Calc more accurate inverse matrices for cat and pre-calc D50 <-> D65 (#…

…354)

* Calc more accurate inverse matrices for cat and pre-calc D50 <-> D65

When applying the inverse CAT transform, the inverse should be
calculated at double precision to match the precision of the values
used.

* Update matrices using a JS implementation

package.json

@@ -81,6 +81,7 @@
 		"core-js": "^3.30.1",
 		"eslint": "latest",
 		"htest.dev": "^0.0.8",
+		"mathjs": "^12.1.0",
 		"postcss": "latest",
 		"postcss-cli": "latest",
 		"postcss-nesting": "latest",

scripts/cat-mat.js

@@ -0,0 +1,50 @@
+import { create, all } from 'mathjs'
+const config = {}
+const math = create(all, config)
+
+const d50 = [0.3457 / 0.3585, 1.00000, (1.0 - 0.3457 - 0.3585) / 0.3585]
+const d65 = [0.3127 / 0.3290, 1.00000, (1.0 - 0.3127 - 0.3290) / 0.3290]
+
+const bradford = [
+    [0.8951000, 0.2664000, -0.1614000],
+    [-0.7502000, 1.7135000, 0.0367000],
+    [0.0389000, -0.0685000, 1.0296000]
+]
+
+const von_kries = [
+    [0.4002400, 0.7076000, -0.0808100],
+    [-0.2263000, 1.1653200, 0.0457000],
+    [0.0000000, 0.0000000, 0.9182200]
+]
+
+const cat02 = [
+    [0.7328000, 0.4296000, -0.1624000],
+    [-0.7036000, 1.6975000, 0.0061000],
+    [0.0030000, 0.0136000, 0.9834000]
+]
+
+const cat16 = [
+    [  0.401288,  0.650173, -0.051461 ],
+    [ -0.250268,  1.204414,  0.045854 ],
+    [ -0.002079,  0.048952,  0.953127 ]
+]
+
+console.log('===== bradford =====')
+console.log(bradford)
+console.log('===== bradford inverse =====')
+console.log(math.inv(bradford))
+
+console.log('===== von kries =====')
+console.log(von_kries)
+console.log('===== von kries inverse =====')
+console.log(math.inv(von_kries))
+
+console.log('===== cat02 =====')
+console.log(cat02)
+console.log('===== cat02 inverse =====')
+console.log(math.inv(cat02))
+
+console.log('===== cat16 =====')
+console.log(cat16)
+console.log('===== cat16 inverse =====')
+console.log(math.inv(cat16))

src/CATs.js

@@ -53,9 +53,9 @@ defineCAT({
 		[  0.0000000,  0.0000000,  0.9182200 ]
 	],
 	fromCone_M: [
-		[  1.8599364, -1.1293816,  0.2198974 ],
-		[  0.3611914,  0.6388125, -0.0000064 ],
-		[  0.0000000,  0.0000000,  1.0890636 ]
+		[ 1.8599363874558397, -1.1293816185800916,   0.21989740959619328 ],
+		[ 0.3611914362417676,  0.6388124632850422,  -0.000006370596838649899 ],
+		[ 0,                   0,                    1.0890636230968613 ]
 	]
 });
 
@@ -70,9 +70,9 @@ defineCAT({
 	],
 	// and back
 	fromCone_M: [
-		[  0.9869929, -0.1470543,  0.1599627 ],
-		[  0.4323053,  0.5183603,  0.0492912 ],
-		[ -0.0085287,  0.0400428,  0.9684867 ]
+		[  0.9869929054667121, -0.14705425642099013, 0.15996265166373122 ],
+		[  0.4323052697233945,  0.5183602715367774,  0.049291228212855594 ],
+		[ -0.00852866457517732, 0.04004282165408486, 0.96848669578755 ]
 	]
 });
 
@@ -85,9 +85,9 @@ defineCAT({
 		[  0.0030000,  0.0136000,  0.9834000 ]
 	],
 	fromCone_M: [
-		[  1.0961238, -0.2788690,  0.1827452 ],
-		[  0.4543690,  0.4735332,  0.0720978 ],
-		[ -0.0096276, -0.0056980,  1.0153256 ]
+		[  1.0961238208355142,   -0.27886900021828726, 0.18274517938277307 ],
+		[  0.4543690419753592,    0.4735331543074117,  0.07209780371722911 ],
+		[ -0.009627608738429355, -0.00569803121611342, 1.0153256399545427 ]
 	]
 });
 
@@ -100,9 +100,9 @@ defineCAT({
 	],
 	// the extra precision is needed to avoid roundtripping errors
 	fromCone_M: [
-		[  1.862067855087233e+0, -1.011254630531685e+0,   1.491867754444518e-1 ],
-		[  3.875265432361372e-1,  6.214474419314753e-1,  -8.973985167612518e-3 ],
-		[ -1.584149884933386e-2, -3.412293802851557e-2,   1.049964436877850e+0 ]
+		[  1.862067855087233,   -1.0112546305316845,  0.14918677544445172 ],
+		[  0.3875265432361372,   0.6214474419314753, -0.008973985167612521 ],
+		[ -0.01584149884933386, -0.03412293802851557, 1.0499644368778496 ]
 	]
 });
 

src/adapt.js

@@ -36,17 +36,17 @@ export default function adapt (W1, W2, XYZ, options = {}) {
 	if (!env.M) {
 		if (env.W1 === WHITES.D65 && env.W2 === WHITES.D50) {
 			env.M = [
-				[  1.0479298208405488,    0.022946793341019088,  -0.05019222954313557 ],
-				[  0.029627815688159344,  0.990434484573249,     -0.01707382502938514 ],
-				[ -0.009243058152591178,  0.015055144896577895,   0.7518742899580008  ]
+				[ 1.0479297925449969, 0.022946870601609652, -0.05019226628920524 ],
+				[ 0.02962780877005599, 0.9904344267538799, -0.017073799063418826 ],
+				[ -0.009243040646204504, 0.015055191490298152, 0.7518742814281371 ]
 			];
 		}
 		else if (env.W1 === WHITES.D50 && env.W2 === WHITES.D65) {
 
 			env.M = [
-				[  0.9554734527042182,   -0.023098536874261423,  0.0632593086610217   ],
-				[ -0.028369706963208136,  1.0099954580058226,    0.021041398966943008 ],
-				[  0.012314001688319899, -0.020507696433477912,  1.3303659366080753   ]
+				[ 0.947386632323667, 0.28196156725620036, -0.1708280666484637 ],
+				[ -0.7357288996314816, 1.6804471734451398, 0.035992069603406264 ],
+				[ 0.029218329379919382, -0.05145129980782719, 0.7733468362356041 ]
 			];
 		}
 	}