c57fb729-4086-4f19-b229-bd092f035b97 41 4 15 decimal

&[DATE] &[TIME] - &[FILENAME]

2D LINEAR INTERPOLATION

°C XX 2050100150200250300350400450500550600113 mat :

мм YY 1520254050658010012515020025030035040045050060070080090010001400231 mat :

Вт/м MM 491725354556688194109124140410192839506275891031191351525112031425467819511112814516351223354760759010612314216118161426385166819811513315317319571629435874901081271471691912148173146627896115135156179202226919345067851041241461681922172431021385574931141361591832082352631123426180101132156182209238267298142850729511915418221224227430834316335782107133173204236270305342380183967951241531912242592963333734142245771081401732082442813203614034462549841171521872232623013433854304762754911271632002392803223654104575053058981361752152562993433894364865373467112154197241286333382432484537593387512417021726431336441647052658364243831371882382903433974535115716336964791150205259315372430490552616681749521001632222813404004635275926607298017013321529136443951459167075083391810982313 mat :

YY rows 23

MM rows 23

XX cols 13

MM cols 13

Mike's initial solution:

X Y M x y bilinearmk V 01 matrix : k 1 X length range V k el Y M k col y linterp : for X transpose V x linterp 31 line :

Mike's final proposal:

X Y M x y bilinear0 X x margin X 2 el X 1 el > x X 2 el ≤ k 2 : x X X length 1 - el ≥ k X length : k 3 : X k el x < k k 1 + : while 21 line if if x X 2 el ≥ k 2 : x X X length 1 - el ≤ k X length : k 3 : X k el x > k k 1 + : while 21 line if if if k 1 - 21 line : i X x margin : j Y y margin : dx12 X i 1 + el X i el - : dy12 Y j 1 + el Y j el - : dxx1 x X i el - : dyy1 y Y j el - : dx2x X i 1 + el x - : dy2y Y j 1 + el y - : dy2y dx2x M i j el * dxx1 M i 1 + j el * + (* dyy1 dx2x M i j 1 + el * dxx1 M i 1 + j 1 + el * + (* + dx12 dy12 * / eval 101 line :

xx 75 :

yy 215 :

XX YY MM xx yy bilinearmk 40.8

XX YY MM transpose xx yy bilinear0 40.8

x1 x x2 y1 y y2 Q11 Q12 Q21 Q22 finterpol dx12 x2 x1 - : dy12 y2 y1 - : dxx1 x x1 - : dyy1 y y1 - : dx2x x2 x - : dy2y y2 y - : dy2y dx2x Q11 * dxx1 Q21 * + (* dyy1 dx2x Q12 * dxx1 Q22 * + (* + dx12 dy12 * / eval 71 line :

Ioan's corrections on Mike's proposal:

X Y M x y bilinear X x margin Xl X length : X 2 el X 1 el > x X 2 el ≤ k 2 : x X Xl 1 - el ≥ k Xl : k 3 : X k el x < k k 1 + : while 21 line if if x X 2 el ≥ k 2 : x X Xl 1 - el ≤ k Xl : k 3 : X k el x > k k 1 + : while 21 line if if if k 1 - 31 line : i X x margin : j Y y margin : dx12 X i 1 + el X i el - : dy12 Y j 1 + el Y j el - : dxx1 x X i el - : dyy1 y Y j el - : dx2x X i 1 + el x - : dy2y Y j 1 + el y - : dy2y dx2x M j i el * dxx1 M j i 1 + el * + (* dyy1 dx2x M j 1 + i el * dxx1 M j 1 + i 1 + el * + (* + dx12 dy12 * / 101 line :

XX YY MM xx yy bilinearmk 40.8

XX YY MM xx yy bilinear 40.8

XX YY MM 2015 bilinearmk 4

XX YY MM 2015 bilinear 4

XX YY MM 201400 bilinearmk 70

XX YY MM 201400 bilinear 70

XX YY MM 60015 bilinearmk 140

XX YY MM 60015 bilinear 140

XX YY MM 6001400 bilinearmk 1098

XX YY MM 6001400 bilinear 1098

XX YY MM 101800 bilinearmk 62

XX YY MM 101800 bilinear 62

Testing

Testing for speed: Mike's (bilinear0 - test1) vs optimised by Ioan (bilinear - test2)

