zlaed0.f

          SUBROUTINE ZLAED0( QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, RWORK,
         $                   IWORK, INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          INTEGER            INFO, LDQ, LDQS, N, QSIZ
    *     ..
    *     .. Array Arguments ..
          INTEGER            IWORK( * )
          DOUBLE PRECISION   D( * ), E( * ), RWORK( * )
          COMPLEX*16         Q( LDQ, * ), QSTORE( LDQS, * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  Using the divide and conquer method, ZLAED0 computes all eigenvalues
    *  of a symmetric tridiagonal matrix which is one diagonal block of
    *  those from reducing a dense or band Hermitian matrix and
    *  corresponding eigenvectors of the dense or band matrix.
    *
    *  Arguments
    *  =========
    *
    *  QSIZ   (input) INTEGER
    *         The dimension of the unitary matrix used to reduce
    *         the full matrix to tridiagonal form.  QSIZ >= N if ICOMPQ = 1.
    *
    *  N      (input) INTEGER
    *         The dimension of the symmetric tridiagonal matrix.  N >= 0.
    *
    *  D      (input/output) DOUBLE PRECISION array, dimension (N)
    *         On entry, the diagonal elements of the tridiagonal matrix.
    *         On exit, the eigenvalues in ascending order.
    *
    *  E      (input/output) DOUBLE PRECISION array, dimension (N-1)
    *         On entry, the off-diagonal elements of the tridiagonal matrix.
    *         On exit, E has been destroyed.
    *
    *  Q      (input/output) COMPLEX*16 array, dimension (LDQ,N)
    *         On entry, Q must contain an QSIZ x N matrix whose columns
    *         unitarily orthonormal. It is a part of the unitary matrix
    *         that reduces the full dense Hermitian matrix to a
    *         (reducible) symmetric tridiagonal matrix.
    *
    *  LDQ    (input) INTEGER
    *         The leading dimension of the array Q.  LDQ >= max(1,N).
    *
    *  IWORK  (workspace) INTEGER array,
    *         the dimension of IWORK must be at least
    *                      6 + 6*N + 5*N*lg N
    *                      ( lg( N ) = smallest integer k
    *                                  such that 2^k >= N )
    *
    *  RWORK  (workspace) DOUBLE PRECISION array,
    *                               dimension (1 + 3*N + 2*N*lg N + 3*N**2)
    *                        ( lg( N ) = smallest integer k
    *                                    such that 2^k >= N )
    *
    *  QSTORE (workspace) COMPLEX*16 array, dimension (LDQS, N)
    *         Used to store parts of
    *         the eigenvector matrix when the updating matrix multiplies
    *         take place.
    *
    *  LDQS   (input) INTEGER
    *         The leading dimension of the array QSTORE.
    *         LDQS >= max(1,N).
    *
    *  INFO   (output) INTEGER
    *          = 0:  successful exit.
    *          < 0:  if INFO = -i, the i-th argument had an illegal value.
    *          > 0:  The algorithm failed to compute an eigenvalue while
    *                working on the submatrix lying in rows and columns
    *                INFO/(N+1) through mod(INFO,N+1).
    *
    *  =====================================================================
    *
    *  Warning:      N could be as big as QSIZ!
    *
    *     .. Parameters ..
          DOUBLE PRECISION   TWO
          PARAMETER          ( TWO = 2.D+0 )
    *     ..
    *     .. Local Scalars ..
          INTEGER            CURLVL, CURPRB, CURR, I, IGIVCL, IGIVNM,
         $                   IGIVPT, INDXQ, IPERM, IPRMPT, IQ, IQPTR, IWREM,
         $                   J, K, LGN, LL, MATSIZ, MSD2, SMLSIZ, SMM1,
         $                   SPM1, SPM2, SUBMAT, SUBPBS, TLVLS
          DOUBLE PRECISION   TEMP
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           DCOPY, DSTEQR, XERBLA, ZCOPY, ZLACRM, ZLAED7
    *     ..
