dgesc2.f.html

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      SUBROUTINE <a name="DGESC2.1"></a><a href="dgesc2.f.html#DGESC2.1">DGESC2</a>( N, A, LDA, RHS, IPIV, JPIV, SCALE )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK auxiliary routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      INTEGER            LDA, N
      DOUBLE PRECISION   SCALE
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      INTEGER            IPIV( * ), JPIV( * )
      DOUBLE PRECISION   A( LDA, * ), RHS( * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="DGESC2.19"></a><a href="dgesc2.f.html#DGESC2.1">DGESC2</a> solves a system of linear equations
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">            A * X = scale* RHS
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  with a general N-by-N matrix A using the LU factorization with
</span><span class="comment">*</span><span class="comment">  complete pivoting computed by <a name="DGETC2.24"></a><a href="dgetc2.f.html#DGETC2.1">DGETC2</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The order of the matrix A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  A       (input) DOUBLE PRECISION array, dimension (LDA,N)
</span><span class="comment">*</span><span class="comment">          On entry, the  LU part of the factorization of the n-by-n
</span><span class="comment">*</span><span class="comment">          matrix A computed by <a name="DGETC2.34"></a><a href="dgetc2.f.html#DGETC2.1">DGETC2</a>:  A = P * L * U * Q
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDA     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array A.  LDA &gt;= max(1, N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  RHS     (input/output) DOUBLE PRECISION array, dimension (N).
</span><span class="comment">*</span><span class="comment">          On entry, the right hand side vector b.
</span><span class="comment">*</span><span class="comment">          On exit, the solution vector X.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  IPIV    (input) INTEGER array, dimension (N).
</span><span class="comment">*</span><span class="comment">          The pivot indices; for 1 &lt;= i &lt;= N, row i of the
</span><span class="comment">*</span><span class="comment">          matrix has been interchanged with row IPIV(i).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  JPIV    (input) INTEGER array, dimension (N).
</span><span class="comment">*</span><span class="comment">          The pivot indices; for 1 &lt;= j &lt;= N, column j of the
</span><span class="comment">*</span><span class="comment">          matrix has been interchanged with column JPIV(j).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  SCALE    (output) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment">           On exit, SCALE contains the scale factor. SCALE is chosen
</span><span class="comment">*</span><span class="comment">           0 &lt;= SCALE &lt;= 1 to prevent owerflow in the solution.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Further Details
</span><span class="comment">*</span><span class="comment">  ===============
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Based on contributions by
</span><span class="comment">*</span><span class="comment">     Bo Kagstrom and Peter Poromaa, Department of Computing Science,
</span><span class="comment">*</span><span class="comment">     Umea University, S-901 87 Umea, Sweden.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      DOUBLE PRECISION   ONE, TWO
      PARAMETER          ( ONE = 1.0D+0, TWO = 2.0D+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      INTEGER            I, J
      DOUBLE PRECISION   BIGNUM, EPS, SMLNUM, TEMP
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="DLASWP.73"></a><a href="dlaswp.f.html#DLASWP.1">DLASWP</a>, DSCAL
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      INTEGER            IDAMAX
      DOUBLE PRECISION   <a name="DLAMCH.77"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>
      EXTERNAL           IDAMAX, <a name="DLAMCH.78"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          ABS
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">      Set constant to control owerflow
</span><span class="comment">*</span><span class="comment">
</span>      EPS = <a name="DLAMCH.87"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>( <span class="string">'P'</span> )
      SMLNUM = <a name="DLAMCH.88"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>( <span class="string">'S'</span> ) / EPS
      BIGNUM = ONE / SMLNUM
      CALL <a name="DLABAD.90"></a><a href="dlabad.f.html#DLABAD.1">DLABAD</a>( SMLNUM, BIGNUM )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Apply permutations IPIV to RHS
</span><span class="comment">*</span><span class="comment">
</span>      CALL <a name="DLASWP.94"></a><a href="dlaswp.f.html#DLASWP.1">DLASWP</a>( 1, RHS, LDA, 1, N-1, IPIV, 1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Solve for L part
</span><span class="comment">*</span><span class="comment">
</span>      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
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Solve for U part
</span><span class="comment">*</span><span class="comment">
</span>      SCALE = ONE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Check for scaling
</span><span class="comment">*</span><span class="comment">
</span>      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
<span class="comment">*</span><span class="comment">
</span>      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
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Apply permutations JPIV to the solution (RHS)
</span><span class="comment">*</span><span class="comment">
</span>      CALL <a name="DLASWP.127"></a><a href="dlaswp.f.html#DLASWP.1">DLASWP</a>( 1, RHS, LDA, 1, N-1, JPIV, -1 )
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="DGESC2.130"></a><a href="dgesc2.f.html#DGESC2.1">DGESC2</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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