Cumulative trapezoidal numerical integration

cumtrapz

Cumulative trapezoidal numerical integration

Syntax

• 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. To compute the integral with other than unit spacing, multiply Z by the spacing increment.

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

For matrices, cumtrapz(Y) is a matrix the same size as Y 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 whose first nonsingleton dimension is length(X). cumtrapz operates across this dimension.

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

Example

• Y = [0 1 2; 3 4 5];
  
  cumtrapz(Y,1)
  ans =
            0         0         0
      1.5000   2.5000    3.5000
  
  cumtrapz(Y,2)
  ans =
            0    0.5000    2.0000
          0    3.5000    8.0000