The cl-grnm Reference Manual

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The cl-grnm Reference Manual

This is the cl-grnm Reference Manual, version 0.1.0, generated automatically by Declt version 2.4 "Will Decker" on Wed Jun 20 11:09:48 2018 GMT+0.


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1 Introduction

cl-grnm

Common-Lisp implementations of the grid-restrained and traditional Nelder-Mead algorithms

Authorship

This package was originally written by Mario S. Mommer (2006), and this fork is maintained by Rigetti Computing.

Introduction

These common lisp sources contain two variants of the Nelder-Mead algorithm. The original algorithm [1] and a provably convergent, reliable variant by A. Bürmen et al [4], called the "Grid Restrained Nelder Mead Algorithm" (GRNMA).

It should be mentioned that other, provably convergent variant exist [2,3], which aren't included here. The only reasons are lack of time, and the fact that the implemented variant does not require a simple descent condition, putting it closer to the original.

Other than that, and based on the article [4], the performance of these methods seems to be about equal in terms of number of function evaluations. As a side effect of the additional reliability, both tend to be a lot more efficient than the original algorithm even when it does not fail. In particular when the number of dimensions increases. As a test, one might try the GRNM,

(grnm-optimize #'standard-quadratic (make-array 30 :initial-element 1.0d0) :verbose t)

and compare with the original Nelder-Mead,

(nm-optimize #'standard-quadratic (make-array 30 :initial-element 1.0d0) :verbose t)

and observe the difference in number of function evaluations (the last value returned).

(This exercise also serves to illustrate the overall deficiencies of direct search algorithms when applied to higher dimensional problems.)

This software is provided under the MIT license; see LICENSE.txt for details.

Usage

This implementation of the grid restrained Nelder-Mead algorithm expects at least two parameters: the objective function, and an initial guess. It returns four values:

The objective function should accept a double-float array as its argument.

The initial guess will usually be an array of double-float numbers (but instead an object of the class NM-SIMPLEX may also be provided; see below). For example,

(grnm-optimize #'rosenbrock #(40.0d0 40.0d0))

finds the minimum of the Rosenbrock function, and

(grnm-optimize #'standard-quadratic (make-array 30 :initial-element 1.0d0))

finds the minimum of the standard quadratic function in 30 dimensions.

A few keyword arguments can customize the behavior. These are

:verbose (default: NIL)

Pass T here if you want to see some progress report. The amount of output can be controlled by setting verbose-level to 1 or 2. The difference is that with 1 (the default) only the best value of the simplex is shown, while with 2 the whole simplex is printed on each iteration.

:converged-p (default: burmen-et-al-convergence-test)

The burmen-et-al-convergence-test is, as the name suggests, the convergence test used in the article by Bürmen et al. It accepts a few parameters: tol-x, tol-f and rel; please see the article for further details.

Another convergence criterion that can be given is (pp-volume-test <tol>), which returns true once the parallelogram(!) spanned by the vertices of the simplex has a volume lower than <tol> to the power of N, where N is the dimension of the problem. This is a rather expensive test, as it involves computing a QR decomposition of an N by N matrix on each call.

If you are not in the mood of taking prisoners, you might as well pass (constantly NIL) as the convergence criterion. This has as a consequence that the iteration continues until the simplex collapses, which in floating-point arithmetic happens in finite time. The grid restrained Nelder-Mead algorithm should have converged by then.

:max-function-calls (default: NIL)

Maximum number of objective function evaluations. After that many function evaluations, this implementation of the algorithm will declare convergence to have occurred.

The actual number of function calls might be slightly larger (at most by N), as the relevant condition is only checked in certain situations.

Utilities/Misc

NM-optimize

Apart from the grid-restrained Nelder Mead algorithm, the traditional variant is also provided. The corresponding function is named NM-optimize, and its usage is the same as for GRNM-optimize.

The only difference is that :max-function-calls has a default value of 100000. Otherwise the algorithm might well iterate forever.

initial-simplex <initial guess> :displace <displacement>

Constructs an initial simplex with the double-float array <initial guess> as on of its corners.

