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Extreme Optimization Numerical Libraries for .NET
Usability
The Extreme Optimization Numerical Libraries for .NET
breaks new ground in usability and productivity for numerical software
development. We spent a great deal of time and effort on maximizing the
usability of our API.
Usability is a broad subject. We will briefly discuss some of its aspects and
how they are implemented in the Extreme Optimization Mathematics Library for
.NET. The resources at the bottom of this page
give more information.
Consistency
Consistency both with Microsoft's
Design Guidelines for Developing Class Libraries and internally,
ensures that you can reuse what you have learnt building applications for the
.NET framework. Some examples of consistency with the .NET framework design
guidelines are:
- The library is fully compliant with the Common Language Specification (CLS).
- The order of parameters in constructors and methods is consistent. Required
parameters appear before optional parameters. Optional parameters always appear
in the same order.
- When an exception is thrown, it is of the right type. For example,
DimensionMismatchException, which indicates that the size of
vectors and/or matrices aren't compatible for the requested operation, inherits
from ArgumentException.
- All operator overloads have static (shared in Visual Basic) method equivalents.
- All ToString
methods are culture-aware.
- Boolean parameters always default to false.
Examples of internal consistency include:
- All classes that implement numerical integration and solving equations inherit
from an abstract base class,
IterativeAlgorithm, which specifies properties and
methods shared by all these classes.
- Matrices and matrix decompositions all inherit from an abstract base class:
LinearTransformation. Regardless of the type of matrix or
decomposition, the syntax and semantics of the operation is the same.
Transparency
Transparency means that the code is self-explanatory. It also means that, with
the use of context sensitive help or Intellisense, you should be able to choose
the correct classes, methods, and parameter values.
The classes in the Extreme Optimization Mathematics Library for .NET are
organized in namespaces according to their function. For example, all matrix
and vector classes reside in the
Extreme.Mathematics.LinearAlgebra namespace, while all
numerical integrators reside in
Extreme.Mathematics.Calculus.
Members and method parameters have descriptive, meaningful names. We don't use
abbreviations (LUDecomposition,
not LUDecomp) or transcriptions of mathematical notation (Predictions,
not Yhat ). By using expressive names for language elements, you
don't need to spend mental resources on translating their meaning.
Progressive API's
A progressive API makes it easy to write code incrementally, starting from a simple core scenario and moving on
to increasingly complex ones. At each stage, the tools needed for the next step are available as methods and properties of
objects that have been created up to that point. Only rarely is it necessary to construct a new object.
For example, a basic regression analysis can be written in only a few lines of code. The classes that represent regression
analysis have methods and properties that let you perform other common tasks: inspect the computed model, perform validation tests for the model and
retrieve objects that represent the regression parameters. These objects in turn expose detailed information about the regression
parameters, and let you compute confidence intervals and perform tests on those parameters.
This is in contrast to many other libraries where you have to pull together functions from several, unrelated locations
and then write the code that connects them.
Extensibility
Extensibility allows you to create specialized versions of objects in the
library with minimal effort.
For example, to create a specialized
Matrix type, only two members, the GetValue and SetValue methods, must be implemented. All
operations on matrices, from arithmetic operations to decompositions, and from
solving equations to retrieving rows, columns or submatrices, will work on your
specialized matrix type. You may provide your own optimized implementations of
almost any other method, but that choice is yours.
Other examples of extensibility include:
- To create a new
Vector type, only the GetValue
and SetValue
methods must be implemented. You can evaluate arithmetic operations,
norms, and other properties without writing any more code.
- To create a new
Curve, you must supply the
ValueAt
method. You may want to also define the derivative function and the integral.
Both will be evaluated numerically if no implementation is supplied.
- To create a class of functions for curve fitting, all you need to do is derive
from
FunctionBasis and implement the
FillValues
method.
- The AdaptiveIntegrator
class lets you supply your own integration rule tailored to a specific type of
integrand.
- Functionality that is common between different classes is implemented using
abstract base classes rather than interfaces. The
IterativeAlgorithm mentioned above and LinearTransformation are examples. This
means that future extensions can be implemented without having to define new
interfaces.
Correspondence
Correspondence of objects in the library with the mathematical concepts you use
to describe your problems makes translating your solution into code that much
easier.
Resources
Framework
Design Guidelines: Conventions, Idioms, and Patterns for Reusable .NET
Libraries by Krzysztof Cwalina and Brad
Abrams.
Design Guidelines for Developing Class Libraries from Microsoft.
Measuring
API Usability by Steven Clarke. Dr. Dobbs Journal Special
Windows/.NET supplement, May 2004.
Steven Clarke's Weblog
has information on the Cognitive Dimensions framework for API
usability.
Brad Abrams and Krzysztof Cwalina post
updates to the design guidelines on a regular basis.
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