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"""
Ensures a consistent ordering of corners returned by cv2.findChessboardCornersSB
for asymmetrical chessboards.

For patterns with dims i, j where i > j and i is odd the script ensures the corner 
order to start at a black square running along the positive i axis.

The detected corners are used to create a canonical chessboard view. This
view is analysed by looking at the 2x2 blocks associated with each corner.
A characteristic value is computed from each 2x2 block and if the series

cheind

# Estimate the population size using capture-recapture method
# Assumes: experiment twice, closed population

import numpy as np
import matplotlib.pyplot as plt

T = 1000  # true pop size
N1 = 50  # size of sample 1
N2 = 30  # size of sample 2

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import numpy as np


def cv_to_ndc(fx, fy, cx, cy, near, far, w, h):
    """Returns the 4x4 projection matrix that converts from OpenCV camera
    coordinates to OpenGL NDC coordinates.

    This takes into account that cameras in
        - OpenCV has +z into scene, +y down the image
        - OpenGL has -z into scene, +y up the image

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import numpy as np
import matplotlib.pyplot as plt


def sierpinski_triangle():
    """Generates a Sierpinski triangle.

    Given 3 anchor points and a trace point, the
    next trace point is half-way between its current
    location and a randomly chosen anchor.

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import argparse
import platform
import sys
import subprocess
from pathlib import Path


def describe() -> dict:
    meta = {
        "python": "py" + ".".join(platform.python_version_tuple()[:2]),

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import numpy as np
import matplotlib.pyplot as plt
import dataclasses


@dataclasses.dataclass
class MotionEstimate:
    coeffs: np.ndarray  # 3x1
    t0: float
    degree: int = dataclasses.field(init=False)

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import torch

def sample_entropy(
    x: torch.Tensor, m: int = 2, r: float = None, stride: int = 1, subsample: int = 1
):
    """Returns the (batched) sample entropy of the given time series.

    Sample entropy is a measure of complexity of sequences that can be related
    to predictability. Sample entropy (SE) is defined as the negative logarithm of
    the following ratio:

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from scipy.optimize import linprog
import numpy as np
import pandas as pd


def print_metrics(df):
    print('Total staff costs', df.to_numpy().sum())
    print('Management cost ratio')
    print(df.MgtStaffCosts / df.to_numpy().sum())
    print('Partner cost ratio')

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import numpy as np
from itertools import count

def perm_matrix(perm_indices):
    '''Returns the permutation matrix corresponding to given permutation indices

    Here `perm_indices` defines the permutation order in the following sense: 
    value `j` at index `i` will move row/column `j` of the original matrix to 
    row/column `i`in the permuated matrix P*M/M*P^T.
    

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