Cholesky decomposition: Difference between revisions
Added AutoHotkey
(With Numeric.LinearAlgebra) |
Alpha bravo (talk | contribs) (Added AutoHotkey) |
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( 9.89949, 1.62455, 1.84971, 1.39262))
</pre>
=={{header|AutoHotkey}}==
<lang AutoHotkey>Cholesky_Decomposition(A){
L := [], n := A.Count()
L[1,1] := Sqrt(A[1,1])
loop % n {
k := A_Index
loop % n-1 {
i := A_Index+1
Sigma := 0, j := 0
while (++j <= k-1)
Sigma += L[i, j] * L[k, j]
L[i, k] := (A[i, k] - Sigma) / L[k, k]
Sigma := 0, j := 0
while (++j <= k-1)
Sigma += (L[k, j])**2
L[k, k] := Sqrt(A[k, k] - Sigma)
}
}
loop % n{
k := A_Index
loop % n
L[k, A_Index] := L[k, A_Index] ? L[k, A_Index] : 0
}
return L
}
ShowMatrix(L){
for r, obj in L{
row := ""
for c, v in obj
row .= Format("{:.3f}", v) ", "
output .= "[" trim(row, ", ") "]`n,"
}
return "[" Trim(output, "`n,") "]"
}</lang>
Examples:<lang AutoHotkey>A := [[25, 15, -5]
, [15, 18, 0]
, [-5, 0 , 11]]
L1 := Cholesky_Decomposition(A)
A := [[18, 22, 54, 42]
, [22, 70, 86, 62]
, [54, 86, 174, 134]
, [42, 62, 134, 106]]
L2 := Cholesky_Decomposition(A)
MsgBox % Result := ShowMatrix(L1) "`n----`n" ShowMatrix(L2) "`n----"
return</lang>
{{out}}
<pre>[[5.000, 0.000, 0.000]
,[3.000, 3.000, 0.000]
,[-1.000, 1.000, 3.000]]
----
[[4.243, 0.000, 0.000, 0.000]
,[5.185, 6.566, 0.000, 0.000]
,[12.728, 3.046, 1.650, 0.000]
,[9.899, 1.625, 1.850, 1.393]]
----</pre>
=={{header|BBC BASIC}}==
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