prod

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

  

  or

  

• if orientation is equal to 2 or "c" then:

  

  or

  

• if orientation is equal to n then

  

• 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 summation 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.

Remark

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

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 or(B)

See Also

• cumprod
• sum