```      SUBROUTINE SGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE )
*
*  -- LAPACK auxiliary routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
INTEGER            LDA, N
REAL               SCALE
*     ..
*     .. Array Arguments ..
INTEGER            IPIV( * ), JPIV( * )
REAL               A( LDA, * ), RHS( * )
*     ..
*
*  Purpose
*  =======
*
*  SGESC2 solves a system of linear equations
*
*            A * X = scale* RHS
*
*  with a general N-by-N matrix A using the LU factorization with
*  complete pivoting computed by SGETC2.
*
*  Arguments
*  =========
*
*  N       (input) INTEGER
*          The order of the matrix A.
*
*  A       (input) REAL array, dimension (LDA,N)
*          On entry, the  LU part of the factorization of the n-by-n
*          matrix A computed by SGETC2:  A = P * L * U * Q
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= max(1, N).
*
*  RHS     (input/output) REAL array, dimension (N).
*          On entry, the right hand side vector b.
*          On exit, the solution vector X.
*
*  IPIV    (input) INTEGER array, dimension (N).
*          The pivot indices; for 1 <= i <= N, row i of the
*          matrix has been interchanged with row IPIV(i).
*
*  JPIV    (input) INTEGER array, dimension (N).
*          The pivot indices; for 1 <= j <= N, column j of the
*          matrix has been interchanged with column JPIV(j).
*
*  SCALE    (output) REAL
*           On exit, SCALE contains the scale factor. SCALE is chosen
*           0 <= SCALE <= 1 to prevent owerflow in the solution.
*
*  Further Details
*  ===============
*
*  Based on contributions by
*     Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*     Umea University, S-901 87 Umea, Sweden.
*
*  =====================================================================
*
*     .. Parameters ..
REAL               ONE, TWO
PARAMETER          ( ONE = 1.0E+0, TWO = 2.0E+0 )
*     ..
*     .. Local Scalars ..
INTEGER            I, J
REAL               BIGNUM, EPS, SMLNUM, TEMP
*     ..
*     .. External Subroutines ..
*     ..
*     .. External Functions ..
INTEGER            ISAMAX
REAL               SLAMCH
EXTERNAL           ISAMAX, SLAMCH
*     ..
*     .. Intrinsic Functions ..
INTRINSIC          ABS
*     ..
*     .. Executable Statements ..
*
*      Set constant to control owerflow
*
EPS = SLAMCH( 'P' )
SMLNUM = SLAMCH( 'S' ) / EPS
BIGNUM = ONE / SMLNUM
*
*     Apply permutations IPIV to RHS
*
CALL SLASWP( 1, RHS, LDA, 1, N-1, IPIV, 1 )
*
*     Solve for L part
*
DO 20 I = 1, N - 1
DO 10 J = I + 1, N
RHS( J ) = RHS( J ) - A( J, I )*RHS( I )
10    CONTINUE
20 CONTINUE
*
*     Solve for U part
*
SCALE = ONE
*
*     Check for scaling
*
I = ISAMAX( N, RHS, 1 )
IF( TWO*SMLNUM*ABS( RHS( I ) ).GT.ABS( A( N, N ) ) ) THEN
TEMP = ( ONE / TWO ) / ABS( RHS( I ) )
CALL SSCAL( N, TEMP, RHS( 1 ), 1 )
SCALE = SCALE*TEMP
END IF
*
DO 40 I = N, 1, -1
TEMP = ONE / A( I, I )
RHS( I ) = RHS( I )*TEMP
DO 30 J = I + 1, N
RHS( I ) = RHS( I ) - RHS( J )*( A( I, J )*TEMP )
30    CONTINUE
40 CONTINUE
*
*     Apply permutations JPIV to the solution (RHS)
*
CALL SLASWP( 1, RHS, LDA, 1, N-1, JPIV, -1 )
RETURN
*
*     End of SGESC2
*
END

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