author | Shantanu <shantanu@fossee.in> |
Wed, 18 Nov 2009 18:37:15 +0530 | |
changeset 313 | f5bcb974a665 |
parent 284 | 3c191accbb32 |
child 340 | 347ff2714deb |
permissions | -rw-r--r-- |
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\documentclass[12pt]{article} |
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\title{Matrices and Solution of Equations} |
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\author{FOSSEE} |
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\begin{document} |
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\date{} |
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\vspace{-1in} |
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\begin{center} |
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\LARGE{Interpolation, Differentiation and Integration}\\ |
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\large{FOSSEE} |
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\end{center} |
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\section{} |
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Loading a data file |
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\begin{verbatim} |
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In [2]: x, y = loadtxt('points.txt', unpack = True) |
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#load data file directly into Arrays. |
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\end{verbatim} |
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\section{} |
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Interploate |
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\begin{verbatim} |
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In []: from scipy.interpolate import splrep |
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In []: tck = splrep(x,y) #get spline curve representation for x,y. |
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In []: from scipy.interpolate import splev |
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#To evaluate spline and it's derivatives. |
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In []: Xnew = arange(0.01,3,0.02) |
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#missing set of points |
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In []: Ynew = splev(Xnew, tck) |
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#Value of function at Xnew |
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In []: plot(Xnew, Ynew) |
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\end{verbatim} |
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|
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\section{Differentiation} |
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Taylor series - finite difference approximations |
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$f(x+h)=f(x)+hf^{'}(x)$ Forward |
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\begin{verbatim} |
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In []: x = linspace(0, 2*pi, 100) |
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In []: y = sin(x) |
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In []: deltax = x[1] - x[0] |
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In []: fD = (y[1:] - y[:-1]) / deltax |
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#fD is the required forward difference |
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\end{verbatim} |
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|
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\section{Quadrature} |
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$\int_0^1(sin(x) + x^2)$ |
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In []: def f(x): |
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return sin(x)+x**2 |
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In []: from scipy.integrate import quad |
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In []: quad(f, 0, 1) |
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\end{document} |
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