SLATEC Routines --- CHICO ---

*DECK CHICO
      SUBROUTINE CHICO (A, LDA, N, KPVT, RCOND, Z)
C***BEGIN PROLOGUE  CHICO
C***PURPOSE  Factor a complex Hermitian matrix by elimination with sym-
C            metric pivoting and estimate the condition of the matrix.
C***LIBRARY   SLATEC (LINPACK)
C***CATEGORY  D2D1A
C***TYPE      COMPLEX (SSICO-S, DSICO-D, CHICO-C, CSICO-C)
C***KEYWORDS  CONDITION NUMBER, HERMITIAN, LINEAR ALGEBRA, LINPACK,
C             MATRIX FACTORIZATION
C***AUTHOR  Moler, C. B., (U. of New Mexico)
C***DESCRIPTION
C
C     CHICO factors a complex Hermitian matrix by elimination with
C     symmetric pivoting and estimates the condition of the matrix.
C
C     If  RCOND  is not needed, CHIFA is slightly faster.
C     To solve  A*X = B , follow CHICO by CHISL.
C     To compute  INVERSE(A)*C , follow CHICO by CHISL.
C     To compute  INVERSE(A) , follow CHICO by CHIDI.
C     To compute  DETERMINANT(A) , follow CHICO by CHIDI.
C     To compute  INERTIA(A), follow CHICO 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     Output
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        RCOND   REAL
C                an estimate of the reciprocal condition of  A .
C                For the system  A*X = B , relative perturbations
C                in  A  and  B  of size  EPSILON  may cause
C                relative perturbations in  X  of size  EPSILON/RCOND .
C                If  RCOND  is so small that the logical expression
C                           1.0 + RCOND .EQ. 1.0
C                is true, then  A  may be singular to working
C                precision.  In particular,  RCOND  is zero  if
C                exact singularity is detected or the estimate
C                underflows.
C
C        Z       COMPLEX(N)
C                a work vector whose contents are usually unimportant.
C                If  A  is close to a singular matrix, then  Z  is
C                an approximate null vector in the sense that
C                NORM(A*Z) = RCOND*NORM(A)*NORM(Z) .
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, CDOTC, CHIFA, CSSCAL, SCASUM
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  CHICO