Force a Matrix to 'symmetricMatrix' Without Symmetry Checks

Force a square matrix x to a symmetricMatrix, without a symmetry check as it would be applied for as(x, "symmetricMatrix").

forceSymmetric(x, uplo)

Arguments

x

any square matrix (of numbers), either “"traditional"” (matrix) or inheriting from Matrix.

uplo

optional string, "U" or "L" indicating which “triangle” half of x should determine the result. The default is "U" unless x already has a uplo slot (i.e., when it is symmetricMatrix, or triangularMatrix), where the default will be x@uplo.

Value

a square matrix inheriting from class symmetricMatrix.

See also

symmpart for the symmetric part of a matrix, or the coercions as(x, <symmetricMatrix class>).

Examples

 ## Hilbert matrix
 i <- 1:6
 h6 <- 1/outer(i - 1L, i, "+")
 sd <- sqrt(diag(h6))
 hh <- t(h6/sd)/sd # theoretically symmetric
 isSymmetric(hh, tol=0) # FALSE; hence
#> [1] FALSE
 try( as(hh, "symmetricMatrix") ) # fails, but this works fine:
#> 6 x 6 Matrix of class "dsyMatrix"
#>           [,1]      [,2]      [,3]      [,4]      [,5]      [,6]
#> [1,] 1.0000000 0.8660254 0.7453560 0.6614378 0.6000000 0.5527708
#> [2,] 0.8660254 1.0000000 0.9682458 0.9165151 0.8660254 0.8206518
#> [3,] 0.7453560 0.9682458 1.0000000 0.9860133 0.9583148 0.9270248
#> [4,] 0.6614378 0.9165151 0.9860133 1.0000000 0.9921567 0.9749960
#> [5,] 0.6000000 0.8660254 0.9583148 0.9921567 1.0000000 0.9949874
#> [6,] 0.5527708 0.8206518 0.9270248 0.9749960 0.9949874 1.0000000
 H6 <- forceSymmetric(hh)

 ## result can be pretty surprising:
 (M <- Matrix(1:36, 6))
#> 6 x 6 Matrix of class "dgeMatrix"
#>      [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,]    1    7   13   19   25   31
#> [2,]    2    8   14   20   26   32
#> [3,]    3    9   15   21   27   33
#> [4,]    4   10   16   22   28   34
#> [5,]    5   11   17   23   29   35
#> [6,]    6   12   18   24   30   36
 forceSymmetric(M) # symmetric, hence very different in lower triangle
#> 6 x 6 Matrix of class "dsyMatrix"
#>      [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,]    1    7   13   19   25   31
#> [2,]    7    8   14   20   26   32
#> [3,]   13   14   15   21   27   33
#> [4,]   19   20   21   22   28   34
#> [5,]   25   26   27   28   29   35
#> [6,]   31   32   33   34   35   36
 (tm <- tril(M))
#> 6 x 6 Matrix of class "dtrMatrix"
#>      [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,]    1    .    .    .    .    .
#> [2,]    2    8    .    .    .    .
#> [3,]    3    9   15    .    .    .
#> [4,]    4   10   16   22    .    .
#> [5,]    5   11   17   23   29    .
#> [6,]    6   12   18   24   30   36
 forceSymmetric(tm)
#> 6 x 6 Matrix of class "dsyMatrix"
#>      [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,]    1    2    3    4    5    6
#> [2,]    2    8    9   10   11   12
#> [3,]    3    9   15   16   17   18
#> [4,]    4   10   16   22   23   24
#> [5,]    5   11   17   23   29   30
#> [6,]    6   12   18   24   30   36