library("mlt")
library("numDeriv")

### 10.1080/15598608.2013.772835
### rho = exp(logrho)
### 1 = rho = exp(0) is identical to .Logistic
lg <- mlt:::.GammaFrailty(logrho = 0)
x <- -30:30 / 20
p <- 1:99 / 100
tol <- sqrt(.Machine$double.eps)
stopifnot(max(abs(lg$p(x) - mlt:::.Logistic()$p(x))) < tol)

stopifnot(max(abs(lg$d(x) - mlt:::.Logistic()$d(x))) < tol)

stopifnot(max(abs(lg$dd(x) - mlt:::.Logistic()$dd(x))) < tol)

stopifnot(max(abs(lg$ddd(x) - mlt:::.Logistic()$ddd(x))) < tol)

stopifnot(max(abs(lg$dd2d(x) - mlt:::.Logistic()$dd2d(x))) < tol)

stopifnot(max(abs(lg$q(p) - mlt:::.Logistic()$q(p))) < tol)

### 0 = rho = exp(-infty) is identical to .MinExtrVal
tol <- (.Machine$double.eps)^(1 / 2.5)
lg <- mlt:::.GammaFrailty(logrho = -18)
stopifnot(max(abs(lg$p(x) - mlt:::.MinExtrVal()$p(x))) < tol)

stopifnot(max(abs(lg$d(x) - mlt:::.MinExtrVal()$d(x))) < tol)

stopifnot(max(abs(lg$dd(x) - mlt:::.MinExtrVal()$dd(x))) < tol)

stopifnot(max(abs(lg$ddd(x) - mlt:::.MinExtrVal()$ddd(x))) < tol)

stopifnot(max(abs(lg$dd2d(x) - mlt:::.MinExtrVal()$dd2d(x))) < tol)

stopifnot(max(abs(lg$q(p) - mlt:::.MinExtrVal()$q(p))) < tol)

### logitalpha = logit(1) is identical to .MinExtrVal
tol <- (.Machine$double.eps)^(1 / 2.5)
lg <- mlt:::.PositiveStableFrailty(logitalpha = 50)
stopifnot(max(abs(lg$p(x) - mlt:::.MinExtrVal()$p(x))) < tol)

stopifnot(max(abs(lg$d(x) - mlt:::.MinExtrVal()$d(x))) < tol)

stopifnot(max(abs(lg$dd(x) - mlt:::.MinExtrVal()$dd(x))) < tol)

stopifnot(max(abs(lg$ddd(x) - mlt:::.MinExtrVal()$ddd(x))) < tol)

stopifnot(max(abs(lg$dd2d(x) - mlt:::.MinExtrVal()$dd2d(x))) < tol)

stopifnot(max(abs(lg$q(p) - mlt:::.MinExtrVal()$q(p))) < tol)

### log.p in quantile
prb <- 1:9 / 10
d <- eval(formals(mlt:::.distr)$which)
q1 <- sapply(d, function(w) mlt:::.distr(which = w)$q(prb))
q2 <- sapply(d, function(w) mlt:::.distr(which = w)$q(log(prb), log.p = TRUE))
stopifnot(isTRUE(all.equal(q1, q2)))

x <- -20:20 + .5
d1 <- sapply(d, function(w) grad(mlt:::.distr(which = w)$p, x))
d2 <- sapply(d, function(w) mlt:::.distr(which = w)$d(x))
stopifnot(isTRUE(all.equal(d1, d2)))

d1 <- sapply(d, function(w) grad(mlt:::.distr(which = w)$d, x))
d2 <- sapply(d, function(w) mlt:::.distr(which = w)$dd(x))
stopifnot(isTRUE(all.equal(d1, d2)))

d1 <- sapply(d, function(w) grad(mlt:::.distr(which = w)$dd, x))
d2 <- sapply(d, function(w) mlt:::.distr(which = w)$ddd(x))
stopifnot(isTRUE(all.equal(d1, d2)))

prm <- -7:7
q1 <- sapply(prm, function(p) mlt:::.GammaFrailty(p)$q(prb))
q2 <- sapply(prm, function(p) mlt:::.GammaFrailty(p)$q(log(prb), log.p = TRUE))
stopifnot(isTRUE(all.equal(q1, q2)))

d1 <- sapply(prm, function(p) grad(mlt:::.GammaFrailty(p)$p, x))
d2 <- sapply(prm, function(p) mlt:::.GammaFrailty(p)$d(x))
stopifnot(isTRUE(all.equal(d1, d2)))

d1 <- sapply(prm, function(p) grad(mlt:::.GammaFrailty(p)$d, x))
d2 <- sapply(prm, function(p) mlt:::.GammaFrailty(p)$dd(x))
stopifnot(isTRUE(all.equal(d1, d2)))

d1 <- sapply(prm, function(p) grad(mlt:::.GammaFrailty(p)$dd, x))
d2 <- sapply(prm, function(p) mlt:::.GammaFrailty(p)$ddd(x))
stopifnot(isTRUE(all.equal(d1, d2)))

q1 <- sapply(prm, function(p) mlt:::.InvGaussFrailty(p)$q(prb))
q2 <- sapply(prm, function(p) mlt:::.InvGaussFrailty(p)$q(log(prb), log.p = TRUE))
stopifnot(isTRUE(all.equal(q1, q2)))

d1 <- sapply(prm, function(p) grad(mlt:::.InvGaussFrailty(p)$p, x))
d2 <- sapply(prm, function(p) mlt:::.InvGaussFrailty(p)$d(x))
stopifnot(isTRUE(all.equal(d1, d2)))

d1 <- sapply(prm, function(p) grad(mlt:::.InvGaussFrailty(p)$d, x))
d2 <- sapply(prm, function(p) mlt:::.InvGaussFrailty(p)$dd(x))
stopifnot(isTRUE(all.equal(d1, d2)))

d1 <- sapply(prm, function(p) grad(mlt:::.InvGaussFrailty(p)$dd, x))
d2 <- sapply(prm, function(p) mlt:::.InvGaussFrailty(p)$ddd(x))
stopifnot(isTRUE(all.equal(d1, d2)))

q1 <- sapply(prm, function(p) mlt:::.PositiveStableFrailty(p)$q(prb))
q2 <- sapply(prm, function(p) mlt:::.PositiveStableFrailty(p)$q(log(prb), log.p = TRUE))
stopifnot(isTRUE(all.equal(q1, q2)))

d1 <- sapply(prm, function(p) grad(mlt:::.PositiveStableFrailty(p)$p, x))
d2 <- sapply(prm, function(p) mlt:::.PositiveStableFrailty(p)$d(x))
stopifnot(isTRUE(all.equal(d1, d2)))

d1 <- sapply(prm, function(p) grad(mlt:::.PositiveStableFrailty(p)$d, x))
d2 <- sapply(prm, function(p) mlt:::.PositiveStableFrailty(p)$dd(x))
stopifnot(isTRUE(all.equal(d1, d2)))

d1 <- sapply(prm, function(p) grad(mlt:::.PositiveStableFrailty(p)$dd, x))
d2 <- sapply(prm, function(p) mlt:::.PositiveStableFrailty(p)$ddd(x))
stopifnot(isTRUE(all.equal(d1, d2)))