dsteqr.f.html

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      SUBROUTINE <a name="DSTEQR.1"></a><a href="dsteqr.f.html#DSTEQR.1">DSTEQR</a>( COMPZ, N, D, E, Z, LDZ, WORK, 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">     .. Scalar Arguments ..
</span>      CHARACTER          COMPZ
      INTEGER            INFO, LDZ, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      DOUBLE PRECISION   D( * ), E( * ), WORK( * ), Z( LDZ, * )
<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="DSTEQR.18"></a><a href="dsteqr.f.html#DSTEQR.1">DSTEQR</a> computes all eigenvalues and, optionally, eigenvectors of a
</span><span class="comment">*</span><span class="comment">  symmetric tridiagonal matrix using the implicit QL or QR method.
</span><span class="comment">*</span><span class="comment">  The eigenvectors of a full or band symmetric matrix can also be found
</span><span class="comment">*</span><span class="comment">  if <a name="DSYTRD.21"></a><a href="dsytrd.f.html#DSYTRD.1">DSYTRD</a> or <a name="DSPTRD.21"></a><a href="dsptrd.f.html#DSPTRD.1">DSPTRD</a> or <a name="DSBTRD.21"></a><a href="dsbtrd.f.html#DSBTRD.1">DSBTRD</a> has been used to reduce this matrix to
</span><span class="comment">*</span><span class="comment">  tridiagonal form.
</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">  COMPZ   (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'N':  Compute eigenvalues only.
</span><span class="comment">*</span><span class="comment">          = 'V':  Compute eigenvalues and eigenvectors of the original
</span><span class="comment">*</span><span class="comment">                  symmetric matrix.  On entry, Z must contain the
</span><span class="comment">*</span><span class="comment">                  orthogonal matrix used to reduce the original matrix
</span><span class="comment">*</span><span class="comment">                  to tridiagonal form.
</span><span class="comment">*</span><span class="comment">          = 'I':  Compute eigenvalues and eigenvectors of the
</span><span class="comment">*</span><span class="comment">                  tridiagonal matrix.  Z is initialized to the identity
</span><span class="comment">*</span><span class="comment">                  matrix.
</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.  N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  D       (input/output) DOUBLE PRECISION array, dimension (N)
</span><span class="comment">*</span><span class="comment">          On entry, the diagonal elements of the tridiagonal matrix.
</span><span class="comment">*</span><span class="comment">          On exit, if INFO = 0, the eigenvalues in ascending order.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  E       (input/output) DOUBLE PRECISION array, dimension (N-1)
</span><span class="comment">*</span><span class="comment">          On entry, the (n-1) subdiagonal elements of the tridiagonal
</span><span class="comment">*</span><span class="comment">          matrix.
</span><span class="comment">*</span><span class="comment">          On exit, E has been destroyed.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Z       (input/output) DOUBLE PRECISION array, dimension (LDZ, N)
</span><span class="comment">*</span><span class="comment">          On entry, if  COMPZ = 'V', then Z contains the orthogonal
</span><span class="comment">*</span><span class="comment">          matrix used in the reduction to tridiagonal form.
</span><span class="comment">*</span><span class="comment">          On exit, if INFO = 0, then if  COMPZ = 'V', Z contains the
</span><span class="comment">*</span><span class="comment">          orthonormal eigenvectors of the original symmetric matrix,
</span><span class="comment">*</span><span class="comment">          and if COMPZ = 'I', Z contains the orthonormal eigenvectors
</span><span class="comment">*</span><span class="comment">          of the symmetric tridiagonal matrix.
</span><span class="comment">*</span><span class="comment">          If COMPZ = '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">          eigenvectors are desired, then  LDZ &gt;= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK    (workspace) DOUBLE PRECISION array, dimension (max(1,2*N-2))
</span><span class="comment">*</span><span class="comment">          If COMPZ = 'N', then WORK 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:  the algorithm has failed to find all the eigenvalues in
</span><span class="comment">*</span><span class="comment">                a total of 30*N iterations; if INFO = i, then i
</span><span class="comment">*</span><span class="comment">                elements of E have not converged to zero; on exit, D
</span><span class="comment">*</span><span class="comment">                and E contain the elements of a symmetric tridiagonal
</span><span class="comment">*</span><span class="comment">                matrix which is orthogonally similar to the original
</span><span class="comment">*</span><span class="comment">                matrix.
