prod(x [,squeeze:T] [,silent:T,undefval:U]), x REAL or LOGICAL or a structure with REAL or LOGICAL components, U a REAL scalar prod(x, dimensions:J [,squeeze:T] [,silent:T,undefval:U]), vector of positive integers J prod(x, margins:K [,squeeze:F] [,silent:T,undefval:U]), vector of positive integers K prod(x1,x2,... [,silent:T,undefval:U]), x1, x2, ... REAL or LOGICAL vectors, all the same type. |

prod(x) computes the product of the elements of a REAL or LOGICAL vector x. If x is LOGICAL, True is interpreted as 1 and False as 0 and hence prod(x) has value 1 if all elements of x are True and 0 if any is False. If x is a m by n matrix, prod(x) computes a row vector (1 by n matrix) consisting of the product of the elements in each column of x. If x is an array with dimensions n1, n2, n3, ..., y <- prod(x) computes an array with dimensions 1, n2, n3, ... such that y[1,j,k,...] = prod(x[i,j,k,...], i=1,...,n1). This is consistent with what happens when x is a matrix. Note: MacAnova3.35 and earlier produced a result with dimensions n2, n3, ... . prod(x, squeeze:T) does the same, except the first dimension of the result (of length 1) is squeezed out unless the result is a scalar. In particular, if x is a matrix, prod(x,squeeze:T) will be identical to vector(prod(x)), and if x is an array, prod(x,squeeze:T) will be identical to array(prod(x),dim(x)[-1]). prod(NULL) is NULL. prod(a,b,c,...) is equivalent to prod(vector(a,b,c,...)) if a, b, c, ... are all vectors. They must all have the same type, REAL or LOGICAL or be NULL. prod(NULL, NULL, ..., NULL) is NULL. prod(x, silent:T) or prod(a,b,c,...,silent:T) does the same but suppresses warning messages about MISSING values or overflows. If all the elements of a vector x are MISSING, prod(x) is 1.0. prod(x, undefval:U), where U is a REAL scalar does the same, except the returned value is U when all the elements of x are MISSING. If x is a structure, prod(x) computes a structure, each of whose components is prod() applied to that component of x. prod(x, dimensions:J [,squeeze:T] [,silent:T] [undefval:U]) computes products over the dimensions in J = vector(j1,j2,...,jn) where j1, ..., jn are distinct positive integers <= ndims(x). Without 'squeeze:T', the result has the same number of dimensions as x, with dimensions j1, j2, ..., jn of length 1. With 'squeeze:T', these dimensions are removed from the result. The order of j1, j2, ... is ignored. It is an error if max(J) > ndims(x) or if there are duplicate elements in J. For example, if x is a matrix, prod(x, dimensions:2) computes the row products as a nrows(x) by 1 matrix and prod(x, dimensions:2,squeeze:T) computes them as a one dimensional vector. prod(x, margins:K [,squeeze:F] [,silent:T] [undefval:U]) computes products over the dimensions not in K = vector(k1, k2, ..., km), where k1, ..., km are distinct positive integers <= ndims(x). This computes marginal products for the margins specified in K. Without 'squeeze:F', only the dimensions in K are retained in the result. Otherwise the other dimensions are retained but have length 1. This is opposite from the default with 'dimensions:J'. It is an error if max(K) > ndims(x) or if there are duplicate elements in K. Examples: Cmd> x # matrix with labels B1 B2 A1 18 15 A2 17 26 A3 18 19 Cmd> prod(x) # products down columns B1 B2 (1) 5508 7410 Cmd> prod(x)/x # elements in row are products of other rows of x B1 B2 A1 306 494 A2 324 285 A3 306 390 Cmd> prod(x,dimensions:2) # products accross rows (1) A1 270 A2 442 A3 342 Cmd> prod(x,margins:1) # same as a vector A1 A2 A3 270 442 342 See also topics sum(), 'NULL'.

Gary Oehlert 2003-01-15