dlasq1 (l) - Linux Manuals

dlasq1: computes the singular values of a real N-by-N bidiagonal matrix with diagonal D and off-diagonal E

NAME

DLASQ1 - computes the singular values of a real N-by-N bidiagonal matrix with diagonal D and off-diagonal E

SYNOPSIS

SUBROUTINE DLASQ1(
N, D, E, WORK, INFO )

    
INTEGER INFO, N

    
DOUBLE PRECISION D( * ), E( * ), WORK( * )

PURPOSE

DLASQ1 computes the singular values of a real N-by-N bidiagonal matrix with diagonal D and off-diagonal E. The singular values are computed to high relative accuracy, in the absence of denormalization, underflow and overflow. The algorithm was first presented in
"Accurate singular values and differential qd algorithms" by K. V. Fernando and B. N. Parlett, Numer. Math., Vol-67, No. 2, pp. 191-230, 1994,
and the present implementation is described in "An implementation of the dqds Algorithm (Positive Case)", LAPACK Working Note.

ARGUMENTS

N (input) INTEGER
The number of rows and columns in the matrix. N >= 0.
D (input/output) DOUBLE PRECISION array, dimension (N)
On entry, D contains the diagonal elements of the bidiagonal matrix whose SVD is desired. On normal exit, D contains the singular values in decreasing order.
E (input/output) DOUBLE PRECISION array, dimension (N)
On entry, elements E(1:N-1) contain the off-diagonal elements of the bidiagonal matrix whose SVD is desired. On exit, E is overwritten.
WORK (workspace) DOUBLE PRECISION array, dimension (4*N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: the algorithm failed = 1, a split was marked by a positive value in E = 2, current block of Z not diagonalized after 30*N iterations (in inner while loop) = 3, termination criterion of outer while loop not met (program created more than N unreduced blocks)

Pages related to dlasq1

  • dlasq1 (3)
  • dlasq2 (l) - computes all the eigenvalues of the symmetric positive definite tridiagonal matrix associated with the qd array Z to high relative accuracy are computed to high relative accuracy, in the absence of denormalization, underflow and overflow
  • dlasq3 (l) - checks for deflation, computes a shift (TAU) and calls dqds
  • dlasq4 (l) - computes an approximation TAU to the smallest eigenvalue using values of d from the previous transform
  • dlasq5 (l) - computes one dqds transform in ping-pong form, one version for IEEE machines another for non IEEE machines
  • dlasq6 (l) - computes one dqd (shift equal to zero) transform in ping-pong form, with protection against underflow and overflow
  • dlas2 (l) - computes the singular values of the 2-by-2 matrix [ F G ] [ 0 H ]
  • dlascl (l) - multiplies the M by N real matrix A by the real scalar CTO/CFROM
  • dlascl2 (l) - performs a diagonal scaling on a vector
  • 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