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// Copyright ©2019 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 f32
import "gonum.org/v1/gonum/internal/math32"
// L2NormUnitary is the level 2 norm of x.
func L2NormUnitary(x []float32) (sum float32) {
var scale float32
var sumSquares float32 = 1
for _, v := range x {
if v == 0 {
continue
}
absxi := math32.Abs(v)
if math32.IsNaN(absxi) {
return math32.NaN()
}
if scale < absxi {
s := scale / absxi
sumSquares = 1 + sumSquares*s*s
scale = absxi
} else {
s := absxi / scale
sumSquares += s * s
}
}
if math32.IsInf(scale, 1) {
return math32.Inf(1)
}
return scale * math32.Sqrt(sumSquares)
}
// L2NormInc is the level 2 norm of x.
func L2NormInc(x []float32, n, incX uintptr) (sum float32) {
var scale float32
var sumSquares float32 = 1
for ix := uintptr(0); ix < n*incX; ix += incX {
val := x[ix]
if val == 0 {
continue
}
absxi := math32.Abs(val)
if math32.IsNaN(absxi) {
return math32.NaN()
}
if scale < absxi {
s := scale / absxi
sumSquares = 1 + sumSquares*s*s
scale = absxi
} else {
s := absxi / scale
sumSquares += s * s
}
}
if math32.IsInf(scale, 1) {
return math32.Inf(1)
}
return scale * math32.Sqrt(sumSquares)
}
// L2DistanceUnitary is the L2 norm of x-y.
func L2DistanceUnitary(x, y []float32) (sum float32) {
var scale float32
var sumSquares float32 = 1
for i, v := range x {
v -= y[i]
if v == 0 {
continue
}
absxi := math32.Abs(v)
if math32.IsNaN(absxi) {
return math32.NaN()
}
if scale < absxi {
s := scale / absxi
sumSquares = 1 + sumSquares*s*s
scale = absxi
} else {
s := absxi / scale
sumSquares += s * s
}
}
if math32.IsInf(scale, 1) {
return math32.Inf(1)
}
return scale * math32.Sqrt(sumSquares)
}
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