Datasets:

andreacenzato
/

Ground-Wing

import numpy as np
import pandas as pd
import warnings
import os

from sklearn.pipeline import Pipeline
from sklearn.compose import ColumnTransformer
from sklearn.preprocessing import OneHotEncoder,KBinsDiscretizer
from skmultilearn.model_selection import iterative_train_test_split
from scipy import interpolate
from scipy.stats import qmc



def check_bounds(sample,bounds):
    sample_ok = True
    for i in range(len(sample)):
        if not bounds[i][0] <= sample[i] <= bounds[i][1]:
            sample_ok = False
    return sample_ok

def check_feasibility(p_set:list,bounds:list)->bool:
    """
        Checks if a set of parameters is suitable for geometry generation
    """
    # Calculate forward displacement of wingtip
    forward_disp = -np.tan(np.deg2rad(p_set[4]))*1000

    # Check that angle of attack and twist angle sum does not exceed limits
    if not bounds[0][0] < p_set[0] + p_set[1] < bounds[0][1]:
        return False
    # Check forward displacement
    if forward_disp + p_set[2] > bounds[2][1]:
        return False
    # Check backwards displacement
    if forward_disp + p_set[2] < bounds[3][0]:
        return False
    # Check if outboard chord is too large
    if p_set[3] - p_set[2] - forward_disp > bounds[3][1]:
        return False
    return True 

def check_feasibility_batch(points,bounds):
    """
        Checks if each set of parameters is suitable for geometry generation
    """

    feas_bounds = np.array([check_bounds(point,bounds) for point in points])
    feas_constrains = np.array([check_feasibility(point,bounds) for point in points])

    return np.logical_and(feas_bounds,feas_constrains)

def build_F_inv(p_index, p_bounds, sens_funcs, num_points=200):

    a, b = p_bounds[p_index]
    # grid on axis i
    xs = np.linspace(a, b, num_points)
    ds = sens_funcs[p_index](xs)  # sensitivities at grid points
    ds = np.maximum(ds, 1e-12) # Ensure no zeros are present, to avoid duplicates in cdf
    if np.all(ds == ds[0]):
        ds = np.ones_like(ds)
    pdf = ds
    cdf_vals = np.cumsum(pdf)
    cdf_vals = cdf_vals / cdf_vals[-1]  # normalize to [0,1]
    inv_cdf = interpolate.make_interp_spline(cdf_vals,xs,k=1)
    def F_inv(u):
        u = np.clip(u, 0.0, 1.0)
        return inv_cdf(u)
    return F_inv

# -----------------------------
# Warp using empirical per-axis CDF inverse
# -----------------------------
def warp_samples(X, F_inv_funcs):
    M = X.shape[0]
    X_warped = np.empty_like(X)
    for i in range(len(F_inv_funcs)):
        X_warped[:, i] = F_inv_funcs[i](X[:, i])
    return X_warped

def clip_samples(X,bounds):
    for i in range(len(bounds)):
        X[:,i] = np.interp(X[:,i],(X[:,i].min(),X[:,i].max()),(bounds[i][0],bounds[i][1]))
    return X

def compute_sample_weights(samples, sens_funcs, bounds):
    """
    Compute importance weights based on sensitivity functions.
    Samples with higher sensitivity values get higher weights.
    Args:
        samples: Array of shape (n_samples, n_dims)
        sens_funcs: List of sensitivity functions, one per dimension
        bounds: Parameter bounds
    Returns:
        weights: Array of shape (n_samples,) with normalized weights
    """
    n_samples = samples.shape[0]
    weights = np.ones(n_samples)

    # Multiply sensitivity values across all dimensions
    for i in range(samples.shape[1]):
        sens_values = sens_funcs[i](samples[:, i])
        # Ensure positive values
        sens_values = np.maximum(sens_values, 1e-12)
        weights *= sens_values

    # Normalize weights to sum to 1
    weights = weights / weights.sum()

    return weights

# -----------------------------
# Maximin subset selection in warped space
# -----------------------------
def maximin_subset(points, k):
    n = points.shape[0]
    selected = []
    available = np.ones(n,dtype=bool)

    # 1) Start with the point farthest from the centroid
    mean_pt = np.mean(points, axis=0)
    dists_to_mean = np.linalg.norm(points - mean_pt, axis=1)
    first = int(np.argmax(dists_to_mean))
    selected.append(first)
    available[first] = False

    # 2) Iteratively add points maximizing distance to the current set
    for _ in range(1, k):
        # Compute, for each candidate in 'remaining', the distance to its nearest
        # point in 'selected'
        cand_indices = np.nonzero(available)[0]
        cand_points = points[cand_indices]  # shape (m, d)
        selected_points = points[np.array(selected)]  # shape (s, d)

        # Compute pairwise distances: (m, s)
        dist_matrix = np.linalg.norm(
            cand_points[:, None, :] - selected_points[None, :, :], axis=2
        )
        # For each candidate, distance to the nearest selected point
        min_dist_to_selected = dist_matrix.min(axis=1)

        # Pick the candidate with the maximum of these minima
        pos = int(np.argmax(min_dist_to_selected))
        chosen = int(cand_indices[pos])

        selected.append(chosen)
        available[chosen] = False

    return np.array(selected, dtype=int)

def weighted_maximin_selection(points, weights, k):
    """
    Select k points using weighted maximin strategy.
    Combines space coverage (maximin) with importance sampling (weights).
    Args:
        points: Array of shape (n_samples, n_dims)
        weights: Array of shape (n_samples,) with sample importance weights
        k: Number of points to select
    Returns:
        selected_indices: Array of selected point indices
    """
    n = points.shape[0]
    selected = []
    available = np.ones(n, dtype=bool)

