random_init_polynomial {genscore}

Randomly generate an initial point in the domain defined by a single polynomial with no negative coefficient.

Description

Randomly generate an initial point in the domain defined by a single polynomial with no negative coefficient.

Usage

random_init_polynomial(domain)

Arguments

domain

A list returned from make_domain() that represents the domain. Currently only supports domain$type == "polynomial" && length(domain$ineqs) == 1. If domain$ineqs[[1]]$uniform == FALSE, domain$ineqs[[1]]$coeffs must not contain negative numbers.

Details

If inequality is uniform, find the uniform bound for each component and generate each coordinate using random_init_uniform(). Otherwise, first randomly generate centered laplace variables for components with coefficient 0 (free variables). Then assign a quota of eq$const / length(nonzero_coefficient) to each coordinate (so that each
frac_pow(x[i], eq$power_numers[i], eq$power_denoms[i], eq$abs) * eq$coeffs[i] is compared to quota). Deal with components with exp() term first, and generate each coordinate while fulfilling quota if possible; if not, randomly generate from
[-0.01,0.01]/abs(eq$power_numers[i]). Then recalculate the new quota which subtracts the exp() terms from eq$const, and this time divided by the number of remaining components. If quota becomes negative and eq$larger == FALSE, each component, after frac_pow() is assumed to give a negative number. This is not possible if the term has the form x^{even_number/even_number}, or if the term is not log() in the case where eq$nonnegative == TRUE || eq$abs == TRUE. Change quota to a positive smaller in absolute value for these bad terms and generate. Finally, recalculate quota as before and generate the rest of the "good" components.

In some extreme domains the function may fail to generate a point within the domain. Also, it is not guaranteed that the function returns a point in an area with a high probability density.

Value

A p vector inside the domain defined by domain.

Examples

p <- 30
poly_d <- function(ex, abs, nng){
   return (make_domain("polynomial", p=p, 
                       ineqs=list(list(expression=ex, abs=abs, nonnegative=nng))))
}

random_init_polynomial(poly_d(paste("sum(exp(x))<=", p*1.01), abs=TRUE, nng=TRUE))
random_init_polynomial(poly_d(paste("sum(exp(x))<=", p*1.01), abs=FALSE, nng=FALSE))
random_init_polynomial(poly_d(paste("sum(exp(x))>", p*1.01), abs=TRUE, nng=TRUE))
random_init_polynomial(poly_d(paste("sum(exp(x))>", p*1.01), abs=TRUE, nng=FALSE))
random_init_polynomial(poly_d(paste("sum(log(x))<=", 0.01), abs=TRUE, nng=TRUE))
random_init_polynomial(poly_d(paste("sum(log(x))>", 0.01), abs=TRUE, nng=TRUE))
random_init_polynomial(poly_d(paste("sum(x^2)<=", 0.01), abs=TRUE, nng=TRUE))
random_init_polynomial(poly_d(paste("sum(x^2)>", 0.01), abs=TRUE, nng=TRUE))

random_init_polynomial(poly_d(paste("exp(x)<=", 1.01), abs=TRUE, nng=TRUE))
random_init_polynomial(poly_d(paste("exp(x)<=", 1.01), abs=FALSE, nng=FALSE))
random_init_polynomial(poly_d(paste("exp(x)>", 1.01), abs=TRUE, nng=TRUE))
random_init_polynomial(poly_d(paste("exp(x)>", 1.01), abs=TRUE, nng=FALSE))
random_init_polynomial(poly_d(paste("log(x)<=", 0.01), abs=TRUE, nng=TRUE))
random_init_polynomial(poly_d(paste("log(x)>", 0.01), abs=TRUE, nng=TRUE))
random_init_polynomial(poly_d(paste("x^2<=", 0.01), abs=TRUE, nng=TRUE))
random_init_polynomial(poly_d(paste("x^2>", 0.01), abs=TRUE, nng=TRUE))

random_init_polynomial(poly_d("x1^2+x2^2+log(x3)<-2", abs=TRUE, nng=TRUE))
random_init_polynomial(poly_d("x1^2+x2^2+log(x3)>-2", abs=FALSE, nng=FALSE))
random_init_polynomial(poly_d("x1^(3/5)+x2^2+x3^(1/3)<-2", abs=FALSE, nng=FALSE))
random_init_polynomial(poly_d("x1^(3/5)+x2^2+x3^(1/3)>-2", abs=FALSE, nng=FALSE))
random_init_polynomial(poly_d("x1^(3/5)+1.2*exp(2*x2)+2.3*exp(-3*x3)<-2", abs=FALSE, nng=FALSE))
random_init_polynomial(poly_d("x1^(3/5)+1.2*exp(2*x2)+2.3*exp(-3*x3)<2", abs=TRUE, nng=FALSE))
random_init_polynomial(poly_d("x1^(3/5)+1.2*exp(2*x2)+2.3*exp(-3*x3)>-2", abs=TRUE, nng=FALSE))
random_init_polynomial(poly_d("x1^(3/5)+2.3*log(x4)+1.3*exp(2*x2)+0.7*exp(-3*x3)<-2", 
                       abs=TRUE, nng=FALSE))
random_init_polynomial(poly_d("x1^(3/5)+2.3*log(x4)+1.3*exp(2*x2)+0.7*exp(-3*x3)>-2", 
                       abs=FALSE, nng=FALSE))
random_init_polynomial(poly_d(
   "x1^(3/5)+0.9*x2^(2/3)+2.7*x3^(-3/2)+1.1*x4^(-5)+1.1*exp(2x5)+1.3*exp(-3x6)+0.7*log(x7)<-2", 
                       abs=TRUE, nng=FALSE))
random_init_polynomial(poly_d(
   "x1^(3/5)+0.9*x2^(2/3)+2.7*x3^(-3/2)+1.1*x4^(-5)+1.1*exp(2x5)+1.3*exp(-3x6)+0.7*log(x7)<-2", 
                       abs=FALSE, nng=TRUE))
random_init_polynomial(poly_d(
   "x1^(3/5)+0.9*x2^(2/3)+2.7*x3^(-3/2)+1.1*x4^(-5)+1.1*exp(2x5)+1.3*exp(-3x6)+0.7*log(x7)>-2", 
                       abs=TRUE, nng=FALSE))
random_init_polynomial(poly_d(
   "x1^(3/5)+0.9*x2^(2/3)+2.7*x3^(-3/2)+1.1*x4^(-5)+1.1*exp(2x5)+1.3*exp(-3x6)+0.7*log(x7)>2", 
                       abs=TRUE, nng=TRUE))
random_init_polynomial(poly_d(
   "x1^(3/5)+0.9*x2^(2/3)+2.7*x3^(-3/2)+1.1*x4^(-5)+1.1*exp(2x5)+1.3*exp(-3x6)+0.7*log(x7)>2", 
                       abs=FALSE, nng=FALSE))