</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, TWO, THREE
      PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0,
     $                   THREE = 3.0D0 )
      INTEGER            MAXIT
      PARAMETER          ( MAXIT = 30 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      INTEGER            I, ICOMPZ, II, ISCALE, J, JTOT, K, L, L1, LEND,
     $                   LENDM1, LENDP1, LENDSV, LM1, LSV, M, MM, MM1,
     $                   NM1, NMAXIT
      DOUBLE PRECISION   ANORM, B, C, EPS, EPS2, F, G, P, R, RT1, RT2,
     $                   S, SAFMAX, SAFMIN, SSFMAX, SSFMIN, TST
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.92"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      DOUBLE PRECISION   <a name="DLAMCH.93"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>, <a name="DLANST.93"></a><a href="dlanst.f.html#DLANST.1">DLANST</a>, <a name="DLAPY2.93"></a><a href="dlapy2.f.html#DLAPY2.1">DLAPY2</a>
      EXTERNAL           <a name="LSAME.94"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="DLAMCH.94"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>, <a name="DLANST.94"></a><a href="dlanst.f.html#DLANST.1">DLANST</a>, <a name="DLAPY2.94"></a><a href="dlapy2.f.html#DLAPY2.1">DLAPY2</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="DLAE2.97"></a><a href="dlae2.f.html#DLAE2.1">DLAE2</a>, <a name="DLAEV2.97"></a><a href="dlaev2.f.html#DLAEV2.1">DLAEV2</a>, <a name="DLARTG.97"></a><a href="dlartg.f.html#DLARTG.1">DLARTG</a>, <a name="DLASCL.97"></a><a href="dlascl.f.html#DLASCL.1">DLASCL</a>, <a name="DLASET.97"></a><a href="dlaset.f.html#DLASET.1">DLASET</a>, <a name="DLASR.97"></a><a href="dlasr.f.html#DLASR.1">DLASR</a>,
     $                   <a name="DLASRT.98"></a><a href="dlasrt.f.html#DLASRT.1">DLASRT</a>, DSWAP, <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">     .. Intrinsic Functions ..
</span>      INTRINSIC          ABS, MAX, SIGN, 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">     Test the input parameters.
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
<span class="comment">*</span><span class="comment">
</span>      IF( <a name="LSAME.109"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( COMPZ, <span class="string">'N'</span> ) ) THEN
         ICOMPZ = 0
      ELSE IF( <a name="LSAME.111"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( COMPZ, <span class="string">'V'</span> ) ) THEN
         ICOMPZ = 1
      ELSE IF( <a name="LSAME.113"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( COMPZ, <span class="string">'I'</span> ) ) THEN
         ICOMPZ = 2
      ELSE
         ICOMPZ = -1
      END IF
      IF( ICOMPZ.LT.0 ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( ( LDZ.LT.1 ) .OR. ( ICOMPZ.GT.0 .AND. LDZ.LT.MAX( 1,
     $         N ) ) ) THEN
         INFO = -6
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.127"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="DSTEQR.127"></a><a href="dsteqr.f.html#DSTEQR.1">DSTEQR</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>      IF( N.EQ.0 )
     $   RETURN
<span class="comment">*</span><span class="comment">
</span>      IF( N.EQ.1 ) THEN
         IF( ICOMPZ.EQ.2 )
     $      Z( 1, 1 ) = ONE
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Determine the unit roundoff and over/underflow thresholds.
</span><span class="comment">*</span><span class="comment">
</span>      EPS = <a name="DLAMCH.144"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>( <span class="string">'E'</span> )
      EPS2 = EPS**2
      SAFMIN = <a name="DLAMCH.146"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>( <span class="string">'S'</span> )
      SAFMAX = ONE / SAFMIN
      SSFMAX = SQRT( SAFMAX ) / THREE
      SSFMIN = SQRT( SAFMIN ) / EPS2
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Compute the eigenvalues and eigenvectors of the tridiagonal
</span><span class="comment">*</span><span class="comment">     matrix.
</span><span class="comment">*</span><span class="comment">
</span>      IF( ICOMPZ.EQ.2 )
     $   CALL <a name="DLASET.155"></a><a href="dlaset.f.html#DLASET.1">DLASET</a>( <span class="string">'Full'</span>, N, N, ZERO, ONE, Z, LDZ )
<span class="comment">*</span><span class="comment">
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