dlasd9 (l) - Linux Manuals

dlasd9: find the square roots of the roots of the secular equation,

NAME

DLASD9 - find the square roots of the roots of the secular equation,

SYNOPSIS

SUBROUTINE DLASD9(
ICOMPQ, LDU, K, D, Z, VF, VL, DIFL, DIFR, DSIGMA, WORK, INFO )

    
INTEGER ICOMPQ, INFO, K, LDU

    
DOUBLE PRECISION D( * ), DIFL( * ), DIFR( LDU, * ), DSIGMA( * ), VF( * ), VL( * ), WORK( * ), Z( * )

PURPOSE

DLASD9 finds the square roots of the roots of the secular equation, as defined by the values in DSIGMA and Z. It makes the
appropriate calls to DLASD4, and stores, for each element in D, the distance to its two nearest poles (elements in DSIGMA). It also updates the arrays VF and VL, the first and last components of all the right singular vectors of the original bidiagonal matrix.

DLASD9 is called from DLASD7.

ARGUMENTS

ICOMPQ (input) INTEGER
Specifies whether singular vectors are to be computed in factored form in the calling routine:

ICOMPQ = 0 Compute singular values only.

ICOMPQ = 1 Compute singular vector matrices in factored form also. K (input) INTEGER The number of terms in the rational function to be solved by DLASD4. K >= 1.

D (output) DOUBLE PRECISION array, dimension(K)
D(I) contains the updated singular values.
DSIGMA (input) DOUBLE PRECISION array, dimension(K)
The first K elements of this array contain the old roots of the deflated updating problem. These are the poles of the secular equation.
Z (input) DOUBLE PRECISION array, dimension (K)
The first K elements of this array contain the components of the deflation-adjusted updating row vector.
VF (input/output) DOUBLE PRECISION array, dimension(K)
On entry, VF contains information passed through SBEDE8.f On exit, VF contains the first K components of the first components of all right singular vectors of the bidiagonal matrix.
VL (input/output) DOUBLE PRECISION array, dimension(K)
On entry, VL contains information passed through SBEDE8.f On exit, VL contains the first K components of the last components of all right singular vectors of the bidiagonal matrix.
DIFL (output) DOUBLE PRECISION array, dimension (K).
On exit, DIFL(I) = D(I) - DSIGMA(I).
DIFR (output) DOUBLE PRECISION array,
dimension (LDU, 2) if ICOMPQ =1 and dimension (K) if ICOMPQ = 0. On exit, DIFR(I, 1) = D(I) - DSIGMA(I+1), DIFR(K, 1) is not defined and will not be referenced.

If ICOMPQ = 1, DIFR(1:K, 2) is an array containing the normalizing factors for the right singular vector matrix.

WORK (workspace) DOUBLE PRECISION array,
dimension at least (3 * K) Workspace.
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = 1, an singular value did not converge

FURTHER DETAILS

Based on contributions by

Ming Gu and Huan Ren, Computer Science Division, University of
California at Berkeley, USA

Pages related to dlasd9

  • 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
  • dlasd5 (l) - 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
  • 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,
  • 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
  • dlasdq (l) - computes the singular value decomposition (SVD) of a real (upper or lower) bidiagonal matrix with diagonal D and offdiagonal E, accumulating the transformations if desired