DPODI(3)

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

NAME
dpodi - Compute the determinant and inverse of a certain real symmetric positive definite matrix using the factors computed by DPOCO, DPOFA or DQRDC.

LIBRARY
SLATEC (LINPACK)

CATEGORY
D2B1B, D3B1B

TYPE
DOUBLE PRECISION (SPODI-S, DPODI-D, CPODI-C)

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

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

DESCRIPTION
DPODI computes the determinant and inverse of a certain double precision symmetric positive definite matrix (see below) using the factors computed by DPOCO, DPOFA or DQRDC. On Entry A DOUBLE PRECISION(LDA, N) the output A from DPOCO or DPOFA or the output X from DQRDC. 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 DPOCO or DPOFA was used to factor A , then DPODI produces the upper half of INVERSE(A) . If DQRDC was used to decompose X , then DPODI produces the upper half of inverse(TRANS(X)*X) where TRANS(X) is the transpose. Elements of A below the diagonal are unchanged. If the units digit of JOB is zero, A is unchanged. DET DOUBLE PRECISION(2) determinant of A or of TRANS(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 DPOCO or DPOFA 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
DAXPY, DSCAL

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)