Someone who is not an employee of TMW cannot see the code. (I can't, as I am not an employee.) And if someone is an employee, they generally do not give specifics of code that is not an m-file. But, this is one of those simple codes that are mainly simple heuristics, an ad hoc algorithm that gets the job done. Nothing more is needed. And a basic rule when writing code is that if a simple code is sufficient, then just write the simple code. Get the job done, and move onto more difficult problems.
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
As such, the islocalmax function detects if both immediate neighbors of an element are less than the element in the middle. So, without any parameters set, all that is required should be a tiny amount of excess.
A little experimentation should be sufficient to determine the basic rules the code will follow.
So only the number 3 was flagged. An element at the end can not be a local max, by that definition, since the immediate elements on either side are not less than it.
This next test shows that an inequality is required. All elements of a constant vector are not local maxima.
How about a case where there is an internal region that is greater than the neightbors, but is constant? We should see three local maxima in this next test. Only the third maximum is a true extremum in my eyes, because the first two cases are not distiinct from the immediate neighbors. But the other two cases still would seem to qualify, depending on how the inequality test is structured.
V = [1 2 2 1 3 3 3 1 3 4 3 1];
islocalmax(V)
ans =
0 1 0 0 0 1 0 0 0 1 0 0
Next, remember that we cannot have a local maximum at either end of a vector.
A perturbation by eps is all that is required to introduce a max though.
V(5) = 1 + eps
V =
0 0 0 1.0000 1.0000 1.0000
Unless, of course, one has decided to adjust the tolerance for a peak, using the "minprominence" property.
islocalmax(V,'minprominence',2*eps)
So all that does is adjust the test for inequality that is applied, using a tolerance.
Anyway, I would argue there is surely no serious mathematics behind this code, beyond a set of simple tests of inequality. There are several options in the code that will make those tests more complex, but still nothing sophisticated, just more complicated. Yes, I might apply diff to the vector to perform some of those tests, but diff is just a simple forward difference engine.
