naginterfaces.library.opt.bounds_mod_deriv_easy¶
- naginterfaces.library.opt.bounds_mod_deriv_easy(ibound, funct2, bl, bu, x, data=None)[source]¶
bounds_mod_deriv_easy
is an easy-to-use modified Newton algorithm for finding a minimum of a function , subject to fixed upper and lower bounds on the independent variables , when first derivatives of are available. It is intended for functions which are continuous and which have continuous first and second derivatives (although it will usually work even if the derivatives have occasional discontinuities).For full information please refer to the NAG Library document for e04kz
https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/e04/e04kzf.html
- Parameters
- iboundint
Indicates whether the facility for dealing with bounds of special forms is to be used. It must be set to one of the following values:
If you are supplying all the and individually.
If there are no bounds on any .
If all the bounds are of the form .
If and .
- funct2callable (fc, gc) = funct2(xc, data=None)
You must supply this function to calculate the values of the function and its first derivatives at any point .
It should be tested separately before being used in conjunction with
bounds_mod_deriv_easy
(see submoduleopt
).- Parameters
- xcfloat, ndarray, shape
The point at which the function and derivatives are required.
- dataarbitrary, optional, modifiable in place
User-communication data for callback functions.
- Returns
- fcfloat
The value of the function at the current point ,
- gcfloat, array-like, shape
must be set to the value of the first derivative at the point , for .
- blfloat, array-like, shape
The lower bounds .
If is set to , you must set to , for . (If a lower bound is not specified for a particular , the corresponding should be set to .)
If is set to , you must set to ;
bounds_mod_deriv_easy
will then set the remaining elements of equal to .- bufloat, array-like, shape
The upper bounds .
If is set to , you must set to , for . (If an upper bound is not specified for a particular , the corresponding should be set to .)
If is set to , you must set to ;
bounds_mod_deriv_easy
will then set the remaining elements of equal to .- xfloat, array-like, shape
must be set to a guess at the th component of the position of the minimum, for . The function checks the gradient at the starting point, and is more likely to detect any error in your programming if the initial are nonzero and mutually distinct.
- dataarbitrary, optional
User-communication data for callback functions.
- Returns
- blfloat, ndarray, shape
The lower bounds actually used by
bounds_mod_deriv_easy
.- bufloat, ndarray, shape
The upper bounds actually used by
bounds_mod_deriv_easy
.- xfloat, ndarray, shape
The lowest point found during the calculations of the position of the minimum.
- ffloat
The value of corresponding to the final point stored in .
- gfloat, ndarray, shape
The value of corresponding to the final point stored in , for ; the value of for variables not on a bound should normally be close to zero.
- Raises
- NagValueError
- (errno )
On entry, and for some .
- (errno )
On entry, and .
- (errno )
On entry, .
Constraint: .
- (errno )
On entry, .
Constraint: .
- (errno )
There have been function evaluations.
- (errno )
The modulus of a variable has become very large. There may be a mistake in , your problem has no finite solution, or the problem needs rescaling.
- (errno )
It is very likely that you have made an error forming the gradient.
- Warns
- NagAlgorithmicWarning
- (errno )
The conditions for a minimum have not all been satisfied, but a lower point could not be found.
- (errno )
It is probable that a local minimum has been found, but it cannot be guaranteed.
- (errno )
It is possible that a local minimum has been found, but it cannot be guaranteed.
- (errno )
It is unlikely that a local minimum has been found.
- (errno )
It is very unlikely that a local minimum has been found.
- Notes
No equivalent traditional C interface for this routine exists in the NAG Library.
bounds_mod_deriv_easy
is applicable to problems of the form:when first derivatives are known.
Special provision is made for problems which actually have no bounds on the , problems which have only non-negativity bounds, and problems in which and . You must supply a function to calculate the values of and its first derivatives at any point .
From a starting point you supplied there is generated, on the basis of estimates of the gradient of the curvature of , a sequence of feasible points which is intended to converge to a local minimum of the constrained function.
- References
Gill, P E and Murray, W, 1976, Minimization subject to bounds on the variables, NPL Report NAC 72, National Physical Laboratory