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| lasd5(3) | LAPACK | lasd5(3) |
NAME
lasd5 - lasd5: D&C step: secular equation, 2x2
SYNOPSIS
Functions
subroutine dlasd5 (i, d, z, delta, rho, dsigma, work)
DLASD5 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.
subroutine slasd5 (i, d, z, delta, rho, dsigma, work)
SLASD5 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.
Detailed Description
Function Documentation
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)
DLASD5 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.
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.
Parameters
I is INTEGER
The index of the eigenvalue to be computed. I = 1 or I = 2.
D
D is DOUBLE PRECISION array, dimension ( 2 )
The original eigenvalues. We assume 0 <= D(1) < D(2).
Z
Z is DOUBLE PRECISION array, dimension ( 2 )
The components of the updating vector.
DELTA
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.
RHO
RHO is DOUBLE PRECISION
The scalar in the symmetric updating formula.
DSIGMA
DSIGMA is DOUBLE PRECISION
The computed sigma_I, the I-th updated eigenvalue.
WORK
WORK is DOUBLE PRECISION array, dimension ( 2 )
WORK contains (D(j) + sigma_I) in its j-th component.
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
Definition at line 115 of file dlasd5.f.
subroutine slasd5 (integer i, real, dimension( 2 ) d, real, dimension( 2 ) z, real, dimension( 2 ) delta, real rho, real dsigma, real, dimension( 2 ) work)
SLASD5 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.
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.
Parameters
I is INTEGER
The index of the eigenvalue to be computed. I = 1 or I = 2.
D
D is REAL array, dimension (2)
The original eigenvalues. We assume 0 <= D(1) < D(2).
Z
Z is REAL array, dimension (2)
The components of the updating vector.
DELTA
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.
RHO
RHO is REAL
The scalar in the symmetric updating formula.
DSIGMA
DSIGMA is REAL
The computed sigma_I, the I-th updated eigenvalue.
WORK
WORK is REAL array, dimension (2)
WORK contains (D(j) + sigma_I) in its j-th component.
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
Definition at line 115 of file slasd5.f.
Author
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| Sun Jan 12 2025 15:13:37 | Version 3.12.1 |
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