/usr/include/openturns/swig/GaussLegendre_doc.i is in libopenturns-dev 1.9-5.
This file is owned by root:root, with mode 0o644.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 | %feature("docstring") OT::GaussLegendre
"Tensorized integration algorithm of Gauss-Legendre.
Available constructors:
GaussLegendre(*dimension=1*)
GaussLegendre(*discretization*)
Parameters
----------
dimension : int, :math:`dimension>0`
The dimension of the functions to integrate. The default discretization is *GaussLegendre-DefaultMarginalIntegrationPointsNumber* in each dimension, see :class:`~openturns.ResourceMap`.
discretization : sequence of int
The number of nodes in each dimension. The sequence must be non-empty and must contain only positive values.
Notes
-----
The Gauss-Legendre algorithm enables to approximate the definite integral:
.. math::
\\\\int_{\\\\vect{a}}^\\\\vect{b} f(\\\\vect{t})\\\\di{\\\\vect{t}}
with :math:`f: \\\\Rset^d \\\\mapsto \\\\Rset^p`, :math:`\\\\vect{a}, \\\\vect{b}\\\\in\\\\Rset^d` using a fixed tensorized Gauss-Legendre approximation:
.. math::
\\\\int_{\\\\vect{a}}^\\\\vect{b} f(\\\\vect{t})\\\\di{\\\\vect{t}} = \\\\sum_{\\\\vect{n}\\\\in \\\\cN}\\\\left(\\\\prod_{i=1}^d w^{N_i}_{n_i}\\\\right)f(\\\\xi^{N_1}_{n_1},\\\\dots,\\\\xi^{N_d}_{n_d})
where :math:`\\\\xi^{N_i}_{n_i}` is the :math:`n_i`th node of the :math:`N_i`-points Gauss-Legendre 1D integration rule and :math:`w^{N_i}_{n_i}` the associated weight.
Examples
--------
Create a Gauss-Legendre algorithm:
>>> import openturns as ot
>>> algo = ot.GaussLegendre(2)
>>> algo = ot.GaussLegendre([2, 4, 5])"
// ---------------------------------------------------------------------
%feature("docstring") OT::GaussLegendre::integrate
"Evaluation of the integral of :math:`f` on an interval.
Available usages:
integrate(*f, interval*)
integrate(*f, interval, xi*)
Parameters
----------
f : :class:`~openturns.Function`, :math:`f: \\\\Rset^d \\\\mapsto \\\\Rset^p`
The integrand function.
interval : :class:`~openturns.Interval`, :math:`interval \\\\in \\\\Rset^d`
The integration domain.
xi : :class:`~openturns.Sample`
The integration nodes.
Returns
-------
value : :class:`~openturns.Point`
Approximation of the integral.
Examples
--------
>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x'], ['sin(x)'])
>>> a = -2.5
>>> b = 4.5
>>> algoGL = ot.GaussLegendre([10])
>>> value = algoGL.integrate(f, ot.Interval(a, b))[0]
>>> print(value)
-0.590...
"
// ---------------------------------------------------------------------
%feature("docstring") OT::GaussLegendre::getDiscretization
"Accessor to the discretization of the tensorized rule.
Returns
-------
discretization : :class:`~openturns.Indices`
The number of integration point in each dimension."
// ---------------------------------------------------------------------
%feature("docstring") OT::GaussLegendre::getNodes
"Accessor to the integration nodes.
Returns
-------
nodes : :class:`~openturns.Sample`
The tensorized Gauss-Legendre integration nodes on :math:`[0,1]^d` where :math:`d>0` is the dimension of the integration algorithm."
// ---------------------------------------------------------------------
%feature("docstring") OT::GaussLegendre::getWeights
"Accessor to the integration weights.
Returns
-------
weights : :class:`~openturns.Point`
The tensorized Gauss-Legendre integration weights on :math:`[0,1]^d` where :math:`d>0` is the dimension of the integration algorithm."
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