    # 1) Start with weighted probability selection for the first point
    # This ensures we start in a high-sensitivity region
    probs = weights / weights.sum()
    first = np.random.choice(n, p=probs)
    selected.append(first)
    available[first] = False

    # 2) Iteratively add points balancing distance and weight
    for _ in range(1, k):
        cand_indices = np.nonzero(available)[0]
        if len(cand_indices) == 0:
            break

        cand_points = points[cand_indices]
        cand_weights = weights[cand_indices]
        selected_points = points[np.array(selected)]

        # Compute pairwise distances to selected points
        dist_matrix = np.linalg.norm(
            cand_points[:, None, :] - selected_points[None, :, :], axis=2
        )
        # For each candidate, distance to the nearest selected point
        min_dist_to_selected = dist_matrix.min(axis=1)

        # Normalize distances to [0, 1]
        if min_dist_to_selected.max() > 0:
            norm_dists = min_dist_to_selected / min_dist_to_selected.max()
        else:
            norm_dists = np.ones_like(min_dist_to_selected)

        # Normalize weights to [0, 1]
        if cand_weights.max() > 0:
            norm_weights = cand_weights / cand_weights.max()
        else:
            norm_weights = np.ones_like(cand_weights)

        # Combined score: balance distance (70%) and weight (30%)
        # Adjust these ratios to prioritize coverage vs sensitivity
        scores = 0.7 * norm_dists + 0.3 * norm_weights

        # Pick the candidate with the highest combined score
        pos = int(np.argmax(scores))
        chosen = int(cand_indices[pos])

        selected.append(chosen)
        available[chosen] = False

    return np.array(selected, dtype=int)

def weighted_maximin_selection_with_weight(points, weights, k, coverage_weight=0.5):
    """
    Select k points using weighted maximin strategy with adjustable balance.
    Combines space coverage (maximin) with importance sampling (weights).
    Args:
        points: Array of shape (n_samples, n_dims)
        weights: Array of shape (n_samples,) with sample importance weights
        k: Number of points to select
        coverage_weight: Weight for coverage (0-1). Higher = more coverage, less sensitivity bias
    Returns:
        selected_indices: Array of selected point indices
    """
    n = points.shape[0]
    selected = []
    available = np.ones(n, dtype=bool)

    # 1) Start with weighted probability selection for the first point
    probs = weights / weights.sum()
    first = np.random.choice(n, p=probs)
    selected.append(first)
    available[first] = False

    # 2) Iteratively add points balancing distance and weight
    sensitivity_weight = 1.0 - coverage_weight

    for i in range(1, k):
        if i % 10 == 0:
            print(f"Selected {i} of {k} samples...")
        cand_indices = np.nonzero(available)[0]
        if len(cand_indices) == 0:
            break

        cand_points = points[cand_indices]
        cand_weights = weights[cand_indices]
        selected_points = points[np.array(selected)]

        # Compute pairwise distances to selected points
        dist_matrix = np.linalg.norm(
            cand_points[:, None, :] - selected_points[None, :, :], axis=2
        )
        min_dist_to_selected = dist_matrix.min(axis=1)

        # Normalize distances to [0, 1]
        if min_dist_to_selected.max() > 0:
            norm_dists = min_dist_to_selected / min_dist_to_selected.max()
        else:
            norm_dists = np.ones_like(min_dist_to_selected)

        # Normalize weights to [0, 1]
        if cand_weights.max() > 0:
            norm_weights = cand_weights / cand_weights.max()
        else:
            norm_weights = np.ones_like(cand_weights)

        # Combined score with adjustable balance
        scores = coverage_weight * norm_dists + sensitivity_weight * norm_weights

        # Pick the candidate with the highest combined score
        pos = int(np.argmax(scores))
        chosen = int(cand_indices[pos])

        selected.append(chosen)
        available[chosen] = False

    return np.array(selected, dtype=int)

def iterative_split(samples, N, M, bound_names, max_attempts = 12):
    df = pd.DataFrame(data=samples, columns=bound_names)
    continuos_cols = [c for c in bound_names if c in ["CS","OS"]]

    with warnings.catch_warnings(record=True) as rw:
        bin_numeric = KBinsDiscretizer(n_bins=20,encode="ordinal",strategy='uniform')
        one_hot_encode = OneHotEncoder(handle_unknown="error",sparse_output=False,)
        col_trans1 = ColumnTransformer(transformers=[("bin_numeric",bin_numeric,continuos_cols)],remainder="passthrough",verbose_feature_names_out=False)
        col_trans2 = ColumnTransformer(transformers=[("one_hot_encode",one_hot_encode,df.columns)],remainder="drop",verbose_feature_names_out=False)
        pp = Pipeline([("col_trans1",col_trans1),("col_trans2",col_trans2)])
        pp.set_output(transform="pandas")
        one_hot_labels : pd.DataFrame = pp.fit_transform(df) # type: ignore

