*> \brief \b SORGBR
*
* =========== DOCUMENTATION ===========
*
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*
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*
* Definition:
* ===========
*
* SUBROUTINE SORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
*
* .. Scalar Arguments ..
* CHARACTER VECT
* INTEGER INFO, K, LDA, LWORK, M, N
* ..
* .. Array Arguments ..
* REAL A( LDA, * ), TAU( * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] VECT
*> \verbatim
*> VECT is 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.
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix Q or P**T to be returned.
*> M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is 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).
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*> K is 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.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*> A is 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,M).
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*> TAU is 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.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is REAL array, dimension (MAX(1,LWORK))
*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is 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.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup realGBcomputational
*
* =====================================================================
SUBROUTINE SORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
*
* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
CHARACTER VECT
INTEGER INFO, K, LDA, LWORK, M, N
* ..
* .. Array Arguments ..
REAL A( LDA, * ), TAU( * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
* ..
* .. Local Scalars ..
LOGICAL LQUERY, WANTQ
INTEGER I, IINFO, J, LWKOPT, MN
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL SORGLQ, SORGQR, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. Executable Statements ..
*
* Test the input arguments
*
INFO = 0
WANTQ = LSAME( VECT, 'Q' )
MN = MIN( M, N )
LQUERY = ( LWORK.EQ.-1 )
IF( .NOT.WANTQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN
INFO = -1
ELSE IF( M.LT.0 ) THEN
INFO = -2
ELSE IF( N.LT.0 .OR. ( WANTQ .AND. ( N.GT.M .OR. N.LT.MIN( M,
$ K ) ) ) .OR. ( .NOT.WANTQ .AND. ( M.GT.N .OR. M.LT.
$ MIN( N, K ) ) ) ) THEN
INFO = -3
ELSE IF( K.LT.0 ) THEN
INFO = -4
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
INFO = -6
ELSE IF( LWORK.LT.MAX( 1, MN ) .AND. .NOT.LQUERY ) THEN
INFO = -9
END IF
*
IF( INFO.EQ.0 ) THEN
WORK( 1 ) = 1
IF( WANTQ ) THEN
IF( M.GE.K ) THEN
CALL SORGQR( M, N, K, A, LDA, TAU, WORK, -1, IINFO )
ELSE
IF( M.GT.1 ) THEN
CALL SORGQR( M-1, M-1, M-1, A( 2, 2 ), LDA, TAU, WORK,
$ -1, IINFO )
END IF
END IF
ELSE
IF( K.LT.N ) THEN
CALL SORGLQ( M, N, K, A, LDA, TAU, WORK, -1, IINFO )
ELSE
IF( N.GT.1 ) THEN
CALL SORGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
$ -1, IINFO )
END IF
END IF
END IF
LWKOPT = WORK( 1 )
LWKOPT = MAX (LWKOPT, MN)
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'SORGBR', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
WORK( 1 ) = LWKOPT
RETURN
END IF
*
* Quick return if possible
*
IF( M.EQ.0 .OR. N.EQ.0 ) THEN
WORK( 1 ) = 1
RETURN
END IF
*
IF( WANTQ ) THEN
*
* Form Q, determined by a call to SGEBRD to reduce an m-by-k
* matrix
*
IF( M.GE.K ) THEN
*
* If m >= k, assume m >= n >= k
*
CALL SORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO )
*
ELSE
*
* If m < k, assume m = n
*
* Shift the vectors which define the elementary reflectors one
* column to the right, and set the first row and column of Q
* to those of the unit matrix
*
DO 20 J = M, 2, -1
A( 1, J ) = ZERO
DO 10 I = J + 1, M
A( I, J ) = A( I, J-1 )
10 CONTINUE
20 CONTINUE
A( 1, 1 ) = ONE
DO 30 I = 2, M
A( I, 1 ) = ZERO
30 CONTINUE
IF( M.GT.1 ) THEN
*
* Form Q(2:m,2:m)
*
CALL SORGQR( M-1, M-1, M-1, A( 2, 2 ), LDA, TAU, WORK,
$ LWORK, IINFO )
END IF
END IF
ELSE
*
* Form P**T, determined by a call to SGEBRD to reduce a k-by-n
* matrix
*
IF( K.LT.N ) THEN
*
* If k < n, assume k <= m <= n
*
CALL SORGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO )
*
ELSE
*
* If k >= n, assume m = n
*
* Shift the vectors which define the elementary reflectors one
* row downward, and set the first row and column of P**T to
* those of the unit matrix
*
A( 1, 1 ) = ONE
DO 40 I = 2, N
A( I, 1 ) = ZERO
40 CONTINUE
DO 60 J = 2, N
DO 50 I = J - 1, 2, -1
A( I, J ) = A( I-1, J )
50 CONTINUE
A( 1, J ) = ZERO
60 CONTINUE
IF( N.GT.1 ) THEN
*
* Form P**T(2:n,2:n)
*
CALL SORGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
$ LWORK, IINFO )
END IF
END IF
END IF
WORK( 1 ) = LWKOPT
RETURN
*
* End of SORGBR
*
END