Add python/denoising

python/README.md

@@ -1,5 +1,6 @@
 # Python
 
 | Name                                     | Description                                                              |
-| ---------------------------------------- | ------------------------------------------------------------------ |
+| ---------------------------------------- | ------------------------------------------------------------------------ |
+| [denoising](./denoising)                 | Uni homework implementation of a terrible image denoising implementation |
 | [tram-stat-problem](./tram-stat-problem) | Quick script to visualize a dumb stat problem I was thinking about       |

python/denoising/.gitignore

@@ -0,0 +1,5 @@
+.direnv
+.ipynb_checkpoints
+.envrc
+*.pyc
+*.zip

python/denoising/LICENSE

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+                    GNU GENERAL PUBLIC LICENSE
+                       Version 3, 29 June 2007
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+OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,
+THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
+PURPOSE.  THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM
+IS WITH YOU.  SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
+ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
+
+  16. Limitation of Liability.
+
+  IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
+WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
+THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
+GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
+USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
+DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
+PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
+EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
+SUCH DAMAGES.
+
+  17. Interpretation of Sections 15 and 16.
+
+  If the disclaimer of warranty and limitation of liability provided
+above cannot be given local legal effect according to their terms,
+reviewing courts shall apply local law that most closely approximates
+an absolute waiver of all civil liability in connection with the
+Program, unless a warranty or assumption of liability accompanies a
+copy of the Program in return for a fee.
+
+                     END OF TERMS AND CONDITIONS
+
+            How to Apply These Terms to Your New Programs
+
+  If you develop a new program, and you want it to be of the greatest
+possible use to the public, the best way to achieve this is to make it
+free software which everyone can redistribute and change under these terms.
+
+  To do so, attach the following notices to the program.  It is safest
+to attach them to the start of each source file to most effectively
+state the exclusion of warranty; and each file should have at least
+the "copyright" line and a pointer to where the full notice is found.
+
+    <one line to give the program's name and a brief idea of what it does.>
+    Copyright (C) <year>  <name of author>
+
+    This program is free software: you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with this program.  If not, see <https://www.gnu.org/licenses/>.
+
+Also add information on how to contact you by electronic and paper mail.
+
+  If the program does terminal interaction, make it output a short
+notice like this when it starts in an interactive mode:
+
+    <program>  Copyright (C) <year>  <name of author>
+    This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+    This is free software, and you are welcome to redistribute it
+    under certain conditions; type `show c' for details.
+
+The hypothetical commands `show w' and `show c' should show the appropriate
+parts of the General Public License.  Of course, your program's commands
+might be different; for a GUI interface, you would use an "about box".
+
+  You should also get your employer (if you work as a programmer) or school,
+if any, to sign a "copyright disclaimer" for the program, if necessary.
+For more information on this, and how to apply and follow the GNU GPL, see
+<https://www.gnu.org/licenses/>.
+
+  The GNU General Public License does not permit incorporating your program
+into proprietary programs.  If your program is a subroutine library, you
+may consider it more useful to permit linking proprietary applications with
+the library.  If this is what you want to do, use the GNU Lesser General
+Public License instead of this License.  But first, please read
+<https://www.gnu.org/licenses/why-not-lgpl.html>.

python/denoising/flake.lock

@@ -0,0 +1,43 @@
+{
+  "nodes": {
+    "flake-utils": {
+      "locked": {
+        "lastModified": 1676283394,
+        "narHash": "sha256-XX2f9c3iySLCw54rJ/CZs+ZK6IQy7GXNY4nSOyu2QG4=",
+        "owner": "numtide",
+        "repo": "flake-utils",
+        "rev": "3db36a8b464d0c4532ba1c7dda728f4576d6d073",
+        "type": "github"
+      },
+      "original": {
+        "owner": "numtide",
+        "repo": "flake-utils",
+        "type": "github"
+      }
+    },
+    "nixpkgs": {
+      "locked": {
+        "lastModified": 1676428076,
+        "narHash": "sha256-8caqXsVSUvZqp4/pOLjbWWabzLEV/ZfDUiEv32WumKw=",
+        "owner": "nixos",
+        "repo": "nixpkgs",
+        "rev": "e0a054002198445ef987b55c34cde892cecc0de7",
+        "type": "github"
+      },
+      "original": {
+        "owner": "nixos",
+        "ref": "release-22.11",
+        "repo": "nixpkgs",
+        "type": "github"
+      }
+    },
+    "root": {
+      "inputs": {
+        "flake-utils": "flake-utils",
+        "nixpkgs": "nixpkgs"
+      }
+    }
+  },
+  "root": "root",
+  "version": 7
+}

