Mercurial > hg > octave-nkf
diff scripts/polynomial/residue.m @ 3426:f8dde1807dee
[project @ 2000-01-13 08:40:00 by jwe]
author | jwe |
---|---|
date | Thu, 13 Jan 2000 08:40:53 +0000 |
parents | a4cd1e9d9962 |
children | 434790acb067 |
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--- a/scripts/polynomial/residue.m +++ b/scripts/polynomial/residue.m @@ -23,13 +23,13 @@ ## residue calculates the partial fraction expansion corresponding to the ## ratio of the two polynomials. ## @cindex partial fraction expansion -## +## ## The function @code{residue} returns @var{r}, @var{p}, @var{k}, and ## @var{e}, where the vector @var{r} contains the residue terms, @var{p} ## contains the pole values, @var{k} contains the coefficients of a direct ## polynomial term (if it exists) and @var{e} is a vector containing the ## powers of the denominators in the partial fraction terms. -## +## ## Assuming @var{b} and @var{a} represent polynomials ## @iftex ## @tex @@ -49,19 +49,19 @@ ## @end tex ## @end iftex ## @ifinfo -## +## ## @example ## P(s) M r(m) N ## ---- = SUM ------------- + SUM k(i)*s^(N-i) ## Q(s) m=1 (s-p(m))^e(m) i=1 ## @end example ## @end ifinfo -## +## ## @noindent ## where @var{M} is the number of poles (the length of the @var{r}, ## @var{p}, and @var{e} vectors) and @var{N} is the length of the @var{k} ## vector. -## +## ## The argument @var{tol} is optional, and if not specified, a default ## value of 0.001 is assumed. The tolerance value is used to determine ## whether poles with small imaginary components are declared real. It is @@ -69,7 +69,7 @@ ## imaginary part of a pole to the real part is less than @var{tol}, the ## imaginary part is discarded. If two poles are farther apart than ## @var{tol} they are distinct. For example, -## +## ## @example ## @group ## b = [1, 1, 1]; @@ -81,7 +81,7 @@ ## @result{} e = [1, 2, 1] ## @end group ## @end example -## +## ## @noindent ## which implies the following partial fraction expansion ## @iftex @@ -92,7 +92,7 @@ ## @end tex ## @end iftex ## @ifinfo -## +## ## @example ## s^2 + s + 1 -2 7 3 ## ------------------- = ----- + ------- + -----