# test1 time # time : x 9100015 range y 810013 range r YY XX MM y x bilinear0 : for for # time time - 31 line :

# test2 time # time : x 9100015 range y 810013 range r XX YY MM x y bilinear : for for # time time - 31 line :

k 140 range R k 1 el 1 test1 : R k 2 el 1 test2 : 21 line for

R 2.965 s * 3.085 s * 2.941 s * 3.097 s * 2.951 s * 3.079 s * 2.89 s * 3.065 s * 2.904 s * 3.049 s * 2.908 s * 3.002 s * 2.905 s * 3.033 s * 2.861 s * 3.032 s * 2.903 s * 3.025 s * 2.89 s * 3.047 s * 2.902 s * 3.018 s * 2.902 s * 3.046 s * 2.885 s * 3.032 s * 2.892 s * 3.037 s * 2.895 s * 3.036 s * 2.907 s * 2.997 s * 2.893 s * 3.027 s * 2.9 s * 3.019 s * 2.91 s * 3.032 s * 2.888 s * 3.036 s * 2.887 s * 3.035 s * 2.947 s * 3.068 s * 2.916 s * 3.031 s * 2.905 s * 3.029 s * 2.911 s * 3.031 s * 2.891 s * 3.049 s * 2.902 s * 3.055 s * 2.884 s * 3.042 s * 2.889 s * 3.009 s * 2.895 s * 3.059 s * 2.929 s * 3.055 s * 2.912 s * 3.046 s * 2.925 s * 3.049 s * 2.95 s * 3.065 s * 2.959 s * 3.057 s * 2.93 s * 3.039 s * 2.93 s * 3.058 s * 2.926 s * 3.065 s * 2.928 s * 3.066 s * 2.915 s * 3.227 s * 402 mat

R 2 col sum R 1 col sum - R rows / 0.1376 s *

Testing

Testing for speed: Ioan's version without length() optimization

X Y M x y bilinear X x margin X 2 el X 1 el > x X 2 el ≤ k 2 : x X X length 1 - el ≥ k X length : k 3 : X k el x < k k 1 + : while 21 line if if x X 2 el ≥ k 2 : x X X length 1 - el ≤ k X length : k 3 : X k el x > k k 1 + : while 21 line if if if k 1 - 21 line : i X x margin : j Y y margin : dx12 X i 1 + el X i el - : dy12 Y j 1 + el Y j el - : dxx1 x X i el - : dyy1 y Y j el - : dx2x X i 1 + el x - : dy2y Y j 1 + el y - : dy2y dx2x M j i el * dxx1 M j i 1 + el * + (* dyy1 dx2x M j 1 + i el * dxx1 M j 1 + i 1 + el * + (* + dx12 dy12 * / 101 line :

k 140 range R k 1 el 1 test1 : R k 2 el 1 test2 : 21 line for

R 2.964 s * 3.076 s * 2.969 s * 3.025 s * 2.933 s * 3.028 s * 3.011 s * 3.067 s * 2.954 s * 3.043 s * 2.982 s * 3.059 s * 2.965 s * 3.058 s * 2.988 s * 3.066 s * 2.968 s * 3.071 s * 2.971 s * 3.077 s * 2.973 s * 3.063 s * 2.968 s * 3.041 s * 2.979 s * 3.064 s * 2.959 s * 3.081 s * 2.982 s * 3.065 s * 2.976 s * 3.046 s * 2.95 s * 3.05 s * 2.951 s * 3.07 s * 2.972 s * 3.079 s * 2.96 s * 3.03 s * 3.037 s * 3.088 s * 2.928 s * 3.071 s * 2.964 s * 3.052 s * 2.949 s * 3.055 s * 2.959 s * 3.064 s * 2.981 s * 3.025 s * 2.954 s * 3.063 s * 2.97 s * 3.069 s * 2.956 s * 3.049 s * 2.961 s * 3.065 s * 2.947 s * 3.046 s * 2.989 s * 3.087 s * 2.953 s * 3.06 s * 2.954 s * 3.036 s * 2.92 s * 3.026 s * 2.923 s * 3.003 s * 2.933 s * 3.018 s * 2.921 s * 3.009 s * 2.942 s * 3.015 s * 2.924 s * 3.032 s * 402 mat

R 2 col sum R 1 col sum - R rows / 0.0913 s *