Fitting Simultaneous Equations involving arbitrary function

SPIL just a moment. 0 answers, 0 views
equation-solving fitting
n = {1, 2, 3, 4, 5, 4, 4, 4, 4, 4, 4, 4, 3, 3, 4, 2, 3}

I guessed a function of n. This function is subject to change, so please suggested a different function if required (I can then reproduce "fitFEqnToZero" list, which is written below further down and edit the post).

fC[x_] := a^b*Log[c*x^d] + e

a,b,c,d, and e are arbitrary variables. So please reduce or increase the number of these.

fcForFit = fC /@ n

    {e + a^b Log[c], e + a^b Log[2^d c], e + a^b Log[3^d c], 
 e + a^b Log[4^d c], e + a^b Log[5^d c], e + a^b Log[4^d c], 
 e + a^b Log[4^d c], e + a^b Log[4^d c], e + a^b Log[4^d c], 
 e + a^b Log[4^d c], e + a^b Log[4^d c], e + a^b Log[4^d c], 
 e + a^b Log[3^d c], e + a^b Log[3^d c], e + a^b Log[4^d c], 
 e + a^b Log[2^d c], e + a^b Log[3^d c]}

I used fcForFit to construct the following list of equations (if you have a different function, I can construct again).

    fitFEqnToZero = {-603 + 13.36 qB (e + a^b Log[c]), -940 + 
  22 qB (e + a^b Log[2^d c]), -1401+ 
  22 qB (e + a^b Log[3^d c]) + 
  13 qT (e + a^b Log[3^d c]), -1378 + 
  22 qB (e + a^b Log[4^d c]) + 
  22 qT (e + a^b Log[4^d c]), -1431 + 
  33 qB (e + a^b Log[5^d c]) + 
  22 qT (e + a^b Log[5^d c]), -1649 + 
  11 qB (e + a^b Log[4^d c]) + 
  33 qT (e + a^b Log[4^d c]), -1907 + 
  11 qB (e + a^b Log[4^d c]) + 
  33 qT (e + a^b Log[4^d c]), -1718 + 
  11 qB (e + a^b Log[4^d c]) + 
  33 qT (e + a^b Log[4^d c]), -1718 + 
  11 qB (e + a^b Log[4^d c]) + 
  33 qT (e + a^b Log[4^d c]), -1770 + 
  11 qB (e + a^b Log[4^d c]) + 
  33 qT (e + a^b Log[4^d c]), -1587 + 
  11 qB (e + a^b Log[4^d c]) + 
  33 qT (e + a^b Log[4^d c]), -1640 + 
  11 qB (e + a^b Log[4^d c]) + 
  33 qT (e + a^b Log[4^d c]), -1339 + 
  13 qB (e + a^b Log[3^d c]) + 
  22 qT (e + a^b Log[3^d c]), -1297 + 
  22 qB (e + a^b Log[3^d c]) + 
  11 qT (e + a^b Log[3^d c]), -1501 + 
  19 qB (e + a^b Log[4^d c]) + 
  20 qT (e + a^b Log[4^d c]), -1574 + 
  8 qB (e + a^b Log[2^d c]) + 
  13 qT (e + a^b Log[2^d c]), -1297 + 
  33 qT (e + a^b Log[3^d c])}

Now I want to set fitFEqnToZero[[1]], fitFEqnToZero[[2]]...fitFEqnToZero[[Length[fitFEqnToZero]]]... all to zero and fit simultaneously for the following variables

{qB, a, b, c, d,  e, qT}

with the following constraints

fcoil[1] == 1 && qB <= 2000 && qT <= 2000 && fcoil[2] <= 1 && 
  fcoil[3] <= 1 && fcoil[4] <= 1 && 
  fcoil[5] <= 1}, 

How can I do this? Is Nsolve, NMinimize or other the most appropriate?

If I use NMinimize should I fit to Total[fitFEqnToZero] == 0? Is this effective the same or could this result in some of the elements in list fitFEqnToZero being non-zero?

No Answers Yet


HighResolutionMusic.com - Download Hi-Res Songs

1 The Chainsmokers

Beach House flac

The Chainsmokers. 2018. Writer: Andrew Taggart.
2 (G)I-DLE

POP/STARS flac

(G)I-DLE. 2018. Writer: Riot Music Team;Harloe.
3 Ariana Grande

​Thank U, Next flac

Ariana Grande. 2018. Writer: Crazy Mike;Scootie;Victoria Monét;Tayla Parx;TBHits;Ariana Grande.
4 Anne-Marie

Rewrite The Stars flac

Anne-Marie. 2018. Writer: Benj Pasek;Justin Paul.
5 Clean Bandit

Baby flac

Clean Bandit. 2018. Writer: Jack Patterson;Kamille;Jason Evigan;Matthew Knott;Marina;Luis Fonsi.
6 Nicki Minaj

No Candle No Light flac

Nicki Minaj. 2018. Writer: Denisia “Blu June” Andrews;Kathryn Ostenberg;Brittany "Chi" Coney;Brian Lee;TJ Routon;Tushar Apte;ZAYN;Nicki Minaj.
7 BlackPink

Kiss And Make Up flac

BlackPink. 2018. Writer: Soke;Kny Factory;Billboard;Chelcee Grimes;Teddy Park;Marc Vincent;Dua Lipa.
8 Imagine Dragons

Bad Liar flac

Imagine Dragons. 2018. Writer: Jorgen Odegard;Daniel Platzman;Ben McKee;Wayne Sermon;Aja Volkman;Dan Reynolds.
9 BTS

Waste It On Me flac

BTS. 2018. Writer: Steve Aoki;Jeff Halavacs;Ryan Ogren;Michael Gazzo;Nate Cyphert;Sean Foreman;RM.
10 Halsey

Without Me flac

Halsey. 2018. Writer: Halsey;Delacey;Louis Bell;Amy Allen;Justin Timberlake;Timbaland;Scott Storch.
11 Little Mix

Woman Like Me flac

Little Mix. 2018. Writer: Nicki Minaj;Steve Mac;Ed Sheeran;Jess Glynne.
12 Brooks

Limbo flac

Brooks. 2018.
13 Fitz And The Tantrums

HandClap flac

Fitz And The Tantrums. 2017. Writer: Fitz And The Tantrums;Eric Frederic;Sam Hollander.
14 Backstreet Boys

Chances flac

Backstreet Boys. 2018.
15 Lady Gaga

I'll Never Love Again flac

Lady Gaga. 2018. Writer: Benjamin Rice;Lady Gaga.
16 Diplo

Close To Me flac

Diplo. 2018. Writer: Ellie Goulding;Savan Kotecha;Peter Svensson;Ilya;Swae Lee;Diplo.
17 Rita Ora

Velvet Rope flac

Rita Ora. 2018.
18 Bradley Cooper

Always Remember Us This Way flac

Bradley Cooper. 2018. Writer: Lady Gaga;Dave Cobb.
19 Imagine Dragons

Machine flac

Imagine Dragons. 2018. Writer: Wayne Sermon;Daniel Platzman;Dan Reynolds;Ben McKee;Alex Da Kid.
20 Erika Sirola

Speechless flac

Erika Sirola. 2018. Writer: Teemu Brunila;Stefan Dabruck;Jürgen Dohr;Guido Kramer;Dennis Bierbrodt;Chris Braide;Robin Schulz.

Language

Popular Tags