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// Copyright ©2020 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 c128
import (
"math"
"math/cmplx"
)
// Add is
//
// for i, v := range s {
// dst[i] += v
// }
func Add(dst, s []complex128) {
for i, v := range s {
dst[i] += v
}
}
// AddConst is
//
// for i := range x {
// x[i] += alpha
// }
func AddConst(alpha complex128, x []complex128) {
for i := range x {
x[i] += alpha
}
}
// CumSum is
//
// if len(s) == 0 {
// return dst
// }
// dst[0] = s[0]
// for i, v := range s[1:] {
// dst[i+1] = dst[i] + v
// }
// return dst
func CumSum(dst, s []complex128) []complex128 {
if len(s) == 0 {
return dst
}
dst[0] = s[0]
for i, v := range s[1:] {
dst[i+1] = dst[i] + v
}
return dst
}
// CumProd is
//
// if len(s) == 0 {
// return dst
// }
// dst[0] = s[0]
// for i, v := range s[1:] {
// dst[i+1] = dst[i] * v
// }
// return dst
func CumProd(dst, s []complex128) []complex128 {
if len(s) == 0 {
return dst
}
dst[0] = s[0]
for i, v := range s[1:] {
dst[i+1] = dst[i] * v
}
return dst
}
// Div is
//
// for i, v := range s {
// dst[i] /= v
// }
func Div(dst, s []complex128) {
for i, v := range s {
dst[i] /= v
}
}
// DivTo is
//
// for i, v := range s {
// dst[i] = v / t[i]
// }
// return dst
func DivTo(dst, s, t []complex128) []complex128 {
for i, v := range s {
dst[i] = v / t[i]
}
return dst
}
// DotUnitary is
//
// for i, v := range x {
// sum += cmplx.Conj(v) * y[i]
// }
// return sum
func DotUnitary(x, y []complex128) (sum complex128) {
for i, v := range x {
sum += cmplx.Conj(v) * y[i]
}
return sum
}
// L2DistanceUnitary returns the L2-norm of x-y.
func L2DistanceUnitary(x, y []complex128) (norm float64) {
var scale float64
sumSquares := 1.0
for i, v := range x {
v -= y[i]
if v == 0 {
continue
}
absxi := cmplx.Abs(v)
if math.IsNaN(absxi) {
return math.NaN()
}
if scale < absxi {
s := scale / absxi
sumSquares = 1 + sumSquares*s*s
scale = absxi
} else {
s := absxi / scale
sumSquares += s * s
}
}
if math.IsInf(scale, 1) {
return math.Inf(1)
}
return scale * math.Sqrt(sumSquares)
}
// L2NormUnitary returns the L2-norm of x.
func L2NormUnitary(x []complex128) (norm float64) {
var scale float64
sumSquares := 1.0
for _, v := range x {
if v == 0 {
continue
}
absxi := cmplx.Abs(v)
if math.IsNaN(absxi) {
return math.NaN()
}
if scale < absxi {
s := scale / absxi
sumSquares = 1 + sumSquares*s*s
scale = absxi
} else {
s := absxi / scale
sumSquares += s * s
}
}
if math.IsInf(scale, 1) {
return math.Inf(1)
}
return scale * math.Sqrt(sumSquares)
}
// Sum is
//
// var sum complex128
// for i := range x {
// sum += x[i]
// }
func Sum(x []complex128) complex128 {
var sum complex128
for _, v := range x {
sum += v
}
return sum
}
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