# chifa.f

          SUBROUTINE CHIFA (A, LDA, N, KPVT, INFO)
    C***BEGIN PROLOGUE  CHIFA
    C***PURPOSE  Factor a complex Hermitian matrix by elimination
    C            (symmetric pivoting).
    C***LIBRARY   SLATEC (LINPACK)
    C***CATEGORY  D2D1A
    C***TYPE      COMPLEX (SSIFA-S, DSIFA-D, CHIFA-C, CSIFA-C)
    C***KEYWORDS  HERMITIAN, LINEAR ALGEBRA, LINPACK, MATRIX FACTORIZATION
    C***AUTHOR  Bunch, J., (UCSD)
    C***DESCRIPTION
    C
    C     CHIFA factors a complex Hermitian matrix by elimination
    C     with symmetric pivoting.
    C
    C     To solve  A*X = B , follow CHIFA by CHISL.
    C     To compute  INVERSE(A)*C , follow CHIFA by CHISL.
    C     To compute  DETERMINANT(A) , follow CHIFA by CHIDI.
    C     To compute  INERTIA(A) , follow CHIFA by CHIDI.
    C     To compute  INVERSE(A) , follow CHIFA by CHIDI.
    C
    C     On Entry
    C
    C        A       COMPLEX(LDA,N)
    C                the Hermitian matrix to be factored.
    C                Only the diagonal and upper triangle are used.
    C
    C        LDA     INTEGER
    C                the leading dimension of the array  A .
    C
    C        N       INTEGER
    C                the order of the matrix  A .
    C
    C     On Return
    C
    C        A       a block diagonal matrix and the multipliers which
    C                were used to obtain it.
    C                The factorization can be written  A = U*D*CTRANS(U)
    C                where  U  is a product of permutation and unit
    C                upper triangular matrices , CTRANS(U) is the
    C                conjugate transpose of  U , and  D  is block diagonal
    C                with 1 by 1 and 2 by 2 blocks.
    C
    C        KVPT    INTEGER(N)
    C                an integer vector of pivot indices.
    C
    C        INFO    INTEGER
    C                = 0  normal value.
    C                = K  if the K-th pivot block is singular.  This is
    C                     not an error condition for this subroutine,
    C                     but it does indicate that CHISL or CHIDI may
    C                     divide by zero if called.
    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, CSWAP, ICAMAX
    C***REVISION HISTORY  (YYMMDD)
    C   780814  DATE WRITTEN
    C   890531  Changed all specific intrinsics to generic.  (WRB)
    C   890831  Modified array declarations.  (WRB)
    C   891107  Modified routine equivalence list.  (WRB)
    C   891107  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  CHIFA