CNBFA(3)

SYNOPSIS
SUBROUTINE CNBFA (ABE, LDA, N, ML, MU, IPVT, INFO)

NAME
cnbfa - Factor a band matrix by elimination.

LIBRARY
SLATEC

CATEGORY
D2C2

TYPE
COMPLEX (SNBFA-S, DNBFA-D, CNBFA-C)

KEYWORDS
BANDED, LINEAR EQUATIONS, MATRIX FACTORIZATION, NONSYMMETRIC

AUTHOR
Voorhees, E. A., (LANL)

DESCRIPTION
CNBFA factors a complex band matrix by elimination. CNBFA is usually called by CNBCO, but it can be called directly with a saving in time if RCOND is not needed. On Entry ABE COMPLEX(LDA, NC) contains the matrix in band storage. The rows of the original matrix are stored in the rows of ABE and the diagonals of the original matrix are stored in columns 1 through ML+MU+1 of ABE. NC must be .GE. 2*ML+MU+1 . See the comments below for details. LDA INTEGER the leading dimension of the array ABE. LDA must be .GE. N . N INTEGER the order of the original matrix. ML INTEGER number of diagonals below the main diagonal. 0 .LE. ML .LT. N . MU INTEGER number of diagonals above the main diagonal. 0 .LE. MU .LT. N . More efficient if ML .LE. MU . On Return ABE 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. IPVT INTEGER(N) an integer vector of pivot indices. INFO INTEGER =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 CNBSL will divide by zero if called. Use RCOND in CNBCO 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) DO 20 I = 1, N J1 = MAX(1, I-ML) J2 = MIN(N, I+MU) DO 10 J = J1, J2 K = J - I + ML + 1 ABE(I,K) = A(I,J) 10 CONTINUE 20 CONTINUE This uses columns 1 through ML+MU+1 of ABE . Furthermore, ML additional columns are needed in ABE starting with column ML+MU+2 for elements generated during the triangularization. The total number of columns needed in ABE is 2*ML+MU+1 . Example: If the original matrix is 11 12 13 0 0 0 21 22 23 24 0 0 0 32 33 34 35 0 0 0 43 44 45 46 0 0 0 54 55 56 0 0 0 0 65 66 then N = 6, ML = 1, MU = 2, LDA .GE. 5 and ABE should contain * 11 12 13 + , * = not used 21 22 23 24 + , + = used for pivoting 32 33 34 35 + 43 44 45 46 + 54 55 56 * + 65 66 * * +

REFERENCES
J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. Stewart, LINPACK Users' Guide, SIAM, 1979.

ROUTINES CALLED
CAXPY, CSCAL, CSWAP, ICAMAX

REVISION HISTORY (YYMMDD)
800730 DATE WRITTEN
890531 Changed all specific intrinsics to generic. (WRB)
890831 Modified array declarations. (WRB)
890831 REVISION DATE from Version 3.2
891214 Prologue converted to Version 4.0 format. (BAB)
920501 Reformatted the REFERENCES section. (WRB)