added lapack 3.7.0 with latest patches from git
This commit is contained in:
Werner Saar
287
lapack-netlib/SRC/zgerqf.f
Normal file
287
lapack-netlib/SRC/zgerqf.f
Normal file
@@ -0,0 +1,287 @@
|
||||
*> \brief \b ZGERQF
|
||||
*
|
||||
* =========== DOCUMENTATION ===========
|
||||
*
|
||||
* Online html documentation available at
|
||||
* http://www.netlib.org/lapack/explore-html/
|
||||
*
|
||||
*> \htmlonly
|
||||
*> Download ZGERQF + dependencies
|
||||
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgerqf.f">
|
||||
*> [TGZ]</a>
|
||||
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgerqf.f">
|
||||
*> [ZIP]</a>
|
||||
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgerqf.f">
|
||||
*> [TXT]</a>
|
||||
*> \endhtmlonly
|
||||
*
|
||||
* Definition:
|
||||
* ===========
|
||||
*
|
||||
* SUBROUTINE ZGERQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
* INTEGER INFO, LDA, LWORK, M, N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
|
||||
* ..
|
||||
*
|
||||
*
|
||||
*> \par Purpose:
|
||||
* =============
|
||||
*>
|
||||
*> \verbatim
|
||||
*>
|
||||
*> ZGERQF computes an RQ factorization of a complex M-by-N matrix A:
|
||||
*> A = R * Q.
|
||||
*> \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*16 array, dimension (LDA,N)
|
||||
*> On entry, the M-by-N matrix A.
|
||||
*> On exit,
|
||||
*> if m <= n, the upper triangle of the subarray
|
||||
*> A(1:m,n-m+1:n) contains the M-by-M upper triangular matrix R;
|
||||
*> if m >= n, the elements on and above the (m-n)-th subdiagonal
|
||||
*> contain the M-by-N upper trapezoidal matrix R;
|
||||
*> the remaining elements, 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*16 array, dimension (min(M,N))
|
||||
*> The scalar factors of the elementary reflectors (see Further
|
||||
*> Details).
|
||||
*> \endverbatim
|
||||
*>
|
||||
*> \param[out] WORK
|
||||
*> \verbatim
|
||||
*> WORK is COMPLEX*16 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,M).
|
||||
*> For optimum performance LWORK >= M*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 December 2016
|
||||
*
|
||||
*> \ingroup complex16GEcomputational
|
||||
*
|
||||
*> \par Further Details:
|
||||
* =====================
|
||||
*>
|
||||
*> \verbatim
|
||||
*>
|
||||
*> The matrix Q is represented as a product of elementary reflectors
|
||||
*>
|
||||
*> Q = H(1)**H H(2)**H . . . H(k)**H, 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(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on
|
||||
*> exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i).
|
||||
*> \endverbatim
|
||||
*>
|
||||
* =====================================================================
|
||||
SUBROUTINE ZGERQF( M, N, 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..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INFO, LDA, LWORK, M, N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
|
||||
* ..
|
||||
*
|
||||
* =====================================================================
|
||||
*
|
||||
* .. Local Scalars ..
|
||||
LOGICAL LQUERY
|
||||
INTEGER I, IB, IINFO, IWS, K, KI, KK, LDWORK, LWKOPT,
|
||||
$ MU, NB, NBMIN, NU, NX
|
||||
* ..
|
||||
* .. External Subroutines ..
|
||||
EXTERNAL XERBLA, ZGERQ2, ZLARFB, ZLARFT
|
||||
* ..
|
||||
* .. Intrinsic Functions ..
|
||||
INTRINSIC MAX, MIN
|
||||
* ..
|
||||
* .. External Functions ..
|
||||
INTEGER ILAENV
|
||||
EXTERNAL ILAENV
|
||||
* ..
|
||||
* .. Executable Statements ..
