RWUPDT(3)

SYNOPSIS
SUBROUTINE RWUPDT (N, R, LDR, W, B, ALPHA, COS, SIN)

NAME
rwupdt - Subsidiary to SNLS1 and SNLS1E

LIBRARY
SLATEC

TYPE
SINGLE PRECISION (RWUPDT-S, DWUPDT-D)

AUTHOR
(UNKNOWN)

DESCRIPTION
Given an N by N upper triangular matrix R, this subroutine computes the QR decomposition of the matrix formed when a row is added to R. If the row is specified by the vector W, then RWUPDT determines an orthogonal matrix Q such that when the N+1 by N matrix composed of R augmented by W is premultiplied by (Q TRANSPOSE), the resulting matrix is upper trapezoidal. The orthogonal matrix Q is the product of N transformations G(1)*G(2)* ... *G(N) where G(I) is a Givens rotation in the (I,N+1) plane which eliminates elements in the I-th plane. RWUPDT also computes the product (Q TRANSPOSE)*C where C is the (N+1)-vector (b,alpha). Q itself is not accumulated, rather the information to recover the G rotations is supplied. The subroutine statement is SUBROUTINE RWUPDT(N,R,LDR,W,B,ALPHA,COS,SIN) where N is a positive integer input variable set to the order of R. R is an N by N array. On input the upper triangular part of R must contain the matrix to be updated. On output R contains the updated triangular matrix. LDR is a positive integer input variable not less than N which specifies the leading dimension of the array R. W is an input array of length N which must contain the row vector to be added to R. B is an array of length N. On input B must contain the first N elements of the vector C. On output B contains the first N elements of the vector (Q TRANSPOSE)*C. ALPHA is a variable. On input ALPHA must contain the (N+1)-st element of the vector C. On output ALPHA contains the (N+1)-st element of the vector (Q TRANSPOSE)*C. COS is an output array of length N which contains the cosines of the transforming Givens rotations. SIN is an output array of length N which contains the sines of the transforming Givens rotations.

SEE ALSO
SNLS1, SNLS1E

ROUTINES CALLED
(NONE)

REVISION HISTORY (YYMMDD)
800301 DATE WRITTEN
890831 Modified array declarations. (WRB)
891214 Prologue converted to Version 4.0 format. (BAB)
900326 Removed duplicate information from DESCRIPTION section. (WRB)
900328 Added TYPE section. (WRB)