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Ingy döt Net 2023-07-01 11:58:00 -04:00
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35
Task/Pascal-matrix-generation/REXX/pascal-matrix-generation-1.rexx Normal file
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/*REXX program generates and displays three forms of an NxN Pascal matrix. */
numeric digits 50 /*be able to calculate huge factorials.*/
parse arg N . /*obtain the optional matrix size (N).*/
if N=='' | N=="," then N= 5 /*Not specified? Then use the default.*/
call show N, upp(N), 'Pascal upper triangular matrix'
call show N, low(N), 'Pascal lower triangular matrix'
call show N, sym(N), 'Pascal symmetric matrix'
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
upp: procedure; parse arg N; $= /*gen Pascal upper triangular matrix. */
do i=0 for N; do j=0 for N; $=$ comb(j, i); end; end; return $
/*──────────────────────────────────────────────────────────────────────────────────────*/
low: procedure; parse arg N; $= /*gen Pascal lower triangular matrix. */
do i=0 for N; do j=0 for N; $=$ comb(i, j); end; end; return $
/*──────────────────────────────────────────────────────────────────────────────────────*/
sym: procedure; parse arg N; $= /*generate Pascal symmetric matrix. */
do i=0 for N; do j=0 for N; $=$ comb(i+j, i); end; end; return $
/*──────────────────────────────────────────────────────────────────────────────────────*/
!: procedure; parse arg x; !=1; do j=2 to x; != !*j; end; return !
/*──────────────────────────────────────────────────────────────────────────────────────*/
comb: procedure; parse arg x,y; if x=y then return 1 /* {=} case.*/
if y>x then return 0 /* {>} case.*/
if x-y<y then y= x-y; _= 1; do j=x-y+1 to x; _= _*j; end; return _ / !(y)
/*──────────────────────────────────────────────────────────────────────────────────────*/
show: procedure; parse arg s,@; w=0; #=0 /*get args. */
do x=1 for s**2; w= max(w, 1 + length( word(@,x) ) ); end
say; say center( arg(3), 50, '─') /*show title*/
do r=1 for s; if r==1 then $= '[[' /*row 1 */
else $= ' [' /*rows 2 N*/
do c=1 for s; #= #+1; e= (c==s) /*e ≡ "end".*/
$=$ || right( word(@, #), w) || left(',', \e) || left("]", e)
end /*c*/ /* [↑] row.*/
say $ || left(',', r\==s)left("]", r==s) /*show row. */
end /*r*/
return

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Task/Pascal-matrix-generation/REXX/pascal-matrix-generation-2.rexx Normal file
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/*REXX program generates and displays three forms of an NxN Pascal matrix. */
numeric digits 50 /*be able to calculate huge factorials.*/
parse arg N . /*obtain the optional matrix size (N).*/
if N=='' | N=="," then N= 5 /*Not specified? Then use the default.*/
call show N, Pmat(N, 'upper'), 'Pascal upper triangular matrix'
call show N, Pmat(N, 'lower'), 'Pascal lower triangular matrix'
call show N, Pmat(N, 'sym') , 'Pascal symmetric matrix'
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
Pmat: procedure; parse arg N; $= /*generate a format of a Pascal matrix.*/
arg , ? /*get uppercase version of the 2nd arg.*/
do i=0 for N; do j=0 for N /*pick a format to use [↓] */
if abbrev('UPPER' , ?, 1) then $= $ comb(j , i)
if abbrev('LOWER' , ?, 1) then $= $ comb(i , j)
if abbrev('SYMMETRICAL', ?, 1) then $= $ comb(i+j, j)
end /*j*/ /* ↑ */
end /*i*/ /* │ */
return $ /* └──min. abbreviation is 1 char.*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
!: procedure; parse arg x; !=1; do j=2 to x; != ! * j; end; return !
/*──────────────────────────────────────────────────────────────────────────────────────*/
comb: procedure; parse arg x,y; if x=y then return 1 /* {=} case.*/
if y>x then return 0 /* {>} case.*/
if x-y<y then y=x-y; _= 1; do j=x-y+1 to x; _= _ * j; end; return _ / !(y)
/*──────────────────────────────────────────────────────────────────────────────────────*/
show: procedure; parse arg s,@; w=0; #=0 /*get args. */
do x=1 for s**2; w=max(w,1+length(word(@,x))); end
say; say center( arg(3), 50, '─') /*show title*/
do r=1 for s; if r==1 then $= '[[' /*row 1 */
else $= ' [' /*rows 2 N*/
do c=1 for s; #= # + 1; e= (c==s) /*e ≡ "end".*/
$=$ || right( word(@, #), w) || left(', ',\e) || left("]", e)
end /*c*/ /* [↑] row.*/
say $ || left(',', r\==s)left(']', r==s) /*show row. */
end /*r*/
return