zhbtrd.f man page

zhbtrd.f

Synopsis

Functions/Subroutines

subroutine zhbtrd (VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO)
ZHBTRD

Function/Subroutine Documentation

subroutine zhbtrd (character VECT, character UPLO, integer N, integer KD, complex*16, dimension( ldab, * ) AB, integer LDAB, double precision, dimension( * ) D, double precision, dimension( * ) E, complex*16, dimension( ldq, * ) Q, integer LDQ, complex*16, dimension( * ) WORK, integer INFO)

ZHBTRD  

Purpose:

 ZHBTRD reduces a complex Hermitian band matrix A to real symmetric
 tridiagonal form T by a unitary similarity transformation:
 Q**H * A * Q = T.
Parameters:

VECT

          VECT is CHARACTER*1
          = 'N':  do not form Q;
          = 'V':  form Q;
          = 'U':  update a matrix X, by forming X*Q.

UPLO

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

N

          N is INTEGER
          The order of the matrix A.  N >= 0.

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.

AB

          AB is COMPLEX*16 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.

LDAB

          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= KD+1.

D

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

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'.

Q

          Q is COMPLEX*16 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.

LDQ

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

WORK

          WORK is COMPLEX*16 array, dimension (N)

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.

Date:

December 2016

Further Details:

  Modified by Linda Kaufman, Bell Labs.

Definition at line 165 of file zhbtrd.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

The man page zhbtrd(3) is an alias of zhbtrd.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK