280 lines
7.6 KiB
Fortran
280 lines
7.6 KiB
Fortran
*> \brief \b CGEQRF
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
*> \htmlonly
|
|
*> Download CGEQRF + dependencies
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgeqrf.f">
|
|
*> [TGZ]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgeqrf.f">
|
|
*> [ZIP]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgeqrf.f">
|
|
*> [TXT]</a>
|
|
*> \endhtmlonly
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE CGEQRF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* INTEGER INFO, LDA, LWORK, M, N
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> CGEQRF computes a QR factorization of a complex M-by-N matrix A:
|
|
*>
|
|
*> A = Q * ( R ),
|
|
*> ( 0 )
|
|
*>
|
|
*> where:
|
|
*>
|
|
*> Q is a M-by-M orthogonal matrix;
|
|
*> R is an upper-triangular N-by-N matrix;
|
|
*> 0 is a (M-N)-by-N zero matrix, if M > N.
|
|
*>
|
|
*> \endverbatim
|
|
*
|
|
* Arguments:
|
|
* ==========
|
|
*
|
|
*> \param[in] M
|
|
*> \verbatim
|
|
*> M is INTEGER
|
|
*> The number of rows of the matrix A. M >= 0.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] N
|
|
*> \verbatim
|
|
*> N is INTEGER
|
|
*> The number of columns of the matrix A. N >= 0.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in,out] A
|
|
*> \verbatim
|
|
*> A is COMPLEX array, dimension (LDA,N)
|
|
*> On entry, the M-by-N matrix A.
|
|
*> On exit, the elements on and above the diagonal of the array
|
|
*> contain the min(M,N)-by-N upper trapezoidal matrix R (R is
|
|
*> upper triangular if m >= n); the elements below the diagonal,
|
|
*> with the array TAU, represent the unitary matrix Q as a
|
|
*> product of min(m,n) elementary reflectors (see Further
|
|
*> Details).
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] LDA
|
|
*> \verbatim
|
|
*> LDA is INTEGER
|
|
*> The leading dimension of the array A. LDA >= max(1,M).
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] TAU
|
|
*> \verbatim
|
|
*> TAU is COMPLEX array, dimension (min(M,N))
|
|
*> The scalar factors of the elementary reflectors (see Further
|
|
*> Details).
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] WORK
|
|
*> \verbatim
|
|
*> WORK is COMPLEX 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,N).
|
|
*> For optimum performance LWORK >= 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 November 2019
|
|
*
|
|
*> \ingroup complexGEcomputational
|
|
*
|
|
*> \par Further Details:
|
|
* =====================
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> The matrix Q is represented as a product of elementary reflectors
|
|
*>
|
|
*> Q = H(1) H(2) . . . H(k), where k = min(m,n).
|
|
*>
|
|
*> Each H(i) has the form
|
|
*>
|
|
*> H(i) = I - tau * v * v**H
|
|
*>
|
|
*> where tau is a complex scalar, and v is a complex vector with
|
|
*> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
|
|
*> and tau in TAU(i).
|
|
*> \endverbatim
|
|
*>
|
|
* =====================================================================
|
|
SUBROUTINE CGEQRF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
|
|
*
|
|
* -- LAPACK computational routine (version 3.9.0) --
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
|
* November 2019
|
|
*
|
|
* .. Scalar Arguments ..
|
|
INTEGER INFO, LDA, LWORK, M, N
|
|
* ..
|
|
* .. Array Arguments ..
|
|
COMPLEX A( LDA, * ), TAU( * ), WORK( * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Local Scalars ..
|
|
LOGICAL LQUERY
|
|
INTEGER I, IB, IINFO, IWS, K, LDWORK, LWKOPT, NB,
|
|
$ NBMIN, NX
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL CGEQR2, CLARFB, CLARFT, XERBLA
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC MAX, MIN
|
|
* ..
|
|
* .. External Functions ..
