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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 |
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4 # polynomial 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 |
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9 [nr, nc] = size(v); |
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10 if !((nr == 1 && nc > 1) || (nc == 1 && nr > 1)) |
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11 usage ("roots (v), where v is a nonzero vector"); |
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12 endif |
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13 |
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14 n = nr + nc - 1; |
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15 v = reshape (v, 1, n); |
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16 |
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17 # If v = [ 0 ... 0 v(k+1) ... v(k+l) 0 ... 0 ], we can remove the |
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18 # leading k zeros and n - k - l roots of the polynomial are zero. |
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19 |
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20 f = find (v); |
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21 m = max (size (f)); |
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22 if (m > 0) |
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23 v = v(f(1):f(m)); |
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24 l = max (size (v)); |
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25 if (l > 1) |
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26 A = diag (ones (1, l-2), -1); |
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27 A(1,:) = -v(2:l) ./ v(1); |
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28 r = eig (A); |
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29 if (f(m) < n) |
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30 r = [r; zeros (n - f(m), 1)]; |
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31 endif |
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32 else |
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33 r = zeros (n - f(m), 1); |
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34 endif |
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35 else |
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36 usage ("roots (v), where v is a nonzero vector"); |
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37 endif |
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38 |
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39 endfunction |
