islocalmin

Find local minima

Syntax

TF = islocalmin(A)

TF = islocalmin(A,dim)

TF = islocalmin(___,Name,Value)

[TF,P] = islocalmin(___)

Description

TF = islocalmin(A) returns a logical array whose elements are 1 (true) when a local minimum is detected in the corresponding element of an array, table, or timetable.

TF = islocalmin(A,dim) specifies the dimension of A to operate along. For example, islocalmin(A,2) finds local minima of each row of a matrix A.

TF = islocalmin(___,Name,Value) specifies additional parameters for finding local minima using one or more name-value pair arguments. For example, islocalmin(A,'SamplePoints',t) finds local minima of A with respect to the time stamps contained in the time vector t.

[TF,P] = islocalmin(___) also returns the prominence corresponding to each element of A for any of the previous syntaxes.

Examples

Local Minima in Vector

Compute and plot the local minima of a vector of data.

x = 1:100;
A = (1-cos(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.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical | table | timetable

dim — Operating dimension

positive integer scalar

Operating 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

Name-Value Pair Arguments

Specify optional comma-separated 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.

Example: TF = islocalmin(A,'MinProminence',2)

'MinProminence' — Minimum prominence

nonnegative scalar

Minimum prominence, specified as the comma-separated pair consisting of 'MinProminence' and a nonnegative scalar. islocalmin returns only local minima whose prominence is at least the value specified. The default minimum prominence value is size(A,dim) for input A and operating dimension dim.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

'window' — Window length

positive integer scalar | two-element vector of positive integers | positive duration scalar | two-element vector of positive durations

Window length, specified as a positive integer scalar, a two-element vector of positive integers, a positive duration scalar, or a two-element vector of positive durations.

When window is a positive integer scalar, then the window is centered about the current element and contains window-1 neighboring elements. If window is even, then the window is centered about the current and previous elements. If window is a two-element vector of positive integers [b f], then the window contains the current element, b elements backward, and f elements forward.

When A is a timetable or when 'SamplePoints' is specified as a datetime or duration vector, window must be of type duration, and the window is computed relative to the sample points.

When the window length is also specified as an output argument, the output value matches the input value.

Data Types: double | single | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | duration

'ProminenceWindow' — Prominence window

positive integer scalar | two-element vector of positive integers | positive duration scalar | two-element vector of positive durations

Prominence window, specified as the comma-separated pair consisting of 'ProminenceWindow' and a positive integer scalar, a two-element vector of positive integers, a positive duration scalar, or a two-element 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 k-1 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 two-element 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 comma-separated 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' name-value pairs, flat region points are jointly considered a single minimum point.

'MinSeparation' — Minimum separation

0 (default) | nonnegative scalar

Minimum separation between local minima, specified as the comma-separated 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 minima

positive integer scalar

Maximum number of minima detected, specified as the comma-separated 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

'SamplePoints' — Sample points

vector

Sample points, specified as the comma-separated pair consisting of 'SamplePoints' and a vector. The sample points represent the location of the data in A. Sample points do not need to be uniformly sampled, but must be sorted with unique elements. By default, the sample points vector is [1 2 3 ...].

islocalmin does not support this name-value pair when the input data is a timetable.

Data Types: double | single | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | datetime | duration

'DataVariables' — Table variables

variable name | cell array of variable names | numeric vector | logical vector | function handle

Table variables, specified as the comma-separated pair consisting of 'DataVariables' and a variable name, a cell array of variable names, a numeric vector, a logical vector, or a function handle. The 'DataVariables' value indicates which columns of an input table or timetable to operate on. This value can be one of the following:

• A character vector specifying a single table variable name

• A cell array of character vectors where each element is a table variable name

• A vector of table variable indices

• A logical vector whose elements each correspond to a table variable, where true includes the corresponding variable and false excludes it

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

The specified table variables must have numeric or logical type.

Example: 'Age'

Example: {'Height','Weight'}

Example: @isnumeric

Data Types: char | cell | double | single | logical | function_handle

Output Arguments

TF — Local minima indicator

vector | matrix | multidimensional array

Local minima indicator, returned as a vector, matrix, or multidimensional array. TF is the same size as A.

Data Types: logical

P — Prominence

vector | matrix | multidimensional array

Prominence, 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.

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 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).

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' name-value pair.

• The 'MaxNumExtrema', 'MinSeparation', and 'SamplePoints' name-value pairs are not supported.

• The value of 'DataVariables' cannot be a function handle.

For more information, see Tall Arrays.