blob: f3774b5b17065fb66c84966910f04ea15c49eaca [file] [log] [blame]
// Copyright 2015 The Go 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 stats
// Miscellaneous helper algorithms
import (
"fmt"
)
func maxint(a, b int) int {
if a > b {
return a
}
return b
}
func minint(a, b int) int {
if a < b {
return a
}
return b
}
func sumint(xs []int) int {
sum := 0
for _, x := range xs {
sum += x
}
return sum
}
// bisect returns an x in [low, high] such that |f(x)| <= tolerance
// using the bisection method.
//
// f(low) and f(high) must have opposite signs.
//
// If f does not have a root in this interval (e.g., it is
// discontiguous), this returns the X of the apparent discontinuity
// and false.
func bisect(f func(float64) float64, low, high, tolerance float64) (float64, bool) {
flow, fhigh := f(low), f(high)
if -tolerance <= flow && flow <= tolerance {
return low, true
}
if -tolerance <= fhigh && fhigh <= tolerance {
return high, true
}
if mathSign(flow) == mathSign(fhigh) {
panic(fmt.Sprintf("root of f is not bracketed by [low, high]; f(%g)=%g f(%g)=%g", low, flow, high, fhigh))
}
for {
mid := (high + low) / 2
fmid := f(mid)
if -tolerance <= fmid && fmid <= tolerance {
return mid, true
}
if mid == high || mid == low {
return mid, false
}
if mathSign(fmid) == mathSign(flow) {
low = mid
flow = fmid
} else {
high = mid
fhigh = fmid
}
}
}
// bisectBool implements the bisection method on a boolean function.
// It returns x1, x2 ∈ [low, high], x1 < x2 such that f(x1) != f(x2)
// and x2 - x1 <= xtol.
//
// If f(low) == f(high), it panics.
func bisectBool(f func(float64) bool, low, high, xtol float64) (x1, x2 float64) {
flow, fhigh := f(low), f(high)
if flow == fhigh {
panic(fmt.Sprintf("root of f is not bracketed by [low, high]; f(%g)=%v f(%g)=%v", low, flow, high, fhigh))
}
for {
if high-low <= xtol {
return low, high
}
mid := (high + low) / 2
if mid == high || mid == low {
return low, high
}
fmid := f(mid)
if fmid == flow {
low = mid
flow = fmid
} else {
high = mid
fhigh = fmid
}
}
}
// series returns the sum of the series f(0), f(1), ...
//
// This implementation is fast, but subject to round-off error.
func series(f func(float64) float64) float64 {
y, yp := 0.0, 1.0
for n := 0.0; y != yp; n++ {
yp = y
y += f(n)
}
return y
}