LU decomposition: Difference between revisions
→{{header|VBA}}
SqrtNegInf (talk | contribs) (Added Perl example) |
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</pre>
=={{header|VBA}}==
{{trans|Phix}}
<lang vb>Option Base 1
Private Function pivotize(m As Variant) As Variant
Dim n As Integer: n = UBound(m)
Dim im() As Double
ReDim im(n, n)
For i = 1 To n
For j = 1 To n
im(i, j) = 0
Next j
im(i, i) = 1
Next i
For i = 1 To n
mx = m(i, i)
row_ = i
For j = i To n
If m(j, i) > mx Then
mx = m(j, i)
row_ = j
End If
Next j
If i <> Row Then
For j = 1 To n
tmp = im(i, j)
im(i, j) = im(row_, j)
im(row_, j) = tmp
Next j
End If
Next i
pivotize = im
End Function
Private Function lu(a As Variant) As Variant
Dim n As Integer: n = UBound(a)
Dim l() As Double
ReDim l(n, n)
For i = 1 To n
For j = 1 To n
l(i, j) = 0
Next j
Next i
u = l
p = pivotize(a)
a2 = WorksheetFunction.MMult(p, a)
For j = 1 To n
l(j, j) = 1#
For i = 1 To j
sum1 = 0#
For k = 1 To i
sum1 = sum1 + u(k, j) * l(i, k)
Next k
u(i, j) = a2(i, j) - sum1
Next i
For i = j + 1 To n
sum2 = 0#
For k = 1 To j
sum2 = sum2 + u(k, j) * l(i, k)
Next k
l(i, j) = (a2(i, j) - sum2) / u(j, j)
Next i
Next j
Dim res(4) As Variant
res(1) = a
res(2) = l
res(3) = u
res(4) = p
lu = res
End Function
Public Sub main()
a = [{1, 3, 5; 2, 4, 7; 1, 1, 0}]
Debug.Print "== a,l,u,p: =="
result = lu(a)
For i = 1 To 4
For j = 1 To UBound(result(1))
For k = 1 To UBound(result(1), 2)
Debug.Print result(i)(j, k),
Next k
Debug.Print
Next j
Debug.Print
Next i
a = [{11, 9,24, 2; 1, 5, 2, 6; 3,17,18, 1; 2, 5, 7, 1}]
Debug.Print "== a,l,u,p: =="
result = lu(a)
For i = 1 To 4
For j = 1 To UBound(result(1))
For k = 1 To UBound(result(1), 2)
Debug.Print Format(result(i)(j, k), "0.#####"),
Next k
Debug.Print
Next j
Debug.Print
Next i
End Sub</lang>{{out}}
<pre>== a,l,u,p: ==
1 3 5
2 4 7
1 1 0
1 0 0
0,5 1 0
0,5 -1 1
2 4 7
0 1 1,5
0 0 -2
0 1 0
1 0 0
0 0 1
== a,l,u,p: ==
11, 9, 24, 2,
1, 5, 2, 6,
3, 17, 18, 1,
2, 5, 7, 1,
1, 0, 0, 0,
0,27273 1, 0, 0,
0,09091 0,2875 1, 0,
0,18182 0,23125 0,0036 1,
11, 9, 24, 2,
0, 14,54545 11,45455 0,45455
0, 0, -3,475 5,6875
0, 0, 0, 0,51079
1, 0, 0, 0,
0, 0, 1, 0,
0, 1, 0, 0,
0, 0, 0, 1, </pre>
=={{header|zkl}}==
Using the GNU Scientific Library, which does the decomposition without returning the permutations:
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