DDOGLG(3)

SYNOPSIS
SUBROUTINE DDOGLG (N, R, LR, DIAG, QTB, DELTA, X, WA1, WA2)

NAME
ddoglg - Subsidiary to DNSQ and DNSQE

LIBRARY
SLATEC

TYPE
DOUBLE PRECISION (DOGLEG-S, DDOGLG-D)

AUTHOR
(UNKNOWN)

DESCRIPTION
Given an M by N matrix A, an N by N nonsingular diagonal matrix D, an M-vector B, and a positive number DELTA, the problem is to determine the convex combination X of the Gauss-Newton and scaled gradient directions that minimizes (A*X - B) in the least squares sense, subject to the restriction that the Euclidean norm of D*X be at most DELTA. This subroutine completes the solution of the problem if it is provided with the necessary information from the QR factorization of A. That is, if A = Q*R, where Q has orthogonal columns and R is an upper triangular matrix, then DDOGLG expects the full upper triangle of R and the first N components of (Q transpose)*B. The subroutine statement is SUBROUTINE DDOGLG(N,R,LR,DIAG,QTB,DELTA,X,WA1,WA2) where N is a positive integer input variable set to the order of R. R is an input array of length LR which must contain the upper triangular matrix R stored by rows. LR is a positive integer input variable not less than (N*(N+1))/2. DIAG is an input array of length N which must contain the diagonal elements of the matrix D. QTB is an input array of length N which must contain the first N elements of the vector (Q transpose)*B. DELTA is a positive input variable which specifies an upper bound on the Euclidean norm of D*X. X is an output array of length N which contains the desired convex combination of the Gauss-Newton direction and the scaled gradient direction. WA1 and WA2 are work arrays of length N.

SEE ALSO
DNSQ, DNSQE

ROUTINES CALLED
D1MACH, DENORM

REVISION HISTORY (YYMMDD)
800301 DATE WRITTEN
890531 Changed all specific intrinsics to generic. (WRB)
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)