Rewrite the error function w/ analytic derivatives

This greatly speeds up the code and improves convergence. Something's slightly off with the code, though, and the output colors are slightly skewed.

1 files changed, 51 insertions, 0 deletions

diff --git a/test_diff.py b/test_diff.py
new file mode 100644
index 0000000..b634ca6
--- /dev/null
+++ b/test_diff.py
@@ -0,0 +1,51 @@
+import numpy as np
+from scipy.optimize import minimize
+from colour import *
+from colour.colorimetry import STANDARD_OBSERVER_CMFS, ILLUMINANT_SDS
+from colour.models import eotf_inverse_sRGB, sRGB_to_XYZ
+from matplotlib import pyplot as plt
+from gsoc_common import plot_comparison, error_function, model_sd, D65_xy
+
+shape = SpectralShape(360, 830, 1)
+cmfs = STANDARD_OBSERVER_CMFS["CIE 1931 2 Degree Standard Observer"].align(shape)
+
+illuminant = SpectralDistribution(ILLUMINANT_SDS["D65"]).align(shape)
+illuminant_XYZ = sd_to_XYZ(illuminant) / 100
+wvl = np.linspace(0, 1, len(shape.range()))
+
+target = np.array([50, -20, 30]) # Some arbitrary Lab coordinates
+xs = np.linspace(-10, 10, 500)
+h = xs[1] - xs[0]
+
+# This test checks if derivatives are calculated correctly by comparing them
+# to finite differences.
+for c_index in range(3):
+	errors = np.empty(len(xs))
+	derrors = np.empty(len(xs))
+
+	for i, x in enumerate(xs):
+		c = np.array([1.0, 1, 1])
+		c[c_index] = x
+
+		error, derror_dc = error_function(
+			c, target, wvl, cmfs, illuminant, illuminant_XYZ
+		)
+
+		errors[i] = error
+		derrors[i] = derror_dc[c_index]
+
+
+	plt.subplot(2, 3, 1 + c_index)
+	plt.xlabel("c%d" % c_index)
+	plt.ylabel("ΔE")
+	plt.plot(xs, errors)
+
+	plt.subplot(2, 3, 4 + c_index)
+	plt.xlabel("c%d" % c_index)
+	plt.ylabel("dΔE/dc%d" % c_index)
+
+	plt.plot(xs, derrors, "k-")
+	plt.plot(xs[:-1] + h / 2, np.diff(errors) / h, "r:")
+
+
+plt.show()