cumtrapz (MATLAB Function Reference)

Cumulative trapezoidal numerical integration

Z = cumtrapz(Y) 
Z = cumtrapz(X,Y) 
Z = cumtrapz(... dim)

Description

Z = cumtrapz(Y)

computes an approximation of the cumulative integral of Y via the trapezoidal method with unit spacing. (This is similar to cumsum(Y), except that trapezoidal approximation is used.) To compute the integral with other than unit spacing, multiply Z by the spacing increment.

For vectors, cumtrapz(Y) is the cumulative integral of Y.

For matrices, cumtrapz(Y) is a row vector with the cumulative integral over each column.

For multidimensional arrays, cumtrapz(Y) works across the first nonsingleton dimension.

Z = cumtrapz(X,Y)

computes the cumulative integral of Y with respect to X using trapezoidal integration. X and Y must be vectors of the same length, or X must be a column vector and Y an array.

If X is a column vector and Y an array whose first nonsingleton dimension is length(X), cumtrapz(X,Y) operates across this dimension.

Z = cumtrapz(... dim)

integrates across the dimension of Y specified by scalar dim. The length of X must be the same as size(Y,dim).

Example

Example: If Y = [0 1 2; 3 4 5]

cumtrapz(Y,1)
ans =
          0    1.0000    2.0000
    1.5000    2.5000    3.5000

and

cumtrapz(Y,2)
ans =
          0    0.5000    2.0000
    3.0000    3.5000    8.0000