prod product of array elements

## Syntax

    y=prod(x)
                y=prod(x,orientation)
                y=prod(x,outtype)
                y=prod(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=prod(x)` returns in the scalar `y` the product of all the elements of `x`.

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

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

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

  or

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

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

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

  or

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

- if `orientation` is equal to n then

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

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

- `y=prod(x,"m")` is equivalent to `y=prod(x,orientation)` where `orientation` is the index of the first dimension of `x` that is greater than 1.

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"`. This option is used for Matlab compatibility.

This function applies with identical rules to sparse matrices.

## Examples

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

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

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

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

## See also

- cumprod
- sum