dspfa.f
SUBROUTINE DSPFA (AP, N, KPVT, INFO)
C***BEGIN PROLOGUE DSPFA
C***PURPOSE Factor a real symmetric matrix stored in packed form by
C elimination with symmetric pivoting.
C***LIBRARY SLATEC (LINPACK)
C***CATEGORY D2B1A
C***TYPE DOUBLE PRECISION (SSPFA-S, DSPFA-D, CHPFA-C, CSPFA-C)
C***KEYWORDS LINEAR ALGEBRA, LINPACK, MATRIX FACTORIZATION, PACKED,
C SYMMETRIC
C***AUTHOR Bunch, J., (UCSD)
C***DESCRIPTION
C
C DSPFA factors a double precision symmetric matrix stored in
C packed form by elimination with symmetric pivoting.
C
C To solve A*X = B , follow DSPFA by DSPSL.
C To compute INVERSE(A)*C , follow DSPFA by DSPSL.
C To compute DETERMINANT(A) , follow DSPFA by DSPDI.
C To compute INERTIA(A) , follow DSPFA by DSPDI.
C To compute INVERSE(A) , follow DSPFA by DSPDI.
C
C On Entry
C
C AP DOUBLE PRECISION (N*(N+1)/2)
C the packed form of a symmetric matrix A . The
C columns of the upper triangle are stored sequentially
C in a one-dimensional array of length N*(N+1)/2 .
C See comments below for details.
C
C N INTEGER
C the order of the matrix A .
C
C Output
C
C AP a block diagonal matrix and the multipliers which
C were used to obtain it stored in packed form.
C The factorization can be written A = U*D*TRANS(U)
C where U is a product of permutation and unit
C upper triangular matrices, TRANS(U) is the
C transpose of U , and D is block diagonal
C with 1 by 1 and 2 by 2 blocks.
C
C KPVT INTEGER(N)
C an integer vector of pivot indices.
C
C INFO INTEGER
C = 0 normal value.
C = K if the K-th pivot block is singular. This is
C not an error condition for this subroutine,
C but it does indicate that DSPSL or DSPDI may
C divide by zero if called.
C
C Packed Storage
C
C The following program segment will pack the upper
C triangle of a symmetric matrix.
C
C K = 0
C DO 20 J = 1, N
C DO 10 I = 1, J
C K = K + 1
C AP(K) = A(I,J)
C 10 CONTINUE
C 20 CONTINUE
C
C***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W.
C Stewart, LINPACK Users' Guide, SIAM, 1979.
C***ROUTINES CALLED DAXPY, DSWAP, IDAMAX
C***REVISION HISTORY (YYMMDD)
C 780814 DATE WRITTEN
C 890531 Changed all specific intrinsics to generic. (WRB)
C 890831 Modified array declarations. (WRB)
C 891107 Modified routine equivalence list. (WRB)
C 891107 REVISION DATE from Version 3.2
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 900326 Removed duplicate information from DESCRIPTION section.
C (WRB)
C 920501 Reformatted the REFERENCES section. (WRB)
C***END PROLOGUE DSPFA