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`cumprod`

Cumulative product

Usage

`cumprod(A)`

A is a numeric or character array.
The output contains the cumulative products and has the same size as A.
A cumulative product is obtained by multiplying elements in a vector along the first non-singleton dimension of A.

`cumprod(A, dim)`

A is a numeric or character array.
dim should be a positive integer scalar, not equal to inf nor nan.
It obtains the cumulative products along the dim-th dimension of A.
If size(A, dim) == 1 or dim > ndims(A), then the output is the same as A.

`cumprod(A, option)`

A is a numeric or character array.
option should be either 'reverse', 'forward', 'includenan' or 'omitnan'.
Each of these options controls the operation direction or inclusion of NaN in the operation.
See the table below for the available options.

`cumprod(A, dim, option)`

Same as cumprod(A, dim) above. In addition, an option is specified for controlling the operation direction or inclusion of NaN in the operation.
See the table below for the available options.

`cumprod(A, option1, option2)`

Same as cumprod(A, option) above. In addition, a second option is specified.
option2 will override option1 if they contradict with each other.
See the table below for the available options.

`cumprod(A, dim, option1, option2)`

Same as cumprod(A, dim, option) above. In addition, a second option is specified.
option2 will override option1 if they contradict with each other.
See the table below for the available options.

Option	Meaning	Default
`'forward'`	The cumulative products are obtained in the forward direction.	Default for `cumsum`, `cumprod`, `cummin`, `cummax`
`'reverse'`	The cumulative products are obtained in the reverse direction.	Not default for `cumsum`, `cumprod`, `cummin` and `cummax`
`'includenan`'	Include `NaN` in the calculation	Default for `cumsum`, `cumprod`
`'omitnan`'	Omit `NaN` in the calculation	Default for `cummax`, `cummin`

Examples

In the following, the first non-singleton dimension of A is the first dimension. The product operation is performed along the vertical direction. For instance, s(:,1) contains cumulative products of elements of A(:,1).

Input

% Matrix of size [3,4]
a = reshape(1:12,3,4)
% Cumulative products
cumprod(a)

Output

a = 
 1.0000   4.0000   7.0000   10.000
 2.0000   5.0000   8.0000   11.000
 3.0000   6.0000   9.0000   12.000

ans = 
 1.0000   4.0000   7.0000   10.000
 2.0000   20.000   56.000   110.00
 6.0000   120.00   504.00   1320.0

In the following, the product operation is performed along the horizontal direction (2nd dimension). For instance, p(1,:) contains cumulative products of elements of A(1,:).

Input

% Matrix of size [3,4]
A = reshape(1:12,3,4)
% Cumulative products along 2nd dimension
p = cumprod(A,2)

Output

A = 
 1.0000   4.0000   7.0000   10.000
 2.0000   5.0000   8.0000   11.000
 3.0000   6.0000   9.0000   12.000

p = 
 1.0000   4.0000   28.000   280.00
 2.0000   10.000   80.000   880.00
 3.0000   18.000   162.00   1944.0

Cumulative products of the same vector but with different options. Note that cumprod by default includes NaN, therefore NaN appears in the outputs of the 1st and 2nd calls of cumprod. In fact, multiplication with NaN always returns NaN. In the 3rd call of cumprod, NaN is ignored in the multiplication operation.

Input

a = [1:5 nan 6]

% Default options
disp('Include nan, forward')
cumprod(a)

% Include nan, forward direction
disp('Include nan, forward.')
cumprod(a, 'includenan')

% Omit NaN, forward
disp('Omit nan, forward')
cumprod(a, 'omitnan')

% Include nan, forward
disp('Include nan, forward')
cumprod(a, 'forward')

% Include nan, reverse direction
disp('Include nan, reverse')
cumprod(a, 'reverse')

Output

a = 
 1.0000   2.0000   3.0000   4.0000   5.0000   NaN      6.0000

Include nan, forward

ans = 
 1.0000   2.0000   6.0000   24.000   120.00   NaN      NaN   

Include nan, forward.

ans = 
 1.0000   2.0000   6.0000   24.000   120.00   NaN      NaN   

Omit nan, forward

ans = 
 1.0000   2.0000   6.0000   24.000   120.00   120.00   720.00

Include nan, forward

ans = 
 1.0000   2.0000   6.0000   24.000   120.00   NaN      NaN   

Include nan, reverse

ans = 
 NaN      NaN      NaN      NaN      NaN      NaN      6.0000