You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
315 lines
9.3 KiB
315 lines
9.3 KiB
2 years ago
|
*> \brief \b SLAQZ2
|
||
|
|
*
|
||
|
|
* =========== DOCUMENTATION ===========
|
||
|
|
*
|
||
|
|
* Online html documentation available at
|
||
|
|
* http://www.netlib.org/lapack/explore-html/
|
||
|
|
*
|
||
|
|
*> \htmlonly
|
||
|
|
*> Download SLAQZ2 + dependencies
|
||
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slaqz2.f">
|
||
|
|
*> [TGZ]</a>
|
||
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slaqz2.f">
|
||
|
|
*> [ZIP]</a>
|
||
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slaqz2.f">
|
||
|
|
*> [TXT]</a>
|
||
|
|
*> \endhtmlonly
|
||
|
|
*
|
||
|
|
* Definition:
|
||
|
|
* ===========
|
||
|
|
*
|
||
|
|
* SUBROUTINE SLAQZ2( ILQ, ILZ, K, ISTARTM, ISTOPM, IHI, A, LDA, B,
|
||
|
|
* $ LDB, NQ, QSTART, Q, LDQ, NZ, ZSTART, Z, LDZ )
|
||
|
|
* IMPLICIT NONE
|
||
|
|
*
|
||
|
|
* Arguments
|
||
|
|
* LOGICAL, INTENT( IN ) :: ILQ, ILZ
|
||
|
|
* INTEGER, INTENT( IN ) :: K, LDA, LDB, LDQ, LDZ, ISTARTM, ISTOPM,
|
||
|
|
* $ NQ, NZ, QSTART, ZSTART, IHI
|
||
|
|
* REAL :: A( LDA, * ), B( LDB, * ), Q( LDQ, * ), Z( LDZ, * )
|
||
|
|
* ..
|
||
|
|
*
|
||
|
|
*
|
||
|
|
*> \par Purpose:
|
||
|
|
* =============
|
||
|
|
*>
|
||
|
|
*> \verbatim
|
||
|
|
*>
|
||
|
|
*> SLAQZ2 chases a 2x2 shift bulge in a matrix pencil down a single position
|
||
|
|
*> \endverbatim
|
||
|
|
*
|
||
|
|
*
|
||
|
|
* Arguments:
|
||
|
|
* ==========
|
||
|
|
*
|
||
|
|
*>
|
||
|
|
*> \param[in] ILQ
|
||
|
|
*> \verbatim
|
||
|
|
*> ILQ is LOGICAL
|
||
|
|
*> Determines whether or not to update the matrix Q
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] ILZ
|
||
|
|
*> \verbatim
|
||
|
|
*> ILZ is LOGICAL
|
||
|
|
*> Determines whether or not to update the matrix Z
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] K
|
||
|
|
*> \verbatim
|
||
|
|
*> K is INTEGER
|
||
|
|
*> Index indicating the position of the bulge.
|
||
|
|
*> On entry, the bulge is located in
|
||
|
|
*> (A(k+1:k+2,k:k+1),B(k+1:k+2,k:k+1)).
|
||
|
|
*> On exit, the bulge is located in
|
||
|
|
*> (A(k+2:k+3,k+1:k+2),B(k+2:k+3,k+1:k+2)).
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] ISTARTM
|
||
|
|
*> \verbatim
|
||
|
|
*> ISTARTM is INTEGER
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] ISTOPM
|
||
|
|
*> \verbatim
|
||
|
|
*> ISTOPM is INTEGER
|
||
|
|
*> Updates to (A,B) are restricted to
|
||
|
|
*> (istartm:k+3,k:istopm). It is assumed
|
||
|
|
*> without checking that istartm <= k+1 and
|
||
|
|
*> k+2 <= istopm
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] IHI
|
||
|
|
*> \verbatim
|
||
|
|
*> IHI is INTEGER
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[inout] A
|
||
|
|
*> \verbatim
|
||
|
|
*> A is REAL array, dimension (LDA,N)
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] LDA
|
||
|
|
*> \verbatim
|
||
|
|
*> LDA is INTEGER
|
||
|
|
*> The leading dimension of A as declared in
|
||
|
|
*> the calling procedure.
