Shared.ox

Components shared by components of niqlow . ⇩

CV and AV

Volume and Noise Levels

Log Files

Integration, Kernels

Author:: © 2011-2023 Christopher Ferrall

Global variables, functions, enumerations

Variables
BaseTag	static const	Base tags for parallel messaging.
curdir	static const
DIFF_EPS	static const	tolerance level 0: $10^{-8}$.
DIFF_EPS1	static const	tolerance level 1: $5\times 10^{-6}$.
DIFF_EPS2	static const	tolerance level 2: $10^{-4}$.
DIFF_EPS3	static const	tolerance level 3: $10^{-2}$.
IIDZpars	static const	IID normal parameter vector.
mymomlabels	static const	labels for MyMoments
SQRT_EPS	static const	$\sqrt{\epsilon_m}$ $10^{-8}$.
SSQ_TOLER	static const	Euclidean tolerance, $10^{-12}$.
VZero	static const	0 as a vector .
ZeroForSure	static const	used in transitions.
Functions
AV		ActualValue: Returns X->myAV() if it exists or CV(X).
ColLogit		The Multinomial logit smoothing function (over columns).
CV		Return the Current Value of a Quantity: access X.v, X, X() or X(arg).
DeltaV		Row-Difference of a matrix.
Dimensions		Return rows() and columns() as a row vector.
DiscreteNormal		Return Nx1 vector of values corresponding to the 1/(N+1) percentiles of the normal distribution.
DrawOne		Return index of a single draw from the multinomial distribution.
Epanechnikov		Compute the Epanechnikov kernel matrix for a data matrix.
FLogit		The standard logistic cumulative distribution.
GaussianKernel		Compute the Gausian kernel matrix for a data matrix.
HTopen
MyMoments		Print Column Moments.
RowLogit		The Multinomial logit smoothing function (over rows).
SameDims		Check that two objects have same rows and columns.
SumToOne		Return the completed simplex of a vector or double.
TypeCheck		Check that an object is of a required class, or one of a required class.
vararray		Convert an array of strings into a space-separated string.
varlist		Parse a string for variable names; return array of strings.
Enumerations
AggregatorTypes		Tags for Types of vector-valued objective Aggregation.
ConstraintTypes		Tags for Types of Constraints.
ConvergenceResults		Code for solutions to Optimization and Non-Linear System solving.
Names_for_Integers		Pseudonyms for -3, -2, ….
NextTreatmentStates		Possible next treatment phases.
NoiseLevels		Levels of output to produce while executing.
NormalParams		Tags for parameter vectors of normal distribution.
ParallelExecutionModes		Modes of Execution when executing in parallel.
StateTypes		Codes for Type.

CGI : Zauxiliary

. @internal

Public methods
Finalize	static	Finalize the CGI component of the output; Ox output appears below.
GetVar	static	Find and return the CGI key value
Initialize	static	Initialize the processing of CGI post data.
Parse	static	Parse and return the values of a HTML form.
ParseQ	static	Parse the query

CPoint : Point : LinePoint : Zauxiliary

Store a point for a constrained objective.

Public fields
eq		inequalities.
ineq		equalities.
L		Merit value.
Public methods
Vec

Inherited methods from Point:: aggregate, Point, Vstore
Inherited methods from LinePoint:: GetV, LinePoint

Inherited fields from Point:: AggType, F, G, H, J, SE, X
Inherited fields from LinePoint:: step, V, v

Discrete : Quantity

Discrete values: actions, states, auxiliaries.

Public fields
actual		corresponding model vals.
N		Number of different values
pdf		vector of prob.
subv		subvector objected belongs to.
vals	const	range(0,N-1)
Public methods
Discrete		Create a discrete quantity .
GetN
PDF	virtual
SetActual	virtual	Initialize the actual values.
Track	virtual
Update	virtual	The default Discrete Variable update does nothing.

Inherited methods from Quantity:: SetVolume

Inherited fields from Quantity:: L, logf, pos, track, v, Volume

Discretized : Zauxiliary

A continuous discretization of a (potentially) continuous quantity.

Public fields
f		1xM row vector of unique indices into nodes.
nodes	const	Quantity object or points.
p		NxM matrix of weights.
pts		N-array of matrices, either 2x1 or 2x2. first row are node indices, second is weight on the node.
Public methods
Approx		Map vector of values into current nodes.
Discretized		Map a continuous outcome onto a set of discrete nodes.

Equality : Equations : Zauxiliary

A container for equality constraints.

