diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml index 86a6b9ec..9965629e 100644 --- a/.github/workflows/test.yml +++ b/.github/workflows/test.yml @@ -21,9 +21,8 @@ jobs: - {os: "ubuntu-22.04", python-version: "3.10"} - {os: "ubuntu-22.04", python-version: "3.9"} - {os: "ubuntu-20.04", python-version: "3.8"} - - {os: "ubuntu-20.04", python-version: "3.7"} #os: [ubuntu-latest] # TODO: add macos-latest, windows-latest ? - #python-version: [3.7, 3.8, 3.9, 3.10, 3.11] + #python-version: [3.8, 3.9, 3.10, 3.11] timeout-minutes: 30 diff --git a/Makefile b/Makefile index 66f41b1f..8f9d15d1 100644 --- a/Makefile +++ b/Makefile @@ -15,7 +15,8 @@ black-check: ## check black formatting flake8: ## check style with flake8 flake8 dadapy/base.py dadapy/metric_comparisons.py dadapy/clustering.py dadapy/id_estimation.py \ dadapy/density_estimation.py dadapy/id_discrete.py dadapy/data.py dadapy/feature_weighting.py \ - dadapy/kstar.py dadapy/neigh_graph.py dadapy/density_advanced.py tests #dev_scripts examples + dadapy/kstar.py dadapy/neigh_graph.py dadapy/density_advanced.py dadapy/hamming.py \ + tests #dev_scripts examples # to include the "dadapy" folder: pytest tests --doctest-modules dadapy tests/ test: ## run tests quickly with the default Python diff --git a/dadapy/hamming.py b/dadapy/hamming.py new file mode 100644 index 00000000..abf3f015 --- /dev/null +++ b/dadapy/hamming.py @@ -0,0 +1,627 @@ +import os +from time import time + +import numpy as np +from jax import devices as jdevices +from jax import jit, lax +from jax import numpy as jnp +from jax import random +from jax.scipy.special import gammaln +from jax.tree_util import register_pytree_node + +# from jax.experimental.host_callback import call + +jdevices("cpu")[0] # to run JAX on CPU +eps = 1e-7 # good old small epsilon + + +class Hamming: + def __init__( + self, + q=2, # number of states: 2 for binary spins. In the future we can think of extending this to q>2. + coordinates=None, # spins: must be normalized to +-1 to compute distances. + distances=None, # + crossed_distances=0, # 0 means we have one dataset with N samples and N(N-1)/2 (correlated) distances. + verbose=True, # + ): + self.q = q + self.coordinates = coordinates + self.distances = distances + self.crossed_distances = crossed_distances + self.verbose = verbose + + self.r = None + self.r_idx = None + self.D_values = None + self.D_counts = None + self.D_probs = None + self.D_mu_emp = None + self.D_var_emp = None + + def compute_distances( + self, + sort=False, + check_format=True, + ): + """ + Computes all to all distances in dataset and stores them + in the matrix "self.distances" of shape (Ns,Ns), where Ns is the number of samples + """ + if self.q == 2: + self.distances = jcompute_distances( + X1=self.coordinates, + X2=self.coordinates, + crossed_distances=self.crossed_distances, + check_format=check_format, + sort=sort, + ) + + """TODO: MODIFY HISTOGRAM ROUTINE TO DISCARD THE TRIVIAL ZEROS WHEN CROSSED_DISTANCES = 1""" + + def D_histogram( + self, + compute_flag=0, # 1 to compute histogram (else it is loaded) + save=False, # 1 to save computed histogram + resultsfolder="results/hist/", + filename="counts.txt", + ): + """ + Given the computed distances, this routine computes the histogram (Pemp). + It defines + - self.D_values, a vector containing the sampled distances + - self.D_counts, a vector containing how many times each distance was sampled + - self.D_probs, self.counts normalized by the total number of counts observed. + """ + assert self.crossed_distances == 0 + + if save: + os.makedirs(resultsfolder, exist_ok=True) + _filename = resultsfolder + filename + + if compute_flag: + self.D_values, self.D_counts = np.unique(self.distances, return_counts=True) + + if self.crossed_distances == 0: + Nsamples = self.distances.shape[0] + assert self.D_values[0] == 0 # trivial zeros + Nzeros = int( + Nsamples * (Nsamples + 1) / 2 + ) # trivial zeros, Gauss sum of them + self.D_counts[0] -= Nzeros + if self.D_counts[0] == 0: + self.D_values = self.D_values[1:] + self.D_counts = self.D_counts[1:] + self.D_probs = self.D_counts / np.sum(self.D_counts) + + if save: + np.savetxt( + fname=_filename, + X=np.transpose([self.D_values, self.D_counts]), + fmt="%d,%d", + ) + else: + f = np.loadtxt(_filename, delimiter=",", dtype=int) + self.D_values = f[:, 0] + self.D_counts = f[:, 1] + self.D_probs = self.D_counts / np.sum(self.D_counts) + + def set_r_quantile(self, alpha, round=True, precision=10): + """ + Defines + + - self.r as the quantile of order alpha of self.D_probs, + which can be used for rmax or rmin, + to discard distances larger than rmax or smaller than rmin, respectively. + - self.r_idx as the index of self.r in self.D_values + """ + if round: + alpha = np.round(alpha, precision) + self.D_probs = np.round(self.D_probs, precision) + + indices = np.where(np.cumsum(self.D_probs) <= alpha)[0] + if len(indices) == 0: + self.r_idx = 0 + else: + self.r_idx = indices[-1] + + self.r = int(self.D_values[self.r_idx]) + return + + def compute_moments(self): + """ + computes the empirical mean and variance of H.D_probs + """ + self.D_mu_emp = np.dot(self.D_probs, self.D_values) + self.D_var_emp = np.dot(self.D_probs, self.D_values**2) - self.D_mu_emp**2 + + +def check_data_format(X): + e1, e2 = np.unique(X) + assert ( + e1 == -1 and e2 == 1 + ), f"spins have to be formatted to -+1, but {np.unique(X)=}" + + +def jcompute_distances( + X1, + X2, + crossed_distances, + check_format=True, + sort=False, +): + """This routine works for Ising spins variables defined as +-1 (this is faster than scipy)""" + X1 = jnp.array(X1).astype(jnp.int32) + X2 = jnp.array(X2).astype(jnp.int32) + + if check_format: + check_data_format(X1) + check_data_format(X2) + + Ns1, N = X1.shape + Ns2 = X2.shape[0] # the samples in the other dataset must have also N spins... + + distances = jnp.zeros(shape=(Ns1, Ns2), dtype=jnp.int32) + sample_idx = 0 + lower_idx = 0 + pytree = { + "crossed_distances": crossed_distances, + "D": distances, + "X1": X1, + "X2": X2, + "sample_idx": sample_idx, + "lower_idx": lower_idx, # to avoid computing distances twice if crossed_distances=1 + "Ns1": Ns1, # number of samples in dataset 1 + "Ns2": Ns2, # number of samples in dataset 2 + "N": N, # number of spins in each sample + } + + pytree = lax.fori_loop( + lower=0, upper=Ns1, body_fun=_jcompute_distances, init_val=pytree + ) + + if sort: + return np.array(jnp.sort(pytree["D"])) + else: + return np.array(pytree["D"]) + + +@jit +def _jcompute_distances(idx, pytree): + """ + for each data sample indexed by "sample_idx" (row), computes the distance between it and the rest + """ + pytree["sample_idx"] = idx + pytree = lax.cond( + pytree["crossed_distances"], _set_lower_idx_true, _set_lower_idx_false, pytree + ) + pytree = lax.fori_loop( + lower=pytree["lower_idx"], + upper=pytree["Ns2"], + body_fun=compute_row_distances, + init_val=pytree, + ) + return pytree + + +def _set_lower_idx_true(pytree): + """ + if we have two datasets, we have Ns1 * Ns2 distances to compute. + """ + pytree["lower_idx"] = 0 + return pytree + + +def _set_lower_idx_false(pytree): + """ + if we have one dataset, we have Ns(Ns-1)/2 distances to compute (the upper triangular part of "distances") + """ + pytree["lower_idx"] = pytree["sample_idx"] + 1 + return pytree + + +@jit +def compute_row_distances(_idx, pytree): + """ + for each data sample indexed by "sample_idx", computes the distance between it and the rest + """ + pytree["D"] = ( + pytree["D"] + .at[pytree["sample_idx"], _idx] + .set( + jnp.int32( + ( + pytree["N"] + - jnp.dot( + pytree["X1"][pytree["sample_idx"], :], pytree["X2"][_idx, :] + ) + ) + / 2 + ) + ) + ) + return pytree + + +class Optimizer: + """ + Stochastic optimization + """ + + def __init__( + self, + key=0, + d0=0.0, # BID + d0_r=0.0, # BID + random perturbation (*** used by compute_Pmodel instead of d0...) + d1=0.0, # slope + d1_r=0.0, # slope + random pertubation (*** used by compute_Pmodel instead of d1...) + delta=0.0, # optimization step size + KL=jnp.double(0.0), # KL divergence between Pemp(r) and Pmodel(r) + KL_aux=jnp.inf, # auxiliary variable to check when KL decreases + remp=None, # vector with empirical Hamming distances + Pemp=None, # vector with empirical probabilities + Pmodel=None, # vector with model probabilities + Nsteps=0, # Number of steps for the optimization + accepted=0, # Accepted moves + acc_ratio=jnp.double(1.0), # Acceptance ratio + save_logKLs_flag=0, # Flag to save logKLs during optimization + logKLs=None, # Vector with logKLs during optimization + idx=0, # Auxiliary index + mod_divisor=0, # Auxiliary variable to export the log KL + Nsteps_max=1000, # Total number of saved steps (subsample of the total number of steps) + ): + self.key = key + self.d0 = d0 + self.d0_r = d0_r + self.d1 = d1 + self.d1_r = d1_r + self.delta = delta + self.KL = KL + self.KL_aux = KL_aux + self.remp = remp + self.Pemp = Pemp + self.Pmodel = Pmodel + self.Nsteps = Nsteps + self.accepted = accepted + self.acc_ratio = acc_ratio + self.save_logKLs_flag = save_logKLs_flag + self.logKLs = logKLs + self.idx = idx + self.mod_divisor = mod_divisor + self.Nsteps_max = Nsteps_max + + def _tree_flatten(self): + children = ( + self.key, + self.d0, + self.d0_r, + self.d1, + self.d1_r, + self.delta, + self.KL, + self.KL_aux, + self.remp, + self.Pemp, + self.Pmodel, + self.Nsteps, + self.accepted, + self.acc_ratio, + self.save_logKLs_flag, + self.logKLs, + self.idx, + self.mod_divisor, + ) # arrays / dynamic values + aux_data = { + "Nsteps_max": self.Nsteps_max, + } # static values + return (children, aux_data) + + @classmethod + def _tree_unflatten(cls, aux_data, children): + return cls(*children, **aux_data) + + +register_pytree_node(Optimizer, Optimizer._tree_flatten, Optimizer._tree_unflatten) + + +def _compute_Pmodel(idx, Op): + """ + note that this routine uses Op.d0_r and Op.d1_r to compute Pmodel + """ + ID = Op.d0_r + Op.d1_r * Op.remp[idx] + Op.Pmodel = Op.Pmodel.at[idx].set( + jnp.exp( + gammaln(ID + jnp.double(1)) + - gammaln(Op.remp[idx] + 1) + - gammaln(ID - Op.remp[idx] + 1) + - ID * jnp.log(jnp.double(2)) + ) + ) + # call(lambda x: print(f'{x}'),Op.Pmodel[idx]) + return Op + + +@jit +def compute_Pmodel(Op): + Op = lax.fori_loop( + lower=0, upper=Op.Pmodel.shape[0], body_fun=_compute_Pmodel, init_val=Op + ) + Op.Pmodel /= jnp.sum(Op.Pmodel) + return Op + + +@jit +def step(idx, Op): + Op.key, subkey = random.split(Op.key, num=2) + r = random.uniform(subkey, dtype=jnp.float64) + Op.d0_r = Op.d0 * (1 + Op.delta * (r - jnp.double(0.5))) + + Op.key, subkey = random.split(Op.key, num=2) + rr = random.uniform(subkey, dtype=jnp.float64) + Op.d1_r = Op.d1 * (1 + Op.delta * (rr - jnp.double(0.5))) + + Op = compute_Pmodel(Op) + Op = compute_KLd(Op) + Op = lax.cond(Op.KL <= Op.KL_aux, update_state, do_nothing, Op) + logical_condition = jnp.logical_and( + Op.save_logKLs_flag, jnp.mod(idx, Op.mod_divisor) == 0 + ) + Op = lax.cond(logical_condition, save_logKL, do_nothing, Op) + return Op + + +@jit +def compute_KLd(Op): + Op.KL = jnp.sum(Op.Pemp * jnp.log(Op.Pemp / Op.Pmodel)) + return Op + + +@jit +def update_state(Op): + Op.d0 = Op.d0_r + Op.d1 = Op.d1_r + Op.KL_aux = Op.KL + Op.accepted += 1 + return Op + + +@jit +def do_nothing(Op): + return Op + + +@jit +def save_logKL(Op): + Op.logKLs = Op.logKLs.at[Op.idx].set(jnp.log(Op.KL)) + Op.idx += 1 + return Op + + +@jit +def minimize_KL(Op): + Op.logKLs = jnp.empty(shape=(Op.Nsteps_max), dtype=jnp.double) + Op.mod_divisor = Op.Nsteps // Op.Nsteps_max + + Op = lax.fori_loop(lower=0, upper=Op.Nsteps, body_fun=step, init_val=Op) + + # This is necessary to keep the last *accepted* move + Op.d0_r = Op.d0 + Op.d1_r = Op.d1 + Op = compute_Pmodel(Op) + Op = compute_KLd(Op) + Op.acc_ratio = jnp.double(Op.accepted) / jnp.double(Op.Nsteps) + return Op + + +class BID: + def __init__( + self, + H=Hamming(), # instance of Hamming class defined above + Op=None, # instance of Optimizer class defined above + alphamin=0.0, + alphamax=0.2, + seed=1, + d0=jnp.double(0), # BID \equiv d(r=0) (see paper) + d1=jnp.double(0), # slope of d(r) at r=0 + d00=jnp.double(0), # initial value of d0 + d10=jnp.double(0), # initial value of d1 + delta=5e-4, + Nsteps=1e6, + optfolder0="results/opt/", + load_initial_condition_flag=False, + optimization_elapsed_time=None, + export_results=1, + export_logKLs=0, # To export the curve of logKLs during optimization + L=0, # Number of bits / Ising spins + ): + self.H = H + self.Op = Op + self.alphamin = alphamin + self.alphamax = alphamax + self.seed = seed + self.d0 = d0 + self.d1 = d1 + self.d00 = d00 + self.d10 = d10 + self.delta = delta + self.Nsteps = Nsteps + self.optimization_elapsed_time = optimization_elapsed_time # in minutes + self.export_results = export_results + self.export_logKLs = export_logKLs + self.L = L + self.intrinsic_dim = self.d0 + + self.key0 = random.PRNGKey(self.seed) + self.optfolder0 = optfolder0 + self.load_initial_condition_flag = load_initial_condition_flag + + if np.isclose(alphamin, 0): + self.regularize = False + else: + self.regularize = True + + def load_initial_condition( + self, + ): + self.set_filepaths() + _, self.d00, self.d10, _ = self.load_results() + + def set_filepaths( + self, + ): + self.optfolder = self.optfolder0 + self.optfolder += f"alphamin{self.alphamin:.5f}/" + self.optfolder += f"alphamax{self.alphamax:.5f}/" + self.optfolder += f"Nsteps{self.Nsteps}/" + self.optfolder += f"delta{self.delta:.5f}/" + self.optfolder += f"seed{self.seed}/" + self.optfile = self.optfolder + "opt.txt" + self.valfile = self.optfolder + "model_validation.txt" + self.KLfile = self.optfolder + "logKLs_opt.txt" + + def set_idmin( + self, + ): + if self.regularize is False: + self.idmin = 0 + self.rmin = self.H.D_values[0] + else: + self.H.set_r_quantile(self.alphamin) + self.rmin = self.H.r + self.idmin = self.H.r_idx + self.H.r = None + self.H.r_idx = None + + def set_idmax( + self, + ): + self.H.set_r_quantile(self.alphamax) + self.rmax = self.H.r + self.idmax = self.H.r_idx + self.H.r = None + self.H.r_idx = None + + def truncate_hist(self): + self.remp = jnp.array( + self.H.D_values[self.idmin : self.idmax + 1], dtype=jnp.float64 + ) + self.Pemp = jnp.array( + self.H.D_probs[self.idmin : self.idmax + 1], dtype=jnp.float64 + ) + self.Pemp /= jnp.sum(self.Pemp) + self.Pmodel = jnp.zeros(shape=self.Pemp.shape, dtype=jnp.float64) + + def test_initial_condition(self, d0, d1): + self.Op.d0_r = jnp.double(d0) + self.Op.d1_r = jnp.double(d1) + self.Op = compute_Pmodel(self.Op) + self.Op = compute_KLd(self.Op) + return np.log(self.Op.KL) + + def set_initial_condition(self, d00min=0.05, d00max=0.95, d00step=0.05): + # our home-made guess: + d00_guess_list = jnp.array([jnp.double(self.Op.remp[-1])]) + d10_guess_list = jnp.array([jnp.double(1)]) + + if self.L != 0: + # Inspired by Cristopher Erazo: + self.H.compute_moments() + _d00_guess_list = self.L * jnp.arange( + d00min, d00max + eps, d00step, dtype=jnp.double + ) + _d10_guess_list = jnp.double(2) - _d00_guess_list / jnp.double( + self.H.D_mu_emp + ) + + d00_guess_list = jnp.concatenate((d00_guess_list, _d00_guess_list)) + d10_guess_list = np.concatenate((d10_guess_list, _d10_guess_list)) + + logKLs0 = jnp.empty(shape=(len(d00_guess_list)), dtype=jnp.double) + for i in range(len(d00_guess_list)): + logKLs0 = logKLs0.at[i].set( + self.test_initial_condition( + d00_guess_list[i], + d10_guess_list[i], + ) + ) + # print(f'{logKLs0=}') + i0 = jnp.nanargmin(logKLs0) + # print(f'{i0=}') + # print(f'{logKLs0[i0]=}') + self.d00 = d00_guess_list[i0] # ; print(f'{self.d00=}') + self.d10 = d10_guess_list[i0] # ; print(f'{self.d10=}') + self.Op.d0 = self.d00 + self.Op.d1 = self.d10 + self.Op.KL_aux = jnp.exp(logKLs0[i0]) + + def computeBID( + self, + ): + self.set_idmin() + self.set_idmax() + self.truncate_hist() + self.set_filepaths() + if self.export_results: + os.makedirs(self.optfolder, exist_ok=True) + + self.Op = Optimizer( + key=self.key0, + d0=jnp.double(self.d00), + d1=jnp.double(self.d10), + delta=jnp.double(self.delta), + remp=self.remp, + Pemp=self.Pemp, + Pmodel=self.Pmodel, + Nsteps=self.Nsteps, + save_logKLs_flag=self.export_logKLs, + ) + self.set_initial_condition() + + if self.H.verbose == 1: + print("starting optimization") + + starting_time = time() + self.Op = minimize_KL(self.Op) + self.optimization_elapsed_time = (time() - starting_time) / 60.0 + + if self.H.verbose == 1: + print(f"optimization took {self.optimization_elapsed_time:.1f} minutes") + print( + f"d_0={self.Op.d0:.3f},d_1={self.Op.d1:.3f},logKL={jnp.log(self.Op.KL):.2f}" + ) + + if self.export_results: + os.system(f"rm -f {self.optfile}") + print( + f"{self.rmax:d},{self.Op.d0:.8f},{self.Op.d1:8f},{np.log(self.Op.KL):.8f}", + file=open(self.optfile, "a"), + ) + np.savetxt( + fname=self.valfile, + X=np.transpose([self.remp, self.Pemp, self.Op.Pmodel]), + ) + if self.export_logKLs: + np.savetxt(fname=self.KLfile, X=self.Op.logKLs) + + self.d0 = self.Op.d0.item() + self.d1 = self.Op.d1.item() + self.logKL = jnp.log(self.Op.KL).item() + self.Pmodel = np.array(self.Op.Pmodel) + self.intrinsic_dim = self.d0 + + def load_results( + self, + ): + self.set_filepaths() + return np.loadtxt(self.optfile, unpack=True, delimiter=",") + + def load_fit( + self, + ): + self.set_filepaths() + return np.loadtxt(self.valfile, unpack=True) + + def load_logKLs_opt( + self, + ): + self.set_filepaths() + return np.loadtxt(self.KLfile) diff --git a/examples/datasets/hamming/Ising2D/hist/L100_T1.00_Ns5000D_counts.txt b/examples/datasets/hamming/Ising2D/hist/L100_T1.00_Ns5000D_counts.txt new file mode 100644 index 00000000..e3d2bcab --- /dev/null +++ b/examples/datasets/hamming/Ising2D/hist/L100_T1.00_Ns5000D_counts.txt @@ -0,0 +1,55 @@ +0,6666 +1,41186 +2,137369 +3,313850 +4,540111 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a/examples/datasets/hamming/Ising2D/hist/L100_T2.28_Ns5000D_counts.txt b/examples/datasets/hamming/Ising2D/hist/L100_T2.28_Ns5000D_counts.txt