.TH "SRC/slag2.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/slag2.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBslag2\fP (a, lda, b, ldb, safmin, scale1, scale2, wr1, wr2, wi)"
.br
.RI "\fBSLAG2\fP computes the eigenvalues of a 2-by-2 generalized eigenvalue problem, with scaling as necessary to avoid over-/underflow\&. "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine slag2 (real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real safmin, real scale1, real scale2, real wr1, real wr2, real wi)"

.PP
\fBSLAG2\fP computes the eigenvalues of a 2-by-2 generalized eigenvalue problem, with scaling as necessary to avoid over-/underflow\&.  
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\fBPurpose:\fP
.RS 4

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.nf
!>
!> SLAG2 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\&.
!> 
.fi
.PP
 
.RE
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\fBParameters\fP
.RS 4
\fIA\fP 
.PP
.nf
!>          A is REAL 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\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= 2\&.
!> 
.fi
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.br
\fIB\fP 
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.nf
!>          B is REAL 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\&.
!> 
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
!>          LDB is INTEGER
!>          The leading dimension of the array B\&.  LDB >= 2\&.
!> 
.fi
.PP
.br
\fISAFMIN\fP 
.PP
.nf
!>          SAFMIN is REAL
!>          The smallest positive number s\&.t\&. 1/SAFMIN does not
!>          overflow\&.  (This should always be SLAMCH('S') -- it is an
!>          argument in order to avoid having to call SLAMCH frequently\&.)
!> 
.fi
.PP
.br
\fISCALE1\fP 
.PP
.nf
!>          SCALE1 is REAL
!>          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\&.
!> 
.fi
.PP
.br
\fISCALE2\fP 
.PP
.nf
!>          SCALE2 is REAL
!>          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\&.
!> 
.fi
.PP
.br
\fIWR1\fP 
.PP
.nf
!>          WR1 is REAL
!>          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\&.
!> 
.fi
.PP
.br
\fIWR2\fP 
.PP
.nf
!>          WR2 is REAL
!>          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\&.
!> 
.fi
.PP
.br
\fIWI\fP 
.PP
.nf
!>          WI is REAL
!>          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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

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Univ\&. of California Berkeley 

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Univ\&. of Colorado Denver 

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NAG Ltd\&. 
.RE
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Definition at line \fB154\fP of file \fBslag2\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.