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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
50 lines
1.2 KiB
Go
50 lines
1.2 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 integrate
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import "sort"
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// Trapezoidal 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 trapezoidal rule. 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 2.
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//
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// The trapezoidal rule approximates f by a piecewise linear function and
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// estimates
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//
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// \int_x[i]^x[i+1] f(x) dx
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//
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// as
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//
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// (x[i+1] - x[i]) * (f[i] + f[i+1])/2
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//
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// More details on the trapezoidal rule can be found at:
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// https://en.wikipedia.org/wiki/Trapezoidal_rule
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func Trapezoidal(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 < 2:
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panic("integrate: input data too small")
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case !sort.Float64sAreSorted(x):
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panic("integrate: input must be sorted")
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}
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integral := 0.0
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for i := 0; i < n-1; i++ {
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integral += 0.5 * (x[i+1] - x[i]) * (f[i+1] + f[i])
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}
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return integral
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}
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