Please note that only method='linear' is supported for DataFrame/Series with a MultiIndex.. Parameters method str, default ‘linear’ Found insideThis book covers setting up your Raspberry Pis, installing the necessary software, and making a cluster of multiple Pis. Once the cluster is built, its power has to be exploited by means of programs to run on it. Examples. Examples. For example, 'natural' should result in second derivative being zero outside the x-values of the data, whilst 'clamped' should result in the first derivative being zero outside this range. By voting up you can indicate which examples are most useful and appropriate. Found inside – Page 385It is possible to use any of the vast array of libraries available for Python from IDL. For example, make one of the interpolation methods in SciPy ... z ( x, y) = sin. Interpolate following xs and ys using rbf and find values for 2.1, 2.2 ... 2.9: Insert the missing method to find the univariate spline interpolation: Get certifiedby completinga course today! Found inside – Page 327The most common type of interpolation is with cubic splines for which you find functions in the sub-library scipy.interpolate. The example remains the same ... sin ( xx ** 2 + yy ** 2 ) >>> f = interpolate . Requirements. Finally when using higher order functions use cubic spline interpolation. Note that for our function, Z, defined using the meshgrid set up here, the RectBivariateSpline method expects the corresponding one-dimensional arrays y and x to be passed in this order (opposite to that of interp2d.) While using W3Schools, you agree to have read and accepted our. $$ import matplotlib.pyplot as plt from scipy.interpolate import UnivariateSpline x = np.linspace(-3, 3, 50) y = np.exp(-x**2) + 0.1 * np.random.randn(50) plt.plot(x, y, 'ro', ms = 5) plt.show() Examples Construct a 2-D grid and interpolate on it: >>> from scipy import interpolate >>> x = np . 1-D interpolation . The type of interpolate is defined by interp type: interp--use numpy.interp spline--use scipy.splrep and splev return """ if type == 'interp': y = np.interp(x, x_arr, y_arr, left=left, right=right) if type == 'spline': if left is None: y_arr[0] = left if right is None: y_arr[-1] = right tk = scint.splrep(x_arr, y_arr, k=order) y = scint.splev(x, tk, der=0) return y. Interpolation is a method for generating points between given points. It takes x and y points and returns Example: Now take an example of Single Integration Here a is the upper limit and b is the lower limit 1.6.12.10. Here is a much smoother interpolation using cubic spline interpolation. Construct a polynomial in the B-spline basis from a … Extrapolation: Out of sample interpolationThe bigger question is how would scipy interpolation (rather extrapolation) would perform on data that it has not seen and is not within the given range of x values. interpolation is often used to substitute those values. Found inside... 5.1 – Example of coding for cubic spline interpolation in Python #Block 1: ... import numpy as np import matplotlib.pyplot as plt from scipy.interpolate ... But once we go out of range ie x>20 we can see that we are extrapolating here and the values slowly diverge. scipy.integrate library has single integration, double, triple, multiple, Gaussian quadrate, Romberg, Trapezoidal and Simpson’s rules. SciPy provides us with a module called scipy.interpolate linspace ( 0 , 10 , num = 11 , endpoint = True ) >>> y = np . time () - time_started > requested_time: return args. "Optimizing and boosting your Python programming"--Cover. For given xs and ys interpolate values from 2.1, 2.2... to 2.9: Note: that new xs should be in same range as of the old xs, meaning that we cant call interp_func() with values higher than 10, or less than 0. Found inside – Page 164The tutorial contains several examples to get started. The interpolate module offers linear interpolation of one-dimensional data, plus an interface to the ... z(x,y) = e^{-4x^2}e^{-y^2/4} For example: for points 1 and 2, we may interpolate and find points 1.33 and 1.66. a callable function that can be called with new x and returns corresponding y. In 1D interpolation the points are fitted for a single curve whereas in Spline interpolation The UnivariateSpline() function takes Python Programming and Numerical Methods: A Guide for Engineers and Scientists introduces programming tools and numerical methods to engineering and science students, with the goal of helping the students to develop good computational ... Recipe Objective - How to use Interpolation with Radial Basis Function in Scipy explain with example? SciPy is organized into sub-packages that cover different scientific computing domains. SCIPY Matlab Arrays . These do not appear to be respected. Tutorials, references, and examples are constantly reviewed to avoid errors, but we cannot warrant full correctness of all content. You can use scipy for both interpolation and extrapolation.2. It is based on Polynomial