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prod

Product of array elements

Syntax

B = prod(A)
B = prod(A,'all')
B = prod(A,dim)
B = prod(A,vecdim)
B = prod(___,type)
B = prod(___,nanflag)

Description

example

B = prod(A) returns the product of the array elements of A.

  • If A is a vector, then prod(A) returns the product of the elements.

  • If A is a nonempty matrix, then prod(A) treats the columns of A as vectors and returns a row vector of the products of each column.

  • If A is an empty 0-by-0 matrix, prod(A) returns 1.

  • If A is a multidimensional array, then prod(A) acts along the first nonsingleton dimension and returns an array of products. The size of this dimension reduces to 1 while the sizes of all other dimensions remain the same.

prod computes and returns B as single when the input, A, is single. For all other numeric and logical data types, prod computes and returns B as double.

example

B = prod(A,'all') computes the product of all elements of A.

example

B = prod(A,dim) returns the products along dimension dim. For example, if A is a matrix, prod(A,2) is a column vector containing the products of each row.

example

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

example

B = prod(___,type) returns an array in the class specified by type, using any of the input arguments in the previous syntaxes. type can be 'double', 'native', or 'default'.

example

B = prod(___,nanflag) specifies whether to include or omit NaN values from the calculation for any of the previous syntaxes. prod(A,'includenan') includes NaN values in the calculation while prod(A,'omitnan') ignores them.

Examples

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Create a 3-by-3 array whose elements correspond to their linear indices.

A=[1:3:7;2:3:8;3:3:9]
A = 3×3

     1     4     7
     2     5     8
     3     6     9

Find the product of the elements in each column. The length of the first dimension is 1, and the length of the second dimension matches size(A,2).

B = prod(A)
B = 1×3

     6   120   504

Create an array of logical values.

A = [true false; true true]
A = 2x2 logical array

   1   0
   1   1

Find the product of the elements in each column.

B = prod(A)
B = 1×2

     1     0

The output has type double.

class(B)
ans = 
'double'

Create a 3-by-3 array whose elements correspond to their linear indices.

A=[1:3:7;2:3:8;3:3:9]
A = 3×3

     1     4     7
     2     5     8
     3     6     9

Find the product of the elements in each row and reduce the length of the second dimension to 1. The length of the first dimension matches size(A,1), and the length of the second dimension is 1.

dim = 2;
B = prod(A,dim)
B = 3×1

    28
    80
   162

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

A(:,:,1) = [2 4; -2 1];
A(:,:,2) = [1 2; -5 3];
A(:,:,3) = [4 4; 1 -3];
B1 = prod(A,[1 2])
B1 = 
B1(:,:,1) =

   -16


B1(:,:,2) =

   -30


B1(:,:,3) =

   -48

To compute the product over all dimensions of an array, you can either specify each dimension in the vector dimension argument, or use the 'all' option.

B2 = prod(A,[1 2 3])
B2 = -23040
Ball = prod(A,'all')
Ball = -23040

Create a 3-by-3 array of single-precision values.

A = single([1200 1500 1800; 1300 1600 1900; 1400 1700 2000])
A = 3x3 single matrix

        1200        1500        1800
        1300        1600        1900
        1400        1700        2000

Find the product of the elements in each row by multiplying in double precision.

B = prod(A,2,'double')
B = 3×1
109 ×

    3.2400
    3.9520
    4.7600

The output is double precision.

class(B)
ans = 
'double'

Create a 3-by-3 array of 8-bit unsigned integers.

A = uint8([1:3:7;2:3:8;3:3:9])
A = 3x3 uint8 matrix

   1   4   7
   2   5   8
   3   6   9

Find the product of the elements in each column natively in uint8.

B = prod(A,'native')
B = 1x3 uint8 row vector

     6   120   255

The result is an array of 8-bit unsigned integers.

class(B)
ans = 
'uint8'

Create a vector and compute its product, excluding NaN values. If you do not specify 'omitnan', then prod(A) returns NaN.

A = [1 3 2 4 NaN 3 NaN 2];
P = prod(A,'omitnan')
P = 144

Input Arguments

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

Data Types: double | single | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical
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(B,dim) is 1, while the sizes of all other dimensions remain the same.

Consider a two-dimensional input array, A.

  • If dim = 1, then prod(A,1) returns a row vector containing the product of the elements in each column.

  • If dim = 2, then prod(A,2) returns a column vector containing the product of the elements in each row.

prod returns A when dim is greater than ndims(A).

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

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 prod(A,[1 2]) returns a 1-by-1-by-3 array whose elements are the products of each page of A.

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

Output class, specified as 'default', 'double', or 'native', and which defines the data type of the output, B.

typeOutput data type
'default'double, unless the input data type is single. In which case, the output data type is single.
'double'double
'native'same data type as the input array, A

NaN condition, specified as one of these values:

  • 'includenan' — Include NaN values from the input when computing the product, resulting in NaN output.

  • 'omitnan' — Ignore NaN values in the input. If all elements are NaN, then prod returns 1.

Output Arguments

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Product array, returned as a scalar, vector, matrix, or multidimensional array.

The class of B is as follows:

  • If the type argument specifies 'default' or is not used

    • and the input is not single, then the output is double.

    • and the input is single, then the output is single.

  • If the type argument specifies 'double', then the output is double regardless of the input data type.

  • If the type argument specifies 'native', then the output is the same data type as the input.

More About

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First Nonsingleton Dimension

The first nonsingleton dimension is the first dimension of an array whose size is not equal to 1.

For example:

  • If X is a 1-by-n row vector, then the second dimension is the first nonsingleton dimension of X.

  • If X is a 1-by-0-by-n empty array, then the second dimension is the first nonsingleton dimension of X.

  • If X is a 1-by-1-by-3 array, then the third dimension is the first nonsingleton dimension of X.

Extended Capabilities

See Also

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Introduced before R2006a