LU decomposition: Difference between revisions
Rename Perl 6 -> Raku, alphabetize, minor clean-up
(Add Lobster solution) |
Thundergnat (talk | contribs) (Rename Perl 6 -> Raku, alphabetize, minor clean-up) |
||
Line 866:
0 0 0 0.51079
</lang>
=={{header|Fortran}}==
Line 980 ⟶ 979:
|| P.A - L.U || = 0.0000000000000000
</pre>
=={{header|Go}}==
Line 1,398 ⟶ 1,396:
0, 0, 0, 1}
</pre>
=={{header|Haskell}}==
Line 1,534 ⟶ 1,531:
1.0000 5.0000 2.0000 6.0000
</pre>
=={{header|Idris}}==
'''works with Idris 0.10'''
Line 2,444 ⟶ 2,442:
[[File:LUex1.png]]
[[File:LUex2.png]]
=={{header|MATLAB}} / {{header|Octave}}==
Line 2,568 ⟶ 2,565:
</lang>
=={{header|Maxima}}==
Line 2,836 ⟶ 2,834:
0 0 -3.47500 5.68750
0 0 0 0.51079</pre>
=={{header|Phix}}==
Line 3,290 ⟶ 3,150:
[0.0, 1.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 1.0]]</pre>
=={{header|R}}==
Line 3,340 ⟶ 3,199:
; #[0 0 -2]])
</lang>
=={{header|Raku}}==
(formerly Perl 6)
{{works with|Rakudo|2015-11-20}}
Translation of Ruby.
<lang perl6>for ( [1, 3, 5], # Test Matrices
[2, 4, 7],
[1, 1, 0]
),
( [11, 9, 24, 2],
[ 1, 5, 2, 6],
[ 3, 17, 18, 1],
[ 2, 5, 7, 1]
)
-> @test {
say-it 'A Matrix', @test;
say-it( $_[0], @($_[1]) ) for 'P Matrix', 'Aʼ Matrix', 'L Matrix', 'U Matrix' Z, lu @test;
}
sub lu (@a) {
die unless @a.&is-square;
my $n = +@a;
my @P = pivotize @a;
my @Aʼ = mmult @P, @a;
my @L = matrix-ident $n;
my @U = matrix-zero $n;
for ^$n -> $i {
for ^$n -> $j {
if $j >= $i {
@U[$i][$j] = @Aʼ[$i][$j] - [+] map { @U[$_][$j] * @L[$i][$_] }, ^$i
} else {
@L[$i][$j] = (@Aʼ[$i][$j] - [+] map { @U[$_][$j] * @L[$i][$_] }, ^$j) / @U[$j][$j];
}
}
}
return @P, @Aʼ, @L, @U;
}
sub pivotize (@m) {
my $size = +@m;
my @id = matrix-ident $size;
for ^$size -> $i {
my $max = @m[$i][$i];
my $row = $i;
for $i ..^ $size -> $j {
if @m[$j][$i] > $max {
$max = @m[$j][$i];
$row = $j;
}
}
if $row != $i {
@id[$row, $i] = @id[$i, $row]
}
}
@id
}
sub is-square (@m) { so @m == all @m[*] }
sub matrix-zero ($n, $m = $n) { map { [ flat 0 xx $n ] }, ^$m }
sub matrix-ident ($n) { map { [ flat 0 xx $_, 1, 0 xx $n - 1 - $_ ] }, ^$n }
sub mmult(@a,@b) {
my @p;
for ^@a X ^@b[0] -> ($r, $c) {
@p[$r][$c] += @a[$r][$_] * @b[$_][$c] for ^@b;
}
@p
}
sub rat-int ($num) {
return $num unless $num ~~ Rat;
return $num.narrow if $num.narrow.WHAT ~~ Int;
$num.nude.join: '/';
}
sub say-it ($message, @array) {
say "\n$message";
$_».&rat-int.fmt("%7s").say for @array;
}</lang>
{{out}}
<pre>A Matrix
1 3 5
2 4 7
1 1 0
P Matrix
0 1 0
1 0 0
0 0 1
Aʼ Matrix
2 4 7
1 3 5
1 1 0
L Matrix
1 0 0
1/2 1 0
1/2 -1 1
U Matrix
2 4 7
0 1 3/2
0 0 -2
A Matrix
11 9 24 2
1 5 2 6
3 17 18 1
2 5 7 1
P Matrix
1 0 0 0
0 0 1 0
0 1 0 0
0 0 0 1
Aʼ Matrix
11 9 24 2
3 17 18 1
1 5 2 6
2 5 7 1
L Matrix
1 0 0 0
3/11 1 0 0
1/11 23/80 1 0
2/11 37/160 1/278 1
U Matrix
11 9 24 2
0 160/11 126/11 5/11
0 0 -139/40 91/16
0 0 0 71/139
</pre>
=={{header|REXX}}==
Line 4,262 ⟶ 4,260:
0, 1, 0, 0,
0, 0, 0, 1, </pre>
=={{header|zkl}}==
Using the GNU Scientific Library, which does the decomposition without returning the permutations:
| |||