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def __len__(self) -> int:
return len(self.bodies) | physics |
def update_system(self, delta_time: float) -> None:
for body1 in self.bodies:
force_x = 0.0
force_y = 0.0
for body2 in self.bodies:
if body1 != body2:
dif_x = body2.position_x - body1.position_x
dif_y = body2.position_y - body1.position_y
# Calculation of the distance using Pythagoras's theorem
# Extra factor due to the softening technique
distance = (dif_x**2 + dif_y**2 + self.softening_factor) ** (
1 / 2
)
# Newton's law of universal gravitation.
force_x += (
self.gravitation_constant * body2.mass * dif_x / distance**3
)
force_y += (
self.gravitation_constant * body2.mass * dif_y / distance**3
)
# Update the body's velocity once all the force components have been added
body1.update_velocity(force_x, force_y, delta_time * self.time_factor)
# Update the positions only after all the velocities have been updated
for body in self.bodies:
body.update_position(delta_time * self.time_factor) | physics |
def update_step(
body_system: BodySystem, delta_time: float, patches: list[plt.Circle]
) -> None:
# Update the positions of the bodies
body_system.update_system(delta_time)
# Update the positions of the patches
for patch, body in zip(patches, body_system.bodies):
patch.center = (body.position_x, body.position_y) | physics |
def update(frame: int) -> list[plt.Circle]:
update_step(body_system, DELTA_TIME, patches)
return patches | physics |
def example_1() -> BodySystem:
position_x = 0.9700436
position_y = -0.24308753
velocity_x = 0.466203685
velocity_y = 0.43236573
bodies1 = [
Body(position_x, position_y, velocity_x, velocity_y, size=0.2, color="red"),
Body(-position_x, -position_y, velocity_x, velocity_y, size=0.2, color="green"),
Body(0, 0, -2 * velocity_x, -2 * velocity_y, size=0.2, color="blue"),
]
return BodySystem(bodies1, time_factor=3) | physics |
def example_2() -> BodySystem:
moon_mass = 7.3476e22
earth_mass = 5.972e24
velocity_dif = 1022
earth_moon_distance = 384399000
gravitation_constant = 6.674e-11
# Calculation of the respective velocities so that total impulse is zero,
# i.e. the two bodies together don't move
moon_velocity = earth_mass * velocity_dif / (earth_mass + moon_mass)
earth_velocity = moon_velocity - velocity_dif
moon = Body(-earth_moon_distance, 0, 0, moon_velocity, moon_mass, 10000000, "grey")
earth = Body(0, 0, 0, earth_velocity, earth_mass, 50000000, "blue")
return BodySystem([earth, moon], gravitation_constant, time_factor=1000000) | physics |
def example_3() -> BodySystem:
bodies = []
for _ in range(10):
velocity_x = random.uniform(-0.5, 0.5)
velocity_y = random.uniform(-0.5, 0.5)
# Bodies are created pairwise with opposite velocities so that the
# total impulse remains zero
bodies.append(
Body(
random.uniform(-0.5, 0.5),
random.uniform(-0.5, 0.5),
velocity_x,
velocity_y,
size=0.05,
)
)
bodies.append(
Body(
random.uniform(-0.5, 0.5),
random.uniform(-0.5, 0.5),
-velocity_x,
-velocity_y,
size=0.05,
)
)
return BodySystem(bodies, 0.01, 10, 0.1) | physics |
def _is_matrix_spd(matrix: np.ndarray) -> bool:
# Ensure matrix is square.
assert np.shape(matrix)[0] == np.shape(matrix)[1]
# If matrix not symmetric, exit right away.
if np.allclose(matrix, matrix.T) is False:
return False
# Get eigenvalues and eignevectors for a symmetric matrix.
eigen_values, _ = np.linalg.eigh(matrix)
# Check sign of all eigenvalues.
# np.all returns a value of type np.bool_
return bool(np.all(eigen_values > 0)) | linear_algebra |
def _create_spd_matrix(dimension: int) -> Any:
random_matrix = np.random.randn(dimension, dimension)
spd_matrix = np.dot(random_matrix, random_matrix.T)
assert _is_matrix_spd(spd_matrix)
return spd_matrix | linear_algebra |
def conjugate_gradient(
spd_matrix: np.ndarray,
load_vector: np.ndarray,
max_iterations: int = 1000,
tol: float = 1e-8,
) -> Any:
# Ensure proper dimensionality.
assert np.shape(spd_matrix)[0] == np.shape(spd_matrix)[1]
assert np.shape(load_vector)[0] == np.shape(spd_matrix)[0]
assert _is_matrix_spd(spd_matrix)
# Initialize solution guess, residual, search direction.
x0 = np.zeros((np.shape(load_vector)[0], 1))
r0 = np.copy(load_vector)
p0 = np.copy(r0)
# Set initial errors in solution guess and residual.
error_residual = 1e9
error_x_solution = 1e9
error = 1e9
# Set iteration counter to threshold number of iterations.
iterations = 0
while error > tol:
# Save this value so we only calculate the matrix-vector product once.
w = np.dot(spd_matrix, p0)
