# Documentation

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# max

Largest elements in array

## Syntax

M = max(A)
M = max(A,[],dim)
M = max(A,[],nanflag)
M = max(A,[],dim,nanflag)
[M,I] = max(___)
C = max(A,B)
C = max(A,B,nanflag)

## Description

example

M = max(A) returns the largest elements of A.

• If A is a vector, then max(A) returns the largest element of A.

• If A is a matrix, then max(A) is a row vector containing the maximum value of each column.

• If A is a multidimensional array, then max(A) operates along the first array dimension whose size does not equal 1, treating the elements as vectors. The size of this dimension becomes 1 while the sizes of all other dimensions remain the same. If A is an empty array whose first dimension has zero length, then max(A) returns an empty array with the same size as A.

example

M = max(A,[],dim) returns the largest elements along dimension dim. For example, if A is a matrix, then max(A,[],2) is a column vector containing the maximum value of each row.

example

M = max(A,[],nanflag) specifies whether to include or omit NaN values in the calculation. For example, max(A,[],'includenan') includes all NaN values in A while max(A,[],'omitnan') ignores them.

M = max(A,[],dim,nanflag) also specifies the dimension to operate along when using the nanflag option.

example

[M,I] = max(___) finds the indices of the maximum values of A and returns them in output vector I, using any of the input arguments in the previous syntaxes. If the maximum value occurs more than once, then max returns the index corresponding to the first occurrence.

example

C = max(A,B) returns an array with the largest elements taken from A or B.

C = max(A,B,nanflag) also specifies how to treat NaN values.

## Examples

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Create a vector and compute its largest element.

A = [23 42 37 18 52];
M = max(A)
M = 52

Create a complex vector and compute its largest element, that is, the element with the largest magnitude.

A = [-2+2i 4+i -1-3i];
max(A)
ans =
4.0000 + 1.0000i

Create a matrix and compute the largest element in each column.

A = [2 8 4; 7 3 9]
A =

2     8     4
7     3     9

M = max(A)
M =

7     8     9

Create a matrix and compute the largest element in each row.

A = [1.7 1.2 1.5; 1.3 1.6 1.99]
A =

1.7000    1.2000    1.5000
1.3000    1.6000    1.9900

M = max(A,[],2)
M =

1.7000
1.9900

Create a matrix A and compute the largest elements in each column, as well as the row indices of A in which they appear.

A = [1 9 -2; 8 4 -5]
A =

1     9    -2
8     4    -5

[M,I] = max(A)
M =

8     9    -2

I =

2     1     1

Create a matrix and return the largest value between each of its elements compared to a scalar.

A = [1 7 3; 6 2 9]
A =

1     7     3
6     2     9

B = 5;
C = max(A,B)
C =

5     7     5
6     5     9

Create a matrix A and use its column representation, A(:), to find the value and index of the largest element.

A = [8 2 4; 7 3 9]
A =

8     2     4
7     3     9

A(:)
ans =

8
7
2
3
4
9

[M,I] = max(A(:))
M = 9
I = 6

I is the index of A(:) containing the largest element.

Now, use the ind2sub function to extract the row and column indices of A corresponding to the largest element.

[I_row, I_col] = ind2sub(size(A),I)
I_row = 2
I_col = 3

If you need only the maximum value of A and not its index, then call the max function twice.

M = max(max(A))
M = 9

Create a vector and compute its maximum, excluding NaN values.

A = [1.77 -0.005 3.98 -2.95 NaN 0.34 NaN 0.19];
M = max(A,[],'omitnan')
M = 3.9800

max(A) will also produce this result since 'omitnan' is the default option.

Use the 'includenan' flag to return NaN.

M = max(A,[],'includenan')
M = NaN

## Input Arguments

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Input array, specified as a scalar, vector, matrix, or multidimensional array.

• If A is complex, then max(A) returns the complex number with the largest magnitude. If magnitudes are equal, then max(A) returns the value with the largest magnitude and the largest phase angle.

• If A is a scalar, then max(A) returns A.

• If A is a 0-by-0 empty array, then max(A) is as well.

If A has type categorical, then it must be ordinal.

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

Dimension to operate along, 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.

Dimension dim indicates the dimension whose length reduces to 1. The size(M,dim) is 1, while the sizes of all other dimensions remain the same, unless size(A,dim) is 0. If size(A,dim) is 0, then max(A,dim) returns an empty array with the same size as A.

Consider a two-dimensional input array, A:

• If dim = 1, then max(A,[],1) returns a row vector containing the largest element in each column.

• If dim = 2, then max(A,[],2) returns a column vector containing the largest element in each row.

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

Additional input array, specified as a scalar, vector, matrix, or multidimensional array. Numeric inputs A and B must either be the same size or have sizes that are compatible (for example, A is an M-by-N matrix and B is a scalar or 1-by-N row vector). For more information, see Compatible Array Sizes for Basic Operations.

If A and B are datetime, duration, or categorical arrays, then they must be the same size unless one is a scalar.

• A and B must be the same data type unless one is a double. In that case, the data type of the other array can be single, duration, or any integer type.

• If A and B are ordinal categorical arrays, they must have the same sets of categories with the same order.

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

NaN condition, specified as one of these values:

• 'omitnan' — Ignore all NaN values in the input.

• 'includenan' — Include the NaN values in the input for the calculation.

For datetime arrays, you can also use 'omitnat' or 'includenat' to omit and include NaT values, respectively.

The max function does not support the nanflag option for categorical arrays.

Data Types: char

## Output Arguments

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Maximum values, returned as a scalar, vector, matrix, or multidimensional array. size(M,dim) is 1, while the sizes of all other dimensions match the size of the corresponding dimension in A, unless size(A,dim) is 0. If size(A,dim) is 0, then M is an empty array with the same size as A.

Index to maximum values of A, returned as a scalar, vector, matrix, or multidimensional array. I is the same size as M. If the largest element occurs more than once, then I contains the index to the first occurrence of the value.

Maximum elements from A or B, returned as a scalar, vector, matrix, or multidimensional array. The size of C is determined by implicit expansion of the dimensions of A and B. For more information, see Compatible Array Sizes for Basic Operations.

The data type of C depends on the data types of A and B:

• If A and B are the same data type, then C matches the data type of A and B.

• If either A or B is single, then C is single.

• If either A or B is an integer data type with the other a scalar double, then C assumes the integer data type.

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