CSPDI(3)

SYNOPSIS
SUBROUTINE CSPDI (AP, N, KPVT, DET, WORK, JOB)

NAME
cspdi - Compute the determinant and inverse of a complex symmetric matrix stored in packed form using the factors from CSPFA.

LIBRARY
SLATEC (LINPACK)

CATEGORY
D2C1, D3C1

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

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

AUTHOR
Bunch, J., (UCSD)

DESCRIPTION
CSPDI computes the determinant and inverse of a complex symmetric matrix using the factors from CSPFA, where the matrix is stored in packed form. On Entry AP COMPLEX (N*(N+1)/2) the output from CSPFA. N INTEGER the order of the matrix A . KVPT INTEGER(N) the pivot vector from CSPFA. WORK COMPLEX(N) work vector. Contents ignored. JOB INTEGER JOB has the decimal expansion AB where if B .NE. 0, the inverse is computed, if A .NE. 0, the determinant is computed. For example, JOB = 11 gives both. 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 COMPLEX(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. Error Condition A division by zero will occur if the inverse is requested and CSPCO has set RCOND .EQ. 0.0 or CSPFA 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, CDOTU, CSWAP

REVISION HISTORY (YYMMDD)
780814 DATE WRITTEN
890531 Changed all specific intrinsics to generic. (WRB)
890831 Modified array declarations. (WRB)
891107 Corrected category and 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)