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+ SUBROUTINE DGESC2( 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
+ DOUBLE PRECISION SCALE
+* ..
+* .. Array Arguments ..
+ INTEGER IPIV( * ), JPIV( * )
+ DOUBLE PRECISION A( LDA, * ), RHS( * )
+* ..
+*
+* Purpose
+* =======
+*
+* DGESC2 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 DGETC2.
+*
+* Arguments
+* =========
+*
+* N (input) INTEGER
+* The order of the matrix A.
+*
+* A (input) DOUBLE PRECISION array, dimension (LDA,N)
+* On entry, the LU part of the factorization of the n-by-n
+* matrix A computed by DGETC2: A = P * L * U * Q
+*
+* LDA (input) INTEGER
+* The leading dimension of the array A. LDA >= max(1, N).
+*
+* RHS (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION
+* 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 ..
+ DOUBLE PRECISION ONE, TWO
+ PARAMETER ( ONE = 1.0D+0, TWO = 2.0D+0 )
+* ..
+* .. Local Scalars ..
+ INTEGER I, J
+ DOUBLE PRECISION BIGNUM, EPS, SMLNUM, TEMP
+* ..
+* .. External Subroutines ..
+ EXTERNAL DLASWP, DSCAL
+* ..
+* .. External Functions ..
+ INTEGER IDAMAX
+ DOUBLE PRECISION DLAMCH
+ EXTERNAL IDAMAX, DLAMCH
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC ABS
+* ..
+* .. Executable Statements ..
+*
+* Set constant to control owerflow
+*
+ EPS = DLAMCH( 'P' )
+ SMLNUM = DLAMCH( 'S' ) / EPS
+ BIGNUM = ONE / SMLNUM
+ CALL DLABAD( SMLNUM, BIGNUM )
+*
+* Apply permutations IPIV to RHS
+*
+ CALL DLASWP( 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 = IDAMAX( N, RHS, 1 )
+ IF( TWO*SMLNUM*ABS( RHS( I ) ).GT.ABS( A( N, N ) ) ) THEN
+ TEMP = ( ONE / TWO ) / ABS( RHS( I ) )
+ CALL DSCAL( 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 DLASWP( 1, RHS, LDA, 1, N-1, JPIV, -1 )
+ RETURN
+*
+* End of DGESC2
+*
+ END