# Copyright 2018 The JAX Authors.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     https://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

import collections
import functools
import itertools

from absl.testing import absltest
from absl.testing import parameterized

import numpy as np
import scipy
import scipy.special as osp_special

import jax
import jax.numpy as jnp
from jax._src import test_util as jtu
from jax.scipy import special as lsp_special

jax.config.parse_flags_with_absl()


all_shapes = [(), (4,), (3, 4), (3, 1), (1, 4), (2, 1, 4)]

OpRecord = collections.namedtuple(
    "OpRecord",
    ["name", "nargs", "dtypes", "rng_factory", "test_autodiff", "nondiff_argnums", "test_name"])


def op_record(name, nargs, dtypes, rng_factory, test_grad, nondiff_argnums=(), test_name=None):
  test_name = test_name or name
  nondiff_argnums = tuple(sorted(set(nondiff_argnums)))
  return OpRecord(name, nargs, dtypes, rng_factory, test_grad, nondiff_argnums, test_name)


float_dtypes = jtu.dtypes.floating
int_dtypes = jtu.dtypes.integer

# TODO(phawkins): we should probably separate out the function domains used for
# autodiff tests from the function domains used for equivalence testing. For
# example, logit should closely match its scipy equivalent everywhere, but we
# don't expect numerical gradient tests to pass for inputs very close to 0.

JAX_SPECIAL_FUNCTION_RECORDS = [
    op_record(
        "beta", 2, float_dtypes, jtu.rand_default, False
    ),
    op_record(
        "betaln", 2, float_dtypes, jtu.rand_default, False
    ),
    op_record(
        "betainc", 3, float_dtypes, jtu.rand_positive, False
    ),
    op_record(
        "gamma", 1, float_dtypes, jtu.rand_default, True
    ),
    op_record(
        "digamma", 1, float_dtypes, jtu.rand_positive, True
    ),
    op_record(
        "gammainc", 2, float_dtypes, jtu.rand_positive, True
    ),
    op_record(
        "gammaincc", 2, float_dtypes, jtu.rand_positive, True
    ),
    op_record(
        "gammasgn", 1, float_dtypes, jtu.rand_default, True
    ),
    op_record(
        "erf", 1, float_dtypes, jtu.rand_small_positive, True
    ),
    op_record(
        "erfc", 1, float_dtypes, jtu.rand_small_positive, True
    ),
    op_record(
        "erfinv", 1, float_dtypes, jtu.rand_small_positive, True
    ),
    op_record(
        "expit", 1, float_dtypes, jtu.rand_small_positive, True
    ),
    # TODO: gammaln has slightly high error.
    op_record(
        "gammaln", 1, float_dtypes, jtu.rand_positive, False
    ),
    op_record(
        "factorial", 1, float_dtypes, jtu.rand_default, True
    ),
    op_record(
        "fresnel", 1, float_dtypes,
        functools.partial(jtu.rand_default, scale=30), True
    ),
    op_record(
        "i0", 1, float_dtypes, jtu.rand_default, True
    ),
    op_record(
        # Note: values near zero can fail numeric gradient tests.
        "i0e", 1, float_dtypes,
        functools.partial(jtu.rand_not_small, offset=0.1), True
    ),
    op_record(
        "i1", 1, float_dtypes, jtu.rand_default, True
    ),
    op_record(
        "i1e", 1, float_dtypes, jtu.rand_default, True
    ),
    op_record(
        "logit", 1, float_dtypes,
        functools.partial(jtu.rand_uniform, low=0.05, high=0.95), True),
    op_record(
        "log_ndtr", 1, float_dtypes, jtu.rand_default, True
    ),
    op_record(
        "ndtri", 1, float_dtypes,
        functools.partial(jtu.rand_uniform, low=0.0, high=1.0), True,
    ),
    op_record(
        "ndtr", 1, float_dtypes, jtu.rand_default, True
    ),
    # TODO(phawkins): gradient of entr yields NaNs.
    op_record(
        "entr", 1, float_dtypes, jtu.rand_default, False
    ),
    op_record(
        "polygamma", 2, (int_dtypes, float_dtypes),
        jtu.rand_positive, True, (0,)),
    op_record(
        "xlogy", 2, float_dtypes, jtu.rand_positive, True
    ),
    op_record(
        "xlog1py", 2, float_dtypes, jtu.rand_default, True
    ),
    op_record("zeta", 2, float_dtypes, jtu.rand_positive, True),
    # TODO: float64 produces aborts on gpu, potentially related to use of jnp.piecewise
    op_record(
        "expi", 1, [np.float32],
        functools.partial(jtu.rand_not_small, offset=0.1), True),
    op_record("exp1", 1, [np.float32], jtu.rand_positive, True),
    op_record(
        "expn", 2, (int_dtypes, [np.float32]), jtu.rand_positive, True, (0,)),
    op_record("kl_div", 2, float_dtypes, jtu.rand_positive, True),
    op_record(
        "rel_entr", 2, float_dtypes, jtu.rand_positive, True,
    ),
    op_record("poch", 2, float_dtypes, jtu.rand_positive, True),
    op_record(
        "hyp1f1", 3, float_dtypes,
        functools.partial(jtu.rand_uniform, low=0.5, high=30), True
    ),
    op_record("log_softmax", 1, float_dtypes, jtu.rand_default, True),
    op_record("softmax", 1, float_dtypes, jtu.rand_default, True),
]