The displacement can be a an array of double floats or a number. In the first case, the additional vertices of the simplex are build by adding to each component of the <initial guess> the corresponding component in <displacement>. If it is a number, then the additional vertices are build by adding <displacement> to each component of the <initial guess>.

Tips & Tricks

References

[1] J.A. Nelder and R. Mead, "A simplex method for function minimization," The Computer Journal, vol. 7, pp. 308-313, 1965.

[2] P. Tseng, "Fortified-descent simplicial search method: A general approach," SIAM Journal on Optimization, vol. 10, pp. 269-288, 1999.

[3] C.J. Price, I.D. Coope, and D. Byatt, "A convergent variant of the Nelder-Mead algorithm," Journal of Optimization Theory and Applications, vol. 113, pp. 5-19, 2002.

[4] A. Bürmen, J. Puhan and T. Tuma, "Grid Restrained Nelder-Mead Algorithm", Computational Optimization and Applications, vol. 34, no. 3, pp. 359 - 375, 2006


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2 Systems

The main system appears first, followed by any subsystem dependency.


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2.1 cl-grnm

Author

Rigetti Computing and Mario S. Sommer

License

MIT (See LICENSE.txt)

Description

Grid Restrained Nelder-Mead, a multivariate rootfinder.

Version

0.1.0

Source

cl-grnm.asd (file)

Components

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3 Files

Files are sorted by type and then listed depth-first from the systems components trees.


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3.1 Lisp


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3.1.1 cl-grnm.asd

Location

cl-grnm.asd

Systems

cl-grnm (system)

Packages

cl-grnm-asd


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3.1.2 cl-grnm/defpackage.lisp

Parent

cl-grnm (system)

Location

defpackage.lisp

Packages

cl-grnm


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3.1.3 cl-grnm/la.lisp

Dependency

defpackage.lisp (file)

Parent

cl-grnm (system)

Location

la.lisp

Internal Definitions

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3.1.4 cl-grnm/neldermead.lisp

Dependency

la.lisp (file)

Parent

cl-grnm (system)

Location

neldermead.lisp

Exported Definitions
Internal Definitions

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4 Packages

Packages are listed by definition order.


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4.1 cl-grnm-asd

Source

cl-grnm.asd

Use List

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4.2 cl-grnm

Source

defpackage.lisp (file)

Use List

common-lisp

Exported Definitions
Internal Definitions

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5 Definitions

Definitions are sorted by export status, category, package, and then by lexicographic order.


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5.1 Exported definitions


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5.1.1 Functions

Function: burmen-et-al-convergence-test &key TOL-X TOL-F REL
Package

cl-grnm

Source

neldermead.lisp (file)

Function: grnm-optimize OBJECTIVE-FUNCTION INITIAL-GUESS &key MAX-FUNCTION-CALLS CONVERGENCE-P VERBOSE
Package

cl-grnm

Source

neldermead.lisp (file)

Function: initial-simplex X0 &key DISPLACE
Package

cl-grnm

Source

neldermead.lisp (file)

Function: nm-optimize OBJECTIVE-FUNCTION INITIAL-GUESS &key MAX-FUNCTION-CALLS CONVERGENCE-P VERBOSE
Package

cl-grnm

Source

neldermead.lisp (file)

Function: pp-volume-test CSIDE
Package

cl-grnm

Source

neldermead.lisp (file)

Function: rosenbrock V
Package

cl-grnm

Source

neldermead.lisp (file)

Function: standard-quadratic V
Package

cl-grnm

Source

neldermead.lisp (file)


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5.2 Internal definitions


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5.2.1 Special variables

Special Variable: *biglambda*
Package

cl-grnm

Source

neldermead.lisp (file)

Special Variable: *breakdown*
Package

cl-grnm

Source

neldermead.lisp (file)

Special Variable: *psi*
Package

cl-grnm

Source

neldermead.lisp (file)

Special Variable: *smalllambda*
Package

cl-grnm

Source

neldermead.lisp (file)

Special Variable: *tau-a*
Package

cl-grnm

Source

neldermead.lisp (file)

