"""
Utility functions models code
"""
import numpy as np
import pandas as pd
import scipy.linalg
from statsmodels.tools.data import _is_using_pandas
from statsmodels.tools.validation import array_like
def asstr2(s):
if isinstance(s, str):
return s
elif isinstance(s, bytes):
return s.decode('latin1')
else:
return str(s)
def _make_dictnames(tmp_arr, offset=0):
"""
Helper function to create a dictionary mapping a column number
to the name in tmp_arr.
"""
col_map = {}
for i, col_name in enumerate(tmp_arr):
col_map[i + offset] = col_name
return col_map
def drop_missing(Y, X=None, axis=1):
"""
Returns views on the arrays Y and X where missing observations are dropped.
Y : array_like
X : array_like, optional
axis : int
Axis along which to look for missing observations. Default is 1, ie.,
observations in rows.
Returns
-------
Y : ndarray
All Y where the
X : ndarray
Notes
-----
If either Y or X is 1d, it is reshaped to be 2d.
"""
Y = np.asarray(Y)
if Y.ndim == 1:
Y = Y[:, None]
if X is not None:
X = np.array(X)
if X.ndim == 1:
X = X[:, None]
keepidx = np.logical_and(~np.isnan(Y).any(axis),
~np.isnan(X).any(axis))
return Y[keepidx], X[keepidx]
else:
keepidx = ~np.isnan(Y).any(axis)
return Y[keepidx]
# TODO: needs to better preserve dtype and be more flexible
# ie., if you still have a string variable in your array you do not
# want to cast it to float
# TODO: add name validator (ie., bad names for datasets.grunfeld)
def categorical(data, col=None, dictnames=False, drop=False):
"""
Construct a dummy matrix from categorical variables
.. deprecated:: 0.12
Use pandas.get_dummies instead.
Parameters
----------
data : array_like
An array, Series or DataFrame. This can be either a 1d vector of
the categorical variable or a 2d array with the column specifying
the categorical variable specified by the col argument.
col : {str, int, None}
If data is a DataFrame col must in a column of data. If data is a
Series, col must be either the name of the Series or None. For arrays,
`col` can be an int that is the (zero-based) column index
number. `col` can only be None for a 1d array. The default is None.
dictnames : bool, optional
If True, a dictionary mapping the column number to the categorical
name is returned. Used to have information about plain arrays.
drop : bool
Whether or not keep the categorical variable in the returned matrix.
Returns
-------
dummy_matrix : array_like
A matrix of dummy (indicator/binary) float variables for the
categorical data.
dictnames : dict[int, str], optional
Mapping between column numbers and categorical names.
Notes
-----
This returns a dummy variable for *each* distinct variable. If a
a DaataFrame is provided, the names for the new variable is the
old variable name - underscore - category name. So if the a variable
'vote' had answers as 'yes' or 'no' then the returned array would have to
new variables-- 'vote_yes' and 'vote_no'. There is currently
no name checking.
Examples
--------
>>> import numpy as np
>>> import statsmodels.api as sm
Univariate examples
>>> import string
>>> string_var = [string.ascii_lowercase[0:5],
... string.ascii_lowercase[5:10],
... string.ascii_lowercase[10:15],
... string.ascii_lowercase[15:20],
... string.ascii_lowercase[20:25]]
>>> string_var *= 5
>>> string_var = np.asarray(sorted(string_var))
>>> design = sm.tools.categorical(string_var, drop=True)
Or for a numerical categorical variable
>>> instr = np.floor(np.arange(10,60, step=2)/10)
>>> design = sm.tools.categorical(instr, drop=True)
With a structured array
>>> num = np.random.randn(25,2)
>>> struct_ar = np.zeros((25,1),
... dtype=[('var1', 'f4'),('var2', 'f4'),
... ('instrument','f4'),('str_instr','a5')])
>>> struct_ar['var1'] = num[:,0][:,None]
>>> struct_ar['var2'] = num[:,1][:,None]
>>> struct_ar['instrument'] = instr[:,None]
>>> struct_ar['str_instr'] = string_var[:,None]
>>> design = sm.tools.categorical(struct_ar, col='instrument', drop=True)
Or
>>> design2 = sm.tools.categorical(struct_ar, col='str_instr', drop=True)
"""
import warnings
warnings.warn(
"categorical is deprecated. Use pandas Categorical to represent "
