roots求得多项式的所有复根

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1. function r = roots(c)
   
2. %roots(p)可求得多项式p的所有复根.
   
3. %例   x^3+2x^2-3=0
   
4. %   求解
   
5. %      roots([1 2 0 -3])
   
6. %
   
7. %ROOTS  Find polynomial roots.
   
8. %   ROOTS(C) computes the roots of the polynomial whose coefficients
   
9. %   are the elements of the vector C. If C has N+1 components,
   
10. %   the polynomial is C(1)*X^N + ... + C(N)*X + C(N+1).
    
11. %
    
12. %   See also POLY, RESIDUE, FZERO.
    
13. 
    
14. %   J.N. Little 3-17-86
    
15. %   Copyright (c) 1984-98 by The MathWorks, Inc.
    
16. %   $Revision: 5.6 $  $Date: 1997/11/21 23:41:05 $
    
17. 
    
18. % ROOTS finds the eigenvalues of the associated companion matrix.
    
19. 
    
20. if size(c,1)>1 & size(c,2)>1
    
21.     error('Must be a vector.')
    
22. end
    
23. c = c(:).';
    
24. n = size(c,2);
    
25. r = zeros(0,1);
    
26. 
    
27. inz = find(c);
    
28. if isempty(inz),
    
29.     % All elements are zero
    
30.     return
    
31. end
    
32. 
    
33. % Strip leading zeros and throw away.  
    
34. % Strip trailing zeros, but remember them as roots at zero.
    
35. nnz = length(inz);
    
36. c = c(inz(1):inz(nnz));
    
37. r = zeros(n-inz(nnz),1);
    
38. 
    
39. % Polynomial roots via a companion matrix
    
40. n = length(c);
    
41. if n > 1
    
42.     a = diag(ones(1,n-2),-1);
    
43.     a(1,:) = -c(2:n) ./ c(1);
    
44.     r = [r;eig(a)];
    
45. end
    

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