<p> Bivariate algo collapse in utilities ..... bivariate(X,Y,Z,f,x,y) </p>

ed08d2fb-e938-48d1-baa3-62801e22df56 14 3 12 decimal

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

X Y Z f x y bivariate M i 1 X rows range M i el X i el Y i el f : for unest rows A v M 1 el : j 2 M rows range v v M j el stack : for v 51 line : β M transpose M * (1 -^M transpose Z * (* : x y p x y f transpose β * : 31 sys :

bivariate matrix

β Cholesky solver

interpolating poly

Algo style bivariate

Model basis for bivariate f(x,y) ... Mathcad, Mathematica collected otherwise a 1 el a 2 el x * + a 3 el y * + a 4 el x * y * + a 5 el x 2^* + a 6 el y 2^* + a 7 el x 3^* + a 8 el y 3^* + a 9 el x * y 2^* + a 10 el x 2^* y * +

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bivariate model X 6671697061666717 mat transpose : Y 16520016015816317515217 mat transpose : Z 3027441835202617 mat transpose : x y f 1 x y x y * x 2^y 2^16 mat : 41 sys

M X Y Z f x y bivariate 1 el : β X Y Z f x y bivariate 2 el : x y interp X Y Z f x y bivariate 3 el : 31 sys

sanity MCD 11 65160 interp 41.0

M 166165108904356272251712001420050414000016916011040476125600170158110604900249641611639943372126569166175115504356306251671521018444892310476 mat

β 5361.86557086453 113.039202254069 - 19.18258889544 - 0.750568722356 0.066645586492 - 0.094862159359 - 61 mat

β 5361.86557086453 113.039202254069 - 19.18258889544 - 0.750568722356 0.066645586492 - 0.094862159359 - 61 mat :

smart ! ... native Smath x y biv x y f transpose β * :

65160 biv 40.969

1. <= copy RHS
2. paste in foreign
3. Σ in foreign 1 u v u v * u 2^v 2^61 mat β * vectorize 536186557086453100000000000 / 113039202254069 u * 1000000000000 / - 239782361193 v * 12500000000 / - 187642180589 u * v * 250000000000 / 16661396623 u 2^* 250000000000 / - 94862159359 v 2^* 1000000000000 / - 61 mat

u v Biv 1 u v u v * u 2^v 2^61 mat β * vectorize sum :

65160 Biv 40.969

i 16 range :

1 u v u v * u 2^v 2^61 mat β_biv i el * vectorize β_biv 1 el u β_biv 2 el * v β_biv 3 el * u v * β_biv 4 el * u 2^β_biv 5 el * v 2^β_biv 6 el * 61 mat