*> \brief \b SORGBR * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download SORGBR + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * 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. * *> \date April 2012 * *> \ingroup realGBcomputational * * ===================================================================== SUBROUTINE SORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * April 2012 * * .. 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