def _pretty_special_fun_name(case):
  shapes_str = "_".join("x".join(map(str, shape)) if shape else "s"
                        for shape in case["shapes"])
  dtypes_str = "_".join(np.dtype(d).name for d in case["dtypes"])
  name = f"_{case['op']}_{shapes_str}_{dtypes_str}"
  return dict(**case, testcase_name=name)


class LaxScipySpcialFunctionsTest(jtu.JaxTestCase):

  def _GetArgsMaker(self, rng, shapes, dtypes):
    return lambda: [rng(shape, dtype) for shape, dtype in zip(shapes, dtypes)]

  @parameterized.named_parameters(itertools.chain.from_iterable(
    map(_pretty_special_fun_name, jtu.sample_product_testcases(
      [dict(op=rec.name, rng_factory=rec.rng_factory,
            test_autodiff=rec.test_autodiff,
            nondiff_argnums=rec.nondiff_argnums)],
      shapes=itertools.combinations_with_replacement(all_shapes, rec.nargs),
      dtypes=(itertools.combinations_with_replacement(rec.dtypes, rec.nargs)
        if isinstance(rec.dtypes, list) else itertools.product(*rec.dtypes)),
    ))
    for rec in JAX_SPECIAL_FUNCTION_RECORDS
  ))
  @jax.numpy_rank_promotion('allow')  # This test explicitly exercises implicit rank promotion.
  @jax.numpy_dtype_promotion('standard')  # This test explicitly exercises dtype promotion
  def testScipySpecialFun(self, op, rng_factory, shapes, dtypes,
                          test_autodiff, nondiff_argnums):
    scipy_op = getattr(osp_special, op)
    lax_op = getattr(lsp_special, op)
    rng = rng_factory(self.rng())
    args_maker = self._GetArgsMaker(rng, shapes, dtypes)
    args = args_maker()
    self.assertAllClose(scipy_op(*args), lax_op(*args), atol=1e-3, rtol=1e-3,
                        check_dtypes=False)
    self._CompileAndCheck(lax_op, args_maker, rtol=1e-4)

    if test_autodiff:
      def partial_lax_op(*vals):
        list_args = list(vals)
        for i in nondiff_argnums:
          list_args.insert(i, args[i])
        return lax_op(*list_args)

      assert list(nondiff_argnums) == sorted(set(nondiff_argnums))
      diff_args = [x for i, x in enumerate(args) if i not in nondiff_argnums]
      jtu.check_grads(partial_lax_op, diff_args, order=1,
                      atol=.1 if jtu.test_device_matches(["tpu"]) else 1e-3,
                      rtol=.1, eps=1e-3)

