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****** |
i n p u t ******
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w.....work array of size | | |
(nroww,nrow) containing the interesting
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part of a banded matrix | | |
a , with the diagonals or bands of a
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stored in the rows of | | |
w , while columns of a correspond to
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columns of | | |
w . this is the storage mode used in linpack and
results in efficient innermost loops.
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explicitly, | | |
a has nbandl bands below the diagonal
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1 (main) diagonal
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nbandu bands above the diagonal
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and thus, with | | |
middle = nbandu + 1,
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a(i+j,j) | | |
is in w(i+middle,j) for i=-nbandu,...,nbandl
j=1,...,nrow .
for example, the interesting entries of a (1,2)-banded matrix
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of order | | |
9 would appear in the first 1+1+2 = 4 rows of w
as follows.
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all other entries of | | |
w not identified in this way with an en-
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try of |
a are never referenced .
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nroww.....row dimension of the work array | | |
w .
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must be | | |
[char46]ge. nbandl + 1 + nbandu .
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nbandl.....number of bands of | | |
a below the main diagonal
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nbandu.....number of bands of | | |
a above the main diagonal .
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****** |
o u t p u t ******
iflag.....integer indicating success( = 1) or failure ( = 2) .
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w.....contains the lu-factorization of |
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a into a unit lower triangu-
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lar matrix | | |
l and an upper triangular matrix u (both banded)
and stored in customary fashion over the corresponding entries
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of |
a . this makes it possible to solve any particular linear
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system |
a*x = b for x by a
call banslv ( w, nroww, nrow, nbandl, nbandu, b )
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with the solution x | | |
contained in b on return .
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if |
iflag = 2, then
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one of |
nrow-1, nbandl,nbandu failed to be nonnegative, or else
one of the potential pivots was found to be zero indicating
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that |
a does not have an lu-factorization. this implies that
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is singular in case it is totally positive .
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****** |
m e t h o d ******
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gauss elimination | | |
w i t h o u t pivoting is used. the routine is
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intended for use with matrices |
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a which do not require row inter-
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changes during factorization, especially for the | | |
t o t a l l y
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p o s i t i v e | | |
matrices which occur in spline calculations.
the routine should not be used for an arbitrary banded matrix.
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