Special Variable: *tau-r*
Package

cl-grnm

Source

neldermead.lisp (file)

Special Variable: *verbose-level*
Package

cl-grnm

Source

neldermead.lisp (file)


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5.2.2 Macros

Macro: with-matrix-dimensions VARFORMS &body BODY
Package

cl-grnm

Source

la.lisp (file)


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5.2.3 Functions

Function: deep-shrink F S G GAMMA_S CONVERGENCE-P VERBOSE
Package

cl-grnm

Source

neldermead.lisp (file)

Function: default-initial-simplex X0
Package

cl-grnm

Source

neldermead.lisp (file)

Function: ip V W &optional START
Package

cl-grnm

Source

la.lisp (file)

Function: make-matrix M N
Package

cl-grnm

Source

la.lisp (file)

Function: make-vector N &key INITIAL-ELEMENT
Package

cl-grnm

Source

la.lisp (file)

Function: nm-iteration SIMPLEX F &key VERBOSE GAMMA_REFLECT GAMMA_EXPAND GAMMA_OUTER_CONTRACTION GAMMA_INNER_CONTRACTION GAMMA_SHRINK
Package

cl-grnm

Source

neldermead.lisp (file)

Function: nm-iteration-burmen-et-al SIMPLEX F GRID &key VERBOSE GAMMA_REFLECT GAMMA_EXPAND GAMMA_OUTER_CONTRACTION GAMMA_INNER_CONTRACTION
Package

cl-grnm

Source

neldermead.lisp (file)

Function: norm V &optional START
Package

cl-grnm

Source

la.lisp (file)

Function: qr-factorization MAT &key WITH-Q
Package

cl-grnm

Source

la.lisp (file)

Function: qrthing-closure S N
Package

cl-grnm

Source

neldermead.lisp (file)

Function: regrid G X1 DMIN FKT
Package

cl-grnm

Source

neldermead.lisp (file)

Function: simplex-qr-thing SIDEV
Package

cl-grnm

Source

neldermead.lisp (file)

Function: v*c VECTOR CONSTANT
Package

cl-grnm

Source

la.lisp (file)

Function: v+w*c V W C
Package

cl-grnm

Source

la.lisp (file)


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5.2.4 Generic functions

Generic Function: best-before-reshape OBJECT
Generic Function: (setf best-before-reshape) NEW-VALUE OBJECT
Package

cl-grnm

Methods
Method: best-before-reshape (CACHED-SIMPLEX-DATA cached-simplex-data)

automatically generated reader method

Source

neldermead.lisp (file)

Method: (setf best-before-reshape) NEW-VALUE (CACHED-SIMPLEX-DATA cached-simplex-data)

automatically generated writer method

Source

neldermead.lisp (file)

Generic Function: cached-slot S SLOT COMPUTER
Package

cl-grnm

Methods
Method: cached-slot (S nm-simplex) SLOT COMPUTER
Source

neldermead.lisp (file)

Generic Function: data OBJECT
Generic Function: (setf data) NEW-VALUE OBJECT
Package

cl-grnm

Methods
Method: data (NM-SIMPLEX nm-simplex)

automatically generated reader method

Source

neldermead.lisp (file)

Method: (setf data) NEW-VALUE (NM-SIMPLEX nm-simplex)

automatically generated writer method

Source

neldermead.lisp (file)

Generic Function: delta OBJECT
Generic Function: (setf delta) NEW-VALUE OBJECT
Package

cl-grnm

Methods
Method: delta (GRID grid)

automatically generated reader method

Source

neldermead.lisp (file)

Method: (setf delta) NEW-VALUE (GRID grid)

automatically generated writer method

Source

neldermead.lisp (file)

Generic Function: dimension S
Package

cl-grnm

Methods
Method: dimension (S nm-simplex)
Source

neldermead.lisp (file)

Generic Function: dmin OBJECT
Generic Function: (setf dmin) NEW-VALUE OBJECT
Package

cl-grnm

Methods
Method: dmin (CACHED-SIMPLEX-DATA cached-simplex-data)

automatically generated reader method

Source

neldermead.lisp (file)

