from __future__ import annotations
from dataclasses import dataclass
from io import BytesIO
from pathlib import Path
import base64
import html
import json
import random
import sys
import matplotlib.pyplot as plt
from matplotlib import colors
from matplotlib.patches import Rectangle
from mplsoccer import Pitch
import numpy as np
import pandas as pd
import torch
from torch import nn
from torch.utils.data import DataLoader, TensorDataset
SCRIPT_DIR = Path(__file__).resolve().parent
PROJECT_ROOT = SCRIPT_DIR.parent
MODEL_DIR = PROJECT_ROOT / "data" / "modeling"
REPORTS_DIR = PROJECT_ROOT / "reports"
REPORT_PATH = REPORTS_DIR / "attack_pv_interaction_gnn_report.html"
JSON_PATH = MODEL_DIR / "attack_pv_interaction_gnn_metrics.json"
MODEL_PATH = MODEL_DIR / "attack_pv_interaction_gnn_bundle.pt"
ATTACK_PRED_PATH = MODEL_DIR / "attack_interaction_gnn_test_predictions.parquet"
PV_PRED_PATH = MODEL_DIR / "pv_interaction_gnn_test_predictions.parquet"
if str(SCRIPT_DIR) not in sys.path:
sys.path.insert(0, str(SCRIPT_DIR))
import train_attack_prediction_ffn as base # noqa: E402
RANDOM_SEED = 42
BATCH_SIZE = 256
MAX_EPOCHS = 260
PATIENCE = 32
LEARNING_RATE = 4e-4
WEIGHT_DECAY = 1e-5
SMOOTH_LAMBDA = 0.005
GATE_ENTROPY_LAMBDA = 0.001
ZONE_ORDER = [
"Deep_Cross__Der_",
"Half_Space__Der_",
"Creativity_Zone",
"Half_Space__Izq_",
"Deep_Cross__Izq_",
"Cross__Der_",
"Cut_Back__Der_",
"Scoring_Zone",
"Cut_Back__Izq_",
"Cross__Izq_",
]
PRETTY_ZONE = {
"Scoring_Zone": "Scoring Zone",
"Creativity_Zone": "Creativity Zone",
"Half_Space__Izq_": "Half-Space Izq",
"Half_Space__Der_": "Half-Space Der",
"Cut_Back__Izq_": "Cut-Back Izq",
"Cut_Back__Der_": "Cut-Back Der",
"Cross__Izq_": "Cross Izq",
"Cross__Der_": "Cross Der",
"Deep_Cross__Izq_": "Deep Cross Izq",
"Deep_Cross__Der_": "Deep Cross Der",
}
ATTACK_PREV_JSON = MODEL_DIR / "attack_distribution_gnn_metrics.json"
PV_PREV_JSON = MODEL_DIR / "pv_distribution_gnn_metrics.json"
@dataclass
class TaskData:
df: pd.DataFrame
global_x: np.ndarray
attack_node_x: np.ndarray
defense_node_x: np.ndarray
y_dist: np.ndarray
baseline_long: np.ndarray
baseline_short: np.ndarray
train_idx: np.ndarray
val_idx: np.ndarray
test_idx: np.ndarray
val_start_date: str
task_name: str
@dataclass
class SplitData:
global_x: np.ndarray
attack_node_x: np.ndarray
defense_node_x: np.ndarray
y_dist: np.ndarray
baseline_long: np.ndarray
baseline_short: np.ndarray
metadata: pd.DataFrame
def _set_seed(seed: int = RANDOM_SEED) -> None:
random.seed(seed)
np.random.seed(seed)
torch.manual_seed(seed)
def _attack_zone_rectangles() -> dict[str, list[tuple[float, float, float, float]]]:
zones: dict[str, list[tuple[float, float, float, float]]] = {}
def add(z: str, x0: float, x1: float, y0: float, y1: float) -> None:
zones.setdefault(z, []).append((x0, y0, x1 - x0, y1 - y0))
add("Scoring_Zone", 83, 100, 37, 63)
add("Cut_Back__Izq_", 83, 100, 63, 79)
add("Cross__Izq_", 83, 100, 79, 100)
add("Cut_Back__Der_", 83, 100, 21, 37)
add("Cross__Der_", 83, 100, 0, 21)
add("Creativity_Zone", 60, 83, 37, 63)
add("Half_Space__Izq_", 60, 83, 63, 79)
add("Deep_Cross__Izq_", 60, 83, 79, 100)
add("Half_Space__Der_", 60, 83, 21, 37)
add("Deep_Cross__Der_", 60, 83, 0, 21)
return zones
ZONES_RECTS = _attack_zone_rectangles()
