zungbr(3)

NAME

ZUNGBR - generate one of the complex unitary matrices Q or

P**H determined by ZGEBRD when reducing a complex matrix A to

bidiagonal form

SYNOPSIS

SUBROUTINE ZUNGBR( VECT, M,  N,  K,  A,  LDA,  TAU,  WORK,
LWORK, INFO )
    CHARACTER      VECT
    INTEGER        INFO, K, LDA, LWORK, M, N
    COMPLEX*16     A( LDA, * ), TAU( * ), WORK( * )

PURPOSE

ZUNGBR generates one of the complex unitary matrices Q or

P**H determined by ZGEBRD when reducing a complex matrix A to

bidiagonal form: A = Q * B * P**H. Q and P**H are defined as

products of elementary reflectors H(i) or G(i) respectively.

If VECT = 'Q', A is assumed to have been an M-by-K matrix,

and Q is of order M:
if m >= k, Q = H(1) H(2) . . . H(k) and ZUNGBR returns the

first n columns of Q, where m >= n >= k;
if m < k, Q = H(1) H(2) . . . H(m-1) and ZUNGBR returns Q

as an M-by-M matrix.

If VECT = 'P', A is assumed to have been a K-by-N matrix,

and P**H is of order N:
if k < n, P**H = G(k) . . . G(2) G(1) and ZUNGBR returns

the first m rows of P**H, where n >= m >= k;
if k >= n, P**H = G(n-1) . . . G(2) G(1) and ZUNGBR re

turns P**H as an N-by-N matrix.

ARGUMENTS

VECT (input) CHARACTER*1

Specifies whether the matrix Q or the matrix P**H

is required, as defined in the transformation applied by ZGEBRD:
= 'Q': generate Q;
= 'P': generate P**H.

M (input) INTEGER

The number of rows of the matrix Q or P**H to be

returned. M >= 0.

N (input) INTEGER

The number of columns of the matrix Q or P**H to

be returned. N >= 0. If VECT = 'Q', M >= N >= min(M,K); if VECT

= 'P', N >= M >= min(N,K).

K (input) INTEGER

If VECT = 'Q', the number of columns in the origi

nal M-by-K matrix reduced by ZGEBRD. If VECT = 'P', the number

of rows in the original K-by-N matrix reduced by ZGEBRD. K >= 0.

A (input/output) COMPLEX*16 array, dimension (LDA,N)

On entry, the vectors which define the elementary

reflectors, as returned by ZGEBRD. On exit, the M-by-N matrix Q

or P**H.

LDA (input) INTEGER

The leading dimension of the array A. LDA >= M.

TAU (input) COMPLEX*16 array, dimension

(min(M,K)) if VECT = 'Q' (min(N,K)) if VECT = 'P'

TAU(i) must contain the scalar factor of the elementary reflector

H(i) or G(i), which determines Q or P**H, as returned by ZGEBRD

in its array argument TAUQ or TAUP.

WORK (workspace/output) COMPLEX*16 array, dimension

(LWORK)

On exit, if INFO = 0, WORK(1) returns the optimal

LWORK.

LWORK (input) INTEGER

The dimension of the array WORK. LWORK >=

max(1,min(M,N)). For optimum performance LWORK >= min(M,N)*NB,

where NB is the optimal blocksize.

If LWORK = -1, then a workspace query is assumed;

the routine only calculates the optimal size of the WORK array,

returns this value as the first entry of the WORK array, and no

error message related to LWORK is issued by XERBLA.

INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille

gal value

LAPACK version 3.0 15 June 2000

ZUNGBR(3)