|
||
|
|
*> \endverbatim
|
||
|
|
*
|
||
|
|
*> \param[inout] B
|
||
|
|
*> \verbatim
|
||
|
|
*> B is REAL array, dimension (LDB,N)
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] LDB
|
||
|
|
*> \verbatim
|
||
|
|
*> LDB is INTEGER
|
||
|
|
*> The leading dimension of B as declared in
|
||
|
|
*> the calling procedure.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] NQ
|
||
|
|
*> \verbatim
|
||
|
|
*> NQ is INTEGER
|
||
|
|
*> The order of the matrix Q
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] QSTART
|
||
|
|
*> \verbatim
|
||
|
|
*> QSTART is INTEGER
|
||
|
|
*> Start index of the matrix Q. Rotations are applied
|
||
|
|
*> To columns k+2-qStart:k+4-qStart of Q.
|
||
|
|
*> \endverbatim
|
||
|
|
*
|
||
|
|
*> \param[inout] Q
|
||
|
|
*> \verbatim
|
||
|
|
*> Q is REAL array, dimension (LDQ,NQ)
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] LDQ
|
||
|
|
*> \verbatim
|
||
|
|
*> LDQ is INTEGER
|
||
|
|
*> The leading dimension of Q as declared in
|
||
|
|
*> the calling procedure.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] NZ
|
||
|
|
*> \verbatim
|
||
|
|
*> NZ is INTEGER
|
||
|
|
*> The order of the matrix Z
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] ZSTART
|
||
|
|
*> \verbatim
|
||
|
|
*> ZSTART is INTEGER
|
||
|
|
*> Start index of the matrix Z. Rotations are applied
|
||
|
|
*> To columns k+1-qStart:k+3-qStart of Z.
|
||
|
|
*> \endverbatim
|
||
|
|
*
|
||
|
|
*> \param[inout] Z
|
||
|
|
*> \verbatim
|
||
|
|
*> Z is REAL array, dimension (LDZ,NZ)
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] LDZ
|
||
|
|
*> \verbatim
|
||
|
|
*> LDZ is INTEGER
|
||
|
|
*> The leading dimension of Q as declared in
|
||
|
|
*> the calling procedure.
|
||
|
|
*> \endverbatim
|
||
|
|
*
|
||
|
|
* Authors:
|
||
|
|
* ========
|
||
|
|
*
|
||
|
|
*> \author Thijs Steel, KU Leuven
|
||
|
|
*
|
||
|
|
*> \date May 2020
|
||
|
|
*
|
||
|
|
*> \ingroup doubleGEcomputational
|
||
|
|
*>
|
||
|
|
* =====================================================================
|
||
|
|
SUBROUTINE SLAQZ2( ILQ, ILZ, K, ISTARTM, ISTOPM, IHI, A, LDA, B,
|
||
|
|
$ LDB, NQ, QSTART, Q, LDQ, NZ, ZSTART, Z, LDZ )
|
||
|
|
IMPLICIT NONE
|
||
|
|
*
|
||
|
|
* Arguments
|
||
|
|
LOGICAL, INTENT( IN ) :: ILQ, ILZ
|
||
|
|
INTEGER, INTENT( IN ) :: K, LDA, LDB, LDQ, LDZ, ISTARTM, ISTOPM,
|
||
|
|
$ NQ, NZ, QSTART, ZSTART, IHI
|
||
|
|
REAL :: A( LDA, * ), B( LDB, * ), Q( LDQ, * ), Z( LDZ, * )
|
||
