func Factors(X, Wo, Ho *sparse.Sparse, tolerance float64, iterations int, limit time.Duration) (W, H *sparse.Sparse, ok bool) {
W = Wo
H = Ho
to := time.Now()
hT := H.T()
wT := W.T()
gW := W.Dot(H.Dot(hT)).Sub(X.Dot(hT))
gH := wT.Dot(W).Dot(H).Sub(wT.Dot(X))
gradient := gW.Stack(gH.T()).Norm(matrix.Fro)
toleranceW := math.Max(0.001, tolerance) * gradient
toleranceH := toleranceW
wFilter := func(r, c int, v float64) bool {
w := W.At(r, c)
return v < 0 || w > 0 // wFilter called with gW as receiver, so v, _ = gW.At(r, c)
}
hFilter := func(r, c int, v float64) bool {
h := H.At(r, c)
return v < 0 || h > 0 // hFilter called with gH as receiver, so v, _ = gH.At(r, c)
}
var (
subOk bool
iW, iH int
)
ok = true
for i := 1; i < iterations; i++ {
projection := sparse.Elements(gW.Filter(wFilter), (gH.Filter(hFilter))).Norm(matrix.Fro)
if projection < tolerance*gradient || time.Now().Sub(to) > limit {
break
}
if W, gW, iW, subOk = subproblem(X.T(), H.T(), W.T(), toleranceW, 1000); iW == 1 {
toleranceW *= 0.1
}
ok = ok && subOk
W = W.T()
gW = gW.T()
if H, gH, iH, subOk = subproblem(X, W, H, toleranceH, 1000); iH == 1 {
toleranceH *= 0.1
}
ok = ok && subOk
}
return
}
func subproblem(X, W, Ho *sparse.Sparse, tolerance float64, iterations int) (H, G *sparse.Sparse, i int, ok bool) {
H = Ho.Copy()
WtV := W.T().Dot(X)
WtW := W.T().Dot(W)
var alpha, beta float64 = 1, 0.1
for i := 0; i < iterations; i++ {
G = WtW.Dot(H).Sub(WtV)
filter := func(r, c int, v float64) bool {
h := H.At(r, c)
return v < 0 || h > 0 // filter called with G as receiver, so v, _ = G.At(r, c)
}
if projection := G.Filter(filter).Norm(matrix.Fro); projection < tolerance {
break
}
}
var (
decrease bool
Hp *sparse.Sparse
)
for j := 0; j < InnerLoop; j++ {
Hn := H.Sub(G.Scalar(alpha))
filter := func(r, c int, v float64) bool {
return v > 0 // filter called with Hn as receiver, so v, _ = Hn.At(r, c)
}
Hn = Hn.Filter(filter)
d := Hn.Sub(H)
gd := G.MulElem(d).Sum()
dQd := WtW.Dot(d).MulElem(d).Sum()
sufficient := 0.99*gd+0.5*dQd < 0
if j == 0 {
decrease = !sufficient
Hp = H.Copy()
}
if decrease {
if sufficient {
H = Hn
ok = true
break
} else {
alpha *= beta
}
} else {
if !sufficient || Hp.Equals(Hn) {
H = Hp
ok = true
break
} else {
alpha /= beta
Hp = Hn.Copy()
}
}
}
return
}