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Reduced row echelon form: Difference between revisions
→{{header|Ursala}}: Added zkl
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rref = @ySzSX msolve; ^plrNCTS\~& ~&iiDlSzyCK9+ :/1.+ 0.!*t</lang>
=={{header|zkl}}==
Direct implementation of the pseudo-code given, lots of generating new rows rather than modifying the rows themselves.
<lang zkl>fcn toReducedRowEchelonForm(m){ // m is modified, the rows are not
lead,rowCount,columnCount := 0,m.len(),m[1].len();
foreach r in (rowCount){
if(columnCount<=lead) break;
i:=r;
while(m[i][lead]==0){
i+=1;
if(rowCount==i){
i=r; lead+=1;
if(columnCount==lead) break;
}
}//while
m.swap(i,r); // Swap rows i and r
if(n:=m[r][lead]) m[r]=m[r].apply('/(n)); //divide row r by M[r,lead]
foreach i in (rowCount){
if(i!=r) // Subtract M[i, lead] multiplied by row r from row i
m[i]=m[i].zipWith('-,m[r].apply('*(m[i][lead])))
}//foreach
lead+=1;
}//foreach
m
}</lang>
<lang zkl>m:=List( T( 1, 2, -1, -4,), // T is read only list
T( 2, 3, -1, -11,),
T(-2, 0, -3, 22,));
printM(m);
println("-->");
printM(toReducedRowEchelonForm(m));
fcn printM(m){ m.pump(Console.println,rowFmt) }
fcn rowFmt(row){ ("%4d "*row.len()).fmt(row.xplode()) }</lang>
{{out}}
<pre>
1 2 -1 -4
2 3 -1 -11
-2 0 -3 22
-->
1 0 0 -8
0 1 0 1
0 0 1 -2
</pre>
{{omit from|GUISS}}
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