pchipInterpolateFit

pchipInterpolateFit(X, Y, [extrapolate=true])

X is a numeric vector representing the x-coordinates (independent variable) of the interpolation points. X must be strictly increasing and contain at least two elements.

Y is a numeric vector of the same length as X, representing the y-coordinates (dependent variable) of the interpolation points.

extrapolate (optional) is a Boolean scalar indicating whether to allow extrapolation when prediction points fall outside the data range. Defaults to true.

This function applies piecewise cubic Hermite interpolation to the given numerical vectors X and Y. PCHIP stands for Piecewise Cubic Hermite Interpolating Polynomial.

Return value: A dictionary with the following keys:

• modelName: A string "PchipInterpolate" indicating the model name.
• X: The DOUBLE vector representing the x-coordinates used for interpolation (i.e., the input X).
• extrapolate: A Boolean scalar. The input extrapolate.
• coeffs: A numeric vector containing the polynomial coefficients fitted from the input data points.
• predict: The prediction function of the model. You can call model.predict(X) or predict(model, X) to make predictions with the generated model.
  • model: The output dictionary of pchipInterpolateFit.
  • X: A numeric vector representing the x-coordinates.

Perform piecewise cubic Hermite interpolation on the given vectors x and y.

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$DOUBLE\(num-1)*0..(num-1)	
}

x_observed = linspace(0.0, 10.0, 11)[1]
y_observed = sin(x_observed)

model = pchipInterpolateFit(x_observed, y_observed)
model;

/* output:
modelName->PchipInterpolate
X->[0,1,2,3,4,5,6,7,8,9,10]
coeffs->#0                 #1                 #2                 #3                
------------------ ------------------ ------------------ ------------------
-0.32911446845195  -0.057707802943105 1.228293256202952  0                 
-0.01011863907468  -0.047589163868426 0.125534244960891  0.841470984807897 
0.708356730424705  -1.476534149190519 0                  0.909297426825682 
0.637878921149598  -0.707803317410469 -0.827998107106924 0.141120008059867 
0.074275580231352  0.053570618892506  -0.329967978479069 -0.756802495307928
-0.571482233207003 1.250991009671215  0                  -0.958924274663138
-0.594663658922633 0.743530436118926  0.787535319721422  -0.279415498198926
-0.174138080617811 0.015904513331029  0.490605215191374  0.656986598718789 
0.434603140426252  -1.011842901807877 0                  0.989358246623382 
0.046813296419378  -0.283076510213506 -0.719876382336998 0.412118485241757 

extrapolate->true
predict->cubicHermiteSplinePredict
*/

Related: predict cubicHermiteSplineFit