def test_to_ndarray(self):
"""
Tests :func:`colour.algebra.common.to_ndarray` definition.
"""
self.assertEqual(to_ndarray(1), np.array([1]))
self.assertEqual(to_ndarray([1]), np.array([1]))
self.assertEqual(to_ndarray((1, )), np.array((1, )))
self.assertEqual(to_ndarray(np.array([1])), np.array([1]))
def test_to_ndarray(self):
"""
Tests :func:`colour.algebra.common.to_ndarray` definition.
"""
self.assertEqual(to_ndarray(1), np.array([1]))
self.assertEqual(to_ndarray([1]), np.array([1]))
self.assertEqual(to_ndarray((1,)), np.array((1,)))
self.assertEqual(to_ndarray(np.array([1])), np.array([1]))
def x(self, value):
"""
Setter for **self.__x** private attribute.
Parameters
----------
value : array_like
Attribute value.
"""
if value is not None:
value = to_ndarray(value)
assert value.ndim == 1, (
'"x" independent variable must have exactly one dimension!')
assert is_uniform(value), (
'"x" independent variable is not uniform!')
if not issubclass(value.dtype.type, np.inexact):
value = value.astype(np.float_)
value_steps = steps(value)[0]
xp1 = value[0] - value_steps * 2
xp2 = value[0] - value_steps
xp3 = value[-1] + value_steps
xp4 = value[-1] + value_steps * 2
self.__xp = np.concatenate(((xp1, xp2), value, (xp3, xp4)))
self.__x = value
def x(self, value):
"""
Setter for **self.__x** private attribute.
Parameters
----------
value : array_like
Attribute value.
"""
if value is not None:
value = to_ndarray(value)
assert value.ndim == 1, (
'"x" independent variable must have exactly one dimension!')
assert is_uniform(value), (
'"x" independent variable is not uniform!')
if not issubclass(value.dtype.type, np.inexact):
value = value.astype(np.float_)
value_steps = steps(value)[0]
xp1 = value[0] - value_steps * 2
xp2 = value[0] - value_steps
xp3 = value[-1] + value_steps
xp4 = value[-1] + value_steps * 2
self.__xp = np.concatenate(((xp1, xp2), value, (xp3, xp4)))
self.__x = value
def to_RGB(self, value):
"""
Setter for **self.__to_RGB** private attribute.
Parameters
----------
value : array_like
Attribute value.
"""
if value is not None:
value = to_ndarray(value)
self.__to_RGB = value
def primaries(self, value):
"""
Setter for **self.__primaries** private attribute.
Parameters
----------
value : array_like, (3, 2)
Attribute value.
"""
if value is not None:
value = to_ndarray(value)
self.__primaries = value
def to_RGB(self, value):
"""
Setter for **self.__to_RGB** private attribute.
Parameters
----------
value : array_like
Attribute value.
"""
if value is not None:
value = to_ndarray(value)
self.__to_RGB = value
def primaries(self, value):
"""
Setter for **self.__primaries** private attribute.
Parameters
----------
value : array_like, (3, 2)
Attribute value.
"""
if value is not None:
value = to_ndarray(value)
self.__primaries = value
def x(self, value):
"""
Setter for **self.__x** private attribute.
Parameters
----------
value : array_like
Attribute value.
"""
if value is not None:
value = to_ndarray(value)
assert value.ndim == 1, (
'"x" independent variable must have exactly one dimension!')
if not issubclass(value.dtype.type, np.inexact):
value = value.astype(np.float_)
self.__x = value
def x(self, value):
"""
Setter for **self.__x** private attribute.
Parameters
----------
value : array_like
Attribute value.
"""
if value is not None:
value = to_ndarray(value)
assert value.ndim == 1, (
'"x" independent variable must have exactly one dimension!')
if not issubclass(value.dtype.type, np.inexact):
value = value.astype(np.float_)
self.__x = value
def __call__(self, x):
"""
Evaluates the Extrapolator1d at given point(s).
Parameters
----------
x : numeric or array_like
Point(s) to evaluate the Extrapolator1d at.
Returns
-------
float or ndarray
Extrapolated points value(s).
"""
xe = self.__evaluate(to_ndarray(x))
if is_numeric(x):
return float(xe)
else:
return xe
def __call__(self, x):
"""
Evaluates the interpolating polynomial at given point(s).
Parameters
----------
x : numeric or array_like
Point(s) to evaluate the interpolant at.
