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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.
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1 function [R, P, I] = cholp(A, piv)
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2 %CHOLP Cholesky factorization with pivoting of a positive semidefinite matrix.
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3 % [R, P] = CHOLP(A) returns an upper triangular matrix R and a
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4 % permutation matrix P such that R'*R = P'*A*P. Only the upper
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5 % triangular part of A is used. If A is not positive semidefinite,
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6 % an error message is printed.
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7 %
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8 % [R, P, I] = CHOLP(A) never produces an error message.
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9 % If A is positive semidefinite then I = 0 and R is the Cholesky factor.
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10 % If A is not positive semidefinite then I is positive and
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11 % R is (I-1)-by-N with P'*A*P - R'*R zero in columns 1:I-1 and
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12 % rows 1:I-1.
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13 % [R, I] = CHOLP(A, 0) forces P = EYE(SIZE(A)), and therefore behaves
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14 % like [R, I] = CHOL(A).
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15
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16 % This routine is based on the LINPACK routine CCHDC. It works
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17 % for both real and complex matrices.
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18 %
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19 % Reference:
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20 % N. J. Higham, Accuracy and Stability of Numerical Algorithms,
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21 % Second edition, Society for Industrial and Applied Mathematics,
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22 % Philadelphia, PA, 2002; sec. 10.3.
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23
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24 if nargin == 1, piv = 1; end
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25
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26 n = length(A);
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27 pp = 1:n;
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28 I = 0;
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29
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30 for k = 1:n
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31
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32 if piv
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33 d = diag(A);
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34 [big, m] = max( d(k:n) );
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35 m = m+k-1;
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36 else
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37 big = A(k,k); m = k;
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38 end
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39 if big < 0, I = k; break, end
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40
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41 % Symmetric row/column permutations.
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42 if m ~= k
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43 A(:, [k m]) = A(:, [m k]);
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44 A([k m], :) = A([m k], :);
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45 pp( [k m] ) = pp( [m k] );
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46 end
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47
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48 if big == 0
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49 if norm(A(k+1:n,k)) ~= 0
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50 I = k; break
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51 else
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52 continue
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53 end
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54 end
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55
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56 A(k,k) = sqrt( A(k,k) );
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57 if k == n, break, end
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58 A(k, k+1:n) = A(k, k+1:n) / A(k,k);
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59
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60 % For simplicity update the whole of the remaining submatrix (rather
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61 % than just the upper triangle).
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62
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63 j = k+1:n;
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64 A(j,j) = A(j,j) - A(k,j)'*A(k,j);
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65
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66 end
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67
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68 R = triu(A);
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69 if I > 0
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70 if nargout < 3, error('Matrix must be positive semidefinite.'), end
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71 R = R(1:I-1,:);
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72 end
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73
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74 if piv == 0
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75 P = I;
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76 else
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77 P = eye(n); P = P(:,pp);
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78 end