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fix(mypy): type annotations for linear algebra algorithms (#4317)

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* fix(mypy): type annotations for linear algebra algorithms

* refactor: remove linear algebra directory from mypy exclude
This commit is contained in:
Dhruv Manilawala 2021-04-05 19:07:38 +05:30 committed by GitHub
parent 20c7518028
commit 8c2986026b
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8 changed files with 100 additions and 74 deletions
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2
.github/workflows/build.yml vendored
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@ -23,7 +23,7 @@ jobs:
python -m pip install mypy pytest-cov -r requirements.txt
# FIXME: #4052 fix mypy errors in the exclude directories and remove them below
- run: mypy --ignore-missing-imports
--exclude '(data_structures|digital_image_processing|dynamic_programming|graphs|linear_algebra|maths|matrix|other|project_euler|scripts|searches|strings*)/$' .
--exclude '(data_structures|digital_image_processing|dynamic_programming|graphs|maths|matrix|other|project_euler|scripts|searches|strings*)/$' .
- name: Run tests
run: pytest --doctest-modules --ignore=project_euler/ --ignore=scripts/ --cov-report=term-missing:skip-covered --cov=. .
- if: ${{ success() }}

17
linear_algebra/src/conjugate_gradient.py
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@ -3,10 +3,12 @@ Resources:
- https://en.wikipedia.org/wiki/Conjugate_gradient_method
- https://en.wikipedia.org/wiki/Definite_symmetric_matrix
"""
from typing import Any
import numpy as np
def _is_matrix_spd(matrix: np.array) -> bool:
def _is_matrix_spd(matrix: np.ndarray) -> bool:
"""
Returns True if input matrix is symmetric positive definite.
Returns False otherwise.
@ -38,10 +40,11 @@ def _is_matrix_spd(matrix: np.array) -> bool:
eigen_values, _ = np.linalg.eigh(matrix)
# Check sign of all eigenvalues.
return np.all(eigen_values > 0)
# np.all returns a value of type np.bool_
return bool(np.all(eigen_values > 0))
def _create_spd_matrix(dimension: np.int64) -> np.array:
def _create_spd_matrix(dimension: int) -> Any:
"""
Returns a symmetric positive definite matrix given a dimension.
@ -64,11 +67,11 @@ def _create_spd_matrix(dimension: np.int64) -> np.array:
def conjugate_gradient(
spd_matrix: np.array,
load_vector: np.array,
spd_matrix: np.ndarray,
load_vector: np.ndarray,
max_iterations: int = 1000,
tol: float = 1e-8,
) -> np.array:
) -> Any:
"""
Returns solution to the linear system np.dot(spd_matrix, x) = b.
@ -141,6 +144,8 @@ def conjugate_gradient(
# Update number of iterations.
iterations += 1
if iterations > max_iterations:
break
return x