  @jtu.sample_product(
      n=[0, 1, 2, 3, 10, 50]
  )
  def testScipySpecialFunBernoulli(self, n):
    dtype = jnp.zeros(0).dtype  # default float dtype.
    scipy_op = lambda: osp_special.bernoulli(n).astype(dtype)
    lax_op = functools.partial(lsp_special.bernoulli, n)
    args_maker = lambda: []
    self._CheckAgainstNumpy(scipy_op, lax_op, args_maker, atol=0, rtol=1E-5)
    self._CompileAndCheck(lax_op, args_maker, atol=0, rtol=1E-5)

  def testGammaSign(self):
    dtype = jnp.zeros(0).dtype  # default float dtype.
    typ = dtype.type
    testcases = [
      (np.arange(-10, 0).astype(dtype), np.array([np.nan] * 10, dtype=dtype)),
      (np.nextafter(np.arange(-5, 0).astype(dtype), typ(-np.inf)),
       np.array([1, -1, 1, -1, 1], dtype=dtype)),
      (np.nextafter(np.arange(-5, 0).astype(dtype), typ(np.inf)),
       np.array([-1, 1, -1, 1, -1], dtype=dtype)),
      (np.arange(0, 10).astype(dtype), np.ones((10,), dtype)),
      (np.nextafter(np.arange(0, 10).astype(dtype), typ(np.inf)),
       np.ones((10,), dtype)),
      (np.nextafter(np.arange(1, 10).astype(dtype), typ(-np.inf)),
       np.ones((9,), dtype)),
      (np.array([-np.inf, -0.0, 0.0, np.inf, np.nan]),
       np.array([np.nan, -1.0, 1.0, 1.0, np.nan]))
    ]
    for inp, out in testcases:
      self.assertArraysEqual(out, lsp_special.gammasgn(inp))
      self.assertArraysEqual(out, jnp.sign(lsp_special.gamma(inp)))
      if jtu.parse_version(scipy.__version__) >= (1, 15):
        self.assertArraysEqual(out, osp_special.gammasgn(inp))
        self.assertAllClose(osp_special.gammasgn(inp),
                            lsp_special.gammasgn(inp))

  def testNdtriExtremeValues(self):
    # Testing at the extreme values (bounds (0. and 1.) and outside the bounds).
    dtype = jnp.zeros(0).dtype  # default float dtype.
    args_maker = lambda: [np.arange(-10, 10).astype(dtype)]
    rtol = 1E-3 if jtu.test_device_matches(["tpu"]) else 1e-5
    self._CheckAgainstNumpy(osp_special.ndtri, lsp_special.ndtri, args_maker, rtol=rtol)
    self._CompileAndCheck(lsp_special.ndtri, args_maker, rtol=rtol)

  def testRelEntrExtremeValues(self):
    # Testing at the extreme values (bounds (0. and 1.) and outside the bounds).
    dtype = jnp.zeros(0).dtype  # default float dtype.
    args_maker = lambda: [np.array([-2, -2, -2, -1, -1, -1, 0, 0, 0]).astype(dtype),
                          np.array([-1, 0, 1, -1, 0, 1, -1, 0, 1]).astype(dtype)]
    rtol = 1E-3 if jtu.test_device_matches(["tpu"]) else 1e-5
    self._CheckAgainstNumpy(osp_special.rel_entr, lsp_special.rel_entr, args_maker, rtol=rtol)
    self._CompileAndCheck(lsp_special.rel_entr, args_maker, rtol=rtol)

  def testBetaParameterDeprecation(self):
    with self.assertNoWarnings():
      lsp_special.beta(1, 1)
      lsp_special.beta(1, b=1)
      lsp_special.beta(a=1, b=1)
    with self.assertRaises(TypeError):
      lsp_special.beta(x=1, y=1)


if __name__ == "__main__":
  absltest.main(testLoader=jtu.JaxTestLoader())