###########################
### Quantile Regression ###
###########################
test_that("sgdi_qr should work with option rs", {
  n = 1e05
  p = 5
  bt0 = rep(5,p)
  x = matrix(rnorm(n*(p-1)), n, (p-1))
  y = cbind(1,x) %*% bt0 + rnorm(n)
  my.dat = data.frame(y=y, x=x)
  out = sgdi_qr(y~., data=my.dat, inference="rs")
  expect_error(print(out), NA)
})
test_that("sgdi_qr should work with option rss", {
  n = 1e05
  p = 5
  bt0 = rep(5,p)
  x = matrix(rnorm(n*(p-1)), n, (p-1))
  y = cbind(1,x) %*% bt0 + rnorm(n)
  my.dat = data.frame(y=y, x=x)
  out = sgdi_qr(y~., data=my.dat, inference="rss")
  expect_error(print(out), NA)
})
test_that("sgdi_qr should work with option rsd", {
  n = 1e05
  p = 5
  bt0 = rep(5,p)
  x = matrix(rnorm(n*(p-1)), n, (p-1))
  y = cbind(1,x) %*% bt0 + rnorm(n)
  my.dat = data.frame(y=y, x=x)
  out = sgdi_qr(y~., data=my.dat, inference="rsd")
  expect_error(print(out), NA)
})
test_that("sgdi_qr option burn matters", {
  n = 1e05
  p = 5
  bt0 = rep(5,p)
  x = matrix(rnorm(n*(p-1)), n, (p-1))
  y = cbind(1,x) %*% bt0 + rnorm(n)
  my.dat = data.frame(y=y, x=x)
  out1 = sgdi_qr(y~., data=my.dat)
  out2 = sgdi_qr(y~., data=my.dat, burn=1000)
  check = max(abs(out1$coefficients - out2$coefficients))
  expect_false(check==0)
})
test_that("sgdi_qr option intercept matters", {
  n = 1e05
  p = 5
  bt0 = rep(5,p)
  x = matrix(rnorm(n*(p-1)), n, (p-1))
  y = cbind(1,x) %*% bt0 + rnorm(n)
  my.dat = data.frame(y=y, x=x)
  out1 = sgdi_qr(y~., data=my.dat)
  out2 = sgdi_qr(y~., data=my.dat, intercept=FALSE)
  check = max(abs(out1$coefficients[1] - out2$coefficients[1]))
  expect_false(check==0)
})
test_that("sgdi_qr option level matters 1", {
  n = 1e05
  p = 5
  bt0 = rep(5,p)
  x = matrix(rnorm(n*(p-1)), n, (p-1))
  y = cbind(1,x) %*% bt0 + rnorm(n)
  my.dat = data.frame(y=y, x=x)
  out1 = sgdi_qr(y~., data=my.dat)
  out2 = sgdi_qr(y~., data=my.dat, level=0.9)
  check = max(abs(out1$ci.lower - out2$ci.lower))
  expect_false(check==0)
})
test_that("sgdi_qr option level matters 2", {
  n = 1e05
  p = 5
  bt0 = rep(5,p)
  x = matrix(rnorm(n*(p-1)), n, (p-1))
  y = cbind(1,x) %*% bt0 + rnorm(n)
  my.dat = data.frame(y=y, x=x)
  out1 = sgdi_qr(y~., data=my.dat)
  out2 = sgdi_qr(y~., data=my.dat, level=0.8)
  check = max(abs(out1$ci.lower - out2$ci.lower))
  expect_false(check==0)
})
test_that("sgdi_qr option level matters 3", {
  n = 1e05
  p = 5
  bt0 = rep(5,p)
  x = matrix(rnorm(n*(p-1)), n, (p-1))
  y = cbind(1,x) %*% bt0 + rnorm(n)
  my.dat = data.frame(y=y, x=x)
  bt_start = bt0*rnorm(5, mean=1, sd=0.25) # Need the same starting value to expect_true
  out1 = sgdi_qr(y~., data=my.dat, bt_start=bt_start)
  out2 = sgdi_qr(y~., data=my.dat, bt_start=bt_start, level=0.7)
  check = max(abs(out1$ci.lower - out2$ci.lower))  
  expect_true(check==0)
})
