Reduced row echelon form: Difference between revisions

<langsyntaxhighlight lang="360asm">* reduced row echelon form 27/08/2015

END RREF</langsyntaxhighlight>

<langsyntaxhighlight Actionscriptlang="actionscript">public function RREF():Matrix {

}</langsyntaxhighlight>

<langsyntaxhighlight Adalang="ada">generic

end Matrices;</langsyntaxhighlight>

<langsyntaxhighlight Adalang="ada">package body Matrices is

end Matrices;</langsyntaxhighlight>

<langsyntaxhighlight Adalang="ada">with Matrices;

end Main;</langsyntaxhighlight>

<langsyntaxhighlight lang="aime">rref(list l, integer rows, columns)

}</langsyntaxhighlight>

<langsyntaxhighlight lang="algol68">MODE FIELD = REAL; # FIELD can be REAL, LONG REAL etc, or COMPL, FRAC etc #

printf((mat repr, mat, $l$))</langsyntaxhighlight>

=={{header|BBC BASIC}}==

<langsyntaxhighlight lang="bbcbasic"> DIM matrix(2,3)

ENDPROC</langsyntaxhighlight>

<langsyntaxhighlight lang="c">#include <stdio.h>

}</langsyntaxhighlight>

<langsyntaxhighlight lang="csharp">using System;

}</langsyntaxhighlight>

<langsyntaxhighlight lang="cpp">#include <algorithm> // for std::swap

}</langsyntaxhighlight>

<langsyntaxhighlight lang="lisp">(defun convert-to-row-echelon-form (matrix)

:finally (return matrix)))))</langsyntaxhighlight>

<langsyntaxhighlight lang="d">import std.stdio, std.algorithm, std.array, std.conv;

}</langsyntaxhighlight>

<langsyntaxhighlight lang="euphoria">function ToReducedRowEchelonForm(sequence M)

{ -2, 0, -3, 22 } })</langsyntaxhighlight>

<langsyntaxhighlight lang="factor">USE: math.matrices.elimination

{ { 1 2 -1 -4 } { 2 3 -1 -11 } { -2 0 -3 22 } } solution .</langsyntaxhighlight>

<langsyntaxhighlight lang="fortran">module Rref

end module Rref</langsyntaxhighlight>

<langsyntaxhighlight lang="fortran">program prg_test

end program prg_test</langsyntaxhighlight>

<langsyntaxhighlight lang="go">package main

}</langsyntaxhighlight>

<langsyntaxhighlight lang="go">package main

}</langsyntaxhighlight>

<langsyntaxhighlight lang="groovy">enum Pivoting {

}</langsyntaxhighlight>

<langsyntaxhighlight lang="groovy">def matrixCopy = { matrix -> matrix.collect { row -> row.collect { it } } }

println()</langsyntaxhighlight>

<langsyntaxhighlight lang="haskell">import Data.List (find)

where (a, _ : b) = splitAt n l</langsyntaxhighlight>

<langsyntaxhighlight lang="unicon">procedure main(A)

end</langsyntaxhighlight>

The reduced row echelon form of a matrix can be obtained using the <code>gauss_jordan</code> verb from the [httphttps://www.jsoftwaregithub.com/wsvnjsoftware/addonsmath_misc/trunkblob/math/miscmaster/linear.ijs linear.ijs script], available as part of the <code>math/misc</code> addon. <code>gauss_jordan</code> and the verb <code>pivot</code> are shown below (in a mediawiki "[Expand]" region) for completeness:

'''SolutionImplementation:'''

<langsyntaxhighlight lang="j" class="mw-collapsible mw-collapsed">NB.*pivot v Pivot at row, column

)</langsyntaxhighlight>

<langsyntaxhighlight lang="j"> require 'math/misc/linear'

0 0 1 _2</langsyntaxhighlight>

0 0</langsyntaxhighlight>

<langsyntaxhighlight lang="j">mat=: 0 ". ];._2 noun define

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0.820513</langsyntaxhighlight>

<langsyntaxhighlight lang="java">import java.util.*;

