257 lines
6.9 KiB
Fortran
257 lines
6.9 KiB
Fortran
*> \brief \b ZUNGTR
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
*> \htmlonly
|
|
*> Download ZUNGTR + dependencies
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zungtr.f">
|
|
*> [TGZ]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zungtr.f">
|
|
*> [ZIP]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zungtr.f">
|
|
*> [TXT]</a>
|
|
*> \endhtmlonly
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE ZUNGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* CHARACTER UPLO
|
|
* INTEGER INFO, LDA, LWORK, N
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> ZUNGTR generates a complex unitary matrix Q which is defined as the
|
|
*> product of n-1 elementary reflectors of order N, as returned by
|
|
*> ZHETRD:
|
|
*>
|
|
*> if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
|
|
*>
|
|
*> if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
|
|
*> \endverbatim
|
|
*
|
|
* Arguments:
|
|
* ==========
|
|
*
|
|
*> \param[in] UPLO
|
|
*> \verbatim
|
|
*> UPLO is CHARACTER*1
|
|
*> = 'U': Upper triangle of A contains elementary reflectors
|
|
*> from ZHETRD;
|
|
*> = 'L': Lower triangle of A contains elementary reflectors
|
|
*> from ZHETRD.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] N
|
|
*> \verbatim
|
|
*> N is INTEGER
|
|
*> The order of the matrix Q. N >= 0.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in,out] A
|
|
*> \verbatim
|
|
*> A is COMPLEX*16 array, dimension (LDA,N)
|
|
*> On entry, the vectors which define the elementary reflectors,
|
|
*> as returned by ZHETRD.
|
|
*> On exit, the N-by-N unitary matrix Q.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] LDA
|
|
*> \verbatim
|
|
*> LDA is INTEGER
|
|
*> The leading dimension of the array A. LDA >= N.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] TAU
|
|
*> \verbatim
|
|
*> TAU is COMPLEX*16 array, dimension (N-1)
|
|
*> TAU(i) must contain the scalar factor of the elementary
|
|
*> reflector H(i), as returned by ZHETRD.
|
|
*> \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 >= N-1.
|
|
*> For optimum performance LWORK >= (N-1)*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 2011
|
|
*
|
|
*> \ingroup complex16OTHERcomputational
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE ZUNGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO )
|
|
*
|
|
* -- LAPACK computational routine (version 3.4.0) --
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
|
* November 2011
|
|
*
|
|
* .. Scalar Arguments ..
|
|
CHARACTER UPLO
|
|
INTEGER INFO, LDA, LWORK, N
|
|
* ..
|
|
* .. Array Arguments ..
|
|
COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
COMPLEX*16 ZERO, ONE
|
|
PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ),
|
|
$ ONE = ( 1.0D+0, 0.0D+0 ) )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
LOGICAL LQUERY, UPPER
|
|
INTEGER I, IINFO, J, LWKOPT, NB
|
|
* ..
|
|
* .. External Functions ..
|
|
LOGICAL LSAME
|
|
INTEGER ILAENV
|
|
EXTERNAL LSAME, ILAENV
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL XERBLA, ZUNGQL, ZUNGQR
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC MAX
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
* Test the input arguments
|
|
*
|
|
INFO = 0
|
|
LQUERY = ( LWORK.EQ.-1 )
|
|
UPPER = LSAME( UPLO, 'U' )
|
|
IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
|
|
INFO = -1
|
|
ELSE IF( N.LT.0 ) THEN
|
|
INFO = -2
|
|
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
|
|
INFO = -4
|
|
ELSE IF( LWORK.LT.MAX( 1, N-1 ) .AND. .NOT.LQUERY ) THEN
|
|
INFO = -7
|
|
END IF
|
|
*
|
|
IF( INFO.EQ.0 ) THEN
|
|
IF( UPPER ) THEN
|
|
NB = ILAENV( 1, 'ZUNGQL', ' ', N-1, N-1, N-1, -1 )
|
|
ELSE
|
|
NB = ILAENV( 1, 'ZUNGQR', ' ', N-1, N-1, N-1, -1 )
|
|
END IF
|
|
LWKOPT = MAX( 1, N-1 )*NB
|
|
WORK( 1 ) = LWKOPT
|
|
END IF
|
|
*
|
|
IF( INFO.NE.0 ) THEN
|
|
CALL XERBLA( 'ZUNGTR', -INFO )
|
|
RETURN
|
|
ELSE IF( LQUERY ) THEN
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Quick return if possible
|
|
*
|
|
IF( N.EQ.0 ) THEN
|
|
WORK( 1 ) = 1
|
|
RETURN
|
|
END IF
|
|
*
|
|
IF( UPPER ) THEN
|
|
*
|
|
* Q was determined by a call to ZHETRD with UPLO = 'U'
|
|
*
|
|
* Shift the vectors which define the elementary reflectors one
|
|
* column to the left, and set the last row and column of Q to
|
|
* those of the unit matrix
|
|
*
|
|
DO 20 J = 1, N - 1
|
|
DO 10 I = 1, J - 1
|
|
A( I, J ) = A( I, J+1 )
|
|
10 CONTINUE
|
|
A( N, J ) = ZERO
|
|
20 CONTINUE
|
|
DO 30 I = 1, N - 1
|
|
A( I, N ) = ZERO
|
|
30 CONTINUE
|
|
A( N, N ) = ONE
|
|
*
|
|
* Generate Q(1:n-1,1:n-1)
|
|
*
|
|
CALL ZUNGQL( N-1, N-1, N-1, A, LDA, TAU, WORK, LWORK, IINFO )
|
|
*
|
|
ELSE
|
|
*
|
|
* Q was determined by a call to ZHETRD with UPLO = 'L'.
|
|
*
|
|
* 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 50 J = N, 2, -1
|
|
A( 1, J ) = ZERO
|
|
DO 40 I = J + 1, N
|
|
A( I, J ) = A( I, J-1 )
|
|
40 CONTINUE
|
|
50 CONTINUE
|
|
A( 1, 1 ) = ONE
|
|
DO 60 I = 2, N
|
|
A( I, 1 ) = ZERO
|
|
60 CONTINUE
|
|
IF( N.GT.1 ) THEN
|
|
*
|
|
* Generate Q(2:n,2:n)
|
|
*
|
|
CALL ZUNGQR( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
|
|
$ LWORK, IINFO )
|
|
END IF
|
|
END IF
|
|
WORK( 1 ) = LWKOPT
|
|
RETURN
|
|
*
|
|
* End of ZUNGTR
|
|
*
|
|
END
|