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* =========== DOCUMENTATION ===========
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*> Download DORGBR + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorgbr.f">
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorgbr.f">
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorgbr.f">
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* SUBROUTINE DORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
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* .. Scalar Arguments ..
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* INTEGER INFO, K, LDA, LWORK, M, N
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* .. Array Arguments ..
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* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
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*> DORGBR generates one of the real orthogonal matrices Q or P**T
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*> determined by DGEBRD when reducing a real matrix A to bidiagonal
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*> form: A = Q * B * P**T. Q and P**T are defined as products of
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*> elementary reflectors H(i) or G(i) respectively.
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*> If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q
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*> if m >= k, Q = H(1) H(2) . . . H(k) and DORGBR returns the first n
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*> columns of Q, where m >= n >= k;
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*> if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q as an
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*> If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T
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*> if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns the first m
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*> rows of P**T, where n >= m >= k;
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*> if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns P**T as
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*> VECT is CHARACTER*1
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*> Specifies whether the matrix Q or the matrix P**T is
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*> required, as defined in the transformation applied by DGEBRD:
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*> = 'P': generate P**T.
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*> The number of rows of the matrix Q or P**T to be returned.
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*> The number of columns of the matrix Q or P**T to be returned.
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*> If VECT = 'Q', M >= N >= min(M,K);
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*> if VECT = 'P', N >= M >= min(N,K).
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*> If VECT = 'Q', the number of columns in the original M-by-K
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*> matrix reduced by DGEBRD.
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*> If VECT = 'P', the number of rows in the original K-by-N
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*> matrix reduced by DGEBRD.
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*> A is DOUBLE PRECISION array, dimension (LDA,N)
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*> On entry, the vectors which define the elementary reflectors,
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*> as returned by DGEBRD.
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*> On exit, the M-by-N matrix Q or P**T.
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*> The leading dimension of the array A. LDA >= max(1,M).
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*> TAU is DOUBLE PRECISION array, dimension
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*> (min(M,K)) if VECT = 'Q'
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*> (min(N,K)) if VECT = 'P'
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*> TAU(i) must contain the scalar factor of the elementary
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*> reflector H(i) or G(i), which determines Q or P**T, as
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*> returned by DGEBRD in its array argument TAUQ or TAUP.
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*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
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*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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*> The dimension of the array WORK. LWORK >= max(1,min(M,N)).
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*> For optimum performance LWORK >= min(M,N)*NB, where NB
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*> is the optimal blocksize.
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*> If LWORK = -1, then a workspace query is assumed; the routine
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*> only calculates the optimal size of the WORK array, returns
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*> this value as the first entry of the WORK array, and no error
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*> message related to LWORK is issued by XERBLA.
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*> = 0: successful exit
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*> < 0: if INFO = -i, the i-th argument had an illegal value
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \ingroup doubleGBcomputational
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* =====================================================================
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SUBROUTINE DORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
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* -- LAPACK computational routine (version 3.4.1) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* .. Scalar Arguments ..
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INTEGER INFO, K, LDA, LWORK, M, N
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* .. Array Arguments ..
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DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
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* =====================================================================
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DOUBLE PRECISION ZERO, ONE
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PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
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* .. Local Scalars ..
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LOGICAL LQUERY, WANTQ
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INTEGER I, IINFO, J, LWKOPT, MN
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* .. External Functions ..
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EXTERNAL LSAME, ILAENV
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* .. External Subroutines ..
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EXTERNAL DORGLQ, DORGQR, XERBLA
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* .. Intrinsic Functions ..
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* .. Executable Statements ..
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* Test the input arguments
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WANTQ = LSAME( VECT, 'Q' )
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LQUERY = ( LWORK.EQ.-1 )
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IF( .NOT.WANTQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN
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ELSE IF( M.LT.0 ) THEN
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ELSE IF( N.LT.0 .OR. ( WANTQ .AND. ( N.GT.M .OR. N.LT.MIN( M,
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$ K ) ) ) .OR. ( .NOT.WANTQ .AND. ( M.GT.N .OR. M.LT.
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$ MIN( N, K ) ) ) ) THEN
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ELSE IF( K.LT.0 ) THEN
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ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
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ELSE IF( LWORK.LT.MAX( 1, MN ) .AND. .NOT.LQUERY ) THEN
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CALL DORGQR( M, N, K, A, LDA, TAU, WORK, -1, IINFO )
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CALL DORGQR( M-1, M-1, M-1, A( 2, 2 ), LDA, TAU, WORK,
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CALL DORGLQ( M, N, K, A, LDA, TAU, WORK, -1, IINFO )
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CALL DORGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
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LWKOPT = MAX (LWKOPT, MN)
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CALL XERBLA( 'DORGBR', -INFO )
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ELSE IF( LQUERY ) THEN
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* Quick return if possible
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IF( M.EQ.0 .OR. N.EQ.0 ) THEN
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* Form Q, determined by a call to DGEBRD to reduce an m-by-k
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* If m >= k, assume m >= n >= k
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CALL DORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO )
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* If m < k, assume m = n
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* Shift the vectors which define the elementary reflectors one
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* column to the right, and set the first row and column of Q
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* to those of the unit matrix
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A( I, J ) = A( I, J-1 )
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CALL DORGQR( M-1, M-1, M-1, A( 2, 2 ), LDA, TAU, WORK,
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* Form P**T, determined by a call to DGEBRD to reduce a k-by-n
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* If k < n, assume k <= m <= n
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CALL DORGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO )
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* If k >= n, assume m = n
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* Shift the vectors which define the elementary reflectors one
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* row downward, and set the first row and column of P**T to
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* those of the unit matrix
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DO 50 I = J - 1, 2, -1
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A( I, J ) = A( I-1, J )
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CALL DORGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,