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dlasda.f(3)				      LAPACK				      dlasda.f(3)

NAME
       dlasda.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dlasda (ICOMPQ, SMLSIZ, N, SQRE, D, E, U, LDU, VT, K, DIFL, DIFR, Z, POLES,
	   GIVPTR, GIVCOL, LDGCOL, PERM, GIVNUM, C, S, WORK, IWORK, INFO)
	   DLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal
	   matrix with diagonal d and off-diagonal e. Used by sbdsdc.

Function/Subroutine Documentation
   subroutine dlasda (integerICOMPQ, integerSMLSIZ, integerN, integerSQRE, double precision,
       dimension( * )D, double precision, dimension( * )E, double precision, dimension( ldu, *
       )U, integerLDU, double precision, dimension( ldu, * )VT, integer, dimension( * )K, double
       precision, dimension( ldu, * )DIFL, double precision, dimension( ldu, * )DIFR, double
       precision, dimension( ldu, * )Z, double precision, dimension( ldu, * )POLES, integer,
       dimension( * )GIVPTR, integer, dimension( ldgcol, * )GIVCOL, integerLDGCOL, integer,
       dimension( ldgcol, * )PERM, double precision, dimension( ldu, * )GIVNUM, double precision,
       dimension( * )C, double precision, dimension( * )S, double precision, dimension( * )WORK,
       integer, dimension( * )IWORK, integerINFO)
       DLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal matrix
       with diagonal d and off-diagonal e. Used by sbdsdc.

       Purpose:

	    Using a divide and conquer approach, DLASDA 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. The
	    algorithm computes the singular values in the SVD B = U * S * VT.
	    The orthogonal matrices U and VT are optionally computed in
	    compact form.

	    A related subroutine, DLASD0, computes the singular values and
	    the singular vectors in explicit form.

       Parameters:
	   ICOMPQ

		     ICOMPQ is INTEGER
		    Specifies whether singular vectors are to be computed
		    in compact form, as follows
		    = 0: Compute singular values only.
		    = 1: Compute singular vectors of upper bidiagonal
			 matrix in compact form.

	   SMLSIZ

		     SMLSIZ is INTEGER
		    The maximum size of the subproblems at the bottom of the
		    computation tree.

	   N

		     N is INTEGER
		    The row dimension of the upper bidiagonal matrix. This is
		    also the dimension of the main diagonal array D.

	   SQRE

		     SQRE is INTEGER
		    Specifies the column dimension of the bidiagonal matrix.
		    = 0: The bidiagonal matrix has column dimension M = N;
		    = 1: The bidiagonal matrix has column dimension M = N + 1.

	   D

		     D is DOUBLE PRECISION array, dimension ( N )
		    On entry D contains the main diagonal of the bidiagonal
		    matrix. On exit D, if INFO = 0, contains its singular values.

	   E

		     E is DOUBLE PRECISION array, dimension ( M-1 )
		    Contains the subdiagonal entries of the bidiagonal matrix.
		    On exit, E has been destroyed.

	   U

		     U is DOUBLE PRECISION array,
		    dimension ( LDU, SMLSIZ ) if ICOMPQ = 1, and not referenced
		    if ICOMPQ = 0. If ICOMPQ = 1, on exit, U contains the left
		    singular vector matrices of all subproblems at the bottom
		    level.

	   LDU

		     LDU is INTEGER, LDU = > N.
		    The leading dimension of arrays U, VT, DIFL, DIFR, POLES,
		    GIVNUM, and Z.

	   VT

		     VT is DOUBLE PRECISION array,
		    dimension ( LDU, SMLSIZ+1 ) if ICOMPQ = 1, and not referenced
		    if ICOMPQ = 0. If ICOMPQ = 1, on exit, VT**T contains the right
		    singular vector matrices of all subproblems at the bottom
		    level.

	   K

		     K is INTEGER array,
		    dimension ( N ) if ICOMPQ = 1 and dimension 1 if ICOMPQ = 0.
		    If ICOMPQ = 1, on exit, K(I) is the dimension of the I-th
		    secular equation on the computation tree.

