optn, optnevn#

Purpose#

Returns optimal matrix dimensions for computing FFT’s.

Format#

n = optnevn(n0)#

Parameters:: n0 (scalar) – the length of a vector or the number of rows or columns in a matrix.
Returns:: n (scalar) – the next optimal size for the given dimension for computing an FFT or RFFT. \(n > n0\).

Examples#

n = optn(231);

The above code assigns n to be equal to 240.

Remarks#

The optn() and optnevn() procedures determine optimal matrix dimensions for computing FFT’s. The Temperton FFT routines (see table following) can handle any matrix whose dimensions can be expressed as:

\[2p \times 3q \times 5r \times 7s\]

where p, q and r are nonnegative integers and s is equal to 0 or 1.

with one restriction: the vector length or matrix column size must be even (p must be positive) when computing RFFT’s.

The fftn(), etc., procedures pad matrices to the next allowable dimensions. However, they generally run faster for matrices whose dimensions are highly composite numbers, that is, products of several factors (to various powers), rather than powers of a single factor. For example, even though it is bigger, a 33600x1 vector can compute as much as 20% faster than a 32768x1 vector, because 33600 is a highly composite number, 2⁶ * 3 * 5² * 7, whereas 32768 is a simple power of 2, 2¹⁵. The optn() and optnevn() procedures are provided so you can take advantage of this fact by hand-sizing matrices to optimal dimensions before computing the FFT.

Use the following table to determine what to call for a given function and matrix:

FFT	Vector	Matrix	Matrix
Function	Length	Rows	Columns
`fftn()`	`optn()`	`optn()`	`optn()`
`rfftn()`	`optnevn()`	`optn()`	`optnevn()`
`rfftnp()`	`optnevn()`	`optn()`	`optnevn()`