func NumericalHessian(f func(linalg.VectorStructure) float64, x linalg.VectorStructure) linalg.MatrixStructure {
hessianValues := make([][]float64, 0)
for i, iValue := range x {
rowValues := make([]float64, 0)
tempRowVector := x.Remove(i)
var value float64
for j, jValue := range x {
tempRowPlusEpsilon := tempRowVector.Insert(i, iValue+GRADIENT_EPSILON)
tempRowMinusEpsilon := tempRowVector.Insert(i, iValue-GRADIENT_EPSILON)
if i == j {
value = (f(tempRowPlusEpsilon) - 2*f(x) + f(tempRowMinusEpsilon)) / (math.Pow(GRADIENT_EPSILON, 2))
// fmt.Println(tempRowPlusEpsilon, tempRowMinusEpsilon, value)
} else {
tempPlus := tempRowPlusEpsilon.Remove(j)
tempMinus := tempRowMinusEpsilon.Remove(j)
tempPlusPlus := tempPlus.Insert(j, jValue+GRADIENT_EPSILON)
tempPlusMinus := tempPlus.Insert(j, jValue-GRADIENT_EPSILON)
tempMinusPlus := tempMinus.Insert(j, jValue+GRADIENT_EPSILON)
tempMinusMinus := tempMinus.Insert(j, jValue-GRADIENT_EPSILON)
value = (f(tempPlusPlus) - f(tempPlusMinus) - f(tempMinusPlus) + f(tempMinusMinus)) / (4 * math.Pow(GRADIENT_EPSILON, 2))
}
rowValues = append(rowValues, value)
}
hessianValues = append(hessianValues, rowValues)
}
return linalg.NewMatrix(hessianValues)
}
// TODO: A lot to optimize in this method.
func NumericalGradient(f func(linalg.VectorStructure) float64, x linalg.VectorStructure) linalg.VectorStructure {
gradientValues := make([]float64, 0)
for i, value := range x {
tempEpsilon := x.Remove(i)
plusEpsilon := tempEpsilon.Insert(i, value+GRADIENT_EPSILON)
minusEpsilon := tempEpsilon.Insert(i, value-GRADIENT_EPSILON)
gradientValues = append(gradientValues, (f(plusEpsilon)-f(minusEpsilon))/(2*GRADIENT_EPSILON))
}
return linalg.NewVector(gradientValues)
}