DLASQ1(3F)							    DLASQ1(3F)

NAME    [Toc]    [Back]

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

SYNOPSIS    [Toc]    [Back]

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

	 INTEGER	INFO, N

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

PURPOSE    [Toc]    [Back]

	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, barring over/underflow or
	denormalization. The algorithm is described 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.

	See also
	"Implementation	of differential	qd algorithms,"	by
	K. V. Fernando and B. N. Parlett, Technical Report,
	Department of Mathematics, University of California at Berkeley,
	1994 (Under preparation).

ARGUMENTS    [Toc]    [Back]

     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 (2*N)

     INFO    (output) INTEGER
	     = 0:  successful exit
	     < 0:  if INFO = -i, the i-th argument had an illegal value
	     > 0:  if INFO = i,	the algorithm did not converge;	 i specifies
	     how many superdiagonals did not converge.
DLASQ1(3F)							    DLASQ1(3F)

NAME    [Toc]    [Back]

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

SYNOPSIS    [Toc]    [Back]

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

	 INTEGER	INFO, N

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

PURPOSE    [Toc]    [Back]

	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, barring over/underflow or
	denormalization. The algorithm is described 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.

	See also
	"Implementation	of differential	qd algorithms,"	by
	K. V. Fernando and B. N. Parlett, Technical Report,
	Department of Mathematics, University of California at Berkeley,
	1994 (Under preparation).

ARGUMENTS    [Toc]    [Back]

     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 (2*N)

     INFO    (output) INTEGER
	     = 0:  successful exit
	     < 0:  if INFO = -i, the i-th argument had an illegal value
	     > 0:  if INFO = i,	the algorithm did not converge;	 i specifies
	     how many superdiagonals did not converge.


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