SciPy and friends can be used for a variety of tasks: NumPy's array type augments the Python language with an efficient data structure useful for numerical work, e. besselLowpassFilter """ import numpy as np import scipy. Smith's text on DSP. This cannot be done with IIR filters, as they have a non-linear phase (non-constant group delay). filtfilt (b, a, x, axis=-1, padtype='odd', padlen=None, method='pad', irlen=None) [source] ¶ Apply a digital filter forward and backward to a signal. signal as sig import sys using the pad method in filtfilt so manual it. zscore(arr, axis=0, ddof=0) function computes the relative Z-score of the input data, relative to the sample mean and standard deviation. Image Processing with SciPy and NumPy — Segmentation. x uses plain MATLAB filter > an is thus genuinely multi-threaded. The objective of this tutorial is to give a brief idea about the usage of SciPy library for scientific computing problems in Python. By continuing to browse this site, you agree to this use. I was using the scipy. Order of Butterworth filter. Pandas provides data structures for efficiently storing sparse data. The Hamming window is defined as: w(n) = α − βcos (2πn)/(N − 1), where α = 0. filtfilt(); ‘lfilter’: scipy. filtfilt¶ scipy. The ‘krogh’, ‘piecewise_polynomial’, ‘spline’, ‘pchip’ and ‘akima’ methods are wrappers around the respective SciPy implementations of similar names. SciPy is a Python-based ecosystem of open-source software for mathematics, science, and engineering. Hosted by Tavis R. Applying a FIR filter 18. fftfilt, filter, filter2. Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A Outline 1 Introduction Image Processing What are SciPy and NumPy? 2 Some Theory Filters The Fourier Transform 3 Doing the Stuff in Python. cheby1 highpass applied to input using FILTFILT looks correct, using FILTER gives a very different and wrong output. scikit-image is a Python package dedicated to image processing, and using natively NumPy arrays as image objects. lfilter_zi (b, a) Compute an initial state zi for the lfilter function that corresponds to the steady state of the step response. signal import lfilter, lfilter_zi, filtfilt, butter from pandas import DataFrame from. This page on FIR filter vs IIR filter describes difference between FIR filter and IIR filter. org distribution. Finding the problem may be arduous, since (a) the R function stats::filter() is not well documented, regarding init, init. The SciPy library depends on NumPy, which provides convenient and fast N-dimensional array manipulation. It includes a use case where we will implement logistic regression using scikit learn. Scikit-image: image processing¶ Author: Emmanuelle Gouillart. Butterworth Lowpass Filter Example. Decimation reduces the original sample rate of a sequence to a lower rate. Author's note: This article was originally called Adventures in Signal Processing with Python (MATLAB? We don't need no stinkin' MATLAB!) — the allusion to The Treasure of the Sierra Madre has been removed, in deference to being a good neighbor to The MathWorks. From DataCamp’s NumPy tutorial, you will have gathered that this library is one of the core libraries for scientific computing in Python. The SciPy library is built to work with NumPy arrays, and provides many user-friendly and efficient numerical routines such as routines for numerical integration and optimization. For tutorials, reference documentation, the SciPy. Given the long release cycle, Statsmodels follows a loose time-based policy for dependencies: minimal dependencies are lagged about one and a half to two years. A 30 point FIR filter with Hamming window is used if ftype is 'fir'. NumPy provides basic FFT functionality, which SciPy extends further, but both include an fft function, based on the Fortran FFTPACK. y, and (b) the Octave filter() spans 700 lines of C, so it is hard to reverse engineer to figure out what it’s doing. Return coefficients for an IIR notch-filter with one or more filter frequencies and according (very narrow) bandwidths to be used with 'filter' or 'filtfilt'. sosfiltfilt(). One workflow the combination of these allow, for example, is to find the locations of steepest descent/ascent in noisy data: (i) filter or fit data, (ii) differentiate smooth data (iii) find coordinate min/max of gradients. Is there a ready made function in numpy/scipy to compute the correlation y=mx+o of an X and Y fast: m, m-err, o, o-err, r-coef,r-coef-err ? numpy and scipy questions are best asked on their lists, not here. This sample code demonstrates the use of the function scipy. Inputs: in - An N-dimensional input array. It provides many user-friendly and efficient numerical routines such as routines for numerical integration, interpolation, optimization, linear algebra and statistics. Symmetric linear-phase FIR filters are constructed, and if phase='zero' (default), the delay of this filter is compensated for, making it