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RedHat 9 (Linux i386) - man page for dlasd3 (redhat section l)

DLASD3(l)					)					DLASD3(l)

NAME
       DLASD3 - find all the square roots of the roots of the secular equation, as defined by the
       values in D and Z

SYNOPSIS
       SUBROUTINE DLASD3( NL, NR, SQRE, K, D, Q, LDQ, DSIGMA, U, LDU, U2, LDU2,  VT,  LDVT,  VT2,
			  LDVT2, IDXC, CTOT, Z, INFO )

	   INTEGER	  INFO, K, LDQ, LDU, LDU2, LDVT, LDVT2, NL, NR, SQRE

	   INTEGER	  CTOT( * ), IDXC( * )

	   DOUBLE	  PRECISION D( * ), DSIGMA( * ), Q( LDQ, * ), U( LDU, * ), U2( LDU2, * ),
			  VT( LDVT, * ), VT2( LDVT2, * ), Z( * )

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  con-
       ceivably  fail  on  hexadecimal	or  decimal machines without guard digits, but we know of
       none.

       DLASD3 is called from DLASD1.

ARGUMENTS
       NL     (input) INTEGER
	      The row dimension of the upper block.  NL >= 1.

       NR     (input) INTEGER
	      The row dimension of the lower block.  NR >= 1.

       SQRE   (input) 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      (input) INTEGER
	      The size of the secular equation, 1 =< K = < N.

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

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

       LDQ    (input) INTEGER
	      The leading dimension of the array Q.  LDQ >= K.

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

       LDU    (input) INTEGER
	      The leading dimension of the array U.  LDU >= N.

       U2     (input) 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   (input) INTEGER
	      The leading dimension of the array U2.  LDU2 >= N.

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

       LDVT   (input) INTEGER
	      The leading dimension of the array VT.  LDVT >= N.

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

       LDVT2  (input) INTEGER
	      The leading dimension of the array VT2.  LDVT2 >= N.

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

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

FURTHER DETAILS
       Based on contributions by
	  Ming Gu and Huan Ren, Computer Science Division, University of
	  California at Berkeley, USA

LAPACK version 3.0			   15 June 2000 				DLASD3(l)


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