Geometric algebra: Difference between revisions
→{{header|Python}}
Line 1,903:
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]</pre>
=={{header|Visual Basic .NET}}==
{{trans|C#}}
<lang vbnet>Option Strict On
Imports System.Text
Module Module1
Structure Vector
Private ReadOnly dims() As Double
Public Sub New(da() As Double)
dims = da
End Sub
Public Shared Operator -(v As Vector) As Vector
Return v * -1.0
End Operator
Public Shared Operator +(lhs As Vector, rhs As Vector) As Vector
Dim result(31) As Double
Array.Copy(lhs.dims, 0, result, 0, lhs.Length)
For i = 1 To result.Length
Dim i2 = i - 1
result(i2) = lhs(i2) + rhs(i2)
Next
Return New Vector(result)
End Operator
Public Shared Operator *(lhs As Vector, rhs As Vector) As Vector
Dim result(31) As Double
For i = 1 To lhs.Length
Dim i2 = i - 1
If lhs(i2) <> 0.0 Then
For j = 1 To lhs.Length
Dim j2 = j - 1
If rhs(j2) <> 0.0 Then
Dim s = ReorderingSign(i2, j2) * lhs(i2) * rhs(j2)
Dim k = i2 Xor j2
result(k) += s
End If
Next
End If
Next
Return New Vector(result)
End Operator
Public Shared Operator *(v As Vector, scale As Double) As Vector
Dim result = CType(v.dims.Clone, Double())
For i = 1 To result.Length
Dim i2 = i - 1
result(i2) *= scale
Next
Return New Vector(result)
End Operator
Default Public Property Index(key As Integer) As Double
Get
Return dims(key)
End Get
Set(value As Double)
dims(key) = value
End Set
End Property
Public ReadOnly Property Length As Integer
Get
Return dims.Length
End Get
End Property
Public Function Dot(rhs As Vector) As Vector
Return (Me * rhs + rhs * Me) * 0.5
End Function
Private Shared Function BitCount(i As Integer) As Integer
i -= ((i >> 1) And &H55555555)
i = (i And &H33333333) + ((i >> 2) And &H33333333)
i = (i + (i >> 4)) And &HF0F0F0F
i += (i >> 8)
i += (i >> 16)
Return i And &H3F
End Function
Private Shared Function ReorderingSign(i As Integer, j As Integer) As Double
Dim k = i >> 1
Dim sum = 0
While k <> 0
sum += BitCount(k And j)
k >>= 1
End While
Return If((sum And 1) = 0, 1.0, -1.0)
End Function
Public Overrides Function ToString() As String
Dim it = dims.GetEnumerator
Dim sb As New StringBuilder("[")
If it.MoveNext() Then
sb.Append(it.Current)
End If
While it.MoveNext
sb.Append(", ")
sb.Append(it.Current)
End While
sb.Append("]")
Return sb.ToString
End Function
End Structure
Function DoubleArray(size As Integer) As Double()
Dim result(size - 1) As Double
For i = 1 To size
Dim i2 = i - 1
result(i2) = 0.0
Next
Return result
End Function
Function E(n As Integer) As Vector
If n > 4 Then
Throw New ArgumentException("n must be less than 5")
End If
Dim result As New Vector(DoubleArray(32))
result(1 << n) = 1.0
Return result
End Function
ReadOnly r As New Random()
Function RandomVector() As Vector
Dim result As New Vector(DoubleArray(32))
For i = 1 To 5
Dim i2 = i - 1
Dim singleton() As Double = {r.NextDouble()}
result += New Vector(singleton) * E(i2)
Next
Return result
End Function
Function RandomMultiVector() As Vector
Dim result As New Vector(DoubleArray(32))
For i = 1 To result.Length
Dim i2 = i - 1
result(i2) = r.NextDouble()
Next
Return result
End Function
Sub Main()
For i = 1 To 5
Dim i2 = i - 1
For j = 1 To 5
Dim j2 = j - 1
If i2 < j2 Then
If E(i2).Dot(E(j2))(0) <> 0.0 Then
Console.Error.WriteLine("Unexpected non-null scalar product")
Return
End If
ElseIf i2 = j2 Then
If E(i2).Dot(E(j2))(0) = 0.0 Then
Console.Error.WriteLine("Unexpected null scalar product")
Return
End If
End If
Next
Next
Dim a = RandomMultiVector()
Dim b = RandomMultiVector()
Dim c = RandomMultiVector()
Dim x = RandomVector()
' (ab)c == a(bc)
Console.WriteLine((a * b) * c)
Console.WriteLine(a * (b * c))
Console.WriteLine()
' a(b+c) == ab + ac
Console.WriteLine(a * (b + c))
Console.WriteLine(a * b + a * c)
Console.WriteLine()
' (a+b)c == ac + bc
