Find (local?) maxima when two maxima are adjacent to each other (maybe using islocalmax or findpeaks?)

In the following bar, I would have two max values (i.e. 37), one at location 1 and one at location 2 in the x-axis.

Would it be still possible to find them with either islocalmax or findpeaks?

freq = [37 37 23 1 1 1];
bar(freq)

m = islocalmax(freq)

m = 1×6 logical array
   0   0   0   0   0   0

Answer 1

[Kevin Holly]

If it wasn't on the edge, you could use the following:

freq = [37 37 23 1 1 1];
m = islocalmax(freq,'FlatSelection','all')

m = 1×6 logical array
   0   0   0   0   0   0

workaround:

freq = [37 37 23 1 1 1];
m = islocalmax([0 freq],'FlatSelection','all')

m = 1×7 logical array
   0   1   1   0   0   0   0

m(1)=[];
m

m = 1×6 logical array
   1   1   0   0   0   0

Answer 2

[Image Analyst]

If it's also a global max, you can do

freq = [37 37 23 1 1 1];
[~, indexes] = find(freq == max(freq))

indexes = 1×2

1 2

Works no matter if the max is inside the array or at one of the ends.

[Sim]

Many thanks @Image Analyst!! If possible I would accept both your and @Kevin Holly's answers... :-)

Answer 3

[John D'Errico]

help islocalmax

 ISLOCALMAX   Detect local maxima in data.
    TF = ISLOCALMAX(A) returns a logical array whose elements are true when
    a local maximum is detected in the corresponding element of A. If A is
    a matrix or a table, ISLOCALMAX operates on each column separately. If
    A is an N-D array, ISLOCALMAX operates along the first array dimension
    whose size does not equal 1.
 
    TF = ISLOCALMAX(A,DIM) specifies the dimension to operate along.
 
    TF = ISLOCALMAX(...,'MinProminence',P) returns only those local maxima
    whose prominence is at least P. The prominence of a local maximum is
    the smaller of the largest decrease in value on the left side and on
    the right side of the local maximum before encountering a larger local
    maximum. For a vector X, the largest prominence is at most
    MAX(X)-MIN(X).
 
    TF = ISLOCALMAX(...,'FlatSelection',F) specifies how local maxima are
    indicated for flat regions containing repeated local maxima values.
    F must be:
        'center'  - (default) middle index of a flat region marked as true.
        'first'   - first index of a flat region marked as true.
        'last'    - last index of a flat region marked as true.
        'all'     - all flat region indices marked as true.
 
    TF = ISLOCALMAX(...,'MinSeparation',S) specifies S as the minimum
    separation between local maxima. S is defined in units of the sample
    points. When S > 0, ISLOCALMAX selects the largest local maximum and
    ignores all other local maximum within S units of it. The process is
    repeated until there are no more local maxima detected. By default, S =
    0.
 
    TF = ISLOCALMAX(...,'MaxNumExtrema',N) detects no more than the N most
    prominent local maxima. By default, N is equal to SIZE(A,DIM).
 
    TF = ISLOCALMAX(...,'SamplePoints',X) specifies the sample points X
    representing the location of the data in A. X must be a numeric or
    datetime vector, and must be sorted with unique elements. If the first
    input is a table, X can also specify a table variable. For example, X
    can specify time stamps for the data in A. By default, ISLOCALMAX uses
    data sampled uniformly at points X = [1 2 3 ... ].
 
    TF = ISLOCALMAX(...,'ProminenceWindow',K) for a positive scalar K
    computes the prominence of each local maxima only within a window of
    width K centered around the maxima.  For flat regions, the window
    extends K/2 units before the first point in the region and K/2 units
    after the last point in the region.
 
    TF = ISLOCALMAX(...,'ProminenceWindow',[NB NF]) for non-negative
    scalars NB and NF computes the prominence of each local maxima only
    within a window from NB units before the local maxima to NF units after
    it.  For flat regions, the window extends NB units before the first
    point in the region and NF units after the last point in the region.
 
    If 'SamplePoints' are specified, the units of the prominence window are
    relative to the sample points.
 
    [TF,P] = ISLOCALMAX(A,...) also returns the prominence for each value
    of A.  Points that are not local maxima have a prominence of 0.
 
    Arguments supported only when first input is table or timetable:
 
    TF = ISLOCALMAX(...,'DataVariables',DV) finds local maxima only in the
    table variables specified by DV. The default is all table variables in
    A. DV must be a table variable name, a cell array of table variable
    names, a vector of table variable indices, a logical vector, a function
    handle that returns a logical scalar (such as @isnumeric), or a table 
    vartype subscript. TF has the same size as A. DV cannot be specified if
    A is not a table or a timetable. Only numeric or logical data variables
    should be specified.
 
    TF = ISLOCALMAX(...,'OutputFormat',FORMAT) specifies the format for the  
    output TF with respect to the table variables. FORMAT must be: 
    'logical'- (default) TF is a logical array matching the size of A. 
    'tabular'  - TF is a table or timetable that is the same height as A with
               logical variables corresponding to specified table variables 
 
    EXAMPLE: Find local maxima in a vector of data.
        x = 1:100;
        A = (1-cos(2*pi*0.01*x)).*sin(2*pi*0.15*x);
        tf = islocalmax(A);
 
    EXAMPLE: Filter out less prominent local maxima.
        A = peaks(256);
        A = A(:, 150);
        tf = islocalmax(A, 'MinProminence', 1);
 
    EXAMPLE: Filter out local maxima too close to each other in time.
        t = hours(linspace(0, 3, 15));
        A = [2 4 6 4 3 7 5 6 5 10 4 -1 -3 -2 0];
        S = minutes(45);
        tf = islocalmax(A, 'MinSeparation', S, 'SamplePoints', t);
 
    EXAMPLE: Detect center points of flat maxima regions.
        x = 0:0.1:10;
        A = min(0.75, sin(pi*x));
        tf = islocalmax(A, 'FlatSelection', 'center');
 
    See also islocalmin, ischange, isoutlier, max, maxk

    Documentation for islocalmax
       doc islocalmax

    Other uses of islocalmax

       gpuArray/islocalmax    tall/islocalmax

Now, look carefully at the elements of that array.

freq = [37 37 23 1 1 1];
m = islocalmax(freq)

m = 1×6 logical array
   0   0   0   0   0   0

Is element 1 a local maximum? NO. Elements 1 and 2 have the same value. NEITHER is local max.

How about element 3? Clearly it is not so. And elements 4,5,6 are shared local minima.

Your vector had NO local maxima. You cannot find something that does not exist.

Change your vector.

freq = [37 38 23 1 2 1];
m = islocalmax(freq)

m = 1×6 logical array
   0   1   0   0   1   0

It should be no surprise that TWO local maxima were found.

So if you want help in finding the local maxima in that vector, then you need to define what a local max means to you.

[Sim]

Thanks @John D'Errico, you are completely right, and many thanks for your great explanation!! ...Also, you are fully right since I did not "define what a local max means to me"..... and I did not express myself in the correct way when writing the question....

What I was looking for was something like the answer of @Image Analyst and/or the workaround proposed by @Kevin Holly....