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dlasd3.f(3)				      LAPACK				      dlasd3.f(3)

NAME
       dlasd3.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dlasd3 (NL, NR, SQRE, K, D, Q, LDQ, DSIGMA, U, LDU, U2, LDU2, VT, LDVT, VT2,
	   LDVT2, IDXC, CTOT, Z, INFO)
	   DLASD3 finds all square roots of the roots of the secular equation, as defined by the
	   values in D and Z, and then updates the singular vectors by matrix multiplication.
	   Used by sbdsdc.

Function/Subroutine Documentation
   subroutine dlasd3 (integerNL, integerNR, integerSQRE, integerK, double precision, dimension( *
       )D, double precision, dimension( ldq, * )Q, integerLDQ, double precision, dimension( *
       )DSIGMA, double precision, dimension( ldu, * )U, integerLDU, double precision, dimension(
       ldu2, * )U2, integerLDU2, double precision, dimension( ldvt, * )VT, integerLDVT, double
       precision, dimension( ldvt2, * )VT2, integerLDVT2, integer, dimension( * )IDXC, integer,
       dimension( * )CTOT, double precision, dimension( * )Z, integerINFO)
       DLASD3 finds all square roots of the roots of the secular equation, as defined by the
       values in D and Z, and then updates the singular vectors by matrix multiplication. Used by
       sbdsdc.

       Purpose:

	    DLASD3 finds all the square roots of the roots of the secular
	    equation, as defined by the values in D and Z.  It makes the
	    appropriate calls to DLASD4 and then updates the singular
	    vectors by matrix multiplication.

	    This code makes very mild assumptions about floating point
	    arithmetic. It will work on machines with a guard digit in
	    add/subtract, or on those binary machines without guard digits
	    which subtract like the Cray XMP, Cray YMP, Cray C 90, or Cray 2.
	    It could conceivably fail on hexadecimal or decimal machines
	    without guard digits, but we know of none.

	    DLASD3 is called from DLASD1.

       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
		    The size of the secular equation, 1 =< K = < N.

	   D

		     D is DOUBLE PRECISION array, dimension(K)
		    On exit the square roots of the roots of the secular equation,
		    in ascending order.

	   Q

		     Q is DOUBLE PRECISION array,
				dimension at least (LDQ,K).

	   LDQ

		     LDQ is INTEGER
		    The leading dimension of the array Q.  LDQ >= K.

	   DSIGMA

		     DSIGMA is DOUBLE PRECISION array, dimension(K)
		    The first K elements of this array contain the old roots
		    of the deflated updating problem.  These are the poles
		    of the secular equation.

	   U

		     U is DOUBLE PRECISION array, dimension (LDU, N)
		    The last N - K columns of this matrix contain the deflated
		    left singular vectors.

	   LDU

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

	   U2

		     U2 is DOUBLE PRECISION array, dimension (LDU2, N)
		    The first K columns of this matrix contain the non-deflated
		    left singular vectors for the split problem.

	   LDU2

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

	   VT

		     VT is DOUBLE PRECISION array, dimension (LDVT, M)
		    The last M - K columns of VT**T contain the deflated
		    right singular vectors.

	   LDVT

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

	   VT2

		     VT2 is DOUBLE PRECISION array, dimension (LDVT2, N)
		    The first K columns of VT2**T contain the non-deflated
		    right singular vectors for the split problem.

	   LDVT2

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

	   IDXC

		     IDXC is INTEGER array, dimension ( N )
		    The permutation used to arrange the columns of U (and rows of
		    VT) into three groups:  the first group contains non-zero
		    entries only at and above (or before) NL +1; the second
		    contains non-zero entries only at and below (or after) NL+2;
		    and the third is dense. The first column of U and the row of
		    VT are treated separately, however.

		    The rows of the singular vectors found by DLASD4
		    must be likewise permuted before the matrix multiplies can
		    take place.

	   CTOT

		     CTOT is INTEGER array, dimension ( 4 )
		    A count of the total number of the various types of columns
		    in U (or rows in VT), as described in IDXC. The fourth column
		    type is any column which has been deflated.

	   Z

		     Z is DOUBLE PRECISION array, dimension (K)
		    The first K elements of this array contain the components
		    of the deflation-adjusted updating row vector.

	   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 224 of file dlasd3.f.

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

Version 3.4.2				 Tue Sep 25 2012			      dlasd3.f(3)
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