dsyevd.f

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*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS, SQRT
*     ..
*     .. Executable Statements ..
*
*     Compute the eigenvalues
*
      SM = A + C
      DF = A - C
      ADF = ABS( DF )
      TB = B + B
      AB = ABS( TB )
      IF( ABS( A ).GT.ABS( C ) ) THEN
         ACMX = A
         ACMN = C
      ELSE
         ACMX = C
         ACMN = A
      END IF
      IF( ADF.GT.AB ) THEN
         RT = ADF*SQRT( ONE+( AB / ADF )**2 )
      ELSE IF( ADF.LT.AB ) THEN
         RT = AB*SQRT( ONE+( ADF / AB )**2 )
      ELSE
*
*        Includes case AB=ADF=0
*
         RT = AB*SQRT( TWO )
      END IF
      IF( SM.LT.ZERO ) THEN
         RT1 = HALF*( SM-RT )
*
*        Order of execution important.
*        To get fully accurate smaller eigenvalue,
*        next line needs to be executed in higher precision.
*
         RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B
      ELSE IF( SM.GT.ZERO ) THEN
         RT1 = HALF*( SM+RT )
*
*        Order of execution important.
*        To get fully accurate smaller eigenvalue,
*        next line needs to be executed in higher precision.
*
         RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B
      ELSE
*
*        Includes case RT1 = RT2 = 0
*
         RT1 = HALF*RT
         RT2 = -HALF*RT
      END IF
      RETURN
*
*     End of DLAE2
*
      END
! ----------------------------------------------------------------------

      SUBROUTINE DLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS,
     $                   WORK, IWORK, INFO )
! ----------------------------------------------------------------------
      Use      numerics
      Implicit None
*
*  -- LAPACK routine (version 2.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     September 30, 1994
*
*     .. Scalar Arguments ..
      INTEGER            ICOMPQ, INFO, LDQ, LDQS, N, QSIZ
*     ..
*     .. Array Arguments ..
      INTEGER            IWORK( * )
      Real(l_)   D( * ), E( * ), Q( LDQ, * ), QSTORE( LDQS, * ),
     $                   WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  DLAED0 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(l_) array, dimension (N)
*         On entry, the main diagonal of the tridiagonal matrix.
*         On exit, its eigenvalues.
*
*  E      (input) Real(l_) array, dimension (N-1)
*         The off-diagonal elements of the tridiagonal matrix.
*         On exit, E has been destroyed.
*
*  Q      (input/output) Real(l_) 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(l_) 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(l_) array,
*                                dimension (1 + 3*N + 2*N*lg N + 2*N**2)
*                        ( lg( N ) = smallest integer k
*                                    such that 2^k >= N )
*
*  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
*                        2 + 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).
*
*  =====================================================================
*
*     .. Parameters ..
      INTEGER            SMLSIZ
      PARAMETER          ( SMLSIZ = 25 )
      Real(l_)   ZERO, ONE, TWO
      PARAMETER          ( ZERO = 0.0_l_, ONE = 1.0_l_, TWO = 20_l_ )
*     ..
*     .. Local Scalars ..
      INTEGER            CURLVL, CURPRB, CURR, I, IGIVCL, IGIVNM,
     $                   IGIVPT, INDXQ, IPERM, IPRMPT, IQ, IQPTR, IWREM,
     $                   J, K, LGN, MATSIZ, MSD2, SMM1, SPM1, SPM2,
     $                   SUBMAT, SUBPBS, TLVLS
      Real(l_)   TEMP
*     ..
*     .. External Subroutines ..
      EXTERNAL           DCOPY, DGEMM, DLACPY, DLAED1, DLAED7, DSTEQR,
     $                   XERBLA
*     ..
*     .. 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
         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( 'DLAED0', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.EQ.0 )
     $   RETURN
*
*     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( 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
      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 DSTEQR( 'I', MATSIZ, D( SUBMAT ), E( SUBMAT ),
     $                   Q( SUBMAT, SUBMAT ), LDQ, WORK, INFO )
            IF( INFO.NE.0 )
     $         GO TO 130
         ELSE
            CALL DSTEQR( '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 DGEMM( '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.
*     DLAED1 is used only for the full eigensystem of a tridiagonal
*     matrix.
*     DLAED7 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 DLAED1( MATSIZ, D( SUBMAT ), Q( SUBMAT, SUBMAT ),
     $                      LDQ, IWORK( INDXQ+SUBMAT ),
     $                      E( SUBMAT+MSD2-1 ), MSD2, WORK,
     $                      IWORK( SUBPBS+1 ), INFO )
            ELSE
               CALL DLAED7( 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 DCOPY( QSIZ, QSTORE( 1, J ), 1, Q( 1, I ), 1 )
  100    CONTINUE
         CALL DCOPY( 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 DCOPY( N, Q( 1, J ), 1, WORK( N*I+1 ), 1 )
  110    CONTINUE
         CALL DCOPY( N, WORK, 1, D, 1 )
         CALL DLACPY( '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 DCOPY( N, WORK, 1, D, 1 )
      END IF
      GO TO 140
*
  130 CONTINUE
      INFO = SUBMAT*( N+1 ) + SUBMAT + MATSIZ - 1
*
  140 CONTINUE
      RETURN
*
*     End of DLAED0
*
      END
! ----------------------------------------------------------------------

      SUBROUTINE DLAED1( N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK,
     $                   INFO )
! ----------------------------------------------------------------------
      Use      numerics
      Implicit None
*
*  -- LAPACK routine (version 2.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     September 30, 1994