new file mode 100644 index 00000000..4e0c1a0d --- /dev/null +++ b/examples/datasets/hamming/Ising2D/hist/L100_T2.28_Ns5000D_counts.txt @@ -0,0 +1,5689 @@ +2104,1 +2107,1 +2108,1 +2118,1 +2124,1 +2128,1 +2133,1 +2134,1 +2140,1 +2143,1 +2150,1 +2152,2 +2153,1 +2154,1 +2157,3 +2158,2 +2160,1 +2162,1 +2163,1 +2166,1 +2169,1 +2170,1 +2172,1 +2173,1 +2174,1 +2176,2 +2177,2 +2178,1 +2180,1 +2181,4 +2182,3 +2183,2 +2186,2 +2187,1 +2188,4 +2189,2 +2191,2 +2193,3 +2194,2 +2195,1 +2196,2 +2197,4 +2198,1 +2199,2 +2200,3 +2201,2 +2202,2 +2203,3 +2204,1 +2205,3 +2206,2 +2207,2 +2208,3 +2209,2 +2211,2 +2212,3 +2214,6 +2215,4 +2216,3 +2217,2 +2218,3 +2219,2 +2220,2 +2221,5 +2222,2 +2223,1 +2224,6 +2225,4 +2226,1 +2227,5 +2228,4 +2229,4 +2230,2 +2231,6 +2232,4 +2233,5 +2234,8 +2235,4 +2236,5 +2237,5 +2238,3 +2239,5 +2240,5 +2241,4 +2242,4 +2243,8 +2244,2 +2245,6 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a/examples/datasets/hamming/Ising2D/hist/L100_T4.00_Ns5000D_counts.txt b/examples/datasets/hamming/Ising2D/hist/L100_T4.00_Ns5000D_counts.txt new file mode 100644 index 00000000..edab85bd --- /dev/null +++ b/examples/datasets/hamming/Ising2D/hist/L100_T4.00_Ns5000D_counts.txt @@ -0,0 +1,586 @@ +4682,1 +4694,2 +4699,1 +4700,2 +4702,1 +4706,1 +4708,1 +4713,1 +4714,1 +4715,1 +4716,3 +4717,4 +4718,1 +4719,1 +4721,4 +4722,1 +4724,2 +4725,1 +4726,2 +4727,2 +4728,3 +4729,5 +4730,1 +4731,5 +4732,4 +4733,4 +4734,3 +4735,7 +4736,7 +4737,6 +4738,3 +4739,5 +4740,9 +4741,8 +4742,6 +4743,9 +4744,8 +4745,14 +4746,6 +4747,13 +4748,12 +4749,18 +4750,14 +4751,12 +4752,18 +4753,17 +4754,15 +4755,20 +4756,21 +4757,30 +4758,21 +4759,26 +4760,32 +4761,37 +4762,30 +4763,35 +4764,38 +4765,39 +4766,41 +4767,47 +4768,50 +4769,52 +4770,57 +4771,63 +4772,93 +4773,73 +4774,71 +4775,86 +4776,82 +4777,96 +4778,94 +4779,119 +4780,93 +4781,103 +4782,125 +4783,141 +4784,141 +4785,121 +4786,151 +4787,161 +4788,160 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a/examples/datasets/hamming/Ising2D/hist/L30_T2.21_Ns5000D_counts.txt b/examples/datasets/hamming/Ising2D/hist/L30_T2.21_Ns5000D_counts.txt new file mode 100644 index 00000000..c0929669 --- /dev/null +++ b/examples/datasets/hamming/Ising2D/hist/L30_T2.21_Ns5000D_counts.txt @@ -0,0 +1,785 @@ +52,1 +56,1 +60,2 +61,4 +62,4 +63,1 +64,6 +65,22 +66,16 +67,17 +68,35 +69,44 +70,51 +71,71 +72,106 +73,116 +74,172 +75,230 +76,222 +77,278 +78,371 +79,489 +80,623 +81,675 +82,779 +83,869 +84,1120 +85,1299 +86,1573 +87,1885 +88,2084 +89,2432 +90,2734 +91,3172 +92,3679 +93,4000 +94,4489 +95,5149 +96,5619 +97,6399 +98,6951 +99,7678 +100,8501 +101,9152 +102,10136 +103,10859 +104,11802 +105,12838 +106,13824 +107,14823 +108,16044 +109,17025 +110,18118 +111,19173 +112,20466 +113,21577 +114,22881 +115,23926 +116,25484 +117,26819 +118,27943 +119,29474 +120,30316 +121,32232 +122,33430 +123,34569 +124,35737 +125,36994 +126,38428 +127,39952 +128,41496 +129,42342 +130,43317 +131,44341 +132,45488 +133,46661 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a/examples/datasets/hamming/Ising2D/hist/L30_T2.40_Ns5000D_counts.txt b/examples/datasets/hamming/Ising2D/hist/L30_T2.40_Ns5000D_counts.txt new file mode 100644 index 00000000..4e857e99 --- /dev/null +++ b/examples/datasets/hamming/Ising2D/hist/L30_T2.40_Ns5000D_counts.txt @@ -0,0 +1,607 @@ +137,1 +143,1 +148,1 +149,2 +151,1 +154,4 +155,2 +156,3 +157,1 +158,1 +159,3 +160,2 +161,8 +162,5 +163,5 +164,6 +165,7 +166,11 +167,5 +168,8 +169,13 +170,14 +171,17 +172,14 +173,23 +174,22 +175,33 +176,15 +177,23 +178,26 +179,34 +180,33 +181,37 +182,39 +183,37 +184,50 +185,50 +186,57 +187,68 +188,66 +189,75 +190,69 +191,80 +192,97 +193,99 +194,107 +195,103 +196,120 +197,131 +198,155 +199,148 +200,173 +201,156 +202,197 +203,189 +204,216 +205,246 +206,257 +207,271 +208,281 +209,312 +210,308 +211,345 +212,368 +213,406 +214,396 +215,423 +216,478 +217,449 +218,518 +219,501 +220,598 +221,581 +222,619 +223,664 +224,744 +225,796 +226,832 +227,802 +228,904 +229,884 +230,900 +231,989 +232,1058 +233,1157 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a/examples/datasets/hamming/Ising2D/hist/L30_T3.70_Ns2000D_counts.txt b/examples/datasets/hamming/Ising2D/hist/L30_T3.70_Ns2000D_counts.txt new file mode 100644 index 00000000..e3af7c76 --- /dev/null +++ b/examples/datasets/hamming/Ising2D/hist/L30_T3.70_Ns2000D_counts.txt @@ -0,0 +1,179 @@ +362,3 +363,2 +364,1 +365,3 +366,3 +367,1 +368,2 +369,6 +370,3 +371,7 +372,13 +373,9 +374,9 +375,18 +376,18 +377,23 +378,30 +379,36 +380,48 +381,55 +382,78 +383,90 +384,103 +385,111 +386,138 +387,170 +388,193 +389,237 +390,281 +391,283 +392,379 +393,427 +394,517 +395,591 +396,732 +397,824 +398,994 +399,1141 +400,1318 +401,1445 +402,1764 +403,1987 +404,2203 +405,2516 +406,2815 +407,3209 +408,3644 +409,4049 +410,4540 +411,4931 +412,5673 +413,6243 +414,6930 +415,7690 +416,8432 +417,9122 +418,10121 +419,10912 +420,12113 +421,13251 +422,14073 +423,15170 +424,16663 +425,17639 +426,18737 +427,20147 +428,21648 +429,22931 +430,24218 +431,25502 +432,26665 +433,28368 +434,29321 +435,30571 +436,32053 +437,33126 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a/examples/datasets/hamming/Ising2D/opt/L100/T2.10/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/opt.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.10/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/opt.txt new file mode 100644 index 00000000..ec48efac --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.10/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/opt.txt @@ -0,0 +1 @@ +1343,729.77185082,1.401922,-8.00081823 diff --git a/examples/datasets/hamming/Ising2D/opt/L100/T2.20/alphamin0.00000/alphamax0.05000/Nsteps1000000/delta0.00050/seed1/model_validation.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.20/alphamin0.00000/alphamax0.05000/Nsteps1000000/delta0.00050/seed1/model_validation.txt new file mode 100644 index 00000000..711cbad5 --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.20/alphamin0.00000/alphamax0.05000/Nsteps1000000/delta0.00050/seed1/model_validation.txt @@ -0,0 +1,375 @@ 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a/examples/datasets/hamming/Ising2D/opt/L100/T2.23/alphamin0.00000/alphamax0.35000/Nsteps1000000/delta0.00050/seed1/opt.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.23/alphamin0.00000/alphamax0.35000/Nsteps1000000/delta0.00050/seed1/opt.txt new file mode 100644 index 00000000..b9b8863c --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.23/alphamin0.00000/alphamax0.35000/Nsteps1000000/delta0.00050/seed1/opt.txt @@ -0,0 +1 @@ +2426,746.05688647,1.664605,-7.28324945 diff --git a/examples/datasets/hamming/Ising2D/opt/L100/T2.23/alphamin0.00000/alphamax0.40000/Nsteps1000000/delta0.00050/seed1/model_validation.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.23/alphamin0.00000/alphamax0.40000/Nsteps1000000/delta0.00050/seed1/model_validation.txt new file mode 100644 index 00000000..0b4cd2c8 --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.23/alphamin0.00000/alphamax0.40000/Nsteps1000000/delta0.00050/seed1/model_validation.txt @@ -0,0 +1,1026 @@ 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a/examples/datasets/hamming/Ising2D/opt/L100/T2.23/alphamin0.00000/alphamax0.40000/Nsteps1000000/delta0.00050/seed1/opt.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.23/alphamin0.00000/alphamax0.40000/Nsteps1000000/delta0.00050/seed1/opt.txt new file mode 100644 index 00000000..da6e6ca8 --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.23/alphamin0.00000/alphamax0.40000/Nsteps1000000/delta0.00050/seed1/opt.txt @@ -0,0 +1 @@ +2534,720.43393672,1.677986,-6.49149505 diff --git a/examples/datasets/hamming/Ising2D/opt/L100/T2.23/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/model_validation.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.23/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/model_validation.txt new file mode 100644 index 00000000..ecbb76cc --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.23/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/model_validation.txt @@ -0,0 +1,1217 @@ 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a/examples/datasets/hamming/Ising2D/opt/L100/T2.26/alphamin0.00000/alphamax0.35000/Nsteps1000000/delta0.00050/seed1/opt.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.26/alphamin0.00000/alphamax0.35000/Nsteps1000000/delta0.00050/seed1/opt.txt new file mode 100644 index 00000000..35925acf --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.26/alphamin0.00000/alphamax0.35000/Nsteps1000000/delta0.00050/seed1/opt.txt @@ -0,0 +1 @@ +3544,571.57394195,1.803290,-4.68026120 diff --git a/examples/datasets/hamming/Ising2D/opt/L100/T2.26/alphamin0.00000/alphamax0.40000/Nsteps1000000/delta0.00050/seed1/model_validation.