# spofa.f

          SUBROUTINE SPOFA (A, LDA, N, INFO)
    C***BEGIN PROLOGUE  SPOFA
    C***PURPOSE  Factor a real symmetric positive definite matrix.
    C***LIBRARY   SLATEC (LINPACK)
    C***CATEGORY  D2B1B
    C***TYPE      SINGLE PRECISION (SPOFA-S, DPOFA-D, CPOFA-C)
    C***KEYWORDS  LINEAR ALGEBRA, LINPACK, MATRIX FACTORIZATION,
    C             POSITIVE DEFINITE
    C***AUTHOR  Moler, C. B., (U. of New Mexico)
    C***DESCRIPTION
    C
    C     SPOFA factors a real symmetric positive definite matrix.
    C
    C     SPOFA is usually called by SPOCO, but it can be called
    C     directly with a saving in time if  RCOND  is not needed.
    C     (Time for SPOCO) = (1 + 18/N)*(Time for SPOFA) .
    C
    C     On Entry
    C
    C        A       REAL(LDA, N)
    C                the symmetric matrix to be factored.  Only the
    C                diagonal and upper triangle are used.
    C
    C        LDA     INTEGER
    C                the leading dimension of the array  A .
    C
    C        N       INTEGER
    C                the order of the matrix  A .
    C
    C     On Return
    C
    C        A       an upper triangular matrix  R  so that  A = TRANS(R)*R
    C                where  TRANS(R)  is the transpose.
    C                The strict lower triangle is unaltered.
    C                If  INFO .NE. 0 , the factorization is not complete.
    C
    C        INFO    INTEGER
    C                = 0  for normal return.
    C                = K  signals an error condition.  The leading minor
    C                     of order  K  is not positive definite.
    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  SDOT
    C***REVISION HISTORY  (YYMMDD)
    C   780814  DATE WRITTEN
    C   890831  Modified array declarations.  (WRB)
    C   890831  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  SPOFA