slaed0.f

          SUBROUTINE SLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS,
         $                   WORK, IWORK, INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          INTEGER            ICOMPQ, INFO, LDQ, LDQS, N, QSIZ
    *     ..
    *     .. Array Arguments ..
          INTEGER            IWORK( * )
          REAL               D( * ), E( * ), Q( LDQ, * ), QSTORE( LDQS, * ),
         $                   WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  SLAED0 computes all eigenvalues and corresponding eigenvectors of a
    *  symmetric tridiagonal matrix using the divide and conquer method.
    *
    *  Arguments
    *  =========
    *
    *  ICOMPQ  (input) INTEGER
    *          = 0:  Compute eigenvalues only.
    *          = 1:  Compute eigenvectors of original dense symmetric matrix
    *                also.  On entry, Q contains the orthogonal matrix used
    *                to reduce the original matrix to tridiagonal form.
    *          = 2:  Compute eigenvalues and eigenvectors of tridiagonal
    *                matrix.
    *
    *  QSIZ   (input) INTEGER
    *         The dimension of the orthogonal 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) REAL array, dimension (N)
    *         On entry, the main diagonal of the tridiagonal matrix.
    *         On exit, its eigenvalues.
    *
    *  E      (input) REAL array, dimension (N-1)
    *         The off-diagonal elements of the tridiagonal matrix.
    *         On exit, E has been destroyed.
    *
    *  Q      (input/output) REAL array, dimension (LDQ, N)
    *         On entry, Q must contain an N-by-N orthogonal matrix.
    *         If ICOMPQ = 0    Q is not referenced.
    *         If ICOMPQ = 1    On entry, Q is a subset of the columns of the
    *                          orthogonal matrix used to reduce the full
    *                          matrix to tridiagonal form corresponding to
    *                          the subset of the full matrix which is being
    *                          decomposed at this time.
    *         If ICOMPQ = 2    On entry, Q will be the identity matrix.
    *                          On exit, Q contains the eigenvectors of the
    *                          tridiagonal matrix.
    *
    *  LDQ    (input) INTEGER
    *         The leading dimension of the array Q.  If eigenvectors are
    *         desired, then  LDQ >= max(1,N).  In any case,  LDQ >= 1.
    *
    *  QSTORE (workspace) REAL array, dimension (LDQS, N)
    *         Referenced only when ICOMPQ = 1.  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.  If ICOMPQ = 1,
    *         then  LDQS >= max(1,N).  In any case,  LDQS >= 1.
    *
    *  WORK   (workspace) REAL array,
    *         If ICOMPQ = 0 or 1, the dimension of WORK must be at least
    *                     1 + 3*N + 2*N*lg N + 2*N**2
    *                     ( lg( N ) = smallest integer k
    *                                 such that 2^k >= N )
    *         If ICOMPQ = 2, the dimension of WORK must be at least
    *                     4*N + N**2.
    *
    *  IWORK  (workspace) INTEGER array,
    *         If ICOMPQ = 0 or 1, 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 )
    *         If ICOMPQ = 2, the dimension of IWORK must be at least
    *                        3 + 5*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).
    *
    *  Further Details
    *  ===============
    *
    *  Based on contributions by
    *     Jeff Rutter, Computer Science Division, University of California
    *     at Berkeley, USA
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          REAL               ZERO, ONE, TWO
          PARAMETER          ( ZERO = 0.E0, ONE = 1.E0, TWO = 2.E0 )
    *     ..
    *     .. Local Scalars ..
          INTEGER            CURLVL, CURPRB, CURR, I, IGIVCL, IGIVNM,
         $                   IGIVPT, INDXQ, IPERM, IPRMPT, IQ, IQPTR, IWREM,
         $                   J, K, LGN, MATSIZ, MSD2, SMLSIZ, SMM1, SPM1,
         $                   SPM2, SUBMAT, SUBPBS, TLVLS
          REAL               TEMP
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           SCOPY, SGEMM, SLACPY, SLAED1, SLAED7, SSTEQR,
         $                   XERBLA
    *     ..
    *     .. External Functions ..
          INTEGER            ILAENV
          EXTERNAL           ILAENV
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          ABS, INT, LOG, MAX, REAL
    *     ..
