formk.f File Reference

Go to the source code of this file.

Functions/Subroutines
subroutine	formk (n, nsub, ind, nenter, ileave, indx2, iupdat, updatd, wn, wn1, m, ws, wy, sy, theta, col, head, info)
	Forms the LEL^T factorization of the indefinite matrix K. More...

Function/Subroutine Documentation

formk()

subroutine formk	(	integer	n,
		integer	nsub,
		integer, dimension(n)	ind,
		integer	nenter,
		integer	ileave,
		integer, dimension(n)	indx2,
		integer	iupdat,
		logical	updatd,
		double precision, dimension(2*m, 2*m)	wn,
		double precision, dimension(2*m, 2*m)	wn1,
		integer	m,
		double precision, dimension(n, m)	ws,
		double precision, dimension(n, m)	wy,
		double precision, dimension(m, m)	sy,
		double precision	theta,
		integer	col,
		integer	head,
		integer	info
	)

This subroutine forms the LEL^T factorization of the indefinite matrix

K = [-D -Y'ZZ'Y/theta L_a'-R_z' ] [L_a -R_z theta*S'AA'S ] where E = [-I 0] [ 0 I]

The matrix K can be shown to be equal to the matrix M^[-1]N occurring in section 5.1 of [1], as well as to the matrix Mbar^[-1] Nbar in section 5.3.

Parameters

n	On entry n is the dimension of the problem. On exit n is unchanged.
nsub	On entry nsub is the number of subspace variables in free set. On exit nsub is not changed.
ind	On entry ind specifies the indices of subspace variables. On exit ind is unchanged.
nenter	On entry nenter is the number of variables entering the free set. On exit nenter is unchanged.
ileave	On entry indx2(ileave),...,indx2(n) are the variables leaving the free set. On exit ileave is unchanged.
indx2	On entry indx2(1),...,indx2(nenter) are the variables entering the free set, while indx2(ileave),...,indx2(n) are the variables leaving the free set. On exit indx2 is unchanged.
iupdat	On entry iupdat is the total number of BFGS updates made so far. On exit iupdat is unchanged.
updatd	On entry 'updatd' is true if the L-BFGS matrix is updated. On exit 'updatd' is unchanged.
wn	On entry wn is unspecified. On exit the upper triangle of wn stores the LEL^T factorization of the 2*col x 2*col indefinite matrix [-D -Y'ZZ'Y/theta L_a'-R_z' ] [L_a -R_z theta*S'AA'S ]
wn1	On entry wn1 stores the lower triangular part of [Y' ZZ'Y L_a'+R_z'] [L_a+R_z S'AA'S ] in the previous iteration. On exit wn1 stores the corresponding updated matrices. The purpose of wn1 is just to store these inner products so they can be easily updated and inserted into wn.
m	On entry m is the maximum number of variable metric corrections used to define 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.
theta	On entry theta is the scaling factor specifying B_0 = theta I. On exit theta is unchanged.
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.
info	On entry info is unspecified. On exit info = 0 for normal return; = -1 when the 1st Cholesky factorization failed; = -2 when the 2st Cholesky factorization failed.

Definition at line 89 of file formk.f.

Referenced by mainlb().

Here is the caller graph for this function: