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// Copyright ©2017 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 spatial_test
import (
"fmt"
"math"
"gonum.org/v1/gonum/floats"
"gonum.org/v1/gonum/mat"
"gonum.org/v1/gonum/stat/spatial"
)
// Euclid is a mat.Matrix whose elements reflects the Euclidean
// distance between a series of unit-separated points strided
// to be arranged in an x by y grid.
type Euclid struct{ x, y int }
func (e Euclid) Dims() (r, c int) { return e.x * e.y, e.x * e.y }
func (e Euclid) At(i, j int) float64 {
d := e.x * e.y
if i < 0 || d <= i || j < 0 || d <= j {
panic("bounds error")
}
if i == j {
return 0
}
x := float64(j%e.x - i%e.x)
y := float64(j/e.x - i/e.x)
return 1 / math.Hypot(x, y)
}
func (e Euclid) T() mat.Matrix { return mat.Transpose{Matrix: e} }
func ExampleGlobalMoransI_areal() {
locality := Euclid{10, 10}
data1 := []float64{
1, 0, 0, 1, 0, 0, 1, 0, 0, 0,
0, 1, 1, 0, 0, 1, 0, 0, 0, 0,
1, 0, 0, 1, 0, 0, 0, 0, 1, 0,
0, 0, 1, 0, 1, 0, 1, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 1, 0, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 1, 0, 1, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 1, 0, 1, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 1, 0,
}
i1, _, z1 := spatial.GlobalMoransI(data1, nil, locality)
data2 := []float64{
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 1, 1, 0, 0, 0, 0, 0,
0, 0, 1, 1, 1, 1, 0, 0, 0, 0,
0, 0, 1, 1, 1, 1, 0, 0, 0, 0,
0, 0, 0, 1, 1, 1, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 0, 0, 1, 0,
0, 0, 0, 0, 0, 0, 0, 1, 1, 1,
0, 0, 0, 0, 0, 0, 0, 1, 1, 1,
0, 0, 0, 0, 0, 0, 0, 1, 1, 1,
}
i2, _, z2 := spatial.GlobalMoransI(data2, nil, locality)
fmt.Printf("%v scattered points Moran's I=%.4v z-score=%.4v\n", floats.Sum(data1), i1, z1)
fmt.Printf("%v clustered points Moran's I=%.4v z-score=%.4v\n", floats.Sum(data2), i2, z2)
// Output:
//
// 24 scattered points Moran's I=-0.02999 z-score=-1.913
// 24 clustered points Moran's I=0.09922 z-score=10.52
}
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