        # Converting to numpy
    df = df.to_numpy()
    one_hot_labels = one_hot_labels.to_numpy() # type: ignore

    # Setup split parameters
    subset_size = N/len(samples)
    subset = []
    attempt = 1
    # Loop to ensure that the extracted subset lenght is correct
    while attempt < max_attempts:
        # Split data 
        _,_,subset,_ = iterative_train_test_split(df,one_hot_labels,subset_size)
        if len(subset) < N:
            if attempt == max_attempts:
                print(f"Failed to obtain desired number of samples!")
            subset_size += 0.025
            attempt += 1
        else:
            break

    print(f"Obtained a subset with {len(subset)} samples in {attempt} attempts!")
    
    return subset

def generate_feasible_samples(bounds, sens_funcs, N=128, M=512, max_attempts=12, p_bases=np.array([0.5,0.5,5,5,1]), coverage_weight=0.5):
    """
    Two-stage sampling approach:
    1. Generate feasible samples with uniform space coverage
    2. Select N samples using weighted maximin (balancing coverage and sensitivity)
    Args:
        bounds: Parameter bounds array
        sens_funcs: List of sensitivity functions
        N: Target number of samples to select
        M: Initial candidate pool size
        max_attempts: Maximum attempts to generate enough feasible samples
        p_bases: Rounding bases for each parameter
        coverage_weight: Weight for space coverage vs sensitivity (0.5 = equal importance)
    Returns:
        X_selected: Selected samples
        M: Final candidate pool size used
    """
    if len(bounds) != len(sens_funcs):
        raise ValueError(f"Expected bounds and sens_funcs to have the same length. Got {bounds.shape} and {sens_funcs.shape}")

    # Filtering input
    bounds = np.asarray(bounds,dtype=float)
    d = len(bounds)

    # Setup sampling loop - generate enough feasible samples for selection
    X_feasible = []
    target_feasible = N * 3  # Generate 3x more samples than needed for good selection pool

    for attempt in range(1, max_attempts+1):
        # STAGE 1: Generate uniform Sobol samples for space coverage
        sampler = qmc.Sobol(d, scramble=True)
        X = sampler.random(n=M)

        # Scale to parameter bounds
        X_scaled = qmc.scale(X, bounds[:, 0]-p_bases/2, bounds[:, 1]+p_bases/2)

        # Round to closest acceptable value
        X_rounded = round_samples(X_scaled, p_bases)

        # Remove duplicates
        X_unique = np.unique(X_rounded, axis=0)

        # Applying feasibility filter
        feas_mask = check_feasibility_batch(X_unique, bounds)
        X_feasible = X_unique[feas_mask]

        # Check if we have enough feasible samples
        if len(X_feasible) >= target_feasible:
            print(f"Generated {len(X_feasible)} feasible samples in {attempt} attempts")
            break
        else:
            # Increase M if not enough points are feasible
            M = int(M * 2)
            if attempt == max_attempts:
                print(f"Warning: Only generated {len(X_feasible)} feasible samples (target was {target_feasible})")

    if len(X_feasible) == 0:
        raise ValueError("Could not generate any feasible samples with the given settings")
    elif len(X_feasible) < N:
        raise ValueError(f"Only {len(X_feasible)} feasible samples could be generated, but N={N} required. Increase M or max_attempts.")

    # STAGE 2: Select N samples using weighted maximin selection
    print(f"Selecting {N} samples from {len(X_feasible)} feasible candidates...")
    weights = compute_sample_weights(X_feasible, sens_funcs, bounds)

    # Adjust the weighted_maximin_selection to use the coverage_weight parameter
    # (We'll pass it directly in the call)
    selected_indices = weighted_maximin_selection_with_weight(X_feasible, weights, N, coverage_weight)
    X_selected = X_feasible[selected_indices]

    print(f"Selected {len(X_selected)} samples balancing space coverage and sensitivity")

    return X_selected, M
     
def validate_samples(samples,bounds,sens_funcs):
    print("Checking if constraints were respected")
    valid = check_feasibility_batch(samples,bounds)
    if any(valid == False):
        raise ValueError("At least one samples does not respect the provided constraints")
    print("Checking if any samples are identical")
    if len(np.unique(samples, axis=0)) != len(samples):
        raise ValueError("At least one identical pair of parameters found")
    print("Validation complete")

def round_samples(samples,p_bases):
    for i in range(len(p_bases)):
        samples[:,i] = round_to_base(samples[:,i],p_bases[i])
    return samples

def round_to_base(x,base=1):
    return base*np.rint(x/base)

def main():

    bound_names = ["CA","OA","CS","OS","AF"]
    N = 50  # target samples
    M = 2048  # candidate pool size
    csv_name = "samples_filling.csv"
    csv_path = "."
    csv_path = os.path.join(csv_path,csv_name)

    # Define parameter bounds
    bounds = np.array([
        [-10.0, 5.0],    # CA
        [-10.0, 10.0],    # OA
        [550.0, 700.0],  # CS
        [350.0, 700.0],  # OS
        [-8.5, 20.0]     # AF
    ], dtype=float)

    d = bounds.shape[0]

    # ========== SENSITIVITY FUNCTION DATA ==========
    # Define your parameter values, lift coefficients (CL), and drag coefficients (CD)
    # Aerodynamic efficiency will be calculated as CL/CD

    # s1: CA parameter
    s1_param_values = np.array([-10,-8,-6,-4,-2,0,2,4,5])
    s1_lift = np.array([2.71597,2.59168,2.38756,2.11036,1.79931,1.46873,1.13276,0.79852,0.63399])  # Replace with CL values
    s1_drag = np.array([0.19559,0.16673,0.13793,0.11181,0.08745,0.06607,0.04852,0.03574,0.03121])  # Replace with CD values

