dgtcon.f.html

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      SUBROUTINE <a name="DGTCON.1"></a><a href="dgtcon.f.html#DGTCON.1">DGTCON</a>( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND,
     $                   WORK, IWORK, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK 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">     Modified to call <a name="DLACN2.8"></a><a href="dlacn2.f.html#DLACN2.1">DLACN2</a> in place of <a name="DLACON.8"></a><a href="dlacon.f.html#DLACON.1">DLACON</a>, 5 Feb 03, SJH.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      CHARACTER          NORM
      INTEGER            INFO, N
      DOUBLE PRECISION   ANORM, RCOND
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      INTEGER            IPIV( * ), IWORK( * )
      DOUBLE PRECISION   D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )
<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="DGTCON.23"></a><a href="dgtcon.f.html#DGTCON.1">DGTCON</a> estimates the reciprocal of the condition number of a real
</span><span class="comment">*</span><span class="comment">  tridiagonal matrix A using the LU factorization as computed by
</span><span class="comment">*</span><span class="comment">  <a name="DGTTRF.25"></a><a href="dgttrf.f.html#DGTTRF.1">DGTTRF</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  An estimate is obtained for norm(inv(A)), and the reciprocal of the
</span><span class="comment">*</span><span class="comment">  condition number is computed as RCOND = 1 / (ANORM * norm(inv(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">  NORM    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          Specifies whether the 1-norm condition number or the
</span><span class="comment">*</span><span class="comment">          infinity-norm condition number is required:
</span><span class="comment">*</span><span class="comment">          = '1' or 'O':  1-norm;
</span><span class="comment">*</span><span class="comment">          = 'I':         Infinity-norm.
</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.  N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  DL      (input) DOUBLE PRECISION array, dimension (N-1)
</span><span class="comment">*</span><span class="comment">          The (n-1) multipliers that define the matrix L from the
</span><span class="comment">*</span><span class="comment">          LU factorization of A as computed by <a name="DGTTRF.44"></a><a href="dgttrf.f.html#DGTTRF.1">DGTTRF</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  D       (input) DOUBLE PRECISION array, dimension (N)
</span><span class="comment">*</span><span class="comment">          The n diagonal elements of the upper triangular matrix U from
</span><span class="comment">*</span><span class="comment">          the LU factorization of A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  DU      (input) DOUBLE PRECISION array, dimension (N-1)
</span><span class="comment">*</span><span class="comment">          The (n-1) elements of the first superdiagonal of U.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  DU2     (input) DOUBLE PRECISION array, dimension (N-2)
</span><span class="comment">*</span><span class="comment">          The (n-2) elements of the second superdiagonal of U.
</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 matrix was
</span><span class="comment">*</span><span class="comment">          interchanged with row IPIV(i).  IPIV(i) will always be either
</span><span class="comment">*</span><span class="comment">          i or i+1; IPIV(i) = i indicates a row interchange was not
</span><span class="comment">*</span><span class="comment">          required.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  ANORM   (input) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment">          If NORM = '1' or 'O', the 1-norm of the original matrix A.
</span><span class="comment">*</span><span class="comment">          If NORM = 'I', the infinity-norm of the original matrix A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  RCOND   (output) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment">          The reciprocal of the condition number of the matrix A,
</span><span class="comment">*</span><span class="comment">          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
</span><span class="comment">*</span><span class="comment">          estimate of the 1-norm of inv(A) computed in this routine.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK    (workspace) DOUBLE PRECISION array, dimension (2*N)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  IWORK   (workspace) INTEGER 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">
</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, ZERO
      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            ONENRM
      INTEGER            I, KASE, KASE1
      DOUBLE PRECISION   AINVNM
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Arrays ..
</span>      INTEGER            ISAVE( 3 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.94"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      EXTERNAL           <a name="LSAME.95"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="DGTTRS.98"></a><a href="dgttrs.f.html#DGTTRS.1">DGTTRS</a>, <a name="DLACN2.98"></a><a href="dlacn2.f.html#DLACN2.1">DLACN2</a>, <a name="XERBLA.98"></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">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Test the input arguments.
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
      ONENRM = NORM.EQ.<span class="string">'1'</span> .OR. <a name="LSAME.105"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( NORM, <span class="string">'O'</span> )
      IF( .NOT.ONENRM .AND. .NOT.<a name="LSAME.106"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( NORM, <span class="string">'I'</span> ) ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( ANORM.LT.ZERO ) THEN
         INFO = -8
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.114"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="DGTCON.114"></a><a href="dgtcon.f.html#DGTCON.1">DGTCON</a>'</span>, -INFO )
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span>      RCOND = ZERO
      IF( N.EQ.0 ) THEN
         RCOND = ONE
         RETURN
      ELSE IF( ANORM.EQ.ZERO ) THEN
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Check that D(1:N) is non-zero.
</span><span class="comment">*</span><span class="comment">
</span>      DO 10 I = 1, N
         IF( D( I ).EQ.ZERO )
     $      RETURN
   10 CONTINUE
<span class="comment">*</span><span class="comment">
</span>      AINVNM = ZERO
      IF( ONENRM ) THEN
         KASE1 = 1
      ELSE
         KASE1 = 2
      END IF
      KASE = 0
   20 CONTINUE
      CALL <a name="DLACN2.143"></a><a href="dlacn2.f.html#DLACN2.1">DLACN2</a>( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
      IF( KASE.NE.0 ) THEN
         IF( KASE.EQ.KASE1 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Multiply by inv(U)*inv(L).
</span><span class="comment">*</span><span class="comment">
</span>            CALL <a name="DGTTRS.149"></a><a href="dgttrs.f.html#DGTTRS.1">DGTTRS</a>( <span class="string">'No transpose'</span>, N, 1, DL, D, DU, DU2, IPIV,
     $                   WORK, N, INFO )
         ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Multiply by inv(L')*inv(U').
</span><span class="comment">*</span><span class="comment">
</span>            CALL <a name="DGTTRS.155"></a><a href="dgttrs.f.html#DGTTRS.1">DGTTRS</a>( <span class="string">'Transpose'</span>, N, 1, DL, D, DU, DU2, IPIV, WORK,
     $                   N, INFO )
         END IF
         GO TO 20
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Compute the estimate of the reciprocal condition number.
</span><span class="comment">*</span><span class="comment">
</span>      IF( AINVNM.NE.ZERO )
     $   RCOND = ( ONE / AINVNM ) / ANORM
<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="DGTCON.168"></a><a href="dgtcon.f.html#DGTCON.1">DGTCON</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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