Information Technology Reference
In-Depth Information
the nonlinear equation solver base class and its generic (say)
solve
method are
seen. This way of programming hides details in numerical algorithms and reduces
complexity. This is of course very important for the reliability of large numerical
codes.
6.5.3
Design of a Numerical Integration Hierarchy
Class
Integrate
is the base class of our numerical integration methods hierarchy.
Specific integration rules are implemented as subclasses. Common to all methods
are the integration limits and the function to be integrated. Other parameters can
differ among the subclasses. The idea of an
init
method with differing argument
lists is not good. We should look for a strategy that handles input data and the ini-
tialization of integration objects in the same way for all subclasses of
Integration
.
To achieve a unified treatment of input data for all subclasses, it may be con-
venient to collect all the parameters in a so-called
parameter class
, here called
Integration prm
:
class Integration_prm
data:
a, b, f
npoints
method
tolerance
...
methods:
constructor()
create()
default()
read()
write()
This outline of the class shows some possible parameters and (at least) five methods:
-
constructor
for creating and initializing an object
-
create
for creating an integration rule object (as a subclass instance in the
Integration
hierarchy), based on the data in this
Integration prm
instance
-
default
for assigning appropriate default values to data members
-
read
for reading values from some kind of user interface
-
write
for dumping the contents of the parameters (for a check)
Observe that our pseudo code does not coincide with a particular programming
language.
20
The base class
Integration
for all integration methods typically has a construc-
tor that takes the bag of parameters (i.e., an
Integration prm
object) and stores it
internally in the class. The base class also offers access to the
integrate
method
20
For example, the
constructor
method will have different names in different languages
(
Integration prm
in Java and C
CC
,
init
in Python).
