def test_lagrange_coefficients(self):
"""
Tests :func:`colour.algebra.interpolation.lagrange_coefficients`
definition.
Notes
-----
- :attr:`LAGRANGE_COEFFICIENTS_A` and :attr:`LAGRANGE_COEFFICIENTS_B`
attributes data is matching :cite:`Fairman1985b`.
References
----------
:cite:`Fairman1985b`
"""
lc = [lagrange_coefficients(i, 3) for i in np.linspace(0.05, 0.95, 19)]
np.testing.assert_almost_equal(lc, LAGRANGE_COEFFICIENTS_A, decimal=7)
lc = [lagrange_coefficients(i, 4) for i in np.linspace(1.05, 1.95, 19)]
np.testing.assert_almost_equal(lc, LAGRANGE_COEFFICIENTS_B, decimal=7)
def test_lagrange_coefficients(self):
"""
Tests :func:`colour.algebra.interpolation.lagrange_coefficients`
definition.
Notes
-----
- :attr:`LAGRANGE_COEFFICIENTS_A` and :attr:`LAGRANGE_COEFFICIENTS_B`
attributes data is matching :cite:`Fairman1985b`.
References
----------
:cite:`Fairman1985b`
"""
lc = [lagrange_coefficients(i, 3) for i in np.linspace(0.05, 0.95, 19)]
np.testing.assert_almost_equal(lc, LAGRANGE_COEFFICIENTS_A, decimal=7)
lc = [lagrange_coefficients(i, 4) for i in np.linspace(1.05, 1.95, 19)]
np.testing.assert_almost_equal(lc, LAGRANGE_COEFFICIENTS_B, decimal=7)
def test_lagrange_coefficients(self):
"""
Tests :func:`colour.algebra.interpolation.lagrange_coefficients`
definition.
Notes
-----
:attr:`LAGRANGE_COEFFICIENTS_A` and :attr:`LAGRANGE_COEFFICIENTS_B`
attributes data is matching [1]_.
References
----------
.. [1] Fairman, H. S. (1985). The calculation of weight factors for
tristimulus integration. Color Research & Application, 10(4),
199–203. doi:10.1002/col.5080100407
"""
lc = [lagrange_coefficients(i, 3) for i in np.linspace(0.05, 0.95, 19)]
np.testing.assert_almost_equal(lc, LAGRANGE_COEFFICIENTS_A, decimal=7)
lc = [lagrange_coefficients(i, 4) for i in np.linspace(1.05, 1.95, 19)]
np.testing.assert_almost_equal(lc, LAGRANGE_COEFFICIENTS_B, decimal=7)
def test_lagrange_coefficients(self):
"""
Tests :func:`colour.algebra.interpolation.lagrange_coefficients`
definition.
Notes
-----
:attr:`LAGRANGE_COEFFICIENTS_A` and :attr:`LAGRANGE_COEFFICIENTS_B`
attributes data is matching [1]_.
References
----------
.. [1] Fairman, H. S. (1985). The calculation of weight factors for
tristimulus integration. Color Research & Application, 10(4),
199–203. doi:10.1002/col.5080100407
"""
lc = [lagrange_coefficients(i, 3)
for i in np.linspace(0.05, 0.95, 19)]
np.testing.assert_almost_equal(lc, LAGRANGE_COEFFICIENTS_A, decimal=7)
lc = [lagrange_coefficients(i, 4)
for i in np.linspace(1.05, 1.95, 19)]
np.testing.assert_almost_equal(lc, LAGRANGE_COEFFICIENTS_B, decimal=7)
def lagrange_coefficients_ASTME202211(
interval=10,
interval_type='inner'):
"""
Computes the *Lagrange Coefficients* for given interval size using practise
*ASTM E2022-11* method [1]_.
Parameters
----------
interval : int
Interval size in nm.
interval_type : unicode, optional
**{'inner', 'boundary'}**,
If the interval is an *inner* interval *Lagrange Coefficients* are
computed for degree 4. Degree 3 is used for a *boundary* interval.
Returns
-------
ndarray
*Lagrange Coefficients*.
See Also
--------
colour.lagrange_coefficients
Examples
--------
>>> lagrange_coefficients_ASTME202211( # doctest: +ELLIPSIS
... 10, 'inner')
array([[-0.028..., 0.940..., 0.104..., -0.016...],
[-0.048..., 0.864..., 0.216..., -0.032...],
[-0.059..., 0.773..., 0.331..., -0.045...],
[-0.064..., 0.672..., 0.448..., -0.056...],
[-0.062..., 0.562..., 0.562..., -0.062...],
[-0.056..., 0.448..., 0.672..., -0.064...],
[-0.045..., 0.331..., 0.773..., -0.059...],
[-0.032..., 0.216..., 0.864..., -0.048...],
[-0.016..., 0.104..., 0.940..., -0.028...]])
>>> lagrange_coefficients_ASTME202211( # doctest: +ELLIPSIS
... 10, 'boundary')
array([[ 0.85..., 0.19..., -0.04...],
[ 0.72..., 0.36..., -0.08...],
[ 0.59..., 0.51..., -0.10...],
[ 0.48..., 0.64..., -0.12...],
[ 0.37..., 0.75..., -0.12...],
[ 0.28..., 0.84..., -0.12...],
[ 0.19..., 0.91..., -0.10...],
[ 0.12..., 0.96..., -0.08...],
[ 0.05..., 0.99..., -0.04...]])
"""
global _LAGRANGE_INTERPOLATING_COEFFICIENTS_CACHE
if _LAGRANGE_INTERPOLATING_COEFFICIENTS_CACHE is None:
_LAGRANGE_INTERPOLATING_COEFFICIENTS_CACHE = CaseInsensitiveMapping()
name_lica = ', '.join((str(interval), interval_type))
if name_lica in _LAGRANGE_INTERPOLATING_COEFFICIENTS_CACHE:
return _LAGRANGE_INTERPOLATING_COEFFICIENTS_CACHE[name_lica]
r_n = np.linspace(1 / interval, 1 - (1 / interval), interval - 1)
d = 3
if interval_type.lower() == 'inner':
r_n += 1
d = 4
lica = _LAGRANGE_INTERPOLATING_COEFFICIENTS_CACHE[name_lica] = (
np.asarray([lagrange_coefficients(r, d) for r in r_n]))
return lica