# The main algorithm.
# Update search direction magnitude.
alpha = np.dot(r0.T, r0) / np.dot(p0.T, w)
# Update solution guess.
x = x0 + alpha * p0
# Calculate new residual.
r = r0 - alpha * w
# Calculate new Krylov subspace scale.
beta = np.dot(r.T, r) / np.dot(r0.T, r0)
# Calculate new A conjuage search direction.
p = r + beta * p0
# Calculate errors.
error_residual = np.linalg.norm(r - r0)
error_x_solution = np.linalg.norm(x - x0)
error = np.maximum(error_residual, error_x_solution)
# Update variables.
x0 = np.copy(x)
r0 = np.copy(r)
p0 = np.copy(p)
# Update number of iterations.
iterations += 1
if iterations > max_iterations:
break
return x | linear_algebra |
def test_conjugate_gradient() -> None:
# Create linear system with SPD matrix and known solution x_true.
dimension = 3
spd_matrix = _create_spd_matrix(dimension)
x_true = np.random.randn(dimension, 1)
b = np.dot(spd_matrix, x_true)
# Numpy solution.
x_numpy = np.linalg.solve(spd_matrix, b)
# Our implementation.
x_conjugate_gradient = conjugate_gradient(spd_matrix, b)
# Ensure both solutions are close to x_true (and therefore one another).
assert np.linalg.norm(x_numpy - x_true) <= 1e-6
assert np.linalg.norm(x_conjugate_gradient - x_true) <= 1e-6 | linear_algebra |
def points_to_polynomial(coordinates: list[list[int]]) -> str:
if len(coordinates) == 0 or not all(len(pair) == 2 for pair in coordinates):
raise ValueError("The program cannot work out a fitting polynomial.")
if len({tuple(pair) for pair in coordinates}) != len(coordinates):
raise ValueError("The program cannot work out a fitting polynomial.")
set_x = {x for x, _ in coordinates}
if len(set_x) == 1:
return f"x={coordinates[0][0]}"
if len(set_x) != len(coordinates):
raise ValueError("The program cannot work out a fitting polynomial.")
x = len(coordinates)
count_of_line = 0
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[float] = []
while count_in_line < x:
count_line.append(a ** (x - (count_in_line + 1)))
count_in_line += 1
matrix.append(count_line)
count_of_line += 1
count_of_line = 0
# put the y values into a vector
vector: list[float] = []
while count_of_line < x:
vector.append(coordinates[count_of_line][1])
count_of_line += 1
count = 0
while count < x:
zahlen = 0
while zahlen < x:
if count == zahlen:
zahlen += 1
if zahlen == x:
break
bruch = matrix[zahlen][count] / matrix[count][count]
for counting_columns, item in enumerate(matrix[count]):
# manipulating all the values in the matrix
matrix[zahlen][counting_columns] -= item * bruch
# manipulating the values in the vector
vector[zahlen] -= vector[count] * bruch
zahlen += 1
count += 1
count = 0
# make solutions
solution: list[str] = []
while count < x:
solution.append(str(vector[count] / matrix[count][count]))
count += 1
count = 0
solved = "f(x)="
while count < x:
remove_e: list[str] = solution[count].split("E")
if len(remove_e) > 1:
solution[count] = f"{remove_e[0]}*10^{remove_e[1]}"
solved += f"x^{x - (count + 1)}*{solution[count]}"
if count + 1 != x:
solved += "+"
count += 1
return solved | linear_algebra |
def __init__(self, components: Collection[float] | None = None) -> None:
if components is None:
components = []
self.__components = list(components) | linear_algebra |
def __len__(self) -> int:
return len(self.__components) | linear_algebra |
def __str__(self) -> str:
return "(" + ",".join(map(str, self.__components)) + ")" | linear_algebra |
def __add__(self, other: Vector) -> Vector:
size = len(self)
if size == len(other):
result = [self.__components[i] + other.component(i) for i in range(size)]
return Vector(result)
else:
raise Exception("must have the same size") | linear_algebra |
def __sub__(self, other: Vector) -> Vector:
size = len(self)
if size == len(other):
result = [self.__components[i] - other.component(i) for i in range(size)]
return Vector(result)
else: # error case
raise Exception("must have the same size") | linear_algebra |
