func forward(x *mat64.Dense) (yHat mat64.Dense) {
z2 := mat64.Dense{} // 3x3
a2 := mat64.Dense{} // 3x3
z3 := mat64.Dense{} // 3x1
z2.Mul(x, w1)
a2.Apply(sigmoidApplyable, &z2)
z3.Mul(&a2, w2)
// yHat is 3x1
yHat.Apply(sigmoidApplyable, &z3)
return
}
// Activate propagates the given input matrix (with) across the network
// a certain number of times (up to maxIterations).
//
// The with matrix should be size * size elements, with only the values
// of input neurons set (everything else should be zero).
//
// If the network is conceptually organised into layers, maxIterations
// should be set to the number of layers.
//
// This function overwrites whatever's stored in its first argument.
func (n *Network) Activate(with *mat64.Dense, maxIterations int) {
// Add bias and feed to activation
biasFunc := func(r, c int, v float64) float64 {
return v + n.biases[r]
}
activFunc := func(r, c int, v float64) float64 {
return n.funcs[r].Forward(v)
}
tmp := new(mat64.Dense)
tmp.Clone(with)
// Main loop
for i := 0; i < maxIterations; i++ {
with.Mul(n.weights, with)
with.Apply(biasFunc, with)
with.Apply(activFunc, with)
}
}
func nnlsSubproblem(V, W, Ho *mat64.Dense, tol float64, outer, inner int) (H, G *mat64.Dense, i int, ok bool) {
H = new(mat64.Dense)
H.Clone(Ho)
var WtV, WtW mat64.Dense
WtV.Mul(W.T(), V)
WtW.Mul(W.T(), W)
alpha, beta := 1., 0.1
decFilt := func(r, c int, v float64) float64 {
// decFilt is applied to G, so v = G.At(r, c).
if v < 0 || H.At(r, c) > 0 {
return v
}
return 0
}
G = new(mat64.Dense)
for i = 0; i < outer; i++ {
G.Mul(&WtW, H)
G.Sub(G, &WtV)
G.Apply(decFilt, G)
if mat64.Norm(G, 2) < tol {
break
}
var (
reduce bool
Hp *mat64.Dense
d, dQ mat64.Dense
)
for j := 0; j < inner; j++ {
var Hn mat64.Dense
Hn.Scale(alpha, G)
Hn.Sub(H, &Hn)
Hn.Apply(posFilt, &Hn)
d.Sub(&Hn, H)
dQ.Mul(&WtW, &d)
dQ.MulElem(&dQ, &d)
d.MulElem(G, &d)
sufficient := 0.99*mat64.Sum(&d)+0.5*mat64.Sum(&dQ) < 0
if j == 0 {
reduce = !sufficient
Hp = H
}
if reduce {
if sufficient {
H = &Hn
ok = true
break
} else {
alpha *= beta
}
} else {
if !sufficient || mat64.Equal(Hp, &Hn) {
H = Hp
break
} else {
alpha /= beta
Hp = &Hn
}
}
}
}
return H, G, i, ok
}
func denormalize(matrix *mat64.Dense, max float64) {
matrix.Apply(func(i, j int, elem float64) float64 {
return elem * max
}, matrix)
}