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SPOFA

       SUBROUTINE SPOFA(A,LDA,N,INFO)
       INTEGER LDA,N,INFO
       REAL A(LDA,1)
 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)
 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     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