non-causal. Chapter 1 Preface Introductory textbook for Kalman lters and Bayesian lters. Standard Analog Filter topologies Up: Some filter concepts Previous: Bandpass filters Contents filtfilt. MATLAB/Octave Python Description; doc help -i % browse with Info: help() Browse help interactively: help help or doc doc: help: Help on using help: help plot: help. lfilter_zi (b, a) Compute an initial state zi for the lfilter function that corresponds to the steady state of the step response. org Mailing Lists: Welcome! Below is a listing of all the public Mailman 2 mailing lists on mail. Hi! I designed a Butterworth 8th order bandpass filter (1-50Hz passband)and tried implementing it using filter. It's becoming increasingly common to use Python for neuroscience data analysis, and I expect it to. Explore Popular Topics Like Government, Sports, Medicine, Fintech, Food, More. They are extracted from open source Python projects. lfilter(); 'sosfiltfilt': scipy. The combined filter has linear phase. m implementation does not work on this type of signal (EEG signal with high level of 60+ Hz noise). This sample code demonstrates the use of the function scipy. In this Python tutorial, we will use Image Processing with SciPy and NumPy. 4, and at this time Python 3. Image Processing with SciPy and NumPy — Segmentation. The pylab module from matplotlib is used to create plots. From DataCamp’s NumPy tutorial, you will have gathered that this library is one of the core libraries for scientific computing in Python. leastsq() is designed for such problems. NumPy/SciPy Application Note. decimate(x, q, n=None, ftype='iir', axis=-1, zero_phase=None) [source] ¶ Downsample the signal after applying an anti-aliasing filter. I write as follows: import scipy. This function uses scipy. lfilter_zi¶ scipy. It applies the filter twice, once forward and once backward, resulting in zero phase delay. Get newsletters and notices that include site news, special offers and exclusive discounts about IT products & services. The SciPy library is built to work with NumPy arrays, and provides many user-friendly and efficient numerical routines such as routines for numerical integration and optimization. FIR filter uses only current and past input digital samples to obtain a current output sample value. First results of axisymmetric numerical studies of the final evolution of degenerate C + O cores are reported. In that, I should initialize data in a vij way, then I should use it to perform matrix vector multiplication. You can vote up the examples you like or vote down the ones you don't like. If sos (default), a series of second-order filters is used for filtering with scipy. Taking the log compresses the range significantly. Type help butter to get more info from Matlab SP toolbox. Hope you like our explanation. signal as sig import sys using the pad method in filtfilt so manual it. If ba, returns numerators/denominators of the transfer functions, used for filtering with scipy. They are extracted from open source Python projects. upfirdn` (which is also new in 0. Gallery About Documentation Support About. You can think of it like Matlab for Python. The SciPy library depends on NumPy, which provides convenient and fast N-dimensional array manipulation. Applying digital filters to speech sounds. sparse improvements. filtfilt, a linear filter that achieves zero phase delay by applying an IIR filter to a signal twice, once forwards and once backwards. Edit (12/1/18): I use Python almost exclusively now. Learn more about why function filtfilt can produce negative values for a positive input data?. From DataCamp’s NumPy tutorial, you will have gathered that this library is one of the core libraries for scientific computing in Python. Type help butter to get more info from Matlab SP toolbox. Hello Junzi Sun, Thank you for such a nice script! However, it seems to me that the filtered it a bit tilted to the right, i. Ein zweiter Vorschlag ist, scipy. filtfilt is the forward-backward filter. This works for many fundamental data types (including Object type). I am trying to understand why I get an array of NaNs after applying a butterworth filter when I make the cutoff frequency too long in the example below. The SciPy library depends on NumPy, which provides convenient and fast N-dimensional array manipulation. It still remains the lingua franca in numerical algorithms. scipy can be compared to other standard scientific-computing libraries, such as the GSL (GNU Scientific Library for C and C++), or Matlab's toolboxes. Smith's text on DSP. Introduction. The image. As a result, input signals get attenuated twice as much. I have an array of date whose sampling rate is 160GHz, and I wish to apply 30kHz-100kHz bandpass filter to the data. sparse supports sparse linear algebra, graph analysis, multiple sparse matrix formats) • signal processing (scipy. lfilter does apply given filter and in Fourier space this is like