CGBFA(3)

SYNOPSIS
SUBROUTINE CGBFA (ABD, LDA, N, ML, MU, IPVT, INFO)

NAME
cgbfa - Factor a band matrix using Gaussian elimination.

LIBRARY
SLATEC (LINPACK)

CATEGORY
D2C2

TYPE
COMPLEX (SGBFA-S, DGBFA-D, CGBFA-C)

KEYWORDS
BANDED, LINEAR ALGEBRA, LINPACK, MATRIX FACTORIZATION

AUTHOR
Moler, C. B., (U. of New Mexico)

DESCRIPTION
CGBFA factors a complex band matrix by elimination. CGBFA is usually called by CGBCO, but it can be called directly with a saving in time if RCOND is not needed. On Entry ABD COMPLEX(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. LDA INTEGER the leading dimension of the array ABD . LDA must be .GE. 2*ML + MU + 1 . 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 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. 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 CGBSL will divide by zero if called. Use RCOND in CGBCO 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 = MAX(1, J-MU) I2 = MIN(N, J+ML) DO 10 I = I1, I2 K = I - J + M ABD(K,J) = A(I,J) 10 CONTINUE 20 CONTINUE 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.

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

ROUTINES CALLED
CAXPY, CSCAL, ICAMAX

REVISION HISTORY (YYMMDD)
780814 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)
900326 Removed duplicate information from DESCRIPTION section. (WRB)
920501 Reformatted the REFERENCES section. (WRB)