# This file is part of Patsy
# Copyright (C) 2012-2013 Nathaniel Smith <njs@pobox.com>
# See file LICENSE.txt for license information.

# There are a number of unit tests in build.py, but this file contains more
# thorough tests of the overall design matrix building system. (These are
# still not exhaustive end-to-end tests, though -- for that see
# test_highlevel.py.)

from __future__ import print_function

import six
import numpy as np
from nose.tools import assert_raises
from patsy import PatsyError
from patsy.util import (atleast_2d_column_default,
                        have_pandas, have_pandas_categorical)
from patsy.desc import Term, INTERCEPT
from patsy.build import *
from patsy.categorical import C
from patsy.user_util import balanced, LookupFactor
from patsy.design_info import DesignMatrix, DesignInfo

if have_pandas:
    import pandas

def assert_full_rank(m):
    m = atleast_2d_column_default(m)
    if m.shape[1] == 0:
        return True
    u, s, v = np.linalg.svd(m)
    rank = np.sum(s > 1e-10)
    assert rank == m.shape[1]
    
def test_assert_full_rank():
    assert_full_rank(np.eye(10))
    assert_full_rank([[1, 0], [1, 0], [1, 0], [1, 1]])
    assert_raises(AssertionError,
                  assert_full_rank, [[1, 0], [2, 0]])
    assert_raises(AssertionError,
                  assert_full_rank, [[1, 2], [2, 4]])
    assert_raises(AssertionError,
                  assert_full_rank, [[1, 2, 3], [1, 10, 100]])
    # col1 + col2 = col3
    assert_raises(AssertionError,
                  assert_full_rank, [[1, 2, 3], [1, 5, 6], [1, 6, 7]])
    
def make_termlist(*entries):
    terms = []
    for entry in entries:
        terms.append(Term([LookupFactor(name) for name in entry]))
    return terms

def check_design_matrix(mm, expected_rank, termlist, column_names=None):
    assert_full_rank(mm)
    assert set(mm.design_info.terms) == set(termlist)
    if column_names is not None:
        assert mm.design_info.column_names == column_names
    assert mm.ndim == 2
    assert mm.shape[1] == expected_rank

def make_matrix(data, expected_rank, entries, column_names=None):
    termlist = make_termlist(*entries)
    def iter_maker():
        yield data
    design_infos = design_matrix_builders([termlist], iter_maker, eval_env=0)
    matrices = build_design_matrices(design_infos, data)
    matrix = matrices[0]
    assert (design_infos[0].term_slices
            == matrix.design_info.term_slices)
    assert (design_infos[0].column_names
            == matrix.design_info.column_names)
    assert matrix.design_info is design_infos[0]
    check_design_matrix(matrix, expected_rank, termlist,
                        column_names=column_names)
    return matrix

def test_simple():
    data = balanced(a=2, b=2)
    x1 = data["x1"] = np.linspace(0, 1, len(data["a"]))
    x2 = data["x2"] = data["x1"] ** 2

    m = make_matrix(data, 2, [["a"]], column_names=["a[a1]", "a[a2]"])
    assert np.allclose(m, [[1, 0], [1, 0], [0, 1], [0, 1]])

    m = make_matrix(data, 2, [[], ["a"]], column_names=["Intercept", "a[T.a2]"])
    assert np.allclose(m, [[1, 0], [1, 0], [1, 1], [1, 1]])

    m = make_matrix(data, 4, [["a", "b"]],
                    column_names=["a[a1]:b[b1]", "a[a2]:b[b1]",
                                  "a[a1]:b[b2]", "a[a2]:b[b2]"])
    assert np.allclose(m, [[1, 0, 0, 0],
                           [0, 0, 1, 0],
                           [0, 1, 0, 0],
                           [0, 0, 0, 1]])

    m = make_matrix(data, 4, [[], ["a"], ["b"], ["a", "b"]],
                    column_names=["Intercept", "a[T.a2]",
                                  "b[T.b2]", "a[T.a2]:b[T.b2]"])
    assert np.allclose(m, [[1, 0, 0, 0],
                           [1, 0, 1, 0],
                           [1, 1, 0, 0],
                           [1, 1, 1, 1]])

