Find nearest SO(3) or orthogonal matrix.

Converts arbitrary 3 x 3 matrices into the nearest SO(3) or orthogonal matrix.

Usage

nearest.SO3(x)
nearest.orthog(x)

Arguments

x

3 x 3 matrices stored in a 3 x 3 x n array)

Details

Uses Stephens' (1979) algorithm to find the nearest (in entry-wise Euclidean sense) SO(3) or orthogonal matrix to a given matrix.

Value

nearest.SO3 produces an orientation-class object holding the closest orientations.

nearest.orthog produces a 3 x 3 x n array of orthogonal matrices.

References

Stephens (1979). Vector correlation. Biometrika 66, 41-48.

Author

Duncan Murdoch

See also

orientation-class

Examples

x <- matrix(rnorm(9), 3,3)
nearest.orthog(x)
#> , , 1
#> 
#>            [,1]        [,2]      [,3]
#> [1,]  0.5590511  0.04878985 0.8276964
#> [2,] -0.3296190 -0.90291392 0.2758583
#> [3,] -0.7607977  0.42704332 0.4886930
#> 
nearest.SO3(x)
#> An object of class "rotmatrix"
#> Slot "x":
#> , , 1
#> 
#>            [,1]         [,2]       [,3]
#> [1,]  0.5824788 -0.784314543  0.2134693
#> [2,] -0.3547565 -0.009004573  0.9349154
#> [3,] -0.7313455 -0.620298005 -0.2834857
#> 
#> 
x <- -x
nearest.orthog(x)
#> , , 1
#> 
#>            [,1]        [,2]       [,3]
#> [1,] -0.5590511 -0.04878985 -0.8276964
#> [2,]  0.3296190  0.90291392 -0.2758583
#> [3,]  0.7607977 -0.42704332 -0.4886930
#> 
nearest.SO3(x)
#> An object of class "rotmatrix"
#> Slot "x":
#> , , 1
#> 
#>            [,1]        [,2]       [,3]
#> [1,] -0.5590511 -0.04878985 -0.8276964
#> [2,]  0.3296190  0.90291392 -0.2758583
#> [3,]  0.7607977 -0.42704332 -0.4886930
#> 
#>