CPODI(3)

SYNOPSIS
SUBROUTINE CPODI (A, LDA, N, DET, JOB)

NAME
cpodi - Compute the determinant and inverse of a certain complex Hermitian positive definite matrix using the factors computed by CPOCO, CPOFA, or CQRDC.

LIBRARY
SLATEC (LINPACK)

CATEGORY
D2D1B, D3D1B

TYPE
COMPLEX (SPODI-S, DPODI-D, CPODI-C)

KEYWORDS
DETERMINANT, INVERSE, LINEAR ALGEBRA, LINPACK, MATRIX, POSITIVE DEFINITE

AUTHOR
Moler, C. B., (U. of New Mexico)

DESCRIPTION
CPODI computes the determinant and inverse of a certain complex Hermitian positive definite matrix (see below) using the factors computed by CPOCO, CPOFA or CQRDC. On Entry A COMPLEX(LDA, N) the output A from CPOCO or CPOFA or the output X from CQRDC. LDA INTEGER the leading dimension of the array A . N INTEGER the order of the matrix A . JOB INTEGER = 11 both determinant and inverse. = 01 inverse only. = 10 determinant only. On Return A If CPOCO or CPOFA was used to factor A then CPODI produces the upper half of INVERSE(A) . If CQRDC was used to decompose X then CPODI produces the upper half of INVERSE(CTRANS(X)*X) where CTRANS(X) is the conjugate transpose. Elements of A below the diagonal are unchanged. If the units digit of JOB is zero, A is unchanged. DET REAL(2) determinant of A or of CTRANS(X)*X if requested. Otherwise not referenced. Determinant = DET(1) * 10.0**DET(2) with 1.0 .LE. DET(1) .LT. 10.0 or DET(1) .EQ. 0.0 . Error Condition a division by zero will occur if the input factor contains a zero on the diagonal and the inverse is requested. It will not occur if the subroutines are called correctly and if CPOCO or CPOFA has set INFO .EQ. 0 .

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

ROUTINES CALLED
CAXPY, CSCAL

REVISION HISTORY (YYMMDD)
780814 DATE WRITTEN
890831 Modified array declarations. (WRB)
890831 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)