def _img_to_base64(fig: plt.Figure) -> str:
buf = BytesIO()
fig.savefig(buf, format="png", dpi=180, bbox_inches="tight", facecolor=fig.get_facecolor())
plt.close(fig)
return base64.b64encode(buf.getvalue()).decode("ascii")
def _normalized_graphs() -> tuple[torch.Tensor, torch.Tensor, torch.Tensor]:
neighbors = {
"Deep_Cross__Der_": ["Half_Space__Der_", "Cross__Der_", "Deep_Cross__Izq_"],
"Half_Space__Der_": ["Deep_Cross__Der_", "Creativity_Zone", "Cut_Back__Der_", "Half_Space__Izq_"],
"Creativity_Zone": ["Half_Space__Der_", "Half_Space__Izq_", "Scoring_Zone", "Cut_Back__Der_", "Cut_Back__Izq_"],
"Half_Space__Izq_": ["Creativity_Zone", "Deep_Cross__Izq_", "Cut_Back__Izq_", "Half_Space__Der_"],
"Deep_Cross__Izq_": ["Half_Space__Izq_", "Cross__Izq_", "Deep_Cross__Der_"],
"Cross__Der_": ["Deep_Cross__Der_", "Cut_Back__Der_", "Cross__Izq_"],
"Cut_Back__Der_": ["Cross__Der_", "Scoring_Zone", "Half_Space__Der_", "Cut_Back__Izq_", "Creativity_Zone"],
"Scoring_Zone": ["Cut_Back__Der_", "Cut_Back__Izq_", "Creativity_Zone"],
"Cut_Back__Izq_": ["Cross__Izq_", "Scoring_Zone", "Half_Space__Izq_", "Cut_Back__Der_", "Creativity_Zone"],
"Cross__Izq_": ["Deep_Cross__Izq_", "Cut_Back__Izq_", "Cross__Der_"],
}
n = len(ZONE_ORDER)
zone_to_idx = {z: i for i, z in enumerate(ZONE_ORDER)}
adj = np.zeros((n, n), dtype=np.float32)
cross = np.eye(n, dtype=np.float32)
edge_pairs: list[tuple[int, int]] = []
for z, neighs in neighbors.items():
i = zone_to_idx[z]
for neigh in neighs:
j = zone_to_idx[neigh]
adj[i, j] = 1.0
cross[i, j] = 1.0
edge_pairs.append((i, j))
deg = np.where(adj.sum(axis=1, keepdims=True) > 0, adj.sum(axis=1, keepdims=True), 1.0)
adj = adj / deg
cross_deg = np.where(cross.sum(axis=1, keepdims=True) > 0, cross.sum(axis=1, keepdims=True), 1.0)
cross = cross / cross_deg
return torch.tensor(adj, dtype=torch.float32), torch.tensor(cross, dtype=torch.float32), torch.tensor(edge_pairs, dtype=torch.long)
ADJ_MATRIX, CROSS_MATRIX, EDGE_INDEX = _normalized_graphs()
def _standardize_global(global_features: pd.DataFrame, train_idx: np.ndarray) -> tuple[np.ndarray, dict]:
fill_values = global_features.iloc[train_idx].median(numeric_only=False)
filled = global_features.fillna(fill_values)
means = filled.iloc[train_idx].mean(axis=0)
stds = filled.iloc[train_idx].std(axis=0, ddof=0).replace(0, 1.0)
scaled = ((filled - means) / stds).to_numpy(dtype=np.float32)
return scaled, {
"fill_values": fill_values.to_dict(),
"means": means.to_dict(),
"stds": stds.to_dict(),
"global_feature_columns": list(global_features.columns),
}
def _standardize_nodes(node_tensor: np.ndarray, train_idx: np.ndarray) -> tuple[np.ndarray, dict]:
train = node_tensor[train_idx]
fill = np.nanmedian(train, axis=0)
filled = np.where(np.isnan(node_tensor), fill[None, :, :], node_tensor)
means = filled[train_idx].mean(axis=0)
stds = filled[train_idx].std(axis=0, ddof=0)
stds = np.where(stds > 0, stds, 1.0)
scaled = (filled - means[None, :, :]) / stds[None, :, :]
return scaled.astype(np.float32), {
"fill_values": fill.tolist(),
"means": means.tolist(),
"stds": stds.tolist(),
}
def _make_split(task: TaskData, idx: np.ndarray) -> SplitData:
return SplitData(
global_x=task.global_x[idx].astype(np.float32),
attack_node_x=task.attack_node_x[idx].astype(np.float32),
