CHPDI(3)

SYNOPSIS
SUBROUTINE CHPDI (AP, N, KPVT, DET, INERT, WORK, JOB)

NAME
chpdi - Compute the determinant, inertia and inverse of a complex Hermitian matrix stored in packed form using the factors obtained from CHPFA.

LIBRARY
SLATEC (LINPACK)

CATEGORY
D2D1A, D3D1A

TYPE
COMPLEX (SSPDI-S, DSPDI-D, CHPDI-C, DSPDI-C)

KEYWORDS
DETERMINANT, HERMITIAN, INVERSE, LINEAR ALGEBRA, LINPACK, MATRIX, PACKED

AUTHOR
Bunch, J., (UCSD)

DESCRIPTION
CHPDI computes the determinant, inertia and inverse of a complex Hermitian matrix using the factors from CHPFA, where the matrix is stored in packed form. On Entry AP COMPLEX (N*(N+1)/2) the output from CHPFA. N INTEGER the order of the matrix A. KVPT INTEGER(N) the pivot vector from CHPFA. WORK COMPLEX(N) work vector. Contents ignored. JOB INTEGER JOB has the decimal expansion ABC where if C .NE. 0, the inverse is computed, if B .NE. 0, the determinant is computed, if A .NE. 0, the inertia is computed. For example, JOB = 111 gives all three. On Return Variables not requested by JOB are not used. AP contains the upper triangle of the inverse of the original matrix, stored in packed form. The columns of the upper triangle are stored sequentially in a one-dimensional array. DET REAL(2) determinant of original matrix. Determinant = DET(1) * 10.0**DET(2) with 1.0 .LE. ABS(DET(1)) .LT. 10.0 or DET(1) = 0.0. INERT INTEGER(3) the inertia of the original matrix. INERT(1) = number of positive eigenvalues. INERT(2) = number of negative eigenvalues. INERT(3) = number of zero eigenvalues. Error Condition A division by zero will occur if the inverse is requested and CHPCO has set RCOND .EQ. 0.0 or CHPFA has set INFO .NE. 0 .

REFERENCES
J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. Stewart, LINPACK Users' Guide, SIAM, 1979.

ROUTINES CALLED
CAXPY, CCOPY, CDOTC, CSWAP

REVISION HISTORY (YYMMDD)
780814 DATE WRITTEN
890531 Changed all specific intrinsics to generic. (WRB)
890831 Modified array declarations. (WRB)
891107 Modified routine equivalence list. (WRB)
891107 REVISION DATE from Version 3.2
891214 Prologue converted to Version 4.0 format. (BAB)
900326 Removed duplicate information from DESCRIPTION section. (WRB)
920501 Reformatted the REFERENCES section. (WRB)