NAG Library Function Document

nag_zero_sparse_nonlin_eqns_easy (c05qsc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{fcn}$ – function, supplied by the userExternal Function

fcn must return the values of the functions $f_i$ at a point $x$.

The specification of fcn is:

void  fcn (Integer n, Integer lindf, const Integer indf[], const double x[], double fvec[], Nag_Comm *comm, Integer *iflag)

1:    $\mathbf{n}$ – IntegerInput

On entry: $n$, the number of equations.

2:    $\mathbf{lindf}$ – IntegerInput

On entry: lindf specifies the number of indices $i$ for which values of $f_i\left(x\right)$ must be computed.

3:    $\mathbf{indf}\left[\mathbf{lindf}\right]$ – const IntegerInput

On entry: indf specifies the indices $i$ for which values of $f_i\left(x\right)$ must be computed. The indices are specified in strictly ascending order.

4:    $\mathbf{x}\left[\mathbf{n}\right]$ – const doubleInput

On entry: the components of the point $x$ at which the functions must be evaluated. $\mathbf{x}\left[i-1\right]$ contains the coordinate $x_i$.

5:    $\mathbf{fvec}\left[\mathbf{n}\right]$ – doubleOutput

On exit: $\mathbf{fvec}\left[i-1\right]$ must contain the function values $f_i\left(x\right)$, for all indices $i$ in indf.

6:    $\mathbf{comm}$ – Nag_Comm *

Pointer to structure of type Nag_Comm; the following members are relevant to fcn.

user – double *

iuser – Integer *

p – Pointer 

The type Pointer will be void *. Before calling nag_zero_sparse_nonlin_eqns_easy (c05qsc) you may allocate memory and initialize these pointers with various quantities for use by fcn when called from nag_zero_sparse_nonlin_eqns_easy (c05qsc) (see Section 3.3.1.1 in How to Use the NAG Library and its Documentation).

7:    $\mathbf{iflag}$ – Integer *Input/Output

On entry: $\mathbf{iflag}>0$.

On exit: in general, iflag should not be reset by fcn. If, however, you wish to terminate execution (perhaps because some illegal point x has been reached), iflag should be set to a negative integer.

Note: fcn should not return floating-point NaN (Not a Number) or infinity values, since these are not handled by nag_zero_sparse_nonlin_eqns_easy (c05qsc). If your code inadvertently does return any NaNs or infinities, nag_zero_sparse_nonlin_eqns_easy (c05qsc) is likely to produce unexpected results.

2:    $\mathbf{n}$ – IntegerInput

On entry: $n$, the number of equations.

Constraint: $\mathbf{n}>0$.

3:    $\mathbf{x}\left[\mathbf{n}\right]$ – doubleInput/Output

On entry: an initial guess at the solution vector. $\mathbf{x}\left[i-1\right]$ must contain the coordinate $x_i$.

On exit: the final estimate of the solution vector.

4:    $\mathbf{fvec}\left[\mathbf{n}\right]$ – doubleOutput

On exit: the function values at the final point returned in x. $\mathbf{fvec}\left[i-1\right]$ contains the function values $f_i$.

5:    $\mathbf{xtol}$ – doubleInput

On entry: the accuracy in x to which the solution is required.

Suggested value: $\sqrt{\epsilon }$, where $\epsilon$ is the machine precision returned by nag_machine_precision (X02AJC).

Constraint: $\mathbf{xtol}\ge 0.0$.

6:    $\mathbf{init}$ – Nag_BooleanInput

On entry: init must be set to Nag_TRUE to indicate that this is the first time nag_zero_sparse_nonlin_eqns_easy (c05qsc) is called for this specific problem. nag_zero_sparse_nonlin_eqns_easy (c05qsc) then computes the dense Jacobian and detects and stores its sparsity pattern (in rcomm and icomm) before proceeding with the iterations. This is noticeably time consuming when n is large. If not enough storage has been provided for rcomm or icomm, nag_zero_sparse_nonlin_eqns_easy (c05qsc) will fail. On exit with $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_NOERROR, NE_NO_IMPROVEMENT, NE_TOO_MANY_FEVALS or NE_TOO_SMALL, $\mathbf{icomm}\left[0\right]$ contains $\mathit{nnz}$, the number of nonzero entries found in the Jacobian. On subsequent calls, init can be set to Nag_FALSE if the problem has a Jacobian of the same sparsity pattern. In that case, the computation time required for the detection of the sparsity pattern will be smaller.

7:    $\mathbf{rcomm}\left[\mathbf{lrcomm}\right]$ – doubleCommunication Array

rcomm MUST NOT be altered between successive calls to nag_zero_sparse_nonlin_eqns_easy (c05qsc).

8:    $\mathbf{lrcomm}$ – IntegerInput

On entry: the dimension of the array rcomm.

Constraint: $\mathbf{lrcomm}\ge 12+\mathit{nnz}$ where $\mathit{nnz}$ is the number of nonzero entries in the Jacobian, as computed by nag_zero_sparse_nonlin_eqns_easy (c05qsc).

9:    $\mathbf{icomm}\left[\mathbf{licomm}\right]$ – IntegerCommunication Array

If $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_NOERROR, NE_NO_IMPROVEMENT, NE_TOO_MANY_FEVALS or NE_TOO_SMALL on exit, $\mathbf{icomm}\left[0\right]$ contains $\mathit{nnz}$ where $\mathit{nnz}$ is the number of nonzero entries in the Jacobian.

icomm MUST NOT be altered between successive calls to nag_zero_sparse_nonlin_eqns_easy (c05qsc).

10:  $\mathbf{licomm}$ – IntegerInput

On entry: the dimension of the array icomm.

Constraint: $\mathbf{licomm}\ge 8\times \mathbf{n}+19+\mathit{nnz}$ where $\mathit{nnz}$ is the number of nonzero entries in the Jacobian, as computed by nag_zero_sparse_nonlin_eqns_easy (c05qsc).

11:  $\mathbf{comm}$ – Nag_Comm *

The NAG communication argument (see Section 3.3.1.1 in How to Use the NAG Library and its Documentation).

12:  $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_INT

On entry, $\mathbf{licomm}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{licomm}\ge 〈\mathit{\text{value}}〉$.

On entry, $\mathbf{lrcomm}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{lrcomm}\ge 〈\mathit{\text{value}}〉$.

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}>0$.

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_NO_IMPROVEMENT

The iteration is not making good progress. This failure exit may indicate that the system does not have a zero, or that the solution is very close to the origin (see Section 7). Otherwise, rerunning nag_zero_sparse_nonlin_eqns_easy (c05qsc) from a different starting point may avoid the region of difficulty. The condition number of the Jacobian is $〈\mathit{\text{value}}〉$.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

NE_REAL

On entry, $\mathbf{xtol}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{xtol}\ge 0.0$.

NE_TOO_MANY_FEVALS

There have been at least $200\times \left(\mathbf{n}+1\right)$ calls to fcn. Consider setting $\mathbf{init}=\mathrm{Nag\_FALSE}$ and restarting the calculation from the point held in x.

NE_TOO_SMALL

No further improvement in the solution is possible. xtol is too small: $\mathbf{xtol}=〈\mathit{\text{value}}〉$.

NE_USER_STOP

iflag was set negative in fcn. $\mathbf{iflag}=〈\mathit{\text{value}}〉$.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

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Example

10.1

Program Text

Program Text (c05qsce.c)

10.2

Program Data

10.3

Program Results

Program Results (c05qsce.r)