Method: (setf dmin) NEW-VALUE (CACHED-SIMPLEX-DATA cached-simplex-data)

automatically generated writer method

Source

neldermead.lisp (file)

Generic Function: dv OBJECT
Generic Function: (setf dv) NEW-VALUE OBJECT
Package

cl-grnm

Methods
Method: dv (CACHED-SIMPLEX-DATA cached-simplex-data)

automatically generated reader method

Source

neldermead.lisp (file)

Method: (setf dv) NEW-VALUE (CACHED-SIMPLEX-DATA cached-simplex-data)

automatically generated writer method

Source

neldermead.lisp (file)

Generic Function: fk S K
Generic Function: (setf fk) NV S K
Package

cl-grnm

Methods
Method: fk (S nm-simplex) K
Method: (setf fk) NV (S nm-simplex) K
Source

neldermead.lisp (file)

Generic Function: fx OBJECT
Generic Function: (setf fx) NEW-VALUE OBJECT
Package

cl-grnm

Methods
Method: fx (NM-SIMPLEX nm-simplex)

automatically generated reader method

Source

neldermead.lisp (file)

Method: (setf fx) NEW-VALUE (NM-SIMPLEX nm-simplex)

automatically generated writer method

Source

neldermead.lisp (file)

Generic Function: grid-z OBJECT
Generic Function: (setf grid-z) NEW-VALUE OBJECT
Package

cl-grnm

Methods
Method: grid-z (GRID grid)

automatically generated reader method

Source

neldermead.lisp (file)

Method: (setf grid-z) NEW-VALUE (GRID grid)

automatically generated writer method

Source

neldermead.lisp (file)

Generic Function: improve S X FX
Package

cl-grnm

Methods
Method: improve (S nm-simplex) X FX
Source

neldermead.lisp (file)

Generic Function: maybe-fill-simplex S F
Package

cl-grnm

Methods
Method: maybe-fill-simplex (S nm-simplex) F
Source

neldermead.lisp (file)

Generic Function: maybe-reshape S G FF &key FORCE
Package

cl-grnm

Methods
Method: maybe-reshape (S nm-simplex) (G grid) FF &key FORCE
Source

neldermead.lisp (file)

Generic Function: pmap OBJECT
Generic Function: (setf pmap) NEW-VALUE OBJECT
Package

cl-grnm

Methods
Method: pmap (NM-SIMPLEX nm-simplex)

automatically generated reader method

Source

neldermead.lisp (file)

Method: (setf pmap) NEW-VALUE (NM-SIMPLEX nm-simplex)

automatically generated writer method

Source

neldermead.lisp (file)

Generic Function: pseudopivot S
Package

cl-grnm

Methods
Method: pseudopivot (S nm-simplex)
Source

neldermead.lisp (file)

Generic Function: q-factor S
Package

cl-grnm

Methods
Method: q-factor (S nm-simplex)
Source

neldermead.lisp (file)

Generic Function: r-factor S
Package

cl-grnm

Methods
Method: r-factor (S nm-simplex)
Source

neldermead.lisp (file)

Generic Function: restrict GRID POINT
Package

cl-grnm

Methods
Method: restrict (GRID grid) POINT
Source

neldermead.lisp (file)

Generic Function: side-vectors S
Package

cl-grnm

Methods
Method: side-vectors (S nm-simplex)
Source

neldermead.lisp (file)

Generic Function: sort-simplex S
Package

cl-grnm

Methods
Method: sort-simplex (S nm-simplex)
Source

neldermead.lisp (file)

Generic Function: x OBJECT
Generic Function: (setf x) NEW-VALUE OBJECT
Package

cl-grnm

Methods
Method: x (NM-SIMPLEX nm-simplex)

automatically generated reader method

Source

neldermead.lisp (file)

Method: (setf x) NEW-VALUE (NM-SIMPLEX nm-simplex)

automatically generated writer method

Source

neldermead.lisp (file)

