NAG Library Function Document

nag_zero_cont_func_bd_1 (c05sdc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     a – doubleInput

On entry: the lower bound of the interval, $a$.

2:     b – doubleInput

On entry: the upper bound of the interval, $b$.

Constraint: $\mathbf{b}\ne \mathbf{a}$.

3:     x – double *Output

On exit: the approximation to the zero.

4:     f – function, supplied by the userExternal Function

f must evaluate the function $f$ whose zero is to be determined.

The specification of f is:

double  f (double x, Nag_User *comm)

1:     x – doubleInput

On entry: the point $x$ at which the function must be evaluated.

2:     comm – Nag_User *

Pointer to a structure of type Nag_User with the following member:

p – Pointer 

On entry/exit: the pointer $\mathbf{comm}\mathbf{\to }\mathbf{p}$ should be cast to the required type, e.g., struct user *s = (struct user *)comm → p, to obtain the original object's address with appropriate type. (See the argument comm below.)

5:     xtol – doubleInput

On entry: the absolute tolerance to which the zero is required (see Section 3).

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

6:     ftol – doubleInput

On entry: a value such that if $\left|f\left(x\right)\right|<\mathbf{ftol}$, $x$ is accepted as the zero. ftol may be specified as 0.0 (see Section 9).

7:     comm – Nag_User *

Pointer to a structure of type Nag_User with the following member:

p – Pointer 

On entry/exit: the pointer $\mathbf{comm}\mathbf{\to }\mathbf{p}$, of type Pointer, allows you to communicate information to and from f(). You must declare an object of the required type, e.g., a structure, and its address assigned to the pointer $\mathbf{comm}\mathbf{\to }\mathbf{p}$ by means of a cast to Pointer in the calling program, e.g., comm.p = (Pointer)&s. The type pointer will be void * with a C compiler that defines void * and char * otherwise.

8:     fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_2_REAL_ARG_EQ

On entry, $\mathbf{a}=⟨\mathit{\text{value}}⟩$ while $\mathbf{b}=⟨\mathit{\text{value}}⟩$. These arguments must satisfy $\mathbf{a}\ne \mathbf{b}$.

NE_FUNC_END_VAL

On entry, f($⟨\mathit{\text{value}}⟩$) and f($⟨\mathit{\text{value}}⟩$) have the same sign, with f($⟨\mathit{\text{value}}⟩$) $\ne 0.0$.

NE_PROBABLE_POLE

Indicates that the function values in the interval $\left(\mathbf{a},\mathbf{b}\right)$ might contain a pole rather than a zero. Reducing xtol may help in distinguishing between a pole and a zero.

NE_REAL_ARG_LE

On entry, xtol must not be less than or equal to 0.0: $\mathbf{xtol}=⟨\mathit{\text{value}}⟩$.

NE_XTOL_TOO_SMALL

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

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (c05sdce.c)

10.2  Program Data

10.3  Program Results

Program Results (c05sdce.r)