*DECK R1MPYQ SUBROUTINE R1MPYQ (M, N, A, LDA, V, W) C***BEGIN PROLOGUE R1MPYQ C***SUBSIDIARY C***PURPOSE Subsidiary to SNSQ and SNSQE C***LIBRARY SLATEC C***TYPE SINGLE PRECISION (R1MPYQ-S, D1MPYQ-D) C***AUTHOR (UNKNOWN) C***DESCRIPTION C C Given an M by N matrix A, this subroutine computes A*Q where C Q is the product of 2*(N - 1) transformations C C GV(N-1)*...*GV(1)*GW(1)*...*GW(N-1) C C and GV(I), GW(I) are Givens rotations in the (I,N) plane which C eliminate elements in the I-th and N-th planes, respectively. C Q itself is not given, rather the information to recover the C GV, GW rotations is supplied. C C The subroutine statement is C C SUBROUTINE R1MPYQ(M,N,A,LDA,V,W) C C where C C M is a positive integer input variable set to the number C of rows of A. C C N is a positive integer input variable set to the number C of columns of A. C C A is an M by N ARRAY. On input A must contain the matrix C to be postmultiplied by the orthogonal matrix Q C described above. On output A*Q has replaced A. C C LDA is a positive integer input variable not less than M C which specifies the leading dimension of the array A. C C V is an input array of length N. V(I) must contain the C information necessary to recover the Givens rotation GV(I) C described above. C C W is an input array of length N. W(I) must contain the C information necessary to recover the Givens rotation GW(I) C described above. C C***SEE ALSO SNSQ, SNSQE C***ROUTINES CALLED (NONE) 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 R1MPYQ