"categorical data and can get_dummies to construct dummy arrays. "
"It will be removed after release 0.13.",
FutureWarning
)
# TODO: add a NameValidator function
if isinstance(col, (list, tuple)):
if len(col) == 1:
col = col[0]
else:
raise ValueError("Can only convert one column at a time")
if (not isinstance(data, (pd.DataFrame, pd.Series)) and
not isinstance(col, (str, int)) and
col is not None):
raise TypeError('col must be a str, int or None')
# Pull out a Series from a DataFrame if provided
if isinstance(data, pd.DataFrame):
if col is None:
raise TypeError('col must be a str or int when using a DataFrame')
elif col not in data:
raise ValueError('Column \'{0}\' not found in data'.format(col))
data = data[col]
# Set col to None since we not have a Series
col = None
if isinstance(data, pd.Series):
if col is not None and data.name != col:
raise ValueError('data.name does not match col '
'\'{0}\''.format(col))
data_cat = pd.Categorical(data)
dummies = pd.get_dummies(data_cat, dtype=float)
col_map = {i: cat for i, cat in enumerate(data_cat.categories) if
cat in dummies}
if not drop:
dummies.columns = list(dummies.columns)
dummies = pd.concat([dummies, data], axis=1)
if dictnames:
return dummies, col_map
return dummies
# Catch array_like for an error
elif not isinstance(data, np.ndarray):
raise NotImplementedError("array_like objects are not supported")
else:
if isinstance(col, int):
offset = data.shape[1] # need error catching here?
tmp_arr = np.unique(data[:, col])
tmp_dummy = (tmp_arr[:, np.newaxis] == data[:, col]).astype(float)
tmp_dummy = tmp_dummy.swapaxes(1, 0)
if drop is True:
offset -= 1
data = np.delete(data, col, axis=1).astype(float)
data = np.column_stack((data, tmp_dummy))
if dictnames is True:
col_map = _make_dictnames(tmp_arr, offset)
return data, col_map
return data
elif col is None and np.squeeze(data).ndim == 1:
tmp_arr = np.unique(data)
tmp_dummy = (tmp_arr[:, None] == data).astype(float)
tmp_dummy = tmp_dummy.swapaxes(1, 0)
if drop is True:
if dictnames is True:
col_map = _make_dictnames(tmp_arr)
return tmp_dummy, col_map
return tmp_dummy
else:
data = np.column_stack((data, tmp_dummy))
if dictnames is True:
col_map = _make_dictnames(tmp_arr, offset=1)
return data, col_map
return data
else:
raise IndexError("The index %s is not understood" % col)
# TODO: add an axis argument to this for sysreg
[docs]def add_constant(data, prepend=True, has_constant='skip'):
"""
Add a column of ones to an array.
Parameters
----------
data : array_like
A column-ordered design matrix.
prepend : bool
If true, the constant is in the first column. Else the constant is
appended (last column).
has_constant : str {'raise', 'add', 'skip'}
Behavior if ``data`` already has a constant. The default will return
data without adding another constant. If 'raise', will raise an
error if any column has a constant value. Using 'add' will add a
column of 1s if a constant column is present.
Returns
-------
array_like
The original values with a constant (column of ones) as the first or
last column. Returned value type depends on input type.
Notes
-----
When the input is a pandas Series or DataFrame, the added column's name
is 'const'.
"""
if _is_using_pandas(data, None):
from statsmodels.tsa.tsatools import add_trend
return add_trend(data, trend='c', prepend=prepend, has_constant=has_constant)
# Special case for NumPy
x = np.asarray(data)
ndim = x.ndim
if ndim == 1:
x = x[:, None]
elif x.ndim > 2:
raise ValueError('Only implemented for 2-dimensional arrays')
is_nonzero_const = np.ptp(x, axis=0) == 0
is_nonzero_const &= np.all(x != 0.0, axis=0)
if is_nonzero_const.any():
if has_constant == 'skip':
return x
elif has_constant == 'raise':
if ndim == 1:
raise ValueError("data is constant.")
else:
columns = np.arange(x.shape[1])
cols = ",".join([str(c) for c in columns[is_nonzero_const]])
raise ValueError(f"Column(s) {cols} are constant.")
x = [np.ones(x.shape[0]), x]
x = x if prepend else x[::-1]
return np.column_stack(x)
[docs]def isestimable(c, d):
"""
True if (Q, P) contrast `c` is estimable for (N, P) design `d`.
