<p> plot(data,char,size,clr) </p>

4ba30f90-55f6-44e5-96e6-2e0393f18ca3 5 15 12 decimal

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

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

Error stem plot for QuickPlot unicolor data Error stemX 1 data rows range : i 1 stemX rows range stem i el data i 1 el data i 2 el data i 1 el 022 mat : for i 1 stem rows 1 - range stem i el stem i el stem i 1 + (1 el 1 el 012 mat stack : for V stem 1 el : j 2 stem rows 1 - range V V stem j el stack : for V V data data rows row stack : 71 line :

much better fit

XY 14 1.5 523 2.5 23452 mat :

X XY 1 col : Y XY 2 col : n X length : degree x φ length : 41 line

poly model x φ 1 x x 1.75^x 2.5^41 mat :

0.1 sec 1 x x 2^x 3^41 mat

0.3 sec 1 x x 1.75^x 2.5^41 mat

data XY . 14 black plot :

Cholesky algebra minimises 'b' in the Legendre LS sense [Least Squares]. The corresponding algebra is universal in CAS [Computer Algebra System]. The method extends to the "ConjugateGradient" fit model function(s). Cholesky algebra is not commutative ... Experiment both φ(x)

t0 1 time :

Chollesky solver j 1 degree range i 1 n range M i j el X i el φ j el : for for Φ M transpose M * : d M transpose Y * : b Φ 1 -^eval d * : 41 line

Φ 1 -^344.479 763.224 - 539.96 112.36 - 763.224 - 1712.027 1220.467 - 255.575 539.96 1220.467 - 874.671 184.017 - 112.36 - 255.575 184.017 - 38.879 44 mat

d 18 34.5 61.551 116.867 41 mat

1 time t0 - 0.3 s *

x c 1 0.5 x ≤ (x 4 ≤ (& cases :

b 26.6172 - 73.9152 55.2643 - 11.9845 41 mat

x λ 11 x ≤ (x 3 ≤ (& cases :

recast the scalar model x fit b x φ * :

PolyOrder 3 :

analytical 1rst derivative ...
slow compute NON-integer monomials x D x fit x diff :

x i^(i 0 PolyOrder sum 1 x 1 x + x 2^+ (* +

Smath QuickPlot scalar fit

x fit x c * x D x λ * data 3 1 sys

1 time t0 - 32.2 s *

options ... acc 100 x fit x X 1 el X 5 el int 6.95

~ 1 min to solve
NON-integer monomials x D x 1.25 2.75 solve x fit x D - 0 ≡ x 1 2.75 solve 21 sys 1.336 2.4951 21 mat 1.1 2.6352 21 mat 21 sys

1 time t0 - 97.2 s *

Relative residuals Residuals i 1 XY rows range Δ i el 1 Y i el X i el fit / - eval : for X Δ augment 21 line :

SSD = "Sum Square Differences" SSD Y i el X i el fit - (2^(i 1 n sum : 0.03

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 :

ε Residuals 0.025 BarSize :

relative residuals

ε Residuals Error 2 1 sys

1 time t0 - 97.8 s *