linearInterpolateFit

linearInterpolateFit(X, Y, [fillValue], [sorted=false])

X is a numeric vector indicating the x-coordinates of the points for interpolation. Note that X must contain no less than two unique values with no NULLs.

Y is a numeric vector indicating the y-coordinates of the points for interpolation. Note that Y must be of the same length as X with no NULLs.

fillValue (optional) specifies how to assign values for the x-coordinate of the points outside the existing data range. The following options are supported:

• A numeric pair in the form (min, max), where min and max represent the values assigned when the x-coordinate of the point X_new is smaller than the minimum of X or larger than the maximum of X, respectively. Specifically:
  • If X_new < Xmin, it is assigned below.
  • If X_new > Xmax, it is assigned above.
• The string "extrapolate" (default), which indicates that extrapolation is performed.

sorted (optional) is a Boolean scalar indicating whether the input X is sorted in ascending order.

• If set to true, X must be in ascending order.
• If set to false (default), the function will sort X and adjust the order of Y accordingly.

Perform linear interpolation/extrapolation on a set of points. Interpolation estimates unknown values that fall between known data points, while extrapolation estimates values beyond the existing data range.

Return value: A dictionary containing the following keys:

• modelName: A string indicating the model name, which is "linearInterpolate".
• sortedX: A DOUBLE vector indicating the input Xsorted in ascending order.
• sortedY: A DOUBLE vector indicating the input Y sorted corresponding to sortedX.
• fillValue: The input fillValue.
• predict: The prediction function of the model, which returns linear interpolation results. It can be called using model.predict(X) or predict(model, X), where:
  • model: A dictionary indicating the output of linearInterpolateFit.
  • X: A numeric vector indicating the x-coordinates of the points to be predicted.

def linspace(start, end, num, endpoint=true){
	if(endpoint) return end$DOUBLE\(num-1), start + end$DOUBLE\(num-1)*0..(num-1)
	else return start + (end-start)$DOUBLE\(num)*0..(num-1)	
}
x = 0..9
y = exp(-x/3.0)
model = linearInterpolateFit(x, y, sorted=true)

/*Output
sortedX->[0.0,1.000000000000,2.000000000000,3.000000000000,4.000000000000,5.000000000000,6.000000000000,7.000000000000,8.000000000000,9.000000000000]
modelName->linearInterpolate
predict->linearInterpolatePredict
fillValue->extrapolate
sortedY->[1.000000000000,0.716531310573,0.513417119032,0.367879441171,0.263597138115,0.188875602837,0.135335283236,0.096971967864,0.069483451222,0.049787068367]
*/

// Enter new values of X to predict the corresponding Y values
model.predict(xnew)

//Output：[1,0.829918786344274,0.67590847226555,0.554039957340832,0.455202047888132,0.367879441171442,0.305310059338013,0.248652831060094,0.203819909893195,0.167459474997182,0.135335283236613,0.112317294013288,0.091474264536084,0.074981154551122,0.061604898080826]