sstevr.f.html

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</span><span class="comment">*</span><span class="comment">          contain the orthonormal eigenvectors of the matrix A
</span><span class="comment">*</span><span class="comment">          corresponding to the selected eigenvalues, with the i-th
</span><span class="comment">*</span><span class="comment">          column of Z holding the eigenvector associated with W(i).
</span><span class="comment">*</span><span class="comment">          Note: the user must ensure that at least max(1,M) columns are
</span><span class="comment">*</span><span class="comment">          supplied in the array Z; if RANGE = 'V', the exact value of M
</span><span class="comment">*</span><span class="comment">          is not known in advance and an upper bound must be used.
</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">  ISUPPZ  (output) INTEGER array, dimension ( 2*max(1,M) )
</span><span class="comment">*</span><span class="comment">          The support of the eigenvectors in Z, i.e., the indices
</span><span class="comment">*</span><span class="comment">          indicating the nonzero elements in Z. The i-th eigenvector
</span><span class="comment">*</span><span class="comment">          is nonzero only in elements ISUPPZ( 2*i-1 ) through
</span><span class="comment">*</span><span class="comment">          ISUPPZ( 2*i ).
</span><span class="comment">*</span><span class="comment">********* Implemented only for RANGE = 'A' or 'I' and IU - IL = N - 1
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK    (workspace/output) REAL array, dimension (MAX(1,LWORK))
</span><span class="comment">*</span><span class="comment">          On exit, if INFO = 0, WORK(1) returns the optimal (and
</span><span class="comment">*</span><span class="comment">          minimal) LWORK.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LWORK   (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The dimension of the array WORK.  LWORK &gt;= 20*N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          If LWORK = -1, then a workspace query is assumed; the routine
</span><span class="comment">*</span><span class="comment">          only calculates the optimal sizes of the WORK and IWORK
</span><span class="comment">*</span><span class="comment">          arrays, returns these values as the first entries of the WORK
</span><span class="comment">*</span><span class="comment">          and IWORK arrays, and no error message related to LWORK or
</span><span class="comment">*</span><span class="comment">          LIWORK is issued by <a name="XERBLA.173"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  IWORK   (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
</span><span class="comment">*</span><span class="comment">          On exit, if INFO = 0, IWORK(1) returns the optimal (and
</span><span class="comment">*</span><span class="comment">          minimal) LIWORK.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LIWORK  (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The dimension of the array IWORK.  LIWORK &gt;= 10*N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          If LIWORK = -1, then a workspace query is assumed; the
</span><span class="comment">*</span><span class="comment">          routine only calculates the optimal sizes of the WORK and
</span><span class="comment">*</span><span class="comment">          IWORK arrays, returns these values as the first entries of
</span><span class="comment">*</span><span class="comment">          the WORK and IWORK arrays, and no error message related to
</span><span class="comment">*</span><span class="comment">          LWORK or LIWORK is issued by <a name="XERBLA.186"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>.
</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:  Internal error
</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">     Inderjit Dhillon, IBM Almaden, USA
</span><span class="comment">*</span><span class="comment">     Osni Marques, LBNL/NERSC, USA
</span><span class="comment">*</span><span class="comment">     Ken Stanley, Computer Science Division, University of
</span><span class="comment">*</span><span class="comment">       California at Berkeley, USA
</span><span class="comment">*</span><span class="comment">     Jason Riedy, Computer Science Division, University of
</span><span class="comment">*</span><span class="comment">       California at Berkeley, 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>      REAL               ZERO, ONE, TWO
      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0, TWO = 2.0E+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            ALLEIG, INDEIG, TEST, LQUERY, VALEIG, WANTZ,
     $                   TRYRAC
      CHARACTER          ORDER
      INTEGER            I, IEEEOK, IMAX, INDIBL, INDIFL, INDISP,
     $                   INDIWO, ISCALE, J, JJ, LIWMIN, LWMIN, NSPLIT
      REAL               BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM,
     $                   TMP1, TNRM, VLL, VUU
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.220"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      INTEGER            <a name="ILAENV.221"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
      REAL               <a name="SLAMCH.222"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>, <a name="SLANST.222"></a><a href="slanst.f.html#SLANST.1">SLANST</a>
      EXTERNAL           <a name="LSAME.223"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="ILAENV.223"></a><a href="hfy-index.html#ILAENV">ILAENV</a>, <a name="SLAMCH.223"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>, <a name="SLANST.223"></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, SSCAL, <a name="SSTEBZ.226"></a><a href="sstebz.f.html#SSTEBZ.1">SSTEBZ</a>, <a name="SSTEMR.226"></a><a href="sstemr.f.html#SSTEMR.1">SSTEMR</a>, <a name="SSTEIN.226"></a><a href="sstein.f.html#SSTEIN.1">SSTEIN</a>, <a name="SSTERF.226"></a><a href="ssterf.f.html#SSTERF.1">SSTERF</a>,
     $                   SSWAP, <a name="XERBLA.227"></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, MIN, SQRT
<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">
</span><span class="comment">*</span><span class="comment">     Test the input parameters.
</span><span class="comment">*</span><span class="comment">
</span>      IEEEOK = <a name="ILAENV.237"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 10, <span class="string">'<a name="SSTEVR.237"></a><a href="sstevr.f.html#SSTEVR.1">SSTEVR</a>'</span>, <span class="string">'N'</span>, 1, 2, 3, 4 )
<span class="comment">*</span><span class="comment">
</span>      WANTZ = <a name="LSAME.239"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBZ, <span class="string">'V'</span> )
      ALLEIG = <a name="LSAME.240"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( RANGE, <span class="string">'A'</span> )
      VALEIG = <a name="LSAME.241"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( RANGE, <span class="string">'V'</span> )
      INDEIG = <a name="LSAME.242"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( RANGE, <span class="string">'I'</span> )
<span class="comment">*</span><span class="comment">
</span>      LQUERY = ( ( LWORK.EQ.-1 ) .OR. ( LIWORK.EQ.-1 ) )
      LWMIN = MAX( 1, 20*N )
      LIWMIN = MAX(1, 10*N )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
      IF( .NOT.( WANTZ .OR. <a name="LSAME.250"></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( N.LT.0 ) THEN
         INFO = -3
      ELSE
         IF( VALEIG ) THEN
            IF( N.GT.0 .AND. VU.LE.VL )
     $         INFO = -7
         ELSE IF( INDEIG ) THEN
            IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN
               INFO = -8
            ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
               INFO = -9
            END IF
         END IF
      END IF
      IF( INFO.EQ.0 ) THEN
         IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
            INFO = -14
         END IF
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( INFO.EQ.0 ) THEN
         WORK( 1 ) = LWMIN
         IWORK( 1 ) = LIWMIN
<span class="comment">*</span><span class="comment">
</span>         IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
            INFO = -17
         ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
            INFO = -19
         END IF
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.286"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="SSTEVR.286"></a><a href="sstevr.f.html#SSTEVR.1">SSTEVR</a>'</span>, -INFO )
         RETURN
      ELSE IF( LQUERY ) THEN
         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
<span class="comment">*</span><span class="comment">
</span>      IF( N.EQ.1 ) THEN
         IF( ALLEIG .OR. INDEIG ) THEN
            M = 1
            W( 1 ) = D( 1 )
         ELSE
            IF( VL.LT.D( 1 ) .AND. VU.GE.D( 1 ) ) THEN
               M = 1
               W( 1 ) = D( 1 )