must be odd. Notes ----- Decreasing the step size too small can result in round-off error. Examples -------- >>> from scipy.misc import derivative >>> def f(x): ... return x**3 + x**2 >>> derivative(f, 1.0, dx=1e-6) 4.9999999999217337 rzm'order' (the number of points used to compute the derivative), must be at least the derivative order 'n' + 1.rrzJ'order' (the number of points used to compute the derivative) must be odd.r g@ig(@ i-igN@ii`iiX g@@giiiigf@iiig@g)r)rr r rr) funcZx0ZdxnargsorderZweightsvalrrrrrr 2s<#           ,c CsNddl}ddl}|j|jtd}t|d}t||}WdQRX|S)aw Get an 8-bit grayscale bit-depth, 512 x 512 derived image for easy use in demos The image is derived from accent-to-the-top.jpg at http://www.public-domain-image.com/people-public-domain-images-pictures/ Parameters ---------- None Returns ------- ascent : ndarray convenient image to use for testing and demonstration Examples -------- >>> import scipy.misc >>> ascent = scipy.misc.ascent() >>> ascent.shape (512, 512) >>> ascent.max() 255 >>> import matplotlib.pyplot as plt >>> plt.gray() >>> plt.imshow(ascent) >>> plt.show() rNz ascent.datrb) pickleospathjoindirname__file__openr r )r2r3fnamefrrrrr{s  Fc Csddl}ddl}t|j|jtdd}|}WdQRX||}t |dd}d|_ |dkrd |dddddfd |ddddd fd |ddddd f d}|S)aw Get a 1024 x 768, color image of a raccoon face. raccoon-procyon-lotor.jpg at http://www.public-domain-image.com Parameters ---------- gray : bool, optional If True return 8-bit grey-scale image, otherwise return a color image Returns ------- face : ndarray image of a racoon face Examples -------- >>> import scipy.misc >>> face = scipy.misc.face() >>> face.shape (768, 1024, 3) >>> face.max() 255 >>> face.dtype dtype('uint8') >>> import matplotlib.pyplot as plt >>> plt.gray() >>> plt.imshow(face) >>> plt.show() rNzface.datr1Zuint8)Zdtype)iir TgzG?gQ?rgQ?r) bz2r3r8r4r5r6r7readZ decompressr shapeastype)Zgrayr;r3r:Zrawdatadatarrrrrs!  Tc CsPddl}|j|jtd}t|}|dt}WdQRX|dd}|S)af Load an electrocardiogram as an example for a one-dimensional signal. The returned signal is a 5 minute long electrocardiogram (ECG), a medical recording of the heart's electrical activity, sampled at 360 Hz. Returns ------- ecg : ndarray The electrocardiogram in millivolt (mV) sampled at 360 Hz. Notes ----- The provided signal is an excerpt (19:35 to 24:35) from the `record 208`_ (lead MLII) provided by the MIT-BIH Arrhythmia Database [1]_ on PhysioNet [2]_. The excerpt includes noise induced artifacts, typical heartbeats as well as pathological changes. .. _record 208: https://physionet.org/physiobank/database/html/mitdbdir/records.htm#208 .. versionadded:: 1.1.0 References ---------- .. [1] Moody GB, Mark RG. The impact of the MIT-BIH Arrhythmia Database. IEEE Eng in Med and Biol 20(3):45-50 (May-June 2001). (PMID: 11446209); :doi:`10.13026/C2F305` .. [2] Goldberger AL, Amaral LAN, Glass L, Hausdorff JM, Ivanov PCh, Mark RG, Mietus JE, Moody GB, Peng C-K, Stanley HE. PhysioBank, PhysioToolkit, and PhysioNet: Components of a New Research Resource for Complex Physiologic Signals. Circulation 101(23):e215-e220; :doi:`10.1161/01.CIR.101.23.e215` Examples -------- >>> from scipy.misc import electrocardiogram >>> ecg = electrocardiogram() >>> ecg array([-0.245, -0.215, -0.185, ..., -0.405, -0.395, -0.385]) >>> ecg.shape, ecg.mean(), ecg.std() ((108000,), -0.16510875, 0.5992473991177294) As stated the signal features several areas with a different morphology. E.g. the first few seconds show the electrical activity of a heart in normal sinus rhythm as seen below. >>> import matplotlib.pyplot as plt >>> fs = 360 >>> time = np.arange(ecg.size) / fs >>> plt.plot(time, ecg) >>> plt.xlabel("time in s") >>> plt.ylabel("ECG in mV") >>> plt.xlim(9, 10.2) >>> plt.ylim(-1, 1.5) >>> plt.show() After second 16 however, the first premature ventricular contractions, also called extrasystoles, appear. These have a different morphology compared to typical heartbeats. The difference can easily be observed in the following plot. >>> plt.plot(time, ecg) >>> plt.xlabel("time in s") >>> plt.ylabel("ECG in mV") >>> plt.xlim(46.5, 50) >>> plt.ylim(-2, 1.5) >>> plt.show() At several points large artifacts disturb the recording, e.g.: >>> plt.plot(time, ecg) >>> plt.xlabel("time in s") >>> plt.ylabel("ECG in mV") >>> plt.xlim(207, 215) >>> plt.ylim(-2, 3.5) >>> plt.show() Finally, examining the power spectrum reveals that most of the biosignal is made up of lower frequencies. At 60 Hz the noise induced by the mains electricity can be clearly observed. >>> from scipy.signal import welch >>> f, Pxx = welch(ecg, fs=fs, nperseg=2048, scaling="spectrum") >>> plt.semilogy(f, Pxx) >>> plt.xlabel("Frequency in Hz") >>> plt.ylabel("Power spectrum of the ECG in mV**2") >>> plt.xlim(f[[0, -1]]) >>> plt.show() rNzecg.datecgigi@)r3r4r5r6r7r r>int)r3Z file_pathfiler@rrrrs Z  N)r)rrrr )F)__doc__Z __future__rrrZnumpyrrrrr r r __all__r r rrrrrrrs$ $ I' -