Returns
-------
float or ndarray
Interpolated value(s).
"""
xi = self.__evaluate(to_ndarray(x))
if is_numeric(x):
return float(xi)
else:
return xi
def __call__(self, x):
"""
Evaluates the Extrapolator1d at given point(s).
Parameters
----------
x : numeric or array_like
Point(s) to evaluate the Extrapolator1d at.
Returns
-------
float or ndarray
Extrapolated points value(s).
"""
xe = self.__evaluate(to_ndarray(x))
if is_numeric(x):
return float(xe)
else:
return xe
def __call__(self, x):
"""
Evaluates the interpolating polynomial at given point(s).
Parameters
----------
x : numeric or array_like
Point(s) to evaluate the interpolant at.
Returns
-------
float or ndarray
Interpolated value(s).
"""
xi = self.__evaluate(to_ndarray(x))
if is_numeric(x):
return float(xi)
else:
return xi
def y(self, value):
"""
Setter for **self.__y** private attribute.
Parameters
----------
value : array_like
Attribute value.
"""
if value is not None:
value = to_ndarray(value)
assert value.ndim == 1, (
'"y" dependent variable must have exactly one dimension!')
assert len(value) >= 6, (
'"y" dependent variable values count must be in domain [6:]!')
if not issubclass(value.dtype.type, np.inexact):
value = value.astype(np.float_)
yp1 = np.ravel((np.dot(self.SPRAGUE_C_COEFFICIENTS[0],
np.array(value[0:6]).reshape(
(6, 1)))) / 209)[0]
yp2 = np.ravel((np.dot(self.SPRAGUE_C_COEFFICIENTS[1],
np.array(value[0:6]).reshape(
(6, 1)))) / 209)[0]
yp3 = np.ravel((np.dot(self.SPRAGUE_C_COEFFICIENTS[2],
np.array(value[-6:]).reshape(
(6, 1)))) / 209)[0]
yp4 = np.ravel((np.dot(self.SPRAGUE_C_COEFFICIENTS[3],
np.array(value[-6:]).reshape(
(6, 1)))) / 209)[0]
self.__yp = np.concatenate(((yp1, yp2), value, (yp3, yp4)))
self.__y = value
def y(self, value):
"""
Setter for **self.__y** private attribute.
Parameters
----------
value : array_like
Attribute value.
"""
if value is not None:
value = to_ndarray(value)
assert value.ndim == 1, (
'"y" dependent variable must have exactly one dimension!')
assert len(value) >= 6, (
'"y" dependent variable values count must be in domain [6:]!')
if not issubclass(value.dtype.type, np.inexact):
value = value.astype(np.float_)
yp1 = np.ravel((np.dot(
self.SPRAGUE_C_COEFFICIENTS[0],
np.array(value[0:6]).reshape((6, 1)))) / 209)[0]
yp2 = np.ravel((np.dot(
self.SPRAGUE_C_COEFFICIENTS[1],
np.array(value[0:6]).reshape((6, 1)))) / 209)[0]
yp3 = np.ravel((np.dot(
self.SPRAGUE_C_COEFFICIENTS[2],
np.array(value[-6:]).reshape((6, 1)))) / 209)[0]
yp4 = np.ravel((np.dot(
self.SPRAGUE_C_COEFFICIENTS[3],
np.array(value[-6:]).reshape((6, 1)))) / 209)[0]
self.__yp = np.concatenate(((yp1, yp2), value, (yp3, yp4)))
self.__y = value
def linear_regression(y, x=None, additional_statistics=False):
"""
Performs the statistics computation about the ideal trend line from given
data using the *least-squares* method.
The equation of the line is :math:`y=b+mx` or
:math:`y=b+m1x1+m1x2+...+mnxn` where the dependent variable :math:`y` value
is a function of the independent variable :math:`x` values.
Parameters
----------
y : array_like
Dependent and already known :math:`y` variable values used to curve
fit an ideal trend line.
x : array_like, optional
Independent :math:`x` variable(s) values corresponding with :math:`y`
variable.
additional_statistics : ndarray
Output additional regression statistics, by default only the :math:`b`
variable and :math:`m` coefficients are returned.
Returns
-------
ndarray, ({{mn, mn-1, ..., b}, {sum_of_squares_residual}})
Regression statistics.
Raises
------
ValueError
If :math:`y` and :math:`x` variables have incompatible dimensions.