def __mul__(self, other: float) -> Vector:
... | linear_algebra |
def __mul__(self, other: Vector) -> float:
... | linear_algebra |
def __mul__(self, other: float | Vector) -> float | Vector:
if isinstance(other, (float, int)):
ans = [c * other for c in self.__components]
return Vector(ans)
elif isinstance(other, Vector) and len(self) == len(other):
size = len(self)
prods = [self.__components[i] * other.component(i) for i in range(size)]
return sum(prods)
else: # error case
raise Exception("invalid operand!") | linear_algebra |
def copy(self) -> Vector:
return Vector(self.__components) | linear_algebra |
def component(self, i: int) -> float:
if isinstance(i, int) and -len(self.__components) <= i < len(self.__components):
return self.__components[i]
else:
raise Exception("index out of range") | linear_algebra |
def change_component(self, pos: int, value: float) -> None:
# precondition
assert -len(self.__components) <= pos < len(self.__components)
self.__components[pos] = value | linear_algebra |
def euclidean_length(self) -> float:
if len(self.__components) == 0:
raise Exception("Vector is empty")
squares = [c**2 for c in self.__components]
return math.sqrt(sum(squares)) | linear_algebra |
def angle(self, other: Vector, deg: bool = False) -> float:
num = self * other
den = self.euclidean_length() * other.euclidean_length()
if deg:
return math.degrees(math.acos(num / den))
else:
return math.acos(num / den) | linear_algebra |
def zero_vector(dimension: int) -> Vector:
# precondition
assert isinstance(dimension, int)
return Vector([0] * dimension) | linear_algebra |
def unit_basis_vector(dimension: int, pos: int) -> Vector:
# precondition
assert isinstance(dimension, int) and (isinstance(pos, int))
ans = [0] * dimension
ans[pos] = 1
return Vector(ans) | linear_algebra |
def axpy(scalar: float, x: Vector, y: Vector) -> Vector:
# precondition
assert (
isinstance(x, Vector)
and isinstance(y, Vector)
and (isinstance(scalar, (int, float)))
)
return x * scalar + y | linear_algebra |
def random_vector(n: int, a: int, b: int) -> Vector:
random.seed(None)
ans = [random.randint(a, b) for _ in range(n)]
return Vector(ans) | linear_algebra |
def __init__(self, matrix: list[list[float]], w: int, h: int) -> None:
self.__matrix = matrix
self.__width = w
self.__height = h | linear_algebra |
def __str__(self) -> str:
ans = ""
for i in range(self.__height):
ans += "|"
for j in range(self.__width):
if j < self.__width - 1:
ans += str(self.__matrix[i][j]) + ","
else:
ans += str(self.__matrix[i][j]) + "|\n"
return ans | linear_algebra |
def __add__(self, other: Matrix) -> Matrix:
if self.__width == other.width() and self.__height == other.height():
matrix = []
for i in range(self.__height):
row = [
self.__matrix[i][j] + other.component(i, j)
for j in range(self.__width)
]
matrix.append(row)
return Matrix(matrix, self.__width, self.__height)
else:
raise Exception("matrix must have the same dimension!") | linear_algebra |
def __sub__(self, other: Matrix) -> Matrix:
if self.__width == other.width() and self.__height == other.height():
matrix = []
for i in range(self.__height):
row = [
self.__matrix[i][j] - other.component(i, j)
for j in range(self.__width)
]
matrix.append(row)
return Matrix(matrix, self.__width, self.__height)
else:
raise Exception("matrices must have the same dimension!") | linear_algebra |
def __mul__(self, other: float) -> Matrix:
... | linear_algebra |
def __mul__(self, other: Vector) -> Vector:
... | linear_algebra |
def __mul__(self, other: float | Vector) -> Vector | Matrix:
if isinstance(other, Vector): # matrix-vector
if len(other) == self.__width:
ans = zero_vector(self.__height)
for i in range(self.__height):
prods = [
self.__matrix[i][j] * other.component(j)
for j in range(self.__width)
]
ans.change_component(i, sum(prods))
return ans
else:
raise Exception(
"vector must have the same size as the "
"number of columns of the matrix!"
