cummax

Cumulative maximum

Syntax

M = cummax(A)

M = cummax(A,dim)

M = cummax(___,direction)

M = cummax(___,nanflag)

Description

M = cummax(A) returns the cumulative maximum elements of A.

• If A is a vector, then M is a vector of the same size and type and contains the cumulative maxima of A.

• If A is a matrix, then M is a matrix of the same size and type and contains the cumulative maxima in each column of A.

• If A is a multidimensional array, then M is an array of the same size and type and contains the cumulative maxima along the first array dimension of A whose size does not equal 1.

• If A is a table or timetable, then cummax(A) returns a table or timetable containing the cumulative maxima of each variable. (since R2023a)

M = cummax(A,dim) returns the cumulative maxima along dimension dim. For example, if A is a matrix, then cummax(A,2) returns the cumulative maxima along the rows of A.

M = cummax(___,direction) specifies the direction for any of the previous syntaxes. For example, cummax(A,2,"reverse") returns the cumulative maxima of A by working from end to beginning of the second dimension of A.

M = cummax(___,nanflag) specifies whether to omit or include NaN values in A. For example, cummax(A,"includenan") includes NaN values when computing each maximum. By default, cummax omits NaN values.

Examples

Cumulative Maximum in Vector

Find the cumulative maxima of a 1-by-10 vector of random integers.

v = randi(10,1,10)

v = 1×10

     9    10     2    10     7     1     3     6    10    10

M = cummax(v)

M = 1×10

     9    10    10    10    10    10    10    10    10    10

Cumulative Maximum in Matrix Columns

Find the cumulative maxima of the columns of a 3-by-3 matrix.

A = [3 5 2; 1 6 3; 7 8 1]

A = 3×3

     3     5     2
     1     6     3
     7     8     1

M = cummax(A)

M = 3×3

     3     5     2
     3     6     3
     7     8     3

Cumulative Maximum in Matrix Rows

Find the cumulative maxima of the rows of a 3-by-3 matrix.

A = [3 5 2; 1 6 3; 7 8 1]

A = 3×3

     3     5     2
     1     6     3
     7     8     1

M = cummax(A,2)

M = 3×3

     3     5     5
     1     6     6
     7     8     8

Reverse Cumulative Maximum

Calculate the cumulative maxima in the third dimension of a 2-by-2-by-3 array. Specify direction as "reverse" to work from the end of the third dimension to the beginning.

A = cat(3,[1 2; 3 4],[9 10; 11 12],[5 6; 7 8])

A = 
A(:,:,1) =

     1     2
     3     4


A(:,:,2) =

     9    10
    11    12


A(:,:,3) =

     5     6
     7     8

M = cummax(A,3,"reverse")

M = 
M(:,:,1) =

     9    10
    11    12


M(:,:,2) =

     9    10
    11    12


M(:,:,3) =

     5     6
     7     8

Cumulative Maximum Including Missing Values

Create a matrix containing NaN values.

A = [3 5 NaN 4; 2 6 2 9; 1 3 0 NaN]

A = 3×4

     3     5   NaN     4
     2     6     2     9
     1     3     0   NaN

Compute the cumulative maxima of the matrix, including NaN values. For matrix columns that contain any NaN value, the cumulative maximum values are NaN as soon as the first NaN value is encountered.

M = cummax(A,"includenan")

M = 3×4

     3     5   NaN     4
     3     6   NaN     9
     3     6   NaN   NaN

Input Arguments

A — Input array

vector | matrix | multidimensional array | table | timetable

Input array, specified as a vector, matrix, multidimensional array, table, or timetable. For complex elements, cummax compares the magnitude of the elements. If magnitudes are equal, cummax also compares the phase angles.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical | duration | table | timetable
Complex Number Support: Yes

dim — Dimension to operate along

positive integer scalar

Dimension to operate along, specified as a positive integer scalar. If you do not specify the dimension, then the default is the first array dimension whose size does not equal 1.

Consider a two-dimensional input array, A:

• cummax(A,1) works on successive elements in the columns of A and returns an array of the same size as A with the cumulative maxima in each column.

  

• cummax(A,2) works on successive elements in the rows of A and returns an array of the same size as A with the cumulative maxima in each row.

  

cummax returns A if dim is greater than ndims(A).

direction — Direction of cumulation

"forward" (default) | "reverse"

Direction of cumulation, specified as one of these values:

• "forward" — Work from 1 to end of the operating dimension.

• "reverse" — Works from end to 1 of the operating dimension.

nanflag — Missing value condition

"omitmissing" (default) | "omitnan" | "includemissing" | "includenan"

Missing value condition, specified as one of these values:

• "omitmissing" or "omitnan" — Ignore NaN values in A when computing the cumulative maxima. If A has consecutive leading NaN values, then the corresponding elements in M are NaN. "omitmissing" and "omitnan" have the same behavior.

• "includemissing" or "includenan" — Include NaN values in A when computing the cumulative maxima. Elements in M are NaN as soon as the first NaN value in A is encountered. "includemissing" and "includenan" have the same behavior.

Tips

• The "reverse" option in many cumulative functions allows quick directional calculations without requiring a flip or reflection of the input array.

Extended Capabilities

Tall Arrays

Calculate with arrays that have more rows than fit in memory.

This function supports tall arrays with the limitations:

The "reverse" direction is not supported.

For more information, see Tall Arrays.

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

The cummax function supports GPU array input with these usage notes and limitations:

• The nanflag argument is not supported.

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Distributed Arrays

Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

Version History

Introduced in R2014b

R2023a: Specify missing value condition

Omit or include missing values in the input array when computing the cumulative maxima by using the "omitmissing" or "includemissing" options. These options have the same behavior as the "omitnan" and "includenan" options, respectively.

R2023a: Perform calculations directly on tables and timetables

The cummax function can calculate on all variables within a table or timetable without indexing to access those variables. All variables must have data types that support the calculation. For more information, see Direct Calculations on Tables and Timetables.