feat(distributions): vectorize ricegamma logpdf, add K→0 fit fallback
- Replace per-term Python loop in _logpdf with a single vectorised kve call (shape N×M) in both ricegamma_gen and logricegamma_gen, giving order-of-magnitude speedup on large batch inputs. - Add adaptive series truncation: n_terms ≈ 3K+30, collapses to n=1 when K=0 so no unnecessary computation. - Cache Gauss-Laguerre quadrature nodes in _cdf to avoid recomputing roots_genlaguerre on every optimiser call. - Add fit() override that re-fits with K fixed to 0 when the MLE estimate falls below _K_ZERO_THRESH (1e-2), avoiding near-zero Rice series numerical issues. - Register logricegamma in the generate_data.py fitting pipeline. - Reduce ricegamma N_SERIES 90→36; adaptive truncation handles accuracy.
This commit is contained in:
@@ -1091,52 +1091,89 @@ class logricegamma_gen(rv_continuous):
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def _logpdf(self, y, alpha, beta, K):
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y = np.asarray(y, dtype=float)
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x = np.exp(y)
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z = 2.0 * x * np.sqrt((1.0 + K) / beta)
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y_flat = y.ravel() # work in 1-D, reshape at end
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# scipy broadcasts shape parameters to match y; extract unique scalar values.
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alpha_s = float(np.ravel(alpha)[0])
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beta_s = float(np.ravel(beta)[0])
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K_s = float(np.ravel(K)[0])
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z = 2.0 * np.exp(y_flat) * np.sqrt((1.0 + K_s) / beta_s)
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# log-prefactor: log(4 x^2 (1+K) e^{-K} / (Γ(α) β^α)), absorbs exp(-z)
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# so each series term uses kve-scaled Bessel values
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log_pre = (
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np.log(4.0) + 2.0 * y + np.log(1.0 + K) - K
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- sc.gammaln(alpha) - alpha * np.log(beta)
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np.log(4.0) + 2.0 * y_flat + np.log(1.0 + K_s) - K_s
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- sc.gammaln(alpha_s) - alpha_s * np.log(beta_s)
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- z
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)
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log_b1Kx2 = np.log(beta) + np.log(1.0 + K) + 2.0 * y # log[beta*(1+K)*x^2]
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log_b1Kx2 = np.log(beta_s) + np.log(1.0 + K_s) + 2.0 * y_flat # log[beta*(1+K)*x^2]
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log1pK = np.log(1.0 + K)
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logK_safe = np.log(np.where(K > 0, K, 1.0))
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log1pK = np.log(1.0 + K_s)
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logK_safe = np.log(K_s) if K_s > 0 else -np.inf
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log_terms = []
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for n in range(self.N_SERIES + 1):
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# log(kve(alpha-1-n, z)) = log(K_{alpha-1-n}(z)) + z
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log_kve_n = logricegamma_gen._log_kve(alpha - 1.0 - n, z)
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# Vectorised: build index array and evaluate all kve orders in one batched call.
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# Adaptive truncation: for small K, high-order terms are negligible.
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# Rule of thumb: N_terms > 3*K + 30; K=0 → only n=0 is non-zero.