    *     .. External Functions ..
          INTEGER            ILAENV
          EXTERNAL           ILAENV
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          ABS, DBLE, INT, LOG, MAX
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input parameters.
    *
          INFO = 0
    *
    *     IF( ICOMPQ .LT. 0 .OR. ICOMPQ .GT. 2 ) THEN
    *        INFO = -1
    *     ELSE IF( ( ICOMPQ .EQ. 1 ) .AND. ( QSIZ .LT. MAX( 0, N ) ) )
    *    $        THEN
          IF( QSIZ.LT.MAX( 0, N ) ) THEN
             INFO = -1
          ELSE IF( N.LT.0 ) THEN
             INFO = -2
          ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN
             INFO = -6
          ELSE IF( LDQS.LT.MAX( 1, N ) ) THEN
             INFO = -8
          END IF
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'ZLAED0', -INFO )
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          IF( N.EQ.0 )
         $   RETURN
    *
          SMLSIZ = ILAENV( 9, 'ZLAED0', ' ', 0, 0, 0, 0 )
    *
    *     Determine the size and placement of the submatrices, and save in
    *     the leading elements of IWORK.
    *
          IWORK( 1 ) = N
          SUBPBS = 1
          TLVLS = 0
       10 CONTINUE
          IF( IWORK( SUBPBS ).GT.SMLSIZ ) THEN
             DO 20 J = SUBPBS, 1, -1
                IWORK( 2*J ) = ( IWORK( J )+1 ) / 2
                IWORK( 2*J-1 ) = IWORK( J ) / 2
       20    CONTINUE
             TLVLS = TLVLS + 1
             SUBPBS = 2*SUBPBS
             GO TO 10
          END IF
          DO 30 J = 2, SUBPBS
             IWORK( J ) = IWORK( J ) + IWORK( J-1 )
       30 CONTINUE
    *
    *     Divide the matrix into SUBPBS submatrices of size at most SMLSIZ+1
    *     using rank-1 modifications (cuts).
    *
          SPM1 = SUBPBS - 1
          DO 40 I = 1, SPM1
             SUBMAT = IWORK( I ) + 1
             SMM1 = SUBMAT - 1
             D( SMM1 ) = D( SMM1 ) - ABS( E( SMM1 ) )
             D( SUBMAT ) = D( SUBMAT ) - ABS( E( SMM1 ) )
       40 CONTINUE
    *
          INDXQ = 4*N + 3
    *
    *     Set up workspaces for eigenvalues only/accumulate new vectors
    *     routine
    *
          TEMP = LOG( DBLE( N ) ) / LOG( TWO )
          LGN = INT( TEMP )
          IF( 2**LGN.LT.N )
         $   LGN = LGN + 1
          IF( 2**LGN.LT.N )
         $   LGN = LGN + 1
          IPRMPT = INDXQ + N + 1
          IPERM = IPRMPT + N*LGN
          IQPTR = IPERM + N*LGN
          IGIVPT = IQPTR + N + 2
          IGIVCL = IGIVPT + N*LGN
    *
          IGIVNM = 1
          IQ = IGIVNM + 2*N*LGN
          IWREM = IQ + N**2 + 1
    *     Initialize pointers
          DO 50 I = 0, SUBPBS
             IWORK( IPRMPT+I ) = 1
             IWORK( IGIVPT+I ) = 1
       50 CONTINUE
          IWORK( IQPTR ) = 1
    *
    *     Solve each submatrix eigenproblem at the bottom of the divide and
    *     conquer tree.
