Reduced row echelon form: Difference between revisions
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''Reduced Row Echelon Form'' (a.k.a. ''row canonical form'') of a matrix, with optimization added. |
''Reduced Row Echelon Form'' (a.k.a. ''row canonical form'') of a matrix, with optimization added. |
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<lang rexx>/*REXX pgm performs Reduced Row Echelon Form (RREF), AKA row canonical form on a matrix)*/ |
<lang rexx>/*REXX pgm performs Reduced Row Echelon Form (RREF), AKA row canonical form on a matrix)*/ |
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cols=0; |
cols= 0; w= 0; @. =0 /*max cols in a row; max width; matrix.*/ |
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mat.=; mat.1= ' 1 2 -1 -4 ' |
mat.=; mat.1= ' 1 2 -1 -4 ' |
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mat.2= ' 2 3 -1 -11 ' |
mat.2= ' 2 3 -1 -11 ' |
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mat.3= ' -2 0 -3 22 ' |
mat.3= ' -2 0 -3 22 ' |
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do r=1 until mat.r==''; _=mat.r /*build @.row.col from (matrix) mat.X*/ |
do r=1 until mat.r==''; _=mat.r /*build @.row.col from (matrix) mat.X*/ |
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do c=1 until _=''; |
do c=1 until _=''; parse var _ @.r.c _ |
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w=max(w, length(@.r.c) + 1) |
w= max(w, length(@.r.c) + 1) /*find the maximum width of an element.*/ |
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end /*c*/ |
end /*c*/ |
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cols=max(cols, c) |
cols= max(cols, c) /*save the maximum number of columns. */ |
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end /*r*/ |
end /*r*/ |
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rows=r |
rows= r-1 /*adjust the row count (from DO loop). */ |
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call showMat 'original matrix' /*display the original |
call showMat 'original matrix' /*display the original matrix──►screen.*/ |
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!= |
!= 1 /*set the working column pointer to 1.*/ |
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/* ┌──────────────────────◄────────────────◄──── Reduced Row Echelon Form on matrix.*/ |
/* ┌──────────────────────◄────────────────◄──── Reduced Row Echelon Form on matrix.*/ |
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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. */ |
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j= |
j= r /*use a subsitute index for the DO loop*/ |
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do while @.j.!==0; j=j + 1 |
do while @.j.!==0; j= j + 1 |
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if j==rows then do; j=r; |
if j==rows then do; j= r; != ! + 1; if cols==! then leave r; end |
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end /*while*/ |
end /*while*/ |
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/* [↓] swap rows J,R (but not if same)*/ |
/* [↓] swap rows J,R (but not if same)*/ |
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do _=1 for cols while j\==r; parse value @.r._ @.j._ with @.j._ @._._ |
do _=1 for cols while j\==r; parse value @.r._ @.j._ with @.j._ @._._ |
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end /*_*/ |
end /*_*/ |
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?=@.r.! |
?= @.r.! |
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do d=1 for cols while ?\=1; @.r.d= @.r.d / ? |
do d=1 for cols while ?\=1; @.r.d= @.r.d / ? |
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end /*d*/ /* [↑] divide row J by @.r.p ──unless≡1*/ |
end /*d*/ /* [↑] divide row J by @.r.p ──unless≡1*/ |
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end /*s*/ |
end /*s*/ |
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end /*k*/ /* [↑] for the rest of numbers in row.*/ |
end /*k*/ /* [↑] for the rest of numbers in row.*/ |
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!=! |
!= !+1 /*bump the working column pointer. */ |
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end /*r*/ |
end /*r*/ |
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exit /*stick a fork in it, we're all done. */ |
exit /*stick a fork in it, we're all done. */ |
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/*──────────────────────────────────────────────────────────────────────────────────────*/ |
/*──────────────────────────────────────────────────────────────────────────────────────*/ |
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showMat: parse arg title; say; |
showMat: parse arg title; say; say center(title, 3 + (cols+1) * w, '─'); say |
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do r=1 for rows; _= |
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do c=1 for cols |
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if @.r.c=='' then do; say "***error*** matrix element isn't defined:" |
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say 'row' r", column" c'.'; exit 13 |
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end |
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_= _ right(@.r.c, w) |
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end /*c*/ |
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say _ /*display a matrix row to the terminal.*/ |
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end /*r*/; return</lang> |
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{{out|output|text= when using the default (internal) input:}} |
{{out|output|text= when using the default (internal) input:}} |
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<pre> |
<pre> |
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