LU decomposition: Difference between revisions

=={{header|Sidef}}==

{{trans|Perl 6}}

<lang ruby>func is_square(m) { m.all { .len == m.len } }

func matrix_zero(n, m=n) { m.of { n.of(0) } }

func matrix_ident(n) { n.of {|i| [(i-1).of(0)..., 1, (n-i).of(0)...] } }

func pivotize(m) {

var size = m.len

var id = matrix_ident(size)

for i in ^size {

var max = m[i][i]

var row = i

for j in range(i, size-1) {

if (m[j][i] > max) {

max = m[j][i]

row = j

}

}

if (row != i) {

id.swap(row, i)

}

}

return id

}

func mmult(a, b) {

var p = []

for r,c in (^a ~X ^b[0]) {

for i in ^b {

p[r][c] := 0 += (a[r][i] * b[i][c])

}

}

return p

}

func lu(a) {

is_square(a) || die "Defined only for square matrices!";

var n = a.len

var P = pivotize(a)

var Aʼ = mmult(P, a)

var L = matrix_ident(n)

var U = matrix_zero(n)

for i,j in (^n ~X ^n) {

if (j >= i) {

U[i][j] = (Aʼ[i][j] - (^i->map { U[_][j] * L[i][_] }.sum(0)))

} else {

L[i][j] = ((Aʼ[i][j] - (^j->map { U[_][j] * L[i][_] }.sum(0))) / U[j][j])

}

}

return [P, Aʼ, L, U]

}

func say_it(message, array) {

say "\n#{message}"

array.each { |row|

say row.map{"%7s" % .as_rat}.join(' ')

}

}

var t = [[

%n(1 3 5),

%n(2 4 7),

%n(1 1 0),

],[

%n(11 9 24 2),

%n( 1 5 2 6),

%n( 3 17 18 1),

%n( 2 5 7 1),

]]

t.each { |test|

say_it('A Matrix', test);

for a in (['P Matrix', 'Aʼ Matrix', 'L Matrix', 'U Matrix'] ~Z lu(test)) {

say_it(a[0], a[1])

}

}</lang>

<pre style="height: 40ex; overflow: scroll">

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>