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

${ y(\mathbf{1},j) = \sum_{\mathbf{i}} x(\mathbf{i},j)}$

or

$y(\mathbf{1},j,k,\ldots) = \sum_{\mathbf{i}} x(\mathbf{i},j,k,\ldots)$
if orientation is equal to 2 or "c" then:

$y(i,\mathbf{1}) = \sum_{\mathbf{j}} x(i,\mathbf{j})$

or

$y(i,\mathbf{1},k,\ldots) = \sum_{j} x(i,\mathbf{j},k,\ldots)$
if orientation is equal to n then

$y(i_1,\ldots,i_{n-1},\mathbf{1},i_{n+1},\ldots) = \sum_{\mathbf{i_n}} x(i_1,\ldots,i_{n-1},\mathbf{i_n},i_{n+1},\ldots)$
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)

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sum

Syntax

Arguments

Description

Examples

See also