dlag2 man page on IRIX

Man page or keyword search:  
man Server   31559 pages
apropos Keyword Search (all sections)
Output format
IRIX logo
[printable version]



DLAG2(3F)							     DLAG2(3F)

NAME
     DLAG2 - compute the eigenvalues of a 2 x 2 generalized eigenvalue problem
     A - w B, with scaling as necessary to avoid over-/underflow

SYNOPSIS
     SUBROUTINE DLAG2( A, LDA, B, LDB, SAFMIN, SCALE1, SCALE2, WR1, WR2, WI )

	 INTEGER       LDA, LDB

	 DOUBLE	       PRECISION SAFMIN, SCALE1, SCALE2, WI, WR1, WR2

	 DOUBLE	       PRECISION A( LDA, * ), B( LDB, * )

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 "s" 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.

ARGUMENTS
     A	     (input) 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.

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

     B	     (input) 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.

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

     SAFMIN  (input) 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.)

     SCALE1  (output) DOUBLE PRECISION
	     A scaling factor used to avoid over-/underflow in the eigenvalue
	     equation which defines the first eigenvalue.  If the eigenvalues

									Page 1

DLAG2(3F)							     DLAG2(3F)

	     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 threshhold if the exact
	     eigenvalue is sufficiently large.

     SCALE2  (output) 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 threshhold if the exact eigenvalue is
	     sufficiently large.

     WR1     (output) 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.

     WR2     (output) 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.

     WI	     (output) 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.

									Page 2

[top]

List of man pages available for IRIX

Copyright (c) for man pages and the logo by the respective OS vendor.

For those who want to learn more, the polarhome community provides shell access and support.

[legal] [privacy] [GNU] [policy] [cookies] [netiquette] [sponsors] [FAQ]
Tweet
Polarhome, production since 1999.
Member of Polarhome portal.
Based on Fawad Halim's script.
....................................................................
Vote for polarhome
Free Shell Accounts :: the biggest list on the net