示例#1
0
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)
}
示例#2
0
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))
		}
	}
}