# Scipy cubic spline plot

A 'spline' is quite a generic term, essentially referring to applications of data interpolation or smoothing. It's a technique that can help you increase the frequency of your data, or to fill in missing time-series values.

In our example below, a dog is sniffing out a treat in the distance. At ten random points over the course of 60 seconds, the dog's collar is emits a statistic showing how far away the dog is from the treat. From this data, we want to estimate the path the dog took to get to the treat.

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We can do this in Python! Firstly, let's create our data, the times that the data was emitted and the subsequent distance statistics. Let's plot what these points look like:. Now, onto the spline creation.

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Below, we're creating the array of points that we want the new spline to pass through. Here, it will be points in order to fill all connections. Next, we apply the spline, giving us values for time and for distance. Let's now plot the new spline over our original data points!

We now have an estimation as to the path the dog took, and therefore also the distance the dog was away from the treat at any point in the 60 seconds. I hope you're able to make use of this technique! Full Code. Creating and Plotting Cubic Splines in Python. Recent Posts See All. Finding Prime numbers using Python.Documentation Help Center. The values of s are determined by cubic spline interpolation of x and y. Use spline to interpolate a sine curve over unevenly-spaced sample points. Use clamped or complete spline interpolation when endpoint slopes are known. To do this, you can specify the values vector y with two extra elements, one at the beginning and one at the end, to define the endpoint slopes.

Create a vector of data y and another vector with the x -coordinates of the data. Interpolate the data using spline and plot the results. Specify the second input with two extra values [0 y 0] to signify that the endpoint slopes are both zero. Use ppval to evaluate the spline fit over points in the interpolation interval.

Create two vectors to represent the census years from to t and the corresponding United States population in millions of people p.

Generate the plot of a circle, with the five data points y :,2The matrix y contains two more columns than does x. Therefore, spline uses y :,1 and y :,end as the endslopes. The circle starts and ends at the point 1,0so that point is plotted twice. Generate sine and cosine curves for a few values between 0 and 1.

Use spline interpolation to sample the functions over a finer mesh. Compare the interpolation results produced by splinepchipand makima for two different data sets. These functions all perform different forms of piecewise cubic Hermite interpolation. Each function differs in how it computes the slopes of the interpolant, leading to different behaviors when the underlying data has flat areas or undulations. Compare the interpolation results on sample data that connects flat regions.

Create vectors of x values, function values at those points yand query points xq.

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Compute interpolations at the query points using splinepchipand makima. Plot the interpolated function values at the query points for comparison. In this case, pchip and makima have similar behavior in that they avoid overshoots and can accurately connect the flat regions. When the underlying function is oscillatory, spline and makima capture the movement between points better than pchipwhich is aggressively flattened near local extrema. The vector x specifies the points at which the data y is given.

The elements of x must be unique. Data Types: single double.

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Function values at x -coordinates, specified as a numeric vector, matrix, or array. If y is a matrix or array, then the values in the last dimension, y :, In that case, the last dimension of y must be the same length as x or have exactly two more elements. If x and y are vectors of the same size, then the not-a-knot end conditions are used. If x or y is a scalar, then it is expanded to have the same length as the other and the not-a-knot end conditions are used. If y is a vector that contains two more values than x has entries, then spline uses the first and last values in y as the endslopes for the cubic spline.

For example, if y is a vector, then:. Query points, specified as a scalar, vector, matrix, or array. The points specified in xq are the x -coordinates for the interpolated function values yq computed by spline.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. I'm wondering how to do it in matplotlib in a simple way. I already had a look at similar question, e. Generating smooth line graph using matplotlibbut direct use of that method produces figure like this. This is basically just reworked from the last example in the section here.

This is pretty much following the circle example here. Viewed 7k times. Generating smooth line graph using matplotlibbut direct use of that method produces figure like this which is of course not what I want.

Kevin Powell Kevin Powell 5 5 silver badges 16 16 bronze badges. See docs. Active Oldest Votes. You need to take a parametric approach, like this: import numpy as np import matplotlib. Thanks a lot! This is exactly what I need. You're a bit faster than me at getting it posted.

Introduction to Splines

KevinPowell Cool. I learned how to "unzip" a list of tuples in answering your question.

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Featured on Meta. Community and Moderator guidelines for escalating issues via new response….Interpolation scipy. Multivariate data interpolation griddata. Spline interpolation in 1-d: Procedural interpolate. Spline interpolation in 1-d: Object-oriented UnivariateSpline. Two-dimensional spline representation: Procedural bisplrep. Two-dimensional spline representation: Object-oriented BivariateSpline. There are several general interpolation facilities available in SciPy, for data in 1, 2, and higher dimensions:.

A class representing an interpolant interp1d in 1-D, offering several interpolation methods. Object-oriented interface for the underlying routines is also available. The interp1d class in scipy. An instance of this class is created by passing the 1-d vectors comprising the data. Behavior at the boundary can be specified at instantiation time.

The following example demonstrates its use, for linear and cubic spline interpolation:. Another set of interpolations in interp1d is nearestpreviousand nextwhere they return the nearest, previous, or next point along the x-axis.

