DSPFA(3)

SYNOPSIS
SUBROUTINE DSPFA (AP, N, KPVT, INFO)

NAME
dspfa - Factor a real symmetric matrix stored in packed form by elimination with symmetric pivoting.

LIBRARY
SLATEC (LINPACK)

CATEGORY
D2B1A

TYPE
DOUBLE PRECISION (SSPFA-S, DSPFA-D, CHPFA-C, CSPFA-C)

KEYWORDS
LINEAR ALGEBRA, LINPACK, MATRIX FACTORIZATION, PACKED, SYMMETRIC

AUTHOR
Bunch, J., (UCSD)

DESCRIPTION
DSPFA factors a double precision symmetric matrix stored in packed form by elimination with symmetric pivoting. To solve A*X = B , follow DSPFA by DSPSL. To compute INVERSE(A)*C , follow DSPFA by DSPSL. To compute DETERMINANT(A) , follow DSPFA by DSPDI. To compute INERTIA(A) , follow DSPFA by DSPDI. To compute INVERSE(A) , follow DSPFA by DSPDI. On Entry AP DOUBLE PRECISION (N*(N+1)/2) the packed form of a symmetric matrix A . The columns of the upper triangle are stored sequentially in a one-dimensional array of length N*(N+1)/2 . See comments below for details. N INTEGER the order of the matrix A . Output AP a block diagonal matrix and the multipliers which were used to obtain it stored in packed form. The factorization can be written A = U*D*TRANS(U) where U is a product of permutation and unit upper triangular matrices, TRANS(U) is the transpose of U , and D is block diagonal with 1 by 1 and 2 by 2 blocks. KPVT INTEGER(N) an integer vector of pivot indices. INFO INTEGER = 0 normal value. = K if the K-th pivot block is singular. This is not an error condition for this subroutine, but it does indicate that DSPSL or DSPDI may divide by zero if called. Packed Storage The following program segment will pack the upper triangle of a symmetric matrix. K = 0 DO 20 J = 1, N DO 10 I = 1, J K = K + 1 AP(K) = A(I,J) 10 CONTINUE 20 CONTINUE

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

ROUTINES CALLED
DAXPY, DSWAP, IDAMAX

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)