SLASD5(3S)SLASD5(3S)NAME
SLASD5 - 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)SYNOPSIS
SUBROUTINE SLASD5( I, D, Z, DELTA, RHO, DSIGMA, WORK )
INTEGER I
REAL DSIGMA, RHO
REAL D( 2 ), DELTA( 2 ), WORK( 2 ), Z( 2 )
IMPLEMENTATION
These routines are part of the SCSL Scientific Library and can be loaded
using either the -lscs or the -lscs_mp option. The -lscs_mp option
directs the linker to use the multi-processor version of the library.
When linking to SCSL with -lscs or -lscs_mp, the default integer size is
4 bytes (32 bits). Another version of SCSL is available in which integers
are 8 bytes (64 bits). This version allows the user access to larger
memory sizes and helps when porting legacy Cray codes. It can be loaded
by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
only one of the two versions; 4-byte integer and 8-byte integer library
calls cannot be mixed.
PURPOSE
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.
ARGUMENTS
I (input) INTEGER
The index of the eigenvalue to be computed. I = 1 or I = 2.
D (input) REAL array, dimension ( 2 )
The original eigenvalues. We assume 0 <= D(1) < D(2).
Z (input) REAL array, dimension ( 2 )
The components of the updating vector.
DELTA (output) REAL array, dimension ( 2 )
Contains (D(j) - lambda_I) in its j-th component. The vector
DELTA contains the information necessary to construct the
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SLASD5(3S)SLASD5(3S)
eigenvectors.
RHO (input) REAL
The scalar in the symmetric updating formula.
DSIGMA (output) REAL The computed lambda_I, the I-th updated
eigenvalue.
WORK (workspace) REAL array, dimension ( 2 )
WORK contains (D(j) + sigma_I) in its j-th component.
FURTHER DETAILS
Based on contributions by
Ren-Cang Li, Computer Science Division, University of California
at Berkeley, USA
SEE ALSOINTRO_LAPACK(3S), INTRO_SCSL(3S)
This man page is available only online.
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