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69 lines
1.7 KiB
Go
69 lines
1.7 KiB
Go
// Copyright ©2016 The Gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package fd_test
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import (
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"fmt"
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"math"
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"gonum.org/v1/gonum/diff/fd"
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"gonum.org/v1/gonum/mat"
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)
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func ExampleDerivative() {
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f := func(x float64) float64 {
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return math.Sin(x)
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}
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// Compute the first derivative of f at 0 using the default settings.
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fmt.Println("f′(0) ≈", fd.Derivative(f, 0, nil))
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// Compute the first derivative of f at 0 using the forward approximation
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// with a custom step size.
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df := fd.Derivative(f, 0, &fd.Settings{
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Formula: fd.Forward,
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Step: 1e-3,
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})
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fmt.Println("f′(0) ≈", df)
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f = func(x float64) float64 {
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return math.Pow(math.Cos(x), 3)
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}
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// Compute the second derivative of f at 0 using
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// the centered approximation, concurrent evaluation,
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// and a known function value at x.
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df = fd.Derivative(f, 0, &fd.Settings{
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Formula: fd.Central2nd,
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Concurrent: true,
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OriginKnown: true,
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OriginValue: f(0),
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})
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fmt.Println("f′′(0) ≈", df)
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// Output:
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// f′(0) ≈ 1
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// f′(0) ≈ 0.9999998333333416
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// f′′(0) ≈ -2.999999981767587
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}
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func ExampleJacobian() {
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f := func(dst, x []float64) {
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dst[0] = x[0] + 1
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dst[1] = 5 * x[2]
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dst[2] = 4*x[1]*x[1] - 2*x[2]
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dst[3] = x[2] * math.Sin(x[0])
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}
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jac := mat.NewDense(4, 3, nil)
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fd.Jacobian(jac, f, []float64{1, 2, 3}, &fd.JacobianSettings{
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Formula: fd.Central,
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Concurrent: true,
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})
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fmt.Printf("J ≈ %.6v\n", mat.Formatted(jac, mat.Prefix(" ")))
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// Output:
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// J ≈ ⎡ 1 0 0⎤
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// ⎢ 0 0 5⎥
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// ⎢ 0 16 -2⎥
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// ⎣ 1.62091 0 0.841471⎦
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}
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