CHIDI(3)

SYNOPSIS
SUBROUTINE CHIDI (A, LDA, N, KPVT, DET, INERT, WORK, JOB)

NAME
chidi - Compute the determinant, inertia and inverse of a complex Hermitian matrix using the factors obtained from CHIFA.

LIBRARY
SLATEC (LINPACK)

CATEGORY
D2D1A, D3D1A

TYPE
COMPLEX (SSIDI-S, DSISI-D, CHIDI-C, CSIDI-C)

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

AUTHOR
Bunch, J., (UCSD)

DESCRIPTION
CHIDI computes the determinant, inertia and inverse of a complex Hermitian matrix using the factors from CHIFA. On Entry A COMPLEX(LDA,N) the output from CHIFA. LDA INTEGER the leading dimension of the array A. N INTEGER the order of the matrix A. KVPT INTEGER(N) the pivot vector from CHIFA. WORK COMPLEX(N) work vector. Contents destroyed. 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. A contains the upper triangle of the inverse of the original matrix. The strict lower triangle is never referenced. 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 may occur if the inverse is requested and CHICO has set RCOND .EQ. 0.0 or CHIFA 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)