Public methods
Equality
print

Inherited methods from Equations:: Equations, norm, penalty

Inherited fields from Equations:: J, L, lam, N, rlabels, v

Equations : Zauxiliary

Code a system of constraints.

Equations are used in systems and constrained optimization.

Public fields
J Jacobian.

L const array of equation labels

lam current multiplier

N const number of equations

rlabels static const lables for equation elements.

v current value

Public methods
Equations Create a system of equations.

norm virtual

penalty virtual

print virtual

GaussianQuadrature : Integration : Zauxiliary

GHK : Integration : Zauxiliary

Smooth Simulation of Multinomial Normal Probabilities and EValues. When using NnotIID an object is created for each choice set $A(\theta).$

Public fields
C	const	J-array of Choleski of M[j]Sigma M[j]'.
CSET
hR	const	half-replication (anti-thetics).
iseed	static	initial seed.
J	const	dimensions on integration, number of feasible options.
L		1xR upper bounds.
M	const	J-array of delta matrices.
nu		JxR matrix of N(0,1) simulated values.
pj		Pj.
pk		incremental simulated prob.
R	const	number of replications.
sigs		vector of standard deviations .
SimJ	const	J-1.
u		1xR uniform values.
vj		Evj.
Volume	static	output level
Public methods
GHK		Set constants for GHK.
SetC		Update array of choice-specific Choleskie's
SetSeed	static
SimDP		Use GHK to simulate choice probabilities and Emaxes for a matrix of index values.
SimProb		Use GHK to simulate state-contingent choice probability when U() includes additive N(0,Σ) errors.

GQH : GaussianQuadrature : Integration : Zauxiliary

Gauss-Hermite Quadrature Integration.

$$\int f(x)exp\{-x²/2\}dx \approx \sum_{m=1}^M \omega_m f(x_m).$$

This can be used to compute the expected value under the normal distribution.

Let $z \sim N(0,1)$.
Since $\phi(z) = (2\pi)^{-0.5} exp{-x^2/2},$ then
$$E[f(z)] \approx (2\pi)^{-0.5}\sum_{m=1}^M \omega_m f(x_m).$$

Example:

GQH::Initialize(8);
println("E[x*x] = ", GQH::wght * sqr(GQH::nodes)  );  // / M_SQRT2PI

Comments:

Thanks to Jason Rheinlander for finding and fixing an error in the previous version.

Public fields
nodes	static	the nodes or mantissa values x_m
order	static	currrent order M
wght	static	corresponding weights ω_m
Public methods
coef	static	Return the polynomial coefficients of H_n polynomial .
Initialize	static	Set the nodes and weights for Gauss-Hermite Quadrature.

GQL : GaussianQuadrature : Integration : Zauxiliary

Gauss-Laguerre Quadrature Integration.

$$\int_0^\infty f(x) e^{-1} dx \approx \sum_{m=0}^{M-1} \omega_m f(x_m)$$

This can be used to compute the expected value under the exponential distribution.

Example:

GQL::Initialize(8);
println("E[x*x] = ", GQL::wght * sqr(GQL::nodes) );

Public fields
nodes	static	the nodes or mantissa values x_m
wght	static	corresponding weights ω_m
Public methods
Initialize	static	Gauss-Laguerre nodes and weights.

InEquality : Equations : Zauxiliary

A container for inequality constraints.

Public methods
InEquality
print

Inherited methods from Equations:: Equations, norm, penalty

Inherited fields from Equations:: J, L, lam, N, rlabels, v

Integration : Zauxiliary

Container for different integration techniques.

LinePoint : Zauxiliary

Holds one line maximization try.

Public fields
step		step length.
V		v value .
v		obj value.
Public methods
Copy	virtual
GetV	virtual
LinePoint

MixPoint : Point : LinePoint : Zauxiliary

Store a point for a mixture objective.

Public fields
Dvar	const
mix		mixture elements.
sp	const
W		weight matrix
WF		free weights.
Public methods
aggregate	virtual	aggregate blackbox objectives into a scalar value.

Inherited methods from Point:: Point, Vstore
Inherited methods from LinePoint:: GetV, LinePoint

Inherited fields from Point:: AggType, F, G, H, J, SE, X
Inherited fields from LinePoint:: step, V, v

Parameter : Quantity

Continuously varying quantity: the base class for parameters of an Objective.

