.TH "laed5" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
laed5 \- laed5: D&C step: secular equation, 2x2
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBdlaed5\fP (i, d, z, delta, rho, dlam)"
.br
.RI "\fBDLAED5\fP used by DSTEDC\&. Solves the 2-by-2 secular equation\&. "
.ti -1c
.RI "subroutine \fBslaed5\fP (i, d, z, delta, rho, dlam)"
.br
.RI "\fBSLAED5\fP used by SSTEDC\&. Solves the 2-by-2 secular equation\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine dlaed5 (integer i, double precision, dimension( 2 ) d, double precision, dimension( 2 ) z, double precision, dimension( 2 ) delta, double precision rho, double precision dlam)"

.PP
\fBDLAED5\fP used by DSTEDC\&. Solves the 2-by-2 secular equation\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 This subroutine computes the I-th eigenvalue of a symmetric rank-one
 modification of a 2-by-2 diagonal matrix

            diag( D )  +  RHO * Z * transpose(Z) \&.

 The diagonal elements in the array D are assumed to satisfy

            D(i) < D(j)  for  i < j \&.

 We also assume RHO > 0 and that the Euclidean norm of the vector
 Z is one\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fII\fP 
.PP
.nf
          I is INTEGER
         The index of the eigenvalue to be computed\&.  I = 1 or I = 2\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is DOUBLE PRECISION array, dimension (2)
         The original eigenvalues\&.  We assume D(1) < D(2)\&.
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
          Z is DOUBLE PRECISION array, dimension (2)
         The components of the updating vector\&.
.fi
.PP
.br
\fIDELTA\fP 
.PP
.nf
          DELTA is DOUBLE PRECISION array, dimension (2)
         The vector DELTA contains the information necessary
         to construct the eigenvectors\&.
.fi
.PP
.br
\fIRHO\fP 
.PP
.nf
          RHO is DOUBLE PRECISION
         The scalar in the symmetric updating formula\&.
.fi
.PP
.br
\fIDLAM\fP 
.PP
.nf
          DLAM is DOUBLE PRECISION
         The computed lambda_I, the I-th updated eigenvalue\&.
.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
\fBContributors:\fP
.RS 4
Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA 
.RE
.PP

.SS "subroutine slaed5 (integer i, real, dimension( 2 ) d, real, dimension( 2 ) z, real, dimension( 2 ) delta, real rho, real dlam)"

.PP
\fBSLAED5\fP used by SSTEDC\&. Solves the 2-by-2 secular equation\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 This subroutine computes the I-th eigenvalue of a symmetric rank-one
 modification of a 2-by-2 diagonal matrix

            diag( D )  +  RHO * Z * transpose(Z) \&.

 The diagonal elements in the array D are assumed to satisfy

            D(i) < D(j)  for  i < j \&.

 We also assume RHO > 0 and that the Euclidean norm of the vector
 Z is one\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fII\fP 
.PP
.nf
          I is INTEGER
         The index of the eigenvalue to be computed\&.  I = 1 or I = 2\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is REAL array, dimension (2)
         The original eigenvalues\&.  We assume D(1) < D(2)\&.
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
          Z is REAL array, dimension (2)
         The components of the updating vector\&.
.fi
.PP
.br
\fIDELTA\fP 
.PP
.nf
          DELTA is REAL array, dimension (2)
         The vector DELTA contains the information necessary
         to construct the eigenvectors\&.
.fi
.PP
.br
\fIRHO\fP 
.PP
.nf
          RHO is REAL
         The scalar in the symmetric updating formula\&.
.fi
.PP
.br
\fIDLAM\fP 
.PP
.nf
          DLAM is REAL
         The computed lambda_I, the I-th updated eigenvalue\&.
.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
\fBContributors:\fP
.RS 4
Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA 
.RE
.PP

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