
"""simple docstring"""





from __future__ import annotations

import math
import random
from collections.abc import Collection
from typing import overload
class 		SCREAMING_SNAKE_CASE_					:




		"""simple docstring"""





		def __init__(	self				,    lowerCAmelCase__ = None):
				if components is None:
						__SCREAMING_SNAKE_CASE				=					[]
				__SCREAMING_SNAKE_CASE				=					list(SCREAMING_SNAKE_CASE__)




		def __len__(	self):
				return len(self.__components)




		def __str__(	self):
				return "(" + ",".join(map(SCREAMING_SNAKE_CASE__				,    self.__components)) + ")"




		def __add__(	self				,    lowerCAmelCase__):
				__SCREAMING_SNAKE_CASE				=					len(self)
				if size == len(SCREAMING_SNAKE_CASE__):
						__SCREAMING_SNAKE_CASE				=					[self.__components[i] + other.component(SCREAMING_SNAKE_CASE__) for i in range(SCREAMING_SNAKE_CASE__)]
						return Vector(SCREAMING_SNAKE_CASE__)
				else:
						raise Exception("""must have the same size""")




		def __sub__(	self				,    lowerCAmelCase__):
				__SCREAMING_SNAKE_CASE				=					len(self)
				if size == len(SCREAMING_SNAKE_CASE__):
						__SCREAMING_SNAKE_CASE				=					[self.__components[i] - other.component(SCREAMING_SNAKE_CASE__) for i in range(SCREAMING_SNAKE_CASE__)]
						return Vector(SCREAMING_SNAKE_CASE__)
				else:  # error case
						raise Exception("""must have the same size""")




		@overload
		def __mul__(	self				,    lowerCAmelCase__):
				...




		@overload
		def __mul__(	self				,    lowerCAmelCase__):
				...




		def __mul__(	self				,    lowerCAmelCase__):
				if isinstance(SCREAMING_SNAKE_CASE__				,    (float, int)):
						__SCREAMING_SNAKE_CASE				=					[c * other for c in self.__components]
						return Vector(SCREAMING_SNAKE_CASE__)
				elif isinstance(SCREAMING_SNAKE_CASE__				,    SCREAMING_SNAKE_CASE__) and len(self) == len(SCREAMING_SNAKE_CASE__):
						__SCREAMING_SNAKE_CASE				=					len(self)
						__SCREAMING_SNAKE_CASE				=					[self.__components[i] * other.component(SCREAMING_SNAKE_CASE__) for i in range(SCREAMING_SNAKE_CASE__)]
						return sum(SCREAMING_SNAKE_CASE__)
				else:  # error case
						raise Exception("""invalid operand!""")




		def       snake_case_	(	self):
				return Vector(self.__components)




		def       snake_case_	(	self				,    lowerCAmelCase__):
				if isinstance(SCREAMING_SNAKE_CASE__				,    SCREAMING_SNAKE_CASE__) and -len(self.__components) <= i < len(self.__components):
						return self.__components[i]
				else:
						raise Exception("""index out of range""")




		def       snake_case_	(	self				,    lowerCAmelCase__				,    lowerCAmelCase__):
				assert -len(self.__components) <= pos < len(self.__components)
				__SCREAMING_SNAKE_CASE				=					value




		def       snake_case_	(	self):
				if len(self.__components) == 0:
						raise Exception("""Vector is empty""")
				__SCREAMING_SNAKE_CASE				=					[c**2 for c in self.__components]
				return math.sqrt(sum(SCREAMING_SNAKE_CASE__))




		def       snake_case_	(	self				,    lowerCAmelCase__				,    lowerCAmelCase__ = False):
				__SCREAMING_SNAKE_CASE				=					self * other
				__SCREAMING_SNAKE_CASE				=					self.euclidean_length() * other.euclidean_length()
				if deg:
						return math.degrees(math.acos(num / den))
				else:
						return math.acos(num / den)



def 		_lowerCAmelCase							(							UpperCamelCase_							):
		assert isinstance(UpperCAmelCase_    ,							UpperCAmelCase_							)
		return Vector([0] * dimension							)



def 		_lowerCAmelCase							(							UpperCamelCase_    ,							UpperCamelCase_							):
		assert isinstance(UpperCAmelCase_    ,							UpperCAmelCase_							) and (isinstance(UpperCAmelCase_    ,							UpperCAmelCase_							))
		__SCREAMING_SNAKE_CASE				=					[0] * dimension
		__SCREAMING_SNAKE_CASE				=					1
		return Vector(UpperCAmelCase_							)



def 		_lowerCAmelCase							(							UpperCamelCase_    ,							UpperCamelCase_    ,							UpperCamelCase_							):
		assert (
		    isinstance(UpperCAmelCase_    ,							UpperCAmelCase_							)
		    and isinstance(UpperCAmelCase_    ,							UpperCAmelCase_							)
		    and (isinstance(UpperCAmelCase_    ,							(int, float)							))
		)
		return x * scalar + y



def 		_lowerCAmelCase							(							UpperCamelCase_    ,							UpperCamelCase_    ,							UpperCamelCase_							):
		random.seed(UpperCAmelCase_							)
		__SCREAMING_SNAKE_CASE				=					[random.randint(UpperCAmelCase_    ,							UpperCAmelCase_							) for _ in range(UpperCAmelCase_							)]
		return Vector(UpperCAmelCase_							)
class 		SCREAMING_SNAKE_CASE_					:




