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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( * )



     #include <sunperf.h>

     void dsbtrd(char vect, char uplo,  int  n,  int  kd,  double
               *dab,  int  ldab, double *d, double *e, double *q,
               int ldq, int *info) ;

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;
               = 'U':  update a matrix X, by forming X*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 ele-
               ments  of  AB are overwritten by the diagonal ele-
               ments 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 off-diagonal elements of T; the
               rest of AB is overwritten by values generated dur-
               ing the reduction.

     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         (input/output) DOUBLE PRECISION  array,  dimension
               (LDQ,N)
               On entry, if VECT = 'U', then Q  must  contain  an
               N-by-N matrix X; if VECT = 'N' or 'V', then Q need
               not be set.

               On exit:  if VECT = 'V',  Q  contains  the  N-by-N
               orthogonal matrix Q; if VECT = 'U', Q contains the
               product X*Q; if VECT = 'N', the  array  Q  is  not
               referenced.

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

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

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

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