I Complete the Python function MySpline that reads in a set of x and y values (each as arrays or lists), and outputs a piecewise-cubic function with natural boundary conditions. The function prototype is cs = MySpline (x, y) The returned function can be called using cs (2.4) or cs ([2.4, 3.7]), for example. You will have to find the parameter values for the as, bs, and cs so that the cubic spline can be evaluated using Pi(x)= a₁_1 (₁+1-x)³ 6h + bx (x₁+1-x)+ci (x-x₁), 6h where hi=i+1-2, and i=1,2,...,n-1. Note that all Python indexing starts at 0, so all the indices can be decremented by 1. However, some care is needed to handle ao,...,an-1. See the documentation for MySpline for some guidance on this issue. + ai The function MySpline is already set up to return a cubic spline function. But it's not a very interesting one, and it does not pass through the points (x, y). The notebook has a small sample set of points to interpolate. Feel free to choose your own set of points. Create a figure that plots the interpolation points overtop of the smooth cubic spline.

I Complete the Python function MySpline that reads in a set of x and y values (each as arrays or lists), and outputs a piecewise-cubic function with natural boundary conditions. The function prototype is cs = MySpline (x, y) The returned function can be called using cs (2.4) or cs ([2.4, 3.7]), for example. You will have to find the parameter values for the as, bs, and cs so that the cubic spline can be evaluated using Pi(x)= a₁_1 (₁+1-x)³ 6h + bx (x₁+1-x)+ci (x-x₁), 6h where hi=i+1-2, and i=1,2,...,n-1. Note that all Python indexing starts at 0, so all the indices can be decremented by 1. However, some care is needed to handle ao,...,an-1. See the documentation for MySpline for some guidance on this issue. + ai The function MySpline is already set up to return a cubic spline function. But it's not a very interesting one, and it does not pass through the points (x, y). The notebook has a small sample set of points to interpolate. Feel free to choose your own set of points. Create a figure that plots the interpolation points overtop of the smooth cubic spline.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

1. I
Complete the Python function MySpline that reads in a set of x and y values (each
as arrays or lists), and outputs a piecewise-cubic function with natural boundary conditions. The
function prototype is
cs MySpline (x, y)
The returned function can be called using cs (2.4) or cs ([2.4, 3.7]), for example. You will
have to find the parameter values for the as, bs, and cs so that the cubic spline can be evaluated
using
Pi(x)= ai-11
+ ai
+ bk (x₁+1-x)+ ci(x − x₁),
6h₁
where hi=i+1; and i = 1,2,..., n - 1. Note that all Python indexing starts at 0, so all the
indices can be decremented by 1. However, some care is needed to handle ao,..., an-1. See the
documentation for MySpline for some guidance on this issue.
(x+1-x)³
6h₁
The function MySpline is already set up to return a cubic spline function. But it's not a very
interesting one, and it does not pass through the points (x, y).
The notebook has a small sample set of points to interpolate. Feel free to choose your own set of
points. Create a figure that plots the interpolation points overtop of the smooth cubic spline.

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