Very similar to the standard integrate function, except that singleton dimensions are ignored.
As described in the integrate function description, integrating over dimensions with a single value (singleton dimensions) returns zero because the area under a single point is zero. In some cases, particularly when you are not sure which dimensions are singleton, this behavior can cause difficulties. The integrate2 function automatically ignores all dimensions with a size of one, which avoids the problem of a zero valued integrals due to singleton dimensions.
|
Syntax |
Description |
|---|---|
|
out = integrate2(A, 1, x1); |
Integrates A over the first dimension in the matrix. x1 is the corresponding position vector. |
|
out = integrate2(A, d, x1, x2, ...); |
Calculates the integral of A over the specified dimension(s) d. d is a vector containing the dimensions over which to integrate. xi is the position vector corresponding to the dimensions of A over which the integration is occurring. If any of the xi vectors only have 1 element, integrate returns 0. For example
|
Example
In the following example, we compare the integrate and integrate2 commands when integrating over matrices with singleton dimensions.
# create 3D matrix of results: data(x,y,z) where # there are 50 'x' sample points, 1 'y' sample points # and 40 'z' sample points. This is typical of data # from a 2D monitor oriented in the XZ plane. x=linspace(-5,5,50); y=0; z=linspace(-3,3,40); X=meshgrid3dx(x,y,z); Z=meshgrid3dz(x,y,z); data = X^2 + Z^2; image(x,z,data,"x","z","data"); ?integrate2(data, [1,2,3], x,y,z); # Integrate2 ignores singleton dimension, giving non-zero result. ?integrate (data, [1,2,3], x,y,z); # Result is zero because of the singleton dimension ?integrate (data, [1,3] , x,z ); # Get the same result as integrate2 by integrating over x and z, but not y. > result: > 680.653 > result: > 0 > result: > 680.653
See Also
List of commands , integrate , conv2 , max , min , interp , find , pinch , round , getdata , sum , length