dsygvx.f.html

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</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 eigenvectors 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">          &gt; 0:  <a name="DPOTRF.169"></a><a href="dpotrf.f.html#DPOTRF.1">DPOTRF</a> or <a name="DSYEVX.169"></a><a href="dsyevx.f.html#DSYEVX.1">DSYEVX</a> returned an error code:
</span><span class="comment">*</span><span class="comment">             &lt;= N:  if INFO = i, <a name="DSYEVX.170"></a><a href="dsyevx.f.html#DSYEVX.1">DSYEVX</a> failed to converge;
</span><span class="comment">*</span><span class="comment">                    i eigenvectors failed to converge.  Their indices
</span><span class="comment">*</span><span class="comment">                    are stored in array IFAIL.
</span><span class="comment">*</span><span class="comment">             &gt; N:   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   ONE
      PARAMETER          ( 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, LQUERY, UPPER, VALEIG, WANTZ
      CHARACTER          TRANS
      INTEGER            LWKMIN, LWKOPT, NB
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.196"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      INTEGER            <a name="ILAENV.197"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
      EXTERNAL           <a name="LSAME.198"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="ILAENV.198"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="DPOTRF.201"></a><a href="dpotrf.f.html#DPOTRF.1">DPOTRF</a>, <a name="DSYEVX.201"></a><a href="dsyevx.f.html#DSYEVX.1">DSYEVX</a>, <a name="DSYGST.201"></a><a href="dsygst.f.html#DSYGST.1">DSYGST</a>, DTRMM, DTRSM, <a name="XERBLA.201"></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
<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>      UPPER = <a name="LSAME.210"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> )
      WANTZ = <a name="LSAME.211"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBZ, <span class="string">'V'</span> )
      ALLEIG = <a name="LSAME.212"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( RANGE, <span class="string">'A'</span> )
      VALEIG = <a name="LSAME.213"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( RANGE, <span class="string">'V'</span> )
      INDEIG = <a name="LSAME.214"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( RANGE, <span class="string">'I'</span> )
      LQUERY = ( LWORK.EQ.-1 )
<span class="comment">*</span><span class="comment">
</span>      INFO = 0
      IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
         INFO = -1
      ELSE IF( .NOT.( WANTZ .OR. <a name="LSAME.220"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBZ, <span class="string">'N'</span> ) ) ) THEN
         INFO = -2
      ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
         INFO = -3
      ELSE IF( .NOT.( UPPER .OR. <a name="LSAME.224"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'L'</span> ) ) ) THEN
         INFO = -4
      ELSE IF( N.LT.0 ) THEN
         INFO = -5
      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -7
      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
         INFO = -9
      ELSE
         IF( VALEIG ) THEN
            IF( N.GT.0 .AND. VU.LE.VL )
     $         INFO = -11
         ELSE IF( INDEIG ) THEN
            IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN
               INFO = -12
            ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
               INFO = -13
            END IF
         END IF
      END IF
      IF (INFO.EQ.0) THEN
         IF (LDZ.LT.1 .OR. (WANTZ .AND. LDZ.LT.N)) THEN
            INFO = -18
         END IF
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( INFO.EQ.0 ) THEN
         LWKMIN = MAX( 1, 8*N )
         NB = <a name="ILAENV.252"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="DSYTRD.252"></a><a href="dsytrd.f.html#DSYTRD.1">DSYTRD</a>'</span>, UPLO, N, -1, -1, -1 )
         LWKOPT = MAX( LWKMIN, ( NB + 3 )*N )
         WORK( 1 ) = LWKOPT
<span class="comment">*</span><span class="comment">
</span>         IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN
            INFO = -20
         END IF
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.262"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="DSYGVX.262"></a><a href="dsygvx.f.html#DSYGVX.1">DSYGVX</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 ) THEN
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Form a Cholesky factorization of B.
</span><span class="comment">*</span><span class="comment">
</span>      CALL <a name="DPOTRF.277"></a><a href="dpotrf.f.html#DPOTRF.1">DPOTRF</a>( UPLO, N, B, LDB, INFO )
      IF( INFO.NE.0 ) THEN
         INFO = N + INFO
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Transform problem to standard eigenvalue problem and solve.
</span><span class="comment">*</span><span class="comment">
</span>      CALL <a name="DSYGST.285"></a><a href="dsygst.f.html#DSYGST.1">DSYGST</a>( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
      CALL <a name="DSYEVX.286"></a><a href="dsyevx.f.html#DSYEVX.1">DSYEVX</a>( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, ABSTOL,
     $             M, W, Z, LDZ, WORK, LWORK, IWORK, IFAIL, INFO )
<span class="comment">*</span><span class="comment">
</span>      IF( WANTZ ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Backtransform eigenvectors to the original problem.
</span><span class="comment">*</span><span class="comment">
</span>         IF( INFO.GT.0 )
     $      M = INFO - 1
         IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
</span><span class="comment">*</span><span class="comment">           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
</span><span class="comment">*</span><span class="comment">
</span>            IF( UPPER ) THEN
               TRANS = <span class="string">'N'</span>
            ELSE
               TRANS = <span class="string">'T'</span>
            END IF
<span class="comment">*</span><span class="comment">
</span>            CALL DTRSM( <span class="string">'Left'</span>, UPLO, TRANS, <span class="string">'Non-unit'</span>, N, M, ONE, B,
     $                  LDB, Z, LDZ )
<span class="comment">*</span><span class="comment">
</span>         ELSE IF( ITYPE.EQ.3 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           For B*A*x=(lambda)*x;
</span><span class="comment">*</span><span class="comment">           backtransform eigenvectors: x = L*y or U'*y
</span><span class="comment">*</span><span class="comment">
</span>            IF( UPPER ) THEN
               TRANS = <span class="string">'T'</span>
            ELSE
               TRANS = <span class="string">'N'</span>
            END IF
<span class="comment">*</span><span class="comment">
</span>            CALL DTRMM( <span class="string">'Left'</span>, UPLO, TRANS, <span class="string">'Non-unit'</span>, N, M, ONE, B,
     $                  LDB, Z, LDZ )
         END IF
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Set WORK(1) to optimal workspace size.
</span><span class="comment">*</span><span class="comment">
</span>      WORK( 1 ) = LWKOPT
<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="DSYGVX.331"></a><a href="dsygvx.f.html#DSYGVX.1">DSYGVX</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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