VBAで実装したベクトルの関数群です。基本的な計算なら対応しています。足し算、引き算、スカラー倍、内積、外積、ノルム、正規化です。

vector.vba

Function vector_plus(vect1, vect2)
  ' ベクトルの足し算
  ans = vect1 ' deep copy (たぶん、ディープコピー)
 
  For i = 0 To UBound(ans)
    ans(i) = vect1(i) + vect2(i)
  Next i
  vector_plus = ans
End Function

Function vector_minus(vect1, vect2)
  ' ベクトルの引き算
  ans = vect1 ' deep copy
 
  For i = 0 To UBound(ans)
    ans(i) = vect1(i) - vect2(i)
  Next i
  vector_minus = ans
End Function
Function vector_times(vect, coefficient)
  ' ベクトルに定数を掛ける
  ans = vect ' deep copy
  
  For i = 0 To UBound(vect)
    ans(i) = coefficient * vect(i)
  Next i
  vector_times = ans
End Function

Function vector_inner(vect1, vect2)
  ' ベクトルの内積
  ans = 0
  For i = 0 To UBound(vect1)
    ans = ans + vect1(i) * vect2(i)
  Next i
  vector_inner = ans
End Function
Function vector_cross(vect1, vect2)
  ' ベクトルの外積
  ans = vect1 ' deep copy

  ans(0) = vect1(1) * vect2(2) - vect1(2) * vect2(1)
  ans(1) = vect1(2) * vect2(0) - vect1(0) * vect2(2)
  ans(2) = vect1(0) * vect2(1) - vect1(1) * vect2(0)
  vector_cross = ans
End Function

Function vector_norm(vect)
  ' ベクトルのノルムを返す
  v = vector_inner(vect, vect)
  vector_norm = v ^ 0.5
End Function

Function vector_normalization(vect)
  ' ベクトルの長さを1とする（正規化する）
  Length = vector_norm(vect)
  vector_normalization = vector_times(vect, 1 / Length)
End Function


Sub vector_test()
    ' セルに表示させるテスト
    Dim a() As Double
    b = 100 ' bは変数
    ReDim a(b) ' aの要素数がbで初期化される
    a(0) = 256
    Cells(1, 4) = a ' 第1要素しか表示されない
    
    c = Range("A1:B2")
    Cells(1, 6) = c
    
    r1 = Array(11, 12, 13)
    r2 = Array(21, 22, 23)
    r3 = Array(31, 32, 33)
    d = Array(r1, r2, r3)
    Cells(1, 1) = r1
    
    Dim e(2, 2) As Double
    e(0, 0) = 100
    e(0, 1) = 200
    e(0, 2) = 300
    e(1, 0) = 400
    e(1, 1) = 500
    e(1, 2) = 600
    Cells(1, 1) = e
    Range("a1") = e
    
    Dim f(2) As Double
    f(0) = 100
    f(1) = 123
    f(1) = 256
    Cells(1, 1) = f
    Range("a1") = f
    
    Dim g As Variant
    g = Array()
    ReDim g(2)
    g(0) = 100
    g(1) = 654
    g(2) = 758
    Cells(1, 1) = g
    Range("a1") = g
    

    v1 = Array(11, 12, 13)
    v2 = Array(21, 22, 23)
    v3 = vector_plus(v1, v2)
    v3 = vector_minus(v1, v2)
    v3 = vector_times(v1, 2)
    v3 = vector_inner(v1, v2)
    v3 = vector_norm(v1)
    v3 = vector_normalization(v1)
    
    v1 = Array(1, 0, 0)
    v2 = Array(0, 1, 0)
    v3 = vector_cross(v1, v2)
    
    v3 = vector_norm(v1)
    v3 = vector_normalization(v1)
End Sub