SUBROUTINE CNBFA (ABE, LDA, N, ML, MU, IPVT, INFO)
C***BEGIN PROLOGUE CNBFA
C***PURPOSE Factor a band matrix by elimination.
C***TYPE COMPLEX (SNBFA-S, DNBFA-D, CNBFA-C)
C***KEYWORDS BANDED, LINEAR EQUATIONS, MATRIX FACTORIZATION,
C***AUTHOR Voorhees, E. A., (LANL)
C CNBFA factors a complex band matrix by elimination.
C CNBFA is usually called by CNBCO, but it can be called
C directly with a saving in time if RCOND is not needed.
C On Entry
C ABE COMPLEX(LDA, NC)
C contains the matrix in band storage. The rows
C of the original matrix are stored in the rows
C of ABE and the diagonals of the original matrix
C are stored in columns 1 through ML+MU+1 of ABE.
C NC must be .GE. 2*ML+MU+1 .
C See the comments below for details.
C LDA INTEGER
C the leading dimension of the array ABE.
C LDA must be .GE. N .
C N INTEGER
C the order of the original matrix.
C ML INTEGER
C number of diagonals below the main diagonal.
C 0 .LE. ML .LT. N .
C MU INTEGER
C number of diagonals above the main diagonal.
C 0 .LE. MU .LT. N .
C More efficient if ML .LE. MU .
C On Return
C ABE an upper triangular matrix in band storage
C and the multipliers which were used to obtain it.
C the factorization can be written A = L*U where
C L is a product of permutation and unit lower
C triangular matrices and U is upper triangular.
C IPVT INTEGER(N)
C an integer vector of pivot indices.
C INFO INTEGER
C =0 normal value
C =K if U(K,K) .EQ. 0.0 . This is not an error
C condition for this subroutine, but it does
C indicate that CNBSL will divide by zero if
C called. Use RCOND in CNBCO for a reliable
C indication of singularity.
C Band Storage
C If A is a band matrix, the following program segment
C will set up the input.
C ML = (band width below the diagonal)
C MU = (band width above the diagonal)
C DO 20 I = 1, N
C J1 = MAX(1, I-ML)
C J2 = MIN(N, I+MU)
C DO 10 J = J1, J2
C K = J - I + ML + 1
C ABE(I,K) = A(I,J)
C 10 CONTINUE
C 20 CONTINUE
C This uses columns 1 through ML+MU+1 of ABE .
C Furthermore, ML additional columns are needed in
C ABE starting with column ML+MU+2 for elements
C generated during the triangularization. The total
C number of columns needed in ABE is 2*ML+MU+1 .
C Example: If the original matrix is
C 11 12 13 0 0 0
C 21 22 23 24 0 0
C 0 32 33 34 35 0
C 0 0 43 44 45 46
C 0 0 0 54 55 56
C 0 0 0 0 65 66
C then N = 6, ML = 1, MU = 2, LDA .GE. 5 and ABE should contain
C * 11 12 13 + , * = not used
C 21 22 23 24 + , + = used for pivoting
C 32 33 34 35 +
C 43 44 45 46 +
C 54 55 56 * +
C 65 66 * * +
C***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W.
C Stewart, LINPACK Users' Guide, SIAM, 1979.
C***ROUTINES CALLED CAXPY, CSCAL, CSWAP, ICAMAX
C***REVISION HISTORY (YYMMDD)
C 800730 DATE WRITTEN
C 890531 Changed all specific intrinsics to generic. (WRB)
C 890831 Modified array declarations. (WRB)
C 890831 REVISION DATE from Version 3.2
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 920501 Reformatted the REFERENCES section. (WRB)
C***END PROLOGUE CNBFA