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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