References
----------
.. [2] http://en.wikipedia.org/wiki/Simple_linear_regression
(Last accessed 24 May 2014)
Examples
--------
Linear regression with the dependent and already known :math:`y` variable:
>>> y = np.array([1, 2, 1, 3, 2, 3, 3, 4, 4, 3])
>>> linear_regression(y) # doctest: +ELLIPSIS
array([ 0.2909090..., 1. ])
Linear regression with the dependent :math:`y` variable and independent
:math:`x` variable:
>>> x1 = np.array([40, 45, 38, 50, 48, 55, 53, 55, 58, 40])
>>> linear_regression(y, x1) # doctest: +ELLIPSIS
array([ 0.1225194..., -3.3054357...])
Multiple linear regression with the dependent :math:`y` variable and
multiple independent :math:`x_i` variables:
>>> x2 = np.array([25, 20, 30, 30, 28, 30, 34, 36, 32, 34])
>>> linear_regression(y, tuple(zip(x1, x2))) # doctest: +ELLIPSIS
array([ 0.0998002..., 0.0876257..., -4.8303807...])
Multiple linear regression with additional statistics:
>>> linear_regression(y, tuple(zip(x1, x2)), True) # doctest: +ELLIPSIS
(array([ 0.0998002..., 0.0876257..., -4.8303807...]), array([ 2.1376249...]))
"""
y = to_ndarray(y)
if x is None:
x = np.arange(1, len(y) + 1)
else:
x = to_ndarray(x)
if len(x) != len(y):
raise ValueError(
'"y" and "x" variables have incompatible dimensions!')
x = np.vstack([np.array(x).T, np.ones(len(x))]).T
result = np.linalg.lstsq(x, y)
if additional_statistics:
return result[0:2]
else:
return result[0]
def linear_regression(y, x=None, additional_statistics=False):
"""
Performs the statistics computation about the ideal trend line from given
data using the *least-squares* method.
The equation of the line is :math:`y=b+mx` or
:math:`y=b+m1x1+m1x2+...+mnxn` where the dependent variable :math:`y` value
is a function of the independent variable :math:`x` values.
Parameters
----------
y : array_like
Dependent and already known :math:`y` variable values used to curve
fit an ideal trend line.
x : array_like, optional
Independent :math:`x` variable(s) values corresponding with :math:`y`
variable.
additional_statistics : ndarray
Output additional regression statistics, by default only the :math:`b`
variable and :math:`m` coefficients are returned.
Returns
-------
ndarray, ({{mn, mn-1, ..., b}, {sum_of_squares_residual}})
Regression statistics.
Raises
------
ValueError
If :math:`y` and :math:`x` variables have incompatible dimensions.
References
----------
.. [2] http://en.wikipedia.org/wiki/Simple_linear_regression
(Last accessed 24 May 2014)
Examples
--------
Linear regression with the dependent and already known :math:`y` variable:
>>> y = np.array([1, 2, 1, 3, 2, 3, 3, 4, 4, 3])
>>> linear_regression(y) # doctest: +ELLIPSIS
array([ 0.2909090..., 1. ])
Linear regression with the dependent :math:`y` variable and independent
:math:`x` variable:
>>> x1 = np.array([40, 45, 38, 50, 48, 55, 53, 55, 58, 40])
>>> linear_regression(y, x1) # doctest: +ELLIPSIS
array([ 0.1225194..., -3.3054357...])
Multiple linear regression with the dependent :math:`y` variable and
multiple independent :math:`x_i` variables:
>>> x2 = np.array([25, 20, 30, 30, 28, 30, 34, 36, 32, 34])
>>> linear_regression(y, tuple(zip(x1, x2))) # doctest: +ELLIPSIS
array([ 0.0998002..., 0.0876257..., -4.8303807...])
Multiple linear regression with additional statistics:
>>> linear_regression(y, tuple(zip(x1, x2)), True) # doctest: +ELLIPSIS
(array([ 0.0998002..., 0.0876257..., -4.8303807...]), array([ 2.1376249...]))
"""
y = to_ndarray(y)
if x is None:
x = np.arange(1, len(y) + 1)
else:
x = to_ndarray(x)
if len(x) != len(y):
raise ValueError(
'"y" and "x" variables have incompatible dimensions!')
x = np.vstack([np.array(x).T, np.ones(len(x))]).T
result = np.linalg.lstsq(x, y)
if additional_statistics:
return result[0:2]
else:
return result[0]
