dlasd5 (l) - Linux Manuals

dlasd5: subroutine compute 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 The diagonal entries in the array D are assumed to satisfy 0 <= D(i) < D(j) for i < j

NAME

DLASD5 - subroutine compute 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 The diagonal entries in the array D are assumed to satisfy 0 <= D(i) < D(j) for i < j

SYNOPSIS

SUBROUTINE DLASD5(
I, D, Z, DELTA, RHO, DSIGMA, WORK )

    
INTEGER I

    
DOUBLE PRECISION DSIGMA, RHO

    
DOUBLE PRECISION D( 2 ), DELTA( 2 ), WORK( 2 ), Z( 2 )

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 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) DOUBLE PRECISION array, dimension ( 2 )
The original eigenvalues. We assume 0 <= D(1) < D(2).
Z (input) DOUBLE PRECISION array, dimension ( 2 )
The components of the updating vector.
DELTA (output) 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 (input) DOUBLE PRECISION
The scalar in the symmetric updating formula. DSIGMA (output) DOUBLE PRECISION The computed sigma_I, the I-th updated eigenvalue.
WORK (workspace) DOUBLE PRECISION 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

Pages related to dlasd5

  • dlasd5 (3)
  • dlasd0 (l) - a divide and conquer approach, DLASD0 computes the singular value decomposition (SVD) of a real upper bidiagonal N-by-M matrix B with diagonal D and offdiagonal E, where M = N + SQRE
  • dlasd1 (l) - computes the SVD of an upper bidiagonal N-by-M matrix B,
  • dlasd2 (l) - merges the two sets of singular values together into a single sorted set
  • dlasd3 (l) - finds all the square roots of the roots of the secular equation, as defined by the values in D and Z
  • dlasd4 (l) - subroutine compute the square root of the I-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix whose entries are given as the squares of the corresponding entries in the array d, and that 0 <= D(i) < D(j) for i < j and that RHO > 0
  • dlasd6 (l) - computes the SVD of an updated upper bidiagonal matrix B obtained by merging two smaller ones by appending a row
  • dlasd7 (l) - merges the two sets of singular values together into a single sorted set
  • dlasd8 (l) - finds the square roots of the roots of the secular equation,
  • dlasd9 (l) - find the square roots of the roots of the secular equation,
  • dlasda (l) - a divide and conquer approach, DLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal N-by-M matrix B with diagonal D and offdiagonal E, where M = N + SQRE