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Reduced row echelon form: Difference between revisions
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=={{header|REXX}}==
''Reduced Row Echelon Form'' (a.k.a. ''row canonical form'') of a matrix, with optimization added.
<lang rexx>/*REXX
cols=0; w=0; @.=0 /*max cols in a row; max width; matrix.*/
mat.=;
do r=1 until mat.r==''; _=mat.r /*build @.row.col from (matrix) mat.X
do c=1 until _=''; parse var _ @.r.c _
w=max(w, length(@.r.c) +1)
end /*c*/
cols=max(cols,c) /*remember max number of cols.*/
end /*r*/
rows=r-1 /*adjust the row count (from DO loop).*/
/* ┌─────────────────────────────────────────◄── Reduced Row Echelon Form on matrix.*/
do r=1 for rows while cols>! /*begin to perform the heavy lifting. */▼
▲ do r=1 for rows while cols>! /*begin to perform the heavy lifting. */
j=r
do while @.j.!==0; j=j+1
if j==rows then do; j=r; !=!+1; if cols==! then leave r; end
end /*while*/
/* [↓] swap rows J,R (but not if same)*/
do _=1 for cols while j\==r; parse value @.r._ @.j._ with @.j._ @._._; end /*_*/
?=@.r.!
do d=1 for cols while ?\=1; @.r.d=@.r.d/?; end /*d*/
/* [↑] divide row J by @.r.p ──unless≡1*/
do k=1 for rows; ?=@.k.! /*subtract (row K) @.r.s from row K.*/
if k==r | ?=0 then iterate /*skip if row K is the same as row R.*/
do s=1 for cols; @.k.s=@.k.s - ?*@.r.s; end /*s*/
end /*k*/ /* [↑] for the rest of numbers in row.*/
!=!+1 /*bump the column pointer. */
end /*r*/
call showMat 'matrix RREF' /*display the reduced row echelon form.*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
showMat: parse arg title; say; say center(title, 3+(cols+1)*w, '─'); say
do r=1 for rows; _=
do c=1 for cols
if @.r.c=='' then do; say "***error
say 'row' row", column" c'.'; exit 13
end
_=_ right(@.r.c,w)
end /*c*/
end /*r*/
return</lang>
{{out|output|text= when using the default (internal) input:}}
<pre>
────original matrix────
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