.TH "lae2" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
lae2 \- lae2: 2x2 eig, step in steqr, stemr
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBdlae2\fP (a, b, c, rt1, rt2)"
.br
.RI "\fBDLAE2\fP computes the eigenvalues of a 2-by-2 symmetric matrix\&. "
.ti -1c
.RI "subroutine \fBslae2\fP (a, b, c, rt1, rt2)"
.br
.RI "\fBSLAE2\fP computes the eigenvalues of a 2-by-2 symmetric matrix\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine dlae2 (double precision a, double precision b, double precision c, double precision rt1, double precision rt2)"

.PP
\fBDLAE2\fP computes the eigenvalues of a 2-by-2 symmetric matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DLAE2  computes the eigenvalues of a 2-by-2 symmetric matrix
    [  A   B  ]
    [  B   C  ]\&.
 On return, RT1 is the eigenvalue of larger absolute value, and RT2
 is the eigenvalue of smaller absolute value\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIA\fP 
.PP
.nf
          A is DOUBLE PRECISION
          The (1,1) element of the 2-by-2 matrix\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is DOUBLE PRECISION
          The (1,2) and (2,1) elements of the 2-by-2 matrix\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is DOUBLE PRECISION
          The (2,2) element of the 2-by-2 matrix\&.
.fi
.PP
.br
\fIRT1\fP 
.PP
.nf
          RT1 is DOUBLE PRECISION
          The eigenvalue of larger absolute value\&.
.fi
.PP
.br
\fIRT2\fP 
.PP
.nf
          RT2 is DOUBLE PRECISION
          The eigenvalue of smaller absolute value\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
  RT1 is accurate to a few ulps barring over/underflow\&.

  RT2 may be inaccurate if there is massive cancellation in the
  determinant A*C-B*B; higher precision or correctly rounded or
  correctly truncated arithmetic would be needed to compute RT2
  accurately in all cases\&.

  Overflow is possible only if RT1 is within a factor of 5 of overflow\&.
  Underflow is harmless if the input data is 0 or exceeds
     underflow_threshold / macheps\&.
.fi
.PP
 
.RE
.PP

.SS "subroutine slae2 (real a, real b, real c, real rt1, real rt2)"

.PP
\fBSLAE2\fP computes the eigenvalues of a 2-by-2 symmetric matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 SLAE2  computes the eigenvalues of a 2-by-2 symmetric matrix
    [  A   B  ]
    [  B   C  ]\&.
 On return, RT1 is the eigenvalue of larger absolute value, and RT2
 is the eigenvalue of smaller absolute value\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIA\fP 
.PP
.nf
          A is REAL
          The (1,1) element of the 2-by-2 matrix\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is REAL
          The (1,2) and (2,1) elements of the 2-by-2 matrix\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is REAL
          The (2,2) element of the 2-by-2 matrix\&.
.fi
.PP
.br
\fIRT1\fP 
.PP
.nf
          RT1 is REAL
          The eigenvalue of larger absolute value\&.
.fi
.PP
.br
\fIRT2\fP 
.PP
.nf
          RT2 is REAL
          The eigenvalue of smaller absolute value\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
  RT1 is accurate to a few ulps barring over/underflow\&.

  RT2 may be inaccurate if there is massive cancellation in the
  determinant A*C-B*B; higher precision or correctly rounded or
  correctly truncated arithmetic would be needed to compute RT2
  accurately in all cases\&.

  Overflow is possible only if RT1 is within a factor of 5 of overflow\&.
  Underflow is harmless if the input data is 0 or exceeds
     underflow_threshold / macheps\&.
.fi
.PP
 
.RE
.PP

.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.