6f6479e7-5946-49a3-a287-e9da95fb44b5 24 4 5 false false 0 decimal

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

PRIMER 3.8

Tc 433.8 556.4 553562 619.6 51 mat :

Pc 31.6 4540 48.6 3851 mat 101.33 * :

α 6.771 6.742 6.844 6.848 7.330 51 mat :

z 0.35 0.1 0.1 0.1 0.35 51 mat :

A 0 0.018 00000 0.125 - 0.045 - 0.045 - 000 0.797 - 0.797 - 0000045 mat :

B 014988274274007153530003943940000045 mat :

x N x x sum / eval 11 line :

P 101.33 :

T 350 :

Tr φ 36 Tr / 42 Tr ln * + 35 - Tr 6^- :

Tr Ψ 0.0364 Tr φ * Tr log10 - :

Tc Pc α T Po 10 Pc log10 0.1183 T Tc / φ * - 7 T Tc / log10 * + α 7 - (T Tc / Ψ * -^:

T x γRK Nc x length : C A B T / + : nul Nc el 0 : C C nul transpose stack : C C C transpose + : j 1 Nc range s kk Clear : s C j kk el x kk el * 1 x j el - (* (kk 1 Nc sum : m 1 Nc 1 - (range n m 1 + (Nc range y j n ≡ (j m ≡ (| 0 C m n el x m el * x n el * if : s s y - : 21 line for for γ j el s exp : 41 line for γ 71 line :

k Tc Pc α T Po vectorize eval : 688.851 101.8051 90.1438 91.5645 14.2433 51 mat

x P T kγ γ T x γRK : γ k * P / vectorize eval 21 line :

Initial guess

Φ 0.5 :

x z k 1 - (Φ * 1 + / vectorize N :

y k x * vectorize N :

x 0.0191 0.0365 0.0412 0.0406 0.8626 51 mat

y 0.3591 0.1017 0.1016 0.1016 0.336 51 mat

x sum 1

y sum 1

know sol

Φo 0.542 :

xo 0.049 0.0973 0.0953 0.1047 0.6538 51 mat :

yo 0.6044 0.1023 0.104 0.096 0.0933 51 mat :

a Φ x y stack eval :

ao Φo xo yo stack eval :

X F X X 1 el X 26 range el N X 711 range el N stack : Φ X 1 el : x X 26 range el : y X 711 range el : 13 mat Φ y * 1 Φ - (x * + z - y x / vectorize x P T kγ - x y - (sum stack eval 31 line :

Modify X for get sum(x)=sum(y)=1

a F normi 5.096

ao F normi 0.0035

HOW TO SOLVE for Φ,x,y ???

Φ x y f 0 ≡

CLOSE ENOUGH TO THE SOLUTION

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X C X 01 ltlt vectorize 11 line :

Borders conditions for each variable

SNRxy Solve Newton Raphson. a N εx εy SNRxy x a : t a : ξ a : y x F eval : 14 mat Nx a length : id Nx identity : J Nx Nx matrix : 13 mat κ 1 N range y normi εy < break c 1 Nx range u x εx id c col * + F eval : r 1 Nx range J r c el u r el y r el - : for 21 line for t x J εx / (1 -^y * - eval : c t C eval : t c t * c ¬ (x * + vectorize eval : 12 mat t x - normi εx < break x t : y x F eval : 12 mat if 41 line if for κ N < t MaxIters rached error if 41 line :

a a 50107 -^105 -^SNRxy : 0.542 0.049 0.0973 0.0953 0.1047 0.6538 0.6044 0.1023 0.104 0.096 0.0933 111 mat

a F 1.4441 1011 -^* 9.999 1012 -^* - 7.53 1013 -^* - 9.898 1012 -^* - 6.209 1012 -^* 7.3663 1010 -^* 4.4932 1010 -^* 1.0303 1011 -^* - 3.596 1010 -^* 5.179 1012 -^* - 1.327 1015 -^* 111 mat

a F normi 7.3663 1010 -^*

a 26 range el sum 1

a 711 range el sum 1