func (Watson) Hess(hess mat64.MutableSymmetric, x []float64) {
dim := len(x)
if dim != hess.Symmetric() {
panic("incorrect size of the Hessian")
}
for j := 0; j < dim; j++ {
for k := j; k < dim; k++ {
hess.SetSym(j, k, 0)
}
}
for i := 1; i <= 29; i++ {
d1 := float64(i) / 29
d2 := 1.0
var s1 float64
for j := 1; j < dim; j++ {
s1 += float64(j) * d2 * x[j]
d2 *= d1
}
d2 = 1.0
var s2 float64
for _, v := range x {
s2 += d2 * v
d2 *= d1
}
t := s1 - s2*s2 - 1
s3 := 2 * d1 * s2
d2 = 2 / d1
th := 2 * d1 * d1 * t
for j := 0; j < dim; j++ {
v := float64(j) - s3
d3 := 1 / d1
for k := 0; k <= j; k++ {
hess.SetSym(k, j, hess.At(k, j)+d2*d3*(v*(float64(k)-s3)-th))
d3 *= d1
}
d2 *= d1
}
}
t1 := x[1] - x[0]*x[0] - 1
hess.SetSym(0, 0, hess.At(0, 0)+8*x[0]*x[0]+2-4*t1)
hess.SetSym(0, 1, hess.At(0, 1)-4*x[0])
hess.SetSym(1, 1, hess.At(1, 1)+2)
}
func (BrownAndDennis) Hess(hess mat64.MutableSymmetric, x []float64) {
if len(x) != 4 {
panic("dimension of the problem must be 4")
}
if len(x) != hess.Symmetric() {
panic("incorrect size of the Hessian")
}
for i := 0; i < 4; i++ {
for j := i; j < 4; j++ {
hess.SetSym(i, j, 0)
}
}
for i := 1; i <= 20; i++ {
d1 := float64(i) / 5
d2 := math.Sin(d1)
t1 := x[0] + d1*x[1] - math.Exp(d1)
t2 := x[2] + d2*x[3] - math.Cos(d1)
t := t1*t1 + t2*t2
s3 := 2 * t1 * t2
r1 := t + 2*t1*t1
r2 := t + 2*t2*t2
hess.SetSym(0, 0, hess.At(0, 0)+r1)
hess.SetSym(0, 1, hess.At(0, 1)+d1*r1)
hess.SetSym(1, 1, hess.At(1, 1)+d1*d1*r1)
hess.SetSym(0, 2, hess.At(0, 2)+s3)
hess.SetSym(1, 2, hess.At(1, 2)+d1*s3)
hess.SetSym(2, 2, hess.At(2, 2)+r2)
hess.SetSym(0, 3, hess.At(0, 3)+d2*s3)
hess.SetSym(1, 3, hess.At(1, 3)+d1*d2*s3)
hess.SetSym(2, 3, hess.At(2, 3)+d2*r2)
hess.SetSym(3, 3, hess.At(3, 3)+d2*d2*r2)
}
for i := 0; i < 4; i++ {
for j := i; j < 4; j++ {
hess.SetSym(i, j, 4*hess.At(i, j))
}
}
}