slasq1(l) [redhat man page]

SLASQ1(l)								 )								 SLASQ1(l)

NAME

       SLASQ1 - compute the singular values of a real N-by-N bidiagonal matrix with diagonal D and off-diagonal E

SYNOPSIS

       SUBROUTINE SLASQ1( N, D, E, WORK, INFO )

	   INTEGER	  INFO, N

	   REAL 	  D( * ), E( * ), WORK( * )

PURPOSE

       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

       "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) 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     (input/output) 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 overwrit-
	     ten.

       WORK  (workspace) REAL 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 itera-
	     tions (in inner while loop) = 3, termination criterion of outer while loop not met (program created more than N unreduced blocks)

LAPACK version 3.0						   15 June 2000 							 SLASQ1(l)

DLASQ1(l)								 )								 DLASQ1(l)

NAME

       DLASQ1 - compute 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 overwrit-
	     ten.

       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 itera-
	     tions (in inner while loop) = 3, termination criterion of outer while loop not met (program created more than N unreduced blocks)

LAPACK version 3.0						   15 June 2000 							 DLASQ1(l)