From an Q x P contrast matrix `C` and an N x P design matrix `D`, checks if
the contrast `C` is estimable by looking at the rank of ``vstack([C,D])``
and verifying it is the same as the rank of `D`.
Parameters
----------
c : array_like
A contrast matrix with shape (Q, P). If 1 dimensional assume shape is
(1, P).
d : array_like
The design matrix, (N, P).
Returns
-------
bool
True if the contrast `c` is estimable on design `d`.
Examples
--------
>>> d = np.array([[1, 1, 1, 0, 0, 0],
... [0, 0, 0, 1, 1, 1],
... [1, 1, 1, 1, 1, 1]]).T
>>> isestimable([1, 0, 0], d)
False
>>> isestimable([1, -1, 0], d)
True
"""
c = array_like(c, 'c', maxdim=2)
d = array_like(d, 'd', ndim=2)
c = c[None, :] if c.ndim == 1 else c
if c.shape[1] != d.shape[1]:
raise ValueError('Contrast should have %d columns' % d.shape[1])
new = np.vstack([c, d])
if np.linalg.matrix_rank(new) != np.linalg.matrix_rank(d):
return False
return True
def pinv_extended(x, rcond=1e-15):
"""
Return the pinv of an array X as well as the singular values
used in computation.
Code adapted from numpy.
"""
x = np.asarray(x)
x = x.conjugate()
u, s, vt = np.linalg.svd(x, False)
s_orig = np.copy(s)
m = u.shape[0]
n = vt.shape[1]
cutoff = rcond * np.maximum.reduce(s)
for i in range(min(n, m)):
if s[i] > cutoff:
s[i] = 1./s[i]
else:
s[i] = 0.
res = np.dot(np.transpose(vt), np.multiply(s[:, np.core.newaxis],
np.transpose(u)))
return res, s_orig
[docs]def recipr(x):
"""
Reciprocal of an array with entries less than or equal to 0 set to 0.
Parameters
----------
x : array_like
The input array.
Returns
-------
ndarray
The array with 0-filled reciprocals.
"""
x = np.asarray(x)
out = np.zeros_like(x, dtype=np.float64)
nans = np.isnan(x.flat)
pos = ~nans
pos[pos] = pos[pos] & (x.flat[pos] > 0)
out.flat[pos] = 1.0 / x.flat[pos]
out.flat[nans] = np.nan
return out
[docs]def recipr0(x):
"""
Reciprocal of an array with entries less than 0 set to 0.
Parameters
----------
x : array_like
The input array.
Returns
-------
ndarray
The array with 0-filled reciprocals.
"""
x = np.asarray(x)
out = np.zeros_like(x, dtype=np.float64)
nans = np.isnan(x.flat)
non_zero = ~nans
non_zero[non_zero] = non_zero[non_zero] & (x.flat[non_zero] != 0)
out.flat[non_zero] = 1.0 / x.flat[non_zero]
out.flat[nans] = np.nan
return out
[docs]def clean0(matrix):
"""
Erase columns of zeros: can save some time in pseudoinverse.
Parameters
----------
matrix : ndarray
The array to clean.
Returns
-------
ndarray
The cleaned array.
"""
colsum = np.add.reduce(matrix**2, 0)
val = [matrix[:, i] for i in np.flatnonzero(colsum)]
return np.array(np.transpose(val))
[docs]def fullrank(x, r=None):
"""
Return an array whose column span is the same as x.
Parameters
----------
x : ndarray
The array to adjust, 2d.
r : int, optional
The rank of x. If not provided, determined by `np.linalg.matrix_rank`.
Returns
-------
ndarray
The array adjusted to have full rank.
Notes
-----
If the rank of x is known it can be specified as r -- no check
is made to ensure that this really is the rank of x.
"""
if r is None:
r = np.linalg.matrix_rank(x)
v, d, u = np.linalg.svd(x, full_matrices=False)
order = np.argsort(d)
order = order[::-1]
value = []
for i in range(r):
value.append(v[:, order[i]])
return np.asarray(np.transpose(value)).astype(np.float64)
[docs]def unsqueeze(data, axis, oldshape):
"""
Unsqueeze a collapsed array.
