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#### 15.5.228 find_max

```find_max(data [, diagonal=diagonal, /degree, /subgrid])```

By default, seeks local maxima in `data` and returns their values. `data` must be numerical and may have multiple dimensions.

If `diagonal` is specified, then it must be an array with one element per dimension of `data`. The elements that are equal to 0 indicate which dimensions are not checked for a local maximum. The elements that are equal to 1 and 2 (after conversion to type `long`) indicate in which dimensions checking is performed. The elements that are equal to 2 indicate in which dimensions checked directions may be diagonal. Elements equal to 1 indicate that no diagonals are allowed in those dimensions. All such directions either have non-zero coordinate offsets only in those dimensions, or have only a single non-zero coordinate offset (i.e., a non-diagnonal or orthogonal direction). Only approved directions are checked. If `diagonal` contains `n1` ones and `n2` twos, then the number of directions per data element that will be considered is equal to `m = 2^n2 - 1 + n1`.

For example, regard a two-dimensional array. We’ll call the first dimension the east-west direction and the second one the north-south dimension. Then, if `diagonal = [1,0]`, values are returned for all points that are local maxima in the east-west direction without regards to any other direction. If `diagonal = [1,1]`, then all points are approved that are local maxima in the east-west direction and also in the north-south direction, without regards to the other (northeast-southwest, southeast-northwest) directions. If `diagonal = [2,2]`, then all directions are checked.

For a three-dimensional array, if `diagonal = [2,2,1]`, then the only checked directions that have a non-zero third coordinate offset are those that are along the 3rd axis. If ```diagonal = [1,1,0]```, then only directions along (and not between) the first two axes are checked.

If `/degree` is specified, then the number of directions per data element where the data shows a local maximum is returned instead. This number always lies between 0 and the total number `m` of directions given above. `find_max(data, /degree) eq m` returns an array with 1s at all positions returned by `find_max(data)`, but the latter form is considerably faster because for each element it stops checking as soon as a direction without a local maximum is found. For noise data in arbitrary numbers of dimensions, on average at most 2 local maximum determinations per data element are performed if `/degree` is not specified, compared to `m`, which is grows exponentially with the number of dimensions in the worst case, if `/degree` is specified.

If `/subgrid` is specified, then the value of the local maximum is taken from a quadratic hypersurface fitted to the local neighborhood of the local maximum.

The used algorithm decides whether a particular data point is a local maximum by looking at its nearest neighbors only. This means that it cannot decide if a region in which all adjacent data values are equal constitutes a local maximum. Such regions are ignored.