applying filter transfer function ONCE. 0) does not extrapolate data at the beginning and the end. Filter the EMG signal to smooth it. This chapter describes how to use scikit-image on various image processing tasks, and insists on the link with other scientific Python modules such as NumPy and SciPy. For example, in the parametric EQ block of a miniDSP plugin, each peak/notch or shelving filter is a single biquad. For tutorials, reference documentation, the SciPy. K- means clustering with scipy K-means clustering is a method for finding clusters and cluster centers in a set of unlabeled data. Any filter that operates in ``real-time'' is a casual filter in that it's output at time t 0 can only depend on events that have occured for t t 0. firwin2 was added. If not, then. Digital filter design functions now include a parameter to specify the sampling rate. We are going to compare the performance of different methods of image processing using three Python libraries (scipy, opencv and scikit-image). Filter a data sequence, x, using a digital filter. The code is on GitHub and he also links to the generators available in SciPy. m has some reverse filtering implemented, but I am unclear on other parts of the function (as I say I am a novice). Actually, the Scipy implementation of the bandwidth estimate does depend on the variance of each data dimension. The SciPy library depends on NumPy, which provides convenient and fast N-dimensional array manipulation. The function uses decimation algorithms 8. filtfilt(); ‘lfilter’: scipy. The option to use Gustafsson's method for choosing the initial conditions of the forward and backward passes was added to `scipy. filtfilt applies the filter twice, whereas scipy. You get twice the attenuation and zero phase shift. • FIR Filter Designer was developed in Python to allow users to take advantage of the new FIR filter implementation • Export filter coefficients to file for immediate use in IADS • Linear phase in passband is desirable for certain analyses • Interactive (TKinter library) Filter Tools (continued). Casual versus non-casual filters. These packages are not. This page on FIR filter vs IIR filter describes difference between FIR filter and IIR filter. Standard Analog Filter topologies Up: Some filter concepts Previous: Bandpass filters Contents filtfilt. Image Processing with SciPy and NumPy — Segmentation. There is, however, an important design called the elliptic filter, which has ripple in both the passband and the stopband. cheby1 highpass applied to input using FILTFILT looks correct, using FILTER gives a very different and wrong output. Iowa Hills Filter design tools (Freeware) This free FIR filter design program uses the Parks McClellan algorithm and Fourier Transform (windows) method to synthesize filters. freqz is used to compute the frequency response, and scipy. •Since all weights are equal, it is called a BOX filter. Compute an initial state zi for the lfilter function that corresponds to the steady state of the step response. Cython >= 0. filtfilt apply the same filter twice and effect is like applying filter transfer function SQUARED. The function `scipy. GpuPy can be transparent, so if a GPU is present on the system where the script is being run, it will simply run faster. 1 1 1 Box filter 1/9 1 1 1 1 1 1 O. Get notifications on updates for this project. jl differentiates between filter coefficients and stateful filters. Magnitude values at zero dB are unaffected by the filter. The function `scipy. So its not the zero phase effect that interested me about the filtfilt, it was the work in minimizing transients. signal) ¶ The function scipy. filters import correlate, convolve from ipywidgets import. scipy is the core package for scientific routines in Python; it is meant to operate efficiently on numpy arrays, so that numpy and scipy work hand in hand. I use a butterworth filter with the filtfilt function. Preferably, do not use sudo pip, as this combination can cause problems. sftrans Transform band edges of a generic lowpass filter (cutoff at W=1) represented in splane zero-pole-gain form. sparse supports sparse linear algebra, graph analysis, multiple sparse matrix formats) • signal processing (scipy. We recommend using an user install, sending the --user flag to pip. Source code for mosaic. Rewrote much of lfilter_zi, and added a docstring that explains what it does. filter_function: string Filtering function to be used. If phase=='zero-double', then this filter is applied twice, once forward, and once backward (also making it non-causal). From Vancouver R Users Group (data analysis / statistics) Public group? This is a. Analog (electronic) filters can be used for these same tasks; however, digital filters can achieve far superior results. This sample code demonstrates the use of the function scipy. lfilter (b, a, x[, axis, zi]) Filter data along one-dimension with an IIR or FIR filter. signal has