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Up-> CppAD utility Poly

Headings-> Syntax Description Include k a z p Type ---..Operations Vector Operation Sequence Example Source

@(@\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }@)@This is cppad-20221105 documentation. Here is a link to its current documentation . Evaluate a Polynomial or its Derivative
Syntax
# include <cppad/utility/poly.hpp>
p = Poly(k, a, z)

Description
Computes the k-th derivative of the polynomial @[@ P(z) = a_0 + a_1 z^1 + \cdots + a_d z^d @]@ If k is equal to zero, the return value is @(@ P(z) @)@.

Include
The file cppad/utility/poly.hpp is included by cppad/cppad.hpp but it can also be included separately with out the rest of the CppAD routines. Including this file defines Poly within the CppAD namespace.

k
The argument k has prototype
    size_t k
It specifies the order of the derivative to calculate.

a
The argument a has prototype
    const Vector &a
(see Vector below). It specifies the vector corresponding to the polynomial @(@ P(z) @)@.

z
The argument z has prototype
    const Type &z
(see Type below). It specifies the point at which to evaluate the polynomial

p
The result p has prototype
    Type p
(see Type below) and it is equal to the k-th derivative of @(@ P(z) @)@; i.e., @[@ p = \frac{k !}{0 !} a_k + \frac{(k+1) !}{1 !} a_{k+1} z^1 + \ldots + \frac{d !}{(d - k) !} a_d z^{d - k} @]@ If @(@ k > d @)@, p = Type(0) .

Type
The type Type is determined by the argument z . It is assumed that multiplication and addition of Type objects are commutative.

Operations
The following operations must be supported where x and y are objects of type Type and i is an int:

x  = i	assignment
x  = y	assignment
x *= y	multiplication compound assignment
x += y	addition compound assignment

Vector
The type Vector must be a SimpleVector class with elements of type Type . The routine CheckSimpleVector will generate an error message if this is not the case.

Operation Sequence
The Type operation sequence used to calculate p is independent of z and the elements of a (it does depend on the size of the vector a ).

Example
The file poly.cpp contains an example and test of this routine.

Source
The file poly.hpp contains the current source code that implements these specifications.

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Input File: include/cppad/utility/poly.hpp