	   DIFL

		     DIFL is DOUBLE PRECISION array, dimension ( LDU, NLVL ),
		    where NLVL = floor(log_2 (N/SMLSIZ))).

	   DIFR

		     DIFR is DOUBLE PRECISION array,
			     dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1 and
			     dimension ( N ) if ICOMPQ = 0.
		    If ICOMPQ = 1, on exit, DIFL(1:N, I) and DIFR(1:N, 2 * I - 1)
		    record distances between singular values on the I-th
		    level and singular values on the (I -1)-th level, and
		    DIFR(1:N, 2 * I ) contains the normalizing factors for
		    the right singular vector matrix. See DLASD8 for details.

	   Z

		     Z is DOUBLE PRECISION array,
			     dimension ( LDU, NLVL ) if ICOMPQ = 1 and
			     dimension ( N ) if ICOMPQ = 0.
		    The first K elements of Z(1, I) contain the components of
		    the deflation-adjusted updating row vector for subproblems
		    on the I-th level.

	   POLES

		     POLES is DOUBLE PRECISION array,
		    dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not referenced
		    if ICOMPQ = 0. If ICOMPQ = 1, on exit, POLES(1, 2*I - 1) and
		    POLES(1, 2*I) contain  the new and old singular values
		    involved in the secular equations on the I-th level.

	   GIVPTR

		     GIVPTR is INTEGER array,
		    dimension ( N ) if ICOMPQ = 1, and not referenced if
		    ICOMPQ = 0. If ICOMPQ = 1, on exit, GIVPTR( I ) records
		    the number of Givens rotations performed on the I-th
		    problem on the computation tree.

	   GIVCOL

		     GIVCOL is INTEGER array,
		    dimension ( LDGCOL, 2 * NLVL ) if ICOMPQ = 1, and not
		    referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I,
		    GIVCOL(1, 2 *I - 1) and GIVCOL(1, 2 *I) record the locations
		    of Givens rotations performed on the I-th level on the
		    computation tree.

	   LDGCOL

		     LDGCOL is INTEGER, LDGCOL = > N.
		    The leading dimension of arrays GIVCOL and PERM.

	   PERM

		     PERM is INTEGER array,
		    dimension ( LDGCOL, NLVL ) if ICOMPQ = 1, and not referenced
		    if ICOMPQ = 0. If ICOMPQ = 1, on exit, PERM(1, I) records
		    permutations done on the I-th level of the computation tree.

	   GIVNUM

		     GIVNUM is DOUBLE PRECISION array,
		    dimension ( LDU,  2 * NLVL ) if ICOMPQ = 1, and not
		    referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I,
		    GIVNUM(1, 2 *I - 1) and GIVNUM(1, 2 *I) record the C- and S-
		    values of Givens rotations performed on the I-th level on
		    the computation tree.

	   C

		     C is DOUBLE PRECISION array,
		    dimension ( N ) if ICOMPQ = 1, and dimension 1 if ICOMPQ = 0.
		    If ICOMPQ = 1 and the I-th subproblem is not square, on exit,
		    C( I ) contains the C-value of a Givens rotation related to
		    the right null space of the I-th subproblem.

	   S

		     S is DOUBLE PRECISION array, dimension ( N ) if
		    ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1
		    and the I-th subproblem is not square, on exit, S( I )
		    contains the S-value of a Givens rotation related to
		    the right null space of the I-th subproblem.

	   WORK

		     WORK is DOUBLE PRECISION array, dimension
		    (6 * N + (SMLSIZ + 1)*(SMLSIZ + 1)).

	   IWORK

		     IWORK is INTEGER array.
		    Dimension must be at least (7 * N).

	   INFO

		     INFO is INTEGER
		     = 0:  successful exit.
		     < 0:  if INFO = -i, the i-th argument had an illegal value.
		     > 0:  if INFO = 1, a singular value did not converge

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       Contributors:
	   Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley,
	   USA

       Definition at line 273 of file dlasda.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      dlasda.f(3)
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