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1 function retval = invhilb (n) |
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2 |
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3 # usage: invhilb (n) |
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4 # |
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5 # Return the inverse of a Hilbert matrix of order n. This is slow but |
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6 # exact. Compare with inv (hilb (n)). |
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7 # |
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8 # See also: hankel, vander, hadamard, hilb, toeplitz |
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9 |
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10 if (nargin != 1) |
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11 error ("usage: invhilb (n)"); |
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12 endif |
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13 |
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14 nmax = length (n); |
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15 if (nmax == 1) |
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16 retval = zeros (n); |
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17 for l = 1:n |
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18 for k = l:n |
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19 tmp = 1; |
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20 for i = 1:n |
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21 tmp = tmp * (i + k - 1); |
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22 endfor |
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23 for i = 1:n |
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24 if (i != k) |
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25 tmp = tmp * (l + i - 1); |
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26 endif |
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27 endfor |
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28 for i = 1:n |
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29 if (i != l) |
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30 tmp = tmp / (i - l); |
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31 endif |
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32 endfor |
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33 for i = 1:n |
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34 if (i != k) |
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35 tmp = tmp / (i - k); |
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36 endif |
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37 endfor |
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38 retval (k, l) = tmp; |
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39 retval (l, k) = tmp; |
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40 endfor |
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41 endfor |
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42 else |
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43 error ("hilb: expecting scalar argument, found something else"); |
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44 endif |
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45 |
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46 endfunction |
