Matrix Manipulation

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Matrix Manipulation

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

## flat()

The flat() function flattens an array to one dimension.

a [3 3 1 1]
1.0000 4.0000 7.0000
2.0000 5.0000 8.0000
3.0000 6.0000 9.0000
flat(a) [9 1 1 1]
1.0000
2.0000
3.0000
4.0000
5.0000
6.0000
7.0000
8.0000
9.0000

The flat function has the following overloads:

> array af::flat(const array& in) – flatten an array

> af_err af_flat(af_array* out, const af_array in) – C interface for flat() function

## flip()

The flip() function flips the contents of an array along a chosen dimension.

a [5 2 1 1]
1.0000 6.0000
2.0000 7.0000
3.0000 8.0000
4.0000 9.0000
5.0000 10.0000
flip(a, 0) [5 2 1 1]
5.0000 10.0000
4.0000 9.0000
3.0000 8.0000
2.0000 7.0000
1.0000 6.0000
flip(a, 1) [5 2 1 1]
6.0000 1.0000
7.0000 2.0000
8.0000 3.0000
9.0000 4.0000
10.0000 5.0000

The flip function has the following overloads:

> array af::flip(const array &in, const unsigned dim) – flips an array along a dimension af_err af_flip(af_array *out, const af_array in, const unsigned dim) – C interface for flip()

## join()

The join() function can join up to 4 arrays together.

a [5 1 1 1]
1.0000
2.0000
3.0000
4.0000
5.0000
join(0, a, a) [10 1 1 1]
1.0000
2.0000
3.0000
4.0000
5.0000
1.0000
2.0000
3.0000
4.0000
5.0000
join(1, a, a) [5 2 1 1]
1.0000 1.0000
2.0000 2.0000
3.0000 3.0000
4.0000 4.0000
5.0000 5.0000

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

## moddims()

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.

a [8 1 1 1]
1.0000
2.0000
1.0000
2.0000
1.0000
2.0000
1.0000
2.0000
af::dim4 new_dims(2, 4);
moddims(a, new_dims) [2 4 1 1]
1.0000 1.0000 1.0000 1.0000
2.0000 2.0000 2.0000 2.0000
moddims(a, a.elements(), 1, 1, 1) [8 1 1 1]
1.0000
2.0000
1.0000
2.0000
1.0000
2.0000
1.0000
2.0000

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

## reorder()

The reorder() function changes the order of the dimensions within the array. This actually alters the underlying data of the array.

a [2 2 3 1]
1.0000 3.0000
2.0000 4.0000
1.0000 3.0000
2.0000 4.0000
1.0000 3.0000
2.0000 4.0000
reorder(a, 1, 0, 2) [2 2 3 1] //equivalent to a transpose
1.0000 2.0000
3.0000 4.0000
1.0000 2.0000
3.0000 4.0000
1.0000 2.0000
3.0000 4.0000
reorder(a, 2, 0, 1) [3 2 2 1]
1.0000 2.0000
1.0000 2.0000
1.0000 2.0000
3.0000 4.0000
3.0000 4.0000
3.0000 4.0000

The reorder function the following several overloads:

> array af::reorder(const array &in, const unsigned x, const unsigned y=1, const unsigned z=2, const unsigned w=3) – Reorders dimensions of an array

> af_err af_reorder(af_array *out, const af_array in, const unsigned x, const unsigned y, const unsigned z, const unsigned w) – C interface for reordering function

## shift()

The shift() function shifts data in a circular buffer fashion along a chosen dimension.

a [3 5 1 1]
0.0000 0.0000 0.0000 0.0000 0.0000
3.0000 4.0000 5.0000 1.0000 2.0000
3.0000 4.0000 5.0000 1.0000 2.0000
shift(a, 0, 2 ) [3 5 1 1]
0.0000 0.0000 0.0000 0.0000 0.0000
1.0000 2.0000 3.0000 4.0000 5.0000
1.0000 2.0000 3.0000 4.0000 5.0000
shift(a, -1, 2 ) [3 5 1 1]
1.0000 2.0000 3.0000 4.0000 5.0000
1.0000 2.0000 3.0000 4.0000 5.0000
0.0000 0.0000 0.0000 0.0000 0.0000

The shift function has the following overloads:

> array af::shift(const array &in, const int x, const int y=0, const int z=0, const int w=0) – Shifts array along specified dimensions

> af_err af_shift(af_array *out, const af_array in, const int x, const int y, const int z, const int w) – C interface for shifting an array

## tile()

The tile() function repeats an array along a dimension

a [3 1 1 1]
1.0000
2.0000
3.0000
tile(a, 2) [6 1 1 1]
1.0000
2.0000
3.0000
1.0000
2.0000
3.0000
tile(a, 2, 2) [6 2 1 1]
1.0000 1.0000
2.0000 2.0000
3.0000 3.0000
1.0000 1.0000
2.0000 2.0000
3.0000 3.0000
af::dim4 tile_dims(1, 2, 3);
tile(a, tile_dims) [3 2 3 1]
1.0000 1.0000
2.0000 2.0000
3.0000 3.0000
1.0000 1.0000
2.0000 2.0000
3.0000 3.0000
1.0000 1.0000
2.0000 2.0000
3.0000 3.0000

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

## transpose()

The transpose() function performs a standard matrix transpose. The input array must have the dimensions of a 2D-matrix.

a [3 3 1 1]
1.0000 3.0000 3.0000
2.0000 1.0000 3.0000
2.0000 2.0000 1.0000
transpose(a) [3 3 1 1]
1.0000 2.0000 2.0000
3.0000 1.0000 2.0000
3.0000 3.0000 1.0000

The transpose function has several overloads:

> array af::transpose(const array &in, const bool conjugate=false) – Transposes a matrix.

> void af::transposeInPlace(array &in, const bool conjugate=false) – Transposes a matrix in-place.

> af_err af_transpose(af_array *out, af_array in, const bool conjugate) – C interface to transpose a matrix.

> af_err af_transpose_inplace(af_array in, const bool conjugate) – C interface to transpose a matrix in-place.

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};
array A = array(3, 2, hA);
af_print(A); // 2x3 matrix
af_print(moddims(A, 2, 3)); // 2x3 matrix
af_print(moddims(A, 6, 1)); // 6x1 column vector
// moddims(A, 2, 2); // fail: wrong number of elements
// moddims(A, 8, 8); // fail: wrong number of elements

The T() and H() methods can be used to form the matrix or vector transpose .

array x = randu(2, 2, f32);
af_print(x.T()); // transpose (real)
array c = randu(2, 2, c32);
af_print(c.T()); // transpose (complex)
af_print(c.H()); // Hermitian (conjugate) 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.

unsigned n=3;
af::array xy = join(1
tile(seq(1, n), n)
flat( transpose(tile(seq(1, n), 1, n)) )
);
xy [9 2 1 1]
1.0000 1.0000
2.0000 1.0000
3.0000 1.0000
1.0000 2.0000
2.0000 2.0000
3.0000 2.0000
1.0000 3.0000
2.0000 3.0000
3.0000 3.0000

# 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!