Public fields
block		0 or pointer to param block.
DoNotConstrain		Flag to ignore constraints.
DoNotVary		Treat as Determined, for now.
f		Current free value f.
ival	const	Initial passed value.
NearFlat	static const	tolerance for too near flat part of transformation.
scale		Scaling value s.
start		Value at start of iteration.
Public methods
Decode	virtual	Default decoding: no scaling, no constraining.
Encode	virtual	Default encoding: no scaling, no constraining.
Menu	virtual
Parameter		Create a new parameter.
ReadCGI	virtual
ReInitialize		Reset the parameter to its hard-coded values.
Reset		Reset the starting value of a parameter.
SetDoNotVary	virtual	Set the value of DoNotVary.
ToggleDoNotVary	virtual	Toggle the value of DoNotVary.

Inherited methods from Quantity:: SetVolume

Inherited fields from Quantity:: L, logf, pos, track, v, Volume

Point : LinePoint : Zauxiliary

Store information about a multidimensional point. An objective or system of equations contains the current point in cur. Algorithms use a point to store temporary values.

Public fields
AggType		form of aggregation of vfunc() into func().
F		Free vector.
G		Gradient
H		Hessian
J		Jacobian
SE		$\sqrt(diag(H^-1f))$.
X		Structural vector.
Public methods
aggregate	virtual	aggregate blackbox objectives into a scalar value.
Point
Vstore	virtual

Inherited methods from LinePoint:: GetV, LinePoint

Inherited fields from LinePoint:: step, V, v

Quantity

Container for discrete variables (DDP) and continuous parameters (FiveO).

Public fields
L	const	Label
logf		Log file dedicated to this qty.
pos		position in vector
track		Data tracking object.
v		Current actual value
Volume		Volume of output.
Public methods
SetVolume		Control variable-specifc output.

SepPoint : Point : LinePoint : Zauxiliary

Store a point for a separable objective.

Public fields
bb	const
Kvar	const
Public methods
aggregate	virtual	aggregate separable objectives into a scalar value.
SepPoint

Inherited methods from Point:: Point, Vstore
Inherited methods from LinePoint:: GetV, LinePoint

Inherited fields from Point:: AggType, F, G, H, J, SE, X
Inherited fields from LinePoint:: step, V, v

SysPoint : Point : LinePoint : Zauxiliary

A system point.

Public methods
SysPoint

Inherited methods from Point:: aggregate, Point, Vstore
Inherited methods from LinePoint:: GetV, LinePoint

Inherited fields from Point:: AggType, F, G, H, J, SE, X
Inherited fields from LinePoint:: step, V, v

Version : Zauxiliary

Checks minimum Ox version and prints copyright info.

Public fields
HTopen	static	HTML log is open.
logdir	static	directory to put log files in.
MPIserver	static	TRUE if running in parallel and in server mode.
tmstmp	static	time stamp for log files.
version	static const	Current niqlow version.
Public methods
Check	static	Check versions and set timestamp, log directory.

Zauxiliary

A container for auxiliary structures, which helps organize the hierarchy of classes.

Global

AggregatorTypes

Tags for Types of vector-valued objective Aggregation. All objectives in FiveO take the form $$f = \Omega_{i=1}^N v_i.$$ where $v$ is the vector returned by the Objective::vfunc() method that the user typically provides for their objective and $\Omega$ is an aggregator If the objective is a System then this is the system of equations. The user's objective is called by Objective::vobj() and the the vector is stored. Then Objective::fobj aggregates the vector into a real number using one of the aggregators below.

Tag	Value	$\Omega$
LINEAR	${\sum}_i\ v_i$
LOGLINEAR	${\sum}_i \ln(v_i)$
MULTIPLICATIVE	${\prod}_i v_i$
MINUSSUMOFSQUARES	$-{\sum}_i v_i^2$
SUMOFSQUARES	${\sum}_i v_i^2$

LINEAR, LOGLINEAR, MULTIPLICATIVE, MINUSSUMOFSQUARES, SUMOFSQUARES, Aggregators

ConstraintTypes

Tags for Types of Constraints. Used by Constrained objectives.

EQUALITY, INEQUALITY, ConstraintTypes

ConvergenceResults

Code for solutions to Optimization and Non-Linear System solving.

NONE, MAXITERATIONS, FAIL, WEAK, SECONDRESET, STRONG, ConvergenceResults

Names_for_Integers

Pseudonyms for -3, -2, ….