    m = make_matrix(data, 4, [[], ["b"], ["a"], ["b", "a"]],
                    column_names=["Intercept", "b[T.b2]",
                                  "a[T.a2]", "b[T.b2]:a[T.a2]"])
    assert np.allclose(m, [[1, 0, 0, 0],
                           [1, 1, 0, 0],
                           [1, 0, 1, 0],
                           [1, 1, 1, 1]])

    m = make_matrix(data, 4, [["a"], ["x1"], ["a", "x1"]],
                    column_names=["a[a1]", "a[a2]", "x1", "a[T.a2]:x1"])
    assert np.allclose(m, [[1, 0, x1[0], 0],
                           [1, 0, x1[1], 0],
                           [0, 1, x1[2], x1[2]],
                           [0, 1, x1[3], x1[3]]])
    
    m = make_matrix(data, 3, [["x1"], ["x2"], ["x2", "x1"]],
                    column_names=["x1", "x2", "x2:x1"])
    assert np.allclose(m, np.column_stack((x1, x2, x1 * x2)))
    
def test_R_bugs():
    data = balanced(a=2, b=2, c=2)
    data["x"] = np.linspace(0, 1, len(data["a"]))
    # For "1 + a:b", R produces a design matrix with too many columns (5
    # instead of 4), because it can't tell that there is a redundancy between
    # the two terms.
    make_matrix(data, 4, [[], ["a", "b"]])
    # For "0 + a:x + a:b", R produces a design matrix with too few columns (4
    # instead of 6), because it thinks that there is a redundancy which
    # doesn't exist.
    make_matrix(data, 6, [["a", "x"], ["a", "b"]])
    # This can be compared with "0 + a:c + a:b", where the redundancy does
    # exist. Confusingly, adding another categorical factor increases the
    # baseline dimensionality to 8, and then the redundancy reduces it to 6
    # again, so the result is the same as before but for different reasons. (R
    # does get this one right, but we might as well test it.)
    make_matrix(data, 6, [["a", "c"], ["a", "b"]])

def test_redundancy_thoroughly():
    # To make sure there aren't any lurking bugs analogous to the ones that R
    # has (see above), we check that we get the correct matrix rank for every
    # possible combination of 2 categorical and 2 numerical factors.
    data = balanced(a=2, b=2, repeat=5)
    data["x1"] = np.linspace(0, 1, len(data["a"]))
    data["x2"] = data["x1"] ** 2

    def all_subsets(l):
        if not l:
            yield tuple()
        else:
            obj = l[0]
            for subset in all_subsets(l[1:]):
                yield tuple(sorted(subset))
                yield tuple(sorted((obj,) + subset))

    all_terms = list(all_subsets(("a", "b", "x1", "x2")))
    all_termlist_templates = list(all_subsets(all_terms))
    print(len(all_termlist_templates))
    # eliminate some of the symmetric versions to speed things up
    redundant = [[("b",), ("a",)],
                 [("x2",), ("x1",)],
                 [("b", "x2"), ("a", "x1")],
                 [("a", "b", "x2"), ("a", "b", "x1")],
                 [("b", "x1", "x2"), ("a", "x1", "x2")]]
    count = 0
    import time
    start = time.time()
    for termlist_template in all_termlist_templates:
        termlist_set = set(termlist_template)
        for dispreferred, preferred in redundant:
            if dispreferred in termlist_set and preferred not in termlist_set:
                break
        else:
            expanded_terms = set()
            for term_template in termlist_template:
                numeric = tuple([t for t in term_template if t.startswith("x")])
                rest = [t for t in term_template if not t.startswith("x")]
                for subset_rest in all_subsets(rest):
                    expanded_terms.add(frozenset(subset_rest + numeric))
            # Because our categorical variables have 2 levels, each expanded
            # term corresponds to 1 unique dimension of variation
            expected_rank = len(expanded_terms)
            if termlist_template in [(), ((),)]:
                # No data dependence, should fail
                assert_raises(PatsyError,
                              make_matrix,
                              data, expected_rank, termlist_template)
            else:
                make_matrix(data, expected_rank, termlist_template)
            count += 1
            if count % 100 == 0:
                print("Completed:", count)
    print("Took %0.2f seconds" % (time.time() - start,))