defense_node_x=task.defense_node_x[idx].astype(np.float32),
y_dist=task.y_dist[idx].astype(np.float32),
baseline_long=task.baseline_long[idx].astype(np.float32),
baseline_short=task.baseline_short[idx].astype(np.float32),
metadata=task.df.iloc[idx].copy().reset_index(drop=True),
)
def _make_loader(split: SplitData, shuffle: bool) -> DataLoader:
dataset = TensorDataset(
torch.from_numpy(split.global_x),
torch.from_numpy(split.attack_node_x),
torch.from_numpy(split.defense_node_x),
torch.from_numpy(split.y_dist),
torch.from_numpy(split.baseline_long),
torch.from_numpy(split.baseline_short),
)
return DataLoader(dataset, batch_size=BATCH_SIZE, shuffle=shuffle)
class IntraGraphBlock(nn.Module):
def __init__(self, in_dim: int, out_dim: int, dropout: float) -> None:
super().__init__()
self.self_lin = nn.Linear(in_dim, out_dim)
self.neigh_lin = nn.Linear(in_dim, out_dim)
self.norm = nn.LayerNorm(out_dim)
self.dropout = nn.Dropout(dropout)
def forward(self, x: torch.Tensor, adj: torch.Tensor) -> torch.Tensor:
neigh = torch.einsum("ij,bjf->bif", adj, x)
h = self.self_lin(x) + self.neigh_lin(neigh)
h = self.norm(h)
h = torch.relu(h)
return self.dropout(h)
class CrossGraphBlock(nn.Module):
def __init__(self, src_dim: int, dst_dim: int, out_dim: int, dropout: float) -> None:
super().__init__()
self.dst_lin = nn.Linear(dst_dim, out_dim)
self.src_lin = nn.Linear(src_dim, out_dim)
self.norm = nn.LayerNorm(out_dim)
self.dropout = nn.Dropout(dropout)
def forward(self, dst: torch.Tensor, src: torch.Tensor, cross_adj: torch.Tensor) -> torch.Tensor:
src_msg = torch.einsum("ij,bjf->bif", cross_adj, src)
h = self.dst_lin(dst) + self.src_lin(src_msg)
h = self.norm(h)
h = torch.relu(h)
return self.dropout(h)
class InteractionDistributionGNN(nn.Module):
def __init__(self, attack_node_dim: int, defense_node_dim: int, global_dim: int, hidden_dim: int = 96, global_hidden: int = 96, num_layers: int = 3) -> None:
super().__init__()
self.global_encoder = nn.Sequential(
nn.Linear(global_dim, 192),
nn.ReLU(),
nn.Dropout(0.10),
nn.Linear(192, global_hidden),
nn.ReLU(),
)
self.attack_encoder = nn.Sequential(nn.Linear(attack_node_dim + global_hidden, hidden_dim), nn.ReLU())
self.defense_encoder = nn.Sequential(nn.Linear(defense_node_dim + global_hidden, hidden_dim), nn.ReLU())
self.attack_blocks = nn.ModuleList([IntraGraphBlock(hidden_dim, hidden_dim, 0.06) for _ in range(num_layers)])
self.defense_blocks = nn.ModuleList([IntraGraphBlock(hidden_dim, hidden_dim, 0.06) for _ in range(num_layers)])
self.cross_to_attack = nn.ModuleList([CrossGraphBlock(hidden_dim, hidden_dim, hidden_dim, 0.05) for _ in range(num_layers)])
self.cross_to_defense = nn.ModuleList([CrossGraphBlock(hidden_dim, hidden_dim, hidden_dim, 0.05) for _ in range(num_layers)])
self.gate_head = nn.Linear(hidden_dim * 2, 1)
self.delta_head = nn.Linear(hidden_dim * 2, 1)
def forward(
self,
attack_node_x: torch.Tensor,
defense_node_x: torch.Tensor,
global_x: torch.Tensor,
baseline_long: torch.Tensor,
baseline_short: torch.Tensor,
adj: torch.Tensor,
cross: torch.Tensor,
) -> tuple[torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor]:
g = self.global_encoder(global_x)
g_rep = g.unsqueeze(1).expand(-1, attack_node_x.size(1), -1)
