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author Antonio Pino Robles <data.script93@gmail.com>
date Fri, 29 May 2015 09:48:36 +0200
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8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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1 function [d,a] = ascent_seq(A)
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2 %ASCENT_SEQ Ascent sequence for square (singular) matrix.
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3 % [d,a] = ASCENT_SEQ(A) returns symbolically computed
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4 % a(i) = dim(null(A^(i-1))) and the ascent sequence d = DIFF(a).
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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5 % A has a square root if in the ascent sequence no two terms are
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6 % the same odd integer.
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7 % This function is intended for singular matrices of small
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8 % dimension with exactly known entries.
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9 % It requires the Symbolic Math Toolbox.
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10
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11 if isempty(ver('symbolic'))
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12 error('The Symbolic Math Toolbox is required.')
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13 end
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14
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15 n = length(A);
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16 a = zeros(n,1);
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17 A = sym(A);
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18 X = sym(eye(n));
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19 for i = 2:n+1
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20 X = X*A;
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21 N = null(X);
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22 if isempty(N), break, end
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23 a(i) = rank(N);
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24 end
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25 d = diff(a);