|
|
INTEGER ILAENV
|
|
EXTERNAL ILAENV
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
* Test the input arguments
|
|
*
|
|
INFO = 0
|
|
NB = ILAENV( 1, 'CGEQRF', ' ', M, N, -1, -1 )
|
|
LWKOPT = N*NB
|
|
WORK( 1 ) = LWKOPT
|
|
LQUERY = ( LWORK.EQ.-1 )
|
|
IF( M.LT.0 ) THEN
|
|
INFO = -1
|
|
ELSE IF( N.LT.0 ) THEN
|
|
INFO = -2
|
|
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
|
|
INFO = -4
|
|
ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN
|
|
INFO = -7
|
|
END IF
|
|
IF( INFO.NE.0 ) THEN
|
|
CALL XERBLA( 'CGEQRF', -INFO )
|
|
RETURN
|
|
ELSE IF( LQUERY ) THEN
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Quick return if possible
|
|
*
|
|
K = MIN( M, N )
|
|
IF( K.EQ.0 ) THEN
|
|
WORK( 1 ) = 1
|
|
RETURN
|
|
END IF
|
|
*
|
|
NBMIN = 2
|
|
NX = 0
|
|
IWS = N
|
|
IF( NB.GT.1 .AND. NB.LT.K ) THEN
|
|
*
|
|
* Determine when to cross over from blocked to unblocked code.
|
|
*
|
|
NX = MAX( 0, ILAENV( 3, 'CGEQRF', ' ', M, N, -1, -1 ) )
|
|
IF( NX.LT.K ) THEN
|
|
*
|
|
* Determine if workspace is large enough for blocked code.
|
|
*
|
|
LDWORK = N
|
|
IWS = LDWORK*NB
|
|
IF( LWORK.LT.IWS ) THEN
|
|
*
|
|
* Not enough workspace to use optimal NB: reduce NB and
|
|
* determine the minimum value of NB.
|
|
*
|
|
NB = LWORK / LDWORK
|
|
NBMIN = MAX( 2, ILAENV( 2, 'CGEQRF', ' ', M, N, -1,
|
|
$ -1 ) )
|
|
END IF
|
|
END IF
|
|
END IF
|
|
*
|
|
IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN
|
|
*
|
|
* Use blocked code initially
|
|
*
|
|
DO 10 I = 1, K - NX, NB
|
|
IB = MIN( K-I+1, NB )
|
|
*
|
|
* Compute the QR factorization of the current block
|
|
* A(i:m,i:i+ib-1)
|
|
*
|
|
CALL CGEQR2( M-I+1, IB, A( I, I ), LDA, TAU( I ), WORK,
|
|
$ IINFO )
|
|
IF( I+IB.LE.N ) THEN
|
|
*
|
|
* Form the triangular factor of the block reflector
|
|
* H = H(i) H(i+1) . . . H(i+ib-1)
|
|
*
|
|
CALL CLARFT( 'Forward', 'Columnwise', M-I+1, IB,
|
|
$ A( I, I ), LDA, TAU( I ), WORK, LDWORK )
|
|
*
|
|
* Apply H**H to A(i:m,i+ib:n) from the left
|
|
*
|
|
CALL CLARFB( 'Left', 'Conjugate transpose', 'Forward',
|
|
$ 'Columnwise', M-I+1, N-I-IB+1, IB,
|
|
$ A( I, I ), LDA, WORK, LDWORK, A( I, I+IB ),
|
|
$ LDA, WORK( IB+1 ), LDWORK )
|
|
END IF
|
|
10 CONTINUE
|
|
ELSE
|
|
I = 1
|
|
END IF
|
|
*
|
|
* Use unblocked code to factor the last or only block.
|
|
*
|
|
IF( I.LE.K )
|
|
$ CALL CGEQR2( M-I+1, N-I+1, A( I, I ), LDA, TAU( I ), WORK,
|
|
$ IINFO )
|
|
*
|
|
WORK( 1 ) = IWS
|
|
RETURN
|
|
*
|
|
* End of CGEQRF
|
|
*
|
|
END
|