python/denoising/flake.nix

@@ -0,0 +1,23 @@
+{
+  inputs = {
+    nixpkgs.url = "github:nixos/nixpkgs/release-22.11";
+    flake-utils.url = "github:numtide/flake-utils";
+  };
+
+  outputs = { self, nixpkgs, flake-utils }:
+    flake-utils.lib.eachDefaultSystem
+      (system:
+        let
+          pkgs = nixpkgs.legacyPackages.${system};
+          pyDeps = p: with p; [ numpy scipy matplotlib pillow ];
+        in
+        rec {
+          devShell = pkgs.mkShell {
+            buildInputs = with pkgs; [
+              (python3.withPackages pyDeps)
+              jupyter
+              pandoc
+            ];
+          };
+        });
+}

python/denoising/modules/decompose.py

@@ -0,0 +1,44 @@
+import numpy as np
+
+def decompose(M):
+  n = len(M)
+
+  U = M.copy()
+  L = np.identity(n)
+
+  for i in range(0, n - 1):
+    for j in range(i + 1, n):
+      L[j, i] = U[j, i] / U[i, i]
+      U[j, i:n] -= L[j, i] * U[i, i:n]
+
+  assert np.allclose(M, L@U)
+
+  return L, U
+
+def solve_lower(m, v):
+  x = np.zeros(len(v))
+
+  for i in range(0, len(v)):
+    x[i] = (v[i] - m[i, :i] @ x[:i]) / m[i, i]
+
+  assert np.allclose(m@x, v)
+
+  return x
+
+def solve_upper(m, v):
+  x = np.zeros(len(v))
+
+  for i in reversed(range(0, len(m))):
+    x[i] = (v[i] - m[i, i+1:] @ x[i+1:]) / m[i, i]
+
+  assert np.allclose(m@x, v)
+
+  return x
+
+def solve(m, v):
+  L, U = decompose(m)
+  x = solve_upper(U, solve_lower(L, v))
+
+  assert np.allclose(m@x, v)
+
+  return x

python/denoising/modules/image_tools.py

@@ -0,0 +1,46 @@
+"""Project 2 tools for generating a noisy image"""
+import matplotlib.pyplot as plt
+import numpy as np
+from PIL import Image  # PIL is an image processing module
+
+
+def create_noisy_image(path="/content/drive/My Drive/", file="sonic.jpg"):
+    """Transform color image to a noisy grayscale image.
+    Plot and save the transformed images.
+
+    The file sonic.jpg must be located in your google drive and the drive must have been
+    "mounted" with:
+
+        from google.colab import drive
+        drive.mount("/content/drive")
+    """
+    image = Image.open(path + file)
+    # Transform RGB image to grayscale
+    image = image.convert("L")
+
+    # get the filename without the extension
+    # (note: the pathlib module offers better ways to do this!)
+    name = file.removesuffix(".jpg")
+
+    image.save(path + name + "_gray.jpg")
+
+    # set images to be plotted in gray scale
+    plt.gray()
+    plt.imshow(image)
+    plt.title("Original image")
+    plt.show()
+
+    # add noise to grayscale image
+    sigma = 2.0
+    img_arr = np.array(image)
+    img_arr_noisy = np.clip(
+        img_arr + sigma * np.random.normal(0, 100, img_arr.shape), 0, 255
+    ).astype(np.uint8)
+    plt.title("Noisy image")
+    plt.imshow(img_arr_noisy)
+
+    # create Image object from numpy array and save to disk
+    image = Image.fromarray(img_arr_noisy, mode="L")
+    image.save(path + name + "_gray_noisy.jpg")
+
+    plt.show()

