[class.gslice.overview]

This class represents a generalized slice out of an array.

A gslice is defined by a starting offset (s), a set of lengths (

{l j), and a set of strides ({d j) .}_{j) .}}_{j), and a set of strides ({d j) .}_{j) .}}

The number of lengths shall equal the number of strides.

A gslice represents a mapping from a set of indices (

{i j), equal in number to the number of strides, to a single index k .}_{j), equal in number to the number of strides, to a single index k .}

It is useful for building multidimensional array classes using the valarray template, which is one-dimensional.

The set of one-dimensional index values specified by a gslice are

k = s + \sum j {i j {d j where the multidimensional indices {i j range in value from 0 to {l i j - 1 .}_{i j - 1 .}}_{j range in value from 0 to {l i j - 1 .}_{i j - 1 .}}}_{j where the multidimensional indices {i j range in value from 0 to {l i j - 1 .}_{i j - 1 .}}_{j range in value from 0 to {l i j - 1 .}_{i j - 1 .}}}}_{j {d j where the multidimensional indices {i j range in value from 0 to {l i j - 1 .}_{i j - 1 .}}_{j range in value from 0 to {l i j - 1 .}_{i j - 1 .}}}_{j where the multidimensional indices {i j range in value from 0 to {l i j - 1 .}_{i j - 1 .}}_{j range in value from 0 to {l i j - 1 .}_{i j - 1 .}}}}

[Example 1:

The gslice specification start = 3 length = {2, 4, 3} stride = {19, 4, 1} yields the sequence of one-dimensional indices

k = 3 + (0, 1) \times 19 + (0, 1, 2, 3) \times 4 + (0, 1, 2) \times 1 which are ordered as shown in the following table:

	 $({i 0, {i 1, {i 2, k) = (0, 0, 0, 3), (0, 0, 1, 4), (0, 0, 2, 5), (0, 1, 0, 7), (0, 1, 1, 8), (0, 1, 2, 9), (0, 2, 0, 11), (0, 2, 1, 12), (0, 2, 2, 13), (0, 3, 0, 15), (0, 3, 1, 16), (0, 3, 2, 17), (1, 0, 0, 22), (1, 0, 1, 23), \dots (1, 3, 2, 36)}_{2, k) = (0, 0, 0, 3), (0, 0, 1, 4), (0, 0, 2, 5), (0, 1, 0, 7), (0, 1, 1, 8), (0, 1, 2, 9), (0, 2, 0, 11), (0, 2, 1, 12), (0, 2, 2, 13), (0, 3, 0, 15), (0, 3, 1, 16), (0, 3, 2, 17), (1, 0, 0, 22), (1, 0, 1, 23), \dots (1, 3, 2, 36)}}_{1, {i 2, k) = (0, 0, 0, 3), (0, 0, 1, 4), (0, 0, 2, 5), (0, 1, 0, 7), (0, 1, 1, 8), (0, 1, 2, 9), (0, 2, 0, 11), (0, 2, 1, 12), (0, 2, 2, 13), (0, 3, 0, 15), (0, 3, 1, 16), (0, 3, 2, 17), (1, 0, 0, 22), (1, 0, 1, 23), \dots (1, 3, 2, 36)}_{2, k) = (0, 0, 0, 3), (0, 0, 1, 4), (0, 0, 2, 5), (0, 1, 0, 7), (0, 1, 1, 8), (0, 1, 2, 9), (0, 2, 0, 11), (0, 2, 1, 12), (0, 2, 2, 13), (0, 3, 0, 15), (0, 3, 1, 16), (0, 3, 2, 17), (1, 0, 0, 22), (1, 0, 1, 23), \dots (1, 3, 2, 36)}}}_{0, {i 1, {i 2, k) = (0, 0, 0, 3), (0, 0, 1, 4), (0, 0, 2, 5), (0, 1, 0, 7), (0, 1, 1, 8), (0, 1, 2, 9), (0, 2, 0, 11), (0, 2, 1, 12), (0, 2, 2, 13), (0, 3, 0, 15), (0, 3, 1, 16), (0, 3, 2, 17), (1, 0, 0, 22), (1, 0, 1, 23), \dots (1, 3, 2, 36)}_{2, k) = (0, 0, 0, 3), (0, 0, 1, 4), (0, 0, 2, 5), (0, 1, 0, 7), (0, 1, 1, 8), (0, 1, 2, 9), (0, 2, 0, 11), (0, 2, 1, 12), (0, 2, 2, 13), (0, 3, 0, 15), (0, 3, 1, 16), (0, 3, 2, 17), (1, 0, 0, 22), (1, 0, 1, 23), \dots (1, 3, 2, 36)}}_{1, {i 2, k) = (0, 0, 0, 3), (0, 0, 1, 4), (0, 0, 2, 5), (0, 1, 0, 7), (0, 1, 1, 8), (0, 1, 2, 9), (0, 2, 0, 11), (0, 2, 1, 12), (0, 2, 2, 13), (0, 3, 0, 15), (0, 3, 1, 16), (0, 3, 2, 17), (1, 0, 0, 22), (1, 0, 1, 23), \dots (1, 3, 2, 36)}_{2, k) = (0, 0, 0, 3), (0, 0, 1, 4), (0, 0, 2, 5), (0, 1, 0, 7), (0, 1, 1, 8), (0, 1, 2, 9), (0, 2, 0, 11), (0, 2, 1, 12), (0, 2, 2, 13), (0, 3, 0, 15), (0, 3, 1, 16), (0, 3, 2, 17), (1, 0, 0, 22), (1, 0, 1, 23), \dots (1, 3, 2, 36)}}}$

That is, the highest-ordered index turns fastest.

— end example]

It is possible to have degenerate generalized slices in which an address is repeated.

[Example 2:

If the stride parameters in the previous example are changed to {1, 1, 1}, the first few elements of the resulting sequence of indices will be

	(0,  0,  0,   3),  
	(0,  0,  1,   4),  
	(0,  0,  2,   5),  
	(0,  1,  0,   4),  
	(0,  1,  1,   5),  
	(0,  1,  2,   6),  
	…

— end example]

If a degenerate slice is used as the argument to the non-const version of operator[](const gslice&), the behavior is undefined.

29 Numerics library [numerics]

29.6 Numeric arrays [numarray]

29.6.6 The gslice class [class.gslice]

29.6.6.1 Overview [class.gslice.overview]