convolutions, wavelets, splines, filters) 23 Scipy vs. Camps, PSU since this is a linear operator, we can take the average around each pixel by convolving the image with this 3x3. linalg import norm from PIL import Image from matplotlib import pyplot as plt, rcParams, rc from scipy. Compute an initial state zi for the lfilter function that corresponds to the steady state of the step response. A filter's frequency response can be plotted using function freqz. In the original code that you've linked to the _compute_covariance method sets the covariance matrix for the Gaussian kernel as the product of the factor provided by calling either scotts_factor or silverman_factor and the data covariance. As the filter order increases, the phase distortion near and in the transition band worsens. The main reason for building the SciPy library is that, it should work. Using lambdas with filter. No matter what i do I get a jump on joining the two ts. py", line 37, in from. I suspect that if you make sure your signals are of length 2^N, you'll get even faster results, since it'll switch to a FFT instead of a DFT. Sample Real world Reconstruct Discrete samples (pixels) Transform. This is the class and function reference of scikit-learn. NumPy/SciPy Application Note. besselLowpassFilter """ import numpy as np import scipy. Help filtfilt >> help filtfilt filtfilt Zero-phase forward and reverse digital IIR filtering. y, and (b) the Octave filter() spans 700 lines of C, so it is hard to reverse engineer to figure out what it’s doing. optimize` improvements * The `scipy. This release contains several great new features and a large number of bug fixes and various improvements, as detailed in the release notes below. Phase of the filter, only used if method='fir'. Glue is a multi-disciplinary tool. Many of the SciPy routines are Python "wrappers", that is, Python routines that provide a Python interface for numerical libraries and routines originally written in Fortran, C, or C++. 0 to 1 for butter vs 0 to π for freqz), leading to errors and confusion. leastsq() is designed for such problems. In case of Butterworth filter (scipy. Magnitude values at zero dB are unaffected by the filter. Inputs: in – An N-dimensional input array. Just keep in. The SciPy stack offers a suite of popular Python packages designed for numerical computing, data transformation, analysis and visualization, which is ideal for many bioinformatic analysis needs. place_poles`, which provides two methods to place poles for linear systems, was added. Im trying to filter my data at different passbands. signalの下にまとまっています。FIRフィルタを設計する関数は、firwin()という1つにまとめられていて引数を変えることでローパス、ハイパス、バンドパス、バンドストップが作れました。firwin()の返り値は、フィルタ係数です。. A short course presenting the application of machine learning methods to large datasets. To apply a filter to a 1-D audio waveform, Matlab provides function filtfilt, which takes as arguments the result [b, a] from butter, the waveform, and a value denoting the order (number of coefficients) of the filter. Compute an initial state zi for the lfilter function that corresponds to the steady state of the step response. Indexing is the way to do these things. first forwards, then backwards. We will deal with reading and writing to image and displaying image. Intuitively, we might think of a cluster as comprising a group of data points whose inter-point distances are small compared with the distances to points outside of the cluster. Y = filtfilt(B, A, X) filters the data in vector X with the filter. 1 What is SciPy? SciPy is both (1) a way to handle large arrays of numerical data in Python (a capability it gets from Numpy) and (2) a way to apply scientific, statistical, and mathematical operations to those arrays of data. The image. lfilter(); 'sosfiltfilt': scipy. lfilter这个函数实现FIR滤波器,主要的参数包括b和a,分别对应分母和分子的系数。. This site uses cookies for analytics, personalized content and ads. SciPy is a Python-based ecosystem of open-source software for mathematics, science, and engineering. The order of the filter is twice the original filter order. It is a hybrid of both Numeric and Numarray incorporating features of both. The SciPy library is built to work with NumPy arrays, and provides many user-friendly and efficient numerical routines such as routines for numerical integration and optimization. This makes these functions consistent with many other functions in scipy. The filter package produces filter constants of the structure shown in Table 1. Parameters path str, Path or file-like object, optional. filtfilt ist der Vorwärts-Rückwärtsfilter. In case of Butterworth filter (scipy. In the chapters where he compares IIR filters (Chebyshev and Butterworth) to FIR filters (windowed-sinc filter), he mostly just mentions execution time as the advantage of Chebyshev filters, saying that FIR filters perform better but are slower. It's great, but it was written in 1997. In the end, it creates an iterator of the ones that return true (vowels). In the wonderful world of integrated circuits, filters play a key role in many important functions within a system design. filtfilt apply the same filter twice and effect is like applying filter transfer function SQUARED. Minimizes numerical precision errors for high-order filters, but is slower. The combined filter has zero phase and a filter order twice that of the. Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A Outline 1 Introduction Image Processing What are SciPy and NumPy? 2 Some Theory Filters The Fourier Transform 3 Doing the Stuff in Python. It applies the filter twice, once forward and once backward, resulting in zero phase delay. There are many types of filter architectures from which to choose, but one of the myriad of decisions which a designer must work through is the choice of using an analog vs. Scipy Filter B A. optimize has multiple solvers, gradient checks, simulated annealing) • sparse matrices (scipy. This I read would help me "zero phase digital filtering ". map(), filter(), lambda, and list comprehensions provide compact, elegant, and efficient ways to encode a few common idioms in programming. lfilter_zi(b, a) [source] ¶ Compute an initial state zi for the lfilter function that corresponds to the steady state of the step response. This cookbook recipe demonstrates the use of scipy. If phase='zero' (default), the delay of this filter is compensated for. kernel_size – A scalar or an N-length list giving the size of the. (Previously it only handled a 1-dimensional array. scipy is the core package for scientific routines in Python; it is meant to operate efficiently on numpy arrays, so that numpy and scipy work hand in hand. y = filtfilt(b,a,x) performs zero-phase digital filtering by processing the input data, x, in both the forward and reverse directions. filtfilt is the forward-backward filter. Spyder and/or Jupyter Notebooks make it simple to do any kind of scientific computing you want. • A band-stop filter works to screen out frequencies that are within a certain range, giving easy passage only to frequencies outside of that range. py", line 37, in from. x uses plain MATLAB filter > an is thus genuinely multi-threaded. In our previous Python Library tutorial, we saw Python Matplotlib. Comparing Python vs Sci Py may also be of use if you are interested in such closely related search terms as scipy vs pythonxy, numpy vs python, numpy vs python speed, numpy vs python array and scipy vs scientific python. Introduction. filtfilt vs filter gives strange results. To this point, the steps to compute filter banks and MFCCs were discussed in terms of their motivations and implementations. filtfilt ist der Vorwärts-Rückwärtsfilter. in (in India). Now we should note that scipy. digital filter. Butterworth Lowpass Filter Example. 6 is the current one. FIR filter uses only current and past input digital samples to obtain a current output sample value. base import MultiSequencePreprocessingMixin class. sparse improvements. filtfilt is an M-file that uses the filter function. filtfilt (b, a, x, axis=-1, padtype='odd', padlen=None, method='pad', irlen=None) [source] ¶ Apply a digital filter forward and backward to a signal. Phase of the filter, only used if method='fir'. In case of Butterworth filter (scipy. mode(array, axis=0) function calculates the mode of the array elements along the specified axis of the array (list in python. Hier ist eine modifizierte Version deines Skripts. To apply a filter to a 1-D audio waveform, Matlab provides function filtfilt, which takes as arguments the result [b, a] from butter, the waveform, and a value denoting the order (number of coefficients) of the filter. It applies the filter twice, once forward and once backward, resulting in zero phase delay. Discrete samples (pixels) Display. This MATLAB function designs a Butterworth IIR digital filter using the specifications supplied in the object d. OK, I Understand. Numerical Routines: SciPy and NumPy¶. curve_fit Function Welcome to Tech Rando! In today's post, I will go over automating decline curve analysis for oil and gas wells, using both an exponential and a hyperbolic line of best fit. We will deal with reading and writing to image and displaying image. Intuitively, we might think of a cluster as comprising a group of data points whose inter-point distances are small compared with the distances to points outside of the cluster. Topics include: brief review of the common issues of machine learning, such as, memorizing/overfitting vs learning, test/train splits, feature engineering, domain knowledge, fast/simple/dumb learners vs slow/complex/smart learners; moving your model from your laptop into a production environment using. After filtering the data in the forward direction, filtfilt reverses the filtered sequence and runs it back through the filter. Now we should note that scipy. More than 5 years have passed since last update. These