dsbgvx.f.html

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</span><span class="comment">*</span><span class="comment">          or equal to zero, then  EPS*|T|  will be used in its place,
</span><span class="comment">*</span><span class="comment">          where |T| is the 1-norm of the tridiagonal matrix obtained
</span><span class="comment">*</span><span class="comment">          by reducing A to tridiagonal form.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          Eigenvalues will be computed most accurately when ABSTOL is
</span><span class="comment">*</span><span class="comment">          set to twice the underflow threshold 2*<a name="DLAMCH.123"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>('S'), not zero.
</span><span class="comment">*</span><span class="comment">          If this routine returns with INFO&gt;0, indicating that some
</span><span class="comment">*</span><span class="comment">          eigenvectors did not converge, try setting ABSTOL to
</span><span class="comment">*</span><span class="comment">          2*<a name="DLAMCH.126"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>('S').
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  M       (output) INTEGER
</span><span class="comment">*</span><span class="comment">          The total number of eigenvalues found.  0 &lt;= M &lt;= N.
</span><span class="comment">*</span><span class="comment">          If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  W       (output) DOUBLE PRECISION array, dimension (N)
</span><span class="comment">*</span><span class="comment">          If INFO = 0, the eigenvalues in ascending order.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Z       (output) DOUBLE PRECISION array, dimension (LDZ, N)
</span><span class="comment">*</span><span class="comment">          If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
</span><span class="comment">*</span><span class="comment">          eigenvectors, with the i-th column of Z holding the
</span><span class="comment">*</span><span class="comment">          eigenvector associated with W(i).  The eigenvectors are
</span><span class="comment">*</span><span class="comment">          normalized so Z**T*B*Z = I.
</span><span class="comment">*</span><span class="comment">          If JOBZ = 'N', then Z is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDZ     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array Z.  LDZ &gt;= 1, and if
</span><span class="comment">*</span><span class="comment">          JOBZ = 'V', LDZ &gt;= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK    (workspace/output) DOUBLE PRECISION array, dimension (7*N)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  IWORK   (workspace/output) INTEGER array, dimension (5*N)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  IFAIL   (output) INTEGER array, dimension (M)
</span><span class="comment">*</span><span class="comment">          If JOBZ = 'V', then if INFO = 0, the first M elements of
</span><span class="comment">*</span><span class="comment">          IFAIL are zero.  If INFO &gt; 0, then IFAIL contains the
</span><span class="comment">*</span><span class="comment">          indices of the eigenvalues that failed to converge.
</span><span class="comment">*</span><span class="comment">          If JOBZ = 'N', then IFAIL is not referenced.
</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">          &lt;= N: if INFO = i, then i eigenvectors failed to converge.
</span><span class="comment">*</span><span class="comment">                  Their indices are stored in IFAIL.
</span><span class="comment">*</span><span class="comment">          &gt; N : <a name="DPBSTF.161"></a><a href="dpbstf.f.html#DPBSTF.1">DPBSTF</a> returned an error code; i.e.,
</span><span class="comment">*</span><span class="comment">                if INFO = N + i, for 1 &lt;= i &lt;= N, then the leading
</span><span class="comment">*</span><span class="comment">                minor of order i of B is not positive definite.
</span><span class="comment">*</span><span class="comment">                The factorization of B could not be completed and
</span><span class="comment">*</span><span class="comment">                no eigenvalues or eigenvectors were computed.
</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">  Based on contributions by
</span><span class="comment">*</span><span class="comment">     Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
</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   ZERO, ONE
      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            ALLEIG, INDEIG, TEST, UPPER, VALEIG, WANTZ
      CHARACTER          ORDER, VECT
      INTEGER            I, IINFO, INDD, INDE, INDEE, INDIBL, INDISP,
     $                   INDIWO, INDWRK, ITMP1, J, JJ, NSPLIT
      DOUBLE PRECISION   TMP1
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.187"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      EXTERNAL           <a name="LSAME.188"></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           DCOPY, DGEMV, <a name="DLACPY.191"></a><a href="dlacpy.f.html#DLACPY.1">DLACPY</a>, <a name="DPBSTF.191"></a><a href="dpbstf.f.html#DPBSTF.1">DPBSTF</a>, <a name="DSBGST.191"></a><a href="dsbgst.f.html#DSBGST.1">DSBGST</a>, <a name="DSBTRD.191"></a><a href="dsbtrd.f.html#DSBTRD.1">DSBTRD</a>,
     $                   <a name="DSTEBZ.192"></a><a href="dstebz.f.html#DSTEBZ.1">DSTEBZ</a>, <a name="DSTEIN.192"></a><a href="dstein.f.html#DSTEIN.1">DSTEIN</a>, <a name="DSTEQR.192"></a><a href="dsteqr.f.html#DSTEQR.1">DSTEQR</a>, <a name="DSTERF.192"></a><a href="dsterf.f.html#DSTERF.1">DSTERF</a>, DSWAP, <a name="XERBLA.192"></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          MIN
<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>      WANTZ = <a name="LSAME.201"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBZ, <span class="string">'V'</span> )
      UPPER = <a name="LSAME.202"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> )
      ALLEIG = <a name="LSAME.203"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( RANGE, <span class="string">'A'</span> )
      VALEIG = <a name="LSAME.204"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( RANGE, <span class="string">'V'</span> )
      INDEIG = <a name="LSAME.205"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( RANGE, <span class="string">'I'</span> )
<span class="comment">*</span><span class="comment">
</span>      INFO = 0
      IF( .NOT.( WANTZ .OR. <a name="LSAME.208"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBZ, <span class="string">'N'</span> ) ) ) THEN
         INFO = -1
      ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
         INFO = -2
      ELSE IF( .NOT.( UPPER .OR. <a name="LSAME.212"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'L'</span> ) ) ) THEN
         INFO = -3
      ELSE IF( N.LT.0 ) THEN
         INFO = -4
      ELSE IF( KA.LT.0 ) THEN
         INFO = -5
      ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN
         INFO = -6
      ELSE IF( LDAB.LT.KA+1 ) THEN
         INFO = -8
      ELSE IF( LDBB.LT.KB+1 ) THEN
         INFO = -10
      ELSE IF( LDQ.LT.1 .OR. ( WANTZ .AND. LDQ.LT.N ) ) THEN
         INFO = -12
      ELSE
         IF( VALEIG ) THEN
            IF( N.GT.0 .AND. VU.LE.VL )
     $         INFO = -14
         ELSE IF( INDEIG ) THEN
            IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN
               INFO = -15
            ELSE IF ( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
               INFO = -16
            END IF
         END IF
      END IF
      IF( INFO.EQ.0) THEN
         IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
            INFO = -21
         END IF
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.245"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="DSBGVX.245"></a><a href="dsbgvx.f.html#DSBGVX.1">DSBGVX</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>      M = 0
      IF( N.EQ.0 )
     $   RETURN