csle_agents.agents.mcs.mcs_utils package

Submodules

csle_agents.agents.mcs.mcs_utils.gls_utils module

class csle_agents.agents.mcs.mcs_utils.gls_utils.GLSUtils[source]

Bases: object

Class with util functions for MCS

lsconvex(alist: List[Union[float, int]], flist: List[Union[float, int]], nmin: int, s: int) → int[source]

Performing the lsconvex :param alist: list of known steps :param flist: function values of known steps :param nmin: :param s: :return: convex

lsrange(xl, xu, x, p, prt, bend)[source]

Defining line search range

Parameters

  • xl – lower bound

  • xu – upper bound

  • x – starting point

  • p – Search direction

  • prt – print command - unused in this implementation sofar

  • bend –

lssat(small: Union[float, int], alist: List[Union[float, int]], flist: List[Union[float, int]], alp: float, amin: float, amax: float, s: int, saturated: int) → Tuple[float, int][source]

Performing the lssat :param small: :param alist: :param flist: :param alp: :param amin: :param amin: :param amax: :param s: :param saturated: :return: alp, saturated

lssort(alist: List[Union[float, int]], flist: List[Union[float, int]])[source]

Performing the lssort

Parameters

  • alist – list of known steps

  • flist – function values of known steps

Returns

metrics and parameters obtained from doing the lssort

csle_agents.agents.mcs.mcs_utils.ls_utils module

class csle_agents.agents.mcs.mcs_utils.ls_utils.LSUtils[source]

Bases: csle_agents.agents.mcs.mcs_utils.ls_utils.UtilHelpers

Class with utility functions for MCS

lsguard(alp: float, alist: List[Union[float, int]], amax: float, amin: float, small: Union[float, int]) → float[source]

Local search guard function

Parameters

  • alp –

  • alist – list of known steps

  • amax – maximum step

  • amin – minimum step

  • small –

Returns

lssplit(i: int, alist: List[Union[float, int]], flist: List[Union[float, int]], short: float) → Tuple[float, float][source]

Local search split function

Parameters

  • i – label index

  • alist – list of known steps

  • flist – function values of known steps

  • short –

Returns

minq(gam: float, c: numpy.ndarray[Any, numpy.dtype[numpy.float64]], G: numpy.ndarray[Any, numpy.dtype[numpy.float64]], xu: numpy.ndarray[Any, numpy.dtype[numpy.float64]], xo: numpy.ndarray[Any, numpy.dtype[numpy.float64]], prt: int, eps: float, ier: int = 0, convex: int = 0) → Tuple[numpy.ndarray[Any, numpy.dtype[numpy.float64]], float, int][source]

Minq Function Minimizes an affine quadratic form subject to simple bounds. Using coordinate searches and reduced subspace minimizations, using LDL^T factorization updates fct = gam + c^T x + 0.5 x^T G x s.t. x in [xu,xo] (xu <= xo is assumed), where G is a symmetric n x n matrix, not necessarily definite (if G is indefinite, only a local minimum is found) if G is sparse, it is assumed that the ordering is such that a sparse modified Cholesky factorization is feasible

Parameters

  • prt – print command

  • xx – initial guess (optional)

  • x – minimizer (but unbounded direction if ier = 1)

  • fct – optimal function value

  • ier – 0 (local minimizer found)

quartic(a: numpy.ndarray[Any, numpy.dtype[numpy.float64]], x: float)[source]

quartic function

Parameters

  • a – vector of function values, normalized by its maximum value

  • x – positional argument generated from alp

Returns

scalar value adjused for quart bool in main code (mcs_agent)

class csle_agents.agents.mcs.mcs_utils.ls_utils.Minq[source]

Bases: object

The minQ class helper for MCS

ldlrk1(L: numpy.ndarray[Any, numpy.dtype[numpy.float64]], d: numpy.ndarray[Any, numpy.dtype[numpy.float64]], alp: float, u: numpy.ndarray[Any, numpy.dtype[numpy.float64]], eps: float = 2.2204e-16) → Tuple[numpy.ndarray[Any, numpy.dtype[numpy.float64]], numpy.ndarray[Any, numpy.dtype[numpy.float64]], numpy.ndarray[Any, numpy.dtype[numpy.float64]]][source]

lslrk1 function

Parameters

  • L – Indication of the end point (or total number of partition of the value x in the i’th dimenstion)

