I wish to establish a consistent notation for my work, which involves combinations of different attributes of a variable $\boldsymbol{x}$ given in the following, including the notation most common in my field (optimization, algorithms, multilinear algebra).
- (multidimensional) indexing: $\boldsymbol{x}_1$, $\boldsymbol{x}_2$, $\boldsymbol{x}_{2,1,3}$
- iterating/updating: $\boldsymbol{x}^{(0)}$, $\boldsymbol{x}^{(k+1)}$
- labeling (often impossible in an ordinal way): $\boldsymbol{x}_{\text{left}}$, $\boldsymbol{x}_{\text{red}}$
If possible, I'd like to refrain from using functional notation and reserve that for other use cases, e.g. operations like vectorization: $\text{vec}(\boldsymbol{X})$. The following existing operations might interfere with reasonable suggestions for my problem:
- selecting: $[\boldsymbol{X}]_{i,j}$ to select the ($i$,$j$)-th element in $\boldsymbol{X}$
- reshaping: $\boldsymbol{X}_{(2)}$ is the 2nd out of multiple possible rearrangements of $\boldsymbol{X}$
- transposing: $\boldsymbol{X}^{{\text{T}}}$ is the transpose of $\boldsymbol{X}$
What might prove to be a clean and intuitive combination of all aspects mentioned? My focus is on clarity rather than brevity.
Toy example: denote the $k$-th iterate of the (4,7)-th entity of $\boldsymbol{x}_{\text{stack}}$. My preference currently gravitates towards $\boldsymbol{x}_{4,7}^{\text{stack},(k)}$ with all of it inside parentheses in case I need to use any of the operations mentioned before.
