plotG(vx,vy,a,b,c)

ea59650a-221c-4bdf-bd19-1f9b7baad041 15 4 5 decimal

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

plotG(vx,vy,a,b,c)

vx vy a b c plotG n vx length : plot vx 1 el vy 1 el a b c augment : i 2 n range plot plot vx i el vy i el a b c augment stack : for plot 41 line :

Step 1: Reduce a data set by a function

vx 01 1.5 3 4.5 51 mat :

vy 2 - 0.04 2.91 1.6 - 1.1 51 mat :

U φ 1 U U 2^U 3^41 mat :

Cholesky companion solver jj 1 U φ length range ii 1 vx length range M ii jj el vx ii el φ jj el : for for Φ M transpose M * : Δ M transpose vy * : β Φ 1 -^eval Δ * : 41 line

β 2.2464470918009 - 7.0674188273767 3.9111967608814 - 0.5560974850113 41 mat :

uu Poly uu φ β * :

Polyfit solves directly from [X, Y] WXYZ is supplementary insight.

x Poly vx vy o 7 red plotG 2 1 sys

The 5 points unknown data set is now reduced to 4 coefficients function ... we have reduced the XY system by another one, now: productive

Step 2: Invent an equivalent system ........that will not be singular

w x y z 41 mat 2.24644709180097 - 7.06741882737669 3.91119676088135 - 0.55609748501128 41 mat :

Invent the 1rst component 5 w * 10 x * + 32.5 y * + 122.5 z * + 0.45

Invent the 2nd component 10 w * 32.5 x * + 122.5 y * + 245 z * + 135.6511 -

Invent the 3rd component 32.5 w * 122.5 x * + 245 y * + 490 z * + 106.9938

Invent the 4th component 122.5 w * 245 x * + 490 y * + 980 z * + 84.817

w x y z Clear 1

LinSolve LinSolve Courtesy NASCH 20180117

Löst ein lineares Gleichungssystem, gegeben als Vektor von Gleichungen, nach allen
unbekannten Variablen auf. Für symbolische Ergebnisse definieren Sie bekannte Größen
mit eigenen Maßeinheiten. Solves a linear system, given as a vector of equations, for any unknown variable. 
Use custom units for parametric (symbolic) solutions. sys LinSolve subtract right hand sides of equations n sys length : i 1 n range Nsys i el sys i el num2str ≡ -(strrep) concat str2num : sys i el num2str trace 21 line for Compute Jacobi matrix and it's determinant u Nsys Unknowns : J Nsys u Jacob : d J det : compute right hand side of linear system i 1 n range RHS i el Nsys i el - J i j el u j el * (j 1 n sum + : for multiply inverse jacobi matrix by rhs i 1 n range r i el J j i alg d / RHS j el * (j 1 n sum : for r 121 line :

RHS J u * G - :

J 1 -^RHS *

Residual(sys): Berechnet den Residuenvektor des Gleichungssystems sys. Die Lösung muss den 
Unbekannten schon zugewiesen sein. Geeignet zur Prüfung von Lösungsverfahren mit eingebetteter
Ergebniszuweisung. Residual(sys): Computes the residual vector of system of equations sys. All variables must
be assigned. Suitable to check solutions with embedded assignment. sys Residual subtract right hand sides of equations Nsys sys num2str ≡ - strrep str2num : 21 line :

Residual(sys,L): Berechnet den Residuenvektor des Gleichungssystems sys für die Lösung L, die
den Unbekannten nicht vorab zugewiesen wurde. Dies erfolgt innerhalb der Funktion. Geeignet zur 
Prüfung von Lösungsverfahren ohne eingebettete Ergebniszuweisung. Residual(sys,L): Computes the residual vector of system of equations sys for a given solution L. 
The solution is assigned to the unknowns and the residual is evaluated. Suitable to check 
solutions without embedded assignment. sys L Residual subtract right hand sides of equations n sys length : u sys Unknowns : Assign solution to unknowns i 1 n range u i el num2str : L i el num2str concat str2num 11 line for Nsys sys num2str ≡ - strrep str2num : 61 line :

vx vy a b c plotG a char ≡ b size ≡ c color ≡ 13 mat n vx length : plot vx 1 el vy 1 el a b c augment : i 2 n range plot plot vx i el vy i el a b c augment stack : for plot 51 line :

Step 3: Construct the linsolve system

WXYZ 5 w * 10 x * + 32.5 y * + 122.5 z * + 0.45 ≡ 10 w * 32.5 x * + 122.5 y * + 245 z * + 135.6511 - ≡ 32.5 w * 122.5 x * + 245 y * + 490 z * + 106.9938 ≡ 122.5 w * 245 x * + 490 y * + 980 z * + 84.817 ≡ 41 mat :

p WXYZ LinSolve :

p 2.24645 - 7.06742 3.9112 - 0.5561 41 mat

Taking into account the rounded WXYZ, LinSolve(WXYZ) will reproduce the β original from the given RHS. Any new value(s)in the RHS will recalculate new 'p' i.e: new β's

WXYZ 5 w * 10 x * + 32.5 y * + 122.5 z * + 0.25 ≡ 10 w * 32.5 x * + 122.5 y * + 245 z * + 135 - ≡ 32.5 w * 122.5 x * + 245 y * + 490 z * + 100 ≡ 122.5 w * 245 x * + 490 y * + 980 z * + 85 ≡ 41 mat :

p WXYZ LinSolve :

Transit/isolate
or spool to file p 2 - 6.8696 3.8499 - 0.5443 41 mat

β 2 - 6.8696 3.8499 - 0.5443 41 mat :

u new u φ β * :

x c 10 x ≤ (x 4.5 ≤ (& cases :

Polyfit solves directly from [X, Y] WXYZ is supplementary insight.

x Poly x c * x new vx vy o 7 black plotG 3 1 sys

What have we achieved ?

The RHS of WXYZ is lot smoother to manipulate

than the Cholesky β's ... all that to better fit

or adapt a fitted data set, for design purpose.

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http://www.hpmuseum.org/cgi-sys/cgiwrap/hpmuseum/archv016.cgi?read=94983

Step 4: The linsolve "compactum" 'V' may be subjected from other intelligentia

[w,x,y,z] solve compactum ... in lexicographic order U 510 32.5 122.5 10 32.5 122.5 245 32.5 122.5 245490 122.5 24549098044 mat : V 0.45 135.6511 - 106.9938 84.817 41 mat : wxyz U 1 -^V * : 15 mat 21 line

[w,x,y,z] solutions and sanity wxyz U wxyz * 12 mat 2.246445 - 7.067419 3.911197 - 0.556098 41 mat 0.45 135.6511 - 106.9938 84.817 41 mat 12 mat