test_redundancy_thoroughly.slow = 1

def test_data_types():
    basic_dict = {"a": ["a1", "a2", "a1", "a2"],
                  "x": [1, 2, 3, 4]}
    # On Python 2, this is identical to basic_dict:
    basic_dict_bytes = dict(basic_dict)
    basic_dict_bytes["a"] = [s.encode("ascii") for s in basic_dict_bytes["a"]]
    # On Python 3, this is identical to basic_dict:
    basic_dict_unicode = {"a": ["a1", "a2", "a1", "a2"],
                          "x": [1, 2, 3, 4]}
    basic_dict_unicode = dict(basic_dict)
    basic_dict_unicode["a"] = [six.text_type(s) for s in basic_dict_unicode["a"]]

    structured_array_bytes = np.array(list(zip(basic_dict["a"],
                                               basic_dict["x"])),
                                      dtype=[("a", "S2"), ("x", int)])
    structured_array_unicode = np.array(list(zip(basic_dict["a"],
                                                 basic_dict["x"])),
                                        dtype=[("a", "U2"), ("x", int)])
    recarray_bytes = structured_array_bytes.view(np.recarray)
    recarray_unicode = structured_array_unicode.view(np.recarray)
    datas = [basic_dict, structured_array_bytes, structured_array_unicode,
             recarray_bytes, recarray_unicode]
    if have_pandas:
        df_bytes = pandas.DataFrame(basic_dict_bytes)
        datas.append(df_bytes)
        df_unicode = pandas.DataFrame(basic_dict_unicode)
        datas.append(df_unicode)
    for data in datas:
        m = make_matrix(data, 4, [["a"], ["a", "x"]],
                        column_names=["a[a1]", "a[a2]", "a[a1]:x", "a[a2]:x"])
        assert np.allclose(m, [[1, 0, 1, 0],
                               [0, 1, 0, 2],
                               [1, 0, 3, 0],
                               [0, 1, 0, 4]])

def test_build_design_matrices_dtype():
    data = {"x": [1, 2, 3]}
    def iter_maker():
        yield data
    builder = design_matrix_builders([make_termlist("x")], iter_maker, 0)[0]

    mat = build_design_matrices([builder], data)[0]
    assert mat.dtype == np.dtype(np.float64)

    mat = build_design_matrices([builder], data, dtype=np.float32)[0]
    assert mat.dtype == np.dtype(np.float32)

    if hasattr(np, "float128"):
        mat = build_design_matrices([builder], data, dtype=np.float128)[0]
        assert mat.dtype == np.dtype(np.float128)

def test_return_type():
    data = {"x": [1, 2, 3]}
    def iter_maker():
        yield data
    builder = design_matrix_builders([make_termlist("x")], iter_maker, 0)[0]
    
    # Check explicitly passing return_type="matrix" works
    mat = build_design_matrices([builder], data, return_type="matrix")[0]
    assert isinstance(mat, DesignMatrix)

    # Check that nonsense is detected
    assert_raises(PatsyError,
                  build_design_matrices, [builder], data,
                  return_type="asdfsadf")

def test_NA_action():
    initial_data = {"x": [1, 2, 3], "c": ["c1", "c2", "c1"]}
    def iter_maker():
        yield initial_data
    builder = design_matrix_builders([make_termlist("x", "c")], iter_maker, 0)[0]

    # By default drops rows containing either NaN or None
    mat = build_design_matrices([builder],
                                {"x": [10.0, np.nan, 20.0],
                                 "c": np.asarray(["c1", "c2", None],
                                                 dtype=object)})[0]
    assert mat.shape == (1, 3)
    assert np.array_equal(mat, [[1.0, 0.0, 10.0]])

