cumsum

Arguments

x

an array of reals, complex, booleans, polynomials or rational fractions.

orientation

This argument can be

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

• or a number with positive integer value

outtype

a string with possible values "native" or "double".

y

scalar or array

Description

Returns the cumulative sum of array elements. For an array x, y=cumsum(x) a matrix y of the same size as x. The value y(i) is the sum of all elements of x(1:i) i.e.:

y=cumsum(x,orientation) returns in y the cumulative 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=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 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];
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