Call: EXTREMUM

function

The function may depend on all of the currently defined Global variables, it must depend on the variable as function of which the extremum is to be searched. The function should return a single variable of type Number.

This argument is mandatory and should be of the type String.

ordinates

A 1-dimensional Matrix which contains the ordinates. This vector must have the same length as the values and the length must be at least 2.

This argument is mandatory.

values

A 1-dimensional Matrix which contains the values. This vector must have the same length as the ordinates and the length must be at least 2.

This argument is mandatory.

extremum

One of the current Global variables. The name can be chosen freely.

The variable doesn't have to have a value before the procedure is called. Any value associated with it before the procedure is called will be lost, if the search is successful.

On successful completion, the value of the variable is set to the abscissa of the extremum and it will then have the type Number.

The variable may be modified even if the search fails.

This argument should be a global variable, not an expression nor a constant.

minimum

The lower end of the parameter range to be searched for an extremum.

This argument is mandatory for an extremum search on a function and must then be of the type Number. The argument should not be specified when searching vectors.

maximum

The upper end of the parameter range to be searched for an extremum.

This argument is mandatory for an extremum search on a function and must then be of the type Number. The argument should not be specified when searching vectors.

options

A String that can contain zero or more of the following options, separated by commata or blanks:

Option	Effect	Notes
`CUBIC`	Cubic vector interpolation	Only with vectors
`LINEAR`	Linear vector interpolation	Only with vectors
`MAXIMUM`	Searches for a maximum	Not default
`MINIMUM`	Searches for a minimum	Default
`NOPLOT`	No plot of the function	Default
`NOPRINT`	No printout	Default
`PLOT`	Makes a plot of the function	Not default
`PRINT`	Prints a progress report	Not default
`QUADRATIC`	Quadratic vector interpolation	Only with vectors

\ε_loc

Specifies the location convergence criterion.

The search is declared to have converged when, between 2 iterations, the location of the extremum changes relatively by less than a fraction \ε_loc or absolutely by less than an amount \ε_loc.

This is an optional parameter of type Number.

Since the function is evaluated in single precision arithmetic, values less than 10\<SUP\>-6\</SUP\> are not meaningful on most computers.

[By default 10\<SUP\>-4\</SUP\>.]

\ε_fun

Specifies the function value convergence criterion.

The search is declared to have converged when, between 2 iterations, the extreme function value changes relatively by less than a fraction \ε_fun or absolutely by less than an amount \ε_fun.

This is an optional parameter of type Number.

Since the function is evaluated in single precision arithmetic, values less than 10\<SUP\>-6\</SUP\> are not meaningful on most computers.

[By default 10\<SUP\>-4\</SUP\>.]

itermax

Maximum number of parabolic search loops.

The search is abandoned if it has not converged on the basis of \ε_loc or \ε_fun within the specified number of iterations,

This is an optional parameter of type Number.

[By default 20.]

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Formatted on 21/01/18 at 16:55.