    # NA_action="a string" also accepted:
    mat = build_design_matrices([builder],
                                {"x": [10.0, np.nan, 20.0],
                                 "c": np.asarray(["c1", "c2", None],
                                                 dtype=object)},
                                NA_action="drop")[0]
    assert mat.shape == (1, 3)
    assert np.array_equal(mat, [[1.0, 0.0, 10.0]])

    # And objects
    from patsy.missing import NAAction
    # allows NaN's to pass through
    NA_action = NAAction(NA_types=[])
    mat = build_design_matrices([builder],
                                {"x": [10.0, np.nan],
                                 "c": np.asarray(["c1", "c2"],
                                                 dtype=object)},
                                NA_action=NA_action)[0]
    assert mat.shape == (2, 3)
    # According to this (and only this) function, NaN == NaN.
    np.testing.assert_array_equal(mat, [[1.0, 0.0, 10.0], [0.0, 1.0, np.nan]])
    
    # NA_action="raise"
    assert_raises(PatsyError,
                  build_design_matrices,
                  [builder],
                  {"x": [10.0, np.nan, 20.0],
                   "c": np.asarray(["c1", "c2", None],
                                   dtype=object)},
                  NA_action="raise")

def test_NA_drop_preserves_levels():
    # Even if all instances of some level are dropped, we still include it in
    # the output matrix (as an all-zeros column)
    data = {"x": [1.0, np.nan, 3.0], "c": ["c1", "c2", "c3"]}
    def iter_maker():
        yield data
    design_info = design_matrix_builders([make_termlist("x", "c")], iter_maker, 0)[0]

    assert design_info.column_names == ["c[c1]", "c[c2]", "c[c3]", "x"]

    mat, = build_design_matrices([design_info], data)

    assert mat.shape == (2, 4)
    assert np.array_equal(mat, [[1.0, 0.0, 0.0, 1.0],
                                [0.0, 0.0, 1.0, 3.0]])

def test_return_type_pandas():
    if not have_pandas:
        return

    data = pandas.DataFrame({"x": [1, 2, 3],
                             "y": [4, 5, 6],
                             "a": ["a1", "a2", "a1"]},
                            index=[10, 20, 30])
    def iter_maker():
        yield data
    int_builder, = design_matrix_builders([make_termlist([])], iter_maker, 0)
    (y_builder, x_builder) = design_matrix_builders([make_termlist("y"),
                                                     make_termlist("x")],
                                                    iter_maker,
                                                    eval_env=0)
    (x_a_builder,) = design_matrix_builders([make_termlist("x", "a")],
                                            iter_maker,
                                            eval_env=0)
    (x_y_builder,) = design_matrix_builders([make_termlist("x", "y")],
                                            iter_maker,
                                            eval_env=0)
    # Index compatibility is always checked for pandas input, regardless of
    # whether we're producing pandas output
    assert_raises(PatsyError,
                  build_design_matrices,
                  [x_a_builder], {"x": data["x"], "a": data["a"][::-1]})
    assert_raises(PatsyError,
                  build_design_matrices,
                  [y_builder, x_builder],
                  {"x": data["x"], "y": data["y"][::-1]})
    # And we also check consistency between data.index and value indexes
    # Creating a mismatch between these is a bit tricky. We want a data object
    # such that isinstance(data, DataFrame), but data["x"].index !=
    # data.index.
    class CheatingDataFrame(pandas.DataFrame):
        def __getitem__(self, key):
            if key == "x":
                return pandas.DataFrame.__getitem__(self, key)[::-1]
            else:
                return pandas.DataFrame.__getitem__(self, key)
    assert_raises(PatsyError,
                  build_design_matrices,
                  [x_builder],
                  CheatingDataFrame(data))

    # A mix of pandas input and unindexed input is fine
    (mat,) = build_design_matrices([x_y_builder],
                                   {"x": data["x"], "y": [40, 50, 60]})
    assert np.allclose(mat, [[1, 40], [2, 50], [3, 60]])