)
elif isinstance(other, (int, float)): # matrix-scalar
matrix = [
[self.__matrix[i][j] * other for j in range(self.__width)]
for i in range(self.__height)
]
return Matrix(matrix, self.__width, self.__height)
return None | linear_algebra |
def height(self) -> int:
return self.__height | linear_algebra |
def width(self) -> int:
return self.__width | linear_algebra |
def component(self, x: int, y: int) -> float:
if 0 <= x < self.__height and 0 <= y < self.__width:
return self.__matrix[x][y]
else:
raise Exception("change_component: indices out of bounds") | linear_algebra |
def change_component(self, x: int, y: int, value: float) -> None:
if 0 <= x < self.__height and 0 <= y < self.__width:
self.__matrix[x][y] = value
else:
raise Exception("change_component: indices out of bounds") | linear_algebra |
def minor(self, x: int, y: int) -> float:
if self.__height != self.__width:
raise Exception("Matrix is not square")
minor = self.__matrix[:x] + self.__matrix[x + 1 :]
for i in range(len(minor)):
minor[i] = minor[i][:y] + minor[i][y + 1 :]
return Matrix(minor, self.__width - 1, self.__height - 1).determinant() | linear_algebra |
def cofactor(self, x: int, y: int) -> float:
if self.__height != self.__width:
raise Exception("Matrix is not square")
if 0 <= x < self.__height and 0 <= y < self.__width:
return (-1) ** (x + y) * self.minor(x, y)
else:
raise Exception("Indices out of bounds") | linear_algebra |
def determinant(self) -> float:
if self.__height != self.__width:
raise Exception("Matrix is not square")
if self.__height < 1:
raise Exception("Matrix has no element")
elif self.__height == 1:
return self.__matrix[0][0]
elif self.__height == 2:
return (
self.__matrix[0][0] * self.__matrix[1][1]
- self.__matrix[0][1] * self.__matrix[1][0]
)
else:
cofactor_prods = [
self.__matrix[0][y] * self.cofactor(0, y) for y in range(self.__width)
]
return sum(cofactor_prods) | linear_algebra |
def square_zero_matrix(n: int) -> Matrix:
ans: list[list[float]] = [[0] * n for _ in range(n)]
return Matrix(ans, n, n) | linear_algebra |
def power_iteration(
input_matrix: np.ndarray,
vector: np.ndarray,
error_tol: float = 1e-12,
max_iterations: int = 100,
) -> tuple[float, np.ndarray]:
# Ensure matrix is square.
assert np.shape(input_matrix)[0] == np.shape(input_matrix)[1]
# Ensure proper dimensionality.
assert np.shape(input_matrix)[0] == np.shape(vector)[0]
# Ensure inputs are either both complex or both real
assert np.iscomplexobj(input_matrix) == np.iscomplexobj(vector)
is_complex = np.iscomplexobj(input_matrix)
if is_complex:
# Ensure complex input_matrix is Hermitian
assert np.array_equal(input_matrix, input_matrix.conj().T)
# Set convergence to False. Will define convergence when we exceed max_iterations
# or when we have small changes from one iteration to next.
convergence = False
lambda_previous = 0
iterations = 0
error = 1e12
while not convergence:
# Multiple matrix by the vector.
w = np.dot(input_matrix, vector)
# Normalize the resulting output vector.
vector = w / np.linalg.norm(w)
# Find rayleigh quotient
# (faster than usual b/c we know vector is normalized already)
vector_h = vector.conj().T if is_complex else vector.T
lambda_ = np.dot(vector_h, np.dot(input_matrix, vector))
# Check convergence.
error = np.abs(lambda_ - lambda_previous) / lambda_
iterations += 1
if error <= error_tol or iterations >= max_iterations:
convergence = True
lambda_previous = lambda_
if is_complex:
lambda_ = np.real(lambda_)
return lambda_, vector | linear_algebra |
def test_power_iteration() -> None:
real_input_matrix = np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]])
real_vector = np.array([41, 4, 20])
complex_input_matrix = real_input_matrix.astype(np.complex128)
imag_matrix = np.triu(1j * complex_input_matrix, 1)
complex_input_matrix += imag_matrix
complex_input_matrix += -1 * imag_matrix.T
complex_vector = np.array([41, 4, 20]).astype(np.complex128)
for problem_type in ["real", "complex"]:
if problem_type == "real":
input_matrix = real_input_matrix
vector = real_vector
elif problem_type == "complex":
input_matrix = complex_input_matrix
vector = complex_vector
# Our implementation.
eigen_value, eigen_vector = power_iteration(input_matrix, vector)
# Numpy implementation.
# Get eigenvalues and eigenvectors using built-in numpy
# eigh (eigh used for symmetric or hermetian matrices).
eigen_values, eigen_vectors = np.linalg.eigh(input_matrix)
# Last eigenvalue is the maximum one.
eigen_value_max = eigen_values[-1]
# Last column in this matrix is eigenvector corresponding to largest eigenvalue.
eigen_vector_max = eigen_vectors[:, -1]
