Login or Register to Ask a Question and Join Our Community

Linux and UNIX Man Pages

Linux & Unix Commands - Search Man Pages

dlagv2(l) [redhat man page]

DLAGV2(l)								 )								 DLAGV2(l)

NAME

       DLAGV2 - compute the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular

SYNOPSIS

       SUBROUTINE DLAGV2( A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, CSL, SNL, CSR, SNR )

	   INTEGER	  LDA, LDB

	   DOUBLE	  PRECISION CSL, CSR, SNL, SNR

	   DOUBLE	  PRECISION A( LDA, * ), ALPHAI( 2 ), ALPHAR( 2 ), B( LDB, * ), BETA( 2 )

PURPOSE

       DLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular. This routine computes
       orthogonal (rotation) matrices given by CSL, SNL and CSR, SNR such that

       1) if the pencil (A,B) has two real eigenvalues (include 0/0 or 1/0
	  types), then

	  [ a11 a12 ] := [  CSL  SNL ] [ a11 a12 ] [  CSR -SNR ]
	  [  0	a22 ]	 [ -SNL  CSL ] [ a21 a22 ] [  SNR  CSR ]

	  [ b11 b12 ] := [  CSL  SNL ] [ b11 b12 ] [  CSR -SNR ]
	  [  0	b22 ]	 [ -SNL  CSL ] [  0  b22 ] [  SNR  CSR ],

       2) if the pencil (A,B) has a pair of complex conjugate eigenvalues,
	  then

	  [ a11 a12 ] := [  CSL  SNL ] [ a11 a12 ] [  CSR -SNR ]
	  [ a21 a22 ]	 [ -SNL  CSL ] [ a21 a22 ] [  SNR  CSR ]

	  [ b11  0  ] := [  CSL  SNL ] [ b11 b12 ] [  CSR -SNR ]
	  [  0	b22 ]	 [ -SNL  CSL ] [  0  b22 ] [  SNR  CSR ]

	  where b11 >= b22 > 0.

ARGUMENTS

       A       (input/output) DOUBLE PRECISION array, dimension (LDA, 2)
	       On entry, the 2 x 2 matrix A.  On exit, A is overwritten by the ``A-part'' of the generalized Schur form.

       LDA     (input) INTEGER
	       THe leading dimension of the array A.  LDA >= 2.

       B       (input/output) DOUBLE PRECISION array, dimension (LDB, 2)
	       On entry, the upper triangular 2 x 2 matrix B.  On exit, B is overwritten by the ``B-part'' of the generalized Schur form.

       LDB     (input) INTEGER
	       THe leading dimension of the array B.  LDB >= 2.

       ALPHAR  (output) DOUBLE PRECISION array, dimension (2)
	       ALPHAI	(output)  DOUBLE  PRECISION  array,   dimension   (2)	BETA	  (output)   DOUBLE   PRECISION   array,   dimension   (2)
	       (ALPHAR(k)+i*ALPHAI(k))/BETA(k) are the eigenvalues of the pencil (A,B), k=1,2, i = sqrt(-1).  Note that BETA(k) may be zero.

       CSL     (output) DOUBLE PRECISION
	       The cosine of the left rotation matrix.

       SNL     (output) DOUBLE PRECISION
	       The sine of the left rotation matrix.

       CSR     (output) DOUBLE PRECISION
	       The cosine of the right rotation matrix.

       SNR     (output) DOUBLE PRECISION
	       The sine of the right rotation matrix.

FURTHER DETAILS

       Based on contributions by
	  Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

LAPACK version 3.0						   15 June 2000 							 DLAGV2(l)

Check Out this Related Man Page

SLAGV2(l)								 )								 SLAGV2(l)

NAME

       SLAGV2 - compute the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular

SYNOPSIS

       SUBROUTINE SLAGV2( A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, CSL, SNL, CSR, SNR )

	   INTEGER	  LDA, LDB

	   REAL 	  CSL, CSR, SNL, SNR

	   REAL 	  A( LDA, * ), ALPHAI( 2 ), ALPHAR( 2 ), B( LDB, * ), BETA( 2 )

PURPOSE

       SLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular. This routine computes
       orthogonal (rotation) matrices given by CSL, SNL and CSR, SNR such that

       1) if the pencil (A,B) has two real eigenvalues (include 0/0 or 1/0
	  types), then

	  [ a11 a12 ] := [  CSL  SNL ] [ a11 a12 ] [  CSR -SNR ]
	  [  0	a22 ]	 [ -SNL  CSL ] [ a21 a22 ] [  SNR  CSR ]

	  [ b11 b12 ] := [  CSL  SNL ] [ b11 b12 ] [  CSR -SNR ]
	  [  0	b22 ]	 [ -SNL  CSL ] [  0  b22 ] [  SNR  CSR ],

       2) if the pencil (A,B) has a pair of complex conjugate eigenvalues,
	  then

	  [ a11 a12 ] := [  CSL  SNL ] [ a11 a12 ] [  CSR -SNR ]
	  [ a21 a22 ]	 [ -SNL  CSL ] [ a21 a22 ] [  SNR  CSR ]

	  [ b11  0  ] := [  CSL  SNL ] [ b11 b12 ] [  CSR -SNR ]
	  [  0	b22 ]	 [ -SNL  CSL ] [  0  b22 ] [  SNR  CSR ]

	  where b11 >= b22 > 0.

ARGUMENTS

       A       (input/output) REAL array, dimension (LDA, 2)
	       On entry, the 2 x 2 matrix A.  On exit, A is overwritten by the ``A-part'' of the generalized Schur form.

       LDA     (input) INTEGER
	       THe leading dimension of the array A.  LDA >= 2.

       B       (input/output) REAL array, dimension (LDB, 2)
	       On entry, the upper triangular 2 x 2 matrix B.  On exit, B is overwritten by the ``B-part'' of the generalized Schur form.

       LDB     (input) INTEGER
	       THe leading dimension of the array B.  LDB >= 2.

       ALPHAR  (output) REAL array, dimension (2)
	       ALPHAI  (output) REAL array, dimension (2) BETA	  (output) REAL array, dimension (2) (ALPHAR(k)+i*ALPHAI(k))/BETA(k) are  the  ei-
	       genvalues of the pencil (A,B), k=1,2, i = sqrt(-1).  Note that BETA(k) may be zero.

       CSL     (output) REAL
	       The cosine of the left rotation matrix.

       SNL     (output) REAL
	       The sine of the left rotation matrix.

       CSR     (output) REAL
	       The cosine of the right rotation matrix.

       SNR     (output) REAL
	       The sine of the right rotation matrix.

FURTHER DETAILS

       Based on contributions by
	  Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

LAPACK version 3.0						   15 June 2000 							 SLAGV2(l)
Man Page