Generic Function: xk S K
Generic Function: (setf xk) NV S K
Package

cl-grnm

Methods
Method: xk (S nm-simplex) K
Method: (setf xk) NV (S nm-simplex) K
Source

neldermead.lisp (file)


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5.2.5 Classes

Class: cached-simplex-data ()
Package

cl-grnm

Source

neldermead.lisp (file)

Direct superclasses

standard-object (class)

Direct methods
Direct slots
Slot: pseudopivot
Slot: q-factor
Slot: side-vectors
Slot: r-factor
Slot: dv
Initargs

:dv

Readers

dv (generic function)

Writers

(setf dv) (generic function)

Slot: dmin
Initargs

:dmin

Readers

dmin (generic function)

Writers

(setf dmin) (generic function)

Slot: best-before-reshape
Initargs

:best-before-reshape

Readers

best-before-reshape (generic function)

Writers

(setf best-before-reshape) (generic function)

Class: grid ()
Package

cl-grnm

Source

neldermead.lisp (file)

Direct superclasses

standard-object (class)

Direct methods
Direct slots
Slot: z
Initargs

:z

Readers

grid-z (generic function)

Writers

(setf grid-z) (generic function)

Slot: delta
Initargs

:delta

Readers

delta (generic function)

Writers

(setf delta) (generic function)

Class: nm-simplex ()
Package

cl-grnm

Source

neldermead.lisp (file)

Direct superclasses

standard-object (class)

Direct methods
Direct slots
Slot: x
Initargs

:x

Readers

x (generic function)

Writers

(setf x) (generic function)

Slot: fx
Initargs

:fx

Readers

fx (generic function)

Writers

(setf fx) (generic function)

Slot: pmap
Initargs

:pmap

Readers

pmap (generic function)

Writers

(setf pmap) (generic function)

Slot: data
Readers

data (generic function)

Writers

(setf data) (generic function)


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Appendix A Indexes


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A.1 Concepts

Jump to:   C   F   L  
Index Entry  Section

C
cl-grnm.asd: The cl-grnm<dot>asd file
cl-grnm/defpackage.lisp: The cl-grnm/defpackage<dot>lisp file
cl-grnm/la.lisp: The cl-grnm/la<dot>lisp file
cl-grnm/neldermead.lisp: The cl-grnm/neldermead<dot>lisp file

F
File, Lisp, cl-grnm.asd: The cl-grnm<dot>asd file
File, Lisp, cl-grnm/defpackage.lisp: The cl-grnm/defpackage<dot>lisp file
File, Lisp, cl-grnm/la.lisp: The cl-grnm/la<dot>lisp file
File, Lisp, cl-grnm/neldermead.lisp: The cl-grnm/neldermead<dot>lisp file

L
Lisp File, cl-grnm.asd: The cl-grnm<dot>asd file
Lisp File, cl-grnm/defpackage.lisp: The cl-grnm/defpackage<dot>lisp file
Lisp File, cl-grnm/la.lisp: The cl-grnm/la<dot>lisp file
Lisp File, cl-grnm/neldermead.lisp: The cl-grnm/neldermead<dot>lisp file

Jump to:   C   F   L  

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A.2 Functions

Jump to:   (  
B   C   D   F   G   I   M   N   P   Q   R   S   V   W   X  
Index Entry  Section

(
(setf best-before-reshape): Internal generic functions
(setf best-before-reshape): Internal generic functions
(setf data): Internal generic functions
(setf data): Internal generic functions
(setf delta): Internal generic functions
(setf delta): Internal generic functions
(setf dmin): Internal generic functions
(setf dmin): Internal generic functions
(setf dv): Internal generic functions
(setf dv): Internal generic functions
(setf fk): Internal generic functions
(setf fk): Internal generic functions
(setf fx): Internal generic functions
(setf fx): Internal generic functions
(setf grid-z): Internal generic functions
(setf grid-z): Internal generic functions
(setf pmap): Internal generic functions
(setf pmap): Internal generic functions
(setf x): Internal generic functions
(setf x): Internal generic functions
(setf xk): Internal generic functions
(setf xk): Internal generic functions

B
best-before-reshape: Internal generic functions
best-before-reshape: Internal generic functions
burmen-et-al-convergence-test: Exported functions