# Check our implementation and numpy gives close answers.
assert np.abs(eigen_value - eigen_value_max) <= 1e-6
# Take absolute values element wise of each eigenvector.
# as they are only unique to a minus sign.
assert np.linalg.norm(np.abs(eigen_vector) - np.abs(eigen_vector_max)) <= 1e-6 | linear_algebra |
def schur_complement(
mat_a: np.ndarray,
mat_b: np.ndarray,
mat_c: np.ndarray,
pseudo_inv: np.ndarray | None = None,
) -> np.ndarray:
shape_a = np.shape(mat_a)
shape_b = np.shape(mat_b)
shape_c = np.shape(mat_c)
if shape_a[0] != shape_b[0]:
raise ValueError(
f"Expected the same number of rows for A and B. \
Instead found A of size {shape_a} and B of size {shape_b}"
)
if shape_b[1] != shape_c[1]:
raise ValueError(
f"Expected the same number of columns for B and C. \
Instead found B of size {shape_b} and C of size {shape_c}"
)
a_inv = pseudo_inv
if a_inv is None:
try:
a_inv = np.linalg.inv(mat_a)
except np.linalg.LinAlgError:
raise ValueError(
"Input matrix A is not invertible. Cannot compute Schur complement."
)
return mat_c - mat_b.T @ a_inv @ mat_b | linear_algebra |
def test_schur_complement(self) -> None:
a = np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]])
b = np.array([[0, 3], [3, 0], [2, 3]])
c = np.array([[2, 1], [6, 3]])
s = schur_complement(a, b, c)
input_matrix = np.block([[a, b], [b.T, c]])
det_x = np.linalg.det(input_matrix)
det_a = np.linalg.det(a)
det_s = np.linalg.det(s)
self.assertAlmostEqual(det_x, det_a * det_s) | linear_algebra |
def test_improper_a_b_dimensions(self) -> None:
a = np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]])
b = np.array([[0, 3], [3, 0], [2, 3]])
c = np.array([[2, 1], [6, 3]])
with self.assertRaises(ValueError):
schur_complement(a, b, c) | linear_algebra |
def test_improper_b_c_dimensions(self) -> None:
a = np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]])
b = np.array([[0, 3], [3, 0], [2, 3]])
c = np.array([[2, 1, 3], [6, 3, 5]])
with self.assertRaises(ValueError):
schur_complement(a, b, c) | linear_algebra |
def test_component(self) -> None:
x = Vector([1, 2, 3])
self.assertEqual(x.component(0), 1)
self.assertEqual(x.component(2), 3)
_ = Vector() | linear_algebra |
def test_str(self) -> None:
x = Vector([0, 0, 0, 0, 0, 1])
self.assertEqual(str(x), "(0,0,0,0,0,1)") | linear_algebra |
def test_size(self) -> None:
x = Vector([1, 2, 3, 4])
self.assertEqual(len(x), 4) | linear_algebra |
def test_euclidean_length(self) -> None:
x = Vector([1, 2])
y = Vector([1, 2, 3, 4, 5])
z = Vector([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
w = Vector([1, -1, 1, -1, 2, -3, 4, -5])
self.assertAlmostEqual(x.euclidean_length(), 2.236, 3)
self.assertAlmostEqual(y.euclidean_length(), 7.416, 3)
self.assertEqual(z.euclidean_length(), 0)
self.assertAlmostEqual(w.euclidean_length(), 7.616, 3) | linear_algebra |
def test_add(self) -> None:
x = Vector([1, 2, 3])
y = Vector([1, 1, 1])
self.assertEqual((x + y).component(0), 2)
self.assertEqual((x + y).component(1), 3)
self.assertEqual((x + y).component(2), 4) | linear_algebra |
def test_sub(self) -> None:
x = Vector([1, 2, 3])
y = Vector([1, 1, 1])
self.assertEqual((x - y).component(0), 0)
self.assertEqual((x - y).component(1), 1)
self.assertEqual((x - y).component(2), 2) | linear_algebra |
def test_mul(self) -> None:
x = Vector([1, 2, 3])
a = Vector([2, -1, 4]) # for test of dot product
b = Vector([1, -2, -1])
self.assertEqual(str(x * 3.0), "(3.0,6.0,9.0)")
self.assertEqual((a * b), 0) | linear_algebra |
def test_zero_vector(self) -> None:
self.assertEqual(str(zero_vector(10)).count("0"), 10) | linear_algebra |
def test_unit_basis_vector(self) -> None:
self.assertEqual(str(unit_basis_vector(3, 1)), "(0,1,0)") | linear_algebra |
def test_axpy(self) -> None:
x = Vector([1, 2, 3])
y = Vector([1, 0, 1])
self.assertEqual(str(axpy(2, x, y)), "(3,4,7)") | linear_algebra |
def test_copy(self) -> None:
