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 // 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⎦ }