colour.utilities.array Module¶

Array Utilities¶

Defines array utilities objects.

colour.utilities.array.as_numeric(x)[source]¶

Converts given \(x\) variable to numeric. In the event where \(x\) cannot be converted, it is passed as is.

Parameters:	x (object) – Variable to convert.
Returns:	\(x\) variable converted to numeric.
Return type:	ndarray

See also

as_stack(), as_shape(), auto_axis()

Examples

>>> as_numeric(np.array([1]))
1.0
>>> as_numeric(np.arange(10))
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])

colour.utilities.array.closest(y, x)[source]¶

Returns closest \(y\) variable element to reference \(x\) variable.

Parameters:	y (array_like) – Variable to search for the closest element. x (numeric) – Reference variable.
Returns:	Closest \(y\) variable element.
Return type:	numeric

Examples

>>> y = np.array([24.31357115,
...               63.62396289,
...               55.71528816,
...               62.70988028,
...               46.84480573,
...               25.40026416])
>>> closest(y, 63)
62.70988028

colour.utilities.array.normalise(x, axis=None, factor=1, clip=True)[source]¶

Normalises given array_like \(x\) variable values and optionally clip them between.

Parameters:	x (array_like) – \(x\) variable to normalise. axis (numeric, optional) – Normalization axis. factor (numeric, optional) – Normalization factor. clip (bool, optional) – Clip values between in domain [0, ‘factor’].
Returns:	Normalised \(x\) variable.
Return type:	ndarray

Examples

>>> x = np.array([0.48224885, 0.31651974, 0.22070513])
>>> normalise(x)  
array([ 1.        ,  0.6563411...,  0.4576581...])

colour.utilities.array.steps(distribution)[source]¶

Returns the steps of given distribution.

Parameters:	distribution (array_like) – Distribution to retrieve the steps.
Returns:	Distribution steps.
Return type:	ndarray

Examples

Uniformly spaced variable:

>>> y = np.array([1, 2, 3, 4, 5])
>>> steps(y)
array([1])

Non-uniformly spaced variable:

>>> y = np.array([1, 2, 3, 4, 8])
>>> steps(y)
array([1, 4])

colour.utilities.array.is_uniform(distribution)[source]¶

Returns if given distribution is uniform.

Parameters:	distribution (array_like) – Distribution to check for uniformity.
Returns:	Is distribution uniform.
Return type:	bool

Examples

Uniformly spaced variable:

>>> y = np.array([1, 2, 3, 4, 5])
>>> is_uniform(y)
True

Non-uniformly spaced variable:

>>> y = np.array([1, 2, 3.1415, 4, 5])
>>> is_uniform(y)
False

colour.utilities.array.in_array(a, b, tolerance=1e-15)[source]¶

Tests whether each element of an array is also present in a second array within given tolerance.

Parameters:	a (array_like) – Array to test the elements from. b (array_like) – The values against which to test each value of array a.
Returns:	A boolean array with a shape describing whether an element of a is present in b within given tolerance.
Return type:	ndarray

References

[1]	Yorke, R. (2014). Python: Change format of np.array or allow tolerance in in1d function. Retrieved March 27, 2015, from http://stackoverflow.com/a/23521245/931625

Examples

>>> a = np.array([0.50, 0.60])
>>> b = np.linspace(0, 10, 101)
>>> np.in1d(a, b)
array([ True, False], dtype=bool)
>>> in_array(a, b)
array([ True,  True], dtype=bool)

colour.utilities.array.tstack(a)[source]¶

Stacks arrays in sequence along the last axis (tail).

Rebuilds arrays divided by tsplit().

Parameters:	a (array_like) – Array to perform the stacking.
Return type:	ndarray

See also

tsplit()

Examples

>>> a = 0
>>> tstack((a, a, a))
array([0, 0, 0])
>>> a = np.arange(0, 6)
>>> tstack((a, a, a))
array([[0, 0, 0],
       [1, 1, 1],
       [2, 2, 2],
       [3, 3, 3],
       [4, 4, 4],
       [5, 5, 5]])
>>> a = np.reshape(a, (1, 6))
>>> tstack((a, a, a))
array([[[0, 0, 0],
        [1, 1, 1],
        [2, 2, 2],
        [3, 3, 3],
        [4, 4, 4],
        [5, 5, 5]]])
>>> a = np.reshape(a, (1, 1, 6))
>>> tstack((a, a, a))
array([[[[0, 0, 0],
         [1, 1, 1],
         [2, 2, 2],
         [3, 3, 3],
         [4, 4, 4],
         [5, 5, 5]]]])

colour.utilities.array.tsplit(a)[source]¶

Splits arrays in sequence along the last axis (tail).

Parameters:	a (array_like) – Array to perform the splitting.
Return type:	ndarray

See also

tstack()

Examples

>>> a = np.array([0, 0, 0])
>>> tsplit(a)
array([0, 0, 0])
>>> a = np.array([[0, 0, 0],
...               [1, 1, 1],
...               [2, 2, 2],
...               [3, 3, 3],
...               [4, 4, 4],
...               [5, 5, 5]])
>>> tsplit(a)
array([[0, 1, 2, 3, 4, 5],
       [0, 1, 2, 3, 4, 5],
       [0, 1, 2, 3, 4, 5]])
>>> a = np.array([[[0, 0, 0],
...                [1, 1, 1],
...                [2, 2, 2],
...                [3, 3, 3],
...                [4, 4, 4],
...                [5, 5, 5]]])
>>> tsplit(a)
array([[[0, 1, 2, 3, 4, 5]],

       [[0, 1, 2, 3, 4, 5]],

       [[0, 1, 2, 3, 4, 5]]])

colour.utilities.array.row_as_diagonal(a)[source]¶

Returns the per row diagonal matrices of the given array.

