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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 — cumulative product of array elements
  • sum — sum of array elements
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Last updated:
Mon Jun 17 17:49:15 CEST 2024