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if K_s == 0.0:
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n_terms = 1
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else:
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n_terms = min(self.N_SERIES + 1, max(1, int(3 * K_s + 30) + 1))
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# K^n: for K=0 only the n=0 term survives (0^0 = 1)
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n_logK = 0.0 if n == 0 else np.where(K > 0, n * logK_safe, -np.inf)
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ns = np.arange(n_terms, dtype=float) # (N,)
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vs = alpha_s - 1.0 - ns # (N,)
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log_gammaln2 = 2.0 * sc.gammaln(ns + 1) # (N,) precomputed
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# ONE call: shape (N, M) where M = y_flat.size
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log_kve_all = logricegamma_gen._log_kve(
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vs[:, np.newaxis], z[np.newaxis, :]
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)
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# K^n coefficient: n=0 → 0.0; K_s=0 & n>0 → -inf (never reached when n_terms=1)
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with np.errstate(invalid='ignore'):
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n_logK = np.where(ns == 0, 0.0, ns * logK_safe) # (N,)
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log_Tn = (
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n_logK
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+ n * log1pK
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- 2.0 * float(sc.gammaln(n + 1))
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+ 2.0 * n * y # x^{2n} factor
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+ (alpha - 1.0 - n) / 2.0 * log_b1Kx2
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+ log_kve_n
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)
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log_terms.append(log_Tn)
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n_logK[:, np.newaxis]
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+ (ns * log1pK)[:, np.newaxis]
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- log_gammaln2[:, np.newaxis]
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+ 2.0 * ns[:, np.newaxis] * y_flat[np.newaxis, :]
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+ (vs / 2.0)[:, np.newaxis] * log_b1Kx2[np.newaxis, :]
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+ log_kve_all
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) # (N, M)
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log_arr = np.stack(log_terms, axis=0) # shape (N_MAX+1, *y.shape)
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max_lt = np.max(log_arr, axis=0) # shape (*y.shape)
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max_lt = np.max(log_Tn, axis=0) # (M,)
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with np.errstate(invalid='ignore'):
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shifted = log_arr - max_lt[np.newaxis, ...]
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log_sum = max_lt + np.log(np.sum(np.exp(shifted), axis=0))
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return log_pre + log_sum
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log_sum = max_lt + np.log(np.sum(np.exp(log_Tn - max_lt), axis=0))
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return (log_pre + log_sum).reshape(y.shape)
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#: K below this threshold triggers collapse to K-distribution (K fixed to 0).
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_K_ZERO_THRESH: float = 1e-2
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def fit(self, data, *args, **kwds):
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"""Fit with automatic K→0 collapse.
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After the unconstrained MLE, if the fitted K is below
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``_K_ZERO_THRESH`` the distribution reduces to the K-distribution
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(K=0). A fresh, cheaper fit is then performed with K fixed to 0,
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which avoids numerical issues from near-zero Rice series terms.
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Skipped when K is already fixed by the caller (``f2`` kwarg).
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"""
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if 'f2' in kwds:
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return super().fit(data, *args, **kwds)
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result = super().fit(data, *args, **kwds)
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if float(result[2]) < self._K_ZERO_THRESH:
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result = super().fit(data, *args, f2=0, **kwds)
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return result
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def _fitstart(self, data, args=None):
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# loc near the data mean; alpha/beta in (0.5, 1) for typical heavy-tail
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# radar clutter; K=1 moderate Rice factor; scale near data std.
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# radar clutter; K=0.5 conservative start (small K → fewer series terms).
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mean_d = float(np.mean(data))
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std_d = float(np.std(data))
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return (0.75, 0.75, 3.0, mean_d, max(std_d * 0.5, 0.1))
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return (0.75, 0.75, 0.5, mean_d, max(std_d * 0.5, 0.1))
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def _rvs(self, alpha, beta, K, size=None, random_state=None):
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# Compound sampler: Omega ~ Gamma(alpha, beta), X|Omega ~ Rice(nu, sigma)
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@@ -1147,6 +1184,10 @@ class logricegamma_gen(rv_continuous):
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z2 = random_state.normal(0.0, sigma, size=size)
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return np.log(np.hypot(z1, z2))
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# Cache for Gauss-Laguerre nodes: keyed by (alpha, N_PTS) to avoid
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# recomputing roots_genlaguerre on every optimizer call.
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_gl_cache: dict = {}
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def _cdf(self, y, alpha, beta, K):
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# Compound representation:
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# P(Y <= y) = E_Omega[ P(X <= e^y | Omega) ]
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@@ -1166,7 +1207,10 @@ class logricegamma_gen(rv_continuous):
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K_s = float(np.ravel(K)[0])
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_N_PTS = 50
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nodes, weights = roots_genlaguerre(_N_PTS, alpha_s - 1.0)
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cache_key = (round(alpha_s, 10), _N_PTS)
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if cache_key not in logricegamma_gen._gl_cache:
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logricegamma_gen._gl_cache[cache_key] = roots_genlaguerre(_N_PTS, alpha_s - 1.0)
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nodes, weights = logricegamma_gen._gl_cache[cache_key]
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# ncx2_arg shape: (*y.shape, N_PTS)
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ncx2_arg = (
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@@ -1202,7 +1246,7 @@ class ricegamma_gen(rv_continuous):
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"""
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#: Number of series terms. Increase for large K (rule: N_SERIES > 3*K + 30).
