2d interpolation of n-dimensional data

I have this set of data (simplified)

x = [1 2 3]

y = [3 7 2]

temp = [22 25 23; 33 25 17; 19 25 26];

each X Y coordinate pair corresponds to a column in temp. So (X,Y) = (1,3) -> [22; 33; 19]. I'm trying to setup a 2D interpolation which gives me interpolated values of temp from input XY. My solution which works, but is slow, is to create a scatteredinterpolant for every row of temp ie

int1 = scatteredinterpolant([1 2 3]', [3 7 2]', [22 25 23]')

int2 = scatteredinterpolant([1 2 3]', [3 7 2]', [33 25 17]')

int3 = scatteredinterpolant([1 2 3]', [3 7 2]', [19 25 26]')

and then using the scatteredinterpolants 3 times. My actual dataset of temp has 30000 elements per coordinate pair, so this goes pretty slow. Any suggestions?

Answer 1

[Sean de Wolski]

You can just change the Values of one scatteredInterpolant object. It won't have to redo the expensive underlying triangulation of x/y then. Example using zeros and ones for your temp.

s = scatteredInterpolant(rand(3,1),rand(3,1),zeros(3,1))

s = 
  scatteredInterpolant with properties:

                 Points: [3×2 double]
                 Values: [3×1 double]
                 Method: 'linear'
    ExtrapolationMethod: 'linear'

s(0.3,0.2)

ans = 0

s.Values = ones(3,1) % swap for your second set of values

s = 
  scatteredInterpolant with properties:

                 Points: [3×2 double]
                 Values: [3×1 double]
                 Method: 'linear'
    ExtrapolationMethod: 'linear'

s(0.3,0.2)

ans = 1

[Curtis Wen]

Its not too much of a time savings since the evaluation of each interp still takes as long, but it does reduce the number of interpolant objects created and reduces my filesize so I'll take it. Thank you!