*> \brief \b DLAQZ2
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
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*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DLAQZ2( 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
* DOUBLE PRECISION :: A( LDA, * ), B( LDB, * ), Q( LDQ, * ), Z( LDZ,
* $ * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DLAQZ2 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 laqz2
*>
* =====================================================================
SUBROUTINE DLAQZ2( 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
DOUBLE PRECISION :: A( LDA, * ), B( LDB, * ), Q( LDQ, * ), Z( LDZ,
$ * )
*
* Parameters
DOUBLE PRECISION :: ZERO, ONE, HALF
PARAMETER( ZERO = 0.0D0, ONE = 1.0D0, HALF = 0.5D0 )
*
* Local variables
DOUBLE PRECISION :: H( 2, 3 ), C1, S1, C2, S2, TEMP
*
* External functions
EXTERNAL :: DLARTG, DROT
*
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 DLARTG( H( 1, 1 ), H( 2, 1 ), C1, S1, TEMP )
H( 2, 1 ) = ZERO
H( 1, 1 ) = TEMP
CALL DROT( 2, H( 1, 2 ), 2, H( 2, 2 ), 2, C1, S1 )
*
CALL DLARTG( H( 2, 3 ), H( 2, 2 ), C1, S1, TEMP )
CALL DROT( 1, H( 1, 3 ), 1, H( 1, 2 ), 1, C1, S1 )
CALL DLARTG( H( 1, 2 ), H( 1, 1 ), C2, S2, TEMP )
*
CALL DROT( IHI-ISTARTM+1, B( ISTARTM, IHI ), 1, B( ISTARTM,
$ IHI-1 ), 1, C1, S1 )
CALL DROT( 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 DROT( IHI-ISTARTM+1, A( ISTARTM, IHI ), 1, A( ISTARTM,
$ IHI-1 ), 1, C1, S1 )
CALL DROT( IHI-ISTARTM+1, A( ISTARTM, IHI-1 ), 1,
$ A( ISTARTM,
$ IHI-2 ), 1, C2, S2 )
IF ( ILZ ) THEN
CALL DROT( NZ, Z( 1, IHI-ZSTART+1 ), 1, Z( 1,
$ IHI-1-ZSTART+
$ 1 ), 1, C1, S1 )
CALL DROT( NZ, Z( 1, IHI-1-ZSTART+1 ), 1, Z( 1,
$ IHI-2-ZSTART+1 ), 1, C2, S2 )
END IF
*
CALL DLARTG( A( IHI-1, IHI-2 ), A( IHI, IHI-2 ), C1, S1,
$ TEMP )
A( IHI-1, IHI-2 ) = TEMP
A( IHI, IHI-2 ) = ZERO
CALL DROT( ISTOPM-IHI+2, A( IHI-1, IHI-1 ), LDA, A( IHI,
$ IHI-1 ), LDA, C1, S1 )
CALL DROT( ISTOPM-IHI+2, B( IHI-1, IHI-1 ), LDB, B( IHI,
$ IHI-1 ), LDB, C1, S1 )
IF ( ILQ ) THEN
CALL DROT( NQ, Q( 1, IHI-1-QSTART+1 ), 1, Q( 1,
$ IHI-QSTART+
$ 1 ), 1, C1, S1 )
END IF
*
CALL DLARTG( B( IHI, IHI ), B( IHI, IHI-1 ), C1, S1, TEMP )
B( IHI, IHI ) = TEMP
B( IHI, IHI-1 ) = ZERO
CALL DROT( IHI-ISTARTM, B( ISTARTM, IHI ), 1, B( ISTARTM,
$ IHI-1 ), 1, C1, S1 )
CALL DROT( IHI-ISTARTM+1, A( ISTARTM, IHI ), 1, A( ISTARTM,
$ IHI-1 ), 1, C1, S1 )
IF ( ILZ ) THEN
CALL DROT( 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 DLARTG( H( 1, 1 ), H( 2, 1 ), C1, S1, TEMP )
H( 2, 1 ) = ZERO
H( 1, 1 ) = TEMP
CALL DROT( 2, H( 1, 2 ), 2, H( 2, 2 ), 2, C1, S1 )
*
* Calculate Z1 and Z2
*
CALL DLARTG( H( 2, 3 ), H( 2, 2 ), C1, S1, TEMP )
CALL DROT( 1, H( 1, 3 ), 1, H( 1, 2 ), 1, C1, S1 )
CALL DLARTG( H( 1, 2 ), H( 1, 1 ), C2, S2, TEMP )
*
* Apply transformations from the right
*
CALL DROT( K+3-ISTARTM+1, A( ISTARTM, K+2 ), 1, A( ISTARTM,
$ K+1 ), 1, C1, S1 )
CALL DROT( K+3-ISTARTM+1, A( ISTARTM, K+1 ), 1, A( ISTARTM,
$ K ), 1, C2, S2 )
CALL DROT( K+2-ISTARTM+1, B( ISTARTM, K+2 ), 1, B( ISTARTM,
$ K+1 ), 1, C1, S1 )
CALL DROT( K+2-ISTARTM+1, B( ISTARTM, K+1 ), 1, B( ISTARTM,
$ K ), 1, C2, S2 )
IF ( ILZ ) THEN
CALL DROT( NZ, Z( 1, K+2-ZSTART+1 ), 1, Z( 1, K+1-ZSTART+
$ 1 ), 1, C1, S1 )
CALL DROT( 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 DLARTG( A( K+2, K ), A( K+3, K ), C1, S1, TEMP )
A( K+2, K ) = TEMP
A( K+3, K ) = ZERO
CALL DLARTG( 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 DROT( ISTOPM-K, A( K+2, K+1 ), LDA, A( K+3, K+1 ), LDA,
$ C1, S1 )
CALL DROT( ISTOPM-K, A( K+1, K+1 ), LDA, A( K+2, K+1 ), LDA,
$ C2, S2 )
*
CALL DROT( ISTOPM-K, B( K+2, K+1 ), LDB, B( K+3, K+1 ), LDB,
$ C1, S1 )
CALL DROT( ISTOPM-K, B( K+1, K+1 ), LDB, B( K+2, K+1 ), LDB,
$ C2, S2 )
IF ( ILQ ) THEN
CALL DROT( NQ, Q( 1, K+2-QSTART+1 ), 1, Q( 1, K+3-QSTART+
$ 1 ), 1, C1, S1 )
CALL DROT( NQ, Q( 1, K+1-QSTART+1 ), 1, Q( 1, K+2-QSTART+
$ 1 ), 1, C2, S2 )
END IF
*
END IF
*
* End of DLAQZ2
*
END SUBROUTINE