		"""simple docstring"""





		def __init__(	self				,    lowerCAmelCase__				,    lowerCAmelCase__				,    lowerCAmelCase__):
				__SCREAMING_SNAKE_CASE				=					matrix
				__SCREAMING_SNAKE_CASE				=					w
				__SCREAMING_SNAKE_CASE				=					h




		def __str__(	self):
				__SCREAMING_SNAKE_CASE				=					""""""
				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




		def __add__(	self				,    lowerCAmelCase__):
				if self.__width == other.width() and self.__height == other.height():
						__SCREAMING_SNAKE_CASE				=					[]
						for i in range(self.__height):
								__SCREAMING_SNAKE_CASE				=					[
								    self.__matrix[i][j] + other.component(SCREAMING_SNAKE_CASE__				,    SCREAMING_SNAKE_CASE__)
								    for j in range(self.__width)
								]
								matrix.append(SCREAMING_SNAKE_CASE__)
						return Matrix(SCREAMING_SNAKE_CASE__				,    self.__width				,    self.__height)
				else:
						raise Exception("""matrix must have the same dimension!""")




		def __sub__(	self				,    lowerCAmelCase__):
				if self.__width == other.width() and self.__height == other.height():
						__SCREAMING_SNAKE_CASE				=					[]
						for i in range(self.__height):
								__SCREAMING_SNAKE_CASE				=					[
								    self.__matrix[i][j] - other.component(SCREAMING_SNAKE_CASE__				,    SCREAMING_SNAKE_CASE__)
								    for j in range(self.__width)
								]
								matrix.append(SCREAMING_SNAKE_CASE__)
						return Matrix(SCREAMING_SNAKE_CASE__				,    self.__width				,    self.__height)
				else:
						raise Exception("""matrices must have the same dimension!""")




		@overload
		def __mul__(	self				,    lowerCAmelCase__):
				...




		@overload
		def __mul__(	self				,    lowerCAmelCase__):
				...




		def __mul__(	self				,    lowerCAmelCase__):
				if isinstance(SCREAMING_SNAKE_CASE__				,    SCREAMING_SNAKE_CASE__):  # matrix-vector
						if len(SCREAMING_SNAKE_CASE__) == self.__width:
								__SCREAMING_SNAKE_CASE				=					zero_vector(self.__height)
								for i in range(self.__height):
										__SCREAMING_SNAKE_CASE				=					[
										    self.__matrix[i][j] * other.component(SCREAMING_SNAKE_CASE__)
										    for j in range(self.__width)
										]
										ans.change_component(SCREAMING_SNAKE_CASE__				,    sum(SCREAMING_SNAKE_CASE__))
								return ans
						else:
								raise Exception(
								    """vector must have the same size as the """
								    """number of columns of the matrix!""")
				elif isinstance(SCREAMING_SNAKE_CASE__				,    (int, float)):  # matrix-scalar
						__SCREAMING_SNAKE_CASE				=					[
						    [self.__matrix[i][j] * other for j in range(self.__width)]
						    for i in range(self.__height)
						]
						return Matrix(SCREAMING_SNAKE_CASE__				,    self.__width				,    self.__height)
				return None




		def       snake_case_	(	self):
				return self.__height




		def       snake_case_	(	self):
				return self.__width




		def       snake_case_	(	self				,    lowerCAmelCase__				,    lowerCAmelCase__):
				if 0 <= x < self.__height and 0 <= y < self.__width:
						return self.__matrix[x][y]
				else:
						raise Exception("""change_component: indices out of bounds""")




		def       snake_case_	(	self				,    lowerCAmelCase__				,    lowerCAmelCase__				,    lowerCAmelCase__):
				if 0 <= x < self.__height and 0 <= y < self.__width:
						__SCREAMING_SNAKE_CASE				=					value
				else:
						raise Exception("""change_component: indices out of bounds""")




		def       snake_case_	(	self				,    lowerCAmelCase__				,    lowerCAmelCase__):
				if self.__height != self.__width:
						raise Exception("""Matrix is not square""")
				__SCREAMING_SNAKE_CASE				=					self.__matrix[:x] + self.__matrix[x + 1 :]
				for i in range(len(SCREAMING_SNAKE_CASE__)):
						__SCREAMING_SNAKE_CASE				=					minor[i][:y] + minor[i][y + 1 :]
				return Matrix(SCREAMING_SNAKE_CASE__				,    self.__width - 1				,    self.__height - 1).determinant()