Zero, One, Two, Three, TrackAll, NotInData, UseCurrent, UseCheckPoint, AggGroup, UseDefault, UseLabel, UnInitialized, Impossible, DoAll, NoMatch, AllFixed, AllRand, UseSubSample, ResetValue, IterationFailed, UseGradient, ErgodicDist, CondProbOne, abbrevsz, xax, yax, zax, Naxes, _lo, _hi, GraphLimits

NextTreatmentStates

Possible next treatment phases.

stayinf, gotonextf, exittreatment, NextTreatmentStates

NoiseLevels

Levels of output to produce while executing.

SILENT, QUIET, LOUD, NOISY, NoiseLevels

NormalParams

Tags for parameter vectors of normal distribution.

Nmu, Nsigma, Nrho, NormalParams

ParallelExecutionModes

Modes of Execution when executing in parallel. See BaseTag

MultiParamVectors: Sending different parameter vectors to nodes to compute overall objective.

OneVector: Sending a single parameter vector to nodes to solve separate sub-problems which will be aggregated by the Client. This involves Objective::vfunc().

MultiParamVectors, OneVector, ParallelModes

StateTypes

Codes for Type. These codes (and their order) determine what calculations to do at the endogenous state $\theta$.

Tags	Value	$\theta$ Type
ORDINARY,INSUBSAMPLE	0	randomly selected for first stage of KW approximation
NOTSASMPLED,IGNOREEXOG	1	approximated if KW or utility does not depend on $\epsilon$
LASTT	2	subsampled AND last period of decision-making
LASTNOTSAMPLED	3	LASTT AND NOTSAMPLED
TERMINAL	4	Terminal state

See also:: MakeTerminal, SubSampleStates

ORDINARY, INSUBSAMPLE, NOTSAMPLED, IGNOREEXOG, LASTT, LASTNOTSAMPLED, TERMINAL, TERMNOTSAMPLED, StateTypeCutoffs

AV

AV ( X , ... )

ActualValue: Returns X->myAV() if it exists or CV(X).

Parameters:

X	anything
...	argument passed to CV()

Returns:

X->myAV() or CV(X)

X               Returns         Notes
Discrete      X->myAV()       (any class with the member function defined)
Other Object    CV(X)

Comments:

This allows user utility to access the current actual value of a state. This also works for StateBlock which will return the items from the Grid of points.

See also:

CV StateVariable::myAV ActionVariable::myAV

BaseTag

static const decl BaseTag

Base tags for parallel messaging.

ColLogit

ColLogit ( x , rho )

The Multinomial logit smoothing function (over columns).

Parameters:

x	m×n matrix.
rho	double [default=1.0] smoothing factor

Returns:

$\exp(\rho x)$./sumr($\exp(\rho x)$)

curdir

static const decl curdir

CV

CV ( X , ... )

Return the Current Value of a Quantity: access X.v, X, X() or X(arg).

Parameters:

a double, integer, static function of the form X() or X(arg), or any object with a member named v.
an array of CV compatible elements will return the horizontal concatenation value of the results as matrix.

...

a single argument can be passed along with X(). Further arguments are ignored

X               Returns         Notes
ActionVariable  X->myCV()       X's column of values in \(\alpha\)
Other Object    X.v             If v is a member
array           row of CV(X)    recursively call CV() or CV(...) for all elements
function        X() or X(...)   simply call function sending optional arguments as array
all else        X               CV() of arithmetic objects is the value itself

Returns:

X.v, X, X(), X(arg)

Comments:

This allows elements of the code to be represented several different ways.
Typically the argument should be the matrix of feasible actions, as this is how CV() is used inside Transit.
No argument is passed by Transitions() and ExogenousTransition

DeltaV

DeltaV ( V )

Row-Difference of a matrix.

Parameters:

V	Nx1 x N matrix vector, N > 1.

Returns:

(N-1)xM matrix, δ = V[i][]-V[i-1][]

Comments:

Dimensions and type are not checked!

DIFF_EPS

static const decl DIFF_EPS

tolerance level 0: $10^{-8}$.

DIFF_EPS1

static const decl DIFF_EPS1

tolerance level 1: $5\times 10^{-6}$. .

DIFF_EPS2

IIDZpars

static const decl IIDZpars

IID normal parameter vector. @NormalParams.

MyMoments

MyMoments ( M , rlabels , oxf )

Print Column Moments.

Parameters:

M	matrix: matrix to compute (column) moments for
rlabels	(optional), array of labels for variables
oxf	int, print to screen (default), file, printed to file

Returns:

matrix of moments

Comments:

See Ox moments()

mymomlabels

static const decl mymomlabels

labels for MyMoments

RowLogit

RowLogit ( x , rho )

The Multinomial logit smoothing function (over rows).

