How to extract the coefficient of x inside the exponential?

syms x
a1=10.0548; a2=-4.4425; a3=-3.2730; a4=-2.2430; b1=0.0; b2=0.0029; b3=0.0379; b4=0.3863; 
y=a1*exp(-b1*x) + a2*exp(-b2*x) + a3*exp(-b3*x) + a4*exp(-b4*x); 

z4 = expand(y4^2);

z4 = vpa(z4,6);

z4 = exp(-0.0758168 x) 10.7127 - exp(-0.0379084 x) 65.8191 - exp(-0.00294242 x) 89.3358 + exp(-0.00588485 x) 19.7354 
- exp(-0.386332 x) 45.1049 + exp(-0.772664 x) 5.03086 + exp(-0.0379084 x) exp(-0.00294242 x) 29.0805
+ exp(-0.0379084 x) exp(-0.386332 x) 14.6825 + exp(-0.00294242 x) exp(-0.386332 x) 19.9285 + 101.099

[c, tx] = coeffs(vpa(z2,6))

qc = arrayfun(@char, tx, 'uniform', 0)
fin = cellfun(@(x)regexprep(x, '\<exp', ''), qc, 'UniformOutput', false)
fin1 = cellfun(@(x)regexprep(x, '\<x', ''), fin, 'UniformOutput', false)
fin2 = cellfun(@(x)regexprep(x, '*+', ''), fin1, 'UniformOutput', false)
fin3 = cellfun(@(x)regexprep(x, '\<(', ''), fin2, 'UniformOutput', false)
fin4 = cellfun(@(x)regexprep(x, '\>)', ''), fin3, 'UniformOutput', false)
fin5 = str2double(fin4)

It gives fin4 as

'-0.037908413650000305494813801487908-0.0029424243719999854107527426094748'	'-0.037908413650000305494813801487908-0.38633213039999958482439978979528'	'-0.037908413650000305494813801487908'	'-0.075816827300000610989627602975816'	'-0.0029424243719999854107527426094748-0.38633213039999958482439978979528'	'-0.0029424243719999854107527426094748'	'-0.0058848487439999708215054852189496'	'-0.38633213039999958482439978979528'	'-0.77266426079999916964879957959056'	'1'

It gives fin5 as

NaN       NaN   -0.0379   -0.0758       NaN   -0.0029   -0.0059   -0.3863   -0.7727    1.0000

Is there any better way to get the coefficennt of x inside the exponetial ?

Thank you.

Answer 1

[David Goodmanson]

Hi Ishan,

Squaring y gives 16 terms involving the product of two exponential functions. Multilying exponentials means adding the two b coefficients in each product, so the task comes down to finding all possible sums of two b coefficients.

b = -[0.0 0.0029 0.0379 .3863]; 
cof = b+b'
% and if you want just the unique ones,
ucof = unique(cof(:))
ucof =
   -0.7726
   -0.4242
   -0.3892
   -0.3863
   -0.0758
   -0.0408
   -0.0379
   -0.0058
   -0.0029
         0

[Ishan Khatri]

Hi David,

Thnak you for such a lucid solution. How I can modify this code to fit cube and fourth power of y?

[David Goodmanson]

Hi Ishan,

here is one way. Start with a variation of the original process:

b = -[0.0 0.0029 0.0379 .3863]; 
bsum = b';           % create a column vector, one sum
bsum = bsum + b      % create a matrix of all pairs of sums
bsum = bsum(:);      % create a column vector, two sums

Now you just repeat the process to get column vectors of three sums, etc. and use unique at the end if desired.