#############################################
### Quantile Regression without Inference ###
#############################################
## NB: Without inference, we do not choose any option on V.hat estimation.
test_that("sgd_qr should work", {
  n = 1e05
  p = 5
  bt0 = rep(5,p)
  x = matrix(rnorm(n*(p-1)), n, (p-1))
  y = cbind(1,x) %*% bt0 + rnorm(n)
  my.dat = data.frame(y=y, x=x)
  out = sgd_qr(y~., data=my.dat, path=F)
  expect_error(print(out), NA)
})
test_that("sgd_qr option burn matters", {
  n = 1e05
  p = 5
  bt0 = rep(5,p)
  x = matrix(rnorm(n*(p-1)), n, (p-1))
  y = cbind(1,x) %*% bt0 + rnorm(n)
  my.dat = data.frame(y=y, x=x)
  out1 = sgd_qr(y~., data=my.dat)
  out2 = sgd_qr(y~., data=my.dat, burn=1000)
  check = max(abs(out1$coefficients - out2$coefficients))
  expect_false(check==0)
})
test_that("sgd_qr option intercept matters", {
  n = 1e05
  p = 5
  bt0 = rep(5,p)
  x = matrix(rnorm(n*(p-1)), n, (p-1))
  y = cbind(1,x) %*% bt0 + rnorm(n)
  my.dat = data.frame(y=y, x=x)
  out1 = sgd_qr(y~., data=my.dat)
  out2 = sgd_qr(y~., data=my.dat, intercept=FALSE)
  check = max(abs(out1$coefficients[1] - out2$coefficients[1]))
  expect_false(check==0)
})
#######################
### Mean Regression ###
#######################
test_that("sgdi_lm should work with option rs", {
  n = 1e05
  p = 5
  bt0 = rep(5,p)
  x = matrix(rnorm(n*(p-1)), n, (p-1))
  y = cbind(1,x) %*% bt0 + rnorm(n)
  my.dat = data.frame(y=y, x=x)
  out = sgdi_lm(y~., data=my.dat, inference="rs")
  expect_error(print(out), NA)
})
test_that("sgdi_lm should work with option rss", {
  n = 1e05
  p = 5
  bt0 = rep(5,p)
  x = matrix(rnorm(n*(p-1)), n, (p-1))
  y = cbind(1,x) %*% bt0 + rnorm(n)
  my.dat = data.frame(y=y, x=x)
  out = sgdi_lm(y~., data=my.dat, inference="rss")
  expect_error(print(out), NA)
})
test_that("sgdi_lm should work with option rsd", {
  n = 1e05
  p = 5
  bt0 = rep(5,p)
  x = matrix(rnorm(n*(p-1)), n, (p-1))
  y = cbind(1,x) %*% bt0 + rnorm(n)
  my.dat = data.frame(y=y, x=x)
  out = sgdi_lm(y~., data=my.dat, inference="rsd")
  expect_error(print(out), NA)
})
test_that("sgdi_lm: bt_start matters", {
  n = 1e05
  p = 5
  bt0 = rep(5,p)
  x = matrix(rnorm(n*(p-1)), n, (p-1))
  y = cbind(1,x) %*% bt0 + rnorm(n)
  my.dat = data.frame(y=y, x=x)
  out1 = sgdi_lm(y~., data=my.dat, bt_start=NULL)
  out2 = sgdi_lm(y~., data=my.dat, bt_start=bt0)
  check = max(abs(out1$coefficients - out2$coefficients))
  expect_false(check==0)
})

test_that("sgdi_lm option burn matters", {
  n = 1e05
  p = 5
  bt0 = rep(5,p)