  • d – the value of the interpolating polynomial

  • alp –

  • u –

  • eps – parameter value for the golden ratio

Returns

class csle_agents.agents.mcs.mcs_utils.ls_utils.UtilHelpers[source]

Bases: object

A class with util functions for MCS

getalp(alpu: float, alpo: float, gTp: float, pTGp: float) → Tuple[float, bool, bool, int][source]

Gives minimizer alp in [alpu,alpo] for a univariate quadratic q(alp)=alp*gTp+0.5*alp^2*pTGp

Parameters

  • alpu –

  • alpo –

  • gTp –

Parm pTGp

Returns

ldldown(L: numpy.ndarray[Any, numpy.dtype[numpy.float64]], d: numpy.ndarray[Any, numpy.dtype[numpy.float64]], j: int) → Tuple[numpy.ndarray[Any, numpy.dtype[numpy.float64]], numpy.ndarray[Any, numpy.dtype[numpy.float64]]][source]

ldldown function

Parameters

  • L – indication of the end point (or total number of partition of the value x in the i’th dimenstion)

  • d – the value of the interpolating polynomial

  • j – label

Returns

the updated end point and the updated value

ldlup(L: numpy.ndarray[Any, numpy.dtype[numpy.float64]], d: numpy.ndarray[Any, numpy.dtype[numpy.float64]], j: int, g: numpy.ndarray[Any, numpy.dtype[numpy.float64]], eps: float) → Tuple[numpy.ndarray[Any, numpy.dtype[numpy.float64]], numpy.ndarray[Any, numpy.dtype[numpy.float64]], numpy.ndarray[Any, numpy.dtype[numpy.float64]]][source]

ldlup function :param L: Indication of the end point (or total number of partition of the value x in the i’th dimenstion) :param d: the value of the interpolating polynomial :param j: label :param g: :param eps: parameter value for the golden ratio :return:

minqsub(nsub: int, free: numpy.ndarray[Any, numpy.dtype[numpy.bool_]], L: numpy.ndarray[Any, numpy.dtype[numpy.float64]], dd: numpy.ndarray[Any, numpy.dtype[numpy.float64]], K: numpy.ndarray[Any, numpy.dtype[numpy.bool_]], G: numpy.ndarray[Any, numpy.dtype[numpy.float64]], n: int, g: numpy.ndarray[Any, numpy.dtype[numpy.float64]], x: numpy.ndarray[Any, numpy.dtype[numpy.float64]], xo: numpy.ndarray[Any, numpy.dtype[numpy.float64]], xu: numpy.ndarray[Any, numpy.dtype[numpy.float64]], convex: int, xx: numpy.ndarray[Any, numpy.dtype[numpy.float64]], fct: float, nfree: int, unfix: int, alp: float, alpu: float, alpo: float, lba: bool, uba: bool, ier: int, subdone: int, eps: float)[source]

Minqsub function

Parameters

  • nsub –

  • free –

  • L – Indication of the end point (or total number of partition of the value x in the i’th dimenstion)

  • dd –

  • n –

  • g –

  • x –

  • xo –

  • xu –

  • convex –

  • xx –

  • fct –

  • nfree –

  • unfix –

  • alp –

  • alpu –

  • alpo –

  • lba –

  • uba –

  • ier –

  • subdone –

  • eps – parameter value for the golden ratio

Returns

csle_agents.agents.mcs.mcs_utils.mcs_fun module

class csle_agents.agents.mcs.mcs_utils.mcs_fun.MCSUtils[source]

Bases: csle_agents.agents.mcs.mcs_utils.mcs_fun.UtilHelpers

Class with utiltiy functions for MCS

addloc(nloc: int, xloc: List[float], x: float) → Tuple[int, List[float]][source]

Adding a location

Parameters

  • nloc –

  • xloc –

  • x –

Returns

locations including the added one

check_box_bound(u: List[int], v: List[int])[source]

Function that checks the bounds of the box :param u: lower bound :param v: upper bound :return: boolean indicating the bound

chkloc(nloc: int, xloc: List[float], x: float) → int[source]

