# cumprod

cumulative product of array elements

## Calling Sequence

    y=cumprod(x)

    y=cumprod(x,orientation)

    y=cumprod(x,outtype)

    y=cumprod(x,orientation,outtype)

## Arguments

x

  an array of reals, complex, booleans, polynomials or rational fractions.

orientation

  it can be either

  - a string with possible values `"*"`, `"r"`, `"c"` or `"m"`

  - a number with positive integer value

outtype

  a string with possible values `"native"` or `"double"`.

y

  scalar or array

## Description

For an array `x`, `y=cumprod(x)` returns in the scalar `y` the cumulative product of all the elements of `x`.

`y=cumprod(x,orientation)` returns in `y` the cumulative product of `x` along the dimension given by `orientation`:

- if `orientation` is equal to 1 or "r" then:

  y(\mathbf{l},j) = \prod_{\mathbf{i}=1}^l x(\mathbf{i},j)

  or

  y(\mathbf{l},j,k,\ldots) = \prod_{\mathbf{i}=1}^l x(\mathbf{i},j,k,\ldots)

- if `orientation` is equal to 2 or "c" then:

  y(i,\mathbf{l}) = \prod_{\mathbf{j}=1}^l x(i,{\mathbf{j})

  or

  y(i,\mathbf{l},k,\ldots) = \prod_{\mathbf{j}=1}^l x(i,\mathbf{j},k,\ldots)

- if `orientation` is equal to n then:

  y(i_1,\ldots,i_{n-1},\mathbf{l},i_{n+1},\ldots) = \prod_{\mathbf{i_n}=1}^l x(i_1,\ldots,i_{n-1},\mathbf{i_n},i_{n+1},\ldots)

- `y=cumprod(x,"*")` is equivalent to `y=cumprod(x)`

- `y=cumprod(x,"m")` is equivalent to `y=cumprod(x,orientation)` where `orientation` is the index of the first dimension of `x` that is greater than 1. This option is used for Matlab compatibility.

The `outtype` argument rules the way the product is done:

- For arrays of floats, of polynomials, of rational fractions, the evaluation is always done using floating points computations. The `"double"` or `"native"` options are equivalent.

- For arrays of integers,

  if `outtype="native"` the evaluation is done using integer computations (modulo 2^b, where b is the number of bits used),

  if `outtype="double"` the evaluation is done using floating point computations.

  The default value is `outtype="native"`.

- For arrays of booleans,

  if `outtype="native"` the evaluation is done using boolean computations (* is replaced by &),

  if `outtype="double"` the evaluation is done using floating point computations (%t values are replaced by 1 and %f values by 0).

  The default value is `outtype="double"`.

## Remark

This function applies, with identical rules to sparse matrices and hypermatrices.

## Examples

    A=[1,2;3,4];
    cumprod(A)
    cumprod(A,1)

    I=uint8([2 95 103;254 9 0])
    cumprod(I) //native evaluation
    cumprod(I,"double")
    cumprod(I,2,"double")

    s=poly(0,"s");
    P=[s,%i+s;s^2,1];
    cumprod(P),
    cumprod(P,2)

    B=[%t %t %f %f];
    cumprod(B) //evaluation in float
    cumprod(B,"native") //similar to and(B)

## See Also

- prod
- cumsum