eradiate.quad
Utility components for quadrature rules.
-
class eradiate.quad.Quad(type, nodes, weights)[source]
A data class storing information about a quadrature rule. Nodes and weights
are defined in the [-1, 1] interval. The reference interval can be changed
using the interval
argument of the eval_nodes()
and
integrate()
functions.
- Parameters:
type (QuadType
) – Quadrature type. If a string is passed, it is converted to a QuadType
.
nodes (ndarray
) – Quadrature rule nodes.
weights (ndarray
) – Quadrature rule weights.
- Fields:
type (QuadType
) – Quadrature type.
nodes (ndarray
) – Quadrature rule nodes.
weights (ndarray
) – Quadrature rule weights.
-
eval_nodes(interval=None)[source]
Compute nodes scaled to a specific interval.
- Parameters:
interval (tuple
of float
, optional) – Interval for which nodes are to be scaled as a 2-tuple. If None
,
the default [-1, 1] is used.
- Returns:
ndarray
– Scaled node values.
-
classmethod gauss_legendre(n)[source]
Initialize a Quad
instance with Gauss-Legendre nodes and
weights.
- Parameters:
n (int
) – Number of quadrature points.
- Returns:
Quad
– Gauss-Legendre quadrature definition.
-
classmethod gauss_lobatto(n)[source]
Initialize a Quad
instance with Gauss-Lobatto nodes and
weights.
- Parameters:
n (int
) – Number of quadrature points.
- Returns:
Quad
– Gauss-Lobatto quadrature definition.
-
integrate(values, interval)[source]
Evaluate quadrature rule, accounting for interval scaling.
- Parameters:
values (ndarray
) – Function values at quadrature nodes.
interval (tuple
of float
, optional) – Interval on which the integral is being computed as a 2-tuple.
If None
, the default [-1, 1] is used.
- Returns:
float
– Quadrature evaluation for the specified interval.
-
classmethod new(type, n)[source]
Initialize a Quad
instance of the specified type.
- Parameters:
type (str
or QuadType
) – Quadrature rule type. If a string is passed, it is converted to
a QuadType
.
n (int
) – Number of quadrature points.
- Returns:
Quad
– Quadrature definition.
-
property str_summary
Return a summarized representation of the current instance.
- Returns:
str
– Instance summary.
-
class eradiate.quad.QuadType(value)[source]
Quadrature rule type flags.