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SPPFA

       SUBROUTINE SPPFA(AP,N,INFO)
       INTEGER N,INFO
       REAL AP(1)
 C
 C     SPPFA FACTORS A REAL SYMMETRIC POSITIVE DEFINITE MATRIX
 C     STORED IN PACKED FORM.
 C
 C     SPPFA IS USUALLY CALLED BY SPPCO, BUT IT CAN BE CALLED
 C     DIRECTLY WITH A SAVING IN TIME IF  RCOND  IS NOT NEEDED.
 C     (TIME FOR SPPCO) = (1 + 18/N)*(TIME FOR SPPFA) .
 C
 C     ON ENTRY
 C
 C        AP      REAL (N*(N+1)/2)
 C                THE PACKED FORM OF A SYMMETRIC MATRIX  A .  THE
 C                COLUMNS OF THE UPPER TRIANGLE ARE STORED SEQUENTIALL
 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     ON RETURN
 C
 C        AP      AN UPPER TRIANGULAR MATRIX  R , STORED IN PACKED
 C                FORM, SO THAT  A = TRANS(R)*R .
 C
 C        INFO    INTEGER
 C                = 0  FOR NORMAL RETURN.
 C                = K  IF THE LEADING MINOR OF ORDER  K  IS NOT
 C                     POSITIVE DEFINITE.
 C
 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     LINPACK.  THIS VERSION DATED 08/14/78 .
 C     CLEVE MOLER, UNIVERSITY OF NEW MEXICO, ARGONNE NATIONAL LAB.
 C
 C     SUBROUTINES AND FUNCTIONS
 C
 C     BLAS SDOT
 C     FORTRAN SQRT
 C