2D Volume Integrate (OriginPro Only)

Description

This function calculates the volume between the plane Z=0 and the matrix surface, which is based on the numerical calculation of two dimensional integration.

To use this function:

Create a new matrix with data.
Activate the matrix.
Select Analysis: Mathematics: 2D Volume Intergrate from the Origin menu to open the integ2 dialog.

In fact, the integ2 X-Function is called to complete the calculation.

Dialog Options

Input Matrix	The operating matrix.
Interpolate for Missing Value	Trim missing values if this parameter is true.

Algorithm

This function computes the volume beneath the matrix surface using a numeric integral method.

For a continuous surface $z=f(x,y),(x,y)\in \sigma$ , the volume beneath it can be computed as:

$\iint_{(\sigma)}f(x,y)dxdy$ ,

Using a numeric method, it can be written as:

$\iint_{(\sigma)}f(x,y)dxdy=\lim_{\Delta x \to 0}\lim_{\Delta y \to 0} \sum_{i=0}^{m-1} \sum_{j=0}^{n-1} f(x_{i,}y_j)\Delta x\Delta y\approx \sum_{i=0}^{m-1} \sum_{j=0}^{n-1} f(x_i,y_j)\Delta x\Delta y$

where the M, N is the number of the rows and columns of the matrix respectively. In the actual process of computing,

$\left( f\left( x_i,y_j\right) +f(x_i,y_{j+1})+f(x_{i+1},y_j)+f(x_{i+1},y_{j+1})\right)/ 4$

is used instead of $f(x_i,y_j)\!$ .