splinefit (MathScript RT Module Function)
Owning Class: approximation
Requires: MathScript RT Module
Syntax
bestfit = splinefit(x, y)
bestfit = splinefit(x, y, balance)
bestfit = splinefit(x, y, balance, weights)
Legacy Name: csaps
Description
Returns the curve fit of data using a weighted cubic spline method with a balance parameter that allows you to trade smoothness for fit accuracy.
Inputs
| Name | Description |
|---|---|
| x | Specifies the independent values. x is a real, double-precision vector. |
| y | Specifies the dependent values. y is a real, double-precision vector. |
| balance | Specifies the balance between the smoothness of the cubic spline fit and the accuracy with which it fits the observations. balance must fall within the range [0, 1]. If balance is 0, the cubic spline fit is equivalent to a linear fit. If balance is 1, the cubic spline fit interpolates between the data points. If balance is out of the range [0, 1], LabVIEW calculates an appropriate value for balance automatically according to the values of x. |
| weights | Specifies the weights for the observations (y, x). weights is an array. size(weights) must equal size(x). If you do not specify weights, LabVIEW sets all elements of weights to 1. If an element in weights is less than 0, LabVIEW uses the absolute value of the element. |
Outputs
| Name | Description |
|---|---|
| bestfit | Returns the values of the fitted curve that LabVIEW evaluates at the points in x. bestfit is a real, double-precision vector. |
Details
This VI minimizes the following function to fit the observations (x, y):
p*sum{w[i]*(y[i] - f(x[i]))^2, i = 0, n-1} + (1 - p)*integral{f''(x)^2(dx), x[0], x[n-1]}
where p is the balance parameter, w[i] is the ith element of weights, y[i] is the ith element of y, x[i] is the ith element of x, integral{f''(x)^2(dx), x[0], x[n-1]} calculates a definite integral of f''(x) with a low limit of x[0] and an upper limit of x[n-1], and f''(x) is the second-order derivative of the cubic spline function, f(x).
If p equals 0, the fitted model is equivalent to a linear model. If p equals 1, the fitting is equivalent to cubic spline interpolation. To make the fitted curve both close to the observations and smooth, p must fall in the range [0, 1]. The closer p is to 0, the smoother the fitted curve. The closer p is to 1, the closer the fitted curve is to the observations.
Examples
X = 0:6;
Y = [pi/2, 0, 1, 0, -1, 0, pi/2];
XX = 0:0.1:6;
YY = spline(X, Y, XX);
YY = YY + 0.2*rand(1, length(YY));
fitY1 = splinefit(XX, YY, 0.7);
fitY2 = splinefit(XX, YY, 0.98);
plot(X, Y, 'o', XX, YY, '-', XX, fitY1, '-', XX, fitY2, '-')