github.com/jingcheng-WU/gonum@v0.9.1-0.20210323123734-f1a2a11a8f7b/integrate/trapezoidal.go (about)

     1  // Copyright ©2016 The Gonum Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  package integrate
     6  
     7  import "sort"
     8  
     9  // Trapezoidal returns an approximate value of the integral
    10  //  \int_a^b f(x) dx
    11  // computed using the trapezoidal rule. The function f is given as a slice of
    12  // samples evaluated at locations in x, that is,
    13  //  f[i] = f(x[i]), x[0] = a, x[len(x)-1] = b
    14  // The slice x must be sorted in strictly increasing order. x and f must be of
    15  // equal length and the length must be at least 2.
    16  //
    17  // The trapezoidal rule approximates f by a piecewise linear function and
    18  // estimates
    19  //  \int_x[i]^x[i+1] f(x) dx
    20  // as
    21  //  (x[i+1] - x[i]) * (f[i] + f[i+1])/2
    22  // More details on the trapezoidal rule can be found at:
    23  // https://en.wikipedia.org/wiki/Trapezoidal_rule
    24  func Trapezoidal(x, f []float64) float64 {
    25  	n := len(x)
    26  	switch {
    27  	case len(f) != n:
    28  		panic("integrate: slice length mismatch")
    29  	case n < 2:
    30  		panic("integrate: input data too small")
    31  	case !sort.Float64sAreSorted(x):
    32  		panic("integrate: input must be sorted")
    33  	}
    34  
    35  	integral := 0.0
    36  	for i := 0; i < n-1; i++ {
    37  		integral += 0.5 * (x[i+1] - x[i]) * (f[i+1] + f[i])
    38  	}
    39  
    40  	return integral
    41  }