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.26/alphamin0.00000/alphamax0.40000/Nsteps1000000/delta0.00050/seed1/model_validation.txt new file mode 100644 index 00000000..bd0afdff --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.26/alphamin0.00000/alphamax0.40000/Nsteps1000000/delta0.00050/seed1/model_validation.txt @@ -0,0 +1,2061 @@ 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b/examples/datasets/hamming/Ising2D/opt/L100/T2.28/alphamin0.00000/alphamax0.35000/Nsteps1000000/delta0.00050/seed1/opt.txt @@ -0,0 +1 @@ +4433,466.81154960,1.880968,-4.68301256 diff --git a/examples/datasets/hamming/Ising2D/opt/L100/T2.28/alphamin0.00000/alphamax0.40000/Nsteps1000000/delta0.00050/seed1/model_validation.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.28/alphamin0.00000/alphamax0.40000/Nsteps1000000/delta0.00050/seed1/model_validation.txt new file mode 100644 index 00000000..f9e6c6a5 --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.28/alphamin0.00000/alphamax0.40000/Nsteps1000000/delta0.00050/seed1/model_validation.txt @@ -0,0 +1,2469 @@ +2.104000000000000000e+03 2.001097615048988861e-07 6.299885934899218258e-06 +2.107000000000000000e+03 2.001097615048988861e-07 6.433815417987039494e-06 +2.108000000000000000e+03 2.001097615048988861e-07 6.478975392808052304e-06 +2.118000000000000000e+03 2.001097615048988861e-07 6.945071665736192574e-06 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a/examples/datasets/hamming/Ising2D/opt/L100/T2.30/alphamin0.00000/alphamax0.40000/Nsteps1000000/delta0.00050/seed1/opt.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.30/alphamin0.00000/alphamax0.40000/Nsteps1000000/delta0.00050/seed1/opt.txt new file mode 100644 index 00000000..20e12a83 --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.30/alphamin0.00000/alphamax0.40000/Nsteps1000000/delta0.00050/seed1/opt.txt @@ -0,0 +1 @@ +4822,512.90428485,1.908076,-7.18779901 diff --git a/examples/datasets/hamming/Ising2D/opt/L100/T2.30/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/model_validation.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.30/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/model_validation.txt new file mode 100644 index 00000000..bb1dcbf1 --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.30/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/model_validation.txt @@ -0,0 +1,2414 @@ 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b/examples/datasets/hamming/Ising2D/opt/L100/T2.32/alphamin0.00000/alphamax0.10000/Nsteps1000000/delta0.00050/seed1/opt.txt @@ -0,0 +1 @@ +4410,680.67608788,1.897357,-7.44869901 diff --git a/examples/datasets/hamming/Ising2D/opt/L100/T2.32/alphamin0.00000/alphamax0.15000/Nsteps1000000/delta0.00050/seed1/model_validation.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.32/alphamin0.00000/alphamax0.15000/Nsteps1000000/delta0.00050/seed1/model_validation.txt new file mode 100644 index 00000000..76fc207e --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.32/alphamin0.00000/alphamax0.15000/Nsteps1000000/delta0.00050/seed1/model_validation.txt @@ -0,0 +1,1594 @@ +2.705000000000000000e+03 5.342981218635599099e-07 3.752884619600193040e-08 +2.742000000000000000e+03 5.342981218635599099e-07 5.809301361842041938e-08 +2.749000000000000000e+03 5.342981218635599099e-07 6.300436050291146102e-08 +2.772000000000000000e+03 5.342981218635599099e-07 8.198764579320966999e-08 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a/examples/datasets/hamming/Ising2D/opt/L100/T2.32/alphamin0.00000/alphamax0.20000/Nsteps1000000/delta0.00050/seed1/opt.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.32/alphamin0.00000/alphamax0.20000/Nsteps1000000/delta0.00050/seed1/opt.txt new file mode 100644 index 00000000..8128a0fa --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.32/alphamin0.00000/alphamax0.20000/Nsteps1000000/delta0.00050/seed1/opt.txt @@ -0,0 +1 @@ +4616,723.96196521,1.879326,-7.68927833 diff --git a/examples/datasets/hamming/Ising2D/opt/L100/T2.32/alphamin0.00000/alphamax0.25000/Nsteps1000000/delta0.00050/seed1/model_validation.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.32/alphamin0.00000/alphamax0.25000/Nsteps1000000/delta0.00050/seed1/model_validation.txt new file mode 100644 index 00000000..2c513ccf --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.32/alphamin0.00000/alphamax0.25000/Nsteps1000000/delta0.00050/seed1/model_validation.txt @@ -0,0 +1,1761 @@ 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b/examples/datasets/hamming/Ising2D/opt/L100/T2.33/alphamin0.00000/alphamax0.05000/Nsteps1000000/delta0.00050/seed1/opt.txt @@ -0,0 +1 @@ +4350,719.79416392,1.911425,-6.96092692 diff --git a/examples/datasets/hamming/Ising2D/opt/L100/T2.33/alphamin0.00000/alphamax0.10000/Nsteps1000000/delta0.00050/seed1/model_validation.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.33/alphamin0.00000/alphamax0.10000/Nsteps1000000/delta0.00050/seed1/model_validation.txt new file mode 100644 index 00000000..372b8dc1 --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.33/alphamin0.00000/alphamax0.10000/Nsteps1000000/delta0.00050/seed1/model_validation.txt @@ -0,0 +1,1362 @@ +2.778000000000000000e+03 8.015399393715590556e-07 7.024253189007868364e-09 +2.966000000000000000e+03 8.015399393715590556e-07 7.949883926562560249e-08 +2.983000000000000000e+03 8.015399393715590556e-07 9.733960477311329807e-08 +3.003000000000000000e+03 8.015399393715590556e-07 1.231052562942207771e-07 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a/examples/datasets/hamming/Ising2D/opt/L100/T2.34/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/opt.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.34/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/opt.txt new file mode 100644 index 00000000..94e689a6 --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.34/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/opt.txt @@ -0,0 +1 @@ +4956,1210.16589235,1.765169,-7.27744535 diff --git a/examples/datasets/hamming/Ising2D/opt/L100/T2.35/alphamin0.00000/alphamax0.05000/Nsteps1000000/delta0.00050/seed1/model_validation.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.35/alphamin0.00000/alphamax0.05000/Nsteps1000000/delta0.00050/seed1/model_validation.txt new file mode 100644 index 00000000..a77b15d8 --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.35/alphamin0.00000/alphamax0.05000/Nsteps1000000/delta0.00050/seed1/model_validation.txt @@ -0,0 +1,939 @@ 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a/examples/datasets/hamming/Ising2D/opt/L100/T2.36/alphamin0.00000/alphamax0.30000/Nsteps1000000/delta0.00050/seed1/opt.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.36/alphamin0.00000/alphamax0.30000/Nsteps1000000/delta0.00050/seed1/opt.txt new file mode 100644 index 00000000..ecf141c5 --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.36/alphamin0.00000/alphamax0.30000/Nsteps1000000/delta0.00050/seed1/opt.txt @@ -0,0 +1 @@ +4851,1521.28978890,1.701886,-8.23387376 diff --git a/examples/datasets/hamming/Ising2D/opt/L100/T2.36/alphamin0.00000/alphamax0.35000/Nsteps1000000/delta0.00050/seed1/model_validation.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.36/alphamin0.00000/alphamax0.35000/Nsteps1000000/delta0.00050/seed1/model_validation.txt new file mode 100644 index 00000000..79bb7599 --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.36/alphamin0.00000/alphamax0.35000/Nsteps1000000/delta0.00050/seed1/model_validation.txt @@ -0,0 +1,1226 @@ 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b/examples/datasets/hamming/Ising2D/opt/L100/T2.36/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/opt.txt @@ -0,0 +1 @@ +4964,1567.94828177,1.690223,-8.18280747 diff --git a/examples/datasets/hamming/Ising2D/opt/L100/T2.37/alphamin0.00000/alphamax0.05000/Nsteps1000000/delta0.00050/seed1/model_validation.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.37/alphamin0.00000/alphamax0.05000/Nsteps1000000/delta0.00050/seed1/model_validation.txt new file mode 100644 index 00000000..1a5074c8 --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.37/alphamin0.00000/alphamax0.05000/Nsteps1000000/delta0.00050/seed1/model_validation.txt @@ -0,0 +1,815 @@ +3.420000000000000000e+03 1.606176774438498366e-06 7.390512547883096475e-10 +3.507000000000000000e+03 1.606176774438498366e-06 5.293288366003410289e-09 +3.557000000000000000e+03 1.606176774438498366e-06 1.533440341505181162e-08 +3.566000000000000000e+03 1.606176774438498366e-06 1.847603006872499336e-08 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a/examples/datasets/hamming/Ising2D/opt/L100/T2.37/alphamin0.00000/alphamax0.25000/Nsteps1000000/delta0.00050/seed1/opt.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.37/alphamin0.00000/alphamax0.25000/Nsteps1000000/delta0.00050/seed1/opt.txt new file mode 100644 index 00000000..fe0ca29d --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.37/alphamin0.00000/alphamax0.25000/Nsteps1000000/delta0.00050/seed1/opt.txt @@ -0,0 +1 @@ +4822,1635.04804478,1.679875,-8.06741435 diff --git a/examples/datasets/hamming/Ising2D/opt/L100/T2.37/alphamin0.00000/alphamax0.30000/Nsteps1000000/delta0.00050/seed1/model_validation.