*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