}</langsyntaxhighlight>

<langsyntaxhighlight lang="javascript">// modifies the matrix in-place

print(m.toReducedRowEchelonForm());</langsyntaxhighlight>

<langsyntaxhighlight lang="scala">// version 1.1.51

}</langsyntaxhighlight>

<langsyntaxhighlight lang="lua">function ToReducedRowEchelonForm ( M )

end</langsyntaxhighlight>

=={{header|Mathematica}}/{{header|Wolfram Language}}==

<langsyntaxhighlight Mathematicalang="mathematica">RowReduce[{{1, 2, -1, -4}, {2, 3, -1, -11}, {-2, 0, -3, 22}}]</langsyntaxhighlight>

<lang Mathematicapre>{{1, 0, 0, -8}, {0, 1, 0, 1}, {0, 0, 1, -2}}</langpre>

<langsyntaxhighlight MATLABlang="matlab">rref([1, 2, -1, -4; 2, 3, -1, -11; -2, 0, -3, 22])</langsyntaxhighlight>

<langsyntaxhighlight lang="maxima">rref(a):=block([p,q,k],[p,q]:matrix_size(a),a:echelon(a),

matrix([1,0,0,0,1/2],[0,1,0,0,-1],[0,0,1,0,-1/2],[0,0,0,1,1],[0,0,0,0,0])</langsyntaxhighlight>

<langsyntaxhighlight lang="objeck">

<langsyntaxhighlight OCamllang="ocaml">let swap_rows m i j =

) m</langsyntaxhighlight>

<langsyntaxhighlight OCamllang="ocaml">let rref m =

show mat</langsyntaxhighlight>

<langsyntaxhighlight lang="octave">A = [ 1, 2, -1, -4; 2, 3, -1, -11; -2, 0, -3, 22];

disp(refA);</langsyntaxhighlight>

PARI has a built-in matrix type, but no commands for row-echelon form. This Ais dimension-limiteda basic one canimplementing be constructed from the builtGauss-in <code>matsolve</code>Jordan command:reduction.

<langsyntaxhighlight lang="parigp">rrefmatrref(M)={

};</langsyntaxhighlight>

<langsyntaxhighlight lang="parigp">rref([1,2,-1,-4;2,3,-1,-11;-2,0,-3,22])</langsyntaxhighlight>

<langsyntaxhighlight lang="perl">sub rref

print display(\@m);</langsyntaxhighlight>

if lead><span style=columnCount"color: then exit end if#000000;">i</span>

<langsyntaxhighlight lang="php"><?php

?></langsyntaxhighlight>

<langsyntaxhighlight PicoLisplang="picolisp">(de reducedRowEchelonForm (Mat)

Mat )</langsyntaxhighlight>

<langsyntaxhighlight lang="python">def ToReducedRowEchelonForm( M):

print ', '.join( (str(rv) for rv in rw) )</langsyntaxhighlight>

<langsyntaxhighlight lang="rsplus">rref <- function(m) {

print(rref(m))</langsyntaxhighlight>

<langsyntaxhighlight lang="racket">

return @m unless $lead < $cols or return @m;

next unless ++$i == $rows or next;

return @m if ++$lead == $cols and return @m;

my@m[$r] »/=» $lv = @m[$r;$lead];

@m[$n] »-=» @m[$r] »*×» (@m[$n;$lead] // 0);

return $num.narrow if $num.narrow.WHAT ~~ Int;

}</langsyntaxhighlight>

Perl 6Raku handles rational numbers internally as a ratio of two integers

[http://unapologetic.wordpress.com/2009/09/03/reduced-row-echelon-form/ reduced row echelon form]

<lang perl6>sub swap_rows shear-row ( @M, \scale, $\r1, $\r2 ) { @M[ $r1,] $r2= @M[r1] =»+» ( @M[ $r2,] $r1»×» ]scale ) };

sub scale_row reduce-row ( @M, $scale, $r ) { @M[$\r] = , \c ) { scale-row @M, 1/@M[$r;c], »*» $scale r };

sub shear_row clear-column ( @M, $scale, $r1 \r, $r2 \c ) { shear-row @M[$r1] =, -@M[$r1_;c].list, »+»$_, (r for @M[$r2].keys.grep: »*» $scale!= )r };

my $column_countcolumn-count = +@( @M[0] );

returnlast if ++$current_colcol == $column_countcolumn-count; # Matrix was all-zeros.

