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NAME
     zsico - compute the UDU factorization and  condition  number
     of  a  symmetric  matrix  A.  If the condition number is not
     needed then xSIFA is slightly faster.  It is typical to fol-
     low  a call to xSICO with a call to xSISL to solve Ax = b or
     to xSIDI to compute the determinant, inverse, and inertia of
     A.

SYNOPSIS
     SUBROUTINE DSICO (DA, LDA, N, IPIVOT, DRCOND, DWORK)

     SUBROUTINE SSICO (SA, LDA, N, IPIVOT, SRCOND, SWORK)

     SUBROUTINE ZSICO (ZA, LDA, N, IPIVOT, DRCOND, ZWORK)

     SUBROUTINE CSICO (CA, LDA, N, IPIVOT, SRCOND, CWORK)



     #include <sunperf.h>

     void dsico(double *da, int lda, int  n,  int  *kpvt,  double
               *rcond) ;

     void ssico(float *sa, int  lda,  int  n,  int  *kpvt,  float
               *rcond) ;

     void zsico(doublecomplex *za, int lda,  int  n,  int  *kpvt,
               double *rcond) ;

     void csico(complex *ca, int lda, int  n,  int  *kpvt,  float
               *rcond) ;

ARGUMENTS
     xA        On entry, the upper triangle of the matrix A.   On
               exit,  a  UDU  factorization of the matrix A.  The
               strict lower triangle of A is not referenced.

     LDA       Leading dimension of the array A as specified in a
               dimension or type statement.  LDA >= max(1,N).

     N         Order of the matrix A.  N >= 0.

     IPIVOT    On exit, a vector of pivot indices.

     xRCOND    On exit, an estimate of the  reciprocal  condition
               number  of  A.  0.0 <= RCOND <= 1.0.  As the value
               of RCOND gets smaller, operations with A  such  as
               solving  Ax  = b may become less stable.  If RCOND
               satisfies RCOND + 1.0 = 1.0 then A may be singular
               to working precision.

     xWORK     Scratch array with a dimension of N.

SAMPLE PROGRAM
           PROGRAM TEST
           IMPLICIT NONE
     C
           INTEGER           LDA, N
           PARAMETER        (N = 4)
           PARAMETER        (LDA = 5)
     C
           DOUBLE PRECISION  A(LDA,N), B(N), RCOND, WORK(N)
           INTEGER           ICOL, IPIVOT(N), IROW
     C
           EXTERNAL          DSICO, DSISL
     C
     C     Initialize the array A to store the matrix A shown below.
     C     Initialize the array B to store the vector b shown below.
     C
     C         -.5   -.5   -.5   -.5        12
     C     A = -.5  -1.5  -1.5  -1.5    b =  6
     C         -.5  -1.5  -2.5  -2.5         6
     C         -.5  -1.5  -2.5  -3.5        12
     C
           DATA A / -5.0D-1, 4*8D8, -5.0D-1, -1.5D0, 3*8D8, -5.0D-1,
          $         -1.5D0, -2.5D0, 2*8D8, -5.0D-1, -1.5D0, -2.5D0,
          $         -3.5D0, 8D8 /
           DATA B / 1.2D1, 6.0D0, 6.0D0, 1.2D1 /
     C
           PRINT 1000
           DO 100, IROW = 1, N
             PRINT 1010, (A(ICOL,IROW), ICOL = 1, IROW),
          $              (A(IROW,ICOL), ICOL = IROW + 1, N)
       100 CONTINUE
           PRINT 1020
           PRINT 1010, ((A(IROW,ICOL), ICOL = 1, N), IROW = 1, N)
           PRINT 1030
           PRINT 1040, B
           CALL DSICO (A, LDA, N, IPIVOT, RCOND, WORK)
           PRINT 1050, RCOND
           IF ((RCOND + 1.0D0) .EQ. RCOND) THEN
             PRINT 1060
           END IF
           PRINT 1070, 1.0D0 / RCOND
           CALL DSISL (A, LDA, N, IPIVOT, B)
           PRINT 1080
           PRINT 1040, B
     C
      1000 FORMAT (1X, 'A in full form:')
      1010 FORMAT (4(3X, F5.1))
      1020 FORMAT (/1X, 'A in symmetric form:  (* in unused elements)')
      1030 FORMAT (/1X, 'b:')
      1040 FORMAT (3X, F5.1)
      1050 FORMAT (/1X, 'Reciprocal condition number of A:', F6.3)
      1060 FORMAT (1X, 'A may be singular to working precision.')
      1070 FORMAT (1X, 'Condition number of A: ', F6.3)
      1080 FORMAT (/1X, 'A**(-1) * b:')
     C
           END

SAMPLE OUTPUT
      A in full form:
         -0.5    -0.5    -0.5    -0.5
         -0.5    -1.5    -1.5    -1.5
         -0.5    -1.5    -2.5    -2.5
         -0.5    -1.5    -2.5    -3.5

      A in symmetric form:  (* in unused elements)
         -0.5    -0.5    -0.5    -0.5
        *****    -1.5    -1.5    -1.5
        *****   *****    -2.5    -2.5
        *****   *****   *****    -3.5

      b:
         12.0
          6.0
          6.0
         12.0

      Reciprocal condition number of A: 0.031
      Condition number of A: 32.000

      A**(-1) * b:
        -30.0
          6.0
          6.0
         -6.0

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