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N_SERIES: int = 90
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N_SERIES: int = 36
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def _shape_info(self):
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return [
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@@ -1250,41 +1294,55 @@ class ricegamma_gen(rv_continuous):
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def _logpdf(self, x, alpha, beta, K):
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x = np.asarray(x, dtype=float)
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z = 2.0 * x * np.sqrt((1.0 + K) / beta)
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x_flat = x.ravel()
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# scipy broadcasts shape params to x's shape; extract scalars
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alpha_s = float(np.ravel(alpha)[0])
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beta_s = float(np.ravel(beta)[0])
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K_s = float(np.ravel(K)[0])
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z = 2.0 * x_flat * np.sqrt((1.0 + K_s) / beta_s)
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# log-prefactor: log(4 x (1+K) e^{-K} / (Γ(α) β^α)), absorbs exp(-z)
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log_pre = (
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np.log(4.0) + np.log(x) + np.log(1.0 + K) - K
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- sc.gammaln(alpha) - alpha * np.log(beta)
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np.log(4.0) + np.log(x_flat) + np.log(1.0 + K_s) - K_s
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- sc.gammaln(alpha_s) - alpha_s * np.log(beta_s)
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- z
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)
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log_b1Kx2 = np.log(beta) + np.log(1.0 + K) + 2.0 * np.log(x)
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log_b1Kx2 = np.log(beta_s) + np.log(1.0 + K_s) + 2.0 * np.log(x_flat)
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log1pK = np.log(1.0 + K_s)
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logK_safe = np.log(K_s) if K_s > 0 else -np.inf
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log1pK = np.log(1.0 + K)
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logK_safe = np.log(np.where(K > 0, K, 1.0))
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# Adaptive truncation: K=0 → only n=0 term survives
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if K_s == 0.0:
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n_terms = 1
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else:
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n_terms = min(self.N_SERIES + 1, max(1, int(3 * K_s + 30) + 1))
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log_terms = []
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for n in range(self.N_SERIES + 1):
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log_kve_n = ricegamma_gen._log_kve(alpha - 1.0 - n, z)
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ns = np.arange(n_terms, dtype=float)
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vs = alpha_s - 1.0 - ns
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log_gammaln2 = 2.0 * sc.gammaln(ns + 1)
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n_logK = 0.0 if n == 0 else np.where(K > 0, n * logK_safe, -np.inf)
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# Single vectorised kve call: shape (n_terms, M)
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log_kve_all = ricegamma_gen._log_kve(vs[:, np.newaxis], z[np.newaxis, :])
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with np.errstate(invalid='ignore'):
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n_logK = np.where(ns == 0, 0.0, ns * logK_safe)
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log_Tn = (
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n_logK
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+ n * log1pK
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- 2.0 * float(sc.gammaln(n + 1))
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+ 2.0 * n * np.log(x) # x^{2n} factor
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+ (alpha - 1.0 - n) / 2.0 * log_b1Kx2
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+ log_kve_n
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n_logK[:, np.newaxis]
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+ (ns * log1pK)[:, np.newaxis]
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- log_gammaln2[:, np.newaxis]
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+ 2.0 * ns[:, np.newaxis] * np.log(x_flat)[np.newaxis, :]
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+ (vs / 2.0)[:, np.newaxis] * log_b1Kx2[np.newaxis, :]
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+ log_kve_all
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)
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log_terms.append(log_Tn)
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log_arr = np.stack(log_terms, axis=0)
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max_lt = np.max(log_arr, axis=0)
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max_lt = np.max(log_Tn, axis=0)
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with np.errstate(invalid='ignore'):
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shifted = log_arr - max_lt[np.newaxis, ...]