Nearest and next can be thought of as a special case of a causal interpolating filter. The following example demonstrates their use, using the same data as in the previous example:. Suppose you have multidimensional data, for instance for an underlying function f x, y you only know the values at points x[i], y[i] that do not form a regular grid. This can be done with griddata — below we try out all of the interpolation methods:.

One can see that the exact result is reproduced by all of the methods to some degree, but for this smooth function the piecewise cubic interpolant gives the best results:. Spline interpolation requires two essential steps: 1 a spline representation of the curve is computed, and 2 the spline is evaluated at the desired points. In order to find the spline representation, there are two different ways to represent a curve and obtain smoothing spline coefficients: directly and parametrically.

The direct method finds the spline representation of a curve in a two- dimensional plane using the function splrep. The default spline order is cubic, but this can be changed with the input keyword, k. For this function only 1 input argument is required.Interpolate data with a piecewise cubic polynomial which is twice continuously differentiable [R58].

The result is represented as a PPoly instance with breakpoints matching the given data. Values must be real, finite and in strictly increasing order. Array containing values of the dependent variable.

## SciPy - Interpolate

It can have arbitrary number of dimensions, but the length along axis see below must match the length of x. Values must be finite. Axis along which y is assumed to be varying. Meaning that for x[i] the corresponding values are np. Default is 0. Boundary condition type. Two additional equations, given by the boundary conditions, are required to determine all coefficients of polynomials on each segment [R59].

Available conditions are:. If bool, determines whether to extrapolate to out-of-bounds points based on first and last intervals, or to return NaNs. In this example the cubic spline is used to interpolate a sampled sinusoid. You can see that the spline continuity property holds for the first and second derivatives and violates only for the third derivative.

Source code. In the second example, the unit circle is interpolated with a spline. A periodic boundary condition is used. Note that a circle cannot be exactly represented by a cubic spline. To increase precision, more breakpoints would be required. A cubic spline can represent this function exactly. To achieve that we need to specify values and first derivatives at endpoints of the interval. It is a good default when there is no information on boundary conditions.

Previous topic scipy. Last updated on Jun 21, Created using Sphinx 1. The same x which was passed to the constructor.Interpolation scipy. Multivariate data interpolation griddata. Spline interpolation in 1-D: Procedural interpolate. Spline interpolation in 1-d: Object-oriented UnivariateSpline. There are several general interpolation facilities available in SciPy, for data in 1, 2, and higher dimensions:.

A class representing an interpolant interp1d in 1-D, offering several interpolation methods. Object-oriented interface for the underlying routines is also available. The interp1d class in scipy. An instance of this class is created by passing the 1-D vectors comprising the data. Behavior at the boundary can be specified at instantiation time. The following example demonstrates its use, for linear and cubic spline interpolation:. Another set of interpolations in interp1d is nearestpreviousand nextwhere they return the nearest, previous, or next point along the x-axis.

Nearest and next can be thought of as a special case of a causal interpolating filter. The following example demonstrates their use, using the same data as in the previous example:. Suppose you have multidimensional data, for instance, for an underlying function f x, y you only know the values at points x[i], y[i] that do not form a regular grid. This can be done with griddata — below, we try out all of the interpolation methods:.

One can see that the exact result is reproduced by all of the methods to some degree, but for this smooth function the piecewise cubic interpolant gives the best results:. Spline interpolation requires two essential steps: 1 a spline representation of the curve is computed, and 2 the spline is evaluated at the desired points.

In order to find the spline representation, there are two different ways to represent a curve and obtain smoothing spline coefficients: directly and parametrically. The direct method finds the spline representation of a curve in a 2-D plane using the function splrep. The default spline order is cubic, but this can be changed with the input keyword, k.

For curves in N-D space the function splprep allows defining the curve parametrically. For this function only 1 input argument is required. The length of each array is the number of curve points, and each array provides one component of the N-D data point. The keyword argument, sis used to specify the amount of smoothing to perform during the spline fit.

Once the spline representation of the data has been determined, functions are available for evaluating the spline splev and its derivatives splevspalde at any point and the integral of the spline between any two points splint. These functions are demonstrated in the example that follows.

The spline-fitting capabilities described above are also available via an objected-oriented interface.Must be increasing; must be strictly increasing if s is 0. Positive smoothing factor used to choose the number of knots. Number of knots will be increased until the smoothing condition is satisfied:. If 0, spline will interpolate through all data points. Whether to check that the input arrays contain only finite numbers. Disabling may give a performance gain, but may result in problems crashes, non-termination or non-sensical results if the inputs do contain infinities or NaNs.

Default is False. The number of data points must be larger than the spline degree k. NaN handling : If the input arrays contain nan values, the result is not useful, since the underlying spline fitting routines cannot deal with nan. A workaround is to use zero weights for not-a-number data points:. Notice the need to replace a nan by a numerical value precise value does not matter as long as the corresponding weight is zero. Continue spline computation with the given smoothing factor s and with the knots found at the last call.

Must be positive. If None defaultweights are all equal. Previous topic scipy. Last updated on Dec 19, Created using Sphinx 2. Author: Kisida