Parameters:

x	m×n matrix.
rho	double [default=1.0] smoothing factor

Returns:

$exp(\rho x)$./sumc($exp(\rho x)$)

SameDims

SameDims ( A , B )

Check that two objects have same rows and columns.

Parameters:

A	matrix
B	matrix

Returns:

TRUE if A and B have the same dimensions

SQRT_EPS

static const decl SQRT_EPS

$\sqrt{\epsilon_m}$ $10^{-8}$.

SSQ_TOLER

static const decl SSQ_TOLER

Euclidean tolerance, $10^{-12}$.

SumToOne

SumToOne ( v )

Return the completed simplex of a vector or double.

Parameters:

v	double or column vector.

Returns:

v | (1-sumc(v))

TypeCheck

TypeCheck ( obj , cname , Fatal , msg )

Check that an object is of a required class, or one of a required class.

Parameters:

obj	object
cname	Class name Array of class names
Fatal	TRUE [default]= end on the error FALSE , only issue warning. SILENT no message, just return outcome
msg	Message to print if not SILENT and class fails to match (default message is "Class fails to match")

Returns:

FALSE if no match
1+i where i is index of first match in the array (so TRUE if first/only matches)

vararray

vararray ( s )

Convert an array of strings into a space-separated string.

Parameters:

sa	a string or an array of strings

Returns:

string

Example:

vararray({"A","B","Joe"})   →  "A B Joe "
vararray("A B Joe ")   →  "A B Joe "

varlist

varlist ( s )

Parse a string for variable names; return array of strings.

Parameters:

string

Returns:

a string if s has a single variable name
an array of variable names

Example:

varlist("A B   Joe")   →  {"A","B","Joe"}
varlist("Joe") → "Joe"

VZero

static const decl VZero

0 as a vector .

ZeroForSure

static const decl ZeroForSure

used in transitions.

CGI

Finalize

static CGI :: Finalize ( )

Finalize the CGI component of the output; Ox output appears below.

GetVar

static CGI :: GetVar ( key )

Find and return the CGI key value

Parameters:

key	string, CGI post keyword

Returns:

value of the key
-1 if key not valid

Initialize

static CGI :: Initialize ( title )

Initialize the processing of CGI post data.

Parameters:

title

string, HTML title

Parse

static CGI :: Parse ( )

Parse and return the values of a HTML form.

Returns:: array of parallel values

ParseQ

static CGI :: ParseQ ( )

Parse the query

CPoint

eq

decl eq [public]

inequalities.

ineq

decl ineq [public]

equalities.

L

decl L [public]

Merit value.

Vec

Discrete

actual

decl actual [public]

corresponding model vals.

Discrete

Discrete :: Discrete ( L , N )

Create a discrete quantity .

Parameters:

L	string a label or name for the variable.
N	positive integer, number of values. N=1 is a constant.
Volume	default=SILENT. NoiseLevels

GetN

Discrete :: GetN ( )

N

decl N [public]

Number of different values

PDF

virtual Discrete :: PDF ( )

pdf

decl pdf [public]

vector of prob. of vals.

SetActual

virtual Discrete :: SetActual ( MaxV , Report )

Initialize the actual values.

Parameters:

MaxV	non-zero double, default = 1.0 N×1 vector, actual
Report	FALSE [default], do not print out current to actual mapping TRUE, print mapping If a double is sent the actual vector to 0,…, MaxV.

Example:

 a = new ActionVariable("att",3);   // None, half-time, full-time
 a -> SetActual();                  // AV(a) = 0  .5  1.0
OR:
 a -> SetActual(40);                // AV(a) = 0  20  40  (hours)

 taxbrack = new StateVariable("s",5);       //lower bound on tax rate brackets
 taxbrack -> SetActual( <0; 20000;  55000; 80000; 165000> );

See also:

Update

subv

decl subv [public]

subvector objected belongs to.

Track

Update

virtual Discrete :: Update ( )

The default Discrete Variable update does nothing. Derived discrete types can define their own Updates which called when parameters of a model (may) have changed. This depends on UpdateTimes

See also:: SetUpdateTime

vals

const decl vals [public]

range(0,N-1)

Discretized

Approx

Discretized :: Approx ( x , trans )

Map vector of values into current nodes.

