//TODO the activation function and his Derviate has to be more general.. to implemente soft-max for example
func (this *ANN) ForwardPropagation(In *Matrix.Matrix) (As, AsDerviate *([]*Matrix.Matrix), Output *Matrix.Matrix) {
if In.GetMRows() == this.Inputs && In.GetNColumns() == 1 {
As1 := make([]*Matrix.Matrix, len(this.Weights)+1, len(this.Weights)+1)
AsDerviate1 := make([]*Matrix.Matrix, len(this.Weights)+1, len(this.Weights)+1)
As := &As1
AsDerviate = &AsDerviate1
sTemp := In.Transpose()
//Add a new column for a Bias Weight
sTemp = sTemp.AddColumn(Matrix.I(1))
holeInput := sTemp.Copy()
As1[0] = sTemp.Transpose()
//Derivate
//sutract, _ := Matrix.Sustract(Matrix.OnesMatrix(As1[0].GetMRows(), 1), As1[0])
//derivate := Matrix.DotMultiplication(As1[0], sutract)
//derivate := holeInput.Apply(this.Derivate)
derivate := this.DarivateActivationLayer(holeInput)
AsDerviate1[0] = derivate.Transpose()
for i := 0; i < len(this.Weights); i++ {
sTemp = Matrix.Product(sTemp, (this.Weights[i]))
//apply the activation functions
holeInput := sTemp.Copy()
sTemp = this.ActivationLayer(sTemp)
//sTemp = sTemp.Apply(this.Activation)
//Add a new column for a Bias Weight
sTemp = sTemp.AddColumn(Matrix.I(1))
(*As)[i+1] = sTemp.Transpose()
//Derivate
//sutract, _ := Matrix.Sustract(Matrix.OnesMatrix((*As)[i+1].GetMRows(), 1), (*As)[i+1])
//derivate := Matrix.DotMultiplication((*As)[i+1], sutract)
derivate := this.DarivateActivationLayer(holeInput)
//derivate := holeInput.Apply(this.Derivate)
(*AsDerviate)[i+1] = derivate.Transpose()
}
Asf := sTemp.Copy()
//Asf = Asf.AddColumn(Matrix.I(1))
(*As)[len(As1)-1] = Asf.Transpose()
Output = sTemp.Transpose().MatrixWithoutLastRow()
return As, AsDerviate, Output
}
return nil, nil, nil
}
func NormalEquation(ts *TrainingSet) *Hypothesis {
// n:=ts.Xs.GetNColumns()
// m:=ts.Xs.GetMRows().
ts.AddX0()
println(ts.Xs.ToString())
Xst := ts.Xs.Transpose()
mult := Matrix.Product(Xst, ts.Xs)
pinv := mult.PInverse()
xT := Matrix.Product(pinv, Xst)
theta := Matrix.Product(xT, ts.Y)
var h1 Hypothesis
h1.ThetaParameters = theta
return &h1
}
func (this *ANN) BackPropagation(As, AsDerviate *[](*Matrix.Matrix), ForwardOutput *Matrix.Matrix, Y *Matrix.Matrix, flen float64) {
ð := this.DerviateCostFunction(ForwardOutput, Y)
this.ð[len(this.ð)-1] = ð
this.AcumatedError, _ = Matrix.Sum(this.CostFunction(ForwardOutput, Y), this.AcumatedError)
for i := len(this.Weights) - 1; i >= 0; i-- {
A := (*As)[i]
Aderviate := (*AsDerviate)[i]
var ðtemp *Matrix.Matrix
if i == len(this.Weights)-1 {
ðtemp = this.ð[i+1].Transpose()
} else {
ðtemp = this.ð[i+1].MatrixWithoutLastRow().Transpose()
}
//Calc ð
//fmt.Println("ð(i+1)", this.ð[i+1].ToString())
//fmt.Println("W(i)", this.Weights[i].ToString())
Product := Matrix.Product(this.Weights[i], ðtemp.Transpose())
//fmt.Println("Product", i, " ", Product.ToString())
this.ð[i] = Matrix.DotMultiplication(Product, Aderviate.AddRowsToDown(Matrix.I(1)))
//Calc of Derivate with respect to the Weights
//ðtemp:= i==len(this.Weights) - 1? this.ð[i+1].Transpose() : this.ð[i+1].MatrixWithoutLastRow().Transpose()
Dw := Matrix.Product(A, ðtemp)
this.Δ[i], _ = Matrix.Sum(this.Δ[i], Dw)
}
return
}
func (this *Hypothesis) Evaluate(x *Matrix.Matrix) (complex128, error) {
x0 := Matrix.NullMatrixP(1, 1)
x0.SetValue(1, 1, 1)
x0 = x0.AddColumn(x)
if x0.GetNColumns() == this.ThetaParameters.GetNColumns() {
xt := x0.Transpose()
res := Matrix.Product(this.ThetaParameters, xt)
return this.H(res.GetValue(1, 1)), nil
}
return 0, errors.New(" The number of parameters is not equal to the parameters of the hypotesis")
}
func (this *Hypothesis) DiffH1Ys(Ts TrainingSet) *Matrix.Matrix {
m := Ts.Xs.GetMRows()
hx := Matrix.NullMatrixP(m, 1)
if this.ThetaParameters.GetNColumns() == Ts.Xs.GetNColumns() {
for i := 1; i <= Ts.Xs.GetMRows(); i++ {
xi := Ts.Xs.GetRow(i)
Thi := Matrix.Product(xi, this.ThetaParameters.Transpose())
hx.SetValue(i, 1, Thi.GetValue(1, 1)-Ts.Y.GetValue(1, i))
}
return hx
}
return nil
}
func (this *Hypothesis) part_DiffH1Ys(i0, i1 int, Ts *TrainingSet, Ret *Matrix.Matrix, RetT *Matrix.Matrix, done chan<- bool) {
di := i1 - i0
if di >= THRESHOLD && runtime.NumGoroutine() < maxGoRoutines {
done2 := make(chan bool, THRESHOLD)
mi := i0 + di/2
go this.part_DiffH1Ys(i0, mi, Ts, Ret, RetT, done2)
go this.part_DiffH1Ys(mi, i1, Ts, Ret, RetT, done2)
<-done2
<-done2
} else {
for i := i0; i <= i1; i++ {
xi := Ts.Xs.GetRow(i)
Thi := Matrix.Product(xi, this.ThetaParameters.Transpose())
temp := this.H(Thi.GetValue(1, 1)) - Ts.Y.GetValue(1, i)
Ret.SetValue(i, 1, temp)
RetT.SetValue(1, i, temp)
}
}
done <- true
}
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
}
