cumsum

Arguments

x

array of booleans, integers, real or complex numbers, polynomials, or rational fractions. Hypermatrices or sparse boolean or numerical matrices are supported as well.

orientation

This argument can be

• either a string with possible values "*", "r", "c" or "m"

• positive integer 1 ≤ orientation ≤ ndims(x): the index of the dimension along which the cumulative sum must be computed. 1 and "r", and 2 and "c", are equivalent.

outtype

Word "native" or "double".

y

Array of size equal to that of x.

Description

y = cumsum(x) computes and provides the partial cumulative sums y(i)=sum(x(1:i)), i.e.:

y = cumsum(x, orientation) returns the partial cumulative sums of x along the dimension given by orientation:

• if orientation is equal to 1 or "r" then:

  , or for a N-Dimensional array:

  

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

  , or for a N-Dimensional array:

  

• if orientation is equal to n then:

  

• y = cumsum(x, "*") is equivalent to y = cumsum(x)

• y = cumsum(x, "m") is equivalent to y = cumsum(x, orientation) where orientation is the index of the first dimension of x that is greater than 1. This option is used for Matlab compatibility.

The outtype argument rules the way the summations are 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 with |),

  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".

When the input x is sparse, please keep in mind that the density of the result y will be almost always close to 100%.

Examples

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

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

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

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

See also

• sum — sum of array elements
• cumprod — cumulative product of array elements