Parameters:

x	column vector of values
trans	TRUE, calculate f and p like output of Transit()

Example:

v = new Discretized(<0;1;2;3>);
v->Approx(<-1.3;1.2;2>,TRUE);

After execution, these value will be set:

v.pts = { < 0				//-1.3 is to left of first node
            1.0 	>,		// all weight on the node
		  < 1 	2			// 1.2 is between 2nd and 3rd nodes
		    0.8 0.2 >,		// 20% of the gap between nodes
		  < 2				// 2 is exactly equal to 3rd node
		    1.0 	> }
v.f = < 0  	1 	2 	3	>	// 4 nodes have positive weight
v.p = < 1.0 0.0 0.0	0.0
		0.0 0.8 0.2 1.0
		0.0 0.0 0.0 1.0	>

Discretized

Discretized :: Discretized ( nodes )

Map a continuous outcome onto a set of discrete nodes.

f

decl f [public]

1xM row vector of unique indices into nodes.

nodes

const decl nodes [public]

Quantity object or points.

p

decl p [public]

NxM matrix of weights.

pts

decl pts [public]

N-array of matrices, either 2x1 or 2x2.
first row are node indices, second is weight on the node.

Equality

Equality :: Equality ( LorNorv )

print

Equality :: print ( )

Equations

Equations :: Equations ( LorN )

Create a system of equations.

Parameters:

LorN	array of strings (labels) string, a list of labels processed by varlist positive integer, number of equations

J

decl J [public]

Jacobian.

L

const decl L [public]

array of equation labels

lam

decl lam [public]

current multiplier

N

const decl N [public]

number of equations

norm

virtual Equations :: norm ( )

penalty

virtual Equations :: penalty ( )

print

rlabels

static const decl rlabels [public]

lables for equation elements.

v

decl v [public]

current value

GHK

C

const decl C [public]

J-array of Choleski of M[j]Sigma M[j]'.

CSET

decl CSET [public]

GHK

GHK :: GHK ( R , J )

Set constants for GHK.

Parameters:

R	integer, number of replications
J	integer, choice dimensions

hR

const decl hR [public]

half-replication (anti-thetics).

iseed

static decl iseed [public]

initial seed.

J

const decl J [public]

dimensions on integration, number of feasible options.

L

decl L [public]

1xR upper bounds.

M

const decl M [public]

J-array of delta matrices. $M[j]$ is $J\times J$. The first row contains a 1 in the $j$ column. The remaining rows contain -1 in the $j$ column and 1 in each non-j column so that deltas can be commuted.

nu

decl nu [public]

JxR matrix of N(0,1) simulated values.

pj

decl pj [public]

Pj.

pk

decl pk [public]

incremental simulated prob. vector.

R

const decl R [public]

number of replications.

SetC

GHK :: SetC ( Sigma )

Update array of choice-specific Choleskie's

Parameters:

Sigma

J×J variance matrix

SetSeed

static GHK :: SetSeed ( newseed )

sigs

decl sigs [public]

vector of standard deviations .

SimDP

GHK :: SimDP ( V )

Use GHK to simulate choice probabilities and Emaxes for a matrix of index values.

Parameters:

V	J×1 vector of choice values

Returns:

2x1 array of J×1 vector of simulated Emaxes and choice probabilities

SimJ

const decl SimJ [public]

J-1.

SimProb

GHK :: SimProb ( j , V )

Use GHK to simulate state-contingent choice probability when U() includes additive N(0,Σ) errors. $Ev$ is this simulated (conditional) value of setting $\alpha^\star = j$: $$Ev_j = \int_{-\infty}^{+\infty} (V_j+z_j) \left[ \int_{-\infty}^{L_{\sim j1}}\cdots \int_{-\infty}^{L_{\sim jJ^-}} f(\delta_{j} | z_j)d\delta_{j} \right] f(z_j)dz_j.$$ Here $\delta_{j}$ is the $J-1$ vector of $z_i-z_j.$ $L_{\sim ji} = -(V_i-V_j)$ is the upper bound on the region of $z_i$ consistent with $j$ being better than $i$. $P_j$ is the same expression except $(V_j+z_j)$ is replaced by $1$.

Bellman routines compute $$Emax = \sim_{j=0}^{J-1} Ev_j P_j.$$

Parameters:

j	integer, option to simulate probability for
V	J×1 vector of choice values Cholesky matrices are updated by (internal) calls to NnotIID::SetC simulated probability and Ev for option j are left in vj and pj

u

decl u [public]

1xR uniform values.

vj

decl vj [public]

Evj.

