default

default: object

Defined in: index.js:45

Type Declaration

adam

adam: (f, x0, options?) => any

Adam (adaptive moment estimation).

Parameters

f

Function

Objective

x0

number[]

Initial parameters

options?

any = {}

{grad, learningRate, maxIter, tol, beta1, beta2, epsilon, verbose}

Returns

any

{x, fx, iterations, converged, history}

AdamOptimizer

AdamOptimizer: typeof AdamOptimizer

createOptimizer

createOptimizer: (name, options) => Optimizer

Convenience function to create optimizer by name

Parameters

name

string

Optimizer name

options?

any = {}

Optimizer options

Returns

Optimizer

Optimizer instance

curveFit

curveFit: (spec) => any

Fit a scalar model to (x, y) data, scipy.optimize.curve_fit style.

Parameters

spec?

model

Function

(x, params) => number for a scalar datum x

options?

any

Remaining keys are passed to leastSquares (jacobian, maxIter, fTol, xTol, gTol, lambda0, lambdaUp, lambdaDown, history)

p0

number[]

Initial parameters

x

number[]

Independent data

y

number[]

Dependent data, same length as x

Returns

any

{params, cov, stdErr, fx, iterations, converged}

gradientDescent

gradientDescent: (f, x0, options?) => any

Plain gradient descent, with optional backtracking line search.

Parameters

f

Function

Objective: (x) => number or (x) => {loss, gradient}

x0

number[]

Initial parameters

options?

any = {}

{grad, learningRate, maxIter, tol, lineSearch, verbose}

Returns

any

{x, fx, iterations, converged, history}

GradientDescent

GradientDescent: typeof GradientDescent

lbfgs

lbfgs: (f, x0, options?) => any

Minimize a function with L-BFGS.

Parameters

f

Function

Objective: (x) => number or (x) => {loss, gradient}

x0

number[]

Initial parameters

options?

c1?

number

Line search sufficient-decrease constant

c2?

number

Line search curvature constant

fTol?

number

Relative function-decrease tolerance

grad?

Function

Gradient: (x) => Array (finite differences otherwise)

maxIter?

number

Maximum iterations

memory?

number

Number of curvature pairs kept

tol?

number

Convergence tolerance on the gradient norm

verbose?

boolean

Returns

any

{x, fx, iterations, fevals, converged, history}

leastSquares

leastSquares: (spec) => any

Minimize 0.5 * sum(r(p)^2) with Levenberg-Marquardt.

Parameters

spec?

bounds?

number[][]

Per-parameter [lo, hi] box bounds (MINUIT transform; null/±Infinity for unbounded sides)

fScale?

number

Residual scale at which the robust losses start to flatten (scipy’s f_scale)

fTol?

number

Relative cost reduction on an accepted step

gTol?

number

Inf-norm of the gradient J^T r

history?

boolean

Record {cost, lambda} per accepted iteration

jacobian?

Function

(p) => m-by-n Array<Array>; central finite differences on the residuals otherwise

lambda0?

number

Initial damping

lambdaDown?

number

Damping decrease factor on acceptance

lambdaUp?

number

Damping increase factor on rejection

loss?

string

‘linear’ | ‘huber’ | ‘soft_l1’ | ‘cauchy’; robust losses down-weight outliers (IRLS, scipy least_squares semantics)

maxIter?

number

Maximum accepted iterations

residuals

Function

(p) => Array of length m

x0

number[]

Initial parameters of length n

xTol?

number

Max relative step component on an accepted step

Returns

any

{x, fx, residuals, iterations, fevals, converged, history?}

methods

methods: () => string[]

List the available minimization methods.

Returns

string[]

minimize

minimize: (spec) => any

Minimize a scalar function of one or more variables.

Parameters

spec?

f

Function

Objective: (x) => number or (x) => {loss, gradient}

grad?