|
|
*
|
||
|
|
* Parameters
|
||
|
|
REAL :: ZERO, ONE, HALF
|
||
|
|
PARAMETER( ZERO = 0.0, ONE = 1.0, HALF = 0.5 )
|
||
|
|
*
|
||
|
|
* Local variables
|
||
|
|
REAL :: H( 2, 3 ), C1, S1, C2, S2, TEMP
|
||
|
|
*
|
||
|
|
* External functions
|
||
|
|
EXTERNAL :: SLARTG, SROT
|
||
|
|
*
|
||
|
|
IF( K+2 .EQ. IHI ) THEN
|
||
|
|
* Shift is located on the edge of the matrix, remove it
|
||
|
|
H = B( IHI-1:IHI, IHI-2:IHI )
|
||
|
|
* Make H upper triangular
|
||
|
|
CALL SLARTG( H( 1, 1 ), H( 2, 1 ), C1, S1, TEMP )
|
||
|
|
H( 2, 1 ) = ZERO
|
||
|
|
H( 1, 1 ) = TEMP
|
||
|
|
CALL SROT( 2, H( 1, 2 ), 2, H( 2, 2 ), 2, C1, S1 )
|
||
|
|
*
|
||
|
|
CALL SLARTG( H( 2, 3 ), H( 2, 2 ), C1, S1, TEMP )
|
||
|
|
CALL SROT( 1, H( 1, 3 ), 1, H( 1, 2 ), 1, C1, S1 )
|
||
|
|
CALL SLARTG( H( 1, 2 ), H( 1, 1 ), C2, S2, TEMP )
|
||
|
|
*
|
||
|
|
CALL SROT( IHI-ISTARTM+1, B( ISTARTM, IHI ), 1, B( ISTARTM,
|
||
|
|
$ IHI-1 ), 1, C1, S1 )
|
||
|
|
CALL SROT( IHI-ISTARTM+1, B( ISTARTM, IHI-1 ), 1, B( ISTARTM,
|
||
|
|
$ IHI-2 ), 1, C2, S2 )
|
||
|
|
B( IHI-1, IHI-2 ) = ZERO
|
||
|
|
B( IHI, IHI-2 ) = ZERO
|
||
|
|
CALL SROT( IHI-ISTARTM+1, A( ISTARTM, IHI ), 1, A( ISTARTM,
|
||
|
|
$ IHI-1 ), 1, C1, S1 )
|
||
|
|
CALL SROT( IHI-ISTARTM+1, A( ISTARTM, IHI-1 ), 1, A( ISTARTM,
|
||
|
|
$ IHI-2 ), 1, C2, S2 )
|
||
|
|
IF ( ILZ ) THEN
|
||
|
|
CALL SROT( NZ, Z( 1, IHI-ZSTART+1 ), 1, Z( 1, IHI-1-ZSTART+
|
||
|
|
$ 1 ), 1, C1, S1 )
|
||
|
|
CALL SROT( NZ, Z( 1, IHI-1-ZSTART+1 ), 1, Z( 1,
|
||
|
|
$ IHI-2-ZSTART+1 ), 1, C2, S2 )
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
CALL SLARTG( A( IHI-1, IHI-2 ), A( IHI, IHI-2 ), C1, S1,
|
||
|
|
$ TEMP )
|
||
|
|
A( IHI-1, IHI-2 ) = TEMP
|
||
|
|
A( IHI, IHI-2 ) = ZERO
|
||
|
|
CALL SROT( ISTOPM-IHI+2, A( IHI-1, IHI-1 ), LDA, A( IHI,
|
||
|
|
$ IHI-1 ), LDA, C1, S1 )
|
||
|
|
CALL SROT( ISTOPM-IHI+2, B( IHI-1, IHI-1 ), LDB, B( IHI,
|
||
|
|
$ IHI-1 ), LDB, C1, S1 )
|
||
|
|
IF ( ILQ ) THEN
|
||
|
|
CALL SROT( NQ, Q( 1, IHI-1-QSTART+1 ), 1, Q( 1, IHI-QSTART+
|
||
|
|
$ 1 ), 1, C1, S1 )
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
CALL SLARTG( B( IHI, IHI ), B( IHI, IHI-1 ), C1, S1, TEMP )
|
||
|
|
B( IHI, IHI ) = TEMP
|
||
|
|
B( IHI, IHI-1 ) = ZERO
|
||
|
|
CALL SROT( IHI-ISTARTM, B( ISTARTM, IHI ), 1, B( ISTARTM,
|
||
|
|
$ IHI-1 ), 1, C1, S1 )
|
||
|
|
CALL SROT( IHI-ISTARTM+1, A( ISTARTM, IHI ), 1, A( ISTARTM,
|
||
|
|
$ IHI-1 ), 1, C1, S1 )
|
||
|
|
IF ( ILZ ) THEN
|
||
|
|
