chpsvx.f.html

来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 302 行 · 第 1/2 页

</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:  D(i,i) is exactly zero.  The factorization
</span><span class="comment">*</span><span class="comment">                       has been completed but the factor D is exactly
</span><span class="comment">*</span><span class="comment">                       singular, so the solution and error bounds could
</span><span class="comment">*</span><span class="comment">                       not be computed. RCOND = 0 is returned.
</span><span class="comment">*</span><span class="comment">                = N+1: D 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">  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">  The packed storage scheme is illustrated by the following example
</span><span class="comment">*</span><span class="comment">  when N = 4, UPLO = 'U':
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Two-dimensional storage of the Hermitian matrix A:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     a11 a12 a13 a14
</span><span class="comment">*</span><span class="comment">         a22 a23 a24
</span><span class="comment">*</span><span class="comment">             a33 a34     (aij = conjg(aji))
</span><span class="comment">*</span><span class="comment">                 a44
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Packed storage of the upper triangle of A:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
</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.198"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      REAL               <a name="CLANHP.199"></a><a href="clanhp.f.html#CLANHP.1">CLANHP</a>, <a name="SLAMCH.199"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>
      EXTERNAL           <a name="LSAME.200"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="CLANHP.200"></a><a href="clanhp.f.html#CLANHP.1">CLANHP</a>, <a name="SLAMCH.200"></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="CHPCON.203"></a><a href="chpcon.f.html#CHPCON.1">CHPCON</a>, <a name="CHPRFS.203"></a><a href="chprfs.f.html#CHPRFS.1">CHPRFS</a>, <a name="CHPTRF.203"></a><a href="chptrf.f.html#CHPTRF.1">CHPTRF</a>, <a name="CHPTRS.203"></a><a href="chptrs.f.html#CHPTRS.1">CHPTRS</a>, <a name="CLACPY.203"></a><a href="clacpy.f.html#CLACPY.1">CLACPY</a>,
     $                   <a name="XERBLA.204"></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.214"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( FACT, <span class="string">'N'</span> )
      IF( .NOT.NOFACT .AND. .NOT.<a name="LSAME.215"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( FACT, <span class="string">'F'</span> ) ) THEN
         INFO = -1
      ELSE IF( .NOT.<a name="LSAME.217"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> ) .AND. .NOT.<a name="LSAME.217"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'L'</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 = -9
      ELSE IF( LDX.LT.MAX( 1, N ) ) THEN
         INFO = -11
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.230"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="CHPSVX.230"></a><a href="chpsvx.f.html#CHPSVX.1">CHPSVX</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 factorization A = U*D*U' or A = L*D*L'.
</span><span class="comment">*</span><span class="comment">
</span>         CALL CCOPY( N*( N+1 ) / 2, AP, 1, AFP, 1 )
         CALL <a name="CHPTRF.239"></a><a href="chptrf.f.html#CHPTRF.1">CHPTRF</a>( UPLO, N, AFP, 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>      ANORM = <a name="CLANHP.251"></a><a href="clanhp.f.html#CLANHP.1">CLANHP</a>( <span class="string">'I'</span>, UPLO, N, AP, RWORK )
<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="CHPCON.255"></a><a href="chpcon.f.html#CHPCON.1">CHPCON</a>( UPLO, N, AFP, 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.259"></a><a href="clacpy.f.html#CLACPY.1">CLACPY</a>( <span class="string">'Full'</span>, N, NRHS, B, LDB, X, LDX )
      CALL <a name="CHPTRS.260"></a><a href="chptrs.f.html#CHPTRS.1">CHPTRS</a>( UPLO, N, NRHS, AFP, 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="CHPRFS.265"></a><a href="chprfs.f.html#CHPRFS.1">CHPRFS</a>( UPLO, N, NRHS, AP, AFP, 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.270"></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="CHPSVX.275"></a><a href="chpsvx.f.html#CHPSVX.1">CHPSVX</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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