# chpdi.f

```      SUBROUTINE CHPDI (AP, N, KPVT, DET, INERT, WORK, JOB)
C***BEGIN PROLOGUE  CHPDI
C***PURPOSE  Compute the determinant, inertia and inverse of a complex
C            Hermitian matrix stored in packed form using the factors
C            obtained from CHPFA.
C***LIBRARY   SLATEC (LINPACK)
C***CATEGORY  D2D1A, D3D1A
C***TYPE      COMPLEX (SSPDI-S, DSPDI-D, CHPDI-C, DSPDI-C)
C***KEYWORDS  DETERMINANT, HERMITIAN, INVERSE, LINEAR ALGEBRA, LINPACK,
C             MATRIX, PACKED
C***AUTHOR  Bunch, J., (UCSD)
C***DESCRIPTION
C
C     CHPDI computes the determinant, inertia and inverse
C     of a complex Hermitian matrix using the factors from CHPFA,
C     where the matrix is stored in packed form.
C
C     On Entry
C
C        AP      COMPLEX (N*(N+1)/2)
C                the output from CHPFA.
C
C        N       INTEGER
C                the order of the matrix A.
C
C        KVPT    INTEGER(N)
C                the pivot vector from CHPFA.
C
C        WORK    COMPLEX(N)
C                work vector.  Contents ignored.
C
C        JOB     INTEGER
C                JOB has the decimal expansion  ABC  where
C                   if  C .NE. 0, the inverse is computed,
C                   if  B .NE. 0, the determinant is computed,
C                   if  A .NE. 0, the inertia is computed.
C
C                For example, JOB = 111  gives all three.
C
C     On Return
C
C        Variables not requested by JOB are not used.
C
C        AP     contains the upper triangle of the inverse of
C               the original matrix, stored in packed form.
C               The columns of the upper triangle are stored
C               sequentially in a one-dimensional array.
C
C        DET    REAL(2)
C               determinant of original matrix.
C               Determinant = DET(1) * 10.0**DET(2)
C               with 1.0 .LE. ABS(DET(1)) .LT. 10.0
C               or DET(1) = 0.0.
C
C        INERT  INTEGER(3)
C               the inertia of the original matrix.
C               INERT(1)  =  number of positive eigenvalues.
C               INERT(2)  =  number of negative eigenvalues.
C               INERT(3)  =  number of zero eigenvalues.
C
C     Error Condition
C
C        A division by zero will occur if the inverse is requested
C        and  CHPCO  has set RCOND .EQ. 0.0
C        or  CHPFA  has set  INFO .NE. 0 .
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, CCOPY, CDOTC, CSWAP
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  CHPDI
```