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dsbtrd

 NAME
      DSBTRD - reduce a real symmetric band matrix A to symmetric
      tridiagonal form T by an orthogonal similarity transforma-
      tion

 SYNOPSIS
      SUBROUTINE DSBTRD( VECT, UPLO, N, KD, AB, LDAB, D, E, Q,
                         LDQ, WORK, INFO )

          CHARACTER      UPLO, VECT

          INTEGER        INFO, KD, LDAB, LDQ, N

          DOUBLE         PRECISION AB( LDAB, * ), D( * ), E( * ),
                         Q( LDQ, * ), WORK( * )

 PURPOSE
      DSBTRD reduces a real symmetric band matrix A to symmetric
      tridiagonal form T by an orthogonal similarity transforma-
      tion: Q**T * A * Q = T.

 ARGUMENTS
      VECT    (input) CHARACTER*1
              = 'N':  do not form Q;
              = 'V':  form Q.

      UPLO    (input) CHARACTER*1
              = 'U':  Upper triangle of A is stored;
              = 'L':  Lower triangle of A is stored.

      N       (input) INTEGER
              The order of the matrix A.  N >= 0.

      KD      (input) INTEGER
              The number of superdiagonals of the matrix A if UPLO
              = 'U', or the number of subdiagonals if UPLO = 'L'.
              KD >= 0.

      AB      (input/output) DOUBLE PRECISION array, dimension (LDAB,N)
              On entry, the upper or lower triangle of the sym-
              metric band matrix A, stored in the first KD+1 rows
              of the array.  The j-th column of A is stored in the
              j-th column of the array AB as follows: if UPLO =
              'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
              if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for
              j<=i<=min(n,j+kd).  On exit, the diagonal elements
              of A are overwritten by the diagonal elements of the
              tridiagonal matrix T; if KD > 0, the elements on the
              first superdiagonal (if UPLO = 'U') or the first
              subdiagonal (if UPLO = 'L') are overwritten by the
              offdiagonal elements of T; the rest of A is

              overwritten by values generated during the reduc-
              tion.

      LDAB    (input) INTEGER
              The leading dimension of the array AB.  LDAB >=
              KD+1.

      D       (output) DOUBLE PRECISION array, dimension (N)
              The diagonal elements of the tridiagonal matrix T.

      E       (output) DOUBLE PRECISION array, dimension (N-1)
              The off-diagonal elements of the tridiagonal matrix
              T: E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if
              UPLO = 'L'.

      Q       (output) DOUBLE PRECISION array, dimension (LDQ,N)
              If VECT = 'V', the N-by-N orthogonal matrix Q.  If
              VECT = 'N', the array Q is not referenced.

      LDQ     (input) INTEGER
              The leading dimension of the array Q.  LDQ >=
              max(1,N) if VECT = 'V'.

      WORK    (workspace) DOUBLE PRECISION array, dimension (N)

      INFO    (output) INTEGER
              = 0:  successful exit
              < 0:  if INFO = -i, the i-th argument had an illegal
              value