    # s2: OA parameter
    s2_param_values = np.array([-10,-8,-6,-4,-2,0,2,4,6,8,10])
    s2_lift = np.array([2.11753,2.00106,1.87441,1.74326,1.60771,1.46873,1.32822,1.18505,1.03937,0.88601,0.72393])  # Replace with CL values
    s2_drag = np.array([0.12137,0.10840,0.09681,0.08580,0.07550,0.06607,0.05760,0.05028,0.04426,0.04071,0.04110])  # Replace with CD values

    # s3: CS parameter
    s3_param_values = np.array([700,675,650,625,600,575,550])
    s3_lift = np.array([1.59557,1.56641,1.53579,1.50281,1.46873,1.43109,1.39120])  # Replace with CL values
    s3_drag = np.array([0.07392,0.07200,0.07008,0.06806,0.06607,0.06395,0.06179])  # Replace with CD values

    # s4: OS parameter
    s4_param_values = np.array([700,650,600,550,500,455,400,350])
    s4_lift = np.array([1.76696,1.72398,1.67319,1.60908,1.53883,1.46873,1.37725,1.29316])  # Replace with CL values
    s4_drag = np.array([0.08746,0.08379,0.07981,0.07517,0.07047,0.06607,0.06063,0.05588])  # Replace with CD values

    # s5: AF parameter
    s5_param_values = np.array([-8.5,-4,0,4,8,12,16,20])
    s5_lift = np.array([1.31019,1.35985,1.39354,1.42229,1.45279,1.48344,1.50923,1.53197])  # Replace with CL values
    s5_drag = np.array([0.05940,0.06138,0.06270,0.06387,0.06528,0.06673,0.06792,0.06904])  # Replace with CD values

    # ========== CREATE INTERPOLATORS FOR LIFT AND DRAG (built once for efficiency) ==========
    _s1_lift_interp = interpolate.make_interp_spline(s1_param_values, s1_lift, k=3)
    _s1_drag_interp = interpolate.make_interp_spline(s1_param_values, s1_drag, k=3)
    _s1_lift_deriv = _s1_lift_interp.derivative()
    _s1_drag_deriv = _s1_drag_interp.derivative()

    _s2_lift_interp = interpolate.make_interp_spline(s2_param_values, s2_lift, k=3)
    _s2_drag_interp = interpolate.make_interp_spline(s2_param_values, s2_drag, k=3)
    _s2_lift_deriv = _s2_lift_interp.derivative()
    _s2_drag_deriv = _s2_drag_interp.derivative()

    _s3_lift_interp = interpolate.make_interp_spline(np.flip(s3_param_values), np.flip(s3_lift), k=3)
    _s3_drag_interp = interpolate.make_interp_spline(np.flip(s3_param_values), np.flip(s3_drag), k=3)
    _s3_lift_deriv = _s3_lift_interp.derivative()
    _s3_drag_deriv = _s3_drag_interp.derivative()

    _s4_lift_interp = interpolate.make_interp_spline(np.flip(s4_param_values), np.flip(s4_lift), k=3)
    _s4_drag_interp = interpolate.make_interp_spline(np.flip(s4_param_values), np.flip(s4_drag), k=3)
    _s4_lift_deriv = _s4_lift_interp.derivative()
    _s4_drag_deriv = _s4_drag_interp.derivative()

    _s5_lift_interp = interpolate.make_interp_spline(s5_param_values, s5_lift, k=3)
    _s5_drag_interp = interpolate.make_interp_spline(s5_param_values, s5_drag, k=3)
    _s5_lift_deriv = _s5_lift_interp.derivative()
    _s5_drag_deriv = _s5_drag_interp.derivative()

    # ========== SENSITIVITY FUNCTIONS ==========
    def s1(p):
        return np.abs(_s1_lift_deriv(p)) + np.abs(_s1_drag_deriv(p))

    def s2(p):
        return np.abs(_s2_lift_deriv(p)) + np.abs(_s2_drag_deriv(p))

    def s3(p):
        return np.abs(_s3_lift_deriv(p)) + np.abs(_s3_drag_deriv(p))

    def s4(p):
        return np.abs(_s4_lift_deriv(p)) + np.abs(_s4_drag_deriv(p))

    def s5(p):
        return np.abs(_s5_lift_deriv(p)) + np.abs(_s5_drag_deriv(p))

    sens_funcs = [s1, s2, s3, s4, s5]

    # Generate the samples using two-stage approach
    # This now returns exactly N samples that balance space coverage and sensitivity
    samples,M = generate_feasible_samples(bounds=bounds,sens_funcs=sens_funcs,N=N,M=M,coverage_weight=0.5)