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.37/alphamin0.00000/alphamax0.30000/Nsteps1000000/delta0.00050/seed1/model_validation.txt new file mode 100644 index 00000000..30ea839c --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.37/alphamin0.00000/alphamax0.30000/Nsteps1000000/delta0.00050/seed1/model_validation.txt @@ -0,0 +1,1110 @@ 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a/examples/datasets/hamming/Ising2D/opt/L100/T2.37/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/opt.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.37/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/opt.txt new file mode 100644 index 00000000..16b9df7c --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.37/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/opt.txt @@ -0,0 +1 @@ +4966,1701.50454020,1.663416,-8.18237916 diff --git a/examples/datasets/hamming/Ising2D/opt/L100/T2.38/alphamin0.00000/alphamax0.05000/Nsteps1000000/delta0.00050/seed1/model_validation.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.38/alphamin0.00000/alphamax0.05000/Nsteps1000000/delta0.00050/seed1/model_validation.txt new file mode 100644 index 00000000..0ba33fd9 --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.38/alphamin0.00000/alphamax0.05000/Nsteps1000000/delta0.00050/seed1/model_validation.txt @@ -0,0 +1,723 @@ 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a/examples/datasets/hamming/Ising2D/opt/L100/T2.39/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/opt.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.39/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/opt.txt new file mode 100644 index 00000000..eadc04ea --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.39/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/opt.txt @@ -0,0 +1 @@ +4970,1974.88733012,1.607918,-8.61059420 diff --git a/examples/datasets/hamming/Ising2D/opt/L100/T2.40/alphamin0.00000/alphamax0.05000/Nsteps1000000/delta0.00050/seed1/model_validation.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.40/alphamin0.00000/alphamax0.05000/Nsteps1000000/delta0.00050/seed1/model_validation.txt new file mode 100644 index 00000000..e0fa8d3b --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.40/alphamin0.00000/alphamax0.05000/Nsteps1000000/delta0.00050/seed1/model_validation.txt @@ -0,0 +1,654 @@ 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a/examples/datasets/hamming/Ising2D/opt/L100/T2.40/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/opt.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.40/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/opt.txt new file mode 100644 index 00000000..b4dd9840 --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.40/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/opt.txt @@ -0,0 +1 @@ +4972,2115.13197884,1.579340,-8.86952598 diff --git a/examples/datasets/hamming/Ising2D/opt/L100/T2.50/alphamin0.00000/alphamax0.05000/Nsteps1000000/delta0.00050/seed1/model_validation.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.50/alphamin0.00000/alphamax0.05000/Nsteps1000000/delta0.00050/seed1/model_validation.txt new file mode 100644 index 00000000..8118aef8 --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.50/alphamin0.00000/alphamax0.05000/Nsteps1000000/delta0.00050/seed1/model_validation.txt @@ -0,0 +1,460 @@ 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a/examples/datasets/hamming/Ising2D/opt/L100/T2.80/alphamin0.00000/alphamax0.30000/Nsteps1000000/delta0.00050/seed1/opt.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.80/alphamin0.00000/alphamax0.30000/Nsteps1000000/delta0.00050/seed1/opt.txt new file mode 100644 index 00000000..71009f3e --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.80/alphamin0.00000/alphamax0.30000/Nsteps1000000/delta0.00050/seed1/opt.txt @@ -0,0 +1 @@ +4950,5267.45164340,0.947203,-9.44364869 diff --git a/examples/datasets/hamming/Ising2D/opt/L100/T2.80/alphamin0.00000/alphamax0.35000/Nsteps1000000/delta0.00050/seed1/model_validation.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.80/alphamin0.00000/alphamax0.35000/Nsteps1000000/delta0.00050/seed1/model_validation.txt new file mode 100644 index 00000000..c785903a --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.80/alphamin0.00000/alphamax0.35000/Nsteps1000000/delta0.00050/seed1/model_validation.txt @@ -0,0 +1,402 @@ 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b/examples/datasets/hamming/Ising2D/opt/L100/T2.80/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/opt.txt @@ -0,0 +1 @@ +4987,5282.11158400,0.944075,-9.57585665 diff --git a/examples/datasets/hamming/Ising2D/opt/L100/T2.90/alphamin0.00000/alphamax0.05000/Nsteps1000000/delta0.00050/seed1/model_validation.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.90/alphamin0.00000/alphamax0.05000/Nsteps1000000/delta0.00050/seed1/model_validation.txt new file mode 100644 index 00000000..4f4a9ae6 --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.90/alphamin0.00000/alphamax0.05000/Nsteps1000000/delta0.00050/seed1/model_validation.txt @@ -0,0 +1,265 @@ +4.546000000000000000e+03 1.635592380954359170e-06 7.593746448964615162e-08 +4.566000000000000000e+03 1.635592380954359170e-06 2.571294807729955906e-07 +4.578000000000000000e+03 1.635592380954359170e-06 5.199970115764631559e-07 +4.579000000000000000e+03 1.635592380954359170e-06 5.509146777733679475e-07 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a/examples/datasets/hamming/Ising2D/opt/L100/T2.90/alphamin0.00000/alphamax0.10000/Nsteps1000000/delta0.00050/seed1/opt.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.90/alphamin0.00000/alphamax0.10000/Nsteps1000000/delta0.00050/seed1/opt.txt new file mode 100644 index 00000000..505a7f43 --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.90/alphamin0.00000/alphamax0.10000/Nsteps1000000/delta0.00050/seed1/opt.txt @@ -0,0 +1 @@ +4889,5646.18499319,0.872834,-8.78908898 diff --git a/examples/datasets/hamming/Ising2D/opt/L100/T2.90/alphamin0.00000/alphamax0.15000/Nsteps1000000/delta0.00050/seed1/model_validation.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.90/alphamin0.00000/alphamax0.15000/Nsteps1000000/delta0.00050/seed1/model_validation.txt new file mode 100644 index 00000000..4ea5dce4 --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.90/alphamin0.00000/alphamax0.15000/Nsteps1000000/delta0.00050/seed1/model_validation.txt @@ -0,0 +1,317 @@ 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a/examples/datasets/hamming/Ising2D/opt/L100/T2.90/alphamin0.00000/alphamax0.25000/Nsteps1000000/delta0.00050/seed1/opt.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.90/alphamin0.00000/alphamax0.25000/Nsteps1000000/delta0.00050/seed1/opt.txt new file mode 100644 index 00000000..3da5d6ab --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.90/alphamin0.00000/alphamax0.25000/Nsteps1000000/delta0.00050/seed1/opt.txt @@ -0,0 +1 @@ +4941,5721.00076723,0.856671,-9.33100013 diff --git a/examples/datasets/hamming/Ising2D/opt/L100/T2.90/alphamin0.00000/alphamax0.30000/Nsteps1000000/delta0.00050/seed1/model_validation.txt b/examples/datasets/hamming/Ising2D/opt/L100/T2.90/alphamin0.00000/alphamax0.30000/Nsteps1000000/delta0.00050/seed1/model_validation.txt new file mode 100644 index 00000000..c464975a --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T2.90/alphamin0.00000/alphamax0.30000/Nsteps1000000/delta0.00050/seed1/model_validation.txt @@ -0,0 +1,361 @@ 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b/examples/datasets/hamming/Ising2D/opt/L100/T3.30/alphamin0.00000/alphamax0.30000/Nsteps1000000/delta0.00050/seed1/opt.txt new file mode 100644 index 00000000..95b3c8cb --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T3.30/alphamin0.00000/alphamax0.30000/Nsteps1000000/delta0.00050/seed1/opt.txt @@ -0,0 +1 @@ +4962,7052.88807030,0.589907,-9.52557364 diff --git a/examples/datasets/hamming/Ising2D/opt/L100/T3.30/alphamin0.00000/alphamax0.35000/Nsteps1000000/delta0.00050/seed1/model_validation.txt b/examples/datasets/hamming/Ising2D/opt/L100/T3.30/alphamin0.00000/alphamax0.35000/Nsteps1000000/delta0.00050/seed1/model_validation.txt new file mode 100644 index 00000000..a54f5730 --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T3.30/alphamin0.00000/alphamax0.35000/Nsteps1000000/delta0.00050/seed1/model_validation.txt @@ -0,0 +1,314 @@ +4.631000000000000000e+03 2.304123037884532863e-07 1.531722336854088782e-08 +4.634000000000000000e+03 2.304123037884532863e-07 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a/examples/datasets/hamming/Ising2D/opt/L100/T3.30/alphamin0.00000/alphamax0.40000/Nsteps1000000/delta0.00050/seed1/opt.txt b/examples/datasets/hamming/Ising2D/opt/L100/T3.30/alphamin0.00000/alphamax0.40000/Nsteps1000000/delta0.00050/seed1/opt.txt new file mode 100644 index 00000000..f1b9a45f --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T3.30/alphamin0.00000/alphamax0.40000/Nsteps1000000/delta0.00050/seed1/opt.txt @@ -0,0 +1 @@ +4981,7060.48983353,0.588312,-9.54405068 diff --git