Documentation

max

Maximum elements of an array

Description

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M = max(A) returns the maximum elements of an array.

• If A is a vector, then max(A) returns the maximum 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.

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M = max(A,[],dim) returns the maximum element 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.

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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.

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[M,I] = max(___) also returns the index into the operating dimension that corresponds to the maximum value of A for any of the previous syntaxes.

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M = max(A,[],'all') finds the maximum over all elements of A. This syntax is valid for MATLAB® versions R2018b and later.

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M = max(A,[],vecdim) computes the maximum over the dimensions specified in the vector vecdim. For example, if A is a matrix, then max(A,[],[1 2]) computes the maximum over all elements in A, since every element of a matrix is contained in the array slice defined by dimensions 1 and 2.

M = max(A,[],'all',nanflag) computes the maximum over all elements of A when using the nanflag option.

M = max(A,[],vecdim,nanflag) specifies multiple dimensions to operate along when using the nanflag option.

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[M,I] = max(A,[],___,'linear') returns the linear index into A that corresponds to the maximum value in A.

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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 = 2×3

2     8     4
7     3     9

M = max(A)
M = 1×3

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 = 2×3

1.7000    1.2000    1.5000
1.3000    1.6000    1.9900

M = max(A,[],2)
M = 2×1

1.7000
1.9900

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

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 = 2×3

1     9    -2
8     4    -5

[M,I] = max(A)
M = 1×3

8     9    -2

I = 1×3

2     1     1

Create a 3-D array and compute the maximum over each page of data (rows and columns).

A(:,:,1) = [2 4; -2 1];
A(:,:,2) = [9 13; -5 7];
A(:,:,3) = [4 4; 8 -3];
M1 = max(A,[],[1 2])
M1 =
M1(:,:,1) =

4

M1(:,:,2) =

13

M1(:,:,3) =

8

Starting in R2018b, to compute the maximum over all dimensions of an array, you can either specify each dimension in the vector dimension argument, or use the 'all' option.

M2 = max(A,[],[1 2 3])
M2 = 13
Mall = max(A,[],'all')
Mall = 13

Create a matrix A and return the maximum value of each row in the matrix M. Use the 'linear' option to also return the linear indices I such that M = A(I).

A = [1 2 3; 4 5 6]
A = 2×3

1     2     3
4     5     6

[M,I] = max(A,[],2,'linear')
M = 2×1

3
6

I = 2×1

5
6

maxvals = A(I)
maxvals = 2×1

3
6

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 = 2×3

1     7     3
6     2     9

B = 5;
C = max(A,B)
C = 2×3

5     7     5
6     5     9

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).

Vector of dimensions, specified as a vector of positive integers. Each element represents a dimension of the input array. The lengths of the output in the specified operating dimensions are 1, while the others remain the same.

Consider a 2-by-3-by-3 input array, A. Then max(A,[],[1 2]) returns a 1-by-1-by-3 array whose elements are the maximums computed over each page of A. Data Types: double | single | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

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. If all elements are NaN, then max returns the first one.

• '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.

For categorical arrays, you can also use 'omitundefined' or 'includeundefined' to omit and include undefined values, respectively.

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, returned as a scalar, vector, matrix, or multidimensional array. I is the same size as the first output.

When 'linear' is not specified, I is the index into the operating dimension. When 'linear' is specified, I contains the linear indices of A corresponding to the maximum values.

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.