func (this *TrainingSet) Variance_sum(i0, i1 int, mean *Matrix.Matrix, res **Matrix.Matrix, sustract *Matrix.Matrix, done chan<- bool) {
di := i1 - i0
if di >= THRESHOLD {
mi := i0 + di/2
done2 := make(chan bool, THRESHOLD)
res1 := Matrix.NullMatrixP(1, this.Xs.GetNColumns())
res2 := Matrix.NullMatrixP(1, this.Xs.GetNColumns())
go this.Variance_sum(i0, mi, mean, &res1, sustract, done2)
go this.Variance_sum(mi, i1, mean, &res1, sustract, done2)
<-done2
<-done2
SP, _ := Matrix.Sum(res1, res2)
*res = SP
} else {
for i := i0; i <= i1; i++ {
xsi := this.Xs.GetRow(i)
Sustract, _ := Matrix.Sustract(mean, xsi)
Square := Matrix.DotMultiplication(Sustract, Sustract)
sustract.SetRow(i, Sustract)
SP, _ := Matrix.Sum(Square, *res)
*res = SP
}
}
done <- true
}
func DSoftmax(X *Matrix.Matrix) *Matrix.Matrix {
Total := 1 / X.TaxicabNorm()
Y := X.Scalar(complex(Total, 0))
S, _ := Matrix.Sustract(Matrix.FixValueMatrix(X.GetNColumns(), X.GetNColumns(), 1.0), X)
YD := Matrix.DotMultiplication(Y, S)
return YD
}
func DerivateHalfDistance(T, O *Matrix.Matrix) *Matrix.Matrix {
r, _ := Matrix.Sustract(T, O)
return r
}
func GradientDescent(alpha complex128, Tolerance complex128, ts *TrainingSet, f func(x complex128) complex128) *Hypothesis {
n := ts.Xs.GetNColumns()
m := ts.Xs.GetMRows()
//Xsc:=ts.Xs.Copy()
ts.AddX0() // add the parametrer x0, with value 1, to all elements of the training set
t := Matrix.NullMatrixP(1, n+1) // put 0 to the parameters theta
thetaP := t
//thetaP:=Matrix.RandomMatrix(1,n+1) // Generates a random values of parameters theta
var h1 Hypothesis
h1.H = f
h1.ThetaParameters = thetaP
var Error complex128
Error = complex(1.0, 0)
var it = 1
diferencia, diferenciaT := h1.Parallel_DiffH1Ys(ts)
jt := Matrix.Product(diferenciaT, diferencia).Scalar(1/complex(2.0*float64(m), 0.0)).GetValue(1, 1)
alpha = 1 / jt
for cmplx.Abs(Error) >= cmplx.Abs(Tolerance) { // Until converges
ThetaPB := h1.ThetaParameters.Copy() //for Error Calc
//diff:=h1.DiffH1Ys(ts)
_, diffT := h1.Parallel_DiffH1Ys(ts) //h(x)-y
product := Matrix.Product(diffT, ts.Xs) //Sum( (hi(xi)-yi)*xij) in matrix form
h1.Sum = product
alpha_it := alpha / (cmplx.Sqrt(complex(float64(it), 0.0))) // re-calc alpha
scalar := product.Scalar(-alpha_it / complex(float64(m), 0.0))
//println("Delta", scalar.ToString())
ThetaTemp, _ := Matrix.Sum(h1.ThetaParameters, scalar) //Theas=Theas-alfa/m*Sum( (hi(xi)-yi)*xij) update the parameters
h1.ThetaParameters = ThetaTemp
diffError, _ := Matrix.Sustract(ThetaPB, h1.ThetaParameters) //diff between theta's Vector , calc the error
Error = complex(diffError.FrobeniusNorm(), 0) //Frobenius Norm
//Error=diffError.InfinityNorm() //Infinty Norm
//println("->", h1.ThetaParameters.ToString())
//println("Error", Error)
/*if it > 10 {
break
}*/
it++
}
h1.M = m
return &h1
}