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

sum(x) computes the sum of the elements of a REAL or LOGICAL vector x. If x is LOGICAL, True is interpreted as 1.0 and False as 0.0 and sum(x) is the number of elements of x that are True. If x is a m by n matrix, sum(x) computes a row vector (1 by n matrix) consisting of the sum of the elements in each column of x. If x is an array with dimensions n1, n2, n3, ..., y <- sum(x) computes an array with dimensions 1, n2, n3, ... such that y[1,j,k,...] = sum(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, ... . sum(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, sum(x,squeeze:T) will be identical to vector(sum(x)), and if x is an array, sum(x,squeeze:T) will be identical to array(sum(x),dim(x)[-1]). sum(NULL) is NULL. See topic 'NULL'. sum(a,b,c,...) is equivalent to sum(vector(a,b,c,...)) if a, b, c, ... are all vectors. They must all have the same type, REAL or LOGICAL or be NULL. sum(NULL, NULL, ..., NULL) is NULL. sum(x, silent:T) or sum(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, sum(x) is 0.0. sum(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. sum(x, dimensions:J [,squeeze:T] [,silent:T] [,undefval:U]) sums 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, sum(x, dimensions:2) computes the row sums as a nrows(x) by 1 matrix and sum(x, dimensions:2,squeeze:T) computes them as a one dimensional vector. sum(x, margins:K [,squeeze:F] [,silent:T] [,undefval:U]) sums over the dimensions not in K = vector(k1, k2, ..., km), where k1, ..., km are distinct positive integers <= ndims(x). This computes marginal totals 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. If x is a structure, sum(x [,dimensions:J or margins:K] [,squeeze:T or F] [,silent:T] [,undefval:U]) computes a structure, each of whose components is sum() applied to that component of x. All the components of x be of the same type, REAL or LOGICAL. Examples: If x is a n by m matrix Cmd> r <- x - sum(x)/sum(!ismissing(x)) computes the matrix of the residuals of x[i,j] from the column means. When there are no MISSING values, divide by nrows(x) If x is a n by 4 by 5 array, Cmd r <- x - sum(x)/sum(!ismissing(x)) computes an array with r[i,j,k] = the residual of x[i,j,k] from the mean of all x[i,j,k] with the same values for j and k. That is, it treats x analogously to a 4 by 5 array of vectors of length n. See topic 'arithmetic'. When there are no MISSING values, divide by dim(x)[1]. If z is a vector of integers, Cmd> sum(z == run(min(z),max(z))') computes a row vector giving the frequency distribution of the values in z. Cmd> a # 2 by 2 by 3 array with labels C1 C2 C3 A1 B1 9 5 7 B2 9 12 11 A2 B1 4 11 10 B2 11 15 9 Cmd> sum(a,dimensions:2) # sum over dimension 2; 2 by 1 by 3 result C1 C2 C3 A1 (1) 18 17 18 A2 (1) 15 26 19 Cmd> sum(a,margins:vector(1,3),squeeze:F) # same as preceding C1 C2 C3 A1 (1) 18 17 18 A2 (1) 15 26 19 Cmd> sum(a,dimensions:2,squeeze:T) # sum over dim 2; 2 by 3 result C1 C2 C3 A1 18 17 18 A2 15 26 19 Cmd> sum(a,margins:vector(1,3)) # same as preceding C1 C2 C3 A1 18 17 18 A2 15 26 19 See also prod(), tabs()

Gary Oehlert 2003-01-15