method unscale_row ( @M: $scale,my $rowcol )= {0;

for @M[$row].keys =-> @M[$row] »/» $scale;{

method unshear_row ( @M:.clear-column( $scalerow, $r1, $r2col ) {;

@M[$r1] = @M[$r1] »-» (return @M[if ++$r2]col »*»== $scale )column-count;

<langsyntaxhighlight lang="rexx">/*REXX pgm performs Reduced Row Echelon Form (RREF), AKA row canonical form on a matrix)*/

cols= 0; w= 0; @. =0 /*max cols in a row; max width; matrix.*/

do c=1 until _=''; parse var _ @.r.c _

w= max(w, length(@.r.c) + 1) /*find the maximum width of an element.*/

cols= max(cols, c) /*save the maximum number of columns. */

rows= r - 1 /*adjust the row count (from DO loop). */

call showMat 'original matrix' /*display the original matrix to screenmatrix──►screen.*/

!=1 1 /*set the working column pointer to 1.*/

j=r 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

?= @.r.!

!= ! + 1 /*bump the working column pointer. */

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' r", column" c'.'; exit 13

end

_= _ right(@.r.c, w)

end /*c*/

say _ say _ /*display a matrix row to the terminal.*/

end /*r*/; return</langsyntaxhighlight>

<langsyntaxhighlight lang="ring">

<langsyntaxhighlight lang="ruby"># returns an 2-D array where each element is a Rational

print_matrix convert_to(reduced, :to_f)</langsyntaxhighlight>

<langsyntaxhighlight lang="sage">sage: m = matrix(ZZ, [[1,2,-1,-4],[2,3,-1,-11],[-2,0,-3,22]])

[ 0 0 1 -2] </langsyntaxhighlight>

<langsyntaxhighlight lang="scheme">(define (reduced-row-echelon-form matrix)

indices)))</langsyntaxhighlight>

<langsyntaxhighlight lang="scheme">(define matrix

(newline)</langsyntaxhighlight>

<syntaxhighlight lang="text">((1 0 0 -8) (0 1 0 1) (0 0 1 -2))</langsyntaxhighlight>

<langsyntaxhighlight lang="seed7">const type: matrix is array array float;

end func;</langsyntaxhighlight>

{{trans|Perl 6Raku}}

<langsyntaxhighlight lang="ruby">func rref (M) {

}</langsyntaxhighlight>

<langsyntaxhighlight lang="tcl">package require Tcl 8.5

print_matrix [toRREF $m]</langsyntaxhighlight>

<langsyntaxhighlight lang="ti83">rref([[1,2,-1,-4][2,3,-1,-11][-2,0,-3,22]])</langsyntaxhighlight>

<langsyntaxhighlight lang="ti89b">rref([1,2,–1,–4; 2,3,–1,–11; –2,0,–3,22])</langsyntaxhighlight>

<langsyntaxhighlight Ursalalang="ursala">#import std

<-2.,0.,-3.,22.>></langsyntaxhighlight>

<langsyntaxhighlight Ursalalang="ursala">#import lin

rref = @ySzSX msolve; ^plrNCTS\~& ~&iiDlSzyCK9+ :/1.+ 0.!*t</langsyntaxhighlight>

{{trans|Phix}}<langsyntaxhighlight lang="vb">Private Function ToReducedRowEchelonForm(M As Variant) As Variant

End Sub</langsyntaxhighlight>{{out}}

<langsyntaxhighlight lang="vfp">

<langsyntaxhighlight lang="zkl">var [const] GSL=Import("zklGSL"); // libGSL (GNU Scientific Library)

}</langsyntaxhighlight>

<langsyntaxhighlight lang="zkl">A:=GSL.Matrix(3,4).set( 1, 2, -1, -4,

toReducedRowEchelonForm(A).format(5,1).println();</langsyntaxhighlight>

<langsyntaxhighlight lang="zkl">fcn toReducedRowEchelonForm(m){ // m is modified, the rows are not

}</langsyntaxhighlight>

<langsyntaxhighlight lang="zkl">m:=List( T( 1, 2, -1, -4,), // T is read only list

fcn rowFmt(row){ ("%4d "*row.len()).fmt(row.xplode()) }</langsyntaxhighlight>