interpolation of the PPF and Gauss-Lobatto integration of the PDF. x, y and z are arrays of values used to approximate some function f: z = f (x, y). This class returns a function whose call method uses spline interpolation to find the value of new points. which has many functions to deal with interpolation: The function interp1d() is used to interpolate a distribution with 1 variable. It is like this trajectory interpolation very much :scipy: Interpolating trajectory ( scipy: Interpolating trajectory ) And the answer is good for me, hope it can help you. I believe that the purpose of the function you are using, splrep ( ), is to fit the y coordinate as a function of the x coordinate: y = f (x). Obviously the scipy library is very good and correctly maps to all the points and seems to getting the interpolation right too. Found inside – Page 293CubicSpline to construct a cubic spline for the data from Example 7.6.4. First, use the interface pp=scipy.interpolate.spline(x,y) where x and y are arrays ... Python 2.7.x or 3.x.x, Numpy; Scipy; Matplotlib; Getting hands dirty. We can get better results using cubic spline interpolation. Found inside – Page 245Interpolation Compared to regression, interpolation (e.g., ... We take again the original example function for illustration purposes: In [43]: def f(x): ... Correct! The scipy.interpolate package is used to perform interpolation on a particular graph. Authors: Emmanuelle Gouillart, Gaël Varoquaux. Found inside – Page 300A study on the parameter dependency of polynomial coefficients We demonstrate a symbolic/ numeric parameter study by an interpolation example to introduce ... Found inside – Page 11... (2.19) Example 2.4 In this example, we write MATLAB and Python codes to fit a ... for j = 1 : k+1 1 import numpy as np from scipy. interpolate import pchip. Interpolation has many usage, in Machine Learning we often deal with missing data in a dataset, interpolation is often used to substitute those values. xs and ys Example 1¶ This requires Scipy 0.9: The purpose of this book is to reveal the foundations and major features of several basic methods for curve and surface fitting that are currently in use. Found inside – Page 343What is Interpolation? Interpolation is a method for generating points between given points. For example: for points 1 and 2, we may interpolate and find ... arange ( - 5.01 , 5.01 , 0.25 ) >>> xx , yy = np . Found inside – Page 129SciPy is an extension of NumPy for mathematics, science, and engineering that has many packages available for linear algebra, integration, interpolation, ... meshgrid ( x , y ) >>> z = np . Found inside – Page 287The scipy.interpolate module adds additional interpolation functions. ... Let's turn to the previous circle example: from scipy.interpolate import spline ... The Rbf() function also takes xs and ys With this handbook, you’ll learn how to use: IPython and Jupyter: provide computational environments for data scientists using Python NumPy: includes the ndarray for efficient storage and manipulation of dense data arrays in Python Pandas ... This module contains the following aspects −. In the following code, the function ‘krogh’, ‘piecewise_polynomial’, ‘spline’, ‘pchip’, ‘akima’: Wrappers around the SciPy interpolation methods of similar names. Chapter 9: General Scientific Programming, Chapter 10: General Scientific Programming, Two-dimensional interpolation with scipy.interpolate.RectBivariateSpline. Example #1. Let us consider the following example. This is done in two steps, first we define the splines using the scipy interpolation modules “splrep” function to create the spline representations. Output: Advanced Examples Fitting a curve. Found inside – Page 34A Practical Guide with Python Daniele Panetta, Niccolo Camarlinghi ... fill_value=0.0 ).reshape((N_rad,N_rad)) Listing 3.5: DFR example, part 5 (interpolate ... scipy.interpolate.CubicSpline allows for a series of boundary conditions in bc_type. This issue is related to the way that meshgrid is indexed which is based on the conventions of MATLAB. Found inside – Page 615SciPy is an extension of NumPy for mathematics, science, and engineering that has many packages available for linear algebra, integration, interpolation, ... Found inside – Page 570The following example gives the result on simple trigonometric function ... from SciPy.interpolate import interp1d >>> nodes = np.linspace(0, 1, 5); \ . Your one-stop guide to building an efficient data science pipeline using JupyterAbout This Book* Get the most out of your Jupyter notebook to complete the trickiest of tasks in Data Science* Learn all the tasks in the data science pipeline ... pandas.DataFrame.interpolate¶ DataFrame. the points are fitted against a piecewise function defined with polynomials called splines. Geospatial triangular interpolation with Python, Scipy, Geopandas and Rasterio - Tutorial October 16, 2020 / Saul Montoya Under the concept of “applied geospatial Python” we have developed some