Find local minima
specifies additional parameters for finding local minima using one or more
namevalue pair 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
for any
of the previous syntaxes.
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*')
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
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*')
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*')
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
A
— Input dataInput data, specified as a vector, matrix, multidimensional array, table, or timetable.
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
 logical
 table
 timetable
dim
— Operating dimensionOperating dimension, specified as a positive integer scalar. By default,
islocalmin
operates along the first dimension whose
size does not equal 1.
For example, if A
is a matrix, then
islocalmin(A,1)
operates along the rows of
A
, computing local minima for each column.
islocalmin(A,2)
operates along the columns of
A
, computing local minima for each row.
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
Specify optional
commaseparated pairs of Name,Value
arguments. Name
is
the argument name and Value
is the corresponding value.
Name
must appear inside quotes. You can specify several name and value
pair arguments in any order as
Name1,Value1,...,NameN,ValueN
.
TF = islocalmin(A,'MinProminence',2)
'SamplePoints'
— Sample pointsSample points, specified as the commaseparated pair consisting of
'SamplePoints'
and a vector. The sample points
represent the xaxis locations of the data in
A
, and must be sorted and contain unique
elements. Sample points do not need to be uniformly sampled. The default
sample points vector is [1 2 3 ...]
.
Note
This namevalue pair is not supported when the input data is a timetable
. Timetables always 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: islocalmax(T,'SamplePoints',0:0.1:10)
Data Types: double
 single
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
 datetime
 duration
'DataVariables'
— Table variables to operate onvartype
subscriptTable 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
. Other variables in the table not
specified by 'DataVariables'
are not operated on, so
the output contains false
values for those
variables.
Option  Description  Examples 

Variable name  A character vector or scalar string 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"])
'MinProminence'
— Minimum prominenceMinimum prominence, specified as the commaseparated pair consisting
of 'MinProminence'
and a nonnegative scalar.
islocalmin
returns only local minima whose
prominence is at least the value specified.
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
'ProminenceWindow'
— Prominence windowProminence window, specified as the commaseparated pair consisting of
'ProminenceWindow'
and 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 [b f]
of
positive integers, 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 when
'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.
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
 duration
'FlatSelection'
— Flat region indicator'center'
(default)  'first'
 'last'
 'all'
Flat region indicator for when a local minimum value is repeated
consecutively, specified as the commaseparated pair consisting of
'FlatSelection'
and one of the following:
'center'
— Indicate only the center
element of a flat region as the local minimum. The element
of TF
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
of TF
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 of
TF
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 of
TF
corresponding to all parts of the
flat are 1.
When using the 'MinSeparation'
or
'MaxNumExtrema'
namevalue pairs, flat region
points are jointly considered a single minimum point.
'MinSeparation'
— Minimum separationMinimum separation between local minima, specified as the
commaseparated pair consisting of 'MinSeparation'
and 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
.
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
 duration
'MaxNumExtrema'
— Maximum number of minimaMaximum number of minima detected, specified as the commaseparated
pair consisting of 'MaxNumExtrema'
and a positive
integer scalar. islocalmin
finds no more than the
specified number of most prominent minima, which is the length of the
operating dimension by default.
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
TF
— Local minima indicatorLocal minima indicator, returned as a vector, matrix, or multidimensional
array. TF
is the same size as
A
.
Data Types: logical
P
— ProminenceProminence, returned as a vector, matrix, or multidimensional
array. P
is the same size as A
.
If the input data has a signed or unsigned integer type, then
P
is an unsigned integer.
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 to the left and to the right of 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)
.
Usage notes and limitations:
Tall timetables are not supported.
You must specify a value for the 'ProminenceWindow'
namevalue pair.
The 'MaxNumExtrema'
, 'MinSeparation'
, and 'SamplePoints'
namevalue pairs are not supported.
The value of 'DataVariables'
cannot be a function handle.
For more information, see Tall Arrays.
Usage notes and limitations:
You must enable support for variablesize arrays.
The 'ProminenceWindow'
namevalue pair is not
supported.
Find Local
Extrema  ischange
 islocalmax
 isoutlier
 min
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