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vws

Description

Package documentation

Author(s)

Maintainer: Andrew M. Raimandrew.raim@gmail.com

See Also

Useful links:

• https://github.com/andrewraim/vws

Categorical Distribution

Description

Draw variates from a categorical distribution.

Usage

r_categ(n, p, log = FALSE, one_based = FALSE)

Arguments

Value

A vector ofn draws.

Examples

p = c(0.1, 0.2, 0.3, 0.4)lp = log(p)set.seed(1234)r_categ(50, p, log = FALSE, one_based = FALSE)r_categ(50, p, log = FALSE, one_based = TRUE)set.seed(1234)r_categ(50, lp, log = TRUE, one_based = FALSE)r_categ(50, lp, log = TRUE, one_based = TRUE)

Gumbel Distribution

Description

Functions for the Gumbel distribution with density

f(x \mid \mu, \sigma) =\frac{1}{\sigma}\exp\{ -\{ (x - \mu) / \sigma + e^{-(x - \mu) / \sigma} \} \}

Usage

r_gumbel(n, mu = 0, sigma = 1)d_gumbel(x, mu = 0, sigma = 1, log = FALSE)p_gumbel(q, mu = 0, sigma = 1, lower = TRUE, log = FALSE)q_gumbel(p, mu = 0, sigma = 1, lower = TRUE, log = FALSE)

Arguments

Value

d_gumbel computes the density,r_gumbel generates random deviates,p_gumbel computes the CDF, andq_gumbel computes quantiles. A vector isreturned by each.

Examples

mu = 1sigma = 2x = r_gumbel(100000, mu, sigma)xx = seq(min(x), max(x), length.out = 100)plot(density(x))lines(xx, d_gumbel(xx, mu, sigma), lty = 2, col = "blue", lwd = 2)plot(ecdf(x))lines(xx, p_gumbel(xx, mu, sigma), lty = 2, col = "blue", lwd = 2)pp = seq(0, 1, length.out = 102) |> head(-1) |> tail(-1)qq = quantile(x, probs = pp)plot(pp, qq)lines(pp, q_gumbel(pp, mu, sigma), lty = 2, col = "blue", lwd = 2)

Printing

Description

Functions to print messages using ansprintf syntax.

Usage

printf(fmt, ...)logger(fmt, ..., dt_fmt = "%Y-%m-%d %H:%M:%S", join = " - ")fprintf(file, fmt, ...)

Arguments

Value

None (invisibleNULL); functions are called for side effects.

Examples

printf("Hello world %f %d\n", 0.1, 5)logger("Hello world\n")logger("Hello world %f %d\n", 0.1, 5)logger("Hello world %f %d\n", 0.1, 5, dt_fmt = "%H:%M:%S")logger("Hello world %f %d\n", 0.1, 5, join = " >> ")logger("Hello world %f %d\n", 0.1, 5, join = " ")

Log-Sum-Exp

Description

Compute arithmetic on the log-scale in a more stable way than directlytaking logarithm and exponentiating.

Usage

log_sum_exp(x)log_add2_exp(x, y)log_sub2_exp(x, y)

Arguments

Details

The functionlog_sum_exp computeslog(sum(exp(x))) using the method inStackExchange posthttps://stats.stackexchange.com/a/381937.

The functionslog_add2_exp andlog_sub2_exp computelog(exp(x) + exp(y)) andlog(exp(x) - exp(y)), respectively.The functionlog_sub2_exp expects that each element ofx islarger than or equal to its corresponding element iny. Otherwise,NaN will be returned with a warning.

Value

log_add2_exp andlog_sub2_exp return a vector of pointwise resultswhoseith element is the result based onx[i] andy[i].log_sum_exp returns a single scalar.

Examples

pi = 1:6 / sum(1:6)x = log(2*pi)log(sum(exp(x)))log_sum_exp(x)# Result should be 0x = c(-Inf -Inf, 0)log_sum_exp(x)# Result should be -Infx = c(-Inf -Inf, -Inf)log_sum_exp(x)# Result should be Infx = c(-Inf -Inf, Inf)log_sum_exp(x)# Result should be 5 on the original scaleout = log_add2_exp(log(3), log(2))exp(out)# Result should be 7 on the original scaleout = log_sub2_exp(log(12), log(5))exp(out)

Hybrid Univariate Optimization

Description

Use Brent's method if a bounded search interval is specified. Otherwise useBFGS method.

Usage

optimize_hybrid(f, init, lower, upper, maximize = FALSE, maxiter = 10000L)

Arguments

Value

A list with the following elements.

Examples

f = function(x) { x^2 }optimize_hybrid(f, init = 0, lower = -1, upper = 2, maximize = FALSE)optimize_hybrid(f, init = 0, lower = -1, upper = Inf, maximize = FALSE)optimize_hybrid(f, init = 0, lower = -Inf, upper = 1, maximize = FALSE)optimize_hybrid(f, init = 0, lower = 0, upper = Inf, maximize = FALSE)optimize_hybrid(f, init = 0, lower = -Inf, upper = 0, maximize = FALSE)f = function(x) { 1 - x^2 }optimize_hybrid(f, init = 0, lower = -1, upper = 1, maximize = TRUE)optimize_hybrid(f, init = 0, lower = -1, upper = 0, maximize = TRUE)optimize_hybrid(f, init = 0, lower = 0, upper = 1, maximize = TRUE)

Rectangular transformation

Description

A transformation from unconstrained\mathbb{R}^d to a rectangle in\mathbb{R}^d, and its inverse transformation.

Usage

rect(z, a, b)inv_rect(x, a, b)

Arguments

Value

A vector of lengthd.

Examples

n = 20x = seq(-5, 5, length.out = n)# Transform x to the interval [-1, 1]a = rep(-1, n)b = rep(+1, n)z = inv_rect(x, a, b)print(z)xx = rect(z, a, b)stopifnot(all(abs(x - xx) < 1e-8))# Transform x to the interval [-Inf, 1]a = rep(-Inf, n)b = rep(+1, n)z = inv_rect(x, a, b)print(z)xx = rect(z, a, b)stopifnot(all(abs(x - xx) < 1e-8))# Transform x to the interval [-1, Inf]a = rep(-1, n)b = rep(+Inf, n)z = inv_rect(x, a, b)print(z)xx = rect(z, a, b)stopifnot(all(abs(x - xx) < 1e-8))# Transform x to the interval [-Inf, Inf]a = rep(-Inf, n)b = rep(+Inf, n)z = inv_rect(x, a, b)print(z)xx = rect(z, a, b)stopifnot(all(abs(x - xx) < 1e-8))

Produce a sequence of knots

Description

Produce knots which defineN equally-spaced intervals between(finite) endpointslo andhi.

Usage

seq_knots(lo, hi, N, endpoints = FALSE)

Arguments

Value

A vector that represents a sequence of knots. Ifendpoints = TRUE, itcontainsN+1 evenly-spaced knots that representN regions withendpoints included. Ifendpoints = FALSE, the endpoints are excluded.

Examples

seq_knots(0, 1, N = 5)seq_knots(0, 1, N = 5, endpoints = TRUE)# Trivial case: make endpoints for just one intervalseq_knots(0, 1, N = 1)seq_knots(0, 1, N = 1, endpoints = TRUE)# The following calls throw errorstryCatch({  seq_knots(0, 1, N = 0)}, error = function(e) { print(e) })tryCatch({  seq_knots(0, Inf, N = 5)}, error = function(e) { print(e) })tryCatch({  seq_knots(-Inf, 1, N = 5)}, error = function(e) { print(e) })