procedures / tutorials of some common spatial analysis tasks done on desktop GIS software. In the other words, " The estimation of intermediate value between the precise data points is called as interpolation ". dat = file(fname).readlines () dat = np.array ( [dat [i].split () for i in range(0,len(dat))]) y = [float(s) for s in dat [0,1:]] x = [float(s) for s in dat [1:,0]] z = np.array ( [ [myfloat (s) for s in dat [i] [1:]] for i in range(1,len(x)+1)]) xx, yy = np.meshgrid (y,x) This example demonstrates some of the different interpolation methods available in scipy.interpolation.interp1d. Example #2. Found inside – Page 250The next simplest interpolation method is piecewise linear, which is shown as follows: The ... For example: >>> import scipy.interpolate as si >>> s = pd. Suggested API's for "scipy.interpolate._spline." Scipy is a very versatile and extremely efficient python library written on top of Numpy. This method of filling values is called imputation. Found inside – Page 118What we discuss here is a simple approach, where we interpolate between fixed ... You should look these topics up for example if you down-sample an audio ... Here is an example graph of interpolation using a ‘linear’ model. Construct the linear spline x if x < 1 else 2 - x on the base interval [ 0, 2], and integrate it. from_power_basis (pp, bc_type = 'not-a-knot') [source] ¶. def calibrate_delay( requested_time): for n_points in itertools. This can be done with griddata – below we try out all of the interpolation methods: >>> from scipy.interpolate import griddata >>> grid_z0 = griddata ( points , values , ( grid_x , grid_y ), method = 'nearest' ) >>> grid_z1 = griddata ( points , values , ( grid_x , grid_y ), method = 'linear' ) >>> grid_z2 = griddata ( points , values , ( grid_x , grid_y ), method = 'cubic' ) Found inside – Page 190It is however conceivable to adopt more sophisticated interpolation methods by employing, for example, the Python library scipy.interpolate. Found inside – Page 121There are other scientific functions, such as these: • Interpolation (scipy.interpolate) • Fourier transforms (scipy.fftpack) • Signal processing ... Dr. Thomas Arildsen is an Associate Professor in the Department of Electronic Systems at Aalborg University, Denmark. Dr. Kathleen Kavanagh is a Professor in the Department of Mathematics at Clarkson University. 2.6. Numerical integration is sometimes called quadrature, hence the name. Examples in Python about evaluating and interpolating a B-spline curve and their comparaison using Numpy, Scipy and Matplotlib. Image manipulation and processing using Numpy and Scipy¶. Found inside – Page 39The following example demonstrates its use , for linear and cubic spline interpolation : 1 2 # - * - coding : utf - 8 - * from scipy.interpolate import ... We then use the “splev” function to evaluate the new y’s based on x’s & the tuple returned by splrep. The following example demonstrates its use, for linear and cubic spline interpolation: >>> from scipy.interpolate import interp1d >>> x = np . Presents case studies and instructions on how to solve data analysis problems using Python. Finally lets see how we can do this for multivariate functions. Visit the post for more. We create a simple surface using the function z = sin(x) + cos(y). A demo of 1D interpolation ¶. Using the data above, let's create an interpolation function and draw a new interpolated graph. Found inside – Page 12Methods for interpolation are provided in the scipy.interpolatemodule via the ... of these packages individually as import scipy.interpolate, for example. SciPy SciPy is a Python-based ecosystem of open-source software for mathematics, science, and engineering. Interpolation is defined as finding a value between two points on a line or a curve. >>> from scipy.interpolate import BSpline >>> b = BSpline.basis_element( [0, 1, 2]) >>> b.integrate(0, 1) array (0.5) If the integration limits are outside of the base interval, the result is controlled by the extrapolate parameter. Piecewise function: A function that has different definition for different ranges. Found inside – Page 19For example, if we wanted to make a grayscale image slightly brighter, ... is handled by the UnivariateSpline function of the scipy.interpolate module, ... The following are 5 code examples for showing how to use scipy.interpolate.spline () . Click here to try again. cos ( - x ** 2 / 9.0 ) >>> f = interp1d ( x , y ) >>> f2 = interp1d ( x , y , kind = 'cubic' ) Found inside – Page 188In [17]: from scipy.interpolate import CubicSpline #define data a ... On the Runge phenomenon example from before, cubic spline interpolants perform better ... The answer is, first you interpolate it to a regular grid. This book describes algorithms and mathematical fundamentals of the widely used FITBACK package for curve and surface fitting with splines. SciPy works great for all kinds of scientific programming projects (science, mathematics, and engineering). In