matupd.f File Reference

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Functions/Subroutines
subroutine	matupd (n, m, ws, wy, sy, ss, d, r, itail, iupdat, col, head, theta, rr, dr, stp, dtd)
	This subroutine updates matrices WS and WY, and forms the middle matrix in B. More...

Function/Subroutine Documentation

matupd()

subroutine matupd	(	integer	n,
		integer	m,
		double precision, dimension(n, m)	ws,
		double precision, dimension(n, m)	wy,
		double precision, dimension(m, m)	sy,
		double precision, dimension(m, m)	ss,
		double precision, dimension(n)	d,
		double precision, dimension(n)	r,
		integer	itail,
		integer	iupdat,
		integer	col,
		integer	head,
		double precision	theta,
		double precision	rr,
		double precision	dr,
		double precision	stp,
		double precision	dtd
	)

This subroutine updates matrices WS and WY, and forms the middle matrix in B.

Parameters

n	On entry n is the number of variables. On exit n is unchanged.
m	On entry m is the maximum number of variable metric corrections allowed in the limited memory matrix. On exit m is unchanged.
ws	On entry this stores S, a set of s-vectors, that defines the limited memory BFGS matrix. On exit this array is unchanged.
wy	On entry this stores Y, a set of y-vectors, that defines the limited memory BFGS matrix. On exit this array is unchanged.
sy	On entry this stores S'Y, that defines the limited memory BFGS matrix. On exit this array is unchanged.
ss	On entry this stores S'S, that defines the limited memory BFGS matrix. On exit this array is unchanged.
d	Search direction at the current iteration. After the line search, the new s-vector is stp*d; matupd stores it as a column of WS (writing d directly, since the stp scaling is folded into the stored ss diagonal entry below).
r	The accepted gradient difference y = g_{k+1} - g_k. Stored as a column of WY.
itail	On entry the column index in WS/WY that the previous update wrote. On exit the column index this update wrote; advances cyclically modulo m.
iupdat	Total number of L-BFGS updates performed so far (incremented by mainlb before each matupd call). When iupdat <= m, col simply grows; when iupdat > m, the history wraps and the oldest column is discarded.
col	On entry col is the actual number of variable metric corrections stored so far. On exit col is unchanged.
head	On entry head is the location of the first s-vector (or y-vector) in S (or Y). On exit col is unchanged.
theta	On entry theta is the scaling factor specifying B_0 = theta I. On exit theta is unchanged.
rr	Squared 2-norm of r (i.e. ||y||^2 = y'y). Used to set theta := rr/dr = y'y / (s'y), the standard initial Hessian scaling for the next L-BFGS update.
dr	Inner product d'r = s'y / stp (the curvature condition; must be positive for the update to be safely accepted – mainlb checks this and skips matupd if dr <= eps*rr).
stp	Line-search step length. Used to recover the s-vector from d (s = stp*d) when computing ss(col,col) = stp^2 * d'd.
dtd	Squared 2-norm of d (i.e. d'd). Combined with stp to form ss(col,col) = stp^2 * dtd = ||s||^2 for the new column.

Definition at line 64 of file matupd.f.

Referenced by mainlb().

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