CALL SROT( NZ, Z( 1, IHI-ZSTART+1 ), 1, Z( 1, IHI-1-ZSTART+
|
||
|
|
$ 1 ), 1, C1, S1 )
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* Normal operation, move bulge down
|
||
|
|
*
|
||
|
|
H = B( K+1:K+2, K:K+2 )
|
||
|
|
*
|
||
|
|
* Make H upper triangular
|
||
|
|
*
|
||
|
|
CALL SLARTG( H( 1, 1 ), H( 2, 1 ), C1, S1, TEMP )
|
||
|
|
H( 2, 1 ) = ZERO
|
||
|
|
H( 1, 1 ) = TEMP
|
||
|
|
CALL SROT( 2, H( 1, 2 ), 2, H( 2, 2 ), 2, C1, S1 )
|
||
|
|
*
|
||
|
|
* Calculate Z1 and Z2
|
||
|
|
*
|
||
|
|
CALL SLARTG( H( 2, 3 ), H( 2, 2 ), C1, S1, TEMP )
|
||
|
|
CALL SROT( 1, H( 1, 3 ), 1, H( 1, 2 ), 1, C1, S1 )
|
||
|
|
CALL SLARTG( H( 1, 2 ), H( 1, 1 ), C2, S2, TEMP )
|
||
|
|
*
|
||
|
|
* Apply transformations from the right
|
||
|
|
*
|
||
|
|
CALL SROT( K+3-ISTARTM+1, A( ISTARTM, K+2 ), 1, A( ISTARTM,
|
||
|
|
$ K+1 ), 1, C1, S1 )
|
||
|
|
CALL SROT( K+3-ISTARTM+1, A( ISTARTM, K+1 ), 1, A( ISTARTM,
|
||
|
|
$ K ), 1, C2, S2 )
|
||
|
|
CALL SROT( K+2-ISTARTM+1, B( ISTARTM, K+2 ), 1, B( ISTARTM,
|
||
|
|
$ K+1 ), 1, C1, S1 )
|
||
|
|
CALL SROT( K+2-ISTARTM+1, B( ISTARTM, K+1 ), 1, B( ISTARTM,
|
||
|
|
$ K ), 1, C2, S2 )
|
||
|
|
IF ( ILZ ) THEN
|
||
|
|
CALL SROT( NZ, Z( 1, K+2-ZSTART+1 ), 1, Z( 1, K+1-ZSTART+
|
||
|
|
$ 1 ), 1, C1, S1 )
|
||
|
|
CALL SROT( NZ, Z( 1, K+1-ZSTART+1 ), 1, Z( 1, K-ZSTART+1 ),
|
||
|
|
$ 1, C2, S2 )
|
||
|
|
END IF
|
||
|
|
B( K+1, K ) = ZERO
|
||
|
|
B( K+2, K ) = ZERO
|
||
|
|
*
|
||
|
|
* Calculate Q1 and Q2
|
||
|
|
*
|
||
|
|
CALL SLARTG( A( K+2, K ), A( K+3, K ), C1, S1, TEMP )
|
||
|
|
A( K+2, K ) = TEMP
|
||
|
|
A( K+3, K ) = ZERO
|
||
|
|
CALL SLARTG( A( K+1, K ), A( K+2, K ), C2, S2, TEMP )
|
||
|
|
A( K+1, K ) = TEMP
|
||
|
|
A( K+2, K ) = ZERO
|
||
|
|
*
|
||
|
|
* Apply transformations from the left
|
||
|
|
*
|
||
|
|
CALL SROT( ISTOPM-K, A( K+2, K+1 ), LDA, A( K+3, K+1 ), LDA,
|
||
|
|
$ C1, S1 )
|
||
|
|
CALL SROT( ISTOPM-K, A( K+1, K+1 ), LDA, A( K+2, K+1 ), LDA,
|
||
|
|
$ C2, S2 )
|
||
|
|
*
|
||
|
|
CALL SROT( ISTOPM-K, B( K+2, K+1 ), LDB, B( K+3, K+1 ), LDB,
|
||
|
|
$ C1, S1 )
|
||
|
|
CALL SROT( ISTOPM-K, B( K+1, K+1 ), LDB, B( K+2, K+1 ), LDB,
|
||
|
|
$ C2, S2 )
|
||
|
|
IF ( ILQ ) THEN
|
||
|
|
CALL SROT( NQ, Q( 1, K+2-QSTART+1 ), 1, Q( 1, K+3-QSTART+
|
||
|
|
$ 1 ), 1, C1, S1 )
|
||
|
|
CALL SROT( NQ, Q( 1, K+1-QSTART+1 ), 1, Q( 1, K+2-QSTART+
|
||
|
|
$ 1 ), 1, C2, S2 )
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* End of SLAQZ2
|
||
|
|
*
|
||
|
|
END SUBROUTINE
|