cgtsvx.f.html

来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 317 行 · 第 1/2 页

</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  X       (output) COMPLEX array, dimension (LDX,NRHS)
</span><span class="comment">*</span><span class="comment">          If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDX     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array X.  LDX &gt;= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  RCOND   (output) REAL
</span><span class="comment">*</span><span class="comment">          The estimate of the reciprocal condition number of the matrix
</span><span class="comment">*</span><span class="comment">          A.  If RCOND is less than the machine precision (in
</span><span class="comment">*</span><span class="comment">          particular, if RCOND = 0), the matrix is singular to working
</span><span class="comment">*</span><span class="comment">          precision.  This condition is indicated by a return code of
</span><span class="comment">*</span><span class="comment">          INFO &gt; 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  FERR    (output) REAL array, dimension (NRHS)
</span><span class="comment">*</span><span class="comment">          The estimated forward error bound for each solution vector
</span><span class="comment">*</span><span class="comment">          X(j) (the j-th column of the solution matrix X).
</span><span class="comment">*</span><span class="comment">          If XTRUE is the true solution corresponding to X(j), FERR(j)
</span><span class="comment">*</span><span class="comment">          is an estimated upper bound for the magnitude of the largest
</span><span class="comment">*</span><span class="comment">          element in (X(j) - XTRUE) divided by the magnitude of the
</span><span class="comment">*</span><span class="comment">          largest element in X(j).  The estimate is as reliable as
</span><span class="comment">*</span><span class="comment">          the estimate for RCOND, and is almost always a slight
</span><span class="comment">*</span><span class="comment">          overestimate of the true error.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  BERR    (output) REAL array, dimension (NRHS)
</span><span class="comment">*</span><span class="comment">          The componentwise relative backward error of each solution
</span><span class="comment">*</span><span class="comment">          vector X(j) (i.e., the smallest relative change in
</span><span class="comment">*</span><span class="comment">          any element of A or B that makes X(j) an exact solution).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK    (workspace) COMPLEX array, dimension (2*N)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  RWORK   (workspace) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INFO    (output) INTEGER
</span><span class="comment">*</span><span class="comment">          = 0:  successful exit
</span><span class="comment">*</span><span class="comment">          &lt; 0:  if INFO = -i, the i-th argument had an illegal value
</span><span class="comment">*</span><span class="comment">          &gt; 0:  if INFO = i, and i is
</span><span class="comment">*</span><span class="comment">                &lt;= N:  U(i,i) is exactly zero.  The factorization
</span><span class="comment">*</span><span class="comment">                       has not been completed unless i = N, but the
</span><span class="comment">*</span><span class="comment">                       factor U is exactly singular, so the solution
</span><span class="comment">*</span><span class="comment">                       and error bounds could not be computed.
</span><span class="comment">*</span><span class="comment">                       RCOND = 0 is returned.
</span><span class="comment">*</span><span class="comment">                = N+1: U is nonsingular, but RCOND is less than machine
</span><span class="comment">*</span><span class="comment">                       precision, meaning that the matrix is singular
</span><span class="comment">*</span><span class="comment">                       to working precision.  Nevertheless, the
</span><span class="comment">*</span><span class="comment">                       solution and error bounds are computed because
</span><span class="comment">*</span><span class="comment">                       there are a number of situations where the
</span><span class="comment">*</span><span class="comment">                       computed solution can be more accurate than the
</span><span class="comment">*</span><span class="comment">                       value of RCOND would suggest.
