.TH "lasd5" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
lasd5 \- lasd5: D&C step: secular equation, 2x2
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBdlasd5\fP (i, d, z, delta, rho, dsigma, work)"
.br
.RI "\fBDLASD5\fP computes the square root of the i-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix\&. Used by sbdsdc\&. "
.ti -1c
.RI "subroutine \fBslasd5\fP (i, d, z, delta, rho, dsigma, work)"
.br
.RI "\fBSLASD5\fP computes the square root of the i-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix\&. Used by sbdsdc\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine dlasd5 (integer i, double precision, dimension( 2 ) d, double precision, dimension( 2 ) z, double precision, dimension( 2 ) delta, double precision rho, double precision dsigma, double precision, dimension( 2 ) work)"

.PP
\fBDLASD5\fP computes the square root of the i-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix\&. Used by sbdsdc\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> This subroutine computes the square root of the I-th eigenvalue
!> of a positive symmetric rank-one modification of a 2-by-2 diagonal
!> matrix
!>
!>            diag( D ) * diag( D ) +  RHO * Z * transpose(Z) \&.
!>
!> The diagonal entries in the array D are assumed to satisfy
!>
!>            0 <= 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 0 <= 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 )
!>         Contains (D(j) - sigma_I) in its  j-th component\&.
!>         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
\fIDSIGMA\fP 
.PP
.nf
!>          DSIGMA is DOUBLE PRECISION
!>         The computed sigma_I, the I-th updated eigenvalue\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is DOUBLE PRECISION array, dimension ( 2 )
!>         WORK contains (D(j) + sigma_I) in its  j-th component\&.
!> 
.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

.PP
Definition at line \fB115\fP of file \fBdlasd5\&.f\fP\&.
.SS "subroutine slasd5 (integer i, real, dimension( 2 ) d, real, dimension( 2 ) z, real, dimension( 2 ) delta, real rho, real dsigma, real, dimension( 2 ) work)"

.PP
\fBSLASD5\fP computes the square root of the i-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix\&. Used by sbdsdc\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> This subroutine computes the square root of the I-th eigenvalue
!> of a positive symmetric rank-one modification of a 2-by-2 diagonal
!> matrix
!>
!>            diag( D ) * diag( D ) +  RHO * Z * transpose(Z) \&.
!>
!> The diagonal entries in the array D are assumed to satisfy
!>
!>            0 <= 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 0 <= 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)
!>         Contains (D(j) - sigma_I) in its  j-th component\&.
!>         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
\fIDSIGMA\fP 
.PP
.nf
!>          DSIGMA is REAL
!>         The computed sigma_I, the I-th updated eigenvalue\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is REAL array, dimension (2)
!>         WORK contains (D(j) + sigma_I) in its  j-th component\&.
!> 
.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

.PP
Definition at line \fB115\fP of file \fBslasd5\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.