LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ dsbtrd()

subroutine dsbtrd ( character vect,
character uplo,
integer n,
integer kd,
double precision, dimension( ldab, * ) ab,
integer ldab,
double precision, dimension( * ) d,
double precision, dimension( * ) e,
double precision, dimension( ldq, * ) q,
integer ldq,
double precision, dimension( * ) work,
integer info )

DSBTRD

Download DSBTRD + dependencies [TGZ] [ZIP] [TXT]

Purpose:
!>
!> DSBTRD reduces a real symmetric band matrix A to symmetric
!> tridiagonal form T by an orthogonal similarity transformation:
!> Q**T * A * Q = T.
!>
Parameters
[in]VECT
!>          VECT is CHARACTER*1
!>          = 'N':  do not form Q;
!>          = 'V':  form Q;
!>          = 'U':  update a matrix X, by forming X*Q.
!>
[in]UPLO
!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>
[in]N
!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>
[in]KD
!>          KD is INTEGER
!>          The number of superdiagonals of the matrix A if UPLO = 'U',
!>          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
!>
[in,out]AB
!>          AB is DOUBLE PRECISION array, dimension (LDAB,N)
!>          On entry, the upper or lower triangle of the symmetric 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 AB 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
!>          off-diagonal elements of T; the rest of AB is overwritten by
!>          values generated during the reduction.
!>
[in]LDAB
!>          LDAB is INTEGER
!>          The leading dimension of the array AB.  LDAB >= KD+1.
!>
[out]D
!>          D is DOUBLE PRECISION array, dimension (N)
!>          The diagonal elements of the tridiagonal matrix T.
!>
[out]E
!>          E is 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'.
!>
[in,out]Q
!>          Q is 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.
!>
[in]LDQ
!>          LDQ is INTEGER
!>          The leading dimension of the array Q.
!>          LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'.
!>
[out]WORK
!>          WORK is DOUBLE PRECISION array, dimension (N)
!>
[out]INFO
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
!>
!>  Modified by Linda Kaufman, Bell Labs.
!>