For practical consideration, ICC has imposed L*a*b* encoding range of -128 to +127 for values a* and b* [link]. In reality, those out of range colors are not imaginary but visible and they can be encoded in a PCS of XYZ icc profile.
[ Negative primaries ]
ProPhoto primaries have either a* or b* that exceed the -128 to 127 range, as shown below.
Red: 0.797668, 0.288040, 0.000000 [Lab 60.608273, 139.168888, 104.497022]
Green: 0.135193, 0.711884, 0.000000 [Lab 87.576439, -186.694184, 150.993860]
Blue: 0.031342, 0.000092, 0.824905 [Lab 0.082699, 90.249204, -172.271644]
[ colprof ]
colprof with options -a, -u and -un
-a lxXgsmGS Algorithm type override
l = Lab cLUT (def.), x = XYZ cLUT, X = display XYZ cLUT + matrix
g = gamma+matrix, s = shaper+matrix, m = matrix only,
G = single gamma+matrix, S = single shaper+matrix
Option -al
Default option, cLUT profile will be created with PCS of L*a*b*. Profiles that are generated with this option support all the four rendering intents.
Option -ax
This option allows cLUT profile to be created with PCS of XYZ which offers better accuracy for input devices such as displays, scanners and cameras. In general, it avoids clipping of values above the white point that can occur in L*a*b* based cLUT input profile.
Option -u
Forces cLUT profile absolute.
Option -un
Forces cLUT profile absolute but cLUT white & black points will not be extrapolated with matrix.
 |
| cLUT Lab bsed Profiles, illustrated with Lab co-ordinates, relative rendering and showing white point at L=100 (same scale) |
-qh -al 2,336,270
-qh -al -u 3,148,510
-qh -al -un 2,538,190
-qh -ax 2.230,620
-qh -ax -u 2,443,380
-qh -ax -un 2,360,950
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