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partial cumulative sums of the elements of an array


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



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


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.


Word "native" or "double".


Array of size equal to that of x.


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

y(i) = ∑u=1→i x(u)

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:

    y(i,j) = ∑u=1→i x(u,j), or for a N-Dimensional array:

    y(i,j,k,…) = ∑u=1→i x(u,j,k,…)

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

    y(i,j) = ∑u=1→j x(i,u), or for a N-Dimensional array:

    y(i,j,k,…) = ∑u=1→j x(i,u,k,…)

  • if orientation is equal to n then:

    y(i₁,…,iₙ₋₁, iₙ,iₙ₊₁,…) = ∑u=1…iₙ  x(i₁,…,iₙ₋₁, u,iₙ₊₁,…)

  • 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%.


A = [1,2;3,4];

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

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