Matlab code made by Tinna Lif Gunnarsdottir.

Part 1 is here

SMPTE RP-177:1993 Rec709 to Rec2020 NPM/TRA. P3 to Rec2020 TRA has a problem with the color red.

**COLOR REC 2020 NPM & NPM INV (Matlab)**

%COLOR REC 2020 NPM & NPM INV R = [0.708 ; 0.292 ; 0.000]; G = [0.170 ; 0.797 ; 0.0330]; B = [0.131 ; 0.046 ; 0.8230]; P = [R G B] ; %White Point D65 X = 0.3127; Y = 0.3290; Z = 0.3583; W = [X/Y ; 1 ; Z/Y]; CC = P \ W; C = [CC(1,1) 0 0 ; 0 CC(2,1) 0 ; 0 0 CC(3,1)]; format long NPM = P * C NPM_inv = inv(NPM)

```
NPM =
0.636958048301291 0.144616903586208 0.168880975164172
0.262700212011267 0.677998071518871 0.059301716469862
0 0.028072693049088 1.060985057710791
NPM_inv =
1.716651187971268 -0.355670783776393 -0.253366281373660
-0.666684351832489 1.616481236634939 0.015768545813911
0.017639857445311 -0.042770613257809 0.942103121235474
```

**From REC709 D65 to Rec-2020 (Matlab)**

%From REC 709 D65 to REC-2020 R_7 = [0.640 ; 0.330 ; 0.030]; G_7 = [0.300 ; 0.600 ; 0.100]; B_7 = [0.150 ; 0.060 ; 0.790]; P_7 = [R_7 G_7 B_7]; % White Point D65 X_7 = 0.3127; Y_7 = 0.3290; Z_7 = 0.3583; W_7 = [X_7/Y_7 ; 1 ; Z_7/Y_7]; CC_7 = P_7 \ W_7; % P inv C_7 = [ CC_7(1,1) 0 0 ; 0 CC_7(2,1) 0 ; 0 0 CC_7(3,1)]; NPM_7 = P_7 * C_7 TRA_7 = NPM \ NPM_7 % Rec709 source, NPM/2020 dest, and inv

```
NPM_7 =
0.412390799265959 0.357584339383878 0.180480788401834
0.212639005871510 0.715168678767756 0.072192315360734
0.019330818715592 0.119194779794626 0.950532152249661
TRA_7 =
0.627403895934699 0.329283038377884 0.043313065687417
0.069097289358232 0.919540395075459 0.011362315566309
0.016391438875150 0.088013307877226 0.895595253247624
```

**Python REC709 D65 to Rec-2020 (Python)**

import numpy as np # COLOR REC 2020 NPM & NPM INV R = np.array([0.708, 0.292, 0.000]) G = np.array([0.170, 0.797, 0.033]) B = np.array([0.131, 0.046, 0.823]) P = np.column_stack((R, G, B)) # White Point D65 X = 0.3127 Y = 0.3290 Z = 0.3583 W = np.array([X/Y, 1, Z/Y]) # Compute CC CC = np.linalg.solve(P, W) # Create C matrix C = np.diag(CC) # Compute NPM and NPM_inv NPM = np.dot(P, C) NPM_inv = np.linalg.inv(NPM) # From REC 709 D65 to REC-2020 R_7 = np.array([0.640, 0.330, 0.030]) G_7 = np.array([0.300, 0.600, 0.100]) B_7 = np.array([0.150, 0.060, 0.790]) P_7 = np.column_stack((R_7, G_7, B_7)) # White Point D65 X_7 = 0.3127 Y_7 = 0.3290 Z_7 = 0.3583 W_7 = np.array([X_7/Y_7, 1, Z_7/Y_7]) # Compute CC_7 CC_7 = np.linalg.solve(P_7, W_7) # Create C_7 matrix C_7 = np.diag(CC_7) # Compute NPM_7 NPM_7 = np.dot(P_7, C_7) # Compute TRA_7 TRA_7 = np.linalg.solve(NPM, NPM_7) # Print results with high precision np.set_printoptions(precision=15) print("NPM:") print(NPM) print("\nNPM_inv:") print(NPM_inv) print("\nNPM_7:") print(NPM_7) print("\nTRA_7:") print(TRA_7)

Download and install Python

Run cmd on windows or terminal on mac

Install NumPy

pip3 install numpy

Copy and paste code into a text editor like nano, notepad++(win), bbedit(mac) and save it as rec709torec2020.py

Run the code

python3 rec709torec2020.py

The result is the same as in Matlab

```
NPM:
[[0.636958048301291 0.144616903586208 0.168880975164172]
[0.262700212011267 0.677998071518871 0.059301716469862]
[0. 0.028072693049088 1.060985057710791]]
```

```
NPM_inv:
[[ 1.716651187971268 -0.355670783776392 -0.25336628137366 ]
[-0.666684351832489 1.616481236634939 0.015768545813911]
[ 0.017639857445311 -0.042770613257809 0.942103121235474]]
```

```
NPM_7:
[[0.412390799265959 0.357584339383878 0.180480788401834]
[0.21263900587151 0.715168678767756 0.072192315360734]
[0.019330818715592 0.119194779794626 0.95053215224966 ]]
```

```
TRA_7:
[[0.627403895934699 0.329283038377884 0.043313065687417]
[0.069097289358232 0.919540395075459 0.011362315566309]
[0.01639143887515 0.088013307877226 0.895595253247624]]
```