Partial fraction decomposition v1

Function used for partial fraction decomposition.

Description

Some improvements have been made to the early version.
% (1) For the fraction bellow：
% s+2
% F(s) = ----------------
% s(s+1)^2(s+3)
% Input：
% >> num_input = [1 2];
% >> den_input = [1 0;1 1;1 1;1 3];
% >> frac_decomp(num_input,den_input)
%
% Result is：
% roots and counts:
% [ 0, 1]
% [ -3, 1]
% [ -1, 2]
%
% symbolic Expression:
%
% 1. s + 2.
% --------------------
% 2
% s (s + 3.) (s + 1.)
% Final Expression:
%
% 0.667 0.0833 0.500 0.750
% ----- + ------ - --------- - ------
% s s + 3. 2 s + 1.
% (s + 1.)
%
% (2) For the following fraction：
% 1
% F(s) = ------------------
% (s+1)^2(s+2s+2)
%
% Input：
% >> num_input = [1];
% >> den_input = [0 1 1;0 1 1;1 2 2];
% >> frac_decomp(num_input,den_input)
%
% Results is:
% roots and counts:
% [ -1+i, 1]
% [ -1-i, 1]
% [ -1, 2]
%
% symbolic Expression:
%
% 1.
% -----------------------------------------
% 2
% (s + 1. - 1. I) (s + 1. + 1. I) (s + 1.)
% Final Expression:
%
% 0. - 0.500 I 0. + 0.500 I 1.00 - 0. I
% - ------------- - ------------- + -----------
% s + 1. - 1. I s + 1. + 1. I 2
% (s + 1.)
%
% (3) For the following fraction:
% -4 s + 8
% ---------------
% 2 s^2 + 6 s + 8
%
% Input:
% >> b = [-4 8];
% >> a = [2 6 8];
% >> frac_decomp(b,a)
%
% Result:
% roots and count:
% [ -3/2+1/2*i*7^(1/2), 1]
% [ -3/2-1/2*i*7^(1/2), 1]
%
% symbolic Expression:
%
% -2. s + 4.
% ---------------------------------------
% (s + 1.50 - 1.32 I) (s + 1.50 + 1.32 I)
% Final Expression:
%
% 1.00 + 2.65 I 1.00 - 2.65 I
% - ----------------- - -----------------
% s + 1.50 - 1.32 I s + 1.50 + 1.32 I

• MATLAB release: MATLAB 7.1.0 (R14SP3)

[xianfa zeng]

Well, I didn't take into account the case that the fraction is nonproper. But you can do it by yourself.