Determinant and permanent: Difference between revisions
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=={{header|VBA}}==
{{trans|Phix}}
As an extra, the results of the built in WorksheetFuction.MDeterm are shown. The latter does not work for scalars.
<lang vb>Option Base 1
Private Function minor(a As Variant, x As Integer, y As Integer) As Variant
Dim l As Integer: l = UBound(a) - 1
Dim result() As Double
If l > 0 Then ReDim result(l, l)
For i = 1 To l
For j = 1 To l
result(i, j) = a(i - (i >= x), j - (j >= y))
Next j
Next i
minor = result
End Function
Private Function det(a As Variant)
If IsArray(a) Then
If UBound(a) = 1 Then
On Error GoTo err
det = a(1, 1)
Exit Function
End If
Else
det = a
Exit Function
End If
Dim sgn_ As Integer: sgn_ = 1
Dim res As Integer: res = 0
Dim i As Integer
For i = 1 To UBound(a)
res = res + sgn_ * a(1, i) * det(minor(a, 1, i))
sgn_ = sgn_ * -1
Next i
det = res
Exit Function
err:
det = a(1)
End Function
Private Function perm(a As Variant) As Double
If IsArray(a) Then
If UBound(a) = 1 Then
On Error GoTo err
perm = a(1, 1)
Exit Function
End If
Else
perm = a
Exit Function
End If
Dim res As Double
Dim i As Integer
For i = 1 To UBound(a)
res = res + a(1, i) * perm(minor(a, 1, i))
Next i
perm = res
Exit Function
err:
perm = a(1)
End Function
Public Sub main()
Dim tests(13) As Variant
tests(1) = [{1, 2; 3, 4}]
'--Determinant: -2, permanent: 10
tests(2) = [{2, 9, 4; 7, 5, 3; 6, 1, 8}]
'--Determinant: -360, permanent: 900
tests(3) = [{ 1, 2, 3, 4; 4, 5, 6, 7; 7, 8, 9, 10; 10, 11, 12, 13}]
'--Determinant: 0, permanent: 29556
tests(4) = [{ 0, 1, 2, 3, 4; 5, 6, 7, 8, 9; 10, 11, 12, 13, 14; 15, 16, 17, 18, 19; 20, 21, 22, 23, 24}]
'--Determinant: 0, permanent: 6778800
tests(5) = [{5}]
'--Determinant: 5, permanent: 5
tests(6) = [{1,0,0; 0,1,0; 0,0,1}]
'--Determinant: 1, permanent: 1
tests(7) = [{0,0,1; 0,1,0; 1,0,0}]
'--Determinant: -1, Permanent: 1
tests(8) = [{4,3; 2,5}]
'--Determinant: 14, Permanent: 26
tests(9) = [{2,5; 4,3}]
'--Determinant: -14, Permanent: 26
tests(10) = [{4,4; 2,2}]
'--Determinant: 0, Permanent: 16
tests(11) = [{7, 2, -2, 4; 4, 4, 1, 7; 11, -8, 9, 10; 10, 5, 12, 13}]
'--det: -4319 permanent: 10723
tests(12) = [{-2, 2, -3; -1, 1, 3; 2 , 0, -1}]
'--det: 18 permanent: 10
tests(13) = 13
Debug.Print "Determinant", "Builtin det", "Permanent"
For i = 1 To 12
Debug.Print det(tests(i)), WorksheetFunction.MDeterm(tests(i)), perm(tests(i))
Next i
Debug.Print det(tests(13)), "error", perm(tests(13))
End Sub</lang>{{out}}
<pre>Determinant Builtin det Permanent
-2 -2 10
-360 -360 900
0 0 29556
0 0 6778800
5 5 5
1 1 1
-1 -1 1
14 14 26
-14 -14 26
0 0 16
-4319 -4319 10723
18 18 10
13 error 13 </pre>
=={{header|zkl}}==
<lang zkl>var [const] GSL=Import("zklGSL"); // libGSL (GNU Scientific Library)
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