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SGEFA

       SUBROUTINE SGEFA(A,LDA,N,IPVT,INFO)
       INTEGER LDA,N,IPVT(1),INFO
       REAL A(LDA,1)
 C
 C     SGEFA FACTORS A REAL MATRIX BY GAUSSIAN ELIMINATION.
 C
 C     SGEFA IS USUALLY CALLED BY SGECO, BUT IT CAN BE CALLED
 C     DIRECTLY WITH A SAVING IN TIME IF  RCOND  IS NOT NEEDED.
 C     (TIME FOR SGECO) = (1 + 9/N)*(TIME FOR SGEFA) .
 C
 C     ON ENTRY
 C
 C        A       REAL(LDA, N)
 C                THE MATRIX TO BE FACTORED.
 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 AND THE MULTIPLIERS
 C                WHICH WERE USED TO OBTAIN IT.
 C                THE FACTORIZATION CAN BE WRITTEN  A = L*U  WHERE
 C                L  IS A PRODUCT OF PERMUTATION AND UNIT LOWER
 C                TRIANGULAR MATRICES AND  U  IS UPPER TRIANGULAR.
 C
 C        IPVT    INTEGER(N)
 C                AN INTEGER VECTOR OF PIVOT INDICES.
 C
 C        INFO    INTEGER
 C                = 0  NORMAL VALUE.
 C                = K  IF  U(K,K) .EQ. 0.0 .  THIS IS NOT AN ERROR
 C                     CONDITION FOR THIS SUBROUTINE, BUT IT DOES
 C                     INDICATE THAT SGESL OR SGEDI WILL DIVIDE BY ZER
 C                     IF CALLED.  USE  RCOND  IN SGECO FOR A RELIABLE
 C                     INDICATION OF SINGULARITY.
 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 SAXPY,SSCAL,ISAMAX
 C