DPBFA(3)

SYNOPSIS
SUBROUTINE DPBFA (ABD, LDA, N, M, INFO)

NAME
dpbfa - Factor a real symmetric positive definite matrix stored in in band form.

LIBRARY
SLATEC (LINPACK)

CATEGORY
D2B2

TYPE
DOUBLE PRECISION (SPBFA-S, DPBFA-D, CPBFA-C)

KEYWORDS
BANDED, LINEAR ALGEBRA, LINPACK, MATRIX FACTORIZATION, POSITIVE DEFINITE

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

DESCRIPTION
DPBFA factors a double precision symmetric positive definite matrix stored in band form. DPBFA is usually called by DPBCO, but it can be called directly with a saving in time if RCOND is not needed. On Entry ABD DOUBLE PRECISION(LDA, N) the matrix to be factored. The columns of the upper triangle are stored in the columns of ABD and the diagonals of the upper triangle are stored in the rows of ABD . See the comments below for details. LDA INTEGER the leading dimension of the array ABD . LDA must be .GE. M + 1 . N INTEGER the order of the matrix A . M INTEGER the number of diagonals above the main diagonal. 0 .LE. M .LT. N . On Return ABD an upper triangular matrix R , stored in band form, so that A = TRANS(R)*R . INFO INTEGER = 0 for normal return. = K if the leading minor of order K is not positive definite. Band Storage If A is a symmetric positive definite band matrix, the following program segment will set up the input. M = (band width above diagonal) DO 20 J = 1, N I1 = MAX(1, J-M) DO 10 I = I1, J K = I-J+M+1 ABD(K,J) = 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
DDOT

REVISION HISTORY (YYMMDD)
780814 DATE WRITTEN
890531 Changed all specific intrinsics to generic. (WRB)
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)