Volume

static decl Volume [public]

output level

GQH

coef

static GQH :: coef ( n )

Return the polynomial coefficients of H_n polynomial . Element 0 is the coefficient on x^n in the H polynomial, element n is the constant (i.e. x^0) coefficient.

Parameters:

n	the order of the polynomial

Returns:

Hermite polynomial coefficients, 1/2 yields probabilists Hermite polynomial coefficients.as a 1-by-(n+1) row vector

Initialize

static GQH :: Initialize ( order )

Set the nodes and weights for Gauss-Hermite Quadrature.

$$\int f(x) e^{-x^} dx \approx \sum_{m=1}^M \omega_m f(x_m).$$ This can be used to compute the expected value under the normal distribution.

Let $z \sim N(0,1)$.
Since $\phi(z) = (2\pi)^{-0.5}\exp{-x^2/2}$,then
$$E[f(z)] \approx (2\pi)^{-0.5}\sum_{m=1}^M \omega_m f(x_m).$$

Parameters:

order

integer, M

Example:

GHQ::Initialize(8);
println("E[x*x] = ", GQH::wght * sqr(GQH::nodes)  );  // / M_SQRT2PI

nodes

static decl nodes [public]

the nodes or mantissa values x_m

order

static decl order [public]

currrent order M

wght

static decl wght [public]

corresponding weights ω_m

GQL

Initialize

static GQL :: Initialize ( order )

Gauss-Laguerre nodes and weights.

∫_₀^+∞ f(x)exp(-x) ≅ ∑_m ω_m f(x_m)

Parameters:

order

integer, 2-6, 8, 10, 20, 32

nodes

static decl nodes [public]

the nodes or mantissa values x_m

wght

static decl wght [public]

corresponding weights ω_m

InEquality

InEquality :: InEquality ( LorNorv )

print

InEquality :: print ( )

LinePoint

Copy

virtual LinePoint :: Copy ( h )

GetV

virtual LinePoint :: GetV ( )

LinePoint

LinePoint :: LinePoint ( )

step

decl step [public]

step length.

V

decl V [public]

v value .

v

decl v [public]

obj value.

MixPoint

aggregate

aggregate blackbox objectives into a scalar value.

Parameters:

inV=0,	if no argument, V data member holds individual values matrix of separable values to be aggregated within columns
outv=0,	if no argument, objective stored in this.v address to return objective The matrix passed as `inV` should be `N×M`.

See also:

AggregatorTypes, Objective::SetAggregation

Dvar

const decl Dvar [public]

mix

decl mix [public]

mixture elements.

sp

const decl sp [public]

W

decl W [public]

weight matrix

WF

decl WF [public]

free weights.

Parameter

block

decl block [public]

0 or pointer to param block.

Decode

virtual Parameter :: Decode ( f )

Default decoding: no scaling, no constraining.

Returns:: v

DoNotConstrain

decl DoNotConstrain [public]

Flag to ignore constraints.

DoNotVary

decl DoNotVary [public]

Treat as Determined, for now.

Encode

virtual Parameter :: Encode ( )

Default encoding: no scaling, no constraining.

v = start;
scale = 1.0;
f = v;

Returns:: v

f

decl f [public]

Current free value f.

ival

const decl ival [public]

Initial passed value.

NearFlat

static const decl NearFlat [public]

tolerance for too near flat part of transformation.

Parameter

Parameter :: Parameter ( L , ival )

Create a new parameter.

Parameters:

L	parameter label
ival	initial value Typically a user would create an object of class derived from this base class. This function is called by those derived classes to set common elements of paramters.

ReadCGI

ReInitialize

Parameter :: ReInitialize ( )

Reset the parameter to its hard-coded values.

This does this:

	v = start = scale = CV(ival);
	f = 1.0;
    Encode();

Typically this is called by a method of the Objective to re-initialize some or all of the parameters that belong to it.

Reset

Parameter :: Reset ( newv , IsCode )

Reset the starting value of a parameter.

Parameters:

newv	value to reset at
IsCode	TRUE [default] newv is a free value FALSE newv is structural

Returns:

the new starting structural value

See also:

ReInitialize

scale

decl scale [public]

Scaling value s.

SetDoNotVary

virtual Parameter :: SetDoNotVary ( setting )

Set the value of DoNotVary.

Parameters:

setting

TRUE or FALSE

start

decl start [public]

Value at start of iteration.

ToggleDoNotVary

virtual Parameter :: ToggleDoNotVary ( )

Toggle the value of DoNotVary.

