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annotate mftoolbox/sqrtm_triang_min_norm.m @ 0:8f23314345f4 draft

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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 R = sqrtm_triang_min_norm(T)
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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2 %SQRTM_TRIANG_MIN_NORM Estimated min norm square root of triangular matrix.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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3 % R = SQRTM_TRIANG_MIN_NORM(T) computes a primary square root of the
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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4 % upper triangular matrix T and attempts to minimize its 1-norm.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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6 if ~isequal(T,triu(T)), error('T must be upper triangular'), end
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7
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8 n = length(T);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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9 rp = zeros(n,1);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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10 rm = zeros(n,1);
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11
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12 R = zeros(n);
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13 for j=1:n
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14 rp(j) = sqrt(T(j,j));
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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15 rm(j) = -sqrt(T(j,j));
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16 for i=j-1:-1:1
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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17 rp(i) = (T(i,j) - R(i,i+1:j-1)*rp(i+1:j-1))/(R(i,i) + rp(j));
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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18 rm(i) = (T(i,j) - R(i,i+1:j-1)*rm(i+1:j-1))/(R(i,i) + rm(j));
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19 end
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20 if norm(rp(1:j),1) <= norm(rm(1:j),1)
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21 R(1:j,j) = rp(1:j);
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22 else
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23 R(1:j,j) = rm(1:j);
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24 end
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25 end