LAPACK 3.3.0

dgesc2.f

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00001       SUBROUTINE DGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE )
00002 *
00003 *  -- LAPACK auxiliary routine (version 3.2.2) --
00004 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00005 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00006 *     June 2010
00007 *
00008 *     .. Scalar Arguments ..
00009       INTEGER            LDA, N
00010       DOUBLE PRECISION   SCALE
00011 *     ..
00012 *     .. Array Arguments ..
00013       INTEGER            IPIV( * ), JPIV( * )
00014       DOUBLE PRECISION   A( LDA, * ), RHS( * )
00015 *     ..
00016 *
00017 *  Purpose
00018 *  =======
00019 *
00020 *  DGESC2 solves a system of linear equations
00021 *
00022 *            A * X = scale* RHS
00023 *
00024 *  with a general N-by-N matrix A using the LU factorization with
00025 *  complete pivoting computed by DGETC2.
00026 *
00027 *  Arguments
00028 *  =========
00029 *
00030 *  N       (input) INTEGER
00031 *          The order of the matrix A.
00032 *
00033 *  A       (input) DOUBLE PRECISION array, dimension (LDA,N)
00034 *          On entry, the  LU part of the factorization of the n-by-n
00035 *          matrix A computed by DGETC2:  A = P * L * U * Q
00036 *
00037 *  LDA     (input) INTEGER
00038 *          The leading dimension of the array A.  LDA >= max(1, N).
00039 *
00040 *  RHS     (input/output) DOUBLE PRECISION array, dimension (N).
00041 *          On entry, the right hand side vector b.
00042 *          On exit, the solution vector X.
00043 *
00044 *  IPIV    (input) INTEGER array, dimension (N).
00045 *          The pivot indices; for 1 <= i <= N, row i of the
00046 *          matrix has been interchanged with row IPIV(i).
00047 *
00048 *  JPIV    (input) INTEGER array, dimension (N).
00049 *          The pivot indices; for 1 <= j <= N, column j of the
00050 *          matrix has been interchanged with column JPIV(j).
00051 *
00052 *  SCALE   (output) DOUBLE PRECISION
00053 *          On exit, SCALE contains the scale factor. SCALE is chosen
00054 *          0 <= SCALE <= 1 to prevent owerflow in the solution.
00055 *
00056 *  Further Details
00057 *  ===============
00058 *
00059 *  Based on contributions by
00060 *     Bo Kagstrom and Peter Poromaa, Department of Computing Science,
00061 *     Umea University, S-901 87 Umea, Sweden.
00062 *
00063 *  =====================================================================
00064 *
00065 *     .. Parameters ..
00066       DOUBLE PRECISION   ONE, TWO
00067       PARAMETER          ( ONE = 1.0D+0, TWO = 2.0D+0 )
00068 *     ..
00069 *     .. Local Scalars ..
00070       INTEGER            I, J
00071       DOUBLE PRECISION   BIGNUM, EPS, SMLNUM, TEMP
00072 *     ..
00073 *     .. External Subroutines ..
00074       EXTERNAL           DLASWP, DSCAL
00075 *     ..
00076 *     .. External Functions ..
00077       INTEGER            IDAMAX
00078       DOUBLE PRECISION   DLAMCH
00079       EXTERNAL           IDAMAX, DLAMCH
00080 *     ..
00081 *     .. Intrinsic Functions ..
00082       INTRINSIC          ABS
00083 *     ..
00084 *     .. Executable Statements ..
00085 *
00086 *      Set constant to control owerflow
00087 *
00088       EPS = DLAMCH( 'P' )
00089       SMLNUM = DLAMCH( 'S' ) / EPS
00090       BIGNUM = ONE / SMLNUM
00091       CALL DLABAD( SMLNUM, BIGNUM )
00092 *
00093 *     Apply permutations IPIV to RHS
00094 *
00095       CALL DLASWP( 1, RHS, LDA, 1, N-1, IPIV, 1 )
00096 *
00097 *     Solve for L part
00098 *
00099       DO 20 I = 1, N - 1
00100          DO 10 J = I + 1, N
00101             RHS( J ) = RHS( J ) - A( J, I )*RHS( I )
00102    10    CONTINUE
00103    20 CONTINUE
00104 *
00105 *     Solve for U part
00106 *
00107       SCALE = ONE
00108 *
00109 *     Check for scaling
00110 *
00111       I = IDAMAX( N, RHS, 1 )
00112       IF( TWO*SMLNUM*ABS( RHS( I ) ).GT.ABS( A( N, N ) ) ) THEN
00113          TEMP = ( ONE / TWO ) / ABS( RHS( I ) )
00114          CALL DSCAL( N, TEMP, RHS( 1 ), 1 )
00115          SCALE = SCALE*TEMP
00116       END IF
00117 *
00118       DO 40 I = N, 1, -1
00119          TEMP = ONE / A( I, I )
00120          RHS( I ) = RHS( I )*TEMP
00121          DO 30 J = I + 1, N
00122             RHS( I ) = RHS( I ) - RHS( J )*( A( I, J )*TEMP )
00123    30    CONTINUE
00124    40 CONTINUE
00125 *
00126 *     Apply permutations JPIV to the solution (RHS)
00127 *
00128       CALL DLASWP( 1, RHS, LDA, 1, N-1, JPIV, -1 )
00129       RETURN
00130 *
00131 *     End of DGESC2
00132 *
00133       END
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