Barsize

4499e953-4505-4d48-8165-92ebbcd36d53 76 8 12 decimal

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

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 :

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 * -^: 31 sys

plot Tc 1 el Pc 1 el α 1 el x Po Tc 2 el Pc 2 el α 2 el x Po Tc 3 el Pc 3 el α 3 el x Po Tc 4 el Pc 4 el α 4 el x Po Tc 5 el Pc 5 el α 5 el x Po 51 sys :

plot 207 2 + 100 black 1 5 mat 2 1 sys

Tc 1 el Pc 1 el α 1 el 207 Po 1.9989288

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 :

A B T / + 0 0.44371429 0.25142857 0.78285714 0.78285714 00 0.07785714 0.10642857 0.10642857 000 0.32871429 0.32871429 0000045 mat

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 0.019 0.037 0.041 0.041 0.863 51 mat

y 0.359 0.102 0.102 0.102 0.336 51 mat

x sum 1

y sum 1

know sol

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 :

x N 0.01906029 0.03654282 0.04121825 0.0405856 0.86259304 51 mat

Φo 0.542 :

a Φ x y stack :

ao Φo xo yo stack eval :

ao F normi 0.0035

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

HOW TO SOLVE for Φ,x,y ???

Φ x y f 0 ≡

CLOSE ENOUGH TO THE SOLUTION

_________________________________________________________________________________________

dummy C dummy 01 ltlt vectorize :

same dummy 01 ltlt vectorize 11 line dummy 01 ltlt vectorize 21 sys

Borders conditions for each variable

SNRxy Solve Newton Raphson. a N εx εy SNRxy x a : t a : y x F : 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 F εx id c col * + : r 1 Nx range J r c el u r el y r el - : for 31 line for t x J εx / (1 -^y * - : c t C : t c t * c ¬ (x * + vectorize : 12 mat t x - normi εx < break x t : y x F : 12 mat if 41 line if for κ N ≤ t MaxIter 'N' reached error if 41 line :

id c col 11 mat

eitherone y normi εy < y normi εy ≤ 21 sys

syntax incorrect
... computes ... x εx id c col * + F x F εx id c col * + 21 sys

eitherone t x - normi εx < t x - normi εx ≤ 21 sys

MaxIter 'N' NOT computed
.....  OK  but freak ! κ N < κ N ≤ 21 sys

t0 1 time :

a a 50107 -^107 -^SNRxy : 0.9458 0.1498 0.0005 0.0444 0.9918 0.0027 0.2026 0.0872 0.4633 0.0573 0.1895 111 mat

a F 0.1516 - 0.0175 - 0.3402 0.0005 - 0.1706 - 10.4158 - 195.3882 11.2984 0.8503 - 84.2248 3.2528 1015 -^* - 111 mat

1 time t0 - min 0

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

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 26 range el sum 1

a 711 range el sum 1

Barsize

Bar plot unicolor style, bar width user. data dt BarSize v data 2 col : t v bar t dt - 0 t dt - v t dt + v t dt + 042 mat : j 1 data rows range j 1 ≡ B data j 1 el data j 2 el bar : B B data j 1 el data j 2 el bar stack : if 11 line for B 41 line :

FindRoot from external forloop 'j' algo style collapse in utilities

j xx yy sol FindRoot ranged algo style j j Φ 0.542 : ε 1015 -^: 12 mat system xx P T kγ j el v u / - 0 ≡ z j el Φ v * 1 Φ - (u * + (- 0 ≡ 21 sys : init u xx j el ≡ v yy j el ≡ 21 mat : 12 mat sol j el system init ε FindRoot : 31 line for sol 31 line :

iter 1172133164951661771381782 mat :

.......... Cyclic user iterations ..........

t0 1 time :

z 0.35 0.1 0.1 0.1 0.35 51 mat :

xx 0.048977472517297 0.097304371601828 0.095276460075385 0.104676253625487 0.653763906282262 51 mat :

yy 0.604369589644057 0.102277855731298 0.103991478386474 0.096048479408724 0.093313894691373 51 mat :

solve for [j, vectors (xx, yy] as received from above

x j 1 xx rows range x j el j xx yy sol j el (1 el : for x 21 line :

y j 1 yy rows range y j el j xx yy sol j el (2 el : for y 21 line :

plug in [xx, yy]

isolate [x, y] Φ 0.542 : x x : y y : 13 mat

x 0.048977472517307 0.097304371601828 0.095276460075395 0.10467625362548 0.653763906282258 51 mat

y 0.604369589644047 0.102277855731298 0.103991478386474 0.096048479408724 0.093313894691377 51 mat

'x' .....

Check sanity 'kγ, xy'

'y' ...

kγ y x / vectorize x P T kγ - :

xy z Φ y * 1 Φ - (x * + (- :

iter iter 0.25 BarSize :

1 time t0 - 16 s *

kγ 14 round vectorize 0.000000000000 0.000000000000 0.000000000000 0.000000000000 0.000000000000 51 mat

xy 14 round vectorize 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 51 mat

iter 2 1 sys

Mathcad solution