slasd2.f(3)							      LAPACK							       slasd2.f(3)

NAME

       slasd2.f -

SYNOPSIS

   Functions/Subroutines
       subroutine slasd2 (NL, NR, SQRE, K, D, Z, ALPHA, BETA, U, LDU, VT, LDVT, DSIGMA, U2, LDU2, VT2, LDVT2, IDXP, IDX, IDXC, IDXQ, COLTYP, INFO)
	   SLASD2

Function/Subroutine Documentation
   subroutine slasd2 (integerNL, integerNR, integerSQRE, integerK, real, dimension( * )D, real, dimension( * )Z, realALPHA, realBETA, real,
       dimension( ldu, * )U, integerLDU, real, dimension( ldvt, * )VT, integerLDVT, real, dimension( * )DSIGMA, real, dimension( ldu2, * )U2,
       integerLDU2, real, dimension( ldvt2, * )VT2, integerLDVT2, integer, dimension( * )IDXP, integer, dimension( * )IDX, integer, dimension( *
       )IDXC, integer, dimension( * )IDXQ, integer, dimension( * )COLTYP, integerINFO)
       SLASD2

       Purpose:

	    SLASD2 merges the two sets of singular values together into a single
	    sorted set.  Then it tries to deflate the size of the problem.
	    There are two ways in which deflation can occur:  when two or more
	    singular values are close together or if there is a tiny entry in the
	    Z vector.  For each such occurrence the order of the related secular
	    equation problem is reduced by one.

	    SLASD2 is called from SLASD1.

       Parameters:
	   NL

		     NL is INTEGER
		    The row dimension of the upper block.  NL >= 1.

	   NR

		     NR is INTEGER
		    The row dimension of the lower block.  NR >= 1.

	   SQRE

		     SQRE is INTEGER
		    = 0: the lower block is an NR-by-NR square matrix.
		    = 1: the lower block is an NR-by-(NR+1) rectangular matrix.

		    The bidiagonal matrix has N = NL + NR + 1 rows and
		    M = N + SQRE >= N columns.

	   K

		     K is INTEGER
		    Contains the dimension of the non-deflated matrix,
		    This is the order of the related secular equation. 1 <= K <=N.

	   D

		     D is REAL array, dimension (N)
		    On entry D contains the singular values of the two submatrices
		    to be combined.  On exit D contains the trailing (N-K) updated
		    singular values (those which were deflated) sorted into
		    increasing order.

	   Z

		     Z is REAL array, dimension (N)
		    On exit Z contains the updating row vector in the secular
		    equation.

	   ALPHA

		     ALPHA is REAL
		    Contains the diagonal element associated with the added row.

	   BETA

		     BETA is REAL
		    Contains the off-diagonal element associated with the added
		    row.

	   U

		     U is REAL array, dimension (LDU,N)
		    On entry U contains the left singular vectors of two
		    submatrices in the two square blocks with corners at (1,1),
		    (NL, NL), and (NL+2, NL+2), (N,N).
		    On exit U contains the trailing (N-K) updated left singular
		    vectors (those which were deflated) in its last N-K columns.

	   LDU

		     LDU is INTEGER
		    The leading dimension of the array U.  LDU >= N.

	   VT

		     VT is REAL array, dimension (LDVT,M)
		    On entry VT**T contains the right singular vectors of two
		    submatrices in the two square blocks with corners at (1,1),
		    (NL+1, NL+1), and (NL+2, NL+2), (M,M).
		    On exit VT**T contains the trailing (N-K) updated right singular
		    vectors (those which were deflated) in its last N-K columns.
		    In case SQRE =1, the last row of VT spans the right null
		    space.

	   LDVT

		     LDVT is INTEGER
		    The leading dimension of the array VT.  LDVT >= M.

	   DSIGMA

		     DSIGMA is REAL array, dimension (N)
		    Contains a copy of the diagonal elements (K-1 singular values
		    and one zero) in the secular equation.

	   U2

		     U2 is REAL array, dimension (LDU2,N)
		    Contains a copy of the first K-1 left singular vectors which
		    will be used by SLASD3 in a matrix multiply (SGEMM) to solve
		    for the new left singular vectors. U2 is arranged into four
		    blocks. The first block contains a column with 1 at NL+1 and
		    zero everywhere else; the second block contains non-zero
		    entries only at and above NL; the third contains non-zero
		    entries only below NL+1; and the fourth is dense.

	   LDU2

		     LDU2 is INTEGER
		    The leading dimension of the array U2.  LDU2 >= N.

	   VT2

		     VT2 is REAL array, dimension (LDVT2,N)
		    VT2**T contains a copy of the first K right singular vectors
		    which will be used by SLASD3 in a matrix multiply (SGEMM) to
		    solve for the new right singular vectors. VT2 is arranged into
		    three blocks. The first block contains a row that corresponds
		    to the special 0 diagonal element in SIGMA; the second block
		    contains non-zeros only at and before NL +1; the third block
		    contains non-zeros only at and after  NL +2.

	   LDVT2

		     LDVT2 is INTEGER
		    The leading dimension of the array VT2.  LDVT2 >= M.

	   IDXP

		     IDXP is INTEGER array, dimension (N)
		    This will contain the permutation used to place deflated
		    values of D at the end of the array. On output IDXP(2:K)
		    points to the nondeflated D-values and IDXP(K+1:N)
		    points to the deflated singular values.

	   IDX

		     IDX is INTEGER array, dimension (N)
		    This will contain the permutation used to sort the contents of
		    D into ascending order.

	   IDXC

		     IDXC is INTEGER array, dimension (N)
		    This will contain the permutation used to arrange the columns
		    of the deflated U matrix into three groups:  the first group
		    contains non-zero entries only at and above NL, the second
		    contains non-zero entries only below NL+2, and the third is
		    dense.

	   IDXQ

		     IDXQ is INTEGER array, dimension (N)
		    This contains the permutation which separately sorts the two
		    sub-problems in D into ascending order.  Note that entries in
		    the first hlaf of this permutation must first be moved one
		    position backward; and entries in the second half
		    must first have NL+1 added to their values.

	   COLTYP

		     COLTYP is INTEGER array, dimension (N)
		    As workspace, this will contain a label which will indicate
		    which of the following types a column in the U2 matrix or a
		    row in the VT2 matrix is:
		    1 : non-zero in the upper half only
		    2 : non-zero in the lower half only
		    3 : dense
		    4 : deflated

		    On exit, it is an array of dimension 4, with COLTYP(I) being
		    the dimension of the I-th type columns.

	   INFO

		     INFO is INTEGER
		     = 0:  successful exit.
		     < 0:  if INFO = -i, the i-th argument had an illegal value.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

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

       Definition at line 268 of file slasd2.f.

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

Version 3.4.1							  Sun May 26 2013						       slasd2.f(3)