Many different kinds of matrix manipulation routines are available:
- flat() - flatten an array to one dimension
- flip() - flip an array along a dimension
- join() - join up to 4 arrays
- moddims() - change the dimensions of an array without changing the data
- reorder() - changes the dimension order within the array
- shift() - shifts data along a dimension
- tile() - repeats an array along a dimension
- transpose() - performs a matrix transpose
- array() to adjust the dimensions of an array
- transpose a matrix or vector with shorthand notation
The flat() function flattens an array to one dimension.
The flat function has the following overloads:
The flip() function flips the contents of an array along a chosen dimension.
The flip function has the following overloads:
The join() function can join up to 4 arrays together.
8 join(0, a, a) [10 1 1 1]
20 join(1, a, a) [5 2 1 1]
The join function has several overloads:
- array af::join(const int dim, const array &first, const array &second) – Joins 2 arrays along a dimension
- array af::join(const int dim, const array &first, const array &second, const array &third) – Joins 3 arrays along a dimension.
- array af::join(const int dim, const array &first, const array &second, const array &third, const array &fourth) – Joins 4 arrays along a dimension
- af_err af_join(af_array *out, const int dim, const af_array first, const af_array second) – C interface function to join 2 arrays along a dimension
- af_err af_join_many(af_array *out, const int dim, const unsigned n_arrays, const af_array *inputs) – C interface function to join up to 10 arrays along a dimension
The moddims() function changes the dimensions of an array without changing its data or order. It is important to remember that the function only modifies the metadata associated with the array and does not actually modify the content of the array.
11 af::dim4 new_dims(2, 4);
12 moddims(a, new_dims) [2 4 1 1]
13 1.0000 1.0000 1.0000 1.0000
14 2.0000 2.0000 2.0000 2.0000
16 moddims(a, a.elements(), 1, 1, 1) [8 1 1 1]
The moddims function has several overloads:
- array af::moddims(const array &in, const unsigned ndims, const dim_t *const dims) – mods number of dimensions to match ndims as specidied in the array dims
- array af::moddims(const array &in, const dim4 &dims) – mods dimensions as specified by dims
- array af::moddims(const array &in, const dim_t d0, const dim_t d1=1, const dim_t d2=1, const dim_t d3=1) – mods dimensions of an array
- af_err af_moddims(af_array *out, const af_array in, const unsigned ndims, const dim_t *const dims) – C interface to mod dimensions of an array
The reorder() function changes the order of the dimensions within the array. This actually alters the underlying data of the array.
12 reorder(a, 1, 0, 2) [2 2 3 1] //equivalent to a transpose
23 reorder(a, 2, 0, 1) [3 2 2 1]
The reorder function the following several overloads:
The shift() function shifts data in a circular buffer fashion along a chosen dimension.
2 0.0000 0.0000 0.0000 0.0000 0.0000
3 3.0000 4.0000 5.0000 1.0000 2.0000
4 3.0000 4.0000 5.0000 1.0000 2.0000
6 shift(a, 0, 2 ) [3 5 1 1]
7 0.0000 0.0000 0.0000 0.0000 0.0000
8 1.0000 2.0000 3.0000 4.0000 5.0000
9 1.0000 2.0000 3.0000 4.0000 5.0000
11 shift(a, -1, 2 ) [3 5 1 1]
12 1.0000 2.0000 3.0000 4.0000 5.0000
13 1.0000 2.0000 3.0000 4.0000 5.0000
14 0.0000 0.0000 0.0000 0.0000 0.0000
The shift function has the following overloads:
The tile() function repeats an array along a dimension
14 tile(a, 2, 2) [6 2 1 1]
22 af::dim4 tile_dims(1, 2, 3);
23 tile(a, tile_dims) [3 2 3 1]
The tile function has several overloads:
- array af::tile(const array &in, const unsigned x, const unsigned y=1, const unsigned z=1, const unsigned w=1) – Tiles array along specified dimensions
- array af::tile(const array &in, const dim4 &dims) – Tile an array according to a dim4 object
- af_err af_tile(af_array *out, const af_array in, const unsigned x, const unsigned y, const unsigned z, const unsigned w) – C interface for tiling an array
The transpose() function performs a standard matrix transpose. The input array must have the dimensions of a 2D-matrix.
The transpose function has several overloads:
array() can be used to create a (shallow) copy of a matrix with different dimensions. The number of elements must remain the same as the original array.
int hA[] = {1, 2, 3, 4, 5, 6};
The T() and H() methods can be used to form the matrix or vector transpose .
Combining re-ordering functions to enumerate grid coordinates
By using a combination of the array restructuring functions, we can quickly code complex manipulation patterns with a few lines of code. For example, consider generating _(x,y)_ coordinates for a grid where each axis goes from 1 to n. Instead of using several loops to populate our arrays we can just use a small combination of the above functions.
4 flat( transpose(tile(seq(1, n), 1, n)) )
Conclusion
Functions provided by arrayfire offer ease and flexibility for efficiently manipulating the structure of arrays. The provided functions can be used as building blocks to generate, shift, or prepare data to any form imaginable!