SLATEC Routines --- R1MPYQ ---

*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