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diff scripts/polynomial/residue.m @ 20200:f1d0f506ee78 stable

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doc: Update more docstrings to have one sentence summary as first line. Reviewed optimization, polynomial, signal script directories. * scripts/optimization/fminbnd.m, scripts/optimization/fminsearch.m, scripts/optimization/fminunc.m, scripts/optimization/fsolve.m, scripts/optimization/fzero.m, scripts/optimization/glpk.m, scripts/optimization/lsqnonneg.m, scripts/optimization/pqpnonneg.m, scripts/optimization/qp.m, scripts/optimization/sqp.m, scripts/polynomial/compan.m, scripts/polynomial/mkpp.m, scripts/polynomial/mpoles.m, scripts/polynomial/pchip.m, scripts/polynomial/poly.m, scripts/polynomial/polyaffine.m, scripts/polynomial/polyder.m, scripts/polynomial/polyeig.m, scripts/polynomial/polyfit.m, scripts/polynomial/polygcd.m, scripts/polynomial/polyint.m, scripts/polynomial/polyout.m, scripts/polynomial/polyval.m, scripts/polynomial/ppder.m, scripts/polynomial/ppint.m, scripts/polynomial/ppjumps.m, scripts/polynomial/ppval.m, scripts/polynomial/residue.m, scripts/polynomial/roots.m, scripts/polynomial/spline.m, scripts/polynomial/splinefit.m, scripts/polynomial/unmkpp.m, scripts/signal/arch_fit.m, scripts/signal/arch_rnd.m, scripts/signal/arma_rnd.m, scripts/signal/autoreg_matrix.m, scripts/signal/bartlett.m, scripts/signal/blackman.m, scripts/signal/detrend.m, scripts/signal/diffpara.m, scripts/signal/durbinlevinson.m, scripts/signal/fftconv.m, scripts/signal/fftfilt.m, scripts/signal/fftshift.m, scripts/signal/filter2.m, scripts/signal/freqz.m, scripts/signal/hamming.m, scripts/signal/hanning.m, scripts/signal/hurst.m, scripts/signal/ifftshift.m, scripts/signal/periodogram.m, scripts/signal/sinc.m, scripts/signal/sinetone.m, scripts/signal/sinewave.m, scripts/signal/spectral_adf.m, scripts/signal/spectral_xdf.m, scripts/signal/spencer.m, scripts/signal/stft.m, scripts/signal/synthesis.m, scripts/signal/unwrap.m, scripts/signal/yulewalker.m: Update more docstrings to have one sentence summary as first line.
author Rik <rik@octave.org>
date Mon, 04 May 2015 21:50:57 -0700
parents 9fc020886ae9
children 83792dd9bcc1
line wrap: on
line diff
--- a/scripts/polynomial/residue.m	Mon May 04 14:22:02 2015 -0700
+++ b/scripts/polynomial/residue.m	Mon May 04 21:50:57 2015 -0700
@@ -23,6 +23,8 @@
 ## @deftypefnx {Function File} {[@var{b}, @var{a}] =} residue (@var{r}, @var{p}, @var{k}, @var{e})
 ## The first calling form computes the partial fraction expansion for the
 ## quotient of the polynomials, @var{b} and @var{a}.
+##
+## The quotient is defined as
 ## @tex
 ## $$
 ## {B(s)\over A(s)} = \sum_{m=1}^M {r_m\over (s-p_m)^e_m}
@@ -33,18 +35,18 @@
 ##
 ## @example
 ## @group
-## B(s)    M       r(m)         N
-## ---- = SUM -------------  + SUM k(i)*s^(N-i)
-## A(s)   m=1 (s-p(m))^e(m)    i=1
+## B(s)    M       r(m)        N
+## ---- = SUM ------------- + SUM k(i)*s^(N-i)
+## A(s)   m=1 (s-p(m))^e(m)   i=1
 ## @end group
 ## @end example
 ##
 ## @end ifnottex
 ## @noindent
-## where @math{M} is the number of poles (the length of the @var{r},
-## @var{p}, and @var{e}), the @var{k} vector is a polynomial of order @math{N-1}
-## representing the direct contribution, and the @var{e} vector specifies
-## the multiplicity of the m-th residue's pole.
+## where @math{M} is the number of poles (the length of the @var{r}, @var{p},
+## and @var{e}), the @var{k} vector is a polynomial of order @math{N-1}
+## representing the direct contribution, and the @var{e} vector specifies the
+## multiplicity of the m-th residue's pole.
 ##
 ## For example,
 ##
@@ -79,11 +81,11 @@
 ##
 ## @end ifnottex
 ##
-## The second calling form performs the inverse operation and computes
-## the reconstituted quotient of polynomials, @var{b}(s)/@var{a}(s),
-## from the partial fraction expansion; represented by the residues,
-## poles, and a direct polynomial specified by @var{r}, @var{p} and
-## @var{k}, and the pole multiplicity @var{e}.
+## The second calling form performs the inverse operation and computes the
+## reconstituted quotient of polynomials, @var{b}(s)/@var{a}(s), from the
+## partial fraction expansion; represented by the residues, poles, and a direct
+## polynomial specified by @var{r}, @var{p} and @var{k}, and the pole
+## multiplicity @var{e}.
 ##
 ## If the multiplicity, @var{e}, is not explicitly specified the multiplicity is
 ## determined by the function @code{mpoles}.