GNU Free Documentation License, Version 1.2

- User documentation for dense matrices (and DenseMatImpl)
- Maintainer documentation for the class DenseMatImpl
- Bugs and Shortcomings

A normal user should never need to know about the class DenseMatImpl; see below for notes aimed at library maintainers.

An dense martrix object is a matrix represented in the most natural
way: as a *2-dimensional array* of its entries. For instance a
DenseMat of 4 rows and 3 columns will contain 12=4x3 entries.
Contrast this with the a `SparseMatrix`

where the values (and
positions) of only the non-zero entries are recorded.

To create a `DenseMat`

you need to specify its ring R and dimensions
(`r`

rows and `c`

columns). By default the matrix is filled with
zeroes; alternatively the entries may be initialized from a `vector`

of `vector`

.

NewDenseMat(R, r, c) -- an r-by-c matrix filled with zero(R) NewDenseMat(R, VV) -- a matrix whose (i,j) entry is VV[i][j] NewDenseMatTranspose(R, VV) -- a matrix whose (i,j) entry is VV[j][i]

To create a copy of a matrix, MatrixView, ConstMatrixView use the call

NewDenseMat(M);

Currently a `DenseMat`

has no special operations in addition to those
for a general `matrix`

. Here is a brief summary of those operations

BaseRing(M) -- the ring to which the matrix entries belong NumRows(M) -- the number of rows in M (may be zero) NumCols(M) -- the number of columns in M (may be zero) cout << M -- print out the value of the matrix M(i,j) -- a copy of entry (i,j) in the matrix SetEntry(M,i,j,value) -- set entry (i,j) of matrix M to value

The implementation is really quite straightforward (apart from keeping
proper track of `RingElemRawPtr`

s when exceptions may occur).

`DenseMatImpl`

is a concrete class derived from `MatrixBase`

(see
`matrix`

). As such it supplies definitions for all pure virtual
functions.
`DenseMatImpl`

represents the value of a matrix as an object of type

vector< vector<RingElemRawPtr> >

The convention used is that the outer vector has an entry for each row,
and each inner vector contains the values of that row. The indices of
a matrix entry correspond directly to the `vector<>`

indices needed to
get at the value of that entry. The advantage of using a vector of
vector is that resizing is relatively simple (compared to mapping the
entries into a single vector whose length is equal to the total number
of matrix entries).

Note that each entry in a `DenseMatImpl`

is a `RingElemRawPtr`

, so
care must be taken to handle exceptions in a way which doesn't leak
memory.

A `DenseMatImpl`

object keeps explicit track of its own size (in the data
members `myNumRows`

and `myNumColumns`

). This makes life easier when
handling matrices one of whose dimensions is zero. The space overhead
should normally be utterly negligible.

Member functions accepting indices use CoCoA_ASSERT to check the validity of the index values. This is useful during debugging but should cost nothing when compiled with debugging turned off.

Using `RingElemRawPtr`

may not have been my brightest idea (because
it becomes hard to make all functions fully exception clean).

The pseudo-ctor from vector of vector should probably be a template fn; this would offer better flexibility to the user (e.g. could initialize from a vector of vector of int).

This is a first implementation: simplicity was paramount, efficiency disregarded.