libraries do not come with the python. Set up Butterworth filter. decimate function and noticed that it seemed to have some unusual edge effects using the default IIR Chebychev filter. Algorithms vs LP or MIP. m has some reverse filtering implemented, but I am unclear on other parts of the function (as I say I am a novice). (As a quick aside, you'll note that we use scipy. Spyder and/or Jupyter Notebooks make it simple to do any kind of scientific computing you want. filtfilt (b, a, x[, axis, padtype, padlen]) A forward-backward filter. with "filtfilt" instead of. All the tests will be done using timeit. to_netcdf (path=None, mode='w', format=None, group=None, engine=None, encoding=None, unlimited_dims=None, compute=True) ¶ Write dataset contents to a netCDF file. linalg import norm from PIL import Image from matplotlib import pyplot as plt, rcParams, rc from scipy. Or you can leave the the filter output uncorrected, then you have a linear phase causal filter. lfilter_zi (b, a) [source] ¶ Construct initial conditions for lfilter for step response steady-state. How to plot the frequency spectrum with scipy Spectrum analysis is the process of determining the frequency domain representation of a time domain signal and most commonly employs the Fourier transform. The objective of this tutorial is to give a brief idea about the usage of SciPy library for scientific computing problems in Python. Symmetric linear-phase FIR filters are constructed, and if phase='zero' (default), the delay of this filter is compensated for, making it non-causal. Added more datasets for examples. (Formerly known as the IPython Notebook)¶ The IPython Notebook is now known as the Jupyter Notebook. filtfilt¶ scipy. The option to use Gustafsson's method for choosing the initial conditions of the forward and backward passes was added to `scipy. resample_poly`. It applies the filter twice, once forward and once backward, resulting in zero phase delay. Hosted by Tavis R. Once loaded, an image may be processed using library routines or by mathematical operations that would take advantage of the speed and conciseness of numpy and scipy. lfiltic (b, a, y[, x]) Construct initial conditions for lfilter. Discrete samples (pixels) Display. Cheby1 lowpass applied using FILTER looks correct and unsig FILTFILT is very different and wrong output. A short course presenting the application of machine learning methods to large datasets. This sample code demonstrates the use of the function scipy. filtfilt() implements filter() twice. Before applying the filter, the function can pad the data along the given axis in one of three ways. Whereas, the filter function gives the output that is of same length as that of the input \(x\). signal has convolutions, wavelets, splines, filters) 23 Scipy vs. Previously, digital filters could only be specified using normalized frequency, but different functions used different scales (e. In other words, the signal filtered with filtfilt has an peak magnitude that is 0. 24 is required to build the code from github but not from a source distribution. This library contains a collection of tools and techniques that can be used to solve on a computer mathematical models of problems in Science and Engineering. filtfilt (b, a, x, axis=-1, padtype='odd', padlen=None, method='pad', irlen=None) [source] ¶ Apply a digital filter forward and backward to a signal. 4; % Threshold frequency (in Nyquist units of 1/(2*dt)) [b a] = butter(N,Wn) % Coefficients for 2N-order low-pass Butterworth filter % Use v = filter(b,a,u) to filter the time series u. sparse improvements Iterating over and slicing of CSC and CSR matrices is now faster by up to ~35%. If ‘minimum’, then a. y, and (b) the Octave filter() spans 700 lines of C, so it is hard to reverse engineer to figure out what it's doing. The function `scipy. filtfilt(b, a, x, axis=-1, padtype='odd', padlen=None) [source] ¶ A forward-backward filter. Gonzalez and Richard E. signal package. A filter's frequency response can be plotted using function freqz. Casual versus non-casual filters. How does the reverse filtering affect the total filter order? If I use a second order butterworth, does the filtfilt function act like a fourth order butterworth (without the shift) or has the reverse filtering no effect on the total filter order? Thnaks for your advice. Flexible Data Ingestion. While I don't make it a. Smooth data with a Savitzky-Golay smoothing filter. decimate lowpass filters the input to guard against aliasing and downsamples the result. SciPy is a Python library of mathematical routines. This chapter describes how to use scikit-image on various image processing tasks, and insists on the link with other scientific Python modules such as NumPy and SciPy. SciPy, a scientific library for Python is an open source, BSD-licensed library for mathematics, science and engineering. This sample code demonstrates the use of the function scipy.