x = Vector([1, 0, 0, 0, 0, 0])
y = x.copy()
self.assertEqual(str(x), str(y)) | linear_algebra |
def test_change_component(self) -> None:
x = Vector([1, 0, 0])
x.change_component(0, 0)
x.change_component(1, 1)
self.assertEqual(str(x), "(0,1,0)") | linear_algebra |
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)) | linear_algebra |
def test_minor(self) -> None:
a = Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]], 3, 3)
minors = [[-3, -14, -10], [-5, -10, -5], [-2, -1, 0]]
for x in range(a.height()):
for y in range(a.width()):
self.assertEqual(minors[x][y], a.minor(x, y)) | linear_algebra |
def test_cofactor(self) -> None:
a = Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]], 3, 3)
cofactors = [[-3, 14, -10], [5, -10, 5], [-2, 1, 0]]
for x in range(a.height()):
for y in range(a.width()):
self.assertEqual(cofactors[x][y], a.cofactor(x, y)) | linear_algebra |
def test_determinant(self) -> None:
a = Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]], 3, 3)
self.assertEqual(-5, a.determinant()) | linear_algebra |
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)) | linear_algebra |
def test_change_component_matrix(self) -> None:
a = Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]], 3, 3)
a.change_component(0, 2, 5)
self.assertEqual("|1,2,5|\n|2,4,5|\n|6,7,8|\n", str(a)) | linear_algebra |
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) | linear_algebra |
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)) | linear_algebra |
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)) | linear_algebra |
def test_square_zero_matrix(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(square_zero_matrix(5)),
) | linear_algebra |
def scaling(scaling_factor: float) -> list[list[float]]:
scaling_factor = float(scaling_factor)
return [[scaling_factor * int(x == y) for x in range(2)] for y in range(2)] | linear_algebra |
def rotation(angle: float) -> list[list[float]]:
c, s = cos(angle), sin(angle)
return [[c, -s], [s, c]] | linear_algebra |
def projection(angle: float) -> list[list[float]]:
c, s = cos(angle), sin(angle)
cs = c * s
return [[c * c, cs], [cs, s * s]] | linear_algebra |
def reflection(angle: float) -> list[list[float]]:
c, s = cos(angle), sin(angle)
cs = c * s
return [[2 * c - 1, 2 * cs], [2 * cs, 2 * s - 1]] | linear_algebra |
def is_hermitian(matrix: np.ndarray) -> bool:
return np.array_equal(matrix, matrix.conjugate().T) | linear_algebra |
def rayleigh_quotient(a: np.ndarray, v: np.ndarray) -> Any:
v_star = v.conjugate().T
v_star_dot = v_star.dot(a)
assert isinstance(v_star_dot, np.ndarray)
return (v_star_dot.dot(v)) / (v_star.dot(v)) | linear_algebra |
def tests() -> None:
a = np.array([[2, 2 + 1j, 4], [2 - 1j, 3, 1j], [4, -1j, 1]])
v = np.array([[1], [2], [3]])
assert is_hermitian(a), f"{a} is not hermitian."
print(rayleigh_quotient(a, v))
a = np.array([[1, 2, 4], [2, 3, -1], [4, -1, 1]])
assert is_hermitian(a), f"{a} is not hermitian."
assert rayleigh_quotient(a, v) == float(3) | linear_algebra |
def __init__(self, list_of_points: list[tuple[float, float]]):
self.list_of_points = list_of_points
# Degree determines the flexibility of the curve.
# Degree = 1 will produce a straight line.
self.degree = len(list_of_points) - 1 | graphics |
def basis_function(self, t: float) -> list[float]:
assert 0 <= t <= 1, "Time t must be between 0 and 1."
output_values: list[float] = []
for i in range(len(self.list_of_points)):
# basis function for each i
output_values.append(
comb(self.degree, i) * ((1 - t) ** (self.degree - i)) * (t**i)
)
# the basis must sum up to 1 for it to produce a valid Bezier curve.
assert round(sum(output_values), 5) == 1
return output_values | graphics |
def bezier_curve_function(self, t: float) -> tuple[float, float]:
assert 0 <= t <= 1, "Time t must be between 0 and 1."
basis_function = self.basis_function(t)
x = 0.0
y = 0.0
for i in range(len(self.list_of_points)):
