# cpbfa.f

          SUBROUTINE CPBFA (ABD, LDA, N, M, INFO)
    C***BEGIN PROLOGUE  CPBFA
    C***PURPOSE  Factor a complex Hermitian positive definite matrix stored
    C            in band form.
    C***LIBRARY   SLATEC (LINPACK)
    C***CATEGORY  D2D2
    C***TYPE      COMPLEX (SPBFA-S, DPBFA-D, CPBFA-C)
    C***KEYWORDS  BANDED, LINEAR ALGEBRA, LINPACK, MATRIX FACTORIZATION,
    C             POSITIVE DEFINITE
    C***AUTHOR  Moler, C. B., (U. of New Mexico)
    C***DESCRIPTION
    C
    C     CPBFA factors a complex Hermitian positive definite matrix
    C     stored in band form.
    C
    C     CPBFA is usually called by CPBCO, but it can be called
    C     directly with a saving in time if  RCOND  is not needed.
    C
    C     On Entry
    C
    C        ABD     COMPLEX(LDA, N)
    C                the matrix to be factored.  The columns of the upper
    C                triangle are stored in the columns of ABD and the
    C                diagonals of the upper triangle are stored in the
    C                rows of ABD .  See the comments below for details.
    C
    C        LDA     INTEGER
    C                the leading dimension of the array  ABD .
    C                LDA must be .GE. M + 1 .
    C
    C        N       INTEGER
    C                the order of the matrix  A .
    C
    C        M       INTEGER
    C                the number of diagonals above the main diagonal.
    C                0 .LE. M .LT. N .
    C
    C     On Return
    C
    C        ABD     an upper triangular matrix  R , stored in band
    C                form, so that  A = CTRANS(R)*R .
    C
    C        INFO    INTEGER
    C                = 0  for normal return.
    C                = K  if the leading minor of order  K  is not
    C                     positive definite.
    C
    C     Band Storage
    C
    C           If  A  is a Hermitian positive definite band matrix,
    C           the following program segment will set up the input.
    C
    C                   M = (band width above diagonal)
    C                   DO 20 J = 1, N
    C                      I1 = MAX(1, J-M)
    C                      DO 10 I = I1, J
    C                         K = I-J+M+1
    C                         ABD(K,J) = A(I,J)
    C                10    CONTINUE
    C                20 CONTINUE
    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  CDOTC
    C***REVISION HISTORY  (YYMMDD)
    C   780814  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   900326  Removed duplicate information from DESCRIPTION section.
    C           (WRB)
    C   920501  Reformatted the REFERENCES section.  (WRB)
    C***END PROLOGUE  CPBFA