e04fc_ad_f : NAG AD Library Routine Document, Mark 26

Fortran Interface

Subroutine e04fc_a1w_f (

ad_handle, m, n, lsqfun, lsqmon, iprint, maxcal, eta, xtol, stepmx, x, fsumsq, fvec, fjac, ldfjac, s, v, ldv, niter, nf, iuser, ruser, ifail)

Integer, Intent (In)	::	m, n, iprint, maxcal, ldfjac, ldv
Integer, Intent (Inout)	::	iuser(*), ifail
Integer, Intent (Out)	::	niter, nf
Type (nagad_a1w_w_rtype), Intent (In)	::	eta, xtol, stepmx
Type (nagad_a1w_w_rtype), Intent (Inout)	::	x(n), fjac(ldfjac,n), v(ldv,n), ruser(*)
Type (nagad_a1w_w_rtype), Intent (Out)	::	fsumsq, fvec(m), s(n)
Type (c_ptr), Intent (In)	::	ad_handle
External	::	lsqfun, lsqmon

Subroutine lsqfun (

ad_handle, iflag, m, n, xc, fvec, iuser, ruser)

Integer, Intent (In)	::	m, n
Integer, Intent (Inout)	::	iflag, iuser(*)
Type (nagad_a1w_w_rtype), Intent (Inout)	::	xc(n), ruser(*), fvec(m)
Type (c_ptr), Intent (In)	::	ad_handle

Subroutine lsqmon (

ad_handle, m, n, xc, fvec, fjac, ldfjac, s, igrade, niter, nf, iuser, ruser)

Integer, Intent (In)	::	m, n, ldfjac, igrade, niter, nf
Integer, Intent (Inout)	::	iuser(*)
Type (nagad_a1w_w_rtype), Intent (Inout)	::	xc(n), fvec(m), fjac(ldfjac,n), s(n), ruser(*)
Type (c_ptr), Intent (In)	::	ad_handle

C++ Header Interface

#include <nagad.h>

void e04fc_a1w_f_ (

void *&ad_handle, const Integer &m, const Integer &n,
void (NAG_CALL lsqfun)(void *&ad_handle, Integer &iflag, const Integer &m, const Integer &n, nagad_a1w_w_rtype xc[], nagad_a1w_w_rtype fvec[], Integer iuser[], nagad_a1w_w_rtype ruser[]),
void (NAG_CALL lsqmon)(void *&ad_handle, const Integer &m, const Integer &n, nagad_a1w_w_rtype xc[], nagad_a1w_w_rtype fvec[], nagad_a1w_w_rtype fjac[], const Integer &ldfjac, nagad_a1w_w_rtype s[], const Integer &igrade, const Integer &niter, const Integer &nf, Integer iuser[], nagad_a1w_w_rtype ruser[]),
const Integer &iprint, const Integer &maxcal, const nagad_a1w_w_rtype &eta, const nagad_a1w_w_rtype &xtol, const nagad_a1w_w_rtype &stepmx, nagad_a1w_w_rtype x[], nagad_a1w_w_rtype &fsumsq, nagad_a1w_w_rtype fvec[], nagad_a1w_w_rtype fjac[], const Integer &ldfjac, nagad_a1w_w_rtype s[], nagad_a1w_w_rtype v[], const Integer &ldv, Integer &niter, Integer &nf, Integer iuser[], nagad_a1w_w_rtype ruser[], Integer &ifail)

Description

e04fcf is a comprehensive algorithm for finding an unconstrained minimum of a sum of squares of

m

nonlinear functions in

n

variables

(m \geq n)

. No derivatives are required.

The routine is intended for functions which have continuous first and second derivatives (although it will usually work even if the derivatives have occasional discontinuities). For further information see Section 3 in the documentation for e04fcf .

References

Arguments

e04fc_a1w_f provides access to all the arguments available in the primal routine. There are also additional arguments specific to AD. A tooltip popup for each argument can be found by hovering over the argument name in Section 2 and a summary of the arguments are provided below:

ad_handle – a handle to the AD configuration data object, as created by x10aa_a1w_f.
m – the number $m$ of residuals, $f_{i} (x)$ , and the number $n$ of variables, $x_{j}$ .
n – the number $m$ of residuals, $f_{i} (x)$ , and the number $n$ of variables, $x_{j}$ .
lsqfun – lsqfun must calculate the vector of values $f_{i} (x)$ at any point $x$ .
lsqmon – If $iprint \geq 0$ , you must supply lsqmon which is suitable for monitoring the minimization process.
iprint – the frequency with which lsqmon is to be called.
maxcal – the limit you set on the number of times that lsqfun may be called by routine.
eta – specifies how accurately the linear minimizations are to be performed.
xtol – the accuracy in $x$ to which the solution is required.
stepmx – an estimate of the Euclidean distance between the solution and the starting point supplied by you.
x – on entry: $x (j)$ must be set to a guess at the $j$ th component of the position of the minimum, for $j = 1, 2, \dots, n$ . on exit: the final point $x^{(k)}$ .
fsumsq – on exit: the value of $F (x)$ , the sum of squares of the residuals $f_{i} (x)$ , at the final point given in x.
fvec – on exit: the value of the residual $f_{i} (x)$ at the final point given in x, for $i = 1, 2, \dots, m$ .
fjac – on exit: the estimate of the first derivative $\frac{\partial f_{i}}{\partial x_{j}}$ at the final point given in x, for $j = 1, 2, \dots, n$ , for $i = 1, 2, \dots, m$ .
ldfjac – the first dimension of the array fjac.
s – on exit: the singular values of the estimated Jacobian matrix at the final point.
v – on exit: the matrix $V$ associated with the singular value decomposition. $J = U S V^{T}$ . of the estimated Jacobian matrix at the final point, stored by columns.
ldv – the first dimension of the array v.
niter – on exit: the number of iterations which have been performed in routine.
nf – on exit: the number of times that the residuals have been evaluated (i.e., number of calls of lsqfun).
iuser – may be used to pass information to user-supplied argument(s).
ruser – may be used to pass information to user-supplied argument(s).
ifail – on entry: ifail must be set to $0$ , $- 1 or 1$ . on exit: ifail = 0 unless the routine detects an error or a warning has been flagged (see Section 6).

Language	Source File	Data	Results
Fortan	e04fc_a1w_fe.f90	e04fc_a1w_fe.d	e04fc_a1w_fe.r
C++	e04fc_a1w_hcppe.cpp	e04fc_a1w_hcppe.d	e04fc_a1w_hcppe.r

NAG AD Library Routine Document

e04fc_a1w_f (lsq_uncon_mod_func_comp_a1w)

▸▿ Contents

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

6

Error Indicators and Warnings

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

NAG AD Library Routine Document

e04fc_a1w_f (lsq_uncon_mod_func_comp_a1w)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example