# For all points, sum up the product of i-th basis function and i-th point.
x += basis_function[i] * self.list_of_points[i][0]
y += basis_function[i] * self.list_of_points[i][1]
return (x, y) | graphics |
def plot_curve(self, step_size: float = 0.01):
from matplotlib import pyplot as plt # type: ignore
to_plot_x: list[float] = [] # x coordinates of points to plot
to_plot_y: list[float] = [] # y coordinates of points to plot
t = 0.0
while t <= 1:
value = self.bezier_curve_function(t)
to_plot_x.append(value[0])
to_plot_y.append(value[1])
t += step_size
x = [i[0] for i in self.list_of_points]
y = [i[1] for i in self.list_of_points]
plt.plot(
to_plot_x,
to_plot_y,
color="blue",
label="Curve of Degree " + str(self.degree),
)
plt.scatter(x, y, color="red", label="Control Points")
plt.legend()
plt.show() | graphics |
def convert_to_2d(
x: float, y: float, z: float, scale: float, distance: float
) -> tuple[float, float]:
if not all(isinstance(val, (float, int)) for val in locals().values()):
raise TypeError(
"Input values must either be float or int: " f"{list(locals().values())}"
)
projected_x = ((x * distance) / (z + distance)) * scale
projected_y = ((y * distance) / (z + distance)) * scale
return projected_x, projected_y | graphics |
def rotate(
x: float, y: float, z: float, axis: str, angle: float
) -> tuple[float, float, float]:
if not isinstance(axis, str):
raise TypeError("Axis must be a str")
input_variables = locals()
del input_variables["axis"]
if not all(isinstance(val, (float, int)) for val in input_variables.values()):
raise TypeError(
"Input values except axis must either be float or int: "
f"{list(input_variables.values())}"
)
angle = (angle % 360) / 450 * 180 / math.pi
if axis == "z":
new_x = x * math.cos(angle) - y * math.sin(angle)
new_y = y * math.cos(angle) + x * math.sin(angle)
new_z = z
elif axis == "x":
new_y = y * math.cos(angle) - z * math.sin(angle)
new_z = z * math.cos(angle) + y * math.sin(angle)
new_x = x
elif axis == "y":
new_x = x * math.cos(angle) - z * math.sin(angle)
new_z = z * math.cos(angle) + x * math.sin(angle)
new_y = y
else:
raise ValueError("not a valid axis, choose one of 'x', 'y', 'z'")
return new_x, new_y, new_z | graphics |
def covid_stats(url: str = "https://www.worldometers.info/coronavirus/") -> covid_data:
xpath_str = '//div[@class = "maincounter-number"]/span/text()'
return covid_data(*html.fromstring(requests.get(url).content).xpath(xpath_str)) | web_programming |
def get_hackernews_story(story_id: str) -> dict:
url = f"https://hacker-news.firebaseio.com/v0/item/{story_id}.json?print=pretty"
return requests.get(url).json() | web_programming |
def hackernews_top_stories(max_stories: int = 10) -> list[dict]:
url = "https://hacker-news.firebaseio.com/v0/topstories.json?print=pretty"
story_ids = requests.get(url).json()[:max_stories]
return [get_hackernews_story(story_id) for story_id in story_ids] | web_programming |
def hackernews_top_stories_as_markdown(max_stories: int = 10) -> str:
stories = hackernews_top_stories(max_stories)
return "\n".join("* [{title}]({url})".format(**story) for story in stories) | web_programming |
def get_imdb_top_250_movies(url: str = "") -> dict[str, float]:
url = url or "https://www.imdb.com/chart/top/?ref_=nv_mv_250"
soup = BeautifulSoup(requests.get(url).text, "html.parser")
titles = soup.find_all("td", attrs="titleColumn")
ratings = soup.find_all("td", class_="ratingColumn imdbRating")
return {
title.a.text: float(rating.strong.text)
for title, rating in zip(titles, ratings)
} | web_programming |
def write_movies(filename: str = "IMDb_Top_250_Movies.csv") -> None:
movies = get_imdb_top_250_movies()
with open(filename, "w", newline="") as out_file:
writer = csv.writer(out_file)
writer.writerow(["Movie title", "IMDb rating"])
for title, rating in movies.items():
writer.writerow([title, rating]) | web_programming |
def quote_of_the_day() -> list:
return requests.get(API_ENDPOINT_URL + "/today").json() | web_programming |
def random_quotes() -> list:
return requests.get(API_ENDPOINT_URL + "/random").json() | web_programming |
def fetch_jobs(location: str = "mumbai") -> Generator[tuple[str, str], None, None]:
soup = BeautifulSoup(requests.get(url + location).content, "html.parser")
# This attribute finds out all the specifics listed in a job
for job in soup.find_all("div", attrs={"data-tn-component": "organicJob"}):
job_title = job.find("a", attrs={"data-tn-element": "jobTitle"}).text.strip()
company_name = job.find("span", {"class": "company"}).text.strip()
yield job_title, company_name | web_programming |