    # with return_type="dataframe", we get out DataFrames with nice indices
    # and nice column names and design_info
    y_df, x_df = build_design_matrices([y_builder, x_builder], data,
                                       return_type="dataframe")
    assert isinstance(y_df, pandas.DataFrame)
    assert isinstance(x_df, pandas.DataFrame)
    assert np.array_equal(y_df, [[4], [5], [6]])
    assert np.array_equal(x_df, [[1], [2], [3]])
    assert np.array_equal(y_df.index, [10, 20, 30])
    assert np.array_equal(x_df.index, [10, 20, 30])
    assert np.array_equal(y_df.columns, ["y"])
    assert np.array_equal(x_df.columns, ["x"])
    assert y_df.design_info.column_names == ["y"]
    assert x_df.design_info.column_names == ["x"]
    assert y_df.design_info.term_names == ["y"]
    assert x_df.design_info.term_names == ["x"]
    # Same with mix of pandas and unindexed info, even if in different
    # matrices
    y_df, x_df = build_design_matrices([y_builder, x_builder],
                                       {"y": [7, 8, 9], "x": data["x"]},
                                       return_type="dataframe")
    assert isinstance(y_df, pandas.DataFrame)
    assert isinstance(x_df, pandas.DataFrame)
    assert np.array_equal(y_df, [[7], [8], [9]])
    assert np.array_equal(x_df, [[1], [2], [3]])
    assert np.array_equal(y_df.index, [10, 20, 30])
    assert np.array_equal(x_df.index, [10, 20, 30])
    assert np.array_equal(y_df.columns, ["y"])
    assert np.array_equal(x_df.columns, ["x"])
    assert y_df.design_info.column_names == ["y"]
    assert x_df.design_info.column_names == ["x"]
    assert y_df.design_info.term_names == ["y"]
    assert x_df.design_info.term_names == ["x"]
    # Check categorical works for carrying index too
    (x_a_df,) = build_design_matrices([x_a_builder],
                                      {"x": [-1, -2, -3], "a": data["a"]},
                                      return_type="dataframe")
    assert isinstance(x_a_df, pandas.DataFrame)
    assert np.array_equal(x_a_df, [[1, 0, -1], [0, 1, -2], [1, 0, -3]])
    assert np.array_equal(x_a_df.index, [10, 20, 30])
    # And if we have no indexed input, then we let pandas make up an index as
    # per its usual rules:
    (x_y_df,) = build_design_matrices([x_y_builder],
                                      {"y": [7, 8, 9], "x": [10, 11, 12]},
                                      return_type="dataframe")
    assert isinstance(x_y_df, pandas.DataFrame)
    assert np.array_equal(x_y_df, [[10, 7], [11, 8], [12, 9]])
    assert np.array_equal(x_y_df.index, [0, 1, 2])

    # If 'data' is a DataFrame, then that suffices, even if no factors are
    # available.
    (int_df,) = build_design_matrices([int_builder], data,
                                      return_type="dataframe")
    assert isinstance(int_df, pandas.DataFrame)
    assert np.array_equal(int_df, [[1], [1], [1]])
    assert int_df.index.equals(pandas.Index([10, 20, 30]))

    import patsy.build
    had_pandas = patsy.build.have_pandas
    try:
        patsy.build.have_pandas = False
        # return_type="dataframe" gives a nice error if pandas is not available
        assert_raises(PatsyError,
                      build_design_matrices,
                      [x_builder], {"x": [1, 2, 3]}, return_type="dataframe")
    finally:
        patsy.build.have_pandas = had_pandas

    x_df, = build_design_matrices([x_a_builder],
                                  {"x": [1.0, np.nan, 3.0],
                                   "a": np.asarray([None, "a2", "a1"],
                                                   dtype=object)},
                                  NA_action="drop",
                                  return_type="dataframe")
    assert x_df.index.equals(pandas.Index([2]))

