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5f0141ca4c
Changes made in dsp/fourier/internal/fftpack break the formatting used there, so these are reverted. There will be complaints in CI. [git-generate] gofmt -w . go generate gonum.org/v1/gonum/blas go generate gonum.org/v1/gonum/blas/gonum go generate gonum.org/v1/gonum/unit go generate gonum.org/v1/gonum/unit/constant go generate gonum.org/v1/gonum/graph/formats/dot go generate gonum.org/v1/gonum/graph/formats/rdf go generate gonum.org/v1/gonum/stat/card git checkout -- dsp/fourier/internal/fftpack
73 lines
1.8 KiB
Go
73 lines
1.8 KiB
Go
// Copyright ©2019 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 integrate
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import "sort"
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// Simpsons returns an approximate value of the integral
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//
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// \int_a^b f(x)dx
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//
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// computed using the Simpsons's method. The function f is given as a slice of
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// samples evaluated at locations in x, that is,
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//
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// f[i] = f(x[i]), x[0] = a, x[len(x)-1] = b
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//
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// The slice x must be sorted in strictly increasing order. x and f must be of
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// equal length and the length must be at least 3.
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//
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// See https://en.wikipedia.org/wiki/Simpson%27s_rule#Composite_Simpson's_rule_for_irregularly_spaced_data
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// for more information.
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func Simpsons(x, f []float64) float64 {
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n := len(x)
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switch {
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case len(f) != n:
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panic("integrate: slice length mismatch")
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case n < 3:
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panic("integrate: input data too small")
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case !sort.Float64sAreSorted(x):
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panic("integrate: must be sorted")
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}
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var integral float64
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for i := 1; i < n-1; i += 2 {
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h0 := x[i] - x[i-1]
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h1 := x[i+1] - x[i]
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if h0 == 0 || h1 == 0 {
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panic("integrate: repeated abscissa")
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}
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h0p2 := h0 * h0
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h0p3 := h0 * h0 * h0
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h1p2 := h1 * h1
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h1p3 := h1 * h1 * h1
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hph := h0 + h1
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a0 := (2*h0p3 - h1p3 + 3*h1*h0p2) / (6 * h0 * hph)
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a1 := (h0p3 + h1p3 + 3*h0*h1*hph) / (6 * h0 * h1)
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a2 := (-h0p3 + 2*h1p3 + 3*h0*h1p2) / (6 * h1 * hph)
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integral += a0 * f[i-1]
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integral += a1 * f[i]
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integral += a2 * f[i+1]
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}
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if n%2 == 0 {
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h0 := x[n-2] - x[n-3]
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h1 := x[n-1] - x[n-2]
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if h0 == 0 || h1 == 0 {
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panic("integrate: repeated abscissa")
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}
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h1p2 := h1 * h1
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h1p3 := h1 * h1 * h1
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hph := h0 + h1
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a0 := -1 * h1p3 / (6 * h0 * hph)
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a1 := (h1p2 + 3*h0*h1) / (6 * h0)
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a2 := (2*h1p2 + 3*h0*h1) / (6 * hph)
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integral += a0 * f[n-3]
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integral += a1 * f[n-2]
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integral += a2 * f[n-1]
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}
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return integral
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}
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