Shift data to operate on specified dimension

`[x,perm,nshifts] = shiftdata(x,dim)`

`[x,perm,nshifts] = shiftdata(x,dim)`

shifts
data `x`

to permute dimension `dim`

to
the first column using the same permutation as the built-in `filter`

function.
The vector `perm`

returns the permutation vector
that is used.

If `dim`

is missing or empty, then the first
non-singleton dimension is shifted to the first column, and the number
of shifts is returned in `nshifts`

.

`shiftdata`

is meant to be used in tandem with `unshiftdata`

,
which shifts the data back to its original shape. These functions
are useful for creating functions that work along a certain dimension,
like `filter`

, `goertzel`

, `sgolayfilt`

,
and `sosfilt`

.

This example shifts `x`

, a 3-x-3 magic square,
permuting dimension `2`

to the first column. `unshiftdata`

shifts `x`

back
to its original shape.

1. Create a 3-x-3 magic square:

x = fi(magic(3)) x = 8 1 6 3 5 7 4 9 2

2. Shift the matrix `x`

to work along the second
dimension:

[x,perm,nshifts] = shiftdata(x,2)

The permutation vector, `perm`

, and the number
of shifts, `nshifts`

, are returned along with the
shifted matrix, `x`

:

x = 8 3 4 1 5 9 6 7 2 perm = 2 1 nshifts = []

3. Shift the matrix back to its original shape:

y = unshiftdata(x,perm,nshifts) y = 8 1 6 3 5 7 4 9 2

This example shows how `shiftdata`

and `unshiftdata`

work
when you define `dim`

as empty.

1. Define `x`

as a row vector:

x = 1:5 x = 1 2 3 4 5

2. Define `dim`

as empty to shift the first
non-singleton dimension of `x`

to the first column:

[x,perm,nshifts] = shiftdata(x,[])

`x`

is returned as a column vector, along with `perm`

,
the permutation vector, and `nshifts`

, the number
of shifts:

x = 1 2 3 4 5 perm = [] nshifts = 1

3. Using `unshiftdata`

, restore `x`

to
its original shape:

y = unshiftdata(x,perm,nshifts) y = 1 2 3 4 5

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