Arbitrary-precision interval arithmetic (iv) and integrals

Taras Boychuk

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Feb 3, 2020, 5:55:55 AM2/3/20

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Is it possible to calculate integrals using Arbitrary-precision interval arithmetic?

This code doesn't work:

from mpmath import quad, iv

L1 = iv.mpf('.1')

L2 = iv.mpf('2')

f = lambda x: 1 / 2

a = quad(f, [L1, L2])

print(a)

What is a correct way?

Kris Kuhlman

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Feb 3, 2020, 9:54:41 AM2/3/20

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I don't think this works as expected in mpmath. (http://mpmath.org/doc/current/contexts.html#arbitrary-precision-interval-arithmetic-iv)

Note: The support for interval arithmetic in mpmath is still experimental, and many functions do not yet properly support intervals. Please use this feature with caution.

The c library Arb does support this, and there is a python wrapper for the library.

http://fredrikj.net/blog/2017/11/new-rigorous-numerical-integration-in-arb/

Kris

Taras Boychuk

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Feb 3, 2020, 12:41:37 PM2/3/20

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Maybe. But if you replace L1 = iv.mpf('.1') with L1 = iv.mpf('1') if works. Even if replace it with L1 = iv.mpf(1/9) it works. So integration is implemented.

понеділок, 3 лютого 2020 р. 12:55:55 UTC+2 користувач Taras Boychuk написав:

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