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. Input Y can be complex.
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 Ymust 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. Inputs X and Y can be complex.
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, using any of the input arguments in the previous syntaxes. The length of X must be the same as size(Y,dim).
Examples
Example 1
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
Example 2
This example uses two complex inputs:
z = exp(1i*pi*(0:100)/100);
ct = cumtrapz(z,1./z);
ct(end)
ans =
0.0000 + 3.1411i
See Also
[URL='http://www.mathworks.com/help/matlab/ref/cumsum.html']cumsum[/url] | [URL='http://www.mathworks.com/help/matlab/ref/trapz.html']trapz[/url]
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. Input Y can be complex.
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 Ymust 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. Inputs X and Y can be complex.
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, using any of the input arguments in the previous syntaxes. The length of X must be the same as size(Y,dim).
Examples
Example 1
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
Example 2
This example uses two complex inputs:
z = exp(1i*pi*(0:100)/100);
ct = cumtrapz(z,1./z);
ct(end)
ans =
0.0000 + 3.1411i
See Also
[URL='http://www.mathworks.com/help/matlab/ref/cumsum.html']cumsum[/url] | [URL='http://www.mathworks.com/help/matlab/ref/trapz.html']trapz[/url]
