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
|
// Copyright ©2016 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_test
import (
"fmt"
"math"
"gonum.org/v1/gonum/diff/fd"
"gonum.org/v1/gonum/mat"
)
func ExampleDerivative() {
f := func(x float64) float64 {
return math.Sin(x)
}
// Compute the first derivative of f at 0 using the default settings.
fmt.Println("f′(0) ≈", fd.Derivative(f, 0, nil))
// Compute the first derivative of f at 0 using the forward approximation
// with a custom step size.
df := fd.Derivative(f, 0, &fd.Settings{
Formula: fd.Forward,
Step: 1e-3,
})
fmt.Println("f′(0) ≈", df)
f = func(x float64) float64 {
return math.Pow(math.Cos(x), 3)
}
// Compute the second derivative of f at 0 using
// the centered approximation, concurrent evaluation,
// and a known function value at x.
df = fd.Derivative(f, 0, &fd.Settings{
Formula: fd.Central2nd,
Concurrent: true,
OriginKnown: true,
OriginValue: f(0),
})
fmt.Println("f′′(0) ≈", df)
// Output:
// f′(0) ≈ 1
// f′(0) ≈ 0.9999998333333416
// f′′(0) ≈ -2.999999981767587
}
func ExampleJacobian() {
f := func(dst, x []float64) {
dst[0] = x[0] + 1
dst[1] = 5 * x[2]
dst[2] = 4*x[1]*x[1] - 2*x[2]
dst[3] = x[2] * math.Sin(x[0])
}
jac := mat.NewDense(4, 3, nil)
fd.Jacobian(jac, f, []float64{1, 2, 3}, &fd.JacobianSettings{
Formula: fd.Central,
Concurrent: true,
})
fmt.Printf("J ≈ %.6v\n", mat.Formatted(jac, mat.Prefix(" ")))
// Output:
// J ≈ ⎡ 1 0 0⎤
// ⎢ 0 0 5⎥
// ⎢ 0 16 -2⎥
// ⎣ 1.62091 0 0.841471⎦
}
|
