# 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