cptsvx.f.html

来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 261 行 · 第 1/2 页

</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) COMPLEX array, dimension (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:  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.158"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      REAL               <a name="CLANHT.159"></a><a href="clanht.f.html#CLANHT.1">CLANHT</a>, <a name="SLAMCH.159"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>
      EXTERNAL           <a name="LSAME.160"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="CLANHT.160"></a><a href="clanht.f.html#CLANHT.1">CLANHT</a>, <a name="SLAMCH.160"></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="CLACPY.163"></a><a href="clacpy.f.html#CLACPY.1">CLACPY</a>, <a name="CPTCON.163"></a><a href="cptcon.f.html#CPTCON.1">CPTCON</a>, <a name="CPTRFS.163"></a><a href="cptrfs.f.html#CPTRFS.1">CPTRFS</a>, <a name="CPTTRF.163"></a><a href="cpttrf.f.html#CPTTRF.1">CPTTRF</a>, <a name="CPTTRS.163"></a><a href="cpttrs.f.html#CPTTRS.1">CPTTRS</a>,
     $                   SCOPY, <a name="XERBLA.164"></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.174"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( FACT, <span class="string">'N'</span> )
      IF( .NOT.NOFACT .AND. .NOT.<a name="LSAME.175"></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.187"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="CPTSVX.187"></a><a href="cptsvx.f.html#CPTSVX.1">CPTSVX</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 CCOPY( N-1, E, 1, EF, 1 )
         CALL <a name="CPTTRF.198"></a><a href="cpttrf.f.html#CPTTRF.1">CPTTRF</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="CLANHT.210"></a><a href="clanht.f.html#CLANHT.1">CLANHT</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="CPTCON.214"></a><a href="cptcon.f.html#CPTCON.1">CPTCON</a>( N, DF, EF, ANORM, RCOND, RWORK, 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.218"></a><a href="clacpy.f.html#CLACPY.1">CLACPY</a>( <span class="string">'Full'</span>, N, NRHS, B, LDB, X, LDX )
      CALL <a name="CPTTRS.219"></a><a href="cpttrs.f.html#CPTTRS.1">CPTTRS</a>( <span class="string">'Lower'</span>, 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="CPTRFS.224"></a><a href="cptrfs.f.html#CPTRFS.1">CPTRFS</a>( <span class="string">'Lower'</span>, N, NRHS, D, E, DF, EF, 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.229"></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="CPTSVX.234"></a><a href="cptsvx.f.html#CPTSVX.1">CPTSVX</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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