    *     .. 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
             INFO = -2
          ELSE IF( N.LT.0 ) THEN
             INFO = -3
          ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN
             INFO = -7
          ELSE IF( LDQS.LT.MAX( 1, N ) ) THEN
             INFO = -9
          END IF
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'SLAED0', -INFO )
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          IF( N.EQ.0 )
         $   RETURN
    *
          SMLSIZ = ILAENV( 9, 'SLAED0', ' ', 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
          IF( ICOMPQ.NE.2 ) THEN
    *
    *        Set up workspaces for eigenvalues only/accumulate new vectors
    *        routine
    *
             TEMP = LOG( REAL( 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
          END IF
    *
    *     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
             IF( ICOMPQ.EQ.2 ) THEN
                CALL SSTEQR( 'I', MATSIZ, D( SUBMAT ), E( SUBMAT ),
         $                   Q( SUBMAT, SUBMAT ), LDQ, WORK, INFO )
                IF( INFO.NE.0 )
         $         GO TO 130
             ELSE
                CALL SSTEQR( 'I', MATSIZ, D( SUBMAT ), E( SUBMAT ),
         $                   WORK( IQ-1+IWORK( IQPTR+CURR ) ), MATSIZ, WORK,
         $                   INFO )
                IF( INFO.NE.0 )
         $         GO TO 130
                IF( ICOMPQ.EQ.1 ) THEN
                   CALL SGEMM( 'N', 'N', QSIZ, MATSIZ, MATSIZ, ONE,
         $                     Q( 1, SUBMAT ), LDQ, WORK( IQ-1+IWORK( IQPTR+
         $                     CURR ) ), MATSIZ, ZERO, QSTORE( 1, SUBMAT ),
         $                     LDQS )
                END IF
                IWORK( IQPTR+CURR+1 ) = IWORK( IQPTR+CURR ) + MATSIZ**2
                CURR = CURR + 1
             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.
    *     SLAED1 is used only for the full eigensystem of a tridiagonal
    *     matrix.
    *     SLAED7 handles the cases in which eigenvalues only or eigenvalues
    *     and eigenvectors of a full symmetric matrix (which was reduced to
    *     tridiagonal form) are desired.
    *
                IF( ICOMPQ.EQ.2 ) THEN
                   CALL SLAED1( MATSIZ, D( SUBMAT ), Q( SUBMAT, SUBMAT ),
         $                      LDQ, IWORK( INDXQ+SUBMAT ),
         $                      E( SUBMAT+MSD2-1 ), MSD2, WORK,
         $                      IWORK( SUBPBS+1 ), INFO )
                ELSE
                   CALL SLAED7( ICOMPQ, MATSIZ, QSIZ, TLVLS, CURLVL, CURPRB,
         $                      D( SUBMAT ), QSTORE( 1, SUBMAT ), LDQS,
         $                      IWORK( INDXQ+SUBMAT ), E( SUBMAT+MSD2-1 ),
         $                      MSD2, WORK( IQ ), IWORK( IQPTR ),
         $                      IWORK( IPRMPT ), IWORK( IPERM ),
         $                      IWORK( IGIVPT ), IWORK( IGIVCL ),
         $                      WORK( IGIVNM ), WORK( IWREM ),
         $                      IWORK( SUBPBS+1 ), INFO )
                END IF
                IF( INFO.NE.0 )
         $         GO TO 130
                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.
    *
          IF( ICOMPQ.EQ.1 ) THEN
             DO 100 I = 1, N
                J = IWORK( INDXQ+I )
                WORK( I ) = D( J )
                CALL SCOPY( QSIZ, QSTORE( 1, J ), 1, Q( 1, I ), 1 )
      100    CONTINUE
             CALL SCOPY( N, WORK, 1, D, 1 )
          ELSE IF( ICOMPQ.EQ.2 ) THEN
             DO 110 I = 1, N
                J = IWORK( INDXQ+I )
                WORK( I ) = D( J )
                CALL SCOPY( N, Q( 1, J ), 1, WORK( N*I+1 ), 1 )
      110    CONTINUE
             CALL SCOPY( N, WORK, 1, D, 1 )
             CALL SLACPY( 'A', N, N, WORK( N+1 ), N, Q, LDQ )
          ELSE
             DO 120 I = 1, N
                J = IWORK( INDXQ+I )
                WORK( I ) = D( J )
      120    CONTINUE
             CALL SCOPY( N, WORK, 1, D, 1 )
          END IF
          GO TO 140
    *
      130 CONTINUE
          INFO = SUBMAT*( N+1 ) + SUBMAT + MATSIZ - 1
    *
      140 CONTINUE
          RETURN
    *
    *     End of SLAED0
    *
          END