83
linear_algebra/src/lib.py
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@ -22,6 +22,7 @@ Overview:
import math
import random
from typing import Collection, Optional, Union, overload
class Vector:
@ -45,7 +46,7 @@ class Vector:
TODO: compare-operator
"""
def __init__(self, components=None):
def __init__(self, components: Optional[Collection[float]] = None) -> None:
"""
input: components or nothing
simple constructor for init the vector
@ -54,7 +55,7 @@ class Vector:
components = []
self.__components = list(components)
def set(self, components):
def set(self, components: Collection[float]) -> None:
"""
input: new components
changes the components of the vector.
@ -65,13 +66,13 @@ class Vector:
else:
raise Exception("please give any vector")
def __str__(self):
def __str__(self) -> str:
"""
returns a string representation of the vector
"""
return "(" + ",".join(map(str, self.__components)) + ")"
def component(self, i):
def component(self, i: int) -> float:
"""
input: index (start at 0)
output: the i-th component of the vector.
@ -81,22 +82,22 @@ class Vector:
else:
raise Exception("index out of range")
def __len__(self):
def __len__(self) -> int:
"""
returns the size of the vector
"""
return len(self.__components)
def euclidLength(self):
def euclidLength(self) -> float:
"""
returns the euclidean length of the vector
"""
summe = 0
summe: float = 0
for c in self.__components:
summe += c ** 2
return math.sqrt(summe)
def __add__(self, other):
def __add__(self, other: "Vector") -> "Vector":
"""
input: other vector
assumes: other vector has the same size
@ -109,7 +110,7 @@ class Vector:
else:
raise Exception("must have the same size")
def __sub__(self, other):
def __sub__(self, other: "Vector") -> "Vector":
"""
input: other vector
assumes: other vector has the same size
@ -122,7 +123,15 @@ class Vector:
else: # error case
raise Exception("must have the same size")
def __mul__(self, other):
@overload
def __mul__(self, other: float) -> "Vector":
...
@overload
def __mul__(self, other: "Vector") -> float:
...
def __mul__(self, other: Union[float, "Vector"]) -> Union[float, "Vector"]:
"""
mul implements the scalar multiplication
and the dot-product
@ -132,20 +141,20 @@ class Vector:
return Vector(ans)
elif isinstance(other, Vector) and (len(self) == len(other)):
size = len(self)
summe = 0
summe: float = 0
for i in range(size):
summe += self.__components[i] * other.component(i)
return summe
else: # error case
raise Exception("invalid operand!")
def copy(self):
def copy(self) -> "Vector":
"""
copies this vector and returns it.
"""
return Vector(self.__components)
def changeComponent(self, pos, value):
def changeComponent(self, pos: int, value: float) -> None:
"""
input: an index (pos) and a value
changes the specified component (pos) with the
@ -156,7 +165,7 @@ class Vector:
self.__components[pos] = value
def zeroVector(dimension):
def zeroVector(dimension: int) -> Vector:
"""
returns a zero-vector of size 'dimension'
"""
@ -165,7 +174,7 @@ def zeroVector(dimension):
return Vector([0] * dimension)
def unitBasisVector(dimension, pos):
def unitBasisVector(dimension: int, pos: int) -> Vector:
"""
returns a unit basis vector with a One
at index 'pos' (indexing at 0)
@ -177,7 +186,7 @@ def unitBasisVector(dimension, pos):
return Vector(ans)
def axpy(scalar, x, y):
def axpy(scalar: float, x: Vector, y: Vector) -> Vector:
"""
input: a 'scalar' and two vectors 'x' and 'y'
output: a vector
@ -192,7 +201,7 @@ def axpy(scalar, x, y):
return x * scalar + y
def randomVector(N, a, b):
def randomVector(N: int, a: int, b: int) -> Vector:
"""
input: size (N) of the vector.
random range (a,b)
@ -200,7 +209,7 @@ def randomVector(N, a, b):
random integer components between 'a' and 'b'.
"""
random.seed(None)
ans = [random.randint(a, b) for i in range(N)]
ans = [random.randint(a, b) for _ in range(N)]
return Vector(ans)
@ -222,7 +231,7 @@ class Matrix:
operator - _ implements the matrix-subtraction
"""
def __init__(self, matrix, w, h):
def __init__(self, matrix: list[list[float]], w: int, h: int) -> None:
"""
simple constructor for initializing
the matrix with components.
@ -231,7 +240,7 @@ class Matrix:
self.__width = w
self.__height = h
def __str__(self):
def __str__(self) -> str:
"""
returns a string representation of this
matrix.
@ -246,7 +255,7 @@ class Matrix:
ans += str(self.__matrix[i][j]) + "|\n"
return ans
def changeComponent(self, x, y, value):
def changeComponent(self, x: int, y: int, value: float) -> None:
"""
changes the x-y component of this matrix
"""
@ -255,7 +264,7 @@ class Matrix:
else:
raise Exception("changeComponent: indices out of bounds")
def component(self, x, y):
def component(self, x: int, y: int) -> float:
"""
returns the specified (x,y) component
"""
@ -264,13 +273,13 @@ class Matrix:
else:
raise Exception("changeComponent: indices out of bounds")
def width(self):
def width(self) -> int:
"""
getter for the width
"""
return self.__width
def height(self):
def height(self) -> int:
"""
getter for the height
"""
@ -303,7 +312,15 @@ class Matrix:
else:
raise Exception("matrix is not square")
def __mul__(self, other):
@overload
def __mul__(self, other: float) -> "Matrix":
...
@overload
def __mul__(self, other: Vector) -> Vector:
...
def __mul__(self, other: Union[float, Vector]) -> Union[Vector, "Matrix"]:
"""
implements the matrix-vector multiplication.
implements the matrix-scalar multiplication
@ -312,7 +329,7 @@ class Matrix:
if len(other) == self.__width:
ans = zeroVector(self.__height)
for i in range(self.__height):
summe = 0
summe: float = 0
for j in range(self.__width):
summe += other.component(j) * self.__matrix[i][j]
ans.changeComponent(i, summe)
@ -330,7 +347,7 @@ class Matrix:
]
return Matrix(matrix, self.__width, self.__height)
def __add__(self, other):
def __add__(self, other: "Matrix") -> "Matrix":
"""
implements the matrix-addition.
"""
@ -345,7 +362,7 @@ class Matrix:
else:
raise Exception("matrix must have the same dimension!")
def __sub__(self, other):
def __sub__(self, other: "Matrix") -> "Matrix":
"""
implements the matrix-subtraction.
"""
@ -361,19 +378,21 @@ class Matrix:
raise Exception("matrix must have the same dimension!")
def squareZeroMatrix(N):
def squareZeroMatrix(N: int) -> Matrix:
"""
returns a square zero-matrix of dimension NxN
"""
ans = [[0] * N for i in range(N)]
ans: list[list[float]] = [[0] * N for _ in range(N)]
return Matrix(ans, N, N)
def randomMatrix(W, H, a, b):
def randomMatrix(W: int, H: int, a: int, b: int) -> Matrix:
"""
returns a random matrix WxH with integer components
between 'a' and 'b'
"""
random.seed(None)
matrix = [[random.randint(a, b) for j in range(W)] for i in range(H)]
matrix: list[list[float]] = [
[random.randint(a, b) for _ in range(W)] for _ in range(H)
]
return Matrix(matrix, W, H)