    # Validate the samples
    validate_samples(samples,bounds,sens_funcs)

     # Add column for profile
    profile_sampler = qmc.Sobol(1,scramble=True)
    profile_samples = profile_sampler.random(n=len(samples))
    profile_samples = qmc.scale(profile_samples,0.5,12.5)
    profile_samples = round_to_base(profile_samples,base=1)

    samples = np.c_[profile_samples,samples]
    
    print("Saving to file...")
    try: 
        np.savetxt(csv_name,samples,delimiter=",",header="P,"+",".join(bound_names),fmt='%f')
        print(f"Saved {csv_name}!")
    except:
        raise RuntimeError("Could not save .csv file")

if __name__ == "__main__":
    main()
    

	import numpy as np
	import pandas as pd
	import warnings
	import os

	from sklearn.pipeline import Pipeline
	from sklearn.compose import ColumnTransformer
	from sklearn.preprocessing import OneHotEncoder,KBinsDiscretizer
	from skmultilearn.model_selection import iterative_train_test_split
	from scipy import interpolate
	from scipy.stats import qmc



	def check_bounds(sample,bounds):
	sample_ok = True
	for i in range(len(sample)):
	if not bounds[i][0] <= sample[i] <= bounds[i][1]:
	sample_ok = False
	return sample_ok

	def check_feasibility(p_set:list,bounds:list)->bool:
	"""
	Checks if a set of parameters is suitable for geometry generation
	"""
	# Calculate forward displacement of wingtip
	forward_disp = -np.tan(np.deg2rad(p_set[4]))*1000

	# Check that angle of attack and twist angle sum does not exceed limits
	if not bounds[0][0] < p_set[0] + p_set[1] < bounds[0][1]:
	return False
	# Check forward displacement
	if forward_disp + p_set[2] > bounds[2][1]:
	return False
	# Check backwards displacement
	if forward_disp + p_set[2] < bounds[3][0]:
	return False
	# Check if outboard chord is too large
	if p_set[3] - p_set[2] - forward_disp > bounds[3][1]:
	return False
	return True

	def check_feasibility_batch(points,bounds):
	"""
	Checks if each set of parameters is suitable for geometry generation
	"""

	feas_bounds = np.array([check_bounds(point,bounds) for point in points])
	feas_constrains = np.array([check_feasibility(point,bounds) for point in points])

	return np.logical_and(feas_bounds,feas_constrains)

	def build_F_inv(p_index, p_bounds, sens_funcs, num_points=200):

	a, b = p_bounds[p_index]
	# grid on axis i
	xs = np.linspace(a, b, num_points)
	ds = sens_funcs[p_index](xs) # sensitivities at grid points
	ds = np.maximum(ds, 1e-12) # Ensure no zeros are present, to avoid duplicates in cdf
	if np.all(ds == ds[0]):
	ds = np.ones_like(ds)
	pdf = ds
	cdf_vals = np.cumsum(pdf)
	cdf_vals = cdf_vals / cdf_vals[-1] # normalize to [0,1]
	inv_cdf = interpolate.make_interp_spline(cdf_vals,xs,k=1)
	def F_inv(u):
	u = np.clip(u, 0.0, 1.0)
	return inv_cdf(u)
	return F_inv

	# -----------------------------
	# Warp using empirical per-axis CDF inverse
	# -----------------------------
	def warp_samples(X, F_inv_funcs):
	M = X.shape[0]
	X_warped = np.empty_like(X)
	for i in range(len(F_inv_funcs)):
	X_warped[:, i] = F_inv_funcs[i](X[:, i])
	return X_warped

	def clip_samples(X,bounds):
	for i in range(len(bounds)):
	X[:,i] = np.interp(X[:,i],(X[:,i].min(),X[:,i].max()),(bounds[i][0],bounds[i][1]))
	return X

	def compute_sample_weights(samples, sens_funcs, bounds):
	"""
	Compute importance weights based on sensitivity functions.
	Samples with higher sensitivity values get higher weights.

	Args:
	samples: Array of shape (n_samples, n_dims)
	sens_funcs: List of sensitivity functions, one per dimension
	bounds: Parameter bounds

	Returns:
	weights: Array of shape (n_samples,) with normalized weights
	"""
	n_samples = samples.shape[0]
	weights = np.ones(n_samples)

	# Multiply sensitivity values across all dimensions
	for i in range(samples.shape[1]):
	sens_values = sens_funcs[i](samples[:, i])
	# Ensure positive values
	sens_values = np.maximum(sens_values, 1e-12)
	weights *= sens_values

	# Normalize weights to sum to 1
	weights = weights / weights.sum()

	return weights

	# -----------------------------
	# Maximin subset selection in warped space
	# -----------------------------
	def maximin_subset(points, k):
	n = points.shape[0]
	selected = []
	available = np.ones(n,dtype=bool)

	# 1) Start with the point farthest from the centroid
	mean_pt = np.mean(points, axis=0)
	dists_to_mean = np.linalg.norm(points - mean_pt, axis=1)
	first = int(np.argmax(dists_to_mean))
	selected.append(first)
	available[first] = False

	# 2) Iteratively add points maximizing distance to the current set
	for _ in range(1, k):
	# Compute, for each candidate in 'remaining', the distance to its nearest
	# point in 'selected'
	cand_indices = np.nonzero(available)[0]
	cand_points = points[cand_indices] # shape (m, d)
	selected_points = points[np.array(selected)] # shape (s, d)

	# Compute pairwise distances: (m, s)
	dist_matrix = np.linalg.norm(
	cand_points[:, None, :] - selected_points[None, :, :], axis=2
	)
	# For each candidate, distance to the nearest selected point
	min_dist_to_selected = dist_matrix.min(axis=1)

	# Pick the candidate with the maximum of these minima
	pos = int(np.argmax(min_dist_to_selected))
	chosen = int(cand_indices[pos])

	selected.append(chosen)
	available[chosen] = False

	return np.array(selected, dtype=int)

	def weighted_maximin_selection(points, weights, k):
	"""
	Select k points using weighted maximin strategy.
	Combines space coverage (maximin) with importance sampling (weights).

