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annotate toolbox/compan.m @ 2:c124219d7bfa draft

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Re-add the 1995 toolbox after noticing the statement in the ~higham/mctoolbox/ webpage.
author Antonio Pino Robles <data.script93@gmail.com>
date Thu, 07 May 2015 18:36:24 +0200
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1 function A = compan(p)
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2 %COMPAN Companion matrix.
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3 % COMPAN(P) is a companion matrix. There are three cases.
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4 % If P is a scalar then COMPAN(P) is the P-by-P matrix COMPAN(1:P+1).
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5 % If P is an (n+1)-vector, COMPAN(P) is the n-by-n companion matrix
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6 % whose first row is -P(2:n+1)/P(1).
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7 % If P is a square matrix, COMPAN(P) is the companion matrix
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8 % of the characteristic polynomial of P, computed as
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9 % COMPAN(POLY(P)).
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10
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11 % References:
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12 % J.H. Wilkinson, The Algebraic Eigenvalue Problem,
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13 % Oxford University Press, 1965, p. 12.
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14 % G.H. Golub and C.F. Van Loan, Matrix Computations, second edition,
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15 % Johns Hopkins University Press, Baltimore, Maryland, 1989,
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16 % sec 7.4.6.
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17 % C. Kenney and A.J. Laub, Controllability and stability radii for
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18 % companion form systems, Math. Control Signals Systems, 1 (1988),
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19 % pp. 239-256. (Gives explicit formulas for the singular values of
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20 % COMPAN(P).)
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21
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22 [n,m] = size(p);
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23
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24 if n == m & n > 1
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25 % Matrix argument.
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26 A = compan(poly(p));
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27 return
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28 end
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29
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30 n = max(n,m);
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31 % Handle scalar p.
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32 if n == 1
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33 n = p+1;
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34 p = 1:n;
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35 end
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36
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37 p = p(:)'; % Ensure p is a row vector.
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38
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39 % Construct matrix of order n-1.
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40 if n == 2
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41 A = 1;
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42 else
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43 A = diag(ones(1,n-2),-1);
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44 A(1,:) = -p(2:n)/p(1);
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45 end