1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
|
// Root-finding algorithms.
//
// Copyright (C) 2020 Juan Marín Noguera
//
// This file is part of Solvned.
//
// Solvned is free software: you can redistribute it and/or modify it under the
// terms of the GNU Lesser General Public License as published by the Free
// Software Foundation, either version 3 of the License, or (at your option) any
// later version.
//
// Solvned is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
// A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
// details.
//
// You should have received a copy of the GNU Lesser General Public License
// along with Solvned. If not, see <https://www.gnu.org/licenses/>.
package mstep
import "math"
func NewtonRoot1D(
x0, tolerance float64, f, df func(float64) (float64, bool),
) (float64, bool) {
prev := x0
for {
fprev, ok := f(prev)
if !ok {
return 0, false
}
dfprev, ok := df(prev)
if !ok {
return 0, false
}
off := fprev / dfprev
next := prev - off
if math.Abs(off) <= tolerance {
return next, true
}
prev = next
}
}
func SecantRoot1D(
x0, x1, tolerance float64, f func(float64) (float64, bool),
) (float64, bool) {
prev := x0
fprev, ok := f(prev)
if !ok {
return 0, false
}
cur := x1
fcur, ok := f(cur)
if !ok {
return 0, false
}
for {
off := fcur * (prev - cur) / (fprev - fcur)
next := cur - off
if math.Abs(off) <= tolerance {
return next, true
}
fnext, ok := f(next)
if !ok {
return 0, false
}
prev, fprev, cur, fcur = cur, fcur, next, fnext
}
}
|
