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comparison doc/interpreter/sparse.txi @ 5681:233d98d95659

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[project @ 2006-03-16 17:48:55 by dbateman]
author dbateman
date Thu, 16 Mar 2006 17:48:56 +0000
parents f37b562ec93c
children 3d8d8ce93c2c
comparison
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5680:cc6a965ae4ca 5681:233d98d95659
743 The band density is defined as the number of non-zero values in the matrix 743 The band density is defined as the number of non-zero values in the matrix
744 divided by the number of non-zero values in the matrix. The banded matrix 744 divided by the number of non-zero values in the matrix. The banded matrix
745 solvers can be entirely disabled by using @dfn{spparms} to set @code{bandden} 745 solvers can be entirely disabled by using @dfn{spparms} to set @code{bandden}
746 to 1 (i.e. @code{spparms ("bandden", 1)}). 746 to 1 (i.e. @code{spparms ("bandden", 1)}).
747 747
748 All of the solvers above, expect the banded solvers, calculate an 748 The QR solver factorizes the problem with a Dulmage-Mendhelsohn, to
749 estimate of the condition number. This can be used to detect numerical 749 seperate the problem into blocks that can be treated as over-determined,
750 stability problems in the solution and force a minimum norm solution 750 multiple well determined blocks, and a final over-determined block. For
751 to be used. However, for narrow banded matrices, the cost of 751 matrices with blocks of strongly connectted nodes this is a big win as
752 calculating the condition number is significant, and can in fact exceed 752 LU decomposition can be used for many blocks. It also significantly
753 the cost of factoring the matrix. Therefore the condition number is 753 improves the chance of finding a solution to over-determined problems
754 not calculated for banded matrices, and therefore unless the factorization 754 rather than just returning a vector of @dfn{NaN}'s.
755 is exactly singular, these numerical instabilities won't be detected. 755
756 In cases where, this might be a problem the user is recommended to disable 756 All of the solvers above, can calculate an estimate of the condition
757 the banded solvers as above, at a significant cost in terms of speed. 757 number. This can be used to detect numerical stability problems in the
758 solution and force a minimum norm solution to be used. However, for
759 narrow banded, triangular or diagonal matrices, the cost of
760 calculating the condition number is significant, and can in fact
761 exceed the cost of factoring the matrix. Therefore the condition
762 number is not calculated in these case, and octave relies on simplier
763 techniques to detect sinular matrices or the underlying LAPACK code in
764 the case of banded matrices.
758 765
759 The user can force the type of the matrix with the @code{matrix_type} 766 The user can force the type of the matrix with the @code{matrix_type}
760 function. This overcomes the cost of discovering the type of the matrix. 767 function. This overcomes the cost of discovering the type of the matrix.
761 However, it should be noted incorrectly identifying the type of the matrix 768 However, it should be noted incorrectly identifying the type of the matrix
762 will lead to unpredictable results, and so @code{matrix_type} should be 769 will lead to unpredictable results, and so @code{matrix_type} should be