att = self.attack_encoder(torch.cat([attack_node_x, g_rep], dim=-1))
dfn = self.defense_encoder(torch.cat([defense_node_x, g_rep], dim=-1))
for att_block, dfn_block, cross_att, cross_dfn in zip(self.attack_blocks, self.defense_blocks, self.cross_to_attack, self.cross_to_defense):
att = att + att_block(att, adj) + cross_att(att, dfn, cross)
dfn = dfn + dfn_block(dfn, adj) + cross_dfn(dfn, att, cross)
pair = torch.cat([att, dfn], dim=-1)
gate = torch.sigmoid(self.gate_head(pair)).squeeze(-1)
mixed = gate * baseline_short + (1.0 - gate) * baseline_long
delta = self.delta_head(pair).squeeze(-1)
logits = torch.log(torch.clamp(mixed, min=1e-6)) + delta
pred = torch.softmax(logits, dim=1)
return pred, delta, gate, mixed
def _distribution_loss(pred: torch.Tensor, target: torch.Tensor, delta: torch.Tensor, gate: torch.Tensor) -> tuple[torch.Tensor, dict[str, float]]:
eps = 1e-8
kl = torch.nn.functional.kl_div(torch.log(torch.clamp(pred, min=eps)), target, reduction="batchmean")
smooth = torch.mean((delta[:, EDGE_INDEX[:, 0]] - delta[:, EDGE_INDEX[:, 1]]) ** 2)
gate_entropy = -torch.mean(gate * torch.log(torch.clamp(gate, min=eps)) + (1 - gate) * torch.log(torch.clamp(1 - gate, min=eps)))
loss = kl + (SMOOTH_LAMBDA * smooth) + (GATE_ENTROPY_LAMBDA * gate_entropy)
return loss, {"kl": float(kl.item()), "smooth": float(smooth.item()), "gate_entropy": float(gate_entropy.item())}
def _train_model(task: TaskData) -> tuple[InteractionDistributionGNN, list[dict[str, float]]]:
train = _make_split(task, task.train_idx)
val = _make_split(task, task.val_idx)
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
model = InteractionDistributionGNN(
attack_node_dim=train.attack_node_x.shape[2],
defense_node_dim=train.defense_node_x.shape[2],
global_dim=train.global_x.shape[1],
).to(device)
optimizer = torch.optim.AdamW(model.parameters(), lr=LEARNING_RATE, weight_decay=WEIGHT_DECAY)
train_loader = _make_loader(train, shuffle=True)
val_loader = _make_loader(val, shuffle=False)
best_state = None
best_val = float("inf")
patience_left = PATIENCE
history: list[dict[str, float]] = []
adj = ADJ_MATRIX.to(device)
cross = CROSS_MATRIX.to(device)
for epoch in range(1, MAX_EPOCHS + 1):
model.train()
running = 0.0
n_batches = 0
for global_x, attack_node_x, defense_node_x, y_dist, baseline_long, baseline_short in train_loader:
global_x = global_x.to(device)
attack_node_x = attack_node_x.to(device)
defense_node_x = defense_node_x.to(device)
y_dist = y_dist.to(device)
baseline_long = baseline_long.to(device)
baseline_short = baseline_short.to(device)
optimizer.zero_grad()
pred, delta, gate, mixed = model(attack_node_x, defense_node_x, global_x, baseline_long, baseline_short, adj, cross)
loss, parts = _distribution_loss(pred, y_dist, delta, gate)
loss.backward()
optimizer.step()
running += float(loss.item())
n_batches += 1
val_metrics = _evaluate_loader(model, val_loader, device)
history.append({"epoch": epoch, "train_loss": running / max(n_batches, 1), "val_loss": val_metrics["loss"], "val_kl": val_metrics["kl"]})
if val_metrics["loss"] < best_val - 1e-6:
best_val = val_metrics["loss"]
best_state = {k: v.detach().cpu().clone() for k, v in model.state_dict().items()}
patience_left = PATIENCE
else:
patience_left -= 1
if patience_left <= 0:
