202 lines
5.0 KiB
Fortran
202 lines
5.0 KiB
Fortran
*> \brief \b SORGL2
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
*> \htmlonly
|
|
*> Download SORGL2 + dependencies
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sorgl2.f">
|
|
*> [TGZ]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sorgl2.f">
|
|
*> [ZIP]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sorgl2.f">
|
|
*> [TXT]</a>
|
|
*> \endhtmlonly
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE SORGL2( M, N, K, A, LDA, TAU, WORK, INFO )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* INTEGER INFO, K, LDA, M, N
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* REAL A( LDA, * ), TAU( * ), WORK( * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> SORGL2 generates an m by n real matrix Q with orthonormal rows,
|
|
*> which is defined as the first m rows of a product of k elementary
|
|
*> reflectors of order n
|
|
*>
|
|
*> Q = H(k) . . . H(2) H(1)
|
|
*>
|
|
*> as returned by SGELQF.
|
|
*> \endverbatim
|
|
*
|
|
* Arguments:
|
|
* ==========
|
|
*
|
|
*> \param[in] M
|
|
*> \verbatim
|
|
*> M is INTEGER
|
|
*> The number of rows of the matrix Q. M >= 0.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] N
|
|
*> \verbatim
|
|
*> N is INTEGER
|
|
*> The number of columns of the matrix Q. N >= M.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] K
|
|
*> \verbatim
|
|
*> K is INTEGER
|
|
*> The number of elementary reflectors whose product defines the
|
|
*> matrix Q. M >= K >= 0.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in,out] A
|
|
*> \verbatim
|
|
*> A is REAL array, dimension (LDA,N)
|
|
*> On entry, the i-th row must contain the vector which defines
|
|
*> the elementary reflector H(i), for i = 1,2,...,k, as returned
|
|
*> by SGELQF in the first k rows of its array argument A.
|
|
*> On exit, the m-by-n matrix Q.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] LDA
|
|
*> \verbatim
|
|
*> LDA is INTEGER
|
|
*> The first dimension of the array A. LDA >= max(1,M).
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] TAU
|
|
*> \verbatim
|
|
*> TAU is REAL array, dimension (K)
|
|
*> TAU(i) must contain the scalar factor of the elementary
|
|
*> reflector H(i), as returned by SGELQF.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] WORK
|
|
*> \verbatim
|
|
*> WORK is REAL array, dimension (M)
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] INFO
|
|
*> \verbatim
|
|
*> INFO is INTEGER
|
|
*> = 0: successful exit
|
|
*> < 0: if INFO = -i, the i-th argument has an illegal value
|
|
*> \endverbatim
|
|
*
|
|
* Authors:
|
|
* ========
|
|
*
|
|
*> \author Univ. of Tennessee
|
|
*> \author Univ. of California Berkeley
|
|
*> \author Univ. of Colorado Denver
|
|
*> \author NAG Ltd.
|
|
*
|
|
*> \ingroup realOTHERcomputational
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE SORGL2( M, N, K, A, LDA, TAU, WORK, 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 ..
|
|
INTEGER INFO, K, LDA, M, N
|
|
* ..
|
|
* .. Array Arguments ..
|
|
REAL A( LDA, * ), TAU( * ), WORK( * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
REAL ONE, ZERO
|
|
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
INTEGER I, J, L
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL SLARF, SSCAL, XERBLA
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC MAX
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
* Test the input arguments
|
|
*
|
|
INFO = 0
|
|
IF( M.LT.0 ) THEN
|
|
INFO = -1
|
|
ELSE IF( N.LT.M ) THEN
|
|
INFO = -2
|
|
ELSE IF( K.LT.0 .OR. K.GT.M ) THEN
|
|
INFO = -3
|
|
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
|
|
INFO = -5
|
|
END IF
|
|
IF( INFO.NE.0 ) THEN
|
|
CALL XERBLA( 'SORGL2', -INFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Quick return if possible
|
|
*
|
|
IF( M.LE.0 )
|
|
$ RETURN
|
|
*
|
|
IF( K.LT.M ) THEN
|
|
*
|
|
* Initialise rows k+1:m to rows of the unit matrix
|
|
*
|
|
DO 20 J = 1, N
|
|
DO 10 L = K + 1, M
|
|
A( L, J ) = ZERO
|
|
10 CONTINUE
|
|
IF( J.GT.K .AND. J.LE.M )
|
|
$ A( J, J ) = ONE
|
|
20 CONTINUE
|
|
END IF
|
|
*
|
|
DO 40 I = K, 1, -1
|
|
*
|
|
* Apply H(i) to A(i:m,i:n) from the right
|
|
*
|
|
IF( I.LT.N ) THEN
|
|
IF( I.LT.M ) THEN
|
|
A( I, I ) = ONE
|
|
CALL SLARF( 'Right', M-I, N-I+1, A( I, I ), LDA,
|
|
$ TAU( I ), A( I+1, I ), LDA, WORK )
|
|
END IF
|
|
CALL SSCAL( N-I, -TAU( I ), A( I, I+1 ), LDA )
|
|
END IF
|
|
A( I, I ) = ONE - TAU( I )
|
|
*
|
|
* Set A(i,1:i-1) to zero
|
|
*
|
|
DO 30 L = 1, I - 1
|
|
A( I, L ) = ZERO
|
|
30 CONTINUE
|
|
40 CONTINUE
|
|
RETURN
|
|
*
|
|
* End of SORGL2
|
|
*
|
|
END
|