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// Copyright ©2017 The Gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package fd
import "gonum.org/v1/gonum/mat"
// Watson implements the Watson's function.
// Dimension of the problem should be 2 <= dim <= 31. For dim == 9, the problem
// of minimizing the function is very ill conditioned.
//
// This is copied from gonum.org/v1/optimize/functions for testing Hessian-like
// derivative methods.
//
// References:
// - Kowalik, J.S., Osborne, M.R.: Methods for Unconstrained Optimization
// Problems. Elsevier North-Holland, New York, 1968
// - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
// optimization software. ACM Trans Math Softw 7 (1981), 17-41
type Watson struct{}
func (Watson) Func(x []float64) (sum float64) {
for i := 1; i <= 29; i++ {
d1 := float64(i) / 29
d2 := 1.0
var s1 float64
for j := 1; j < len(x); 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
sum += t * t
}
t := x[1] - x[0]*x[0] - 1
sum += x[0]*x[0] + t*t
return sum
}
func (Watson) Grad(grad, x []float64) {
if len(x) != len(grad) {
panic("incorrect size of the gradient")
}
for i := range grad {
grad[i] = 0
}
for i := 1; i <= 29; i++ {
d1 := float64(i) / 29
d2 := 1.0
var s1 float64
for j := 1; j < len(x); 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
for j := range x {
grad[j] += d2 * (float64(j) - s3) * t
d2 *= d1
}
}
t := x[1] - x[0]*x[0] - 1
grad[0] += x[0] * (2 - 4*t)
grad[1] += 2 * t
}
func (Watson) Hess(hess mat.MutableSymmetric, x []float64) {
dim := len(x)
if dim != hess.SymmetricDim() {
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)
}
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