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comparison scripts/polynomial/residue.m @ 8517:81d6ab3ac93c

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Allow documentation tobe built for other formats than tex and info
author sh@sh-laptop
date Wed, 14 Jan 2009 20:44:25 -0500
parents 836618fee9d6
children eb63fbe60fab
comparison
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8516:e2a179415bac 8517:81d6ab3ac93c
29 ## {B(s)\over A(s)} = \sum_{m=1}^M {r_m\over (s-p_m)^e_m} 29 ## {B(s)\over A(s)} = \sum_{m=1}^M {r_m\over (s-p_m)^e_m}
30 ## + \sum_{i=1}^N k_i s^{N-i}. 30 ## + \sum_{i=1}^N k_i s^{N-i}.
31 ## $$ 31 ## $$
32 ## @end tex 32 ## @end tex
33 ## @end iftex 33 ## @end iftex
34 ## @ifinfo 34 ## @ifnottex
35 ## 35 ##
36 ## @example 36 ## @example
37 ## B(s) M r(m) N 37 ## B(s) M r(m) N
38 ## ---- = SUM ------------- + SUM k(i)*s^(N-i) 38 ## ---- = SUM ------------- + SUM k(i)*s^(N-i)
39 ## A(s) m=1 (s-p(m))^e(m) i=1 39 ## A(s) m=1 (s-p(m))^e(m) i=1
40 ## @end example 40 ## @end example
41 ## @end ifinfo 41 ## @end ifnottex
42 ## 42 ##
43 ## @noindent 43 ## @noindent
44 ## where @math{M} is the number of poles (the length of the @var{r}, 44 ## where @math{M} is the number of poles (the length of the @var{r},
45 ## @var{p}, and @var{e}), the @var{k} vector is a polynomial of order @math{N-1} 45 ## @var{p}, and @var{e}), the @var{k} vector is a polynomial of order @math{N-1}
46 ## representing the direct contribution, and the @var{e} vector specifies 46 ## representing the direct contribution, and the @var{e} vector specifies
67 ## $$ 67 ## $$
68 ## {s^2+s+1\over s^3-5s^2+8s-4} = {-2\over s-2} + {7\over (s-2)^2} + {3\over s-1} 68 ## {s^2+s+1\over s^3-5s^2+8s-4} = {-2\over s-2} + {7\over (s-2)^2} + {3\over s-1}
69 ## $$ 69 ## $$
70 ## @end tex 70 ## @end tex
71 ## @end iftex 71 ## @end iftex
72 ## @ifinfo 72 ## @ifnottex
73 ## 73 ##
74 ## @example 74 ## @example
75 ## s^2 + s + 1 -2 7 3 75 ## s^2 + s + 1 -2 7 3
76 ## ------------------- = ----- + ------- + ----- 76 ## ------------------- = ----- + ------- + -----
77 ## s^3 - 5s^2 + 8s - 4 (s-2) (s-2)^2 (s-1) 77 ## s^3 - 5s^2 + 8s - 4 (s-2) (s-2)^2 (s-1)
78 ## @end example 78 ## @end example
79 ## 79 ##
80 ## @end ifinfo 80 ## @end ifnottex
81 ## 81 ##
82 ## @deftypefnx {Function File} {[@var{b}, @var{a}] =} residue (@var{r}, @var{p}, @var{k}) 82 ## @deftypefnx {Function File} {[@var{b}, @var{a}] =} residue (@var{r}, @var{p}, @var{k})
83 ## @deftypefnx {Function File} {[@var{b}, @var{a}] =} residue (@var{r}, @var{p}, @var{k}, @var{e}) 83 ## @deftypefnx {Function File} {[@var{b}, @var{a}] =} residue (@var{r}, @var{p}, @var{k}, @var{e})
84 ## Compute the reconstituted quotient of polynomials, 84 ## Compute the reconstituted quotient of polynomials,
85 ## @var{b}(s)/@var{a}(s), from the partial fraction expansion; 85 ## @var{b}(s)/@var{a}(s), from the partial fraction expansion;
126 ## $$ 126 ## $$
127 ## {-2\over s-2} + {7\over (s-2)^2} + {3\over s-1} + s = {s^4-5s^3+9s^2-3s+1\over s^3-5s^2+8s-4} 127 ## {-2\over s-2} + {7\over (s-2)^2} + {3\over s-1} + s = {s^4-5s^3+9s^2-3s+1\over s^3-5s^2+8s-4}
128 ## $$ 128 ## $$
129 ## @end tex 129 ## @end tex
130 ## @end iftex 130 ## @end iftex
131 ## @ifinfo 131 ## @ifnottex
132 ## 132 ##
133 ## @example 133 ## @example
134 ## -2 7 3 s^4 - 5s^3 + 9s^2 - 3s + 1 134 ## -2 7 3 s^4 - 5s^3 + 9s^2 - 3s + 1
135 ## ----- + ------- + ----- + s = -------------------------- 135 ## ----- + ------- + ----- + s = --------------------------
136 ## (s-2) (s-2)^2 (s-1) s^3 - 5s^2 + 8s - 4 136 ## (s-2) (s-2)^2 (s-1) s^3 - 5s^2 + 8s - 4
137 ## @end example 137 ## @end example
138 ## @end ifinfo 138 ## @end ifnottex
139 ## @seealso{poly, roots, conv, deconv, mpoles, polyval, polyderiv, polyinteg} 139 ## @seealso{poly, roots, conv, deconv, mpoles, polyval, polyderiv, polyinteg}
140 ## @end deftypefn 140 ## @end deftypefn
141 141
142 ## Author: Tony Richardson <arichard@stark.cc.oh.us> 142 ## Author: Tony Richardson <arichard@stark.cc.oh.us>
143 ## Author: Ben Abbott <bpabbott@mac.com> 143 ## Author: Ben Abbott <bpabbott@mac.com>