Function

Gradient: (x) => Array (gradient methods only)

method?

string

One of methods()

options?

any

Remaining keys are passed to the method (maxIter, tol, learningRate, fTol, xTol, history, verbose, …)

x0

number[]

Initial parameters

Returns

any

{x, fx, iterations, converged, method, …}

minimizeScalar

minimizeScalar: (f, options?) => any

Minimize a univariate function.

Parameters

f

Function

Objective: (x: number) => number

options?

bracket?

number[]

[a, b] to auto-bracket from, or a full bracketing triple [a, b, c] with f(b) <= f(a), f(b) <= f(c)

maxIter?

number

Maximum iterations

method?

string

‘brent’ or ‘golden’

xTol?

number

Relative tolerance on x

Returns

any

{x, fx, iterations, fevals, converged}

momentumDescent

momentumDescent: (f, x0, options?) => any

Gradient descent with momentum.

Parameters

f

Function

Objective

x0

number[]

Initial parameters

options?

any = {}

{grad, learningRate, maxIter, tol, momentum, verbose}

Returns

any

{x, fx, iterations, converged, history}

MomentumOptimizer

MomentumOptimizer: typeof MomentumOptimizer

nelderMead

nelderMead: (f, x0, options?) => any

Minimize a function using the Nelder-Mead downhill simplex method.

Parameters

f

Function

Objective: (x) => number (or (x) => {loss, …})

x0

number[]

Initial parameters

options?

chi?

number

Expansion coefficient

fTol?

number

Convergence tolerance on f spread across the simplex

history?

boolean

Record {x, fx, simplex} per iteration

maxIter?

number

Maximum iterations

nonZeroDelta?

number

Relative perturbation for nonzero x0 entries

psi?

number

Contraction coefficient

rho?

number

Reflection coefficient

sigma?

number

Reduction (shrink) coefficient

xTol?

number

Convergence tolerance on x spread across the simplex

zeroDelta?

number

Absolute perturbation for zero x0 entries

Returns

any

{x, fx, iterations, fevals, converged, history?}

numericalGradient

numericalGradient: (f, x, options?) => number[]

Approximate the gradient of a scalar function by central finite differences.

Parameters

f

Function

Scalar function (x: Array) => number

x

number[]

Point at which to evaluate the gradient

options?

h?

number

Step size

Returns

number[]

Gradient approximation

numericalHessian

numericalHessian: (f, x, options?) => number[][]

Central finite-difference Hessian of a scalar function.

Parameters

f

Function

(x: Array) => number

x

number[]

Point of length n

options?

step?

number

Relative step size

Returns

number[][]

n-by-n symmetric Hessian

numericalJacobian

numericalJacobian: (f, x, options?) => number[][]

Central finite-difference Jacobian of a vector-valued function. Per-component step h_j = step * max(1, |x_j|).

Parameters

f

Function

(x: Array) => Array of length m

x

number[]

Point of length n

options?

step?

number

Relative step size

Returns

number[][]

m-by-n Jacobian

rmsprop

rmsprop: (f, x0, options?) => any

RMSProp.

Parameters

f

Function

Objective

x0

number[]

Initial parameters

options?

any = {}

{grad, learningRate, maxIter, tol, decay, epsilon, verbose}

Returns

any

{x, fx, iterations, converged, history}

RMSProp

RMSProp: typeof RMSProp

rootScalar

rootScalar: (f, options?) => any

Find a root of a univariate function inside a sign-changing bracket.

Parameters

f

Function

Function: (x: number) => number

options?

bracket

number[]

[a, b] with f(a) and f(b) of opposite signs (required)

maxIter?

number

Maximum iterations

method?

string

‘brent’ or ‘bisect’

rTol?

number

Relative tolerance on x

xTol?

number

Absolute tolerance on x

Returns

any

{x, fx, iterations, fevals, converged}

solve

solve: (A, b) => number[]

Solve the linear system A x = b.

Parameters

A

number[][]

n-by-n coefficient matrix (not mutated)

b

number[]

Right-hand side of length n (not mutated)

Returns

number[]

Solution vector x

Throws

If A is not square, b has the wrong length, or A is singular