SORGBR - generate one of the real orthogonal matrices Q or P**T determined by SGEBRD when reducing a real matrix A to bidiagonal form

SUBROUTINE SORGBR(

VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )

CHARACTER VECT

INTEGER INFO, K, LDA, LWORK, M, N

REAL A( LDA, * ), TAU( * ), WORK( * )

SORGBR generates one of the real orthogonal matrices Q or P**T determined by SGEBRD when reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and P**T 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 SORGBR returns the first n columns of Q, where m >= n >= k;

if m < k, Q = H(1) H(2) . . . H(m-1) and SORGBR returns Q as an M-by-M matrix.

If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T is of order N:

if k < n, P**T = G(k) . . . G(2) G(1) and SORGBR returns the first m rows of P**T, where n >= m >= k;

if k >= n, P**T = G(n-1) . . . G(2) G(1) and SORGBR returns P**T as an N-by-N matrix.

VECT (input) CHARACTER*1

Specifies whether the matrix Q or the matrix P**T is required, as defined in the transformation applied by SGEBRD:

= 'Q': generate Q;

= 'P': generate P**T.

M (input) INTEGER

The number of rows of the matrix Q or P**T to be returned. M >= 0.

N (input) INTEGER

The number of columns of the matrix Q or P**T 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 original M-by-K matrix reduced by SGEBRD. If VECT = 'P', the number of rows in the original K-by-N matrix reduced by SGEBRD. K >= 0.

A (input/output) REAL array, dimension (LDA,N)

On entry, the vectors which define the elementary reflectors, as returned by SGEBRD. On exit, the M-by-N matrix Q or P**T.

LDA (input) INTEGER

The leading dimension of the array A. LDA >= max(1,M).

TAU (input) REAL 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**T, as returned by SGEBRD in its array argument TAUQ or TAUP.

WORK (workspace/output) REAL 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 illegal value