SGBFA - SGBFA factors a real band matrix by elimination.
SGBFA is usually called by SBGCO, but it can be called directly with a
saving in time if RCOND is not needed.
ABD REAL(LDA, N)
contains the matrix in band storage. The columns
of the matrix are stored in the columns of ABD and
the diagonals of the matrix are stored in rows
ML+1 through 2*ML+MU+1 of ABD .
See the comments below for details.
the leading dimension of the array ABD .
LDA must be .GE. 2*ML + MU + 1 .
the order of the original matrix.
number of diagonals below the main diagonal.
0 .LE. ML .LT. N .
number of diagonals above the main diagonal.
0 .LE. MU .LT. N .
More efficient if ML .LE. MU . On Return
ABD an upper triangular matrix in band storage and
the multipliers which were used to obtain it.
The factorization can be written A = L*U , where
L is a product of permutation and unit lower
triangular matrices and U is upper triangular.
an integer vector of pivot indices.
= 0 normal value.
= K if U(K,K) .EQ. 0.0 . This is not an error
condition for this subroutine, but it does
indicate that SGBSL will divide by zero if
called. Use RCOND in SBGCO for a reliable
indication of singularity. Band Storage
If A is a band matrix, the following program segment
will set up the input.
ML = (band width below the diagonal)
MU = (band width above the diagonal)
M = ML + MU + 1
DO 20 J = 1, N
I1 = MAX0(1, J-MU)
I2 = MIN0(N, J+ML)
DO 10 I = I1, I2
K = I - J + M
ABD(K,J) = A(I,J)
This uses rows ML+1 through 2*ML+MU+1 of ABD .
In addition, the first ML rows in ABD are used for
elements generated during the triangularization.
The total number of rows needed in ABD is 2*ML+MU+1 .
The ML+MU by ML+MU upper left triangle and the
ML by ML lower right triangle are not referenced. LINPACK. This
version dated 08/14/78 . Cleve Moler, University of New Mexico, Argonne
National Lab. Subroutines and Functions BLAS SAXPY,SSCAL,ISAMAX Fortran
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