Cholesky decomposition: Difference between revisions
Frink
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12.72792 3.04604 1.64974 0.00000
9.89949 1.62455 1.84971 1.39262</pre>
=={{header|Frink}}==
Frink's package [https://frinklang.org/fsp/colorize.fsp?f=Matrix.frink Matrix.frink] contains routines for Cholesky-Crout decomposition of a square Hermitian matrix (which can be real or complex.) This code is adapted from that more powerful class to work on raw 2-dimensional arrays. This also demonstrates Frink's layout routines.
<syntaxhighlight lang="frink">Cholesky[array] :=
{
n = length[array]
L = new array[[n,n], 0]
for j = 0 to n-1
{
sum = 0
for k = 0 to j-1
sum = sum + (L@j@k)^2
L@j@j = sqrt[array@j@j - sum]
for i = j+1 to n-1
{
sum = 0
for k = 0 to j-1
sum = sum + L@i@k * L@j@k
L@i@j = (1 / L@j@j * (array@i@j -sum))
}
}
return L
}
A = [[ 25, 15, -5],
[ 15, 18, 0],
[ -5, 0, 11]]
println[formatTable[[[formatMatrix[A], "->", formatMatrix[Cholesky[A]]]]]]
B = [[18, 22, 54, 42],
[22, 70, 86, 62],
[54, 86, 174, 134],
[42, 62, 134, 106]]
println[formatTable[[[formatMatrix[B], "->", formatMatrix[formatFix[Cholesky[B], 1, 5]]]]]]</syntaxhighlight>
{{out}}
<pre>
┌ ┐ ┌ ┐
│25 15 -5│ │ 5 0 0│
│ │ │ │
│15 18 0│ -> │ 3 3 0│
│ │ │ │
│-5 0 11│ │-1 1 3│
└ ┘ └ ┘
┌ ┐ ┌ ┐
│18 22 54 42│ │ 4.24264 0.00000 0.00000 0.00000│
│ │ │ │
│22 70 86 62│ │ 5.18545 6.56591 0.00000 0.00000│
│ │ -> │ │
│54 86 174 134│ │12.72792 3.04604 1.64974 0.00000│
│ │ │ │
│42 62 134 106│ │ 9.89949 1.62455 1.84971 1.39262│
└ ┘ └ ┘
</pre>
=={{header|Go}}==
===Real===
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