# [Maxima] About submatrix and its meaning

Leo Butler l.butler at ed.ac.uk
Wed Nov 18 04:16:52 CST 2009

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On Sun, 15 Nov 2009, Stefano Ferri wrote:

< 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)
< )\$

I agree that 'submatrix' is a horrible name.

I would suggest

return(genmatrix(lambda([i,j],_m[_rows[i],_cols[j]]),length(_rows),length(_cols)));

in place of the last 5 lines.

To amplify RJF's comment...
It would be nice if Maxima had a function devoted to argument checking
(q: does it, and I am ignorant?), or even better, if it understood the
syntax

foo(x::list) := ....

Leo

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