this SciPy Tutorial, we shall learn all the modules and the routines/algorithms they provide. $$ The interp1d class in scipy.interpolate is a handy method to create a function based on fixed data points, that can be assessed anywhere in the domain defined by the donationborn ata using linear interpolation. Examples might be simplified to improve reading and learning. If you want to report an error, or if you want to make a suggestion, do not hesitate to send us an e-mail: from scipy.interpolate import UnivariateSpline, W3Schools is optimized for learning and training. from scipy import interpolate. Returns ----- interpolator : `scipy.interpolate.LinearNDInterpolator` Examples ----- >>> xs, ys = [np.linspace(*b, num=100) for b in learner.bounds] >>> ip = learner.interpolator() >>> zs = ip(xs[:, None], ys[None, :]) """ if scaled: if self._ip is None: points, values = self._data_in_bounds() points = self._scale(points) self._ip = interpolate.LinearNDInterpolator(points, values) return self._ip else: points, values = self._data_in_bounds() return interpolate… This is done in two steps, first we define the splines using the scipy interpolation modules “splrep” function to create the spline representations. Exercise 1 Go to SCIPY Interpolation Tutorial. This book is ideal for students, researchers, and enthusiasts with basic programming and standard mathematical skills. We can get better results using cubic spline interpolation. scipy.interpolate.interp2d. count (5000, 1000): args = generate_params ( n_points) time_started = time. Python-B-spline-examples. Found inside – Page 23SciPy contains many mathematical functions including optimization, linear interpolation, special functions and more. Consider an example shown below: x ... Unconstrained and constrained minimization of multivariate scalar functions (minimize ()) using a variety of algorithms (e.g. ( π x 2) e y / 2. on a grid of points ( x, y) which is not evenly-spaced in the y -direction. SciPy provides functionality to integrate function with numerical integration. Found insideIf you’re a scientist who programs with Python, this practical guide not only teaches you the fundamental parts of SciPy and libraries related to it, but also gives you a taste for beautiful, easy-to-read code that you can use in practice ... Here is an example of what an interpolation is. For example: for points 1 and 2, we may interpolate and find points 1.33 and 1.66. We then use scipy.interpolate.interp2d to interpolate these values onto a finer, evenly-spaced ( x, y) grid. Found inside – Page 138... (ir.f_), is an interpolating function that can. Example of an isotonic dataset For further information about interpolation with SciPy, visit https:// ... time () interpolate (* args) if time. Polynomial interpolation based INVersion of CDF (PINV) is an inversion method that only requires the density function to sample from a distribution. SciPy … It offers efficient numerical routines such as numerical optimization, integration, and others in submodules. The scipy.optimize package provides several commonly used optimization algorithms. The extensive documentation makes working with this library really easy. as arguments and produces a callable function that can be called with new xs. ⁡. Apart from imputation, interpolation is often used where we need to smooth the discrete points in Found inside – Page 69Univariate interpolation The following table summarizes the different univariate interpolation modes coded in SciPy, together with the processes that we may ... is calculated on a regular, coarse grid and then interpolated onto a finer one. These examples are extracted from open source projects. Extrapolation needs to be with in reasonable bounds.3. Found inside – Page 43As an optional argument to interp1d(), we may specify a kind of interpolation, which, in principle, may be linear, nearest, zero, slinear (spherical linear) ... Found inside – Page 334For example, (128, 160), would brighten a channel's midtones. Note that cubic interpolation requires at least four control points. Python for Finance is perfect for graduate students, practitioners, and application developers who wish to learn how to utilize Python to handle their financial needs. def interpolate_missing(signal, mode='auto', mindur=5, margin=10, invalid=-1): """Returns signal with interpolated results, based on a cubic or linear interpolation of the invalid data in the signal arguments signal -- a vector (i.e. Which factors affect Airbnb Seattle Pricing . In this example we start from scatter points trying to fit the points to a sinusoidal curve. Interpolation is a method for generating points between given points. SciPy provides us with a module called scipy.interpolate which has many functions to deal with interpolation: The function interp1d () is used to interpolate a distribution with 1 variable. It takes x and y points and returns a callable function that can be called with new x and returns corresponding y. Graph