Hi, when I try this code on Sage 8.0:
u = var('u'); D = RealDistribution('gaussian',1); f(u) = D.distribution_function(u)
I get the following error message:
TypeError: unable to simplify to float approximation
What I want is to get the numerical approximation of integral_numerical(f(u), u, a, b), for some fixed values a and b.
Thanks.
No need to define a symbolic variable like u in your example.
The following should be what you want.
sage: D = RealDistribution('gaussian', 1)
sage: f = D.distribution_function
sage: def prob(a, b):
....: return integral_numerical(f, (a, b))
....:
sage: prob(1.4, 1.5)
(0.013949457964912993, 1.5487009413687183e-16)
where the output is an estimation of the integral and of the error term in computing it numerically.
Thanks! Now I want to pass another function into the argument of f, i.e., I want to obtain a numerical approximation of $\int_{a}^{b}f(g(u))\mathrm{d}u$ for some function $g$. How can I do this?
You could do the following.
sage: D = RealDistribution('gaussian', 1)
sage: f = D.distribution_function
sage: def prob(a, b):
....: return integral_numerical(f, (a, b))
....:
sage: def probg(g, a, b):
....: return integral_numerical(lambda x: f(g(x)), (a, b))
....:
sage: g = lambda x: x^2
sage: a, b = 0.7, 0.8
sage: probg(g, a, b)
(0.03401903789457926, 3.7768719146157604e-16)
Asked: 2017-11-21 16:13:55 +0100
Seen: 630 times
Last updated: Nov 21 '17
Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.
Tip: don't tick the "Community wiki" checkbox when posting questions. If it is ticked, upvotes to the question don't earn you karma. You need karma to be able to post links, to upvote questions and answers, etc.