python/denoising/modules/tridiagonal.py

@@ -0,0 +1,222 @@
+import numpy as np
+import scipy as sp
+
+def assert_valid_tridiagonal(a, c, e):
+  """
+  Validates a tridiagonal matrix.
+  """
+  assert len(a) == len(c) + 1 == len(e) + 1
+
+def create(a, c, e):
+  """
+  Validates a tridiagonal matrix before creating it.
+  """
+  assert_valid_tridiagonal(a, c, e)
+  return (a, c, e)
+
+
+def decompose(a, c, e):
+  """
+  Computes the LU decomposition of a tridiagonal matrix.
+  """
+  assert_valid_tridiagonal(a, c, e)
+
+  α = np.zeros(len(c))
+  β = a.copy()
+
+  for i in range(len(c)):
+    α[i] = e[i] / β[i]
+    β[i + 1] -= c[i] * α[i]
+
+  # Sanity check
+  if len(a) <= 10:
+    assert np.allclose(
+      to_array(a, c, e),
+      to_array(*from_lower(α)) @ to_array(*from_upper(β, c))
+    )
+
+  return (α, β)
+
+def to_csr(a, c, e):
+  """
+  Converts a tridiagonal matrix into a scipy csr sparse matrix.
+  """
+  assert_valid_tridiagonal(a, c, e)
+
+  return sp.sparse.diags((a, c, e), offsets=(0, 1, -1), format="csr")
+
+def to_array(a, c, e):
+  """
+  Converts a tridiagonal matrix into a numpy matrix.
+  """
+  assert_valid_tridiagonal(a, c, e)
+  return to_csr(a, c, e).toarray()
+
+def from_lower(α):
+  """
+  Turns the lower vector of a decomposition into a tridiagonal matrix.
+
+  Example ussage:
+  ```py 
+  α, β = decompose(m)
+  print(from_lower(α))
+  ```
+  """
+  return create(np.ones(len(α) + 1), np.zeros(len(α)), α) 
+
+def from_upper(β, c):
+  """
+  Turns the upper vectors of a decomposition into a tridiagonal matrix.
+
+  Example ussage:
+  ```py 
+  α, β = decompose((a, c, e))
+  print(from_upper(β, c))
+  ```
+  """
+  return create(β, c, np.zeros(len(c)))
+
+def solve_lower(α, rhs):
+  """
+  Solve a linear system of equations Mx = v
+  where M is a lower triangular matrix constructed
+  by LU decomposing a tridiagonal matrix.
+  """
+  x = np.zeros_like(rhs)
+
+  x[0] = rhs[0]
+
+  for i in range(1, len(rhs)):
+    x[i] = rhs[i] - α[i - 1] * x[i - 1]
+
+  if len(α) <= 10:
+    assert np.allclose(to_array(*from_lower(α)) @ x, rhs)
+
+  return x
+
+def solve_upper(β, c, rhs):
+  """
+  Solve a linear system of equations Mx = v
+  where M is an upper triangular matrix constructed
+  by LU decomposing a tridiagonal matrix.
+  """
+  x = np.zeros_like(rhs)
+
+  x[-1] = rhs[-1] / β[-1]
+
+  for i in reversed(range(len(rhs) - 1)):
+    x[i] = (rhs[i] - c[i] * x[i+1]) / β[i]
+
+  if len(β) <= 10:
+    assert np.allclose(to_array(*from_upper(β, c)) @ x, rhs)
+
+  return x
+
+def solve(a, c, e, rhs):
+  """
+  Solves a system of linear equations defined by a tridiagonal matrix.
+  """
+  assert_valid_tridiagonal(a, c, e)
+
+  α, β = decompose(a, c, e)
+  x = solve_upper(β, c, solve_lower(α, rhs))
+
+  if len(α) <= 10:
+    assert np.allclose(to_array(a, c, e)@x, rhs)
+
+  return x
+
+def multiply_vector(a, c, e, x):
+  """
+  Performs a matrix-vector multiplication where the matrix is tridiagonal.
+  """
+  assert_valid_tridiagonal(a, c, e)
+  assert len(x) == len(a)
+
+  result = np.zeros_like(x)
+  for i in range(len(x)):
+    result[i] = a[i] * x[i]
+    if i > 0:
+      result[i] += e[i - 1] * x[i - 1]
+    if i < len(x) - 1:
+      result[i] += c[i] * x[i + 1]
+
+  # Sanity check
+  if len(a) <= 10:
+    assert np.allclose(to_array(a, c, e) @ x, result)
+
+  return result
+
+def largest_eigenvalue(a, c, e, initial_x, kmax):
+  """
+  Computes the largest eigenvalue of a positive definite tridiagonal matrix.
+  """
+  assert_valid_tridiagonal(a, c, e)
+
+  x = initial_x
+  for _ in range(kmax):
+    q = multiply_vector(a, c, e, x)
+    assert not np.allclose(q, 0) # Sanity check
+    x = q/np.linalg.norm(q)
+
+  # Computes the eigenvalue from the eigenvector
+  eigenvalue = (x @ multiply_vector(a, c, e, x)) / (x @ x)
+
+  # Sanity check
+  if len(initial_x) <= 10:
+    actual_eigenvalues, _ = np.linalg.eig(to_array(a, c, e))
+    assert np.allclose(
+      0,
+      np.min(
+        np.abs(
+          actual_eigenvalues - eigenvalue
+        )
+      )
+    )
+
+  return eigenvalue
+
+def add(a, b):
+  """
+  Adds two tridiagonal matrices.
+  """
+  assert_valid_tridiagonal(*a)
+  assert_valid_tridiagonal(*b)
+
+  assert len(a[0]) == len(b[0])
+
+  result = create(a[0] + b[0], a[1] + b[1], a[2] + b[2])
+
+  # Sanity check
+  if len(a[0]) <= 10:
+    assert np.allclose(to_array(*result), to_array(*a) + to_array(*b))
+
+  return result
+
+def identity(n):
+  """
+  Returns the tridiagonal identity n*n matrix.
+  """
+  assert n > 0 # Sanity check
+  return create(np.ones(n), np.zeros(n - 1), np.zeros(n - 1))
+
+def scale(s, m):
+  """
+  Multiplies a tridiagonal matrix by a scalar
+  """
+  assert_valid_tridiagonal(*m)
+
+  result = create(s * m[0], s * m[1], s * m[2])
+
+  # Sanity check
+  if len(m[0]) <= 10:
+    assert np.allclose(result, s * to_array(*m))
+
+  return result
+
+def transpose(a, c, e):
+  """
+  Computes the transpose of a tridiagonal matrix.
+  """
+  return create(a, e, c)
+# main()