— Class: <CONSTANT-FUNCTION>

For a <constant-function> evaluation and derivative computation are trivial.

Superclasses: <FUNCTION>

Direct slots:

• VALUE: Self-explanatory.

— Class: <FUNCTION>

The <function> class is an abstract class for a general function. This function will usually accept vector arguments, the dimensions of domain and image are fixed when defining the function. If the function is differentiable, the gradient matrix can be obtained by evaluating the gradient slot.

Direct slots:

• DOMAIN-DIMENSION: Self-explanatory.
• IMAGE-DIMENSION: Self-explanatory.

— Class: <LINEAR-FUNCTION>

A <linear-function> is determined by a matrix A and a vector b. It represents the map x -> Ax+b.

Superclasses: <FUNCTION>

Direct slots:

• A: Self-explanatory.
• B: Self-explanatory.

— Class: <PERIODIC-POLYGON>

This class implements a periodic polygon.

Superclasses: <POLYGON>

— Class: <POLYGON>

This class implements a function which maps the unit interval to a polygon.

Superclasses: <FUNCTION>

Direct slots:

• POINTS: A vector of points for the polygon.

— Class: <SPECIAL-FUNCTION>

A <special-function> provides its own evaluation and gradient computation.

Superclasses: <FUNCTION>

Direct slots:

• EVALUATOR: Self-explanatory.
• GRADIENT: Self-explanatory.
• JET: Self-explanatory.

— Function: CIRCLE-FUNCTION &OPTIONAL (RADIAL-DISTANCE 1.0) (MIDPOINT (COERCE (QUOTE (0.0 0.0)) (QUOTE DOUBLE-VEC))) (OMEGA 1.0) (PHI0 0.0)

Returns a special function drawing a polar around midpoint with distance given by the function or number radial-distance with angular velocity omega. Without arguments it yields a function mapping R^1 isometrically to S^1.

— Function: CUBIC-SPLINE Y

On a regular partition of the unit interval interpolating values y are given. This function returns an interpolating spline.

— Function: DIFFERENTIABLE-P F &OPTIONAL K

Returns t if f is differentiable or differentiable of the given degree.

— Function: ELLIPSE-MATRIX RADIUS EXCENTRICITY PHI

Returns a matrix A suitable for describing the ellipse as (Ax,x)=1.

— Function: EVALUATE F X

Generic evaluation of functions on an argument. Numbers and arrays are treated as constants. Special evaluation is defined for multivariate polynomials on vectors and for <function> objects.

— Function: EVALUATE-GRADIENT F X

Generic evaluation of gradients of differentiable functions.

— Function: HOMOTOPY FUNC1 FUNC2

Returns a function which uses its first coordinate as a homotopy parameter.

— Function: INTERVAL-METHOD FUNC A B ACCURACY

Finds zeros of functions in 1d by the interval method.

— Function: MAKE-POLYNOMIAL COEFFS

Constructor which simplifies the coefficient list.

— Function: MULTIPLE-EVALUATE FUNC POSITIONS

Multiple evaluations of func may be optimized.

— Function: MULTIPLE-EVALUATE-GRADIENT F POSITIONS

Multiple evaluations may be optimized.

— Function: N-VARIATE-MONOMIALS-OF-DEGREE N DEGREE &OPTIONAL (TYPE (QUOTE =))

Returns n-variate monomials of degree being equal or being lower or equal than deg. Examples: (n-variate-monomials-of-degree 2 2) -> (x2^2 x1*x2 x1^2) (n-variate-monomials-of-degree 2 2 '<=) -> (1 x2 x1 x2^2 x1*x2 x1^2)

— Function: NUMERICAL-COMPLEX-DERIVATIVE F

Computes a very accurate real derivative for functions which can be applied to complex arguments.

— Function: NUMERICAL-GRADIENT FUNC &KEY (SHIFT 1.e-8)

Computes the numerical gradient of func at pos.

— Class: POLYNOMIAL

Multivariate polynomial. The coefficients are represented as nested lists.

Superclasses: <VECTOR>

Direct slots:

• COEFFS: Self-explanatory.

— Function: PROJECT-TO-ELLIPSOID MIDPOINT A

Returns a function which projects to the ellipsoid given by Q(x-midpoint)=1 where Q is the quadratic form associated with the matrix A.

— Function: PROJECT-TO-SPHERE MIDPOINT RADIUS

Returns a function which projects to the sphere with given midpoint and radius.

— Function: SHIFT-POLYNOMIAL POLY DIM

Shifts a polynomial in dimension, e.g. x_1 becomes x_2.

— Function: SPARSE-REAL-DERIVATIVE SPARSE-F

Warning: works only for real-valued functions!

— Function: SPECIAL-1D-FUNCTION F &OPTIONAL DF

Constructs a special function between 1D-spaces from ordinary Lisp functions.

— Function: XN-DISTORTION-FUNCTION F GRAD-F DIM

Returns a function which distorts the xn-coordinate by a factor f(x'). Also grad-f has to be provided.