dlag2()

subroutine dlag2	(	double precision, dimension( lda, * )	a,
		integer	lda,
		double precision, dimension( ldb, * )	b,
		integer	ldb,
		double precision	safmin,
		double precision	scale1,
		double precision	scale2,
		double precision	wr1,
		double precision	wr2,
		double precision	wi )

DLAG2 computes the eigenvalues of a 2-by-2 generalized eigenvalue problem, with scaling as necessary to avoid over-/underflow.

Download DLAG2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:

!>
!> DLAG2 computes the eigenvalues of a 2 x 2 generalized eigenvalue
!> problem  A - w B, with scaling as necessary to avoid over-/underflow.
!>
!> The scaling factor  results in a modified eigenvalue equation
!>
!>     s A - w B
!>
!> where  s  is a non-negative scaling factor chosen so that  w,  w B,
!> and  s A  do not overflow and, if possible, do not underflow, either.
!> 

Parameters

[in]	A	!> A is DOUBLE PRECISION array, dimension (LDA, 2) !> On entry, the 2 x 2 matrix A. It is assumed that its 1-norm !> is less than 1/SAFMIN. Entries less than !> sqrt(SAFMIN)*norm(A) are subject to being treated as zero. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= 2. !>
[in]	B	!> B is DOUBLE PRECISION array, dimension (LDB, 2) !> On entry, the 2 x 2 upper triangular matrix B. It is !> assumed that the one-norm of B is less than 1/SAFMIN. The !> diagonals should be at least sqrt(SAFMIN) times the largest !> element of B (in absolute value); if a diagonal is smaller !> than that, then +/- sqrt(SAFMIN) will be used instead of !> that diagonal. !>
[in]	LDB	!> LDB is INTEGER !> The leading dimension of the array B. LDB >= 2. !>
[in]	SAFMIN	!> SAFMIN is DOUBLE PRECISION !> The smallest positive number s.t. 1/SAFMIN does not !> overflow. (This should always be DLAMCH('S') -- it is an !> argument in order to avoid having to call DLAMCH frequently.) !>
[out]	SCALE1	!> SCALE1 is DOUBLE PRECISION !> A scaling factor used to avoid over-/underflow in the !> eigenvalue equation which defines the first eigenvalue. If !> the eigenvalues are complex, then the eigenvalues are !> ( WR1 +/- WI i ) / SCALE1 (which may lie outside the !> exponent range of the machine), SCALE1=SCALE2, and SCALE1 !> will always be positive. If the eigenvalues are real, then !> the first (real) eigenvalue is WR1 / SCALE1 , but this may !> overflow or underflow, and in fact, SCALE1 may be zero or !> less than the underflow threshold if the exact eigenvalue !> is sufficiently large. !>
[out]	SCALE2	!> SCALE2 is DOUBLE PRECISION !> A scaling factor used to avoid over-/underflow in the !> eigenvalue equation which defines the second eigenvalue. If !> the eigenvalues are complex, then SCALE2=SCALE1. If the !> eigenvalues are real, then the second (real) eigenvalue is !> WR2 / SCALE2 , but this may overflow or underflow, and in !> fact, SCALE2 may be zero or less than the underflow !> threshold if the exact eigenvalue is sufficiently large. !>
[out]	WR1	!> WR1 is DOUBLE PRECISION !> If the eigenvalue is real, then WR1 is SCALE1 times the !> eigenvalue closest to the (2,2) element of A B**(-1). If the !> eigenvalue is complex, then WR1=WR2 is SCALE1 times the real !> part of the eigenvalues. !>
[out]	WR2	!> WR2 is DOUBLE PRECISION !> If the eigenvalue is real, then WR2 is SCALE2 times the !> other eigenvalue. If the eigenvalue is complex, then !> WR1=WR2 is SCALE1 times the real part of the eigenvalues. !>
[out]	WI	!> WI is DOUBLE PRECISION !> If the eigenvalue is real, then WI is zero. If the !> eigenvalue is complex, then WI is SCALE1 times the imaginary !> part of the eigenvalues. WI will always be non-negative. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.