I would like to expose some ideas about the submatrix function
implemented in Maxima.
While submatrix is really useful (I often use in my programs), it is a
function that deletes rows or columns and is different from the
definition everyone could have studied in an Algebra course, where a
submatrix is a matrix with elements to be taken, instead of rows or
columns to be deleted. In other words, given two lists of row and
column indices, by definition a submatrix is created taking all
elements of another matrix whose indices are the couples with the
first element in rows_list and the second in cols_list.
I don't know if such a function is already present in Maxima but I
miss it. Please excuse me if I'm missing something that's already
here!
I wrote a simple function to do that task. It needs 3 parameters: the
first one must be a matrix, the second one a list or rows or a single
integer, the third one a list of columns or a single integer.
I would like to ask to the list if having two function to deal with
submatrices could be useful, above all because of a better alignement
with algebra definitions.
Here's the function:
subm ( _m, _rows, _cols ) := block([i,j,_x],
if not matrixp(_m) then
error("First input must be a matrix"),
if not listp(_rows) and not integerp(_rows) then
error("Second input must be a list of rows or a single integer"),
if not listp(_cols) and not integerp(_cols) then
error("Third input must be a list of columns or a single integer"),
if not listp(_rows) and integerp(_rows) then
_rows : makelist(_x,_x,_rows,_rows),
if not listp(_cols) and integerp(_cols) then
_cols : makelist(_x,_x,_cols,_cols),
for i in _rows do
if not integerp(i) or i<=0 then
error("Elements in rows list must be > 0"),
for i in _cols do
if not integerp(i) or i<=0 then
error("Elements in columns list must be > 0"),
for i in _rows do
if i>matrix_size(_m)[1] then
error("Row indices must be less or equal than the total number of rows"),
for i in _cols do
if i>matrix_size(_m)[2] then
error("Column indices must be less or equal than the total
number of columns"),
_rows : sort(unique(_rows)),
_cols : sort(unique(_cols)),
_outm : zeromatrix(length(_rows),length(_cols)),
for i:1 thru length(_rows) do
for j:1 thru length(_cols) do
_outm[i,j] : _m[_rows[i],_cols[j]],
return(_outm)
)$
It's really simple but for me it's useful. I hope it's not too buggy.
Stefano