islocalmin
Find local minima
Syntax
Description
specifies parameters in addition to any of the input argument combinations in
previous syntaxes for finding local minima using one or more namevalue arguments.
For example, TF
= islocalmin(___,Name,Value
)islocalmin(A,'SamplePoints',t)
finds local minima of
A
with respect to the time stamps contained in the time
vector t
.
[
also returns the prominence corresponding to each element of TF
,P
] = islocalmin(___)A
.
Examples
Local Minima in Vector
Compute and plot the local minima of a vector of data.
x = 1:100;
A = (1cos(2*pi*0.01*x)).*sin(2*pi*0.15*x);
TF = islocalmin(A);
plot(x,A,x(TF),A(TF),'r*')
Minima in Matrix Rows
Create a matrix of data, and compute the local minima for each row.
A = 25*diag(ones(5,1)) + rand(5,5); TF = islocalmin(A,2)
TF = 5x5 logical array
0 0 0 1 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 1 0 0
Separated Minima
Compute the local minima of a vector of data relative to the time stamps in the vector t
. Use the MinSeparation
parameter to compute minima that are at least 45 minutes apart.
t = hours(linspace(0,3,15)); A = [2 4 6 4 3 7 5 6 5 10 4 1 3 2 0]; TF = islocalmin(A,'MinSeparation',minutes(45),'SamplePoints',t); plot(t,A,t(TF),A(TF),'r*')
Flat Minima Regions
Specify a method for indicating consecutive minima values.
Compute the local minima of data that contains consecutive minima values. Indicate the minimum of each flat region based on the first occurrence of that value.
x = 0:0.1:5; A = max(0.75, sin(pi*x)); TF1 = islocalmin(A,'FlatSelection','first'); plot(x,A,x(TF1),A(TF1),'r*')
Indicate the minimum of each flat region with all occurrences of that value.
TF2 = islocalmin(A,'FlatSelection','all'); plot(x,A,x(TF2),A(TF2),'r*')
Prominent Minima
Compute the local minima of a vector of data and their prominence, and then plot them with the data.
x = 1:100; A = peaks(100); A = A(50,:); [TF1,P] = islocalmin(A); P(TF1)
ans = 1×2
2.7585 1.7703
plot(x,A,x(TF1),A(TF1),'r*') axis tight
Compute the most prominent minimum in the data by specifying a minimum prominence requirement.
TF2 = islocalmin(A,'MinProminence',2); plot(x,A,x(TF2),A(TF2),'r*') axis tight
Input Arguments
A
— Input data
vector  matrix  multidimensional array  table  timetable
Input data, specified as a vector, matrix, multidimensional array, table, or timetable.
dim
— Operating dimension
positive integer scalar
Operating dimension, specified as a positive integer scalar. If no value is specified, then the default is the first array dimension whose size does not equal 1.
Consider an m
byn
input matrix,
A
:
islocalmin(A,1)
computes local minima according to the data in each column ofA
and returns anm
byn
matrix.islocalmin(A,2)
computes local minima according to the data in each row ofA
and returns anm
byn
matrix.
For table or timetable input data, dim
is not supported
and operation is along each table or timetable variable separately.
NameValue Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Namevalue arguments must appear after other arguments, but the order of the
pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.
Example: TF = islocalmin(A,'MinProminence',2)
SamplePoints
— Sample points
vector  table variable name  scalar  function handle  table vartype
subscript
Sample points, specified as a vector of sample point values or one of
the options in the following table when the input data is a table. The
sample points represent the xaxis locations of the
data, and must be sorted and contain unique elements. Sample points do
not need to be uniformly sampled. The vector [1 2 3
...]
is the default.
When the input data is a table, you can specify the sample points as a table variable using one of these options.
Option for Table Input  Description  Examples 

Variable name  A character vector or scalar string specifying a single table variable name 

Scalar variable index  A scalar table variable index 

Logical vector  A logical vector whose elements each correspond to a table variable, where


Function handle  A function handle that takes a table variable as input and returns a logical scalar,
which must be 

vartype subscript  A table subscript generated by the 

Note
This namevalue argument is not supported when the input data is a
timetable
. Timetables use the vector of row times as the sample
points. To use different sample points, you must edit the timetable so that the row times
contain the desired sample points.
Example: islocalmin(A,'SamplePoints',0:0.1:10)
Example: islocalmin(T,'SamplePoints',"Var1")
DataVariables
— Table variables to operate on
table variable name  scalar  vector  cell array  function handle  table vartype
subscript
Table variables to operate on, specified as the commaseparated pair
consisting of DataVariables
and one of the options in
this table. The DataVariables
value indicates which
variables of the input table to examine for local minima. The data type
associated with the indicated variables must be numeric or
logical
.
The first output TF
contains
false
for variables not specified by
DataVariables
unless the value of
OutputFormat
is
'tabular'
.
Option  Description  Examples 

Variable name  A character vector or string scalar specifying a single table variable name 

Vector of variable names  A cell array of character vectors or string array, where each element is a table variable name 

Scalar or vector of variable indices  A scalar or vector of table variable indices 

Logical vector  A logical vector whose elements each correspond to a table variable, where