def test_data_mismatch():
    test_cases_twoway = [
        # Data type mismatch
        ([1, 2, 3], [True, False, True]),
        (C(["a", "b", "c"], levels=["c", "b", "a"]),
         C(["a", "b", "c"], levels=["a", "b", "c"])),
        # column number mismatches
        ([[1], [2], [3]], [[1, 1], [2, 2], [3, 3]]),
        ([[1, 1, 1], [2, 2, 2], [3, 3, 3]], [[1, 1], [2, 2], [3, 3]]),
        ]
    test_cases_oneway = [
        ([1, 2, 3], ["a", "b", "c"]),
        ([1, 2, 3], C(["a", "b", "c"])),
        ([True, False, True], C(["a", "b", "c"])),
        ([True, False, True], ["a", "b", "c"]),
        ]
    setup_predict_only = [
        # This is not an error if both are fed in during make_builders, but it
        # is an error to pass one to make_builders and the other to
        # make_matrices.
        (["a", "b", "c"], ["a", "b", "d"]),
        ]
    termlist = make_termlist(["x"])
    def t_incremental(data1, data2):
        def iter_maker():
            yield {"x": data1}
            yield {"x": data2}
        try:
            builders = design_matrix_builders([termlist], iter_maker, 0)
            build_design_matrices(builders, {"x": data1})
            build_design_matrices(builders, {"x": data2})
        except PatsyError:
            pass
        else:
            raise AssertionError
    def t_setup_predict(data1, data2):
        def iter_maker():
            yield {"x": data1}
        builders = design_matrix_builders([termlist], iter_maker, 0)
        assert_raises(PatsyError,
                      build_design_matrices, builders, {"x": data2})
    for (a, b) in test_cases_twoway:
        t_incremental(a, b)
        t_incremental(b, a)
        t_setup_predict(a, b)
        t_setup_predict(b, a)
    for (a, b) in test_cases_oneway:
        t_incremental(a, b)
        t_setup_predict(a, b)
    for (a, b) in setup_predict_only:
        t_setup_predict(a, b)
        t_setup_predict(b, a)

    assert_raises(PatsyError,
                  make_matrix, {"x": [1, 2, 3], "y": [1, 2, 3, 4]},
                  2, [["x"], ["y"]])

def test_data_independent_builder():
    data = {"x": [1, 2, 3]}
    def iter_maker():
        yield data

    # Trying to build a matrix that doesn't depend on the data at all is an
    # error, if:
    # - the index argument is not given
    # - the data is not a DataFrame
    # - there are no other matrices
    null_builder = design_matrix_builders([make_termlist()], iter_maker, 0)[0]
    assert_raises(PatsyError, build_design_matrices, [null_builder], data)

    intercept_builder = design_matrix_builders([make_termlist([])],
                                               iter_maker,
                                               eval_env=0)[0]
    assert_raises(PatsyError, build_design_matrices, [intercept_builder], data)

    assert_raises(PatsyError,
                  build_design_matrices,
                  [null_builder, intercept_builder], data)

    # If data is a DataFrame, it sets the number of rows.
    if have_pandas:
        int_m, null_m = build_design_matrices([intercept_builder,
                                               null_builder],
                                              pandas.DataFrame(data))
        assert np.allclose(int_m, [[1], [1], [1]])
        assert null_m.shape == (3, 0)

    # If there are other matrices that do depend on the data, we make the
    # data-independent matrices have the same number of rows.
    x_termlist = make_termlist(["x"])

    builders = design_matrix_builders([x_termlist, make_termlist()],
                                      iter_maker,
                                      eval_env=0)
    x_m, null_m = build_design_matrices(builders, data)
    assert np.allclose(x_m, [[1], [2], [3]])
    assert null_m.shape == (3, 0)

    builders = design_matrix_builders([x_termlist, make_termlist([])],
                                      iter_maker,
                                      eval_env=0)
    x_m, null_m = build_design_matrices(builders, data)
    x_m, intercept_m = build_design_matrices(builders, data)
    assert np.allclose(x_m, [[1], [2], [3]])
    assert np.allclose(intercept_m, [[1], [1], [1]])

