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# sum

sum of array elements

### Syntax

y = sum(x)
y = sum(x, outtype)
y = sum(x, orientation)
y = sum(x, orientation, outtype)

### Arguments

x
Array of booleans (full or sparse), encoded integers, real or complex numbers (full or sparse), polynomials, or rationals.

orientation
it can be either
• a character "*" (default), "r", "c" or "m"
• a positive integer: Index of the dimension along which the sums must be computed.

outtype
string "native" or "double".

y
scalar or array

### Description

For an array x, y=sum(x) returns in the scalar y the sum of all the elements of x.

y=sum(x,orientation) returns in y the sum 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=sum(x,"*") is equivalent to y=sum(x)

• y=sum(x,"m") is equivalent to y=sum(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 function applies with identical rules to sparse matrices

### Examples

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

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

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

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

• plus — Numerical addition. Text concatenation (gluing)
• cumsum — partial cumulative sums of the elements of an array
• prod — product of array elements