Point

aggregate

virtual Point :: aggregate ( inV , outv )

aggregate blackbox objectives into a scalar value.

Parameters:

inV=0,	if no argument, V data member holds individual values matrix of separable values to be aggregated within columns
outv=0,	if no argument, objective stored in this.v address to return objective The matrix passed as `inV` should be `N×M`.

See also:

AggregatorTypes, Objective::SetAggregation

AggType

decl AggType [public]

form of aggregation of vfunc() into func().

See also:: Objective::SetAggregation, AggregatorTypes

F

decl F [public]

Free vector.

G

decl G [public]

Gradient

H

decl H [public]

Hessian

J

decl J [public]

Jacobian

Point

Point :: Point ( )

SE

decl SE [public]

$\sqrt(diag(H^-1f))$.

Vstore

virtual Point :: Vstore ( inV )

X

decl X [public]

Structural vector.

Quantity

L

const decl L [public]

Label

logf

decl logf [public]

Log file dedicated to this qty.

pos

decl pos [public]

position in vector

SetVolume

Quantity :: SetVolume ( Volume )

Control variable-specifc output.

Parameters:

Volume

new NoiseLevels

Each quantity variable has a volume setting which is initialized to SILENT.

If the new Volume is greater than the current value then a log file is opened if one is not already open.

If the new Volume is SILENT and a log file is already open then the log file is closed.

See also:

logf

track

decl track [public]

Data tracking object.

v

decl v [public]

Current actual value

Volume

decl Volume [public]

Volume of output.

SepPoint

aggregate

virtual SepPoint :: aggregate ( inV , outv )

aggregate separable objectives into a scalar value.

Parameters:

inV=0,	if no argument, V data member holds separable values matrix of separable values to be aggregated within columns
outv=0,	if no argument, objective stored in this.v address to return objective The matrix passed as `inV` should be `(K×NvfuncTerms)×M`.

bb

const decl bb [public]

Kvar

const decl Kvar [public]

SepPoint

SepPoint :: SepPoint ( Kvar , bb )

SysPoint

SysPoint :: SysPoint ( )

Version

Check

static Version :: Check ( indir )

Check versions and set timestamp, log directory.

Parameters:

logdir

str (default="."). A directory path or file prefix to attach to all log files. All log files will receive the same time stamp, which is set here.

Comments:

Only the first call does anything. Any subsequent calls return immediately.

HTopen

static decl HTopen [public]

HTML log is open.

logdir

static decl logdir [public]

directory to put log files in.

MPIserver

static decl MPIserver [public]

TRUE if running in parallel and in server mode.

tmstmp

static decl tmstmp [public]

time stamp for log files.

version

static const decl version [public]

Current niqlow version. @name niqlowversion

Shared.ox

Documentation of Items Defined in Shared.ox ⇧

Global variables, functions, enumerations

CGI : Zauxiliary

CPoint : Point : LinePoint : Zauxiliary

Discrete : Quantity

Discretized : Zauxiliary

Equality : Equations : Zauxiliary

Equations : Zauxiliary

GaussianQuadrature : Integration : Zauxiliary

GHK : Integration : Zauxiliary

GQH : GaussianQuadrature : Integration : Zauxiliary

GQL : GaussianQuadrature : Integration : Zauxiliary

InEquality : Equations : Zauxiliary

Integration : Zauxiliary

LinePoint : Zauxiliary

MixPoint : Point : LinePoint : Zauxiliary

Parameter : Quantity

Point : LinePoint : Zauxiliary

Quantity

SepPoint : Point : LinePoint : Zauxiliary

SysPoint : Point : LinePoint : Zauxiliary

Version : Zauxiliary

Zauxiliary

Global

AV

BaseTag

ColLogit

curdir

CV

DeltaV

DIFF_EPS

DIFF_EPS1

DIFF_EPS2

DIFF_EPS3

Dimensions

DiscreteNormal

DrawOne

Epanechnikov

FLogit

GaussianKernel

HTopen

IIDZpars

MyMoments

mymomlabels

RowLogit

SameDims

SQRT_EPS

SSQ_TOLER

SumToOne

TypeCheck

vararray

varlist

VZero

ZeroForSure

CGI

Finalize

GetVar

Initialize

Parse

ParseQ

CPoint

eq

ineq

L

Vec

Discrete

actual

Discrete

GetN

N

PDF

pdf

SetActual

subv

Track

Update

vals

Discretized

Approx