Curve Fitting Express VI

Owning Palette: Signal Analysis Express VIs

Requires: Full Development System

Computes the coefficients that best represent the input data based on the chosen model type.

Dialog Box Options

Block Diagram Inputs

Block Diagram Outputs

Add to the block diagram

Find on the palette

Dialog Box Options

Parameter	Description
Model Type	Displays the data and results according to a mathematical model type you specify. The model type can be any of the following options: Linear—Finds the slope and intercept of the line that best represents the input data set in the least-squares sense. Quadratic—Finds the polynomial curve of order 2 that best represents the input data set in the least-squares sense. Spline—Returns the spline interpolant of length n. n contains the second derivatives of the spline interpolating function g(x) at the tabulated points , where i = 0, 1, …, n – 1. Polynomial—Finds the set of polynomial fit coefficients that best represents the input data set in the least-squares sense. Polynomial order—Must be greater than or equal to zero. If Polynomial order is less than zero, the Express VI returns an error. The default is 5. This option is available only when you select the Polynomial option. The value of polynomial order must observe the following relationship: 0 m < n – 1, where n is the number of sample points, and m is Polynomial order. General least squares linear—Finds the k-dimension linear curve values and the set of k-dimension linear fit coefficients that best represents the input data set using the least-squares solution. Models—Individual functions of the independent variable. This option is available only when you select the General least squares linear option. In the following equation, the models are the functions of x, namely f₀(x), f₁(x), …, f_{n – 1}(x). where a = {a₀, a₁, a₂, …, a_{n – 1}} Non-linear—Uses the Levenberg-Marquardt algorithm to determine the set of coefficients of the nonlinear model that best represents the input data set in the least-squares sense. The nonlinear model is expressed by a nonlinear function y = f(x,a), where a is the set of coefficients. Independent variable—Specifies the independent variable in Non-linear model. This option is available only when you select the Non-linear option. Maximum iterations—Maximum number of executing iterations. If the Express VI reaches Maximum iterations without finding a solution, the VI returns an error. You must increase Maximum iterations or adjust Initial guesses to find a solution. The default is 500. This option is available only when you select the Non-linear option. Initial guesses—Initial guesses of the solution coefficients. This option is available only when you select the Non-linear option. Current Model—Displays the formula for the currently selected Model Type. This display is available only when you set Model Type to Linear, Quadratic, Spline, Polynomial, or General least squares linear. Non-linear model—String that describes the model equation. This option is available only when you select the Non-linear option.
results	Displays values generated for the parameters based on the options you select and values you enter.
Data Graph	Displays the original data and the best fit. The VI calculates best fit using the following equation. z_i = f(x_i)A where A is the best fit coefficient.
Residue Graph	Displays the difference between the original data and the best fit.
Non-linear	Uses the Levenberg-Marquardt algorithm to determine the set of coefficients of the nonlinear model that best represents the input data set in the least-squares sense. The nonlinear model is expressed by a nonlinear function y = f(x,a), where a is the set of coefficients. Independent variable—Specifies the independent variable in Non-linear model. This option is available only when you select the Non-linear option. Maximum iterations—Maximum number of executing iterations. If the Express VI reaches Maximum iterations without finding a solution, the VI returns an error. You must increase Maximum iterations or adjust Initial guesses to find a solution. The default is 500. This option is available only when you select the Non-linear option. Initial guesses—Initial guesses of the solution coefficients. This option is available only when you select the Non-linear option.

Block Diagram Inputs

Parameter	Description
Signals	Specifies the observed values of the dependent variable.
Locations	Specifies the values of the independent variables.
error in	Describes error conditions that occur before this node runs.

Block Diagram Outputs

Parameter	Description
intercept	Returns the intercept of the calculated best linear fit.
a1	Returns the coefficient of the first-order term.
best fit	Returns the fitted data. The VI calculates best fit using the following equation. z_i = f(x_i)A where A is the best fit coefficient.
residual	Returns the difference between the original data and the best fit.
mean squared error	Returns the mean square error of the best fit.
error out	Contains error information. This output provides standard error out functionality.
polynomial coefficients	Returns the coefficients that describe the best polynomial fit. The total number of elements in polynomial coefficients is m + 1, where m is Polynomial order.
slope	Returns the slope of the calculated best linear fit.
a0	Returns the constant term of the calculated best quadratic fit.
spline interpolant	Returns the second derivative of interpolating function g(x). spline interpolant is the second derivative of interpolating function g(x) at points , i = 0, 1,…, n – 1.
non-linear coefficients	Returns the set of coefficients of the nonlinear model that best represents the input data set in the least-squares sense.
general LS coefficients	Returns the set of coefficients that best represent the input data set in the least-squares sense.
a2	Returns the coefficient of the second-order term.

This Express VI operates similarly to the following VIs and functions:

Linear Fit
Polynomial Interpolation
Spline Interpolation