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log_sum = max_lt + np.log(np.sum(np.exp(shifted), axis=0))
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return log_pre + log_sum
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log_sum = max_lt + np.log(np.sum(np.exp(log_Tn - max_lt), axis=0))
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return (log_pre + log_sum).reshape(x.shape)
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# Cache for Gauss-Laguerre nodes: keyed by (alpha, N_PTS)
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_gl_cache: dict = {}
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def _cdf(self, x, alpha, beta, K):
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# P(X <= x | Omega) = ncx2.cdf(2*(1+K)*x^2/Omega, 2, 2K)
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@@ -1297,7 +1355,11 @@ class ricegamma_gen(rv_continuous):
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beta_s = float(np.ravel(beta)[0])
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K_s = float(np.ravel(K)[0])
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nodes, weights = roots_genlaguerre(50, alpha_s - 1.0)
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_N_PTS = 50
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cache_key = (round(alpha_s, 10), _N_PTS)
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if cache_key not in ricegamma_gen._gl_cache:
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ricegamma_gen._gl_cache[cache_key] = roots_genlaguerre(_N_PTS, alpha_s - 1.0)
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nodes, weights = ricegamma_gen._gl_cache[cache_key]
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ncx2_arg = (
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2.0 * (1.0 + K_s) * (x[..., np.newaxis] ** 2)
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@@ -1315,11 +1377,32 @@ class ricegamma_gen(rv_continuous):
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z2 = random_state.normal(0.0, sigma, size=size)
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return np.hypot(z1, z2)
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#: K below this threshold triggers collapse to K-distribution (K fixed to 0).
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_K_ZERO_THRESH: float = 1e-2
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def fit(self, data, *args, **kwds):
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"""Fit with automatic K→0 collapse.
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After the unconstrained MLE, if the fitted K is below
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``_K_ZERO_THRESH`` a fresh fit is performed with K fixed to 0
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(K-distribution). Skipped when K is already fixed by the caller.
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"""
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if 'f2' in kwds:
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return super().fit(data, *args, **kwds)
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result = super().fit(data, *args, **kwds)
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if float(result[2]) < self._K_ZERO_THRESH:
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result = super().fit(data, *args, f2=0, **kwds)
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return result
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def _fitstart(self, data, args=None):
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# Shapes at scipy's default (1.0); loc = data mean; scale = data std.
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if args is None:
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args = (1.0,) * self.numargs
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return args + (float(np.mean(data)), float(np.std(data)))
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# alpha/beta near 1 for typical heavy-tail clutter; K=0.5 conservative
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# start keeps series short and avoids long first-call overhead.
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mean_d = float(np.mean(data))
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std_d = float(np.std(data))
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return (0.75, 0.75, 0.5, 0.0, max(mean_d * 0.5, 1e-3))
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ricegamma = ricegamma_gen(a=0.0, name='ricegamma', shapes='alpha, beta, K')
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@@ -5,7 +5,7 @@ import sys
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sys.path.insert(0, str(Path(__file__).resolve().parent.parent))
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from etc.fitting import Fitter
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from etc.tools.distributions import logweibull,lognakagami, loggamma_dist, k_dist, lograyleigh, logrice,logk
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from etc.tools.distributions import logweibull,lognakagami, loggamma_dist, k_dist, lograyleigh, logrice,logk, logricegamma
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from etc.tools.statistics import aic_statistic, bic_statistic
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import pandas as pd
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import plotly.io as pio
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@@ -37,7 +37,7 @@ if __name__ == "__main__":
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if not os.path.exists(DATA_FOLDER):
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os.makedirs(DATA_FOLDER)
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dist_list = [weibull_min,nakagami,gamma, rice, rayleigh, k_dist]
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dist_list_log = [logweibull,lognakagami,loggamma_dist,logrice,lograyleigh,logk]
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dist_list_log = [logweibull,lognakagami,loggamma_dist,logrice,lograyleigh,logk,logricegamma]
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statistics_dataframe_aic= pd.DataFrame(columns=[dist.name for dist in dist_list_log])
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statistics_dataframe_bic= pd.DataFrame(columns=[dist.name for dist in dist_list_log])
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