On the Subject of Cruel Ship Review

😨.

The module shows a pair of characters, 6 LEDs of profile pictures and a page counter.

1. For each page: get all the values for the ship from Not Ship Review’s Data Table and put them in one row. Put new rows after existing rows to get 6x6 matrix. Divide this matrix in half both horizontally and vertically to get 4 3x3 matrices. Multiply them in reading order and call the result A.
2. Project A to closest rotation matrix R by doing Singular Value Decomposition:
   1. Set B = A^TA.
   2. Find the eigenvalues of B. Solve the characteristic equation det(B − λI) = 0. This is a cubic equation; it will give three roots λ₁ ≥ λ₂ ≥ λ₃ ≥ 0 (all positive).
   3. Find the eigenvectors of B. For each λ_i:
      1. Set M_i = B − λ_iI.
      2. Reduce M_i to row echelon form using Gaussian elimination (one row should vanish, since det(M_i) = 0 by construction).
      3. Solve for the free variable to get the direction v_i.
      4. Normalize: v_i → v_i / ‖v_i‖.
   4. Assemble V. Set V = [v₁ | v₂ | v₃].
   5. Compute the columns of U. For each i where σ_i = √λ_i: u_i = 1/σ_i * (Av_i).
   6. Assemble U = [u₁ | u₂ | u₃].
   7. Set R = UV^T.
3. For each LED: read the configuration for all pages, divide it in half and count amount of lits in each half. Use table below to find the value of R to submit. First number is the row, second is the column. Submit the numbers in order of LEDs.

   	1	2	3
   1
   2
   3

Clarifications

Numbers must be submitted in ±.#### form and rounded towards 0. If the number is 0, input it as +.0000.

Input system works exactly the same as in Ship Review. However, to get into Submit mode, you should press the white button. You may go back into Read mode with the same button if there’s currently no input. In Read mode, numbered buttons act as a page flipper.

Characters

Here are the characters that may be shown on the module.

Name	Icon	Name	Icon	Name	Icon
Astro		Brightney		Dandy
Bassie		Brusha		Dyle
Blot		Cocoa		Eclipse
Bobbette		Connie		Eggson
Boxten		Cosmo		Ginger

Finn		Scraps		Sprout
Flutter		Shelly		Squirm
Flyte		Ribecca		Teagan
Gigi		R&D		Tisha
Glisten		Rodger		Vee
Goob		Rudie		Waxwell
Looey		Shrimpo		Yatta
Poppy		Soulvester