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factors(8) Scilab Function factors(8)
NAME
factors - numeric real factorization
CALLING SEQUENCE
[lnum,g]=factors(pol [,'flag'])
[lnum,lden,g]=factors(rat [,'flag'])
rat=factors(rat,'flag')
PARAMETERS
pol : real polynomial
rat : real rational polynomial (rat=pol1/pol2)
lnum : list of polynomials (of degrees 1 or 2)
lden : list of polynomials (of degrees 1 or 2)
g : real number
flag : character string 'c' or 'd'
DESCRIPTION
returns the factors of polynomial pol in the list lnum and the "gain" g.
One has pol= g times product of entries of the list lnum (if flag is not
given). If flag='c' is given, then one has |pol(i omega)| =
|g*prod(lnum_j(i omega)|. If flag='d' is given, then one has |pol(exp(i
omega))| = |g*prod(lnum_i(exp(i omega))|. If argument of factors is a 1x1
rational rat=pol1/pol2, the factors of the numerator pol1 and the denomina-
tor pol2 are returned in the lists lnum and lden respectively.
The "gain" is returned as g,i.e. one has: rat= g times (product entries in
lnum) / (product entries in lden).
If flag is 'c' (resp. 'd'), the roots of pol are refected wrt the imaginary
axis (resp. the unit circle), i.e. the factors in lnum are stable polynomi-
als.
Same thing if factors is invoked with a rational arguments: the entries in
lnum and lden are stable polynomials if flag is given. R2=factors(R1,'c')
or R2=factors(R1,'d') with R1 a rational function or SISO syslin list then
the output R2 is a transfer with stable numerator and denominator and with
same magnitude as R1 along the imaginary axis ('c') or unit circle ('d').
EXAMPLE
n=poly([0.2,2,5],'z');
d=poly([0.1,0.3,7],'z');
R=syslin('d',n,d);
R1=factors(R,'d')
roots(R1('num'))
roots(R1('den'))
w=exp(2*%i*%pi*[0:0.1:1]);
norm(abs(horner(R1,w))-abs(horner(R,w)))
SEE ALSO
simp
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