sptsvx.f.html

来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 258 行 · 第 1/2 页

</span><span class="comment">*</span><span class="comment">          This condition is indicated by a return code of 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 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).
</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 any
</span><span class="comment">*</span><span class="comment">          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) REAL array, dimension (2*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:  the leading minor of order i of A is
</span><span class="comment">*</span><span class="comment">                       not positive definite, so the factorization
</span><span class="comment">*</span><span class="comment">                       could not be completed, and the solution has not
</span><span class="comment">*</span><span class="comment">                       been computed. 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
      REAL               ANORM
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.155"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      REAL               <a name="SLAMCH.156"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>, <a name="SLANST.156"></a><a href="slanst.f.html#SLANST.1">SLANST</a>
      EXTERNAL           <a name="LSAME.157"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="SLAMCH.157"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>, <a name="SLANST.157"></a><a href="slanst.f.html#SLANST.1">SLANST</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           SCOPY, <a name="SLACPY.160"></a><a href="slacpy.f.html#SLACPY.1">SLACPY</a>, <a name="SPTCON.160"></a><a href="sptcon.f.html#SPTCON.1">SPTCON</a>, <a name="SPTRFS.160"></a><a href="sptrfs.f.html#SPTRFS.1">SPTRFS</a>, <a name="SPTTRF.160"></a><a href="spttrf.f.html#SPTTRF.1">SPTTRF</a>, <a name="SPTTRS.160"></a><a href="spttrs.f.html#SPTTRS.1">SPTTRS</a>,
     $                   <a name="XERBLA.161"></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><span class="comment">*</span><span class="comment">     Test the input parameters.
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
      NOFACT = <a name="LSAME.171"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( FACT, <span class="string">'N'</span> )
      IF( .NOT.NOFACT .AND. .NOT.<a name="LSAME.172"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( FACT, <span class="string">'F'</span> ) ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( NRHS.LT.0 ) THEN
         INFO = -3
      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
         INFO = -9
      ELSE IF( LDX.LT.MAX( 1, N ) ) THEN
         INFO = -11
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.184"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="SPTSVX.184"></a><a href="sptsvx.f.html#SPTSVX.1">SPTSVX</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 L*D*L' (or U'*D*U) factorization of A.
</span><span class="comment">*</span><span class="comment">
</span>         CALL SCOPY( N, D, 1, DF, 1 )
         IF( N.GT.1 )
     $      CALL SCOPY( N-1, E, 1, EF, 1 )
         CALL <a name="SPTTRF.195"></a><a href="spttrf.f.html#SPTTRF.1">SPTTRF</a>( N, DF, EF, 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>      ANORM = <a name="SLANST.207"></a><a href="slanst.f.html#SLANST.1">SLANST</a>( <span class="string">'1'</span>, N, D, E )
<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="SPTCON.211"></a><a href="sptcon.f.html#SPTCON.1">SPTCON</a>( N, DF, EF, 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="SLACPY.215"></a><a href="slacpy.f.html#SLACPY.1">SLACPY</a>( <span class="string">'Full'</span>, N, NRHS, B, LDB, X, LDX )
      CALL <a name="SPTTRS.216"></a><a href="spttrs.f.html#SPTTRS.1">SPTTRS</a>( N, NRHS, DF, EF, 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="SPTRFS.221"></a><a href="sptrfs.f.html#SPTRFS.1">SPTRFS</a>( N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR,
     $             WORK, 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.226"></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="SPTSVX.231"></a><a href="sptsvx.f.html#SPTSVX.1">SPTSVX</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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