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1 | function Y = sqrt(X) |
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2 | % SQRT Square root. |
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3 | % (Quaternion overloading of standard Matlab function.) |
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4 | |
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5 | % Copyright © 2005, 2006 Stephen J. Sangwine and Nicolas Le Bihan. |
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6 | % See the file : Copyright.m for further details. |
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7 | |
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8 | error(nargchk(1, 1, nargin)), error(nargoutchk(0, 1, nargout)) |
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9 | |
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10 | if isreal(X) |
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11 | |
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12 | % X is a real quaternion, and we compute the square root of an |
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13 | % isomorphic complex number using the standard Matlab square root |
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14 | % function, then construct a quaternion with the same axis as the |
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15 | % original quaternion. |
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16 | |
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17 | Y = isoquaternion(sqrt(isocomplex(X)), X); |
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18 | else |
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19 | |
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20 | % X is a complex quaternion, and therefore we cannot use the method |
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21 | % above for real quaternions, because it is not possible to construct |
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22 | % an isomorphic complex number. Therefore we use polar form and halve |
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23 | % the argument. Note that the modulus and argument here are complex, |
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24 | % so the square root of the modulus is complex. |
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25 | |
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26 | Y = sqrt(abs(X)) .* exp(axis(X) .* angle(X) ./ 2); |
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27 | end; |
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