Fit XYZ data with polynomial equations of specified/maximum degree in X and Y, and rank equations to determine best fit (PRO Only).

Purpose:

• Fit XYZ data with polynomial surface with specified degree in x and y.
• Rank functions up to the specified degree, and determine the best-fit equation.

Installation:
Download the file PolySurfFit.opx, and drag-and-drop it onto the Origin workspace. An icon will appear in the Apps Gallery.
NOTE: This tool requires OriginPro.

Operation:

1. Highlight the Z column in the worksheet.
2. Click the Polynomial Surface Fit icon in the Apps Gallery to open the dialog.
3. Set degree for X and Y to define the polynomial surface function.
   The total degree of the polynomial surface is the maximum of specified X and Y degrees. The degree of X in each term of the function will not be larger than the specified X degree, and degree of Y will not be larger than the specified Y degree.
   e.g. if specified degree of X is 3 and degree of Y is 2, the total degree of the function will be 3, and the polynomial surface function will be:
   poly32(x,y) = c₀₀ + c₁₀ x + c₀₁ y + c₂₀ x² + c₁₁ x y + c₀₂ y² + c₃₀ x³ + c₂₁ x² y + c₁₂ x y²
4. Check Normalize XY if you want to normalize XY data to mean value of 0 and standard deviation of 1.
5. In the Rank Models drop-down list ... 
   • Select None to fit with the specified maximum degrees in X and Y. The workbook will include two sheets: the result sheet with fit statistics and parameters, and the data sheet with fitted data and residuals.
   • Select an option other than None to fit with all possible combinations of degrees in X and Y, to find the best fitting function. Three sheets will be created. The third sheet will be a comparison of results for all fitting models. The best-fit model will show in red.
   • The matrix sheet for fitted surface is hidden by default. You can Show it from Project Explorer.
   For the algorithm of rank models, see Comparing Two Fitting Functions in Origin's online help.
6. Set the XY Grid Settings under the Fitted Surface branch to customize the XY grid size and the range for fitted surface.
7. Click OK to generate a graph of the fitted surface and the results workbook.

Notes:
1. Make sure the column plot designation for inputting Z data is set to Z (Right click on the column, select Set As: Z from the short-cut menu.).
2. Data filters are supported, and hidden rows will be excluded from the analysis.
3. Selecting the Normalize XY option will ensure that coefficients of higher order terms are not so small; X/Y data in the fitted data sheet will be normalized; and mean and standard deviation will be listed in the column's Comments.