Triangular array
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Indexing
Storing a triangular array in a computer requires a mapping from the two-dimensional coordinates (i, j) to a linear memory address. If two triangular arrays of equal size are to be stored (such as in LU decomposition), they can be combined into a standard rectangular array. If there is only one array, or it must be easily appended to, the array may be stored where row i begins at the ith triangular number Ti. Just like a rectangular array, one multiplication is required to find the start of the row, but this multiplication is of two variables (i*(i+1)/2), so some optimizations such as using a sequence of shifts and adds are not available.
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