	Args:
	points: Array of shape (n_samples, n_dims)
	weights: Array of shape (n_samples,) with sample importance weights
	k: Number of points to select

	Returns:
	selected_indices: Array of selected point indices
	"""
	n = points.shape[0]
	selected = []
	available = np.ones(n, dtype=bool)

	# 1) Start with weighted probability selection for the first point
	# This ensures we start in a high-sensitivity region
	probs = weights / weights.sum()
	first = np.random.choice(n, p=probs)
	selected.append(first)
	available[first] = False

	# 2) Iteratively add points balancing distance and weight
	for _ in range(1, k):
	cand_indices = np.nonzero(available)[0]
	if len(cand_indices) == 0:
	break

	cand_points = points[cand_indices]
	cand_weights = weights[cand_indices]
	selected_points = points[np.array(selected)]

	# Compute pairwise distances to selected points
	dist_matrix = np.linalg.norm(
	cand_points[:, None, :] - selected_points[None, :, :], axis=2
	)
	# For each candidate, distance to the nearest selected point
	min_dist_to_selected = dist_matrix.min(axis=1)

	# Normalize distances to [0, 1]
	if min_dist_to_selected.max() > 0:
	norm_dists = min_dist_to_selected / min_dist_to_selected.max()
	else:
	norm_dists = np.ones_like(min_dist_to_selected)

	# Normalize weights to [0, 1]
	if cand_weights.max() > 0:
	norm_weights = cand_weights / cand_weights.max()
	else:
	norm_weights = np.ones_like(cand_weights)

	# Combined score: balance distance (70%) and weight (30%)
	# Adjust these ratios to prioritize coverage vs sensitivity
	scores = 0.7 * norm_dists + 0.3 * norm_weights

	# Pick the candidate with the highest combined score
	pos = int(np.argmax(scores))
	chosen = int(cand_indices[pos])

	selected.append(chosen)
	available[chosen] = False

	return np.array(selected, dtype=int)

	def weighted_maximin_selection_with_weight(points, weights, k, coverage_weight=0.5):
	"""
	Select k points using weighted maximin strategy with adjustable balance.
	Combines space coverage (maximin) with importance sampling (weights).

	Args:
	points: Array of shape (n_samples, n_dims)
	weights: Array of shape (n_samples,) with sample importance weights
	k: Number of points to select
	coverage_weight: Weight for coverage (0-1). Higher = more coverage, less sensitivity bias

	Returns:
	selected_indices: Array of selected point indices
	"""
	n = points.shape[0]
	selected = []
	available = np.ones(n, dtype=bool)

	# 1) Start with weighted probability selection for the first point
	probs = weights / weights.sum()
	first = np.random.choice(n, p=probs)
	selected.append(first)
	available[first] = False

	# 2) Iteratively add points balancing distance and weight
	sensitivity_weight = 1.0 - coverage_weight

	for i in range(1, k):
	if i % 10 == 0:
	print(f"Selected {i} of {k} samples...")
	cand_indices = np.nonzero(available)[0]
	if len(cand_indices) == 0:
	break

	cand_points = points[cand_indices]
	cand_weights = weights[cand_indices]
	selected_points = points[np.array(selected)]

	# Compute pairwise distances to selected points
	dist_matrix = np.linalg.norm(
	cand_points[:, None, :] - selected_points[None, :, :], axis=2
	)
	min_dist_to_selected = dist_matrix.min(axis=1)

	# Normalize distances to [0, 1]
	if min_dist_to_selected.max() > 0:
	norm_dists = min_dist_to_selected / min_dist_to_selected.max()
	else:
	norm_dists = np.ones_like(min_dist_to_selected)

	# Normalize weights to [0, 1]
	if cand_weights.max() > 0:
	norm_weights = cand_weights / cand_weights.max()
	else:
	norm_weights = np.ones_like(cand_weights)

	# Combined score with adjustable balance
	scores = coverage_weight * norm_dists + sensitivity_weight * norm_weights

	# Pick the candidate with the highest combined score
	pos = int(np.argmax(scores))
	chosen = int(cand_indices[pos])

	selected.append(chosen)
	available[chosen] = False

	return np.array(selected, dtype=int)

	def iterative_split(samples, N, M, bound_names, max_attempts = 12):
	df = pd.DataFrame(data=samples, columns=bound_names)
	continuos_cols = [c for c in bound_names if c in ["CS","OS"]]

	with warnings.catch_warnings(record=True) as rw:
	bin_numeric = KBinsDiscretizer(n_bins=20,encode="ordinal",strategy='uniform')
	one_hot_encode = OneHotEncoder(handle_unknown="error",sparse_output=False,)
	col_trans1 = ColumnTransformer(transformers=[("bin_numeric",bin_numeric,continuos_cols)],remainder="passthrough",verbose_feature_names_out=False)
	col_trans2 = ColumnTransformer(transformers=[("one_hot_encode",one_hot_encode,df.columns)],remainder="drop",verbose_feature_names_out=False)
	pp = Pipeline([("col_trans1",col_trans1),("col_trans2",col_trans2)])
	pp.set_output(transform="pandas")
	one_hot_labels : pd.DataFrame = pp.fit_transform(df) # type: ignore