</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>      REAL               ZERO
      PARAMETER          ( ZERO = 0.0E+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            NOFACT, NOTRAN
      CHARACTER          NORM
      REAL               ANORM
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.203"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      REAL               <a name="CLANGT.204"></a><a href="clangt.f.html#CLANGT.1">CLANGT</a>, <a name="SLAMCH.204"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>
      EXTERNAL           <a name="LSAME.205"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="CLANGT.205"></a><a href="clangt.f.html#CLANGT.1">CLANGT</a>, <a name="SLAMCH.205"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           CCOPY, <a name="CGTCON.208"></a><a href="cgtcon.f.html#CGTCON.1">CGTCON</a>, <a name="CGTRFS.208"></a><a href="cgtrfs.f.html#CGTRFS.1">CGTRFS</a>, <a name="CGTTRF.208"></a><a href="cgttrf.f.html#CGTTRF.1">CGTTRF</a>, <a name="CGTTRS.208"></a><a href="cgttrs.f.html#CGTTRS.1">CGTTRS</a>, <a name="CLACPY.208"></a><a href="clacpy.f.html#CLACPY.1">CLACPY</a>,
     $                   <a name="XERBLA.209"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          MAX
<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>      INFO = 0
      NOFACT = <a name="LSAME.217"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( FACT, <span class="string">'N'</span> )
      NOTRAN = <a name="LSAME.218"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( TRANS, <span class="string">'N'</span> )
      IF( .NOT.NOFACT .AND. .NOT.<a name="LSAME.219"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( FACT, <span class="string">'F'</span> ) ) THEN
         INFO = -1
      ELSE IF( .NOT.NOTRAN .AND. .NOT.<a name="LSAME.221"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( TRANS, <span class="string">'T'</span> ) .AND. .NOT.
     $         <a name="LSAME.222"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( TRANS, <span class="string">'C'</span> ) ) THEN
         INFO = -2
      ELSE IF( N.LT.0 ) THEN
         INFO = -3
      ELSE IF( NRHS.LT.0 ) THEN
         INFO = -4
      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
         INFO = -14
      ELSE IF( LDX.LT.MAX( 1, N ) ) THEN
         INFO = -16
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.234"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="CGTSVX.234"></a><a href="cgtsvx.f.html#CGTSVX.1">CGTSVX</a>'</span>, -INFO )
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( NOFACT ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Compute the LU factorization of A.
</span><span class="comment">*</span><span class="comment">
</span>         CALL CCOPY( N, D, 1, DF, 1 )
         IF( N.GT.1 ) THEN
            CALL CCOPY( N-1, DL, 1, DLF, 1 )
            CALL CCOPY( N-1, DU, 1, DUF, 1 )
         END IF
         CALL <a name="CGTTRF.247"></a><a href="cgttrf.f.html#CGTTRF.1">CGTTRF</a>( N, DLF, DF, DUF, DU2, IPIV, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Return if INFO is non-zero.
</span><span class="comment">*</span><span class="comment">
</span>         IF( INFO.GT.0 )THEN
            RCOND = ZERO
            RETURN
         END IF
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Compute the norm of the matrix A.
</span><span class="comment">*</span><span class="comment">
</span>      IF( NOTRAN ) THEN
         NORM = <span class="string">'1'</span>
      ELSE
         NORM = <span class="string">'I'</span>
      END IF
      ANORM = <a name="CLANGT.264"></a><a href="clangt.f.html#CLANGT.1">CLANGT</a>( NORM, N, DL, D, DU )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Compute the reciprocal of the condition number of A.
</span><span class="comment">*</span><span class="comment">
</span>      CALL <a name="CGTCON.268"></a><a href="cgtcon.f.html#CGTCON.1">CGTCON</a>( NORM, N, DLF, DF, DUF, DU2, IPIV, ANORM, RCOND, WORK,
     $             INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Compute the solution vectors X.
</span><span class="comment">*</span><span class="comment">
</span>      CALL <a name="CLACPY.273"></a><a href="clacpy.f.html#CLACPY.1">CLACPY</a>( <span class="string">'Full'</span>, N, NRHS, B, LDB, X, LDX )
      CALL <a name="CGTTRS.274"></a><a href="cgttrs.f.html#CGTTRS.1">CGTTRS</a>( TRANS, N, NRHS, DLF, DF, DUF, DU2, IPIV, X, LDX,
     $             INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Use iterative refinement to improve the computed solutions and
</span><span class="comment">*</span><span class="comment">     compute error bounds and backward error estimates for them.
</span><span class="comment">*</span><span class="comment">
</span>      CALL <a name="CGTRFS.280"></a><a href="cgtrfs.f.html#CGTRFS.1">CGTRFS</a>( TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV,
     $             B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Set INFO = N+1 if the matrix is singular to working precision.
</span><span class="comment">*</span><span class="comment">
</span>      IF( RCOND.LT.<a name="SLAMCH.285"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>( <span class="string">'Epsilon'</span> ) )
     $   INFO = N + 1
<span class="comment">*</span><span class="comment">
</span>      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="CGTSVX.290"></a><a href="cgtsvx.f.html#CGTSVX.1">CGTSVX</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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