Reduced row echelon form: Difference between revisions
Added Algol W
SqrtNegInf (talk | contribs) m (→{{header|Sidef}}: Fix link: Perl 6 --> Raku) |
(Added Algol W) |
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Line 529:
( 0.0000, 1.0000, 0.0000, 1.0000),
( 0.0000, 0.0000, 1.0000, -2.0000))
</pre>
=={{header|ALGOL W}}==
From the pseudo code.
<lang algolw>begin
% replaces M with it's reduced row echelon form %
% M should have bounds ( 0 :: rMax, 0 :: cMax ) %
procedure toReducedRowEchelonForm ( real array M ( *, * )
; integer value rMax, cMax
) ;
begin
integer lead;
lead := 0;
for r := 0 until rMax do begin
integer i;
if lead > cMax then goto done;
i := r;
while M( i, lead ) = 0 do begin
i := i + 1;
if rMax = i then begin
i := r;
lead := lead + 1;
if cMax = lead then goto done
end if_rowCount_eq_i
end while_M_i_lead_eq_0 ;
% Swap rows i and r %
for c := 0 until cMax do begin
real t;
t := M( i, c );
M( i, c ) := M( r, c );
M( r, c ) := t
end swap_rows_i_and_r ;
If M( r, lead ) not = 0 then begin
% divide row r by M[r, lead] %
real rLead;
rLead := M( r, lead );
for c := 0 until cMax do M( r, c ) := M( r, c ) / rLead
end if_M_r_lead_ne_0 ;
for i := 0 until rMax do begin
if i not = r then begin
% Subtract M[i, lead] multiplied by row r from row i %
real iLead;
iLead := M( i, lead );
for c := 0 until cMax do M( i, c ) := M( i, c ) - ( iLead * M( r, c ) )
end if_i_ne_r
end for_i ;
lead := lead + 1
end for_r ;
done:
end toReducedRowEchelonForm ;
% test the toReducedRowEchelonForm procedure %
begin
real array m( 0 :: 2, 0 :: 3 );
M( 0, 0 ) := 1; M( 0, 1 ) := 2; M( 0, 2 ) := -1; M( 0, 3 ) := -4;
M( 1, 0 ) := 2; M( 1, 1 ) := 3; M( 1, 2 ) := -1; M( 1, 3 ) := -11;
M( 2, 0 ) := -2; M( 2, 1 ) := 0; M( 2, 2 ) := -3; M( 2, 3 ) := 22;
toReducedRowEchelonForm( M, 2, 3 );
r_format := "A"; s_w := 0; r_w := 6; r_d := 1; % set output formating %
for r := 0 until 2 do begin
write( M( r, 0 ) );
for c := 1 until 3 do writeon( " ", M( r, c ) );
end for_r
end
end.</lang>
{{out}}
<pre>
1.0 0.0 0.0 -8.0
0.0 1.0 0.0 1.0
0.0 0.0 1.0 -2.0
</pre>
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