NAG AD Library
e04gb (lsq_uncon_quasi_deriv_comp)

1 Purpose

2 Specification

3 Description

3.1 Symbolic Adjoint

3.1.1 Symbolic Strategy

3.1.2 Symbolic Expert Strategy

3.1.3 Mathematical Background

3.1.4 Usable Adjoints

4 References

5 Arguments

1: ad_handle – nag::ad::handle_t Input/Output

On entry: a configuration object that holds information on the differentiation strategy. Details on setting the AD strategy are described in AD handle object and AD Strategies in the NAG AD Library Introduction.

2: m – Integer Input

3: n – Integer Input

4: selct – Integer Input

selct enables you to specify whether the linear minimizations (i.e., minimizations of $F(x^{\left(k\right)}+{\alpha }^{\left(k\right)}{p}^{\left(k\right)})$ with respect to ${\alpha }^{\left(k\right)}$) are to be performed by a routine which just requires the evaluation of the $f_i\left(x\right)$ ($\mathbf{selct}=1$), or by a routine which also requires the first derivatives of the $f_i\left(x\right)$ ($\mathbf{selct}=2$).

5: lsqfun – Callable Input

lsqfun needs to be callable with the specification listed below. This can be a C++ lambda, a functor or a (static member) function pointer. If using a lambda, parameters can be captured safely by reference. No copies of the callable are made internally.

The specification of lsqfun is:

Fortran Interface copy

Subroutine lsqfun ( iflag, m, n, xc, fvec, fjac, ldfjac, iuser, ruser) Integer, Intent (In) :: m, n, ldfjac Integer, Intent (Inout) :: iflag, iuser(*) ADTYPE, Intent (In) :: xc(n) ADTYPE, Intent (Inout) :: fjac(ldfjac,n), ruser(*) ADTYPE, Intent (Out) :: fvec(m) Type (c_ptr), Intent (Inout) :: ad_handle

C++ Interface copy

auto lsqfun = [&]( const handle_t &ad_handle, Integer &iflag, const Integer &m, const Integer &n, const ADTYPE xc[], ADTYPE fvec[], ADTYPE fjac[], const Integer &ldfjac)

1: ad_handle – nag::ad::handle_t Input/Output

On entry: a handle to the AD handle object.

2: iflag – Integer Input/Output

3: m – Integer Input

4: n – Integer Input

5: xc – ADTYPE array Input

6: fvec – ADTYPE array Output

7: fjac – ADTYPE array Output

8: ldfjac – Integer Input

*: iuser($*$) – Integer array User Workspace

*: ruser($*$) – ADTYPE array User Workspace

6: lsqmon – Callable Input

lsqmon needs to be callable with the specification listed below. This can be a C++ lambda, a functor or a (static member) function pointer. If using a lambda, parameters can be captured safely by reference. No copies of the callable are made internally.

If a null pointer is used as the argument, then a NAG supplied routine will be used as the argument for this parameter (C++ only).

For the Fortran interface, the NAG supplied routine e04fd_AD_z may be used as the actual argument for this parameter.

The specification of lsqmon is:

Fortran Interface copy

Subroutine lsqmon ( 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(*) ADTYPE, Intent (In) :: xc(n), fvec(m), fjac(ldfjac,n), s(n) ADTYPE, Intent (Inout) :: ruser(*) Type (c_ptr), Intent (Inout) :: ad_handle

C++ Interface copy

auto lsqmon = [&]( const handle_t &ad_handle, const Integer &m, const Integer &n, const ADTYPE xc[], const ADTYPE fvec[], const ADTYPE fjac[], const Integer &ldfjac, const ADTYPE s[], const Integer &igrade, const Integer &niter, const Integer &nf)

1: ad_handle – nag::ad::handle_t Input/Output

On entry: a handle to the AD handle object.

2: m – Integer Input

3: n – Integer Input

4: xc – ADTYPE array Input

5: fvec – ADTYPE array Input

6: fjac – ADTYPE array Input

7: ldfjac – Integer Input

8: s – ADTYPE array Input

9: igrade – Integer Input

10: niter – Integer Input

11: nf – Integer Input

*: iuser($*$) – Integer array User Workspace

*: ruser($*$) – ADTYPE array User Workspace

7: iprint – Integer Input

8: maxcal – Integer Input

9: eta – ADTYPE Input

10: xtol – ADTYPE Input

11: stepmx – ADTYPE Input

12: x(n) – ADTYPE array Input/Output

Please consult Overwriting of Inputs in the NAG AD Library Introduction.

13: fsumsq – ADTYPE Output

14: fvec(m) – ADTYPE array Output

15: fjac(ldfjac, n) – ADTYPE array Output

16: ldfjac – Integer Input

17: s(n) – ADTYPE array Output

18: v(ldv, n) – ADTYPE array Output

19: ldv – Integer Input

20: niter – Integer Output

21: nf – Integer Output

*: iuser($*$) – Integer array User Workspace

User workspace.

*: ruser($*$) – ADTYPE array User Workspace

User workspace.

22: ifail – Integer Input/Output

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Adjoint modes

10.2 Tangent modes

10.3 Passive mode