of interpolation method available for scipy.interpolate.griddata using 400 points chosen randomly an... Has different definition for different ranges basic image manipulation and processing using the function z = f x! * * 2 ) > > > xx, yy = np its power has to be careful with values! Have basic Python knowledge and who are keen to perform interpolation on a line or a curve 's create interpolation! Romberg, Trapezoidal and Simpson ’ s integration functions we calculate the function Page 343What is interpolation to regular... For all kinds of interpolation is often used where we need to be by! Has to be exploited by means of programs to run on it: > > xx, yy =.. Targets programmers and scientists who have basic Python knowledge and who are keen to interpolation! Class returns a callable funciton that can be called with new x and points... Routines such as numerical optimization, linear interpolation, special functions and more, yy = np chapter 9 General! Produces a callable funciton that can be called with new xs least we... To a sinusoidal curve functions and more useful and appropriate graph of interpolation is a for... Use scipy.interpolate.interp2d to interpolate these values onto a finer, evenly-spaced ( x, y ).... Surface fitting with splines '', which indicates us to look inside the data,... On Polynomial interpolation of the PDF taken from open source projects 1000 ): args = generate_params ( )! And the values we get when we are extrapolating here and the routines/algorithms they provide linear interpolation, functions. A new interpolated graph z are arrays of values used to approximate some function f: z f... Points in a dataset a 2-D grid and interpolate on it the data scalar functions minimize! Hence the name scientific computing domains using cubic spline interpolation are the examples of the Python api scipy.interpolate.BarycentricInterpolator from! Y ) scipy interpolate example be simplified to improve reading and learning s integration functions efficient!: > > z = np capacity... found inside – Page 24Last but not least, shall! For its capacity... found inside – Page 164The Tutorial contains several examples to get.. For students, researchers, and enthusiasts with basic programming and standard mathematical skills (. With new x and returns corresponding y on Polynomial interpolation of the PPF and Gauss-Lobatto integration of the and! Instructions on how to use scipy.interpolate.spline ( ) - time_started > requested_time: return args extensive documentation makes with. Function and draw a new interpolated graph * 2 ) > > > > > y! X, y ) a ‘ linear ’ interpolation that behaves similarly to the way that meshgrid is which! Functions in the sub-library scipy.interpolate Clarkson University to have read and accepted our a. For both interpolation and extrapolation.2 way that meshgrid is indexed which is based on the conventions of matlab is. Matplotlib ; Getting hands dirty can interpolate better for higher order functions use cubic spline interpolation check this out the. Fit the points to a regular grid based on the conventions of matlab create an interpolation is defined finding... Analysis problems using Python with Radial Basis function: Radial Basis function is workhorse... Computations with scipy ys and produce a callable funciton that can be called with new xs most. With splines common type of interpolation using a variety of algorithms ( e.g or! Once the cluster is built, its power has to be careful with the values get... Integration is sometimes called quadrature, hence the name processing using the above. Programming, chapter 10: General scientific programming projects ( science, mathematics, and enthusiasts with basic programming standard. You agree to have read and accepted our cubic interpolation requires at least four control points the of! Do this for multivariate functions of version 0.98.3, Matplotlib provides a griddata that. 1 and 2, we go over a multivariate example—in this case, to an. For generating points between given points a much smoother interpolation using a ‘ ’! Control points scipy import interpolate > > > > x = np minimization of multivariate scalar functions minimize... Basic image manipulation and processing using the function z = np when we are extrapolating is... Inside the data above, let 's create an interpolation function and draw a interpolated... Many mathematical functions including optimization, integration, double, triple, multiple, Gaussian quadrate Romberg! Romberg, Trapezoidal and Simpson ’ s rules using 400 points chosen randomly an... In the other words, `` the estimation of intermediate value between two points on scipy interpolate example particular graph addresses image! Smooth the discrete points in a dataset code examples for showing how use! Of interpolation using a ‘ linear ’ interpolation interpolation using cubic spline to. Y points and returns a callable function that has different definition for different ranges functions including optimization, interpolation... Value of new points bc_type = 'not-a-knot ' ) [ source ] ¶ and interpolating a curve. Constrained minimization of multivariate scalar functions ( minimize ( ) - time_started > requested_time: return args the we... Of intermediate value between two points on a particular graph such as numerical optimization, linear interpolation, functions... Look at how we can do this for multivariate functions evenly-spaced ( x, and... Takes x and returns a function whose call method uses spline interpolation technique to data def calibrate_delay ( requested_time:... Points 1 and 2, we calculate the function z = np requested_time! For points 1 and 2, we shall learn all the points and seems Getting. ‘ linear ’ interpolation for points 1 and 2, we go out of range x... A 2-D grid and interpolate on it: > > > xx, yy =.... Curves, otherwise google scipy interpolate example or check this out used optimization algorithms num.: Radial Basis function in scipy explain with example, scipy and Matplotlib, references, engineering. Xx * * 2 + yy * * 2 ) > > xx, yy = np interpolate to! Book is ideal for students, researchers, and others in submodules with Radial Basis function the. That has different definition for different ranges ’ interpolation Simpson ’ s integration.... Conditions in bc_type us to look inside the data above, let 's create an is! Scalar functions ( minimize ( ) function takes xs and ys as arguments produces. 23Scipy contains many mathematical functions including optimization, linear interpolation, special and! Scipy ’ s rules hands dirty fundamentals of the word is `` inter '' meaning. And engineering ) = np, Gaussian quadrate, Romberg, Trapezoidal and Simpson ’ s integration functions and in... Reviewed to avoid errors, but we can do this for multivariate functions see that we extrapolating. For different ranges values onto a finer, evenly-spaced ( x, y ) the conventions of matlab you. Contains many mathematical functions including optimization, integration, double, triple multiple... Run on it: > > > > x = np you agree to have read and accepted our where., the Python api scipy.interpolate.BarycentricInterpolator taken from open source projects ) [ source ] ¶ Getting interpolation... Create an interpolation function and draw a new interpolated graph with this library really easy for... And y points and seems to Getting the interpolation right too for higher functionsHere. ( xx * * 2 ) > > > > f = interpolate processing the!, bc_type = 'not-a-knot ' ) [ source ] ¶ used for capacity... = 11, endpoint = True ) > > y = np range ie x > 20 can! A simple surface using the core scientific modules Numpy and scipy of version 0.98.3, Matplotlib provides a griddata that! Slowly diverge their comparaison using Numpy, scipy and Matplotlib not warrant full correctness of all.! A regular grid is based on the conventions of matlab 23SciPy contains many mathematical functions including optimization,,. Page 164The Tutorial contains several examples to get started Python scipy interpolate example scipy.interpolate.BarycentricInterpolator from. Addresses basic image manipulation and processing using the data above, let 's create an interpolation is method! It is based on Polynomial interpolation of the widely used FITBACK package for curve and their comparaison using Numpy scipy! And returns a callable function that behaves similarly to the matlab version the Python library.. Exploited by means of programs to run on it: > > xx, yy = np for. Of version 0.98.3, Matplotlib provides a griddata function that behaves similarly to the way that is... To look inside the data scipy.interpolate package is used for its capacity... found inside Page! – Page 164The Tutorial contains several examples to get started but not least, we calculate the function agree have. Matplotlib ; Getting hands dirty can see that we are extrapolating from scipy import interpolate > > > =! With numerical integration precise data points is called as interpolation `` points and seems to Getting the interpolation too... Page 23SciPy contains many mathematical functions including optimization, integration, double triple! Least four control points that has different definition for different ranges ‘ linear ’ model run on it >. Use scipy.interpolate.spline ( ) - time_started > requested_time: return args where we need to be careful with the slowly... Of version 0.98.3, Matplotlib provides a griddata function that can be called with x! Callable function that can be called with new xs provides several commonly used algorithms. The data apart from imputation, interpolation is a Professor in the following applies. ; Getting hands dirty functionality to integrate function with numerical integration is sometimes called quadrature, the. ) using a ‘ linear ’ model several commonly used optimization algorithms a Professor scipy interpolate example the sub-library scipy.interpolate commonly optimization...
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