LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
dgesc2.f
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00001 *> \brief \b DGESC2
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download DGESC2 + dependencies 
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00011 *> [TGZ]</a> 
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00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgesc2.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE DGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       INTEGER            LDA, N
00025 *       DOUBLE PRECISION   SCALE
00026 *       ..
00027 *       .. Array Arguments ..
00028 *       INTEGER            IPIV( * ), JPIV( * )
00029 *       DOUBLE PRECISION   A( LDA, * ), RHS( * )
00030 *       ..
00031 *  
00032 *
00033 *> \par Purpose:
00034 *  =============
00035 *>
00036 *> \verbatim
00037 *>
00038 *> DGESC2 solves a system of linear equations
00039 *>
00040 *>           A * X = scale* RHS
00041 *>
00042 *> with a general N-by-N matrix A using the LU factorization with
00043 *> complete pivoting computed by DGETC2.
00044 *> \endverbatim
00045 *
00046 *  Arguments:
00047 *  ==========
00048 *
00049 *> \param[in] N
00050 *> \verbatim
00051 *>          N is INTEGER
00052 *>          The order of the matrix A.
00053 *> \endverbatim
00054 *>
00055 *> \param[in] A
00056 *> \verbatim
00057 *>          A is DOUBLE PRECISION array, dimension (LDA,N)
00058 *>          On entry, the  LU part of the factorization of the n-by-n
00059 *>          matrix A computed by DGETC2:  A = P * L * U * Q
00060 *> \endverbatim
00061 *>
00062 *> \param[in] LDA
00063 *> \verbatim
00064 *>          LDA is INTEGER
00065 *>          The leading dimension of the array A.  LDA >= max(1, N).
00066 *> \endverbatim
00067 *>
00068 *> \param[in,out] RHS
00069 *> \verbatim
00070 *>          RHS is DOUBLE PRECISION array, dimension (N).
00071 *>          On entry, the right hand side vector b.
00072 *>          On exit, the solution vector X.
00073 *> \endverbatim
00074 *>
00075 *> \param[in] IPIV
00076 *> \verbatim
00077 *>          IPIV is INTEGER array, dimension (N).
00078 *>          The pivot indices; for 1 <= i <= N, row i of the
00079 *>          matrix has been interchanged with row IPIV(i).
00080 *> \endverbatim
00081 *>
00082 *> \param[in] JPIV
00083 *> \verbatim
00084 *>          JPIV is INTEGER array, dimension (N).
00085 *>          The pivot indices; for 1 <= j <= N, column j of the
00086 *>          matrix has been interchanged with column JPIV(j).
00087 *> \endverbatim
00088 *>
00089 *> \param[out] SCALE
00090 *> \verbatim
00091 *>          SCALE is DOUBLE PRECISION
00092 *>          On exit, SCALE contains the scale factor. SCALE is chosen
00093 *>          0 <= SCALE <= 1 to prevent owerflow in the solution.
00094 *> \endverbatim
00095 *
00096 *  Authors:
00097 *  ========
00098 *
00099 *> \author Univ. of Tennessee 
00100 *> \author Univ. of California Berkeley 
00101 *> \author Univ. of Colorado Denver 
00102 *> \author NAG Ltd. 
00103 *
00104 *> \date November 2011
00105 *
00106 *> \ingroup doubleGEauxiliary
00107 *
00108 *> \par Contributors:
00109 *  ==================
00110 *>
00111 *>     Bo Kagstrom and Peter Poromaa, Department of Computing Science,
00112 *>     Umea University, S-901 87 Umea, Sweden.
00113 *
00114 *  =====================================================================
00115       SUBROUTINE DGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE )
00116 *
00117 *  -- LAPACK auxiliary routine (version 3.4.0) --
00118 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00119 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00120 *     November 2011
00121 *
00122 *     .. Scalar Arguments ..
00123       INTEGER            LDA, N
00124       DOUBLE PRECISION   SCALE
00125 *     ..
00126 *     .. Array Arguments ..
00127       INTEGER            IPIV( * ), JPIV( * )
00128       DOUBLE PRECISION   A( LDA, * ), RHS( * )
00129 *     ..
00130 *
00131 *  =====================================================================
00132 *
00133 *     .. Parameters ..
00134       DOUBLE PRECISION   ONE, TWO
00135       PARAMETER          ( ONE = 1.0D+0, TWO = 2.0D+0 )
00136 *     ..
00137 *     .. Local Scalars ..
00138       INTEGER            I, J
00139       DOUBLE PRECISION   BIGNUM, EPS, SMLNUM, TEMP
00140 *     ..
00141 *     .. External Subroutines ..
00142       EXTERNAL           DLASWP, DSCAL
00143 *     ..
00144 *     .. External Functions ..
00145       INTEGER            IDAMAX
00146       DOUBLE PRECISION   DLAMCH
00147       EXTERNAL           IDAMAX, DLAMCH
00148 *     ..
00149 *     .. Intrinsic Functions ..
00150       INTRINSIC          ABS
00151 *     ..
00152 *     .. Executable Statements ..
00153 *
00154 *      Set constant to control owerflow
00155 *
00156       EPS = DLAMCH( 'P' )
00157       SMLNUM = DLAMCH( 'S' ) / EPS
00158       BIGNUM = ONE / SMLNUM
00159       CALL DLABAD( SMLNUM, BIGNUM )
00160 *
00161 *     Apply permutations IPIV to RHS
00162 *
00163       CALL DLASWP( 1, RHS, LDA, 1, N-1, IPIV, 1 )
00164 *
00165 *     Solve for L part
00166 *
00167       DO 20 I = 1, N - 1
00168          DO 10 J = I + 1, N
00169             RHS( J ) = RHS( J ) - A( J, I )*RHS( I )
00170    10    CONTINUE
00171    20 CONTINUE
00172 *
00173 *     Solve for U part
00174 *
00175       SCALE = ONE
00176 *
00177 *     Check for scaling
00178 *
00179       I = IDAMAX( N, RHS, 1 )
00180       IF( TWO*SMLNUM*ABS( RHS( I ) ).GT.ABS( A( N, N ) ) ) THEN
00181          TEMP = ( ONE / TWO ) / ABS( RHS( I ) )
00182          CALL DSCAL( N, TEMP, RHS( 1 ), 1 )
00183          SCALE = SCALE*TEMP
00184       END IF
00185 *
00186       DO 40 I = N, 1, -1
00187          TEMP = ONE / A( I, I )
00188          RHS( I ) = RHS( I )*TEMP
00189          DO 30 J = I + 1, N
00190             RHS( I ) = RHS( I ) - RHS( J )*( A( I, J )*TEMP )
00191    30    CONTINUE
00192    40 CONTINUE
00193 *
00194 *     Apply permutations JPIV to the solution (RHS)
00195 *
00196       CALL DLASWP( 1, RHS, LDA, 1, N-1, JPIV, -1 )
00197       RETURN
00198 *
00199 *     End of DGESC2
00200 *
00201       END
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