a/examples/datasets/hamming/Ising2D/opt/L100/T3.30/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/model_validation.txt b/examples/datasets/hamming/Ising2D/opt/L100/T3.30/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/model_validation.txt new file mode 100644 index 00000000..40051d51 --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T3.30/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/model_validation.txt @@ -0,0 +1,332 @@ 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b/examples/datasets/hamming/Ising2D/opt/L100/T3.40/alphamin0.00000/alphamax0.25000/Nsteps1000000/delta0.00050/seed1/opt.txt @@ -0,0 +1 @@ +4953,7308.47690536,0.538581,-9.46967025 diff --git a/examples/datasets/hamming/Ising2D/opt/L100/T3.40/alphamin0.00000/alphamax0.30000/Nsteps1000000/delta0.00050/seed1/model_validation.txt b/examples/datasets/hamming/Ising2D/opt/L100/T3.40/alphamin0.00000/alphamax0.30000/Nsteps1000000/delta0.00050/seed1/model_validation.txt new file mode 100644 index 00000000..05ac1850 --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T3.40/alphamin0.00000/alphamax0.30000/Nsteps1000000/delta0.00050/seed1/model_validation.txt @@ -0,0 +1,295 @@ +4.633000000000000000e+03 2.710270273578997702e-07 8.539304345352553363e-09 +4.641000000000000000e+03 2.710270273578997702e-07 1.617151061525081530e-08 +4.642000000000000000e+03 2.710270273578997702e-07 1.749737546607902710e-08 +4.655000000000000000e+03 2.710270273578997702e-07 4.774221558120083912e-08 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a/examples/datasets/hamming/Ising2D/opt/L100/T3.40/alphamin0.00000/alphamax0.35000/Nsteps1000000/delta0.00050/seed1/opt.txt b/examples/datasets/hamming/Ising2D/opt/L100/T3.40/alphamin0.00000/alphamax0.35000/Nsteps1000000/delta0.00050/seed1/opt.txt new file mode 100644 index 00000000..d2494991 --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T3.40/alphamin0.00000/alphamax0.35000/Nsteps1000000/delta0.00050/seed1/opt.txt @@ -0,0 +1 @@ +4973,7306.97742631,0.538897,-9.52751008 diff --git a/examples/datasets/hamming/Ising2D/opt/L100/T3.40/alphamin0.00000/alphamax0.40000/Nsteps1000000/delta0.00050/seed1/model_validation.txt b/examples/datasets/hamming/Ising2D/opt/L100/T3.40/alphamin0.00000/alphamax0.40000/Nsteps1000000/delta0.00050/seed1/model_validation.txt new file mode 100644 index 00000000..9ce0a39e --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T3.40/alphamin0.00000/alphamax0.40000/Nsteps1000000/delta0.00050/seed1/model_validation.txt @@ -0,0 +1,314 @@ 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b/examples/datasets/hamming/Ising2D/opt/L100/T3.50/alphamin0.00000/alphamax0.40000/Nsteps1000000/delta0.00050/seed1/opt.txt @@ -0,0 +1 @@ +4982,7523.38793160,0.495485,-9.44510475 diff --git a/examples/datasets/hamming/Ising2D/opt/L100/T3.50/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/model_validation.txt b/examples/datasets/hamming/Ising2D/opt/L100/T3.50/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/model_validation.txt new file mode 100644 index 00000000..b5146115 --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T3.50/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/model_validation.txt @@ -0,0 +1,311 @@ +4.664000000000000000e+03 1.782373578539665020e-07 3.191970451062880506e-08 +4.667000000000000000e+03 1.782373578539665020e-07 4.027452808507231993e-08 +4.668000000000000000e+03 3.564747157079330040e-07 4.349913087140375243e-08 +4.670000000000000000e+03 1.782373578539665020e-07 5.070727850851091738e-08 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a/examples/datasets/hamming/Ising2D/opt/L100/T3.60/alphamin0.00000/alphamax0.40000/Nsteps1000000/delta0.00050/seed1/opt.txt b/examples/datasets/hamming/Ising2D/opt/L100/T3.60/alphamin0.00000/alphamax0.40000/Nsteps1000000/delta0.00050/seed1/opt.txt new file mode 100644 index 00000000..2a5d126f --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T3.60/alphamin0.00000/alphamax0.40000/Nsteps1000000/delta0.00050/seed1/opt.txt @@ -0,0 +1 @@ +4983,7705.15652518,0.459175,-9.46178637 diff --git a/examples/datasets/hamming/Ising2D/opt/L100/T3.60/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/model_validation.txt b/examples/datasets/hamming/Ising2D/opt/L100/T3.60/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/model_validation.txt new file mode 100644 index 00000000..d9d9e9c9 --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T3.60/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/model_validation.txt @@ -0,0 +1,307 @@ 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a/examples/datasets/hamming/Ising2D/opt/L100/T4.00/alphamin0.00000/alphamax0.25000/Nsteps1000000/delta0.00050/seed1/opt.txt b/examples/datasets/hamming/Ising2D/opt/L100/T4.00/alphamin0.00000/alphamax0.25000/Nsteps1000000/delta0.00050/seed1/opt.txt new file mode 100644 index 00000000..67ed0e42 --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T4.00/alphamin0.00000/alphamax0.25000/Nsteps1000000/delta0.00050/seed1/opt.txt @@ -0,0 +1 @@ +4958,8243.99440331,0.351451,-9.38076751 diff --git a/examples/datasets/hamming/Ising2D/opt/L100/T4.00/alphamin0.00000/alphamax0.30000/Nsteps1000000/delta0.00050/seed1/model_validation.txt b/examples/datasets/hamming/Ising2D/opt/L100/T4.00/alphamin0.00000/alphamax0.30000/Nsteps1000000/delta0.00050/seed1/model_validation.txt new file mode 100644 index 00000000..05f5f2c1 --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T4.00/alphamin0.00000/alphamax0.30000/Nsteps1000000/delta0.00050/seed1/model_validation.txt @@ -0,0 +1,260 @@ 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a/examples/datasets/hamming/Ising2D/opt/L100/T4.00/alphamin0.00000/alphamax0.40000/Nsteps1000000/delta0.00050/seed1/opt.txt b/examples/datasets/hamming/Ising2D/opt/L100/T4.00/alphamin0.00000/alphamax0.40000/Nsteps1000000/delta0.00050/seed1/opt.txt new file mode 100644 index 00000000..d0377ee5 --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T4.00/alphamin0.00000/alphamax0.40000/Nsteps1000000/delta0.00050/seed1/opt.txt @@ -0,0 +1 @@ +4984,8264.09234429,0.347261,-9.37643580 diff --git a/examples/datasets/hamming/Ising2D/opt/L100/T4.00/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/model_validation.txt b/examples/datasets/hamming/Ising2D/opt/L100/T4.00/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/model_validation.txt new file mode 100644 index 00000000..523b0b77 --- /dev/null +++ b/examples/datasets/hamming/Ising2D/opt/L100/T4.00/alphamin0.00000/alphamax0.45000/Nsteps1000000/delta0.00050/seed1/model_validation.txt @@ -0,0 +1,284 @@ 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a/examples/datasets/hamming/random_spins/L100/opt/alphamin0.00000/alphamax1.00000/Nsteps100000/delta0.00500/seed1/opt.txt b/examples/datasets/hamming/random_spins/L100/opt/alphamin0.00000/alphamax1.00000/Nsteps100000/delta0.00500/seed1/opt.txt new file mode 100644 index 00000000..ef2d6630 --- /dev/null +++ b/examples/datasets/hamming/random_spins/L100/opt/alphamin0.00000/alphamax1.00000/Nsteps100000/delta0.00500/seed1/opt.txt @@ -0,0 +1 @@ +76,99.57444693,0.008277,-10.85470781 diff --git a/examples/notebook_hamming.ipynb b/examples/notebook_hamming.ipynb new file mode 100644 index 00000000..ed1e173c --- /dev/null +++ b/examples/notebook_hamming.ipynb @@ -0,0 +1,599 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Tutorial: Binary Intrinsic Dimension" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## BID summary:\n", + "\n", + "For non interacting random bit streams of length $N$ it is possible to write the exact probability of observing Hamming distance \n", + "$r = |\\boldsymbol{\\sigma}-\\boldsymbol{\\sigma}'|_H \n", + "%=\\frac{N-\\boldsymbol{\\sigma} \\cdot \\boldsymbol{\\sigma}}{2}\n", + "$ between two i.i.d samples $\\boldsymbol{\\sigma}$ and $\\boldsymbol{\\sigma}'$ as \n", + "\n", + "\\begin{equation}\n", + "P_0(r) = \\frac{1}{2^N} \\binom{N}{r}. \\tag{1}\n", + "\\end{equation}\n", + "\n", + "For interacting spins, our model generalizes the previous expression to \n", + "\n", + "\\begin{equation}\n", + "P(r)=C\\frac{1}{2^{d(r)}}\\binom{d(r)}{r}, \\tag{2}\n", + "\\end{equation}\n", + "where $C$ is the normalization constant. Eq. 2 reduces to 1\n", + "for $ d(r) = N$ and $C=1$. We empirically found that model 2 fits accurately the observed distributions, at least for small distances, if one retains the first two terms of the Taylor expansion:\n", + "\\begin{equation}\n", + " d(r)=d_0+d_1 \\, r \\tag{3}\n", + "\\end{equation}\n", + "where $d_0$ and $d_1$ are variational parameters.\n", + "In order to infer them\n", + "we minimize the Kullbac-Leibler divergence between the empirical probability of Hamming distances $P_{emp}(r)$ and the model $P(r)$ given by Eqs. 2 and 3, \n", + "\n", + "\\begin{equation}\n", + " D_{KL}(P_{emp}||P) = \\sum_{r \\leq r_{max}} P_{emp}(r) \\log{\\frac{P_{emp}(r)}{P(r)}}, \\tag{4}\n", + "\\end{equation}\n", + "where $r_{max}$ is a meta-parameter that allows constraining the fit to small distance if necessary ( i.e., we discard distances $r>r_{max}$ from $P_{emp}$, we show an example below).