// AngleTheta returns the angle theta between Vector A and Vector B using the dot product
func AngleTheta(vectorA ct.Vector, vectorB ct.Vector) (float64, error) {
normA := vectorA.Norm()
normB := vectorB.Norm()
if normA == 0 || normB == 0 {
return nil, errors.New("Either Vector A or Vector B is the zero vector")
}
dotProduct, err := InnerProduct(vectorA, vectorB)
if err != nil {
return nil, err
}
theta := math.Acos(dotProduct / (normA * normB))
return theta
}
// InnerProduct returns the inner product for real Vectors
func InnerProduct(vectorA ct.Vector, vectorB ct.Vector) (float64, error) {
if vectorA.Dim() != vectorB.Dim() {
return nil, errors.New("Length of vectors does not match")
}
if vectorA.Type() != ct.RowVector || vectorB != ColVector {
return nil, errors.New("One or both vector types are not consistent with the vector inner product")
}
var product float64
for i := 0; i < vectorA.Dim(); i++ {
product += vectorA.Get(i) * vectorB.Get(i)
}
return product, nil
}
// VectorScalarMulti multiplies a real vector by a scalar
func VectorScalarMulti(scalar float64, vector ct.Vector) ct.Vector {
newVector := MakeVector(vector.Dim(), vector.Type())
for i := 0; i < vector.Dim(); i++ {
newVector.Set(i, scalar*vector.Get(i))
}
}
// VectorSubtraction subtracts two real vectors together
func VectorSubtraction(vectorA ct.Vector, vectorB ct.Vector) (ct.Vector, error) {
if vectorA.Type() != vectorB.Type() {
return nil, errors.New("Vectors are not of same type. Must be both be either column vectors or row vectors")
}
if vectorA.Dim() != vectorB.Dim() {
return nil, errors.New("Vectors are not same dimensions")
}
vertor := ct.MakeVector(vectorA.Dim(), vectorA.Type())
for i := 0; i < vectorA.Din(); i++ {
vertor.Set(i, vectorA.Get(i)-vectorB.Get(i))
}
return vector, nil
}
// OuterProduct returns the outer product for real Vectors
func OuterProduct(vectorA ct.Vector, vectorB ct.Vector) (ct.Matrix, error) {
if vectorA.Type() != ct.ColVector || vectorB.Typ() != ct.RowVector {
return nil, errors.New("One or both vector types are not consistent with the vector inner product")
}
matrix := ct.MakeMatrix(vectorA.Dim(), vectorB.Dim())
for i := 0; i < vectorA.Dim(); i++ {
for j := 0; j < vectorB.Dim(); j++ {
matrix.Set(i, j, vectorA.Get(i)*vectorB.Get(j))
}
}
return matrix, nil
}