break
if best_state is None:
best_state = {k: v.detach().cpu().clone() for k, v in model.state_dict().items()}
model.load_state_dict(best_state)
return model, history
def _evaluate_loader(model: InteractionDistributionGNN, loader: DataLoader, device: torch.device) -> dict[str, float]:
model.eval()
total = 0.0
total_kl = 0.0
n_batches = 0
adj = ADJ_MATRIX.to(device)
cross = CROSS_MATRIX.to(device)
with torch.no_grad():
for global_x, attack_node_x, defense_node_x, y_dist, baseline_long, baseline_short in loader:
global_x = global_x.to(device)
attack_node_x = attack_node_x.to(device)
defense_node_x = defense_node_x.to(device)
y_dist = y_dist.to(device)
baseline_long = baseline_long.to(device)
baseline_short = baseline_short.to(device)
pred, delta, gate, mixed = model(attack_node_x, defense_node_x, global_x, baseline_long, baseline_short, adj, cross)
loss, parts = _distribution_loss(pred, y_dist, delta, gate)
total += float(loss.item())
total_kl += parts["kl"]
n_batches += 1
return {"loss": total / max(n_batches, 1), "kl": total_kl / max(n_batches, 1)}
def _predict(model: InteractionDistributionGNN, split: SplitData) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
model.eval()
preds: list[np.ndarray] = []
gates: list[np.ndarray] = []
mixeds: list[np.ndarray] = []
loader = _make_loader(split, shuffle=False)
adj = ADJ_MATRIX.to(device)
cross = CROSS_MATRIX.to(device)
with torch.no_grad():
for global_x, attack_node_x, defense_node_x, y_dist, baseline_long, baseline_short in loader:
global_x = global_x.to(device)
attack_node_x = attack_node_x.to(device)
defense_node_x = defense_node_x.to(device)
baseline_long = baseline_long.to(device)
baseline_short = baseline_short.to(device)
pred, delta, gate, mixed = model(attack_node_x, defense_node_x, global_x, baseline_long, baseline_short, adj, cross)
preds.append(pred.cpu().numpy())
gates.append(gate.cpu().numpy())
mixeds.append(mixed.cpu().numpy())
return np.vstack(preds), np.vstack(gates), np.vstack(mixeds)
def _metrics(y_true: np.ndarray, pred_model: np.ndarray, pred_long: np.ndarray, pred_short: np.ndarray) -> dict[str, float]:
def kl_proxy(y, p):
return float(np.mean(np.sum(y * (np.log(np.clip(y, 1e-8, 1.0)) - np.log(np.clip(p, 1e-8, 1.0))), axis=1)))
return {
"model_mae": base._mean_abs_error(y_true, pred_model),
"season_baseline_mae": base._mean_abs_error(y_true, pred_long),
"short8_baseline_mae": base._mean_abs_error(y_true, pred_short),
"model_jsd": base._jsd_mean(y_true, pred_model),
"season_baseline_jsd": base._jsd_mean(y_true, pred_long),
"short8_baseline_jsd": base._jsd_mean(y_true, pred_short),
"model_kl_proxy": kl_proxy(y_true, pred_model),
"season_baseline_kl_proxy": kl_proxy(y_true, pred_long),
"short8_baseline_kl_proxy": kl_proxy(y_true, pred_short),
}
def _load_prev_metrics(path: Path) -> dict[str, float]:
return json.loads(path.read_text(encoding="utf-8"))["test_metrics"]
def _history_plot(history: list[dict[str, float]], title: str) -> str:
hist = pd.DataFrame(history)
fig, ax = plt.subplots(figsize=(7.5, 4.2), facecolor="#F6F7F4")
ax.plot(hist["epoch"], hist["train_loss"], label="Train", color="#2B7A5A", linewidth=2)
ax.plot(hist["epoch"], hist["val_loss"], label="Validacion", color="#D1495B", linewidth=2)
