Request for using my own computed derivatives in NaturalNeighbor.jl

[WillingWeiling]

Dear DanielVandH,

I have been exploring the capabilities of NaturalNeighbor.jl and I was wondering if it would be feasible to utilize custom derivatives as additional known information during the interpolation process. Specifically, I would like to provide my own computed derivatives to enhance the accuracy of the interpolation.
Thank you for your attention to my inquiry. I appreciate the work you have done on NaturalNeighbor.jl and I look forward to hearing your insights on this matter.

Best regards,
Weiling H

[DanielVandH]

Hi @WillingWeiling , thanks for your interest. The interpolate constructor also allows you to pass in your own gradients instead of relying on generating them with derivatives=true. Here is an example:

using NaturalNeighbours 
f = (x, y) -> x^2 + y^2 
df = (x, y) -> (2x, 2y)
x = rand(100)
y = rand(100)
z = f.(x, y)
∇z = df.(x, y) 
itp = interpolate(x, y, z; gradient=∇z)

julia> itp
Natural Neighbour Interpolant
    z: [0.34236037959410437, 0.6409391417100012, 0.2792694577044466, 0.40633019736493853, 0.0014825003910995446, 1.8705036885166058, 0.2833796685769481, 1.4593246638262931, 0.21883478954176305, 0.7157193513420117  …  1.0233750284009104, 0.5668896793818932, 0.7024901459842816, 1.7006307147816409, 0.7477708129900137, 1.09722701646297, 0.21527150358380945, 1.2723403302477225, 0.28273056436535154, 1.281013490332372]
    ∇: [(0.8350983284258899, 0.8197879605341261), (1.6006824475600536, 0.03965184627682539), (0.9765198636683925, 0.4043349931416407), (0.7002460373519068, 1.0653526536470006), (0.07126290698397475, 0.029182180394746737), (1.9119086977347501, 1.9561748095690823), (1.0644855459563665, 0.01972807030017587), (1.5441834861498966, 1.858170071981336), (0.6009112957223604, 0.7171086199735199), (0.8953492854012941, 1.4356974132801934)  …  (0.854979376605338, 1.833714912188694), (1.4897516651971912, 0.21954200866751927), (0.4152962082594305, 1.6240349883369096), (1.6916324673982732, 1.985170636084111), (0.028283158342867543, 1.7292435672611903), (1.6686166433054623, 1.2667385537418099), (0.8963693911208481, 0.24001651817505776), (1.1382351633665064, 1.9477633413397308), (1.0622364857876907, 0.050753381393001895), (1.8755837106400375, 1.267375124306626)]    
    H: nothing

See that the gradient is now in the interpolant, so you can now use e.g. Farin() or Sibson(1). Does that help you?

[WillingWeiling]

Hi@DanielVandH
thank you so much for your assistance. I am grateful to have received your guidance and am confident that it will make a significant difference in my work！ ：）