dlasq1.f (3) Linux Manual Page

dlasq1.f –

Synopsis

Functions/Subroutines

subroutine dlasq1 (N, D, E, WORK, INFO)
DLASQ1 computes the singular values of a real square bidiagonal matrix. Used by sbdsqr.

Function/Subroutine Documentation

subroutine dlasq1 (integerN, double precision, dimension( * )D, double precision, dimension( * )E, double precision, dimension( * )WORK, integerINFO)

DLASQ1 computes the singular values of a real square bidiagonal matrix. Used by sbdsqr.

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.

 

Parameters:

N

 N is INTEGER

 The number of rows and columns in the matrix. N >= 0.

D

 D is 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

 E is 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

 WORK is DOUBLE PRECISION array, dimension (4*N)

INFO

 INFO is 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 100*N

 iterations (in inner while loop) On exit D and E

 represent a matrix with the same singular values

 which the calling subroutine could use to finish the

 computation, or even feed back into DLASQ1

 = 3, termination criterion of outer while loop not met

 (program created more than N unreduced blocks)

 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Definition at line 109 of file dlasq1.f.

Author

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