def get_amazon_product_data(product: str = "laptop") -> DataFrame:
url = f"https://www.amazon.in/laptop/s?k={product}"
header = {
"Accept-Language": "en-US, en;q=0.5",
}
soup = BeautifulSoup(requests.get(url, headers=header).text)
# Initialize a Pandas dataframe with the column titles
data_frame = DataFrame(
columns=[
"Product Title",
"Product Link",
"Current Price of the product",
"Product Rating",
"MRP of the product",
"Discount",
]
)
# Loop through each entry and store them in the dataframe
for item, _ in zip_longest(
soup.find_all(
"div",
attrs={"class": "s-result-item", "data-component-type": "s-search-result"},
),
soup.find_all("div", attrs={"class": "a-row a-size-base a-color-base"}),
):
try:
product_title = item.h2.text
product_link = "https://www.amazon.in/" + item.h2.a["href"]
product_price = item.find("span", attrs={"class": "a-offscreen"}).text
try:
product_rating = item.find("span", attrs={"class": "a-icon-alt"}).text
except AttributeError:
product_rating = "Not available"
try:
product_mrp = (
"₹"
+ item.find(
"span", attrs={"class": "a-price a-text-price"}
).text.split("₹")[1]
)
except AttributeError:
product_mrp = ""
try:
discount = float(
(
(
float(product_mrp.strip("₹").replace(",", ""))
- float(product_price.strip("₹").replace(",", ""))
)
/ float(product_mrp.strip("₹").replace(",", ""))
)
* 100
)
except ValueError:
discount = float("nan")
except AttributeError:
pass
data_frame.loc[len(data_frame.index)] = [
product_title,
product_link,
product_price,
product_rating,
product_mrp,
discount,
]
data_frame.loc[
data_frame["Current Price of the product"] > data_frame["MRP of the product"],
"MRP of the product",
] = " "
data_frame.loc[
data_frame["Current Price of the product"] > data_frame["MRP of the product"],
"Discount",
] = " "
data_frame.index += 1
return data_frame | web_programming |
def convert(number: int) -> str:
if number == 0:
words = "Zero"
return words
else:
digits = math.log10(number)
digits = digits + 1
singles = {}
singles[0] = ""
singles[1] = "One"
singles[2] = "Two"
singles[3] = "Three"
singles[4] = "Four"
singles[5] = "Five"
singles[6] = "Six"
singles[7] = "Seven"
singles[8] = "Eight"
singles[9] = "Nine"
doubles = {}
doubles[0] = ""
doubles[2] = "Twenty"
doubles[3] = "Thirty"
doubles[4] = "Forty"
doubles[5] = "Fifty"
doubles[6] = "Sixty"
doubles[7] = "Seventy"
doubles[8] = "Eighty"
doubles[9] = "Ninety"
teens = {}
teens[0] = "Ten"
teens[1] = "Eleven"
teens[2] = "Twelve"
teens[3] = "Thirteen"
teens[4] = "Fourteen"
teens[5] = "Fifteen"
teens[6] = "Sixteen"
teens[7] = "Seventeen"
teens[8] = "Eighteen"
teens[9] = "Nineteen"
placevalue = {}
placevalue[2] = "Hundred,"
placevalue[3] = "Thousand,"
placevalue[5] = "Lakh,"
placevalue[7] = "Crore,"
temp_num = number
words = ""
counter = 0
digits = int(digits)
while counter < digits:
current = temp_num % 10
if counter % 2 == 0:
addition = ""
if counter in placevalue and current != 0:
addition = placevalue[counter]
if counter == 2:
words = singles[current] + addition + words
elif counter == 0:
if ((temp_num % 100) // 10) == 1:
words = teens[current] + addition + words
temp_num = temp_num // 10
counter += 1
else:
words = singles[current] + addition + words
else:
words = doubles[current] + addition + words
else:
if counter == 1:
if current == 1:
words = teens[number % 10] + words
else:
addition = ""
if counter in placevalue:
addition = placevalue[counter]
words = doubles[current] + addition + words
else:
addition = ""
if counter in placevalue:
if current == 0 and ((temp_num % 100) // 10) == 0:
addition = ""
else:
addition = placevalue[counter]
if ((temp_num % 100) // 10) == 1:
words = teens[current] + addition + words
temp_num = temp_num // 10
counter += 1
else:
words = singles[current] + addition + words
counter += 1
temp_num = temp_num // 10
return words | web_programming |
def __init__(self, content) -> None:
assert isinstance(content, (bytes, str))
self.content = content | web_programming |
def json(self):
return json.loads(self.content) | web_programming |
def mock_response(*args, **kwargs):
assert args[0] == AUTHENTICATED_USER_ENDPOINT
assert "Authorization" in kwargs["headers"]
assert kwargs["headers"]["Authorization"].startswith("token ")
assert "Accept" in kwargs["headers"]
return FakeResponse(b'{"login":"test","id":1}') | web_programming |
def get_movie_data_from_soup(soup: bs4.element.ResultSet) -> dict[str, str]:
return {
"name": soup.h3.a.text,
"genre": soup.find("span", class_="genre").text.strip(),
"rating": soup.strong.text,
"page_link": f"https://www.imdb.com{soup.a.get('href')}",
} | web_programming |
Subsets and Splits