	# Converting to numpy
	df = df.to_numpy()
	one_hot_labels = one_hot_labels.to_numpy() # type: ignore

	# Setup split parameters
	subset_size = N/len(samples)
	subset = []
	attempt = 1
	# Loop to ensure that the extracted subset lenght is correct
	while attempt < max_attempts:
	# Split data
	_,_,subset,_ = iterative_train_test_split(df,one_hot_labels,subset_size)
	if len(subset) < N:
	if attempt == max_attempts:
	print(f"Failed to obtain desired number of samples!")
	subset_size += 0.025
	attempt += 1
	else:
	break

	print(f"Obtained a subset with {len(subset)} samples in {attempt} attempts!")

	return subset

	def generate_feasible_samples(bounds, sens_funcs, N=128, M=512, max_attempts=12, p_bases=np.array([0.5,0.5,5,5,1]), coverage_weight=0.5):
	"""
	Two-stage sampling approach:
	1. Generate feasible samples with uniform space coverage
	2. Select N samples using weighted maximin (balancing coverage and sensitivity)

	Args:
	bounds: Parameter bounds array
	sens_funcs: List of sensitivity functions
	N: Target number of samples to select
	M: Initial candidate pool size
	max_attempts: Maximum attempts to generate enough feasible samples
	p_bases: Rounding bases for each parameter
	coverage_weight: Weight for space coverage vs sensitivity (0.5 = equal importance)

	Returns:
	X_selected: Selected samples
	M: Final candidate pool size used
	"""
	if len(bounds) != len(sens_funcs):
	raise ValueError(f"Expected bounds and sens_funcs to have the same length. Got {bounds.shape} and {sens_funcs.shape}")

	# Filtering input
	bounds = np.asarray(bounds,dtype=float)
	d = len(bounds)

	# Setup sampling loop - generate enough feasible samples for selection
	X_feasible = []
	target_feasible = N * 3 # Generate 3x more samples than needed for good selection pool

	for attempt in range(1, max_attempts+1):
	# STAGE 1: Generate uniform Sobol samples for space coverage
	sampler = qmc.Sobol(d, scramble=True)
	X = sampler.random(n=M)

	# Scale to parameter bounds
	X_scaled = qmc.scale(X, bounds[:, 0]-p_bases/2, bounds[:, 1]+p_bases/2)

	# Round to closest acceptable value
	X_rounded = round_samples(X_scaled, p_bases)

	# Remove duplicates
	X_unique = np.unique(X_rounded, axis=0)

	# Applying feasibility filter
	feas_mask = check_feasibility_batch(X_unique, bounds)
	X_feasible = X_unique[feas_mask]

	# Check if we have enough feasible samples
	if len(X_feasible) >= target_feasible:
	print(f"Generated {len(X_feasible)} feasible samples in {attempt} attempts")
	break
	else:
	# Increase M if not enough points are feasible
	M = int(M * 2)
	if attempt == max_attempts:
	print(f"Warning: Only generated {len(X_feasible)} feasible samples (target was {target_feasible})")

	if len(X_feasible) == 0:
	raise ValueError("Could not generate any feasible samples with the given settings")
	elif len(X_feasible) < N:
	raise ValueError(f"Only {len(X_feasible)} feasible samples could be generated, but N={N} required. Increase M or max_attempts.")

	# STAGE 2: Select N samples using weighted maximin selection
	print(f"Selecting {N} samples from {len(X_feasible)} feasible candidates...")
	weights = compute_sample_weights(X_feasible, sens_funcs, bounds)

	# Adjust the weighted_maximin_selection to use the coverage_weight parameter
	# (We'll pass it directly in the call)
	selected_indices = weighted_maximin_selection_with_weight(X_feasible, weights, N, coverage_weight)
	X_selected = X_feasible[selected_indices]

	print(f"Selected {len(X_selected)} samples balancing space coverage and sensitivity")

	return X_selected, M

	def validate_samples(samples,bounds,sens_funcs):
	print("Checking if constraints were respected")
	valid = check_feasibility_batch(samples,bounds)
	if any(valid == False):
	raise ValueError("At least one samples does not respect the provided constraints")
	print("Checking if any samples are identical")
	if len(np.unique(samples, axis=0)) != len(samples):
	raise ValueError("At least one identical pair of parameters found")
	print("Validation complete")

	def round_samples(samples,p_bases):
	for i in range(len(p_bases)):
	samples[:,i] = round_to_base(samples[:,i],p_bases[i])
	return samples

	def round_to_base(x,base=1):
	return base*np.rint(x/base)

	def main():

	bound_names = ["CA","OA","CS","OS","AF"]
	N = 50 # target samples
	M = 2048 # candidate pool size
	csv_name = "samples_filling.csv"
	csv_path = "."
	csv_path = os.path.join(csv_path,csv_name)

	# Define parameter bounds
	bounds = np.array([
	[-10.0, 5.0], # CA
	[-10.0, 10.0], # OA
	[550.0, 700.0], # CS
	[350.0, 700.0], # OS
	[-8.5, 20.0] # AF
	], dtype=float)

	d = bounds.shape[0]

	# ========== SENSITIVITY FUNCTION DATA ==========
	# Define your parameter values, lift coefficients (CL), and drag coefficients (CD)
	# Aerodynamic efficiency will be calculated as CL/CD

	# s1: CA parameter
	s1_param_values = np.array([-10,-8,-6,-4,-2,0,2,4,5])
	s1_lift = np.array([2.71597,2.59168,2.38756,2.11036,1.79931,1.46873,1.13276,0.79852,0.63399]) # Replace with CL values
	s1_drag = np.array([0.19559,0.16673,0.13793,0.11181,0.08745,0.06607,0.04852,0.03574,0.03121]) # Replace with CD values

