func (BrownBadlyScaled) Hess(hess mat64.MutableSymmetric, x []float64) {
if len(x) != 2 {
panic("dimension of the problem must be 2")
}
if len(x) != hess.Symmetric() {
panic("incorrect size of the Hessian")
}
h00 := 2 + 2*x[1]*x[1]
h01 := 4*x[0]*x[1] - 4
h11 := 2 + 2*x[0]*x[0]
hess.SetSym(0, 0, h00)
hess.SetSym(0, 1, h01)
hess.SetSym(1, 1, h11)
}
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 (PowellBadlyScaled) Hess(hess mat64.MutableSymmetric, x []float64) {
if len(x) != 2 {
panic("dimension of the problem must be 2")
}
if len(x) != hess.Symmetric() {
panic("incorrect size of the Hessian")
}
t1 := 1e4*x[0]*x[1] - 1
s1 := math.Exp(-x[0])
s2 := math.Exp(-x[1])
t2 := s1 + s2 - 1.0001
h00 := 2 * (1e8*x[1]*x[1] + s1*(s1+t2))
h01 := 2 * (1e4*(1+2*t1) + s1*s2)
h11 := 2 * (1e8*x[0]*x[0] + s2*(s2+t2))
hess.SetSym(0, 0, h00)
hess.SetSym(0, 1, h01)
hess.SetSym(1, 1, h11)
}
func (Beale) Hess(hess mat64.MutableSymmetric, x []float64) {
if len(x) != 2 {
panic("dimension of the problem must be 2")
}
if len(x) != hess.Symmetric() {
panic("incorrect size of the Hessian")
}
t1 := 1 - x[1]
t2 := 1 - x[1]*x[1]
t3 := 1 - x[1]*x[1]*x[1]
f1 := 1.5 - x[1]*t1
f2 := 2.25 - x[1]*t2
f3 := 2.625 - x[1]*t3
h00 := 2 * (t1*t1 + t2*t2 + t3*t3)
h01 := 2 * (f1 + x[1]*(2*f2+3*x[1]*f3) - x[0]*(t1+x[1]*(2*t2+3*x[1]*t3)))
h11 := 2 * x[0] * (x[0] + 2*f2 + x[1]*(6*f3+x[0]*x[1]*(4+9*x[1]*x[1])))
hess.SetSym(0, 0, h00)
hess.SetSym(0, 1, h01)
hess.SetSym(1, 1, h11)
}
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))
}
}
}
func (Wood) 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")
}
hess.SetSym(0, 0, 400*(3*x[0]*x[0]-x[1])+2)
hess.SetSym(0, 1, -400*x[0])
hess.SetSym(1, 1, 220.2)
hess.SetSym(0, 2, 0)
hess.SetSym(1, 2, 0)
hess.SetSym(2, 2, 360*(3*x[2]*x[2]-x[3])+2)
hess.SetSym(0, 3, 0)
hess.SetSym(1, 3, 19.8)
hess.SetSym(2, 3, -360*x[2])
hess.SetSym(3, 3, 200.2)
}