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54
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1 function [aa, bb, q, z] = qzhess (a, b) |
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29
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2 |
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72
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3 # Usage: [aa, bb, q, z] = qzhess (a, b) |
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4 # |
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54
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5 # Compute the qz decomposition of the matrix pencil (a - lambda b) |
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6 # |
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7 # result: (for Matlab compatibility): |
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8 # |
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9 # aa = q*a*z and bb = q*b*z, with q, z orthogonal, and |
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10 # v = matrix of generalized eigenvectors. |
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11 # |
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12 # This ought to be done in a compiled program |
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13 # |
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14 # Algorithm taken from Golub and Van Loan, Matrix Computations, 2nd ed. |
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15 |
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72
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16 # Written by A. S. Hodel (scotte@eng.auburn.edu) August 1993. |
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17 |
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54
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18 if (nargin != 2) |
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19 error ("usage: [aa, bb, q, z] = qzhess (a, b)"); |
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20 endif |
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21 |
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22 [na, ma] = size (a); |
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23 [nb, mb] = size (b); |
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24 if (na != ma || na != nb || nb != mb) |
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25 error ("qzhess: incompatible dimensions"); |
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26 endif |
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27 |
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28 # Reduce to hessenberg-triangular form. |
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29
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29 |
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54
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30 [q, bb] = qr (b); |
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31 aa = q' * a; |
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32 q = q'; |
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33 z = eye (na); |
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34 for j = 1:(na-2) |
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35 for i = na:-1:(j+2) |
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36 |
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37 # disp (["zero out aa(", num2str(i), ",", num2str(j), ")"]) |
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38 |
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39 rot = givens (aa (i-1, j), aa (i, j)); |
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40 aa ((i-1):i, :) = rot *aa ((i-1):i, :); |
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41 bb ((i-1):i, :) = rot *bb ((i-1):i, :); |
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42 q ((i-1):i, :) = rot *q ((i-1):i, :); |
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43 |
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44 # disp (["now zero out bb(", num2str(i), ",", num2str(i-1), ")"]) |
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45 |
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46 rot = givens (bb (i, i), bb (i, i-1))'; |
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47 bb (:, (i-1):i) = bb (:, (i-1):i) * rot'; |
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48 aa (:, (i-1):i) = aa (:, (i-1):i) * rot'; |
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49 z (:, (i-1):i) = z (:, (i-1):i) * rot'; |
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50 |
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51 endfor |
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29
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52 endfor |
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53 |
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54
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54 bb (2, 1) = 0.0; |
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55 for i = 3:na |
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56 bb (i, 1:(i-1)) = zeros (1, i-1); |
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57 aa (i, 1:(i-2)) = zeros (1, i-2); |
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58 endfor |
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59 |
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29
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60 endfunction |
