prod

Product of array elements

Syntax

B = prod(A)

B = prod(A,'all')

B = prod(A,dim)

B = prod(A,vecdim)

B = prod(___,outtype)

B = prod(___,nanflag)

Description

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.

B = prod(A,'all') computes the product of all elements of A. This syntax is valid for MATLAB^® versions R2018b and later.

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.

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.

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

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

Product of Elements in Each Column

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

Product of Logical Input

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'

Product of Elements in Each Row

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

Product of Array Page

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

Single-Precision Input Treated as Double

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'

Integer Data Type for Input and Output

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'

Product Excluding NaN

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

A — Input array

vector | matrix | multidimensional array

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

dim — Dimension to operate along

positive integer scalar

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

vecdim — Vector of dimensions

vector of positive integers

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

outtype — Output class

'default' (default) | 'double' | 'native'

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

outtype	Output 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

nanflag — NaN condition

'includenan' (default) | 'omitnan'

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

B — Product array

scalar | vector | matrix | multidimensional array

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

The class of B is as follows:

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

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

More About

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

Tall Arrays

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

This function fully supports tall arrays. For more information, see Tall Arrays.

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• If you supply dim, it must be a constant.

• See Variable-Sizing Restrictions for Code Generation of Toolbox Functions (MATLAB Coder).

GPU Code Generation

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

Usage notes and limitations:

• If you supply dim, it must be a constant.

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™.

Usage notes and limitations:

• 64-bit integers are not supported with the 'native' option.

• The order of the products in prod operation is not defined. Therefore, the prod operation on a GPU array might not return exactly the same answer as the prod operation on the corresponding MATLAB numeric array.

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™.

Usage notes and limitations:

• The order of the products in prod operation is not defined. Therefore, the prod operation on a distributed array might not return exactly the same answer as the prod operation on the corresponding MATLAB numeric array. The difference might be significant when A is a signed integer type and its product is accumulated natively.

For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).