ax.set_xlabel("Epoch")
ax.set_ylabel("Loss")
ax.set_title(title, fontsize=13, fontweight="bold", color="#14342B")
ax.grid(alpha=0.2)
ax.legend(frameon=False)
return _img_to_base64(fig)
def _draw_pitch_distribution(ax: plt.Axes, values: dict[str, float], title: str) -> None:
pitch = Pitch(pitch_type="opta", pitch_length=100, pitch_width=100, line_color="#D9E0DA", linewidth=1.2)
pitch.draw(ax=ax)
ax.set_facecolor("#F6F7F4")
vmax = max(values.values()) if values else 1.0
norm = colors.Normalize(vmin=0.0, vmax=max(vmax, 1e-6))
cmap = plt.cm.Greens
for zone, rects in ZONES_RECTS.items():
value = values.get(zone, 0.0)
for x, y, w, h in rects:
ax.add_patch(Rectangle((x, y), w, h, facecolor=cmap(norm(value)), edgecolor="#FFFFFF", linewidth=1.5, alpha=0.84, zorder=1))
ax.text(x + w / 2, y + h / 2, f"{value * 100:.1f}%", ha="center", va="center", fontsize=8.5, fontweight="bold", color="#16352C", zorder=3)
ax.set_title(title, fontsize=12, fontweight="bold", color="#14342B", pad=10)
def _task_match_quad(row: pd.Series, prefix_target: str) -> str:
fig, axes = plt.subplots(1, 4, figsize=(16, 4.6), facecolor="#F6F7F4")
fig.subplots_adjust(wspace=0.08)
real = {zone: float(row[f"{prefix_target}__{zone}"]) for zone in ZONE_ORDER}
model = {zone: float(row[f"pred_model__{prefix_target}__{zone}"]) for zone in ZONE_ORDER}
season = {zone: float(row[f"pred_season__{prefix_target}__{zone}"]) for zone in ZONE_ORDER}
short8 = {zone: float(row[f"pred_short8__{prefix_target}__{zone}"]) for zone in ZONE_ORDER}
_draw_pitch_distribution(axes[0], real, "Real")
_draw_pitch_distribution(axes[1], model, "Interaccion")
_draw_pitch_distribution(axes[2], season, "Baseline temporada")
_draw_pitch_distribution(axes[3], short8, "Baseline ultimos 8")
fig.suptitle(
f"{row['fecha'].strftime('%Y-%m-%d')} | {row.get('team_name', 'Equipo')} vs {row.get('opponent_name', 'Rival')}",
fontsize=15,
fontweight="bold",
color="#14342B",
y=1.02,
)
return _img_to_base64(fig)
def _render_compare_table(title: str, current: dict[str, float], previous: dict[str, float], season: dict[str, float], short8: dict[str, float]) -> str:
return f"""
{html.escape(title)}
Modelo MAE JSD KL Interaccion GNN {current['model_mae']:.4f} {current['model_jsd']:.4f} {current['model_kl_proxy']:.4f} GNN anterior {previous['model_mae']:.4f} {previous['model_jsd']:.4f} {previous['model_kl_proxy']:.4f} Baseline temporada {season['mae']:.4f} {season['jsd']:.4f} {season['kl']:.4f} Baseline ultimos 8 {short8['mae']:.4f} {short8['jsd']:.4f} {short8['kl']:.4f}
Cada zona tiene dos representaciones: una ofensiva propia y una defensiva del rival. Hay message passing dentro de cada grafo y tambien entre ambos grafos, para modelar explicitamente el matchup zona a zona. Se compara contra los dos baselines y contra la GNN anterior.
{attack_test['model_mae']:.4f}
{pv_test['model_mae']:.4f}
{summary['attack']['previous_test_metrics']['model_mae'] - attack_test['model_mae']:+.4f}
{summary['pv']['previous_test_metrics']['model_mae'] - pv_test['model_mae']:+.4f}
MAE interaccion {base._mean_abs_error(real[None, :], model[None, :]):.4f} | baseline temporada {base._mean_abs_error(real[None, :], season[None, :]):.4f} | baseline ultimos 8 {base._mean_abs_error(real[None, :], short8[None, :]):.4f}