Mercurial > matrix-functions
comparison toolbox/comp.m @ 2:c124219d7bfa draft
Re-add the 1995 toolbox after noticing the statement in the ~higham/mctoolbox/ webpage.
| author | Antonio Pino Robles <data.script93@gmail.com> |
|---|---|
| date | Thu, 07 May 2015 18:36:24 +0200 |
| parents | 8f23314345f4 |
| children |
comparison
equal
deleted
inserted
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| 1:e471a92d17be | 2:c124219d7bfa |
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| 1 function C = comp(A, k) | |
| 2 %COMP Comparison matrices. | |
| 3 % COMP(A) is DIAG(B) - TRIL(B,-1) - TRIU(B,1), where B = ABS(A). | |
| 4 % COMP(A, 1) is A with each diagonal element replaced by its | |
| 5 % absolute value, and each off-diagonal element replaced by minus | |
| 6 % the absolute value of the largest element in absolute value in | |
| 7 % its row. However, if A is triangular COMP(A, 1) is too. | |
| 8 % COMP(A, 0) is the same as COMP(A). | |
| 9 % COMP(A) is often denoted by M(A) in the literature. | |
| 10 | |
| 11 % Reference (e.g.): | |
| 12 % N.J. Higham, A survey of condition number estimation for | |
| 13 % triangular matrices, SIAM Review, 29 (1987), pp. 575-596. | |
| 14 | |
| 15 if nargin == 1, k = 0; end | |
| 16 [m, n] = size(A); | |
| 17 p = min(m, n); | |
| 18 | |
| 19 if k == 0 | |
| 20 | |
| 21 % This code uses less temporary storage than the `high level' definition above. | |
| 22 C = -abs(A); | |
| 23 for j=1:p | |
| 24 C(j,j) = abs(A(j,j)); | |
| 25 end | |
| 26 | |
| 27 elseif k == 1 | |
| 28 | |
| 29 C = A'; | |
| 30 for j=1:p | |
| 31 C(k,k) = 0; | |
| 32 end | |
| 33 mx = max(abs(C)); | |
| 34 C = -mx'*ones(1,n); | |
| 35 for j=1:p | |
| 36 C(j,j) = abs(A(j,j)); | |
| 37 end | |
| 38 if all( A == tril(A) ), C = tril(C); end | |
| 39 if all( A == triu(A) ), C = triu(C); end | |
| 40 | |
| 41 end |