#8321: numerical integration with arbitrary precision
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Reporter: burcin | Owner: burcin
Type: defect | Status: new
Priority: major | Milestone: sage-4.5.3
Component: symbolics | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by maldun):
I think I have the solution for this trac with mpmath:
{{
def _evalf_(self, f, x, a, b, parent = None):
"""
Returns numerical approximation of the integral
EXAMPLES::
sage: from sage.symbolic.integration.integral import
definite_integral
sage: h = definite_integral(sin(x)/x^2, x, 1, 2); h
integrate(sin(x)/x^2, x, 1, 2)
sage: h.n() # indirect doctest
0.4723991772689525...
TESTS:
Check if #3863 is fixed::
sage: integrate(x^2.7 * e^(-2.4*x), x, 0, 3).n()
0.154572952320790
#Check if #8321 is fixed:
sage: d = definite_integral(sin(x)/x^2, x, 1, 2)
sage: d.n(77)
0.4723991772689525199904
"""
#from sage.gsl.integration import numerical_integral
# The gsl routine returns a tuple, which also contains the error.
# We only return the result.
#return numerical_integral(f, a, b)[0]
#Lets try mpmath instead:
import sage.libs.mpmath.all as mpmath
try:
precision = parent.prec()
mpmath.mp.prec = precision
except AttributeError:
precision = mpmath.mp.prec
mp_f = lambda z: \
f(x = mpmath.mpmath_to_sage(z,precision))
return mpmath.call(mpmath.quad,mp_f,[a,b])
}}
The tests just run fine:
{{
sage: sage: sage: from sage.symbolic.integration.integral import
definite_integral
sage: sage: h = definite_integral(sin(x)/x^2, x, 1, 2); h
integrate(sin(x)/x^2, x, 1, 2)
sage: h.n()
0.472399177268953
sage: h.n(77)
0.4723991772689525199904
sage: h.n(100)
0.47239917726895251999041133798
}}
greez maldun
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8321#comment:4>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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