\n", + "We fix $r_{max}$ by taking it as the quantile of order $\\alpha_{max}$ of $P_{emp}$, meaning\n", + "\n", + "\\begin{equation}\n", + "\\alpha_{max} = \\sum_{r=0}^{r_{max}} P_{emp}(r), \\tag{5}\n", + "\\end{equation}\n", + "where $\\alpha_{max} \\in [0,1]$. Ideally nothing depends qualitatively on $\\alpha_{max}$.\n", + "\n", + "\n", + "### NOTE: \n", + "\n", + "In the paper we call $\\alpha^* \\equiv \\alpha_{max}$ and $r^* \\equiv r_{max}$.\n", + "\n", + "In practice we also define $\\alpha_{min}$ and $r_{min}$ by \n", + "\n", + "\\begin{equation}\n", + "\\alpha_{min} = \\sum_{r=0}^{r_{min}} P_{emp}(r), \\tag{6}\n", + "\\end{equation}\n", + "which allow to remove small distances (those with $r the BID imports, to work with JAX double-precision\n", + "os.environ[\"JAX_ENABLE_X64\"] = \"True\"\n", + "from dadapy.hamming import BID, Hamming\n", + "\n", + "# REPRODUCIBILITY\n", + "seed = 1\n", + "np.random.seed(seed=seed)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# RANDOM DATA\n", + "L = 100 # number of bits\n", + "Ns = 5000 # number of samples\n", + "\n", + "# FORMAT NOTE: spins must be normalized to +-1\n", + "X = (2 * np.random.randint(low=0, high=2, size=(Ns, L)) - 1) # X.shape=(Ns,L)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "H.D_values[:idx]=array([25, 26, 27, 28, 29], dtype=int32)\n", + "H.D_counts[:idx]=array([ 4, 6, 34, 52, 120])\n", + "H.D_probs[:idx]=array([3.20e-07, 4.80e-07, 2.72e-06, 4.16e-06, 9.60e-06])\n" + ] + } + ], + "source": [ + "# DEFINING COORDINATES\n", + "H = Hamming(coordinates=X)\n", + "\n", + "# COMPUTING DISTANCES\n", + "H.compute_distances() # stores the matrix of distances between samples in H.distances of shape (Ns,Ns)\n", + "\n", + "# COMPUTING AND SAVING HISTOGRAM OF DISTANCES\n", + "histfolder = f'datasets/hamming/random_spins/L{L}/hist/'\n", + "filename = f'counts.txt'\n", + "H.D_histogram(compute_flag=1, # if 0 the histograms are loaded instead of computed\n", + " save=True, # we compute the histograms once and save time in the future\n", + " resultsfolder=histfolder, # folder where the histograms are saved\n", + " filename=filename, \n", + " )\n", + "\n", + "# \"H.D_histograms\" defines the following attributes\n", + "idx = 5\n", + "print(f'{H.D_values[:idx]=}') # vector containing the sampled distances\n", + "print(f'{H.D_counts[:idx]=}') # vector containing how many times each distance was sampled\n", + "print(f'{H.D_probs[:idx]=}') # same as \"D_counts\" but normalized by the total number of counts observed " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### OPTIMIZATION\n", + "\n", + "(See paper supp. inf for short description about the stochastic optimization performed)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "starting optimization\n", + "optimization took 0.0 minutes\n", + "d_0=99.574,d_1=0.008,logKL=-10.85\n", + "\n", + "B.d0=99.57444692619558\n", + "B.d1=0.008277386221249374\n", + "B.logKL=-10.85470780641487\n", + "B.rmax=76\n", + "\n", + " B.intrinsic_dim=99.57444692619558\n" + ] + } + ], + "source": [ + "# PARAMETER DEFINITIONS FOR OPTIMIZATION\n", + "alphamin = 0 # order of min_quantile, to remove poorly sampled parts of the histogram if necessary (see Supp. Inf. of paper)\n", + "alphamax = 1 # order of max_quantile, to define r* (named rmax in the code).\n", + "delta = 5e-3 # stochastic optimization step size\n", + "Nsteps = int(1e5) # number of optimization steps\n", + "export_results = 1 # flag to export d0,d1,logKL,Pemp,Pmodel after optimization (default=1)\n", + "export_logKLs = 1 # flag to export the logKLs during optimization (default=0)\n", + "optfolder0 = f\"datasets/hamming/random_spins/L{L}/opt/\" # folder where optimization results are saved\n", + "\n", + "B = BID(\n", + " H=H,\n", + " alphamin=alphamin,\n", + " alphamax=alphamax,\n", + " seed=seed,\n", + " delta=delta,\n", + " Nsteps=Nsteps,\n", + " export_results=export_results,\n", + " export_logKLs=export_logKLs,\n", + " optfolder0=optfolder0,\n", + " L=L,\n", + ")\n", + "\n", + "B.computeBID() # results are defined as attributes of B. They are also exported if export_results=1 (default)\n", + "\n", + "print('')\n", + "print(f'{B.d0=}')\n", + "print(f'{B.d1=}')\n", + "print(f'{B.logKL=}')\n", + "print(f'{B.rmax=}')\n", + "\n", + "# Note that B.intrinsic_dim is another alias for B.d0\n", + "print(f'\\n {B.intrinsic_dim=}')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### explicit model validation: " + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig,ax = plt.subplots(1)\n", + "\n", + "# empirical distribution of distances\n", + "ax.plot(B.remp,\n", + " B.Pemp,\n", + " 'x',\n", + " label=r'$P_{emp}(r)$',\n", + " )\n", + "# model fit\n", + "ax.plot(B.remp,\n", + " B.Pmodel,\n", + " '-',\n", + " color='black',\n", + " label=r'$P_{model}(r|d_0,d_1)$',\n", + " )\n", + "plt.ylabel('Probability of observing Hamming distance r')\n", + "plt.xlabel('Hamming distance r')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### KL during optimization\n", + "\n", + "Note that only random moves that minimize (4) are taken, and the rest are discarded. The following plot shows a subsampling of the proposed moves made by the optimizer. " + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "logKLs_opt = B.Op.logKLs # also importable by logKLs_opt = B.load_logKLs_opt()\n", + "figKL,axKL = plt.subplots()\n", + "axKL.plot(logKLs_opt,\n", + " color='black',\n", + " )\n", + "plt.ylabel('logKL during optimization')\n", + "plt.xlabel('1000 equi-spaced steps from the optimization')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2D Ising model\n", + "\n", + "For this model we showed in our paper \n", + "\n", + "- The scaling of the BID with the number of spins\n", + "- The temperature dependence of the BID\n", + "- The fits of the model (2) to the empirical probabilities of distances for different temperatures\n", + "\n", + "Below we show the full distribution of distances of this model, and what happens to the BID estimation when varying the meta paramater $r_{max}$ defined in (4). \n", + "\n", + "Some bibliography about the Ising model: \n", + "\n", + "https://en.wikipedia.org/wiki/Ising_model\n", + "\n", + "https://www.damtp.cam.ac.uk/user/tong/sft/one.pdf\n", + "\n", + "Remember: the exact analytical temperature in the thermodynamic limit (infinite size limit) is $T_c\\approx 2.269$.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [], + "source": [ + "import os\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# this environmental variable must be set the BID imports, to work with JAX double-precision\n", + "os.environ[\"JAX_ENABLE_X64\"] = \"True\"\n", + "from dadapy.hamming import BID, Hamming\n", + "eps = 1E-7" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Histograms of distances show the phase transition:\n", + "\n", + "We can see the phase transition in the histogram of all to all (Hamming-)distances, that becomes bimodal due to the presence of two equivalent low-energy states differing only in an global spin flip. In configuration space $\\mathcal{C} = \\{-1,1\\}^N$, for temperature $T < T_c$, we have two clusters: one in which the mayority of spins point upwards and another in which the mayority of spins point downwards. Thus, in the histogram we have inter-cluster small distances and intra-cluster large distances." + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "figh,axh = plt.subplots(1)\n", + "T_list = np.flip(np.array([1.8,2,2.27,2.28,2.3,4])) # temperature list\n", + "L = 100 # system width or height (you can see size-differences putting here L=30)\n", + "N = L**2 # total number of spins in a two-dimensional square lattice of length L \n", + "Ns = 5000 # number of samples for each temperature\n", + "\n", + "for T_id,T in enumerate(T_list):\n", + " histfolder = f'datasets/hamming/Ising2D/hist/' # folder where we saved previously computed histograms\n", + " filename = f'L{L}_T{T:.2f}_Ns{Ns}D_counts.txt' # we have different histograms for each L,T and Ns\n", + " H = Hamming()\n", + " H.D_histogram(resultsfolder=histfolder,\n", + " filename=filename,\n", + " ) # this loads H.D_values and H.D_probs\n", + " axh.plot(H.D_values/N,\n", + " H.D_probs,\n", + " 'x',\n", + " label=f'{T=:.2f}',\n", + " )\n", + "\n", + "axh.set_yscale('log')\n", + "box = axh.get_position()\n", + "axh.set_position([box.x0, box.y0, box.width * 0.8, box.height])\n", + "axh.legend(loc='center left', bbox_to_anchor=(1, 0.5))\n", + "\n", + "axh.set_xlabel('r/N')\n", + "axh.set_ylabel('P(r)')\n", + "plt.title(f'2D Ising model with {L=}')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### $r_{max}$ dependence \n", + "We cannot fit a bimodal histogram with our unimodal Ansatz, Eq. (2), so one way to proceed is to make a local fit of the first part of each histogram using the meta-parameter $\\alpha_{max}$ defined in Eq. (5). \n", + "Note that any $\\alpha_{max} < \\frac{1}{2}$ will remove the second part of the