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1 function r = roots(v) |
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2 # |
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3 # For a vector v with n components, return the roots of the polynomial |
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4 # v(1)*z^(n-1) + ... + v(n-1) * z + v(n). |
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5 |
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6 # written by KH (Kurt.Hornik@neuro.tuwien.ac.at) on Dec 24, 1993 |
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7 # copyright Dept of Probability Theory and Statistics TU Wien |
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8 # modified by KH on Jan 10, 1994 |
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9 |
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10 [nr, nc] = size(v); |
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11 if !((nr == 1 && nc > 1) || (nc == 1 && nr > 1)) |
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12 error("usage: roots(v), where v is a nonzero vector"); |
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13 endif |
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14 n = nr + nc - 1; |
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15 v = reshape(v,1,n); |
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16 # If v = [ 0 ... 0 v(k+1) ... v(k+l) 0 ... 0 ], we can remove the |
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17 # leading k zeros and n-k-l roots of the polynomial are zero. |
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18 f = find(v); |
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19 m = max(size(f)); |
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20 if (m > 0) |
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21 v = v(f(1):f(m)); |
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22 l = max(size(v)); |
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23 if (l > 1) |
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24 A = diag(ones(1, l-2), -1); |
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25 A(1,:) = -v(2:l) ./ v(1); |
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26 r = eig(A); |
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27 if (f(m) < n) |
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28 r = [r; zeros(n-f(m), 1)]; |
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29 endif |
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30 else |
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31 r = zeros(n-f(m), 1); |
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32 endif |
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33 else |
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34 error("usage: roots(v), where v is a nonzero vector"); |
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35 endif |
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36 |
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37 endfunction |
