Description of matrix

matrix< T, Shape = rectangle<>, Storage = dense<>, Orientation = row_major >		Programmers Guide
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Component type:type

Description

Matrices that occur in real engineering and scientific applications often have special structure, especially in terms of how many zeros are in the matrix, and where the non-zeros are located in the matrix. This means that space and time saving can be acheived by using various types of compressed storage. There are a multitude of matrix storage formats in use today, and the MTL tries to support many of the more common storage formats. The following discussion will describe how the user of MTL can select the type of matrix he or she wishes to use. To create a MTL matrix, one first needs to construct the appropriate matrix type. This is done using the matrix type generation class, which is easier to think of as a function. It takes as input the characteristics of the matrix type that you want and then returns the appropriate MTL matrix. The matrix type generators ``function'' has defaults defined, so in order to create a normal rectangular matrix type, one merely does the following:

 typedef matrix< double >::type MyMatrix;
 MyMatrix A(M, N);

The matrix type generators can take up to four arguments, the element type, the matrix shape, the storage format, and the orientation. The following is the ``prototype'' for the matrix type generators.

 matrix< EltType, Shape, Storage, Orientation >::type

This type of "generative" interface technique was developed by by Krzysztof Czarnecki and Ulrich Eisenecker in their work on the Generative Matrix Computation Library.

*Storage can be made external by specifying such in the storage parameter. eg. dense<external>, packed<external>.

Example

Definition

matrix.h

Template Parameters

Parameter	Description	Default
`EltType`	Valid choices for this argument include `double`, `complex`, and `bool`. In essence, any builtin or user defined type can be used for the `EltType`, however, if one uses the matrix with a particular algorithm, the `EltType` must support the operations required by the algorithm. For MTL algorithms these typically include the usual numerical operators such as addition and multiplication. The `std::complex` class is a good example of what is required in a numerical type. The documentation for each algorithm will include the requirements on the element type.
`Shape`	This argument specifies the general positioning of the non zero elements in the matrix, but does not specify the actual storage format. In addition it specifies certain properties such as symmetry. The choices for this argument include `rectangle`, `banded`, `diagonal`, `triangle`, and `symmetric`. Hermitian is not yet implemented.
`Storage`	The argument specifies the storage scheme used to lay out the matrix elements (and sometimes the element indices) in memory. The storage formats include `dense` , `banded`, `packed` , `banded_view`, `compressed`, `envelope`, and `array`.
`Orientation`	The storage order for an MTL matrix can either be `row_major` or `column_major`.

Model of

Members

Member	Where defined	Description
`enum { Shape_id = Shape::id, Shape_M = Shape::M, Shape_N = Shape::N }`
`type`		The generated type

New members

Notes

See also