Console.WriteLine((a + b) * c)
Console.WriteLine(a * c + b * c)
Console.WriteLine()
' x^2 is real
Console.WriteLine(x * x)
End Sub
End Module</lang>
{{out}}
<pre>[0.574263754349833, -1.04033308353824, -0.776121961159351, 2.00792496222078, 3.16921091358851, 6.73557610270275, -13.4327886840529, -7.74195172209513, -7.21674283588092, -5.86045645950882, 2.22312083899981, 1.32215440847646, -6.14796858424355, -6.31067579900569, -8.24016821785677, -7.13138966213629, 1.70037903072841, -1.61670055512076, -1.53920826677554, 0.0830404550813257, 3.93618132588852, 7.40029585163889, -6.36594388310886, 2.14605789872596, -12.3353817163416, -9.51720072572794, 4.57164353732716, 3.11601890765627, -3.45821025466289, -4.2333151576991, -5.88080545860622, -6.53549242641427]
[0.574263754349836, -1.04033308353825, -0.776121961159348, 2.00792496222078, 3.16921091358851, 6.73557610270275, -13.4327886840529, -7.74195172209514, -7.21674283588092, -5.86045645950883, 2.2231208389998, 1.32215440847646, -6.14796858424355, -6.31067579900569, -8.24016821785676, -7.13138966213629, 1.70037903072841, -1.61670055512076, -1.53920826677554, 0.0830404550813244, 3.93618132588852, 7.40029585163889, -6.36594388310886, 2.14605789872596, -12.3353817163416, -9.51720072572794, 4.57164353732716, 3.11601890765627, -3.4582102546629, -4.2333151576991, -5.88080545860622, -6.53549242641427]
[-4.47297646716049, -5.51675159908628, -2.0422292306007, -2.10280367601528, 4.45365145957714, 3.36803601730516, -1.14571129439412, -0.425208328771765, 1.55145295736126, 1.59542278752789, 5.96209903766593, 3.43000773717995, -1.93701906000176, -0.282031417434974, 2.27435916727966, 5.57909608271093, -4.5313823118833, -5.23492105300004, -1.61573387363407, -2.77225954890565, 2.7749883436186, 2.47317184825279, -1.66854919690689, -1.04001004327011, 0.314038463700274, 0.354414497531512, 6.65882395905864, 4.84274526210668, -1.26994943017024, 0.867830239054973, 5.4316876690133, 8.85070336472853]
[-4.47297646716048, -5.51675159908628, -2.0422292306007, -2.10280367601528, 4.45365145957714, 3.36803601730516, -1.14571129439412, -0.425208328771764, 1.55145295736126, 1.59542278752789, 5.96209903766592, 3.43000773717995, -1.93701906000176, -0.282031417434974, 2.27435916727966, 5.57909608271093, -4.5313823118833, -5.23492105300004, -1.61573387363407, -2.77225954890565, 2.7749883436186, 2.47317184825279, -1.66854919690689, -1.04001004327011, 0.314038463700274, 0.354414497531512, 6.65882395905864, 4.84274526210668, -1.26994943017024, 0.867830239054973, 5.4316876690133, 8.85070336472853]
[-5.22293180574195, -5.83486719133951, -1.69911127655253, -0.239172378976677, 2.88101068267363, 3.97970294192276, -3.56156896393757, -2.61790431554284, -0.736020241689734, -0.776473740587332, 3.0171422268862, 2.15992705303214, -3.20043960767084, -0.644050812810021, 0.714338263909879, 1.74591314489993, -4.38202839888319, -3.26051280533051, -4.05531615492948, -2.93703039040279, 3.56583825504966, 4.17636250632614, -1.11524349520128, -3.21090579244331, 1.27680857237575, 2.37418947249269, 4.48848909104827, 3.7920821695994, -3.71929857788004, 0.286175312382222, 6.0485010014393, 8.27326094456212]
[-5.22293180574195, -5.83486719133951, -1.69911127655253, -0.239172378976677, 2.88101068267363, 3.97970294192276, -3.56156896393757, -2.61790431554284, -0.736020241689734, -0.776473740587333, 3.0171422268862, 2.15992705303214, -3.20043960767084, -0.644050812810022, 0.71433826390988, 1.74591314489993, -4.38202839888319, -3.2605128053305, -4.05531615492948, -2.93703039040279, 3.56583825504966, 4.17636250632614, -1.11524349520128, -3.21090579244331, 1.27680857237575, 2.37418947249269, 4.48848909104827, 3.7920821695994, -3.71929857788004, 0.286175312382223, 6.0485010014393, 8.27326094456212]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]</pre>
| |||