  x = matrix(rnorm(n*(p-1)), n, (p-1))
  y = cbind(1,x) %*% bt0 + rnorm(n)
  my.dat = data.frame(y=y, x=x)
  out1 = sgdi_lm(y~., data=my.dat)
  out2 = sgdi_lm(y~., data=my.dat, burn=1000)
  check = max(abs(out1$coefficients - out2$coefficients))
  expect_false(check==0)
})
test_that("sgdi_lm option intercept matters", {
  n = 1e05
  p = 5
  bt0 = rep(5,p)
  x = matrix(rnorm(n*(p-1)), n, (p-1))
  y = cbind(1,x) %*% bt0 + rnorm(n)
  my.dat = data.frame(y=y, x=x)
  out1 = sgdi_lm(y~., data=my.dat)
  out2 = sgdi_lm(y~., data=my.dat, intercept=FALSE)
  check = max(abs(out1$coefficients[1] - out2$coefficients[1]))
  expect_false(check==0)
})
test_that("sgdi_lm option level matters 1", {
  n = 1e05
  p = 5
  bt0 = rep(5,p)
  x = matrix(rnorm(n*(p-1)), n, (p-1))
  y = cbind(1,x) %*% bt0 + rnorm(n)
  my.dat = data.frame(y=y, x=x)
  out1 = sgdi_lm(y~., data=my.dat)
  out2 = sgdi_lm(y~., data=my.dat, level=0.9)
  check = max(abs(out1$ci.lower - out2$ci.lower))
  expect_false(check==0)
})
test_that("sgdi_lm option level matters 2", {
  n = 1e05
  p = 5
  bt0 = rep(5,p)
  x = matrix(rnorm(n*(p-1)), n, (p-1))
  y = cbind(1,x) %*% bt0 + rnorm(n)
  my.dat = data.frame(y=y, x=x)
  out1 = sgdi_lm(y~., data=my.dat)
  out2 = sgdi_lm(y~., data=my.dat, level=0.8)
  check = max(abs(out1$ci.lower - out2$ci.lower))
  expect_false(check==0)
})
test_that("sgdi_lm option level matters 3", {
  n = 1e05
  p = 5
  bt0 = rep(5,p)
  x = matrix(rnorm(n*(p-1)), n, (p-1))
  y = cbind(1,x) %*% bt0 + rnorm(n)
  my.dat = data.frame(y=y, x=x)
  bt_start = bt0*rnorm(5, mean=1, sd=0.25)  # Need the same starting value to expect_true
  out1 = sgdi_lm(y~., data=my.dat, bt_start = bt_start)
  out2 = sgdi_lm(y~., data=my.dat, bt_start = bt_start, level=0.7)
  check = max(abs(out1$ci.lower - out2$ci.lower))  
  expect_true(check==0)
})
#########################################
### Mean Regression without inference ###
#########################################
test_that("sgd_lm should work", {
  n = 1e05
  p = 5
  bt0 = rep(5,p)
  x = matrix(rnorm(n*(p-1)), n, (p-1))
  y = cbind(1,x) %*% bt0 + rnorm(n)
  my.dat = data.frame(y=y, x=x)
  out = sgd_lm(y~., data=my.dat)
  expect_error(print(out), NA)
})
test_that("sgd_lm option burn matters", {
  n = 1e05
  p = 5
  bt0 = rep(5,p)
  x = matrix(rnorm(n*(p-1)), n, (p-1))
  y = cbind(1,x) %*% bt0 + rnorm(n)
  my.dat = data.frame(y=y, x=x)
  out1 = sgd_lm(y~., data=my.dat)
  out2 = sgd_lm(y~., data=my.dat, burn=1000)
  check = max(abs(out1$coefficients - out2$coefficients))
  expect_false(check==0)
})