C
cached-slot: Internal generic functions
cached-slot: Internal generic functions

D
data: Internal generic functions
data: Internal generic functions
deep-shrink: Internal functions
default-initial-simplex: Internal functions
delta: Internal generic functions
delta: Internal generic functions
dimension: Internal generic functions
dimension: Internal generic functions
dmin: Internal generic functions
dmin: Internal generic functions
dv: Internal generic functions
dv: Internal generic functions

F
fk: Internal generic functions
fk: Internal generic functions
Function, burmen-et-al-convergence-test: Exported functions
Function, deep-shrink: Internal functions
Function, default-initial-simplex: Internal functions
Function, grnm-optimize: Exported functions
Function, initial-simplex: Exported functions
Function, ip: Internal functions
Function, make-matrix: Internal functions
Function, make-vector: Internal functions
Function, nm-iteration: Internal functions
Function, nm-iteration-burmen-et-al: Internal functions
Function, nm-optimize: Exported functions
Function, norm: Internal functions
Function, pp-volume-test: Exported functions
Function, qr-factorization: Internal functions
Function, qrthing-closure: Internal functions
Function, regrid: Internal functions
Function, rosenbrock: Exported functions
Function, simplex-qr-thing: Internal functions
Function, standard-quadratic: Exported functions
Function, v*c: Internal functions
Function, v+w*c: Internal functions
fx: Internal generic functions
fx: Internal generic functions

G
Generic Function, (setf best-before-reshape): Internal generic functions
Generic Function, (setf data): Internal generic functions
Generic Function, (setf delta): Internal generic functions
Generic Function, (setf dmin): Internal generic functions
Generic Function, (setf dv): Internal generic functions
Generic Function, (setf fk): Internal generic functions
Generic Function, (setf fx): Internal generic functions
Generic Function, (setf grid-z): Internal generic functions
Generic Function, (setf pmap): Internal generic functions
Generic Function, (setf x): Internal generic functions
Generic Function, (setf xk): Internal generic functions
Generic Function, best-before-reshape: Internal generic functions
Generic Function, cached-slot: Internal generic functions
Generic Function, data: Internal generic functions
Generic Function, delta: Internal generic functions
Generic Function, dimension: Internal generic functions
Generic Function, dmin: Internal generic functions
Generic Function, dv: Internal generic functions
Generic Function, fk: Internal generic functions
Generic Function, fx: Internal generic functions
Generic Function, grid-z: Internal generic functions
Generic Function, improve: Internal generic functions
Generic Function, maybe-fill-simplex: Internal generic functions
Generic Function, maybe-reshape: Internal generic functions
Generic Function, pmap: Internal generic functions
Generic Function, pseudopivot: Internal generic functions
Generic Function, q-factor: Internal generic functions
Generic Function, r-factor: Internal generic functions
Generic Function, restrict: Internal generic functions
Generic Function, side-vectors: Internal generic functions
Generic Function, sort-simplex: Internal generic functions
Generic Function, x: Internal generic functions
Generic Function, xk: Internal generic functions
grid-z: Internal generic functions
grid-z: Internal generic functions
grnm-optimize: Exported functions

I
improve: Internal generic functions
improve: Internal generic functions
initial-simplex: Exported functions
ip: Internal functions