	# s2: OA parameter
	s2_param_values = np.array([-10,-8,-6,-4,-2,0,2,4,6,8,10])
	s2_lift = np.array([2.11753,2.00106,1.87441,1.74326,1.60771,1.46873,1.32822,1.18505,1.03937,0.88601,0.72393]) # Replace with CL values
	s2_drag = np.array([0.12137,0.10840,0.09681,0.08580,0.07550,0.06607,0.05760,0.05028,0.04426,0.04071,0.04110]) # Replace with CD values

	# s3: CS parameter
	s3_param_values = np.array([700,675,650,625,600,575,550])
	s3_lift = np.array([1.59557,1.56641,1.53579,1.50281,1.46873,1.43109,1.39120]) # Replace with CL values
	s3_drag = np.array([0.07392,0.07200,0.07008,0.06806,0.06607,0.06395,0.06179]) # Replace with CD values

	# s4: OS parameter
	s4_param_values = np.array([700,650,600,550,500,455,400,350])
	s4_lift = np.array([1.76696,1.72398,1.67319,1.60908,1.53883,1.46873,1.37725,1.29316]) # Replace with CL values
	s4_drag = np.array([0.08746,0.08379,0.07981,0.07517,0.07047,0.06607,0.06063,0.05588]) # Replace with CD values

	# s5: AF parameter
	s5_param_values = np.array([-8.5,-4,0,4,8,12,16,20])
	s5_lift = np.array([1.31019,1.35985,1.39354,1.42229,1.45279,1.48344,1.50923,1.53197]) # Replace with CL values
	s5_drag = np.array([0.05940,0.06138,0.06270,0.06387,0.06528,0.06673,0.06792,0.06904]) # Replace with CD values

	# ========== CREATE INTERPOLATORS FOR LIFT AND DRAG (built once for efficiency) ==========
	_s1_lift_interp = interpolate.make_interp_spline(s1_param_values, s1_lift, k=3)
	_s1_drag_interp = interpolate.make_interp_spline(s1_param_values, s1_drag, k=3)
	_s1_lift_deriv = _s1_lift_interp.derivative()
	_s1_drag_deriv = _s1_drag_interp.derivative()

	_s2_lift_interp = interpolate.make_interp_spline(s2_param_values, s2_lift, k=3)
	_s2_drag_interp = interpolate.make_interp_spline(s2_param_values, s2_drag, k=3)
	_s2_lift_deriv = _s2_lift_interp.derivative()
	_s2_drag_deriv = _s2_drag_interp.derivative()

	_s3_lift_interp = interpolate.make_interp_spline(np.flip(s3_param_values), np.flip(s3_lift), k=3)
	_s3_drag_interp = interpolate.make_interp_spline(np.flip(s3_param_values), np.flip(s3_drag), k=3)
	_s3_lift_deriv = _s3_lift_interp.derivative()
	_s3_drag_deriv = _s3_drag_interp.derivative()

	_s4_lift_interp = interpolate.make_interp_spline(np.flip(s4_param_values), np.flip(s4_lift), k=3)
	_s4_drag_interp = interpolate.make_interp_spline(np.flip(s4_param_values), np.flip(s4_drag), k=3)
	_s4_lift_deriv = _s4_lift_interp.derivative()
	_s4_drag_deriv = _s4_drag_interp.derivative()

	_s5_lift_interp = interpolate.make_interp_spline(s5_param_values, s5_lift, k=3)
	_s5_drag_interp = interpolate.make_interp_spline(s5_param_values, s5_drag, k=3)
	_s5_lift_deriv = _s5_lift_interp.derivative()
	_s5_drag_deriv = _s5_drag_interp.derivative()

	# ========== SENSITIVITY FUNCTIONS ==========
	def s1(p):
	return np.abs(_s1_lift_deriv(p)) + np.abs(_s1_drag_deriv(p))

	def s2(p):
	return np.abs(_s2_lift_deriv(p)) + np.abs(_s2_drag_deriv(p))

	def s3(p):
	return np.abs(_s3_lift_deriv(p)) + np.abs(_s3_drag_deriv(p))

	def s4(p):
	return np.abs(_s4_lift_deriv(p)) + np.abs(_s4_drag_deriv(p))

	def s5(p):
	return np.abs(_s5_lift_deriv(p)) + np.abs(_s5_drag_deriv(p))

	sens_funcs = [s1, s2, s3, s4, s5]

	# Generate the samples using two-stage approach
	# This now returns exactly N samples that balance space coverage and sensitivity
	samples,M = generate_feasible_samples(bounds=bounds,sens_funcs=sens_funcs,N=N,M=M,coverage_weight=0.5)

	# Validate the samples
	validate_samples(samples,bounds,sens_funcs)

	# Add column for profile
	profile_sampler = qmc.Sobol(1,scramble=True)
	profile_samples = profile_sampler.random(n=len(samples))
	profile_samples = qmc.scale(profile_samples,0.5,12.5)
	profile_samples = round_to_base(profile_samples,base=1)

	samples = np.c_[profile_samples,samples]

	print("Saving to file...")
	try:
	np.savetxt(csv_name,samples,delimiter=",",header="P,"+",".join(bound_names),fmt='%f')
	print(f"Saved {csv_name}!")
	except:
	raise RuntimeError("Could not save .csv file")

	if __name__ == "__main__":
	main()