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## chbtrd()

subroutine chbtrd | ( | character | vect,
|  | character | uplo,
|  | integer | n,
|  | integer | kd,
|  | complex, dimension( ldab, * ) | ab,
|  | integer | ldab,
|  | real, dimension( * ) | d,
|  | real, dimension( * ) | e,
|  | complex, dimension( ldq, * ) | q,
|  | integer | ldq,
|  | complex, dimension( * ) | work,
|  | integer | info )

CHBTRD

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

Purpose:

      !>
      !> CHBTRD reduces a complex Hermitian band matrix A to real symmetric
      !> tridiagonal form T by a unitary similarity transformation:
      !> Q**H * 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 COMPLEX array, dimension (LDAB,N)
      !>          On entry, the upper or lower triangle of the Hermitian 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 REAL array, dimension (N)
      !>          The diagonal elements of the tridiagonal matrix T.
      !>

  [out]

  E

      !>          E is REAL 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 COMPLEX 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 unitary 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 COMPLEX 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.
      !>