Documentation
¶
Overview ¶
Package spatial provides spatial statistical functions.
Index ¶
Examples ¶
Constants ¶
This section is empty.
Variables ¶
This section is empty.
Functions ¶
func GetisOrdGStar ¶
GetisOrdGStar returns the Local Getis-Ord G*i statistic for element of the weighted data using the provided locality matrix. The returned value is a z-score.
G^*_i = num_i / den_i
num_i = \sum_j (w_{ij} x_j) - \bar X \sum_j w_{ij}
den_i = S \sqrt(((n \sum_j w_{ij}^2 - (\sum_j w_{ij})^2))/(n - 1))
\bar X = (\sum_j x_j) / n
S = \sqrt((\sum_j x_j^2)/n - (\bar X)^2)
GetisOrdGStar will panic if locality is not a square matrix with dimensions the same as the length of data or if i is not a valid index into data.
See doi.org/10.1111%2Fj.1538-4632.1995.tb00912.x.
Weighted Getis-Ord G*i is not currently implemented and GetisOrdGStar will panic if weights is not nil.
Example ¶
package main
import (
"fmt"
"github.com/ArkaGPL/gonum/mat"
"github.com/ArkaGPL/gonum/stat/spatial"
)
func main() {
data := []float64{0, 0, 0, 1, 1, 1, 0, 1, 0, 0}
// The locality here describes spatial neighbor
// relationships including self.
locality := mat.NewDense(10, 10, []float64{
1, 1, 0, 0, 0, 0, 0, 0, 0, 0,
1, 1, 1, 0, 0, 0, 0, 0, 0, 0,
0, 1, 1, 1, 0, 0, 0, 0, 0, 0,
0, 0, 1, 1, 1, 0, 0, 0, 0, 0,
0, 0, 0, 1, 1, 1, 0, 0, 0, 0,
0, 0, 0, 0, 1, 1, 1, 0, 0, 0,
0, 0, 0, 0, 0, 1, 1, 1, 0, 0,
0, 0, 0, 0, 0, 0, 1, 1, 1, 0,
0, 0, 0, 0, 0, 0, 0, 1, 1, 1,
0, 0, 0, 0, 0, 0, 0, 0, 1, 1,
})
for i, v := range data {
fmt.Printf("v=%v G*i=% .4v\n", v, spatial.GetisOrdGStar(i, data, nil, locality))
}
}
Output: v=0 G*i=-1.225 v=0 G*i=-1.604 v=0 G*i=-0.2673 v=1 G*i= 1.069 v=1 G*i= 2.405 v=1 G*i= 1.069 v=0 G*i= 1.069 v=1 G*i=-0.2673 v=0 G*i=-0.2673 v=0 G*i=-1.225
Example (Banded) ¶
package main
import (
"fmt"
"github.com/ArkaGPL/gonum/mat"
"github.com/ArkaGPL/gonum/stat/spatial"
)
func main() {
data := []float64{0, 0, 0, 1, 1, 1, 0, 1, 0, 0}
// The locality here describes spatial neighbor
// relationships including self.
// This example uses the band matrix representation
// to improve time and space efficiency.
locality := mat.NewBandDense(10, 10, 1, 1, []float64{
0, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1, 0,
})
for i, v := range data {
fmt.Printf("v=%v G*i=% .4v\n", v, spatial.GetisOrdGStar(i, data, nil, locality))
}
}
Output: v=0 G*i=-1.225 v=0 G*i=-1.604 v=0 G*i=-0.2673 v=1 G*i= 1.069 v=1 G*i= 2.405 v=1 G*i= 1.069 v=0 G*i= 1.069 v=1 G*i=-0.2673 v=0 G*i=-0.2673 v=0 G*i=-1.225
func GlobalMoransI ¶
GlobalMoransI performs Global Moran's I calculation of spatial autocorrelation for the given data using the provided locality matrix. GlobalMoransI returns Moran's I, Var(I) and the z-score associated with those values. GlobalMoransI will panic if locality is not a square matrix with dimensions the same as the length of data.
See https://doi.org/10.1111%2Fj.1538-4632.2007.00708.x.
Weighted Global Moran's I is not currently implemented and GlobalMoransI will panic if weights is not nil.
Example (Areal) ¶
package main
import (
"fmt"
"math"
"github.com/ArkaGPL/gonum/floats"
"github.com/ArkaGPL/gonum/mat"
"github.com/ArkaGPL/gonum/stat/spatial"
)
// Euclid is a mat.Matrix whose elements refects 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 main() {
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
Example (Banded) ¶
package main
import (
"fmt"
"github.com/ArkaGPL/gonum/mat"
"github.com/ArkaGPL/gonum/stat/spatial"
)
func main() {
data := []float64{0, 0, 0, 1, 1, 1, 0, 1, 0, 0}
// The locality here describes spatial neighbor
// relationships.
// This example uses the band matrix representation
// to improve time and space efficiency.
locality := mat.NewBandDense(10, 10, 1, 1, []float64{
0, 0, 1,
1, 0, 1,
1, 0, 1,
1, 0, 1,
1, 0, 1,
1, 0, 1,
1, 0, 1,
1, 0, 1,
1, 0, 1,
1, 0, 0,
})
i, _, z := spatial.GlobalMoransI(data, nil, locality)
fmt.Printf("Moran's I=%.4v z-score=%.4v\n", i, z)
}
Output: Moran's I=0.1111 z-score=0.6335
Example (Linear) ¶
package main
import (
"fmt"
"github.com/ArkaGPL/gonum/mat"
"github.com/ArkaGPL/gonum/stat/spatial"
)
func main() {
data := []float64{0, 0, 0, 1, 1, 1, 0, 1, 0, 0}
// The locality here describes spatial neighbor
// relationships.
locality := mat.NewDense(10, 10, []float64{
0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 1, 0, 0, 0, 0, 0, 0, 0,
0, 1, 0, 1, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 1, 0, 1, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 1, 0, 0, 0,
0, 0, 0, 0, 0, 1, 0, 1, 0, 0,
0, 0, 0, 0, 0, 0, 1, 0, 1, 0,
0, 0, 0, 0, 0, 0, 0, 1, 0, 1,
0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
})
i, _, z := spatial.GlobalMoransI(data, nil, locality)
fmt.Printf("Moran's I=%.4v z-score=%.4v\n", i, z)
}
Output: Moran's I=0.1111 z-score=0.6335
Types ¶
This section is empty.
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