def test_same_factor_in_two_matrices():
    data = {"x": [1, 2, 3], "a": ["a1", "a2", "a1"]}
    def iter_maker():
        yield data
    t1 = make_termlist(["x"])
    t2 = make_termlist(["x", "a"])
    builders = design_matrix_builders([t1, t2], iter_maker, eval_env=0)
    m1, m2 = build_design_matrices(builders, data)
    check_design_matrix(m1, 1, t1, column_names=["x"])
    assert np.allclose(m1, [[1], [2], [3]])
    check_design_matrix(m2, 2, t2, column_names=["x:a[a1]", "x:a[a2]"])
    assert np.allclose(m2, [[1, 0], [0, 2], [3, 0]])

def test_eval_env_type_builder():
    data = {"x": [1, 2, 3]}
    def iter_maker():
        yield data
    assert_raises(TypeError, design_matrix_builders, [make_termlist("x")], iter_maker, "foo")

def test_categorical():
    data_strings = {"a": ["a1", "a2", "a1"]}
    data_categ = {"a": C(["a2", "a1", "a2"])}
    datas = [data_strings, data_categ]
    if have_pandas_categorical:
        data_pandas = {"a": pandas.Categorical(["a1", "a2", "a2"])}
        datas.append(data_pandas)
    def t(data1, data2):
        def iter_maker():
            yield data1
        builders = design_matrix_builders([make_termlist(["a"])],
                                          iter_maker,
                                          eval_env=0)
        build_design_matrices(builders, data2)
    for data1 in datas:
        for data2 in datas:
            t(data1, data2)

def test_contrast():
    from patsy.contrasts import ContrastMatrix, Sum
    values = ["a1", "a3", "a1", "a2"]
    
    # No intercept in model, full-rank coding of 'a'
    m = make_matrix({"a": C(values)}, 3, [["a"]],
                    column_names=["a[a1]", "a[a2]", "a[a3]"])

    assert np.allclose(m, [[1, 0, 0],
                           [0, 0, 1],
                           [1, 0, 0],
                           [0, 1, 0]])
    
    for s in (Sum, Sum()):
        m = make_matrix({"a": C(values, s)}, 3, [["a"]],
                        column_names=["a[mean]", "a[S.a1]", "a[S.a2]"])
        # Output from R
        assert np.allclose(m, [[1, 1, 0],
                               [1,-1, -1],
                               [1, 1, 0],
                               [1, 0, 1]])
    
    m = make_matrix({"a": C(values, Sum(omit=0))}, 3, [["a"]],
                    column_names=["a[mean]", "a[S.a2]", "a[S.a3]"])
    # Output from R
    assert np.allclose(m, [[1, -1, -1],
                           [1,  0,  1],
                           [1, -1, -1],
                           [1,  1,  0]])

    # Intercept in model, non-full-rank coding of 'a'
    m = make_matrix({"a": C(values)}, 3, [[], ["a"]],
                    column_names=["Intercept", "a[T.a2]", "a[T.a3]"])

    assert np.allclose(m, [[1, 0, 0],
                           [1, 0, 1],
                           [1, 0, 0],
                           [1, 1, 0]])
    
    for s in (Sum, Sum()):
        m = make_matrix({"a": C(values, s)}, 3, [[], ["a"]],
                        column_names=["Intercept", "a[S.a1]", "a[S.a2]"])
        # Output from R
        assert np.allclose(m, [[1, 1, 0],
                               [1,-1, -1],
                               [1, 1, 0],
                               [1, 0, 1]])
    
    m = make_matrix({"a": C(values, Sum(omit=0))}, 3, [[], ["a"]],
                    column_names=["Intercept", "a[S.a2]", "a[S.a3]"])
    # Output from R
    assert np.allclose(m, [[1, -1, -1],
                           [1,  0,  1],
                           [1, -1, -1],
                           [1,  1,  0]])

