<p> plotG(vx,vy,chr,sz,clr) </p>

70ab6251-e6e9-4cb2-896a-0b5b137fa085 29 4 5 decimal

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

vx vy chr sz clr plotG n vx length : plot vx 1 el vy 1 el chr sz clr augment : i 2 n range plot plot vx i el vy i el chr sz clr augment stack : for plot 41 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 :

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 2^x 3^41 mat :

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

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

data X Y . 14 black plotG :

j 1 degree range i 1 n range M i j el X i el φ j el : for for

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).

Φ M transpose M * : d M transpose Y * : b Φ 1 -^eval d * : 31 sys

Φ 1 -^192.2 329 - 17228 - 329 - 571.23 301.905 - 49.556 172 301.905 - 161.143 26.667 - 28 - 49.556 26.667 - 4.444 44 mat

d 18 34.5 75.75 184.125 41 mat

b 17.4 - 40.5714 23.1429 - 441 mat

b grouped modules 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 * : Φ 1 -^eval d * 51 line

r b polyroots (: 0.6316 2.5771 0.4964 i * + 2.5771 0.4964 i * - 31 mat

recast the scalar model x fit b x φ * :

analytical 1rst derivative x D x fit x diff :

PolyOrder 3 :

x D x 1.25 2.75 solve x fit x D - 0 ≡ x 1 2.75 solve 21 sys 1.3468 2.5103 21 mat 1.0847 2.6399 21 mat 21 sys

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

Smath QuickPlot scalar fit

x fit x D data 3 1 sys

x fit x X 1 el X 5 el int 6.9143

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 : 0.06

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

About polynomial fit methods:

1. Pure monomial fit are numerically unstable and should be limited to order < 9.

Same remark applies to fractional monomials.

2. linfitCheby is lot more powerful. ChebyShev polynomials are numerically

very stable. The method optimises a linear combination of those polynomials.

The method supports high order, up to 99 was successful in Mathcad 11.

3. Normalised rational fractions [Padé] will fit more data sets than pure Lagrange

polynomials. They are more numerically stable.

4. Thiele continued fraction is one of the most useful in Engineering domains.

5. Rational linfit is a must as well.

]]>