Sunday, November 29, 2020

HP Prime: Linear Exponential Combination Fit

 HP Prime:  Linear Exponential Combination Fit


The program LINEXPREG attempts to fit bivariate data to the curve:


y = a + b * x + c * e^x


The LSQ (least square) function is used.  The output is a list of three matrices:



*  A matrix of coefficients:  [ [ a ] [ b ] [ c ] ] 


*  A matrix of y values entered


*  A matrix of predicted y values



HP Prime Program LINEXPREG


EXPORT LINEXPREG(lx,ly)

BEGIN

// 2020-11-17 EWS

// x list, y list

LOCAL n,lx2,lx3,mx,my,k,mr,mq;

n:=SIZE(lx);

lx2:=e^(lx);

lx3:={};

FOR k FROM 1 TO n DO

lx3:=CONCAT(lx3,{1,lx(k),lx2(k)});

END;

mx:=list2mat(lx3,3);

my:=list2mat(ly,1);

mq:=LSQ(mx,my);

mr:=mq(1,1)+mq(2,1)*lx+

mq(3,1)*e^(lx);

mr:=list2mat(mr,1);

RETURN {mq,my,mr};

END;


Example





x list:  {0, 1, 2, 3, 4, 5}

y list:  {2, 7, 13, 18, 26, 34}


LINEXPREG({0, 1, 2, 3, 4, 5},{2, 7, 13, 18, 26, 34})


Results:  {coefficients, y values, predicted y values}


coefficients:

[ [ 1.74935499143 ]

[ 5.39455446221 ]

[ 3.66584105034E-2 ] ] 


y values:

[ [ 2 ]

[ 7 ]

[ 13 ]

[ 18 ]

[ 26 ]

[ 34 ] ]


predicted y values:

[ [  1.78601340193 ]

[ 7.24355734477 ]

[ 12.8093349675 ]

[ 18.6693222357 ]

[ 25.3290542368 ]

[ 34.1627178129 ] ] 


Equation:

y = 1.74935499143 + 5.39455446221 * x + 3.66584105034E-2 * e^x


On to the last month of 2020...


Eddie


All original content copyright, © 2011-2020.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 


Casio fx-CG50: Sparse Matrix Builder

Casio fx-CG50: Sparse Matrix Builder Introduction The programs can create a sparse matrix, a matrix where most of the entries have zero valu...