SLATEC Routines --- R1UPDT ---

*DECK R1UPDT
      SUBROUTINE R1UPDT (M, N, S, LS, U, V, W, SING)
C***BEGIN PROLOGUE  R1UPDT
C***SUBSIDIARY
C***PURPOSE  Subsidiary to SNSQ and SNSQE
C***LIBRARY   SLATEC
C***TYPE      SINGLE PRECISION (R1UPDT-S, D1UPDT-D)
C***AUTHOR  (UNKNOWN)
C***DESCRIPTION
C
C     Given an M by N lower trapezoidal matrix S, an M-vector U,
C     and an N-vector V, the problem is to determine an
C     orthogonal matrix Q such that
C
C                   T
C           (S + U*V )*Q
C
C     is again lower trapezoidal.
C
C     This subroutine determines Q as the product of 2*(N - 1)
C     transformations
C
C           GV(N-1)*...*GV(1)*GW(1)*...*GW(N-1)
C
C     where GV(I), GW(I) are Givens rotations in the (I,N) plane
C     which eliminate elements in the I-th and N-th planes,
C     respectively. Q Itself is not accumulated, rather the
C     information to recover the GV, GW rotations is returned.
C
C     The subroutine statement is
C
C       SUBROUTINE R1UPDT(M,N,S,LS,U,V,W,SING)
C
C     where
C
C       M is a positive integer input variable set to the number
C         of rows of S.
C
C       N is a positive integer input variable set to the number
C         of columns of S. N must not exceed M.
C
C       S is an array of length LS. On input S must contain the lower
C         trapezoidal matrix S stored by columns. On output S contains
C         the lower trapezoidal matrix produced as described above.
C
C       LS is a positive integer input variable not less than
C         (N*(2*M-N+1))/2.
C
C       U is an input array of length M which must contain the
C         vector U.
C
C       V is an array of length N. On input V must contain the vector
C         V. On output V(I) contains the information necessary to
C         recover the Givens rotation GV(I) described above.
C
C       W is an output array of length M. W(I) contains information
C         necessary to recover the Givens rotation GW(I) described
C         above.
C
C       SING is a logical output variable. SING is set .TRUE. if any
C         of the diagonal elements of the output S are zero. Otherwise
C         SING is set .FALSE.
C
C***SEE ALSO  SNSQ, SNSQE
C***ROUTINES CALLED  R1MACH
C***REVISION HISTORY  (YYMMDD)
C   800301  DATE WRITTEN
C   890831  Modified array declarations.  (WRB)
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C   900326  Removed duplicate information from DESCRIPTION section.
C           (WRB)
C   900328  Added TYPE section.  (WRB)
C***END PROLOGUE  R1UPDT