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June 2018 Update

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Ingy döt Net 2018-06-22 20:57:24 +00:00
parent ba8067c3b7
commit 22f33d4004
5278 changed files with 84726 additions and 14379 deletions
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49
Task/Reduced-row-echelon-form/REXX/reduced-row-echelon-form.rexx
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@ -3,44 +3,45 @@ cols=0; w=0; @.=0 /*max cols in a row; max width;
mat.=; mat.1= ' 1 2 -1 -4 '
mat.2= ' 2 3 -1 -11 '
mat.3= ' -2 0 -3 22 '
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) /*find the maximum width of an element.*/
end /*c*/
cols=max(cols,c) /*remember max number of cols.*/
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) /*find the maximum width of an element.*/
end /*c*/
cols=max(cols, c) /*save the maximum number of columns. */
end /*r*/
rows=r-1 /*adjust the row count (from DO loop).*/
rows=r - 1 /*adjust the row count (from DO loop).*/
call showMat 'original matrix' /*display the original matrix to screen*/
!=1 /*set the working column pointer to 1.*/
/* ┌─────────────────────────────────────────◄── Reduced Row Echelon Form on matrix.*/
/* ┌──────────────────────◄────────────────◄──── Reduced Row Echelon Form on matrix.*/
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
j=r /*use a subsitute index for the DO loop*/
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 /*_*/
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. */
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
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*** matrix element isn't defined:"
say 'row' row", column" c'.'; exit 13
say 'row' r", column" c'.'; exit 13
end
_=_ right(@.r.c,w)
_=_ right(@.r.c, w)
end /*c*/
say _ /*display a row of the matrix to screen*/
end /*r*/
return
say _ /*display a matrix row to the terminal.*/
end /*r*/; return