Human-readable symmetry operator into matrix and vector

Returns a $3\times 3$ matrix and $3\times 1$ vector corresponding to either a symmetry operator or a centering operator in human-readable, string form.

Usage

op_xyz_to_matrix(op_xyz)

Arguments

op_xyz: A symmetry or centering operation in the form of a human-readable string, e.g. -x+1/2,-y,z+1/2'.

Value

mat_ops A named list including a $3\times 3$ matrix 'R' and a

$3\times 1$ vector 'T'.

Details

A string describing a symmetry or a centering operation has a format similar to, for instance, '-x+1/2,-y,z+1/2'. Such a string corresponds to the symmetry operation represented mathematically by the following matrix and vector: $$ \left(\begin{array}{rrr} -1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1 \end{array}\right)\quad,\quad \left(\begin{array}{r} 1/2 \\ 0 \\ 1/2 \end{array}\right) $$ Where symmetry operations in human-readable form are useful for the subjective reasoning in crystallography, their mathematical counterpart is needed for all practical calculations.

Examples

# Reflection and translation
sop <- '-x,y+1/2,z'
mat_ops <- op_xyz_to_matrix(sop)
print(mat_ops)
#> $R
#>      [,1] [,2] [,3]
#> [1,]   -1    0    0
#> [2,]    0    1    0
#> [3,]    0    0    1
#> 
#> $T
#>      [,1]
#> [1,]  0.0
#> [2,]  0.5
#> [3,]  0.0
#>