cgesc2.f

          SUBROUTINE CGESC2( 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( * )
          COMPLEX            A( LDA, * ), RHS( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  CGESC2 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 CGETC2.
    *
    *
    *  Arguments
    *  =========
    *
    *  N       (input) INTEGER
    *          The number of columns of the matrix A.
    *
    *  A       (input) COMPLEX array, dimension (LDA, N)
    *          On entry, the  LU part of the factorization of the n-by-n
    *          matrix A computed by CGETC2:  A = P * L * U * Q
    *
    *  LDA     (input) INTEGER
    *          The leading dimension of the array A.  LDA >= max(1, N).
    *
    *  RHS     (input/output) COMPLEX 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               ZERO, ONE, TWO
          PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0, TWO = 2.0E+0 )
    *     ..
    *     .. Local Scalars ..
          INTEGER            I, J
          REAL               BIGNUM, EPS, SMLNUM
          COMPLEX            TEMP
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           CLASWP, CSCAL, SLABAD
    *     ..
    *     .. External Functions ..
          INTEGER            ICAMAX
          REAL               SLAMCH
          EXTERNAL           ICAMAX, SLAMCH
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          ABS, CMPLX, REAL
    *     ..
    *     .. Executable Statements ..
    *
    *     Set constant to control overflow
    *
          EPS = SLAMCH( 'P' )
          SMLNUM = SLAMCH( 'S' ) / EPS
          BIGNUM = ONE / SMLNUM
          CALL SLABAD( SMLNUM, BIGNUM )
    *
    *     Apply permutations IPIV to RHS
    *
          CALL CLASWP( 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 = ICAMAX( N, RHS, 1 )
          IF( TWO*SMLNUM*ABS( RHS( I ) ).GT.ABS( A( N, N ) ) ) THEN
             TEMP = CMPLX( ONE / TWO, ZERO ) / ABS( RHS( I ) )
             CALL CSCAL( N, TEMP, RHS( 1 ), 1 )
             SCALE = SCALE*REAL( TEMP )
          END IF
          DO 40 I = N, 1, -1
             TEMP = CMPLX( ONE, ZERO ) / 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 CLASWP( 1, RHS, LDA, 1, N-1, JPIV, -1 )
          RETURN
    *
    *     End of CGESC2
    *
          END