# csico.f

          SUBROUTINE CSICO (A, LDA, N, KPVT, RCOND, Z)
    C***BEGIN PROLOGUE  CSICO
    C***PURPOSE  Factor a complex symmetric matrix by elimination with
    C            symmetric pivoting and estimate the condition number of the
    C            matrix.
    C***LIBRARY   SLATEC (LINPACK)
    C***CATEGORY  D2C1
    C***TYPE      COMPLEX (SSICO-S, DSICO-D, CHICO-C, CSICO-C)
    C***KEYWORDS  CONDITION NUMBER, LINEAR ALGEBRA, LINPACK,
    C             MATRIX FACTORIZATION, SYMMETRIC
    C***AUTHOR  Moler, C. B., (U. of New Mexico)
    C***DESCRIPTION
    C
    C     CSICO factors a complex symmetric matrix by elimination with
    C     symmetric pivoting and estimates the condition of the matrix.
    C
    C     If  RCOND  is not needed, CSIFA is slightly faster.
    C     To solve  A*X = B , follow CSICO by CSISL.
    C     To compute  INVERSE(A)*C , follow CSICO by CSISL.
    C     To compute  INVERSE(A) , follow CSICO by CSIDI.
    C     To compute  DETERMINANT(A) , follow CSICO by CSIDI.
    C
    C     On Entry
    C
    C        A       COMPLEX(LDA, N)
    C                the symmetric 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*TRANS(U)
    C                where  U  is a product of permutation and unit
    C                upper triangular matrices , TRANS(U) is the
    C                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, CDOTU, CSIFA, 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  Corrected category and modified routine equivalence
    C           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  CSICO