Parameters
----------
data : ndarray
The data to unsqueeze.
axis : int
The axis to unsqueeze.
oldshape : tuple[int]
The original shape before the squeeze or reduce operation.
Returns
-------
ndarray
The unsqueezed array.
Examples
--------
>>> from numpy import mean
>>> from numpy.random import standard_normal
>>> x = standard_normal((3,4,5))
>>> m = mean(x, axis=1)
>>> m.shape
(3, 5)
>>> m = unsqueeze(m, 1, x.shape)
>>> m.shape
(3, 1, 5)
>>>
"""
newshape = list(oldshape)
newshape[axis] = 1
return data.reshape(newshape)
def nan_dot(A, B):
"""
Returns np.dot(left_matrix, right_matrix) with the convention that
nan * 0 = 0 and nan * x = nan if x != 0.
Parameters
----------
A, B : ndarray
"""
# Find out who should be nan due to nan * nonzero
should_be_nan_1 = np.dot(np.isnan(A), (B != 0))
should_be_nan_2 = np.dot((A != 0), np.isnan(B))
should_be_nan = should_be_nan_1 + should_be_nan_2
# Multiply after setting all nan to 0
# This is what happens if there were no nan * nonzero conflicts
C = np.dot(np.nan_to_num(A), np.nan_to_num(B))
C[should_be_nan] = np.nan
return C
def maybe_unwrap_results(results):
"""
Gets raw results back from wrapped results.
Can be used in plotting functions or other post-estimation type
routines.
"""
return getattr(results, '_results', results)
class Bunch(dict):
"""
Returns a dict-like object with keys accessible via attribute lookup.
Parameters
----------
*args
Arguments passed to dict constructor, tuples (key, value).
**kwargs
Keyword agument passed to dict constructor, key=value.
"""
def __init__(self, *args, **kwargs):
super(Bunch, self).__init__(*args, **kwargs)
self.__dict__ = self
def _ensure_2d(x, ndarray=False):
"""
Parameters
----------
x : ndarray, Series, DataFrame or None
Input to verify dimensions, and to transform as necesary
ndarray : bool
Flag indicating whether to always return a NumPy array. Setting False
will return an pandas DataFrame when the input is a Series or a
DataFrame.
Returns
-------
out : ndarray, DataFrame or None
array or DataFrame with 2 dimensiona. One dimensional arrays are
returned as nobs by 1. None is returned if x is None.
names : list of str or None
list containing variables names when the input is a pandas datatype.
Returns None if the input is an ndarray.
Notes
-----
Accepts None for simplicity
"""
if x is None:
return x
is_pandas = _is_using_pandas(x, None)
if x.ndim == 2:
if is_pandas:
return x, x.columns
else:
return x, None
elif x.ndim > 2:
raise ValueError('x mst be 1 or 2-dimensional.')
name = x.name if is_pandas else None
if ndarray:
return np.asarray(x)[:, None], name
else:
return pd.DataFrame(x), name
def matrix_rank(m, tol=None, method="qr"):
"""
Matrix rank calculation using QR or SVD
Parameters
----------
m : array_like
A 2-d array-like object to test
tol : float, optional
The tolerance to use when testing the matrix rank. If not provided
an appropriate value is selected.
method : {"ip", "qr", "svd"}
The method used. "ip" uses the inner-product of a normalized version
of m and then computes the rank using NumPy's matrix_rank.
"qr" uses a QR decomposition and is the default. "svd" defers to
NumPy's matrix_rank.
Returns
-------
int
The rank of m.
Notes
-----
When using a QR factorization, the rank is determined by the number of
elements on the leading diagonal of the R matrix that are above tol
in absolute value.
"""
m = array_like(m, "m", ndim=2)
if method == "ip":
m = m[:, np.any(m != 0, axis=0)]
m = m / np.sqrt((m ** 2).sum(0))
m = m.T @ m
return np.linalg.matrix_rank(m, tol=tol, hermitian=True)
elif method == "qr":
r, = scipy.linalg.qr(m, mode="r")
abs_diag = np.abs(np.diag(r))
if tol is None:
tol = abs_diag[0] * m.shape[1] * np.finfo(float).eps
return int((abs_diag > tol).sum())
else:
return np.linalg.matrix_rank(m, tol=tol)