Checking the location

Parameters

  • nloc –

  • xloc –

  • x –

Returns

the location

chrelerr(fbest: float, stop: List[Union[float, int]]) → int[source]

Performing the chrelerr

Parameters

  • fbest –

  • stop –

Returns

flags

chvtr(f: float, vtr: float) → int[source]

Performing te chvtr function

Parameters

  • f –

  • vtr –

Returns

flag

exgain(n: int, n0: numpy.ndarray[Any, numpy.dtype[numpy.float64]], l: numpy.ndarray[Any, numpy.dtype[numpy.int32]], L: numpy.ndarray[Any, numpy.dtype[numpy.int32]], x: numpy.ndarray[Any, numpy.dtype[numpy.float64]], y: numpy.ndarray[Any, numpy.dtype[numpy.float32]], x1: numpy.ndarray[Any, numpy.dtype[numpy.float32]], x2: numpy.ndarray[Any, numpy.dtype[numpy.float32]], fx: float, f0: numpy.ndarray[Any, numpy.dtype[numpy.float32]], f1: numpy.ndarray[Any, numpy.dtype[numpy.float32]], f2: numpy.ndarray[Any, numpy.dtype[numpy.float32]]) → Tuple[numpy.ndarray[Any, numpy.dtype[numpy.float64]], int, float][source]

Determines the splitting index, the splitting value and the expected gain vector e for (potentially) splitting a box by expected gain

Parameters

  • n – dimension of the problem

  • n0 – the ith coordinate has been split n0(i) times in the history of the box

  • l – Pointer to the initial point of the initialization list

  • L – lengths of the initialization list

  • x – base vertex of the box

  • y – opposite vertex of the box

  • x1 – corresponding parameter/coordinate value

  • x2 – corresponding parameter/coordinate value

  • f1 – corresponding function value

  • f2 – corresponding function value

  • fx – function value at the base vertex

  • f0 – function values appertaining to the init. list

Return e

maximal expected gain in function value by changing coordinate i

Return isplit

splitting index

Return splval

Inf if n0(isplit) = 0, splitting value otherwise

fbestloc(fmi: List[float], fbest: float, xmin: List[float], xbest: float, nbasket0: int, stop: List[Union[float, int]]) → Tuple[float, float][source]

The fbestloc function of MCS

Parameters

  • fmi –

  • fbest –

  • xmin –

  • xbest –

  • nbasket0 –

  • stop –

Returns

genbox(par: int, level0: int, nchild: int, f0: float) → Tuple[int, int, int, float][source]

Function that generates a box

Parameters

  • par –

  • level0 –

  • nchild –

  • f0 – inital function value

Returns

Metrics and parameters from generating the box

get_theta0(iinit: int, u: List[Union[float, int]], v: List[Union[float, int]], n: int) → numpy.ndarray[Any, numpy.dtype[numpy.float32]][source]

Function for obtaining initial position

Parameters

  • iinit –

  • u –

  • v –

  • n –

Returns

the initial position theta0

hessian(i: int, k: int, x: List[Union[float, int]], x0: List[Union[float, int]], f: float, f0: float, g: numpy.ndarray[Any, numpy.dtype[numpy.float64]], G: numpy.ndarray[Any, numpy.dtype[numpy.float64]]) → Any[source]

Computes the element G(i,k) of the Hessian of the local quadratic model

Parameters

  • i –

  • k –

  • x – position

  • x0 – initial position

  • f – function values

  • f0 – inital function value

  • g –

  • G –

initbox(theta0: numpy.ndarray[Any, numpy.dtype[numpy.float64]], f0: numpy.ndarray[Any, numpy.dtype[numpy.float32]], l: numpy.ndarray[Any, numpy.dtype[numpy.int32]], L: numpy.ndarray[Any, numpy.dtype[numpy.int32]], istar: numpy.ndarray[Any, numpy.dtype[Union[numpy.float32, numpy.float64]]], u: List[Union[float, int]], v: List[Union[float, int]], isplit: numpy.ndarray[Any, numpy.dtype[numpy.int32]], level: numpy.ndarray[Any, numpy.dtype[numpy.int32]], ipar: numpy.ndarray[Any, numpy.dtype[numpy.int32]], ichild: numpy.ndarray[Any, numpy.dtype[numpy.int32]], f: numpy.ndarray[Any, numpy.dtype[numpy.float32]], nboxes: int, prt: int)[source]

