chbtrd(3)

NAME

chbtrd.f –

SYNOPSIS

Functions/Subroutines

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

Function/Subroutine Documentation

subroutine chbtrd (characterVECT, characterUPLO, integerN, integerKD, complex, dimension( ldab, * )AB, integerLDAB, real, dimension( * )D, real, dimension( * )E, complex, dimension( ldq, * )Q, integerLDQ, complex, dimension( * )WORK, integerINFO)

CHBTRD

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:

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 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 REAL array, dimension (N)
          The diagonal elements of the tridiagonal matrix T.

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’.

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.

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 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:

November 2011

Further Details:

  Modified by Linda Kaufman, Bell Labs.

 

Definition at line 163 of file chbtrd.f.

Author

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