    # Weird ad hoc less-than-full-rank coding of 'a'
    m = make_matrix({"a": C(values, [[7, 12],
                                     [2, 13],
                                     [8, -1]])},
                    2, [["a"]],
                    column_names=["a[custom0]", "a[custom1]"])
    assert np.allclose(m, [[7, 12],
                           [8, -1],
                           [7, 12],
                           [2, 13]])

    m = make_matrix({"a": C(values, ContrastMatrix([[7, 12],
                                                    [2, 13],
                                                    [8, -1]],
                                                   ["[foo]", "[bar]"]))},
                    2, [["a"]],
                    column_names=["a[foo]", "a[bar]"])
    assert np.allclose(m, [[7, 12],
                           [8, -1],
                           [7, 12],
                           [2, 13]])

def test_DesignInfo_subset():
    # For each combination of:
    #   formula, term names, term objects, mixed term name and term objects
    # check that results match subset of full build
    # and that removed variables don't hurt
    all_data = {"x": [1, 2],
                "y": [[3.1, 3.2],
                      [4.1, 4.2]],
                "z": [5, 6]}
    all_terms = make_termlist("x", "y", "z")
    def iter_maker():
        yield all_data
    all_builder = design_matrix_builders([all_terms], iter_maker, 0)[0]
    full_matrix = build_design_matrices([all_builder], all_data)[0]

    def t(which_terms, variables, columns):
        sub_design_info = all_builder.subset(which_terms)
        sub_data = {}
        for variable in variables:
            sub_data[variable] = all_data[variable]
        sub_matrix = build_design_matrices([sub_design_info], sub_data)[0]
        sub_full_matrix = full_matrix[:, columns]
        if not isinstance(which_terms, six.string_types):
            assert len(which_terms) == len(sub_design_info.terms)
        assert np.array_equal(sub_matrix, sub_full_matrix)

    t("~ 0 + x + y + z", ["x", "y", "z"], slice(None))
    t(["x", "y", "z"], ["x", "y", "z"], slice(None))
    # Compatibility: six.PY2 wasn't added until 1.4.0, but six.PY3 exists in
    # all versions.
    if not six.PY3:
        t([unicode("x"), unicode("y"), unicode("z")],
          ["x", "y", "z"], slice(None))
    t(all_terms, ["x", "y", "z"], slice(None))
    t([all_terms[0], "y", all_terms[2]], ["x", "y", "z"], slice(None))

    t("~ 0 + x + z", ["x", "z"], [0, 3])
    t(["x", "z"], ["x", "z"], [0, 3])
    # Compatibility: six.PY2 wasn't added until 1.4.0, but six.PY3 exists in
    # all versions.
    if not six.PY3:
        t([unicode("x"), unicode("z")], ["x", "z"], [0, 3])
    t([all_terms[0], all_terms[2]], ["x", "z"], [0, 3])
    t([all_terms[0], "z"], ["x", "z"], [0, 3])

    t("~ 0 + z + x", ["x", "z"], [3, 0])
    t(["z", "x"], ["x", "z"], [3, 0])
    t([six.text_type("z"), six.text_type("x")], ["x", "z"], [3, 0])
    t([all_terms[2], all_terms[0]], ["x", "z"], [3, 0])
    t([all_terms[2], "x"], ["x", "z"], [3, 0])

    t("~ 0 + y", ["y"], [1, 2])
    t(["y"], ["y"], [1, 2])
    t([six.text_type("y")], ["y"], [1, 2])
    t([all_terms[1]], ["y"], [1, 2])

    # Formula can't have a LHS
    assert_raises(PatsyError, all_builder.subset, "a ~ a")
    # Term must exist
    assert_raises(KeyError, all_builder.subset, "~ asdf")
    assert_raises(KeyError, all_builder.subset, ["asdf"])
    assert_raises(KeyError,
                  all_builder.subset, [Term(["asdf"])])

    # Also check for a minimal DesignInfo (column names only)
    min_di = DesignInfo(["a", "b", "c"])
    min_di_subset = min_di.subset(["c", "a"])
    assert min_di_subset.column_names == ["c", "a"]
    assert min_di_subset.terms is None
