cumsum

cumulative sum of array elements

Syntax

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

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.:

$y(i) = \sum_{k=1}^i x(k)$

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:

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

or

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

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

or

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

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

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cumsum

Syntax

Arguments

Description

Examples

See also