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Create local repository for matrix toolboxes. Step #0 done.
author Antonio Pino Robles <data.script93@gmail.com>
date Wed, 06 May 2015 14:56:53 +0200
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8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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1 function C = circul(v)
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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2 %CIRCUL Circulant matrix.
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3 % C = CIRCUL(V) is the circulant matrix whose first row is V.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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4 % (A circulant matrix has the property that each row is obtained
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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5 % from the previous one by cyclically permuting the entries one step
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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6 % forward; it is a special Toeplitz matrix in which the diagonals
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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7 % `wrap round'.)
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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8 % Special case: if V is a scalar then C = CIRCUL(1:V).
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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9 % The eigensystem of C (N-by-N) is known explicitly. If t is an Nth
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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10 % root of unity, then the inner product of V with W = [1 t t^2 ... t^N]
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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11 % is an eigenvalue of C, and W(N:-1:1) is an eigenvector of C.
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13 % Reference:
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14 % P.J. Davis, Circulant Matrices, John Wiley, 1977.
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16 n = max(size(v));
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18 if n == 1
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19 n = v;
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20 v = 1:n;
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21 end
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23 v = v(:).'; % Make sure v is a row vector.
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8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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25 C = toeplitz( [ v(1) v(n:-1:2) ], v );