def get_qp(self, geometry):
"""
Get quadrature point coordinates and corresponding weights for given
geometry. For built-in quadratures, the integration order is given by
`self.order`.
Parameters
----------
geometry : str
The geometry key describing the integration domain,
see the keys of `sfepy.discrete.quadratures.quadrature_tables`.
Returns
-------
coors : array
The coordinates of quadrature points.
weights: array
The quadrature weights.
"""
if geometry in self.qps:
qp = self.qps[geometry]
else:
if self.mode == 'builtin':
qp = QuadraturePoints.from_table(geometry, self.order)
else:
qp = QuadraturePoints(None,
coors=self.coors, weights=self.weights)
self.qps[geometry] = qp
return qp.coors, qp.weights
def integrate(self, function, order=1, geometry='1_2'):
"""
Integrate numerically a given scalar function.
Parameters
----------
function : callable(coors)
The function of space coordinates to integrate.
order : int, optional
The integration order. For tensor product geometries, this is the
1D (line) order.
geometry : str
The geometry key describing the integration domain. Default
is `'1_2'`, i.e. a line integral in [0, 1]. For other values
see the keys of `sfepy.discrete.quadratures.quadrature_tables`.
Returns
-------
val : float
The value of the integral.
"""
qp = QuadraturePoints.from_table(geometry, order)
fvals = function(qp.coors)
val = nm.sum(fvals * qp.weights)
return val
