SPODI(3)

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

NAME
spodi - Compute the determinant and inverse of a certain real symmetric positive definite matrix using the factors computed by SPOCO, SPOFA or SQRDC.

LIBRARY
SLATEC (LINPACK)

CATEGORY
D2B1B, D3B1B

TYPE
SINGLE 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
SPODI computes the determinant and inverse of a certain real symmetric positive definite matrix (see below) using the factors computed by SPOCO, SPOFA or SQRDC. On Entry A REAL(LDA, N) the output A from SPOCO or SPOFA or the output X from SQRDC. 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 SPOCO or SPOFA was used to factor A , then SPODI produces the upper half of INVERSE(A) . If SQRDC was used to decompose X , then SPODI 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 REAL(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 SPOCO or SPOFA 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
SAXPY, SSCAL

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)