histogram. \n", + "Nonetheless $\\alpha_{max}$ is not a parameter of the system, so our results should be independent of it. \n", + "\n", + "Below we show that the BID is approximately independent of the meta-parameter, and moreover this dependency is smaller the larger the system size! " + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [], + "source": [ + "T_list = np.array([2,2.3,3]) # list of temperatures\n", + "L_list = np.array([30,100]) # list of system-sizes\n", + "\n", + "### OPTIMIZATION PARAMETERS USED FOR THIS EXAMPLE (NEEDED TO LOAD RESULTS)\n", + "Nsteps = int(1E6)\n", + "delta = 5E-4\n", + "seed = 1\n", + "alphamin = 0\n", + "alphamax_list = np.arange(.1,.45+eps,.05) # orders of quantiles of P(r)\n", + "\n", + "### PLACEHOLDERS\n", + "d0_list = np.empty(shape=(len(L_list),\n", + " len(T_list),\n", + " len(alphamax_list)\n", + " ),\n", + ")\n", + "d1_list = np.empty(shape=d0_list.shape)\n", + "rmax_list = np.empty(shape=d0_list.shape) # r^* in the paper\n", + "logKL_list = np.empty(shape=d0_list.shape)\n", + "\n", + "for L_id,L in enumerate(L_list):\n", + " for T_id,T in enumerate(T_list):\n", + " for alphamax_id,alphamax in enumerate(alphamax_list):\n", + " optfolder0 = f'datasets/hamming/Ising2D/opt/L{L}/T{T:.2f}/' # folder to put results\n", + " B = BID(\n", + " alphamin=alphamin,\n", + " alphamax=alphamax,\n", + " seed=seed,\n", + " delta=delta,\n", + " Nsteps=Nsteps,\n", + " optfolder0=optfolder0\n", + " )\n", + " (rmax_list[L_id,T_id,alphamax_id], # r^* in the paper\n", + " d0_list[L_id,T_id,alphamax_id], # BID\n", + " d1_list[L_id,T_id,alphamax_id], # the second variational parameter\n", + " logKL_list[L_id,T_id,alphamax_id], # logarithm of the KL divergence after optimization\n", + " ) = B.load_results()" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "for L_id, L in enumerate(L_list): \n", + " fig, axs = plt.subplots(nrows=1, ncols=2, figsize=(8,3.5))\n", + " ax0, axkl = axs\n", + " for T_id,T in enumerate(T_list):\n", + " lbl = f'{T=:.2f}'\n", + " ax0.plot(alphamax_list,\n", + " d0_list[L_id,T_id,:]/L**2,\n", + " 'o-',\n", + " label=lbl,\n", + " )\n", + " axkl.plot(alphamax_list,\n", + " logKL_list[L_id,T_id,:],\n", + " 'o-',\n", + " label=lbl,\n", + " )\n", + " ax0.set_ylabel(f\"BID/N\")\n", + " ax0.set_xlabel(r'order of quantile ($\\alpha_{max})$')\n", + " ax0.legend()\n", + "\n", + " axkl.set_ylabel(f\"log(KL)\")\n", + " axkl.set_xlabel(r'order of quantile ($\\alpha_{max}$)')\n", + " axkl.legend()\n", + "\n", + " fig.suptitle(f'{L=}')\n", + " plt.tight_layout()\n", + " plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note:\n", + "\n", + "* When studying the BID dependence with system parameters (e.g. here temperature or size), we fix the same $\\alpha_{max}$ for all calculations. \n", + "$r_{max}$ can be completely different when varying the system parameters, and $\\alpha_{max}$ allows to select a $r_{max}$ adaptively and automatically.\n", + "\n", + "* Close to $T_c$ the small size system ($L=30$) has a higher KL divergence for larger scales ($\\alpha_{max}$ close to $\\frac{1}{2}$), where the corresponding histogram has a significant superposition of the two peaks that our model cannot fit. Nonetheless the dependence of the BID with $\\alpha_{max}$ is very mild. Here any $\\alpha_{max}<1/4$ is a safe choice. For $L=100$ we see that any choice of $\\alpha_{max}$ is fine (in which case taking the biggest seems natural, since we fit more data).\n", + "\n", + "* If $\\alpha_{max}$ is too small (say, less than $0.1$) then we throw away almost all data. We would be fitting the initial part of the histogram than can be noisy or not statistically relevant for the problem. \n", + "For example, In dynamical systems we observe that temporal autocorrelations produce long tails on the left part of the histogram (work in progress), which are physically meaningless.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Model validation\n", + "\n", + "In continuous black line the model prediction, in colors the empirical probabilities. \n", + "\n", + "Note that each histogram is cut at some $r_{max}$ depending on the chosen value of $\\alpha_{max}$, and re-normalize by the total number of counts in that regime.\n", + "\n", + "You can see what happens with other temperatures like 1.5, 1.6, 1.7, ... ,4 and or L = 30.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "T = 2\n", + "L = 100\n", + "N = L**2\n", + "alphamax_list = np.arange(.1,.4+eps,.1) # orders of quantiles of P(r)\n", + "\n", + "fig,ax = plt.subplots(1,figsize=(6,4))\n", + "for alphamax_id,alphamax in enumerate(alphamax_list):\n", + " optfolder0 = f'datasets/hamming/Ising2D/opt/L{L}/T{T:.2f}/' # folder to put results\n", + " B = BID(\n", + " alphamin=alphamin,\n", + " alphamax=alphamax,\n", + " seed=seed,\n", + " delta=delta,\n", + " Nsteps=Nsteps,\n", + " optfolder0=optfolder0\n", + " )\n", + " remp,Pemp,Pmodel = B.load_fit() # to do explicit model validation\n", + " ax.plot(remp/N,Pemp,'x',label=r'$\\alpha_{max}=$'+f'{alphamax:.2f}')\n", + " ax.plot(remp/N,Pmodel,'-',color='black')\n", + "\n", + "ax.set_xlabel('r/N')\n", + "ax.set_ylabel('P(r)')\n", + "plt.title('model validation')\n", + "ax.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "venv", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/pyproject.toml b/pyproject.toml index c83df229..41143e43 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -5,9 +5,9 @@ description = "Distance-based Analysis of DAta-manifolds in python" authors = [{ name = "DADApy author"}] license = {file = "LICENSE"} readme = "README.md" -requires-python = ">=3.7" +requires-python = ">=3.8" -dependencies = ["numpy<2.0", "scipy", "scikit-learn", "matplotlib", "seaborn"] +dependencies = ["numpy<2.0", "scipy", "scikit-learn", "matplotlib", "seaborn", "jax", "jaxlib"] [project.urls] homepage = "https://github.com/sissa-data-science/DADApy" @@ -22,4 +22,4 @@ requires = ["setuptools>=61", "numpy<2.0"] build-backend = "setuptools.build_meta" [tool.tox] -envlist = ["py37", "py38", "py39", "py310", "py311", "py12"] +envlist = ["py38", "py39", "py310", "py311", "py12"] diff --git a/requirements.txt b/requirements.txt index a195e8c9..3b364ad6 100644 --- a/requirements.txt +++ b/requirements.txt @@ -7,4 +7,5 @@ numpy scipy scikit-learn joblib -matplotlib \ No newline at end of file +matplotlib +jax \ No newline at end of file diff --git a/tests/test_hamming/results/hist/counts.txt b/tests/test_hamming/results/hist/counts.txt new file mode 100644 index 00000000..f968df4e --- /dev/null +++ b/tests/test_hamming/results/hist/counts.txt @@ -0,0 +1,53 @@ +25,4 +26,6 +27,34 +28,52 +29,120 +30,291 +31,607 +32,1426 +33,2919 +34,5671 +35,10785 +36,19218 +37,33635 +38,56059 +39,89075 +40,135473 +41,198543 +42,278738 +43,375650 +44,486924 +45,607176 +46,726113 +47,830958 +48,918665 +49,975083 +50,993142 +51,974971 +52,920151 +53,832194 +54,722969 +55,606647 +56,486395 +57,375418 +58,278812 +59,198629 +60,135122 +61,88919 +62,55537 +63,33790 +64,19384 +65,11070 +66,5704 +67,2887 +68,1385 +69,658 +70,309 +71,105 +72,46 +73,20 +74,6 +75,2 +76,2 +77,1 \ No newline at end of file diff --git a/tests/test_hamming/test0.py b/tests/test_hamming/test0.py new file mode 100644 index 00000000..8b8a75f4 --- /dev/null +++ b/tests/test_hamming/test0.py @@ -0,0 +1,80 @@ +# Copyright 2021-2023 The DADApy Authors. All Rights Reserved. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. +# ============================================================================== + +"""Module for testing BID routines.""" + +import os + +import numpy as np +import pytest + +# this environmental variable must be set the BID imports +os.environ["JAX_ENABLE_X64"] = "True" +from dadapy.hamming import BID, Hamming # noqa: E402 + +# EXPECTED OUTPUT +d_0 = 99.855 +d_1 = 0.003 +logKL = -12.39 + +# REPRODUCIBILITY +seed = 1 +np.random.seed(seed=seed) + +# DATA +L = 100 # number of bits +Ns = 5000 # number of samples +X = ( + 2 * np.random.randint(low=0, high=2, size=(Ns, L)) - 1 +) # spins must be normalized to +-1 + +# DISTANCE HISTOGRAMS +histfolder = "./tests/test_hamming/results/hist/" +H = Hamming(coordinates=X) + +# REFERENCE HISTOGRAM +H.D_histogram(compute_flag=0, resultsfolder=histfolder) +expected_histogram = H.D_values + +# COMPUTING HISTOGRAM +H.compute_distances() +H.D_histogram(compute_flag=1, resultsfolder=histfolder) + +# PARAMETER DEFINITIONS FOR OPTIMIZATION +eps = 1e-5 # good-old small epsilon +alphamin = 0 # + eps # order of min_quantile, to remove poorly sampled parts of the histogram +alphamax = 1 # - eps # order of max_quantile, to define r* (named rmax here) +delta = 5e-4 # stochastic optimization step +Nsteps = int(1e6) # number of optimization steps +optfolder0 = "results/opt/" # folder where optimization results are saved +export_logKLs = 1 # flag to export the logKLs during optimization + +B = BID( + H, + alphamin=alphamin, + alphamax=alphamax, + seed=seed, + delta=delta, + Nsteps=Nsteps, + export_logKLs=export_logKLs, + optfolder0=optfolder0, + L