13
linear_algebra/src/polynom_for_points.py
View File

@ -1,6 +1,3 @@
from __future__ import annotations
def points_to_polynomial(coordinates: list[list[int]]) -> str:
"""
coordinates is a two dimensional matrix: [[x, y], [x, y], ...]
@ -55,12 +52,12 @@ def points_to_polynomial(coordinates: list[list[int]]) -> str:
if check == 1:
count_of_line = 0
matrix = []
matrix: list[list[float]] = []
# put the x and x to the power values in a matrix
while count_of_line < x:
count_in_line = 0
a = coordinates[count_of_line][0]
count_line: list[int] = []
count_line: list[float] = []
while count_in_line < x:
count_line.append(a ** (x - (count_in_line + 1)))
count_in_line += 1
@ -69,7 +66,7 @@ def points_to_polynomial(coordinates: list[list[int]]) -> str:
count_of_line = 0
# put the y values into a vector
vector: list[int] = []
vector: list[float] = []
while count_of_line < x:
vector.append(coordinates[count_of_line][1])
count_of_line += 1
@ -96,14 +93,14 @@ def points_to_polynomial(coordinates: list[list[int]]) -> str:
# make solutions
solution: list[str] = []
while count < x:
solution.append(vector[count] / matrix[count][count])
solution.append(str(vector[count] / matrix[count][count]))
count += 1
count = 0
solved = "f(x)="
while count < x:
remove_e: list[str] = str(solution[count]).split("E")
remove_e: list[str] = solution[count].split("E")
if len(remove_e) > 1:
solution[count] = remove_e[0] + "*10^" + remove_e[1]
solved += "x^" + str(x - (count + 1)) + "*" + str(solution[count])

7
linear_algebra/src/power_iteration.py
View File

@ -2,8 +2,11 @@ import numpy as np
def power_iteration(
input_matrix: np.array, vector: np.array, error_tol=1e-12, max_iterations=100
) -> [float, np.array]:
input_matrix: np.ndarray,
vector: np.ndarray,
error_tol: float = 1e-12,
max_iterations: int = 100,
) -> tuple[float, np.ndarray]:
"""
Power Iteration.
Find the largest eignevalue and corresponding eigenvector

10
linear_algebra/src/rayleigh_quotient.py
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@ -1,10 +1,12 @@
"""
https://en.wikipedia.org/wiki/Rayleigh_quotient
"""
from typing import Any
import numpy as np
def is_hermitian(matrix: np.array) -> bool:
def is_hermitian(matrix: np.ndarray) -> bool:
"""
Checks if a matrix is Hermitian.
>>> import numpy as np
@ -24,7 +26,7 @@ def is_hermitian(matrix: np.array) -> bool:
return np.array_equal(matrix, matrix.conjugate().T)
def rayleigh_quotient(A: np.array, v: np.array) -> float:
def rayleigh_quotient(A: np.ndarray, v: np.ndarray) -> Any:
"""
Returns the Rayleigh quotient of a Hermitian matrix A and
vector v.
@ -43,7 +45,9 @@ def rayleigh_quotient(A: np.array, v: np.array) -> float:
array([[3.]])
"""
v_star = v.conjugate().T
return (v_star.dot(A).dot(v)) / (v_star.dot(v))
v_star_dot = v_star.dot(A)
assert isinstance(v_star_dot, np.ndarray)
return (v_star_dot.dot(v)) / (v_star.dot(v))
def tests() -> None:

