lasq13

!>
!> 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
!>
!>  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 , LAPACK Working Note.
!> 

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)
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

!>
!> SLASQ1 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
!>
!>  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 , LAPACK Working Note.
!> 

N

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

D

!>          D is REAL 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 REAL 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 REAL 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 SLASQ1
!>             = 3, termination criterion of outer while loop not met
!>                  (program created more than N unreduced blocks)
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.