NAME

zungbr - generate one of the complex unitary matrices Q or P**H determined by CGEBRD when reducing a complex matrix A to bidiagonal form

SYNOPSIS

  SUBROUTINE ZUNGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
  CHARACTER * 1 VECT
  DOUBLE COMPLEX A(LDA,*), TAU(*), WORK(*)
  INTEGER M, N, K, LDA, LWORK, INFO

  SUBROUTINE ZUNGBR_64( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
  CHARACTER * 1 VECT
  DOUBLE COMPLEX A(LDA,*), TAU(*), WORK(*)
  INTEGER*8 M, N, K, LDA, LWORK, INFO

F95 INTERFACE

  SUBROUTINE UNGBR( VECT, M, [N], K, A, [LDA], TAU, [WORK], [LWORK], 
 *       [INFO])
  CHARACTER(LEN=1) :: VECT
  COMPLEX(8), DIMENSION(:) :: TAU, WORK
  COMPLEX(8), DIMENSION(:,:) :: A
  INTEGER :: M, N, K, LDA, LWORK, INFO

  SUBROUTINE UNGBR_64( VECT, M, [N], K, A, [LDA], TAU, [WORK], [LWORK], 
 *       [INFO])
  CHARACTER(LEN=1) :: VECT
  COMPLEX(8), DIMENSION(:) :: TAU, WORK
  COMPLEX(8), DIMENSION(:,:) :: A
  INTEGER(8) :: M, N, K, LDA, LWORK, INFO

C INTERFACE

#include <sunperf.h>

void zungbr(char vect, int m, int n, int k, doublecomplex *a, int lda, doublecomplex *tau, int *info);

void zungbr_64(char vect, long m, long n, long k, doublecomplex *a, long lda, doublecomplex *tau, long *info);

PURPOSE

zungbr generates one of the complex unitary matrices Q or P**H determined by CGEBRD 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 CUNGBR returns the first n columns of Q, where m >= n >= k;

if m < k, Q = H(1) H(2) . . . H(m-1) and CUNGBR 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 CUNGBR 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 CUNGBR returns P**H as an N-by-N matrix.

ARGUMENTS

VECT (input)
Specifies whether the matrix Q or the matrix P**H is required, as defined in the transformation applied by CGEBRD:
```
 = 'Q':  generate Q;
```
```
 = 'P':  generate P**H.
```
M (input)
The number of rows of the matrix Q or P**H to be returned. M > = 0.
N (input)
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)
If VECT = 'Q', the number of columns in the original M-by-K matrix reduced by CGEBRD. If VECT = 'P', the number of rows in the original K-by-N matrix reduced by CGEBRD. K > = 0.
A (input/output)
On entry, the vectors which define the elementary reflectors, as returned by CGEBRD. On exit, the M-by-N matrix Q or P**H.
LDA (input)
The leading dimension of the array A. LDA > = M.
TAU (input)
(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 CGEBRD in its array argument TAUQ or TAUP.
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input)
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)

 = 0:  successful exit

 < 0:  if INFO  = -i, the i-th argument had an illegal value