40
linear_algebra/src/test_linear_algebra.py
View File

@ -12,7 +12,7 @@ from .lib import Matrix, Vector, axpy, squareZeroMatrix, unitBasisVector, zeroVe
class Test(unittest.TestCase):
def test_component(self):
def test_component(self) -> None:
"""
test for method component
"""
@ -21,28 +21,28 @@ class Test(unittest.TestCase):
self.assertEqual(x.component(2), 3)
_ = Vector()
def test_str(self):
def test_str(self) -> None:
"""
test for toString() method
"""
x = Vector([0, 0, 0, 0, 0, 1])
self.assertEqual(str(x), "(0,0,0,0,0,1)")
def test_size(self):
def test_size(self) -> None:
"""
test for size()-method
"""
x = Vector([1, 2, 3, 4])
self.assertEqual(len(x), 4)
def test_euclidLength(self):
def test_euclidLength(self) -> None:
"""
test for the eulidean length
"""
x = Vector([1, 2])
self.assertAlmostEqual(x.euclidLength(), 2.236, 3)
def test_add(self):
def test_add(self) -> None:
"""
test for + operator
"""
@ -52,7 +52,7 @@ class Test(unittest.TestCase):
self.assertEqual((x + y).component(1), 3)
self.assertEqual((x + y).component(2), 4)
def test_sub(self):
def test_sub(self) -> None:
"""
test for - operator
"""
@ -62,7 +62,7 @@ class Test(unittest.TestCase):
self.assertEqual((x - y).component(1), 1)
self.assertEqual((x - y).component(2), 2)
def test_mul(self):
def test_mul(self) -> None:
"""
test for * operator
"""
@ -72,19 +72,19 @@ class Test(unittest.TestCase):
self.assertEqual(str(x * 3.0), "(3.0,6.0,9.0)")
self.assertEqual((a * b), 0)
def test_zeroVector(self):
def test_zeroVector(self) -> None:
"""
test for the global function zeroVector(...)
"""
self.assertTrue(str(zeroVector(10)).count("0") == 10)
def test_unitBasisVector(self):
def test_unitBasisVector(self) -> None:
"""
test for the global function unitBasisVector(...)
"""
self.assertEqual(str(unitBasisVector(3, 1)), "(0,1,0)")
def test_axpy(self):
def test_axpy(self) -> None:
"""
test for the global function axpy(...) (operation)
"""
@ -92,7 +92,7 @@ class Test(unittest.TestCase):
y = Vector([1, 0, 1])
self.assertEqual(str(axpy(2, x, y)), "(3,4,7)")
def test_copy(self):
def test_copy(self) -> None:
"""
test for the copy()-method
"""
@ -100,7 +100,7 @@ class Test(unittest.TestCase):
y = x.copy()
self.assertEqual(str(x), str(y))
def test_changeComponent(self):
def test_changeComponent(self) -> None:
"""
test for the changeComponent(...)-method
"""
@ -109,43 +109,43 @@ class Test(unittest.TestCase):
x.changeComponent(1, 1)
self.assertEqual(str(x), "(0,1,0)")
def test_str_matrix(self):
def test_str_matrix(self) -> None:
A = Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]], 3, 3)
self.assertEqual("|1,2,3|\n|2,4,5|\n|6,7,8|\n", str(A))
def test_determinate(self):
def test_determinate(self) -> None:
"""
test for determinate()
"""
A = Matrix([[1, 1, 4, 5], [3, 3, 3, 2], [5, 1, 9, 0], [9, 7, 7, 9]], 4, 4)
self.assertEqual(-376, A.determinate())
def test__mul__matrix(self):
def test__mul__matrix(self) -> None:
A = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]], 3, 3)
x = Vector([1, 2, 3])
self.assertEqual("(14,32,50)", str(A * x))
self.assertEqual("|2,4,6|\n|8,10,12|\n|14,16,18|\n", str(A * 2))
def test_changeComponent_matrix(self):
def test_changeComponent_matrix(self) -> None:
A = Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]], 3, 3)
A.changeComponent(0, 2, 5)
self.assertEqual("|1,2,5|\n|2,4,5|\n|6,7,8|\n", str(A))
def test_component_matrix(self):
def test_component_matrix(self) -> None:
A = Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]], 3, 3)
self.assertEqual(7, A.component(2, 1), 0.01)
def test__add__matrix(self):
def test__add__matrix(self) -> None:
A = Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]], 3, 3)
B = Matrix([[1, 2, 7], [2, 4, 5], [6, 7, 10]], 3, 3)
self.assertEqual("|2,4,10|\n|4,8,10|\n|12,14,18|\n", str(A + B))
def test__sub__matrix(self):
def test__sub__matrix(self) -> None:
A = Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]], 3, 3)
B = Matrix([[1, 2, 7], [2, 4, 5], [6, 7, 10]], 3, 3)
self.assertEqual("|0,0,-4|\n|0,0,0|\n|0,0,-2|\n", str(A - B))
def test_squareZeroMatrix(self):
def test_squareZeroMatrix(self) -> None:
self.assertEqual(
"|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|" + "\n|0,0,0,0,0|\n",
str(squareZeroMatrix(5)),

2
linear_algebra/src/transformations_2d.py
View File

@ -11,8 +11,6 @@ projection(45) = [[0.27596319193541496, 0.446998331800279],
reflection(45) = [[0.05064397763545947, 0.893996663600558],
[0.893996663600558, 0.7018070490682369]]
"""
from __future__ import annotations
from math import cos, sin