QR decomposition: Difference between revisions
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[[1], [2], [3]]</pre>
=={{header|Futhark}}==
<lang Futhark>
import "lib/github.com/diku-dk/linalg/linalg"
module linalg_f64 = mk_linalg f64
let eye (n: i32): [n][n]f64 =
let arr = map (\ind -> let (i,j) = (ind/n,ind%n) in if (i==j) then 1.0 else 0.0) (iota (n*n))
in unflatten n n arr
let norm v = linalg_f64.dotprod v v |> f64.sqrt
let qr [n] [m] (a: [m][n]f64): ([m][m]f64, [m][n]f64) =
let make_householder [d] (x: [d]f64): [d][d]f64 =
let div = if x[0] > 0 then x[0] + norm x else x[0] - norm x
let v = map (/div) x
let v[0] = 1
let fac = 2.0 / linalg_f64.dotprod v v
in map2 (map2 (-)) (eye d) (map (map (*fac)) (linalg_f64.outer v v))
let step ((x,y):([m][m]f64,[m][n]f64)) (i:i32): ([m][m]f64,[m][n]f64) =
let h = eye m
let h[i:m,i:m] = make_householder y[i:m,i]
let q': [m][m]f64 = linalg_f64.matmul x h
let a': [m][n]f64 = linalg_f64.matmul h y
in (q',a')
let q = eye m
in foldl step (q,a) (iota n)
entry main = qr [[12.0, -51.0, 4.0],[6.0, 167.0, -68.0],[-4.0, 24.0, -41.0]]
</lang>
{{out}}
<pre>
$ ./qr
[[-0.857143f64, 0.394286f64, -0.331429f64], [-0.428571f64, -0.902857f64, 0.034286f64], [0.285714f64, -0.171429f64, -0.942857f64]]
[[-14.000000f64, -21.000000f64, 14.000000f64], [0.000000f64, -175.000000f64, 70.000000f64], [-0.000000f64, 0.000000f64, 35.000000f64]]
</pre>
=={{header|Go}}==
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