Generates the boxes in the initializaiton procedure

Parameters

  • theta0 –

  • f0 – inital function value

  • l – Indication of the mid point

  • L – Indication of the end point (or total number of partition of the value x in the i’th dimenstion)

  • istar –

  • u –

  • v –

  • isplit –

  • level –

  • ipar –

  • ichild –

  • ichild –

  • f – function value of the splitinhg float value

  • nboxes – counter for boxes not in the ‘shopping bas

  • prt – print - unsued in this implementation so far

neighbor(x: numpy.ndarray[Any, numpy.dtype[numpy.float32]], delta: List[float], u: List[Union[float, int]], v: List[Union[float, int]]) → Tuple[List[Any], List[Any]][source]

Computes ‘neighbors’ x1 and x2 of x needed for making triple search and building a local quadratic model such that x(i), x1(i), x2(i) are pairwise distinct for i = 1,…,n

Parameters

  • x – current position

  • delta – radius of neighboring region

  • u –

  • v –

polint1(x: List[float], f: List[float]) → Tuple[float, float][source]

Quadratic polynomial interpolation

Parameters

  • x – positions

  • f – function values

Returns

g, G

splrnk(n: int, n0: numpy.ndarray[Any, numpy.dtype[numpy.float64]], p: numpy.ndarray[Any, numpy.dtype[numpy.int32]], x: numpy.ndarray[Any, numpy.dtype[numpy.float64]], y: numpy.ndarray[Any, numpy.dtype[numpy.float32]]) → Tuple[int, float][source]

Determines the splitting index and splitting value for splitting a box by rank

Parameters

  • n – dimension of the problem

  • p – ranking of estimated variability of the function in the different coordinates

  • x – base vertex of the box

  • y – opposite vertex of the box

:return : splitting index and value at splitting point

strtsw(smax: int, level: List[int], f: List[float], nboxes: int, record: numpy.ndarray[Any, numpy.dtype[Any]]) → Tuple[int, numpy.ndarray[Any, numpy.dtype[numpy.int32]]][source]

Function that does the strtsw

Parameters

  • smax –

  • level –

  • f –

  • nboxes – counter for boxes not in the ‘shopping bas

  • record –

updtrec(j: int, s: int, f: List[float], record: List[int]) → List[int][source]

Updates the pointer record(s) to the best non-split box at level s :param j: label of a box :param s: its level :param f: vector containing the base vertex function values of the already defined boxes. :param record: record list

vertex(j: int, n: int, u: List[Union[float, int]], v: List[Union[float, int]], v1: numpy.ndarray[Any, numpy.dtype[numpy.float64]], x0: numpy.ndarray[Any, numpy.dtype[numpy.float64]], f0: numpy.ndarray[Any, numpy.dtype[numpy.float64]], ipar: numpy.ndarray[Any, numpy.dtype[numpy.int32]], isplit: numpy.ndarray[Any, numpy.dtype[numpy.int32]], ichild: numpy.ndarray[Any, numpy.dtype[numpy.int32]], z: numpy.ndarray[Any, numpy.dtype[numpy.float64]], f: numpy.ndarray[Any, numpy.dtype[numpy.float64]], l: numpy.ndarray[Any, numpy.dtype[numpy.int32]], L: numpy.ndarray[Any, numpy.dtype[numpy.int32]])[source]

Vertex function

Parameters

  • j – label

  • n –

  • u – the initial lower bound (“lower corner” in 3D)

  • v – the initial upper bound (“upper corner” in 3D)

  • v1 –

  • x0 – initial position

  • f0 – inital function value

  • ipar –

  • isplit –

  • ichild –

  • z –

  • f –

  • l – Indication of the mid point

  • L – Indication of the end point (or total number of partition of the value x in the i’th dimenstion)

class csle_agents.agents.mcs.mcs_utils.mcs_fun.UtilHelpers[source]