Parameters:	a (array_like) – Array to perform the diagonal matrices computation.
Return type:	ndarray

References

[1]	Castro, S. (2014). Numpy: Fastest way of computing diagonal for each row of a 2d array. Retrieved August 22, 2014, from http://stackoverflow.com/questions/26511401/numpy-fastest-way-of-computing-diagonal-for-each-row-of-a-2d-array/26517247#26517247

Examples

>>> a = np.array([[0.25891593, 0.07299478, 0.36586996],
...               [0.30851087, 0.37131459, 0.16274825],
...               [0.71061831, 0.67718718, 0.09562581],
...               [0.71588836, 0.76772047, 0.15476079],
...               [0.92985142, 0.22263399, 0.88027331]])
>>> row_as_diagonal(a)
array([[[ 0.25891593,  0.        ,  0.        ],
        [ 0.        ,  0.07299478,  0.        ],
        [ 0.        ,  0.        ,  0.36586996]],

       [[ 0.30851087,  0.        ,  0.        ],
        [ 0.        ,  0.37131459,  0.        ],
        [ 0.        ,  0.        ,  0.16274825]],

       [[ 0.71061831,  0.        ,  0.        ],
        [ 0.        ,  0.67718718,  0.        ],
        [ 0.        ,  0.        ,  0.09562581]],

       [[ 0.71588836,  0.        ,  0.        ],
        [ 0.        ,  0.76772047,  0.        ],
        [ 0.        ,  0.        ,  0.15476079]],

       [[ 0.92985142,  0.        ,  0.        ],
        [ 0.        ,  0.22263399,  0.        ],
        [ 0.        ,  0.        ,  0.88027331]]])

colour.utilities.array.dot_vector(m, v)[source]¶

Convenient wrapper around np.einsum() with the following subscripts: ‘...ij,...j->...i’.

It performs the dot product of two arrays where m parameter is expected to be an array of 3x3 matrices and parameter v an array of vectors.

Parameters:	m (array_like) – Array of 3x3 matrices. v (array_like) – Array of vectors.
Return type:	ndarray

See also

dot_matrix()

Examples

>>> m = np.array([[0.7328, 0.4296, -0.1624],
...               [-0.7036, 1.6975, 0.0061],
...               [0.0030, 0.0136, 0.9834]])
>>> m = np.reshape(np.tile(m, (6, 1)), (6, 3, 3))
>>> v = np.array([0.07049534, 0.10080000, 0.09558313])
>>> v = np.tile(v, (6, 1))
>>> dot_vector(m, v)  
array([[ 0.0794399...,  0.1220905...,  0.0955788...],
       [ 0.0794399...,  0.1220905...,  0.0955788...],
       [ 0.0794399...,  0.1220905...,  0.0955788...],
       [ 0.0794399...,  0.1220905...,  0.0955788...],
       [ 0.0794399...,  0.1220905...,  0.0955788...],
       [ 0.0794399...,  0.1220905...,  0.0955788...]])

colour.utilities.array.dot_matrix(a, b)[source]¶

Convenient wrapper around np.einsum() with the following subscripts: ‘...ij,...jk->...ik’.

It performs the dot product of two arrays where a parameter is expected to be an array of 3x3 matrices and parameter b another array of of 3x3 matrices.

Parameters:	a (array_like) – Array of 3x3 matrices. b (array_like) – Array of 3x3 matrices.
Return type:	ndarray

See also

dot_matrix()

Examples

>>> a = np.array([[0.7328, 0.4296, -0.1624],
...               [-0.7036, 1.6975, 0.0061],
...               [0.0030, 0.0136, 0.9834]])
>>> a = np.reshape(np.tile(a, (6, 1)), (6, 3, 3))
>>> b = a
>>> dot_matrix(a, b)  
array([[[ 0.2342420...,  1.0418482..., -0.2760903...],
        [-1.7099407...,  2.5793226...,  0.1306181...],
        [-0.0044203...,  0.0377490...,  0.9666713...]],

       [[ 0.2342420...,  1.0418482..., -0.2760903...],
        [-1.7099407...,  2.5793226...,  0.1306181...],
        [-0.0044203...,  0.0377490...,  0.9666713...]],

       [[ 0.2342420...,  1.0418482..., -0.2760903...],
        [-1.7099407...,  2.5793226...,  0.1306181...],
        [-0.0044203...,  0.0377490...,  0.9666713...]],

       [[ 0.2342420...,  1.0418482..., -0.2760903...],
        [-1.7099407...,  2.5793226...,  0.1306181...],
        [-0.0044203...,  0.0377490...,  0.9666713...]],

       [[ 0.2342420...,  1.0418482..., -0.2760903...],
        [-1.7099407...,  2.5793226...,  0.1306181...],
        [-0.0044203...,  0.0377490...,  0.9666713...]],

       [[ 0.2342420...,  1.0418482..., -0.2760903...],
        [-1.7099407...,  2.5793226...,  0.1306181...],
        [-0.0044203...,  0.0377490...,  0.9666713...]]])