deeplearning/modulus/modulus-core-v040/_modules/modulus/metrics/general/calibration.html

Source code for modulus.metrics.general.calibration

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from typing import Union

import numpy as np
import torch

from modulus.metrics.general.histogram import histogram, linspace

Tensor = torch.Tensor


[docs]def find_rank( bin_edges: Tensor, counts: Tensor, obs: Union[Tensor, np.ndarray] ) -> Tensor: """Finds the rank of the observation with respect to the given counts and bins. Parameters ---------- bins_edges : Tensor Tensor [N+1, ...] containing bin edges. The leading dimension must represent the N+1 bin edges. counts : Tensor Tensor [N, ...] containing counts, defined over bins. The non-zeroth dimensions of bins and counts must be compatible. obs : Union[Tensor, np.ndarray] Tensor or array containing an observation over which the ranks is computed with respect to. Returns ------- Tensor Tensor of rank for eac of the batched dimensions [...] """ if isinstance(obs, np.ndarray): obs = torch.from_numpy(obs).to(counts.device) if bin_edges.shape[1:] != counts.shape[1:]: raise ValueError( "Expected bins and counts to have compatible non-zeroth dimensions but have shapes" + str(bin_edges.shape[1:]) + " and " + str(counts.shape[1:]) + "." ) if bin_edges.shape[1:] != obs.shape: raise ValueError( "Expected bins and observations to have compatible broadcasting dimensions but have shapes" + str(bin_edges.shape[1:]) + " and " + str(obs.shape) + "." ) if bin_edges.shape[0] != counts.shape[0] + 1: raise ValueError( "Expected zeroth dimension of counts to be equal to the zeroth dimension of bins + 1 but have shapes" + str(bin_edges.shape[0]) + " and " + str(counts.shape[0]) + "+1." ) n = torch.sum(counts, dim=0)[0] bin_mids = 0.5 * (bin_edges[1:] + bin_edges[:-1]) right = torch.sum(counts * (bin_mids <= obs[None, ...]), dim=0) return right / n

def _rank_probability_score_from_counts( rank_bin_edges: Tensor, rank_counts: Tensor ) -> Tensor: """Finds the rank of the observation with respect to the given counts and bins. Computes .. math:: 3 * \int_0^1 (F_X(x) - F_U(x))^2 dx where F represents a cumulative distribution function, X represents the rank distribution and U represents a Uniform distribution. Parameters ---------- rank_bins_edges : Tensor Tensor [N+1, ...] containing rank bin edges. The leading dimension must represent the N+1 bin edges. rank_counts : Tensor Tensor [N, ...] containing rank counts, defined over bins. The non-zeroth dimensions of bin edges and counts must be compatible. Returns ------- Tensor Tensor of the Ranked Probability Score for each batched dimension of the input. """ cdf = torch.cumsum(rank_counts, dim=0) cdf = cdf / cdf[-1] normalization = torch.sum((1.0 - rank_bin_edges[1:]) ** 2, dim=0) return torch.sum((cdf - rank_bin_edges[1:]) ** 2, dim=0) / normalization

[docs]def rank_probability_score(ranks: Tensor) -> Tensor: """ Computes the Rank Probability Score for the passed ranks. Internally, this creates a histogram for the ranks and computes the Rank Probability Score (RPS) using the histogram. With the histogram the RPS is computed as .. math:: \int_0^1 (F_X(x) - F_U(x))^2 dx where F represents a cumulative distribution function, X represents the rank distribution and U represents a Uniform distribution. For computation of the ranks, use _find_rank. Parameters ---------- ranks : Tensor Tensor [B, ...] containing ranks, where the leading dimension represents the batch, or ensemble, dimension. The non-zeroth dimensions are batched over. Returns ------- Tensor Tensor of RPS for each of the batched dimensions [...] """ start = 0.0 * ranks[0, ...] end = start + 1.0 bins = linspace(start, end, 10) bin_edges, bin_counts = histogram(ranks, bins=bins) return _rank_probability_score_from_counts(bin_edges, bin_counts)
© Copyright 2023, NVIDIA Modulus Team. Last updated on Jan 25, 2024.