SUBROUTINE CNBFA (ABE, LDA, N, ML, MU, IPVT, INFO) C***BEGIN PROLOGUE CNBFA C***PURPOSE Factor a band matrix by elimination. C***LIBRARY SLATEC C***CATEGORY D2C2 C***TYPE COMPLEX (SNBFA-S, DNBFA-D, CNBFA-C) C***KEYWORDS BANDED, LINEAR EQUATIONS, MATRIX FACTORIZATION, C NONSYMMETRIC C***AUTHOR Voorhees, E. A., (LANL) C***DESCRIPTION C C CNBFA factors a complex band matrix by elimination. C 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 C On Entry C 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 C LDA INTEGER C the leading dimension of the array ABE. C LDA must be .GE. N . C C N INTEGER C the order of the original matrix. C C ML INTEGER C number of diagonals below the main diagonal. C 0 .LE. ML .LT. N . C 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 C On Return C 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 C IPVT INTEGER(N) C an integer vector of pivot indices. C 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 C Band Storage C C If A is a band matrix, the following program segment C will set up the input. C 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 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 C Example: If the original matrix is C 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 C then N = 6, ML = 1, MU = 2, LDA .GE. 5 and ABE should contain C 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 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