MatrixViews

© 2008 John Abbott
GNU Free Documentation License, Version 1.2



CoCoALib Documentation Index

User documentation for MatrixViews

A MatrixView offers a means to view one or more existing objects as though they were a matrix:

Examples

NB The views do not make copies, so be careful with temporaries! Look at these examples (val is a RingElem):

    // OK
    const vector<RingElem> v(3, val);
    MatrixView MV = RowMat(v);  // MV reads/writes in the vector v
  
    // NO   this compiles, but the vector disappears after the ";"!!
    ConstMatrixView MVGhost = RowMat(vector<RingElem>(3, val));
  
    // OK   NewDenseMat makes a copy of the vector before it disappears
    matrix M = NewDenseMat(RowMat(vector<RingElem>(3, val)));

Pseudo-constructors

Constant MatrixViews

NB no entry is writable

MatrixViews of a vector

You can view a std::vector<RingElem>, all of whose entries belong to the same ring, as a matrix in three ways:

MatrixViews of a matrix

MatrixViews of more matrices

The following pseudo-constructors assemble several matrices into a bigger one; the argument matrices must all have the same BaseRing.

A
B
A B
A 0
0 B
0 A
B 0
A B
C D

NB the boundaries of the four submatrices must be aligned.

Operations on ConstMatrixView, MatrixView

See matrix operations

Maintainer documentation for MatrixViews

Most of the implementations are quite straightforward; the tricky part was getting the design of the abstract classes right (well, I hope it is right now). Below are a few comments on some less obvious aspects of the implementations.

Note: it is a mathematical fact that the determinant of the 0x0 matrix is 1.

ZeroMatImpl and IdentityMatImpl are both derived from MatrixViewBase rather than ConstMatrixViewBase as one might naturally expect. The main reason for this is to simplify the implementation of BlockMat views. I wanted to be lazy and implement ConcatDiag and ConcatAntidiag using BlockMat; while this may not be the best implementation, it is a natural approach and should certainly work as one might reasonably expect. However, the pseudo-ctor BlockMat has just two signatures: if any one of the submatrices is const then whole result becomes const. I didn't want to implement sixteen different signatures for BlockMat, and the easy way out seemed to be to make ZeroMatImpl and IdentityMatImpl non-const. As a consequence there are a number of useless member functions in ZeroMatImpl and IdentityMatImpl. I believe this compromise is reasonable. It seemed reasonable to allow ZeroMatImpl::myAssignZero to succeed.

There is a small problem with creating a matrix from an empty std::vector because there is no indication of what the base ring should be. I have chosen to throw an error if one tries to create a matrix view from an empty vector (in RowMat, ColMat and DiagMat).

The routines which access the (i,j) entry in a BlockMat are messy. I could not see an elegant way to make them simpler (or to avoid repeating similar structure in several places in the code). See Bugs about implementing BlockMat in terms of ConcatVer and ConcatHor.

Bugs, Shortcomings and other ideas

There is an appalling amount of code duplication in the implementations. I do not yet see a good way of reducing this. I hope someone will sooner or later find an elegant way to avoid the duplication. Maybe a diagonal abstract class for ZeroMatImpl, IdentityMatImpl, DiagMatImpl, ConstDiagMatImpl?

It is a great nuisance to have to implement two very similar classes: one for the const case, and the other for the non-const case. Is there a better way?

Add ColMat, RowMat and DiagMat for a free module element?

Should submatrix allow repeated row/col indices? It could lead to some some funny behaviour (e.g. setting one entry may change other entries), so perhaps it would be better to forbid it? Currently, it is forbidden.

The pseudo-ctor for submatrix ought to accept begin/end iterators instead of insisting that the caller put the indices in std::vectors.

Should there be a more general version of BlockMat which allows non-aligned borders? BlockMat could be eliminated and replaced by suitable calls to ConcatVer and ConcatHor.

Tensor product of two matrices: we implement it as a DenseMatrix instead of MatrixView because the latter would give no practical advantage and hide the cost of accessing the entries.

Main changes

2011