Function handle  A function handle that takes a table variable as input and returns a logical scalar 

vartype subscript  A table subscript generated by the 

Example: islocalmin(T,'DataVariables',["Var1" "Var2"
"Var4"])
OutputFormat
— Output data type
'logical'
(default)  'tabular'
Output data type, specified as one of these values:
'logical'
— For table or timetable input data, return the outputTF
as a logical array.'tabular'
— For table input data, return the outputTF
as a table. For timetable input data, return the outputTF
as a timetable.
For vector, matrix, or multidimensional array input data,
OutputFormat
is not supported.
Example: islocalmin(T,'OutputFormat','tabular')
MinProminence
— Minimum prominence
0 (default)  nonnegative scalar
Minimum prominence, specified as a nonnegative scalar.
islocalmin
returns only local minima whose
prominence is at least the value specified.
ProminenceWindow
— Prominence window
positive integer scalar  twoelement vector of positive integers  positive duration scalar  twoelement vector of positive durations
Prominence window, specified as a positive integer scalar, a twoelement vector of positive integers, a positive duration scalar, or a twoelement vector of positive durations. The value defines a window of neighboring points for which to compute the prominence for each local minimum.
When the window value is a positive integer scalar
k, then the window is centered about each local
minimum and contains k1
neighboring elements. If k is even, then the window
is centered about the current and previous elements. If a local minimum
is within a flat region, then islocalmin
treats the
entire flat region as the center point of the window.
When the value is a twoelement vector of positive integers
[b f]
, then the window contains the local
minimum, b
elements backward, and
f
elements forward. If a local minimum is within
a flat region, then the window starts b
elements
before the first point of the region and ends f
elements after the last point of the region.
When the input data is a timetable or SamplePoints
is specified as a datetime
or
duration
vector, the window value must be of type
duration
, and the window is computed relative to
the sample points.
FlatSelection
— Flat region indicator
'center'
(default)  'first'
 'last'
 'all'
Flat region indicator for when a local minimum value is repeated consecutively, specified as one of these values:
'center'
— Indicate only the center element of a flat region as the local minimum. The element ofTF
corresponding to the center of the flat is 1, and is 0 for the remaining flat elements.'first'
— Indicate only the first element of a flat region as the local minimum. The element ofTF
corresponding to the start of the flat is 1, and is 0 for the remaining flat elements.'last'
— Indicate only the last element of a flat region as the local minimum. The element ofTF
corresponding to the end of the flat is 1, and is 0 for the remaining flat elements.'all'
— Indicate all the elements of a flat region as the local minima. The elements ofTF
corresponding to all parts of the flat are 1.
When using the MinSeparation
or
MaxNumExtrema
namevalue arguments, flat region
points are jointly considered a single minimum point.
MinSeparation
— Minimum separation
0 (default)  nonnegative scalar
Minimum separation between local minima, specified as a nonnegative
scalar. The separation value is defined in the same units as the sample
points vector, which is [1 2 3 ...]
by default. When
the separation value is greater than 0, islocalmin
selects the smallest local minimum and ignores all other local minima
within the specified separation. This process is repeated until there
are no more local minima detected.
When the sample points vector has type datetime
,
the separation value must have type duration
.
MaxNumExtrema
— Maximum number of minima
positive integer scalar
Maximum number of minima to detect, specified as a positive integer
scalar. islocalmin
finds no more than the specified
number of the most prominent minima, which is the length of the
operating dimension by default.
Output Arguments
TF
— Local minima indicator
vector  matrix  multidimensional array  table  timetable
Local minima indicator, returned as a vector, matrix, multidimensional array, table, or timetable.
TF
is the same size as A
unless the
value of OutputFormat
is 'tabular'
. If
the value of OutputFormat
is
'tabular'
, then TF
only has variables
corresponding to the DataVariables
specified.
Data Types: logical
P
— Prominence
vector  matrix  multidimensional array  table  timetable
Prominence, returned as a vector, matrix, multidimensional array, table, or timetable.
If
P
is a vector, matrix, or multidimensional array,P
is the same size asA
.If
P
is a table or timetable,P
is the same height asA
and only has variables corresponding to theDataVariables
specified.
If the input data has a signed or unsigned integer type, then
P
is an unsigned integer.
More About
Prominence of Local Minimum
The prominence of a local minimum (or valley) measures how the valley stands out with respect to its depth and location relative to other valleys.
To measure the prominence of a valley, first extend a horizontal line from the valley. Find where the line intersects the data on the left and on the right, which will either be another valley or the end of the data. Mark these locations as the outer endpoints of the left and right intervals. Next, find the highest peak in both the left and right intervals. Take the smaller of these two peaks, and measure the vertical distance from that peak to the valley. This distance is the prominence.
For a vector x
, the largest prominence is at
most max(x)min(x)
.
Extended Capabilities
Tall Arrays
Calculate with arrays that have more rows than fit in memory.
Usage notes and limitations:
Tall timetables are not supported.
You must specify a value for the
ProminenceWindow
namevalue argument.The
MaxNumExtrema
,MinSeparation
, andSamplePoints
namevalue arguments are not supported.The value of
DataVariables
cannot be a function handle.
For more information, see Tall Arrays.
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Usage notes and limitations:
You must enable support for variablesize arrays.
The
ProminenceWindow
andOutputFormat
namevalue arguments are not supported.
ThreadBased Environment
Run code in the background using MATLAB® backgroundPool
or accelerate code with Parallel Computing Toolbox™ ThreadPool
.
This function fully supports threadbased environments. For more information, see Run MATLAB Functions in ThreadBased Environment.
GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.
This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).
Version History
Introduced in R2017bR2022a: Return table or timetable containing logical output
For table or timetable input data, return a tabular output TF
instead
of a logical array by setting the OutputFormat
namevalue argument to
'tabular'
.
R2021b: Specify sample points as table variable
For table input data, specify the sample points as a table variable using the
SamplePoints
namevalue argument.
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