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 B in this dimension reduces to 1, while the sizes of all other dimensions remain the same as in A.

• If A is a table or timetable, then prod(A) returns a one-row table of the products of each variable. (since R2023a)

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") returns the product of all elements of A.

B = prod(A,dim) returns the product 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) returns the product based on the dimensions specified in the vector vecdim. For example, if A is a matrix, then prod(A,[1 2]) returns the product of all elements in A because 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 in A. For example, prod(A,"omitnan") ignores NaN values when computing the product. By default, prod includes NaN values.

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 Missing Values

Create a matrix containing NaN values.

A = [1.77 -0.005 NaN -2.95; NaN 0.34 NaN 0.19]

A = 2×4

    1.7700   -0.0050       NaN   -2.9500
       NaN    0.3400       NaN    0.1900

Compute the products of the matrix, excluding NaN values. For matrix column that contain any NaN value, prod computes with the non-NaN elements. For matrix columns that contain all NaN values, the product is 1.

B = prod(A,"omitnan")

B = 1×4

    1.7700   -0.0017    1.0000   -0.5605

Input Arguments

A — Input array

vector | matrix | multidimensional array | table | timetable

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

Data Types: double | single | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical | 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 of size greater than 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, table, or timetable. In which case, the output data type is single or table, respectively.
"double"	double, unless the input data type is table or timetable. In which case, the output data type is table.
"native"	Same data type as the input array, A, unless the input data type is timetable. In which case, the output data type is table.

nanflag — Missing value condition

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

Missing value condition, specified as one of these values:

• "includemissing" or "includenan" — Include NaN values in A when computing the product. If any element in the operating dimension is NaN, then the corresponding element in B is NaN. "includemissing" and "includenan" have the same behavior.

• "omitmissing" or "omitnan" — Ignore NaN values in A, and compute the product over fewer points. If all elements in the operating dimension are NaN, then the corresponding element in B is 1. "omitmissing" and "omitnan" have the same behavior.

Output Arguments

B — Product array

scalar | vector | matrix | multidimensional array | table

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

The class of B is as follows:

• If the outtype argument specifies "default" or is not used

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

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

  • and the input is table or timetable, then the output is table.

• If the outtype argument specifies "double", then the output is double regardless of the input data type, unless the input is table or timetable.

• If the outtype argument specifies "native", then the output is the same data type as the input, unless the input is timetable. In which case, the output is table.

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 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 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).

Version History

Introduced before R2006a

R2023a: Specify missing value condition

Include or omit missing values in the input array when computing the product by using the "includemissing" or "omitmissing" options. These options have the same behavior as the "includenan" and "omitnan" options, respectively.

R2023a: Perform calculations directly on tables and timetables

The prod 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.

R2018b: Operate on multiple dimensions

Operate on multiple dimensions of the input array at a time. Specify a vector of operating dimensions, or specify the "all" option to operate on all array dimensions.