		def       snake_case_	(	self				,    lowerCAmelCase__				,    lowerCAmelCase__):
				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(SCREAMING_SNAKE_CASE__				,    SCREAMING_SNAKE_CASE__)
				else:
						raise Exception("""Indices out of bounds""")




		def       snake_case_	(	self):
				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:
						__SCREAMING_SNAKE_CASE				=					[
						    self.__matrix[0][y] * self.cofactor(0				,    SCREAMING_SNAKE_CASE__) for y in range(self.__width)
						]
						return sum(SCREAMING_SNAKE_CASE__)



def 		_lowerCAmelCase							(							UpperCamelCase_							):
		__SCREAMING_SNAKE_CASE				=					[[0] * n for _ in range(UpperCAmelCase_							)]
		return Matrix(UpperCAmelCase_    ,							UpperCAmelCase_    ,							UpperCAmelCase_							)



def 		_lowerCAmelCase							(							UpperCamelCase_    ,							UpperCamelCase_    ,							UpperCamelCase_    ,							UpperCamelCase_							):
		random.seed(UpperCAmelCase_							)
		__SCREAMING_SNAKE_CASE				=					[
		    [random.randint(UpperCAmelCase_    ,							UpperCAmelCase_							) for _ in range(UpperCAmelCase_							)] for _ in range(UpperCAmelCase_							)
		]
		return Matrix(UpperCAmelCase_    ,							UpperCAmelCase_    ,							UpperCAmelCase_							)









"""simple docstring"""







from ..utils import (
    OptionalDependencyNotAvailable,
    is_flax_available,
    is_scipy_available,
    is_torch_available,
    is_torchsde_available,
)


try:
			if not is_torch_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			from ..utils.dummy_pt_objects import *  # noqa F403
else:
			from .scheduling_consistency_models import CMStochasticIterativeScheduler
			from .scheduling_ddim import DDIMScheduler
			from .scheduling_ddim_inverse import DDIMInverseScheduler
			from .scheduling_ddim_parallel import DDIMParallelScheduler
			from .scheduling_ddpm import DDPMScheduler
			from .scheduling_ddpm_parallel import DDPMParallelScheduler
			from .scheduling_deis_multistep import DEISMultistepScheduler
			from .scheduling_dpmsolver_multistep import DPMSolverMultistepScheduler
			from .scheduling_dpmsolver_multistep_inverse import DPMSolverMultistepInverseScheduler
			from .scheduling_dpmsolver_singlestep import DPMSolverSinglestepScheduler
			from .scheduling_euler_ancestral_discrete import EulerAncestralDiscreteScheduler
			from .scheduling_euler_discrete import EulerDiscreteScheduler
			from .scheduling_heun_discrete import HeunDiscreteScheduler
			from .scheduling_ipndm import IPNDMScheduler
			from .scheduling_k_dpm_2_ancestral_discrete import KDPMaAncestralDiscreteScheduler
			from .scheduling_k_dpm_2_discrete import KDPMaDiscreteScheduler
			from .scheduling_karras_ve import KarrasVeScheduler
			from .scheduling_pndm import PNDMScheduler
			from .scheduling_repaint import RePaintScheduler
			from .scheduling_sde_ve import ScoreSdeVeScheduler
			from .scheduling_sde_vp import ScoreSdeVpScheduler
			from .scheduling_unclip import UnCLIPScheduler
			from .scheduling_unipc_multistep import UniPCMultistepScheduler
			from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin
			from .scheduling_vq_diffusion import VQDiffusionScheduler

try:
			if not is_flax_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			from ..utils.dummy_flax_objects import *  # noqa F403
else:
			from .scheduling_ddim_flax import FlaxDDIMScheduler
			from .scheduling_ddpm_flax import FlaxDDPMScheduler
			from .scheduling_dpmsolver_multistep_flax import FlaxDPMSolverMultistepScheduler
			from .scheduling_karras_ve_flax import FlaxKarrasVeScheduler
			from .scheduling_lms_discrete_flax import FlaxLMSDiscreteScheduler
			from .scheduling_pndm_flax import FlaxPNDMScheduler
			from .scheduling_sde_ve_flax import FlaxScoreSdeVeScheduler
			from .scheduling_utils_flax import (
			    FlaxKarrasDiffusionSchedulers,
			    FlaxSchedulerMixin,
			    FlaxSchedulerOutput,
			    broadcast_to_shape_from_left,
			)


try:
			if not (is_torch_available() and is_scipy_available()):
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			from ..utils.dummy_torch_and_scipy_objects import *  # noqa F403
else:
			from .scheduling_lms_discrete import LMSDiscreteScheduler

try:
			if not (is_torch_available() and is_torchsde_available()):
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			from ..utils.dummy_torch_and_torchsde_objects import *  # noqa F403
else:
			from .scheduling_dpmsolver_sde import DPMSolverSDEScheduler