M
Macro, with-matrix-dimensions: Internal macros
make-matrix: Internal functions
make-vector: Internal functions
maybe-fill-simplex: Internal generic functions
maybe-fill-simplex: Internal generic functions
maybe-reshape: Internal generic functions
maybe-reshape: Internal generic functions
Method, (setf best-before-reshape): Internal generic functions
Method, (setf data): Internal generic functions
Method, (setf delta): Internal generic functions
Method, (setf dmin): Internal generic functions
Method, (setf dv): Internal generic functions
Method, (setf fk): Internal generic functions
Method, (setf fx): Internal generic functions
Method, (setf grid-z): Internal generic functions
Method, (setf pmap): Internal generic functions
Method, (setf x): Internal generic functions
Method, (setf xk): Internal generic functions
Method, best-before-reshape: Internal generic functions
Method, cached-slot: Internal generic functions
Method, data: Internal generic functions
Method, delta: Internal generic functions
Method, dimension: Internal generic functions
Method, dmin: Internal generic functions
Method, dv: Internal generic functions
Method, fk: Internal generic functions
Method, fx: Internal generic functions
Method, grid-z: Internal generic functions
Method, improve: Internal generic functions
Method, maybe-fill-simplex: Internal generic functions
Method, maybe-reshape: Internal generic functions
Method, pmap: Internal generic functions
Method, pseudopivot: Internal generic functions
Method, q-factor: Internal generic functions
Method, r-factor: Internal generic functions
Method, restrict: Internal generic functions
Method, side-vectors: Internal generic functions
Method, sort-simplex: Internal generic functions
Method, x: Internal generic functions
Method, xk: Internal generic functions

N
nm-iteration: Internal functions
nm-iteration-burmen-et-al: Internal functions
nm-optimize: Exported functions
norm: Internal functions

P
pmap: Internal generic functions
pmap: Internal generic functions
pp-volume-test: Exported functions
pseudopivot: Internal generic functions
pseudopivot: Internal generic functions

Q
q-factor: Internal generic functions
q-factor: Internal generic functions
qr-factorization: Internal functions
qrthing-closure: Internal functions

R
r-factor: Internal generic functions
r-factor: Internal generic functions
regrid: Internal functions
restrict: Internal generic functions
restrict: Internal generic functions
rosenbrock: Exported functions

S
side-vectors: Internal generic functions
side-vectors: Internal generic functions
simplex-qr-thing: Internal functions
sort-simplex: Internal generic functions
sort-simplex: Internal generic functions
standard-quadratic: Exported functions

V
v*c: Internal functions
v+w*c: Internal functions

W
with-matrix-dimensions: Internal macros

X
x: Internal generic functions
x: Internal generic functions
xk: Internal generic functions
xk: Internal generic functions

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A.3 Variables

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Index Entry  Section

*
*biglambda*: Internal special variables
*breakdown*: Internal special variables
*psi*: Internal special variables
*smalllambda*: Internal special variables
*tau-a*: Internal special variables
*tau-r*: Internal special variables
*verbose-level*: Internal special variables

B
best-before-reshape: Internal classes

D
data: Internal classes
delta: Internal classes
dmin: Internal classes
dv: Internal classes

F
fx: Internal classes

P
pmap: Internal classes
pseudopivot: Internal classes

Q
q-factor: Internal classes

R
r-factor: Internal classes

S
side-vectors: Internal classes
Slot, best-before-reshape: Internal classes
Slot, data: Internal classes
Slot, delta: Internal classes
Slot, dmin: Internal classes
Slot, dv: Internal classes
Slot, fx: Internal classes
Slot, pmap: Internal classes
Slot, pseudopivot: Internal classes
Slot, q-factor: Internal classes
Slot, r-factor: Internal classes
Slot, side-vectors: Internal classes
Slot, x: Internal classes
Slot, z: Internal classes
Special Variable, *biglambda*: Internal special variables
Special Variable, *breakdown*: Internal special variables
Special Variable, *psi*: Internal special variables
Special Variable, *smalllambda*: Internal special variables
Special Variable, *tau-a*: Internal special variables
Special Variable, *tau-r*: Internal special variables
Special Variable, *verbose-level*: Internal special variables

X
x: Internal classes

Z
z: Internal classes

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A.4 Data types

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Index Entry  Section

C
cached-simplex-data: Internal classes
cl-grnm: The cl-grnm system
cl-grnm: The cl-grnm package
cl-grnm-asd: The cl-grnm-asd package
Class, cached-simplex-data: Internal classes
Class, grid: Internal classes
Class, nm-simplex: Internal classes

G
grid: Internal classes

N
nm-simplex: Internal classes

P
Package, cl-grnm: The cl-grnm package
Package, cl-grnm-asd: The cl-grnm-asd package

S
System, cl-grnm: The cl-grnm system

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