|
||||
*
|
||||
* Test the input arguments
|
||||
*
|
||||
INFO = 0
|
||||
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
|
||||
END IF
|
||||
*
|
||||
IF( INFO.EQ.0 ) THEN
|
||||
K = MIN( M, N )
|
||||
IF( K.EQ.0 ) THEN
|
||||
LWKOPT = 1
|
||||
ELSE
|
||||
NB = ILAENV( 1, 'ZGERQF', ' ', M, N, -1, -1 )
|
||||
LWKOPT = M*NB
|
||||
END IF
|
||||
WORK( 1 ) = LWKOPT
|
||||
*
|
||||
IF( LWORK.LT.MAX( 1, M ) .AND. .NOT.LQUERY ) THEN
|
||||
INFO = -7
|
||||
END IF
|
||||
END IF
|
||||
*
|
||||
IF( INFO.NE.0 ) THEN
|
||||
CALL XERBLA( 'ZGERQF', -INFO )
|
||||
RETURN
|
||||
ELSE IF( LQUERY ) THEN
|
||||
RETURN
|
||||
END IF
|
||||
*
|
||||
* Quick return if possible
|
||||
*
|
||||
IF( K.EQ.0 ) THEN
|
||||
RETURN
|
||||
END IF
|
||||
*
|
||||
NBMIN = 2
|
||||
NX = 1
|
||||
IWS = M
|
||||
IF( NB.GT.1 .AND. NB.LT.K ) THEN
|
||||
*
|
||||
* Determine when to cross over from blocked to unblocked code.
|
||||
*
|
||||
NX = MAX( 0, ILAENV( 3, 'ZGERQF', ' ', M, N, -1, -1 ) )
|
||||
IF( NX.LT.K ) THEN
|
||||
*
|
||||
* Determine if workspace is large enough for blocked code.
|
||||
*
|
||||
LDWORK = M
|
||||
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, 'ZGERQF', ' ', 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.
|
||||
* The last kk rows are handled by the block method.
|
||||
*
|
||||
KI = ( ( K-NX-1 ) / NB )*NB
|
||||
KK = MIN( K, KI+NB )
|
||||
*
|
||||
DO 10 I = K - KK + KI + 1, K - KK + 1, -NB
|
||||
IB = MIN( K-I+1, NB )
|
||||
*
|
||||
* Compute the RQ factorization of the current block
|
||||
* A(m-k+i:m-k+i+ib-1,1:n-k+i+ib-1)
|
||||
*
|
||||
CALL ZGERQ2( IB, N-K+I+IB-1, A( M-K+I, 1 ), LDA, TAU( I ),
|
||||
$ WORK, IINFO )
|
||||
IF( M-K+I.GT.1 ) THEN
|
||||
*
|
||||
* Form the triangular factor of the block reflector
|
||||
* H = H(i+ib-1) . . . H(i+1) H(i)
|
||||
*
|
||||
CALL ZLARFT( 'Backward', 'Rowwise', N-K+I+IB-1, IB,
|
||||
$ A( M-K+I, 1 ), LDA, TAU( I ), WORK, LDWORK )
|
||||
*
|
||||
* Apply H to A(1:m-k+i-1,1:n-k+i+ib-1) from the right
|
||||
*
|
||||
CALL ZLARFB( 'Right', 'No transpose', 'Backward',
|
||||
$ 'Rowwise', M-K+I-1, N-K+I+IB-1, IB,
|
||||
$ A( M-K+I, 1 ), LDA, WORK, LDWORK, A, LDA,
|
||||
$ WORK( IB+1 ), LDWORK )
|
||||
END IF
|
||||
10 CONTINUE
|
||||
MU = M - K + I + NB - 1
|
||||
NU = N - K + I + NB - 1
|
||||
ELSE
|
||||
MU = M
|
||||
NU = N
|
||||
END IF
|
||||
*
|
||||
* Use unblocked code to factor the last or only block
|
||||
*
|
||||
IF( MU.GT.0 .AND. NU.GT.0 )
|
||||
$ CALL ZGERQ2( MU, NU, A, LDA, TAU, WORK, IINFO )
|
||||
*
|
||||
WORK( 1 ) = IWS
|
||||
RETURN
|
||||
*
|
||||
* End of ZGERQF
|
||||
*
|
||||
END
|
||||
Reference in New Issue
Block a user