package phantom-algebra

An index of type (+'dim,'+len,+'rank,'group) index can be used to index a tensor, each type parameter informs on which kind of tensor can be used ('dim and 'rank), on the type of the resulting vector ('len and 'rank), or on with which indices it can be combined when swizzling. More precisely,

• `dim is the list of tensor dimension compatible with the index, for instance `x` works for all dimension, whereas `w` is only meaningful for a 4-vector.
• `rank is the number of coordinate specified by the index, a tensor can be indexed only if its own rank is equal or superior to the index rank. For instance, xx is a rank 2 tensor and can only index matrices, whereas x is a valid index for both vector and tensor. When slicing, the rank of the slice will be the difference between the tensor rank and the index rank. For a vector v and a matrix m, v.%x is a scalar (1 - 1 = 0) like m.%[xx] ( 2 - 2 = 0) but m.%x is a vector (2-1=0) corresponding to the first row of the matrix
• 'len is the number of indices combined in the aggregated index by swizzling, if 'len > 1 it increases the rank of the resulting tensor by one and sets its dimension to 'len. See the slice function for more information.
• 'group corresponds to the index namespace, only index of the same namespace can be combined by swizzling. Availaibles namespace are `xyzx,`rgba and `stpq.

Index concatenation

XYZW group

RGBA

STPQ group