    *
          CURR = 0
          DO 70 I = 0, SPM1
             IF( I.EQ.0 ) THEN
                SUBMAT = 1
                MATSIZ = IWORK( 1 )
             ELSE
                SUBMAT = IWORK( I ) + 1
                MATSIZ = IWORK( I+1 ) - IWORK( I )
             END IF
             LL = IQ - 1 + IWORK( IQPTR+CURR )
             CALL DSTEQR( 'I', MATSIZ, D( SUBMAT ), E( SUBMAT ),
         $                RWORK( LL ), MATSIZ, RWORK, INFO )
             CALL ZLACRM( QSIZ, MATSIZ, Q( 1, SUBMAT ), LDQ, RWORK( LL ),
         $                MATSIZ, QSTORE( 1, SUBMAT ), LDQS,
         $                RWORK( IWREM ) )
             IWORK( IQPTR+CURR+1 ) = IWORK( IQPTR+CURR ) + MATSIZ**2
             CURR = CURR + 1
             IF( INFO.GT.0 ) THEN
                INFO = SUBMAT*( N+1 ) + SUBMAT + MATSIZ - 1
                RETURN
             END IF
             K = 1
             DO 60 J = SUBMAT, IWORK( I+1 )
                IWORK( INDXQ+J ) = K
                K = K + 1
       60    CONTINUE
       70 CONTINUE
    *
    *     Successively merge eigensystems of adjacent submatrices
    *     into eigensystem for the corresponding larger matrix.
    *
    *     while ( SUBPBS > 1 )
    *
          CURLVL = 1
       80 CONTINUE
          IF( SUBPBS.GT.1 ) THEN
             SPM2 = SUBPBS - 2
             DO 90 I = 0, SPM2, 2
                IF( I.EQ.0 ) THEN
                   SUBMAT = 1
                   MATSIZ = IWORK( 2 )
                   MSD2 = IWORK( 1 )
                   CURPRB = 0
                ELSE
                   SUBMAT = IWORK( I ) + 1
                   MATSIZ = IWORK( I+2 ) - IWORK( I )
                   MSD2 = MATSIZ / 2
                   CURPRB = CURPRB + 1
                END IF
    *
    *     Merge lower order eigensystems (of size MSD2 and MATSIZ - MSD2)
    *     into an eigensystem of size MATSIZ.  ZLAED7 handles the case
    *     when the eigenvectors of a full or band Hermitian matrix (which
    *     was reduced to tridiagonal form) are desired.
    *
    *     I am free to use Q as a valuable working space until Loop 150.
    *
                CALL ZLAED7( MATSIZ, MSD2, QSIZ, TLVLS, CURLVL, CURPRB,
         $                   D( SUBMAT ), QSTORE( 1, SUBMAT ), LDQS,
         $                   E( SUBMAT+MSD2-1 ), IWORK( INDXQ+SUBMAT ),
         $                   RWORK( IQ ), IWORK( IQPTR ), IWORK( IPRMPT ),
         $                   IWORK( IPERM ), IWORK( IGIVPT ),
         $                   IWORK( IGIVCL ), RWORK( IGIVNM ),
         $                   Q( 1, SUBMAT ), RWORK( IWREM ),
         $                   IWORK( SUBPBS+1 ), INFO )
                IF( INFO.GT.0 ) THEN
                   INFO = SUBMAT*( N+1 ) + SUBMAT + MATSIZ - 1
                   RETURN
                END IF
                IWORK( I / 2+1 ) = IWORK( I+2 )
       90    CONTINUE
             SUBPBS = SUBPBS / 2
             CURLVL = CURLVL + 1
             GO TO 80
          END IF
    *
    *     end while
    *
    *     Re-merge the eigenvalues/vectors which were deflated at the final
    *     merge step.
    *
          DO 100 I = 1, N
             J = IWORK( INDXQ+I )
             RWORK( I ) = D( J )
             CALL ZCOPY( QSIZ, QSTORE( 1, J ), 1, Q( 1, I ), 1 )
      100 CONTINUE
          CALL DCOPY( N, RWORK, 1, D, 1 )
    *
          RETURN
    *
    *     End of ZLAED0
    *
          END