Determinant and permanent: Difference between revisions

Content added Content deleted
(→‎{{header|Raku}}: Fix up some internal links)
(→‎{{header|Raku}}: add a test with a Hilbert matrix)
Line 1,909: Line 1,909:
note "Not a square matrix" and return
note "Not a square matrix" and return
if [||] map { @a.elems cmp @a[$_].elems }, ^@a;
if [||] map { @a.elems cmp @a[$_].elems }, ^@a;
[+] map {
sum σ_permutations([^@a]).race.map: {
my $permutation = .key;
my $permutation = .key;
my $term = $op eq 'perm' ?? 1 !! .value;
my $term = $op eq 'perm' ?? 1 !! .value;
for $permutation.kv -> $i, $j { $term *= @a[$i][$j] };
for $permutation.kv -> $i, $j { $term *= @a[$i][$j] };
$term
$term
⚫
}
}, σ_permutations [^@a];
}
}


########### Testing ###########
######### helper subs #########
sub hilbert-matrix (\h) {[(1..h).map(-> \n {[(n..^n+h).map: {(1/$_).FatRat}]})]}

sub rat-or-int ($num) {
return $num unless $num ~~ Rat|FatRat;
return $num.narrow if $num.narrow.WHAT ~~ Int;
$num.nude.join: '/';
⚫
}

sub say-it ($message, @array) {
⚫
my $max;
@array.map: {$max max= max $_».&rat-or-int.comb(/\S+/)».chars};
⚫
say "\n$message";
$_».&rat-or-int.fmt(" %{$max}s").put for @array;
}


########### Testing ###########
my @tests = (
my @tests = (
[
[
Line 1,930: Line 1,945:
[ 10, 11, 12, 13 ]
[ 10, 11, 12, 13 ]
],
],
hilbert-matrix 7
⚫
[
⚫
[ 0, 1, 2, 3, 4 ],
⚫
[ 5, 6, 7, 8, 9 ],
[ 10, 11, 12, 13, 14 ],
[ 15, 16, 17, 18, 19 ],
[ 20, 21, 22, 23, 24 ]
]
);
);

sub dump (@matrix) {
say $_».fmt: "%3s" for @matrix;
⚫
say '';
⚫
}


for @tests -> @matrix {
for @tests -> @matrix {
say 'Matrix:';
say-it 'Matrix:', @matrix;
@matrix.&dump;
say "Determinant:\t", rat-or-int @matrix.&m_arith: <det>;
say "Determinant:\t", @matrix.&m_arith: <det>;
say "Permanent: \t", rat-or-int @matrix.&m_arith: <perm>;
say "Permanent: \t", @matrix.&m_arith: <perm>;
say '-' x 40;
⚫
say '-' x 25;
}</lang>
}</lang>


'''Output'''
'''Output'''
<pre>Matrix:
<pre>Matrix:
[ 1 2]
1 2
[ 3 4]
3 4

Determinant: -2
Determinant: -2
Permanent: 10
Permanent: 10
-------------------------
----------------------------------------

Matrix:
Matrix:
[ 1 2 3 4]
1 2 3 4
[ 4 5 6 7]
4 5 6 7
[ 7 8 9 10]
7 8 9 10
[ 10 11 12 13]
10 11 12 13

Determinant: 0
Determinant: 0
Permanent: 29556
Permanent: 29556
-------------------------
----------------------------------------

Matrix:
Matrix:
[ 0 1 2 3 4]
1 1/2 1/3 1/4 1/5 1/6 1/7
[ 5 6 7 8 9]
1/2 1/3 1/4 1/5 1/6 1/7 1/8
⚫
1/3 1/4 1/5 1/6 1/7 1/8 1/9
[ 10 11 12 13 14]
1/4 1/5 1/6 1/7 1/8 1/9 1/10
[ 15 16 17 18 19]
1/5 1/6 1/7 1/8 1/9 1/10 1/11
[ 20 21 22 23 24]
⚫
1/6 1/7 1/8 1/9 1/10 1/11 1/12

1/7 1/8 1/9 1/10 1/11 1/12 1/13
Determinant: 0
Determinant: 1/2067909047925770649600000
Permanent: 6778800
Permanent: 29453515169174062608487/2067909047925770649600000
-------------------------</pre>
----------------------------------------</pre>


=={{header|REXX}}==
=={{header|REXX}}==
Retrieved from "https://rosettacode.org/wiki/Determinant_and_permanent"