func (g *gradientIterator) optimalStep(d linalg.Vector) float64 {
// The optimal step size is (d'*b - c'*A*d)/(d'*A*d)
// where d is the direction, A is the matrix, x is
// the current approximate solution, and b is all 1's.
dMat := &linalg.Matrix{
Rows: len(d),
Cols: 1,
Data: d,
}
ad := linalg.Vector(g.matrix.Mul(dMat).Data)
summer := kahan.NewSummer64()
for _, x := range d {
summer.Add(x)
}
numerator := summer.Sum() - g.solution.Dot(ad)
denominator := d.Dot(ad)
return numerator / denominator
}
// OptimalStep returns the value a which minimizes
// the squared distance between y and x0+a*x.
func (_ SquareLoss) OptimalStep(x0, x, y linalg.Vector) float64 {
return (x.Dot(y) - x.Dot(x0)) / x.Dot(x)
}