Bases: object

Class with utility functions for MCS

polint(x: Union[List[float], numpy.ndarray[Any, numpy.dtype[numpy.float64]]], f: Union[List[float], numpy.ndarray[Any, numpy.dtype[numpy.float64]], numpy.ndarray[Any, numpy.dtype[numpy.float32]]]) → numpy.ndarray[Any, numpy.dtype[numpy.float64]][source]

Quadratic polynomial interpolation

Parameters

  • x – pairwise distinct support points

  • f – corresponding function values

Return d

the value of the interpolating polynomial

quadmin(a: float, b: float, d: numpy.ndarray[Any, numpy.dtype[numpy.float64]], x0: Union[List[float], numpy.ndarray[Any, numpy.dtype[numpy.float64]]]) → float[source]

The quadmin method

Parameters

  • a –

  • b –

  • d –

  • x0 –

Returns

quadpol(x: float, d: numpy.ndarray[Any, numpy.dtype[numpy.float64]], x0: Union[List[float], numpy.ndarray[Any, numpy.dtype[numpy.float64]]])[source]

Evaluates the quadratic polynomial

Parameters

  • x – starting point

  • d – the value of the interpolating polynomial

  • x0 – initial position

split1(x1: float, x2: float, f1: float, f2: float) → float[source]

The split1 method

Parameters

  • x1 –

  • x2 –

  • f1 –

  • f2 –

Returns

split2(x: float, y: float) → float[source]

The split2 method. Determines a value x1 for splitting the interval [min(x,y),max(x,y)] is modeled on the function subint with safeguards for infinite y

Parameters

  • x –

  • y –

Returns

subint(x1: float, x2: float) → Tuple[float, float][source]

Computes [min(x,y),max(x,y)] that are neither too close nor too far away from x

Parameters

  • x1 – corresponding parameter/coordinate value

  • x2 – corresponding parameter/coordinate value

updtf(n: int, i: int, x1: numpy.ndarray[Any, numpy.dtype[numpy.float64]], x2: numpy.ndarray[Any, numpy.dtype[numpy.float64]], f1: numpy.ndarray[Any, numpy.dtype[numpy.float64]], f2: numpy.ndarray[Any, numpy.dtype[numpy.float64]], fold: Union[float, numpy.ndarray[Any, numpy.dtype[numpy.float64]]], f: numpy.ndarray[Any, numpy.dtype[numpy.float64]]) → Tuple[numpy.ndarray[Any, numpy.dtype[numpy.float64]], numpy.ndarray[Any, numpy.dtype[numpy.float64]], numpy.ndarray[Any, numpy.dtype[numpy.float64]]][source]

updtf function

Parameters

  • n –

  • i –

  • x1 – corresponding parameter/coordinate value

  • x2 – corresponding parameter/coordinate value

  • f1 – corresponding function value

  • f2 – corresponding function value

  • fold – former function value

  • f – function values

Returns

vert1(j: int, z: numpy.ndarray[Any, numpy.dtype[numpy.float64]], f: numpy.ndarray[Any, numpy.dtype[numpy.float64]], x1: float, x2: float, f1: float, f2: float) → Tuple[float, float, float, float, float][source]

The vert1 method

Parameters

  • j – label

  • z –

  • f – function value

  • x1 – corresponding parameter/coordinate value

  • x2 – corresponding parameter/coordinate value

  • f1 – corresponding function value

  • f2 – corresponding function value

Returns

vert2(j: int, x: float, z: numpy.ndarray[Any, numpy.dtype[numpy.float64]], f: numpy.ndarray[Any, numpy.dtype[numpy.float64]], x1: float, x2: float, f1: float, f2: float) → Tuple[float, float, float, float][source]

The vert2 function

Parameters

  • j – label

  • x –

  • z –

  • f – function values

  • x1 – corresponding parameter/coordinate value

  • x2 – corresponding parameter/coordinate value

  • f1 – corresponding function value

  • f2 – corresponding function value

vert3(j: int, x0, f0, L: int, x1: float, x2: float, f1: float, f2: float) → Tuple[float, float, float, float][source]

Vert3 function

Parameters

  • j – label

  • x0 – initial position

  • f0 – inital function value

  • L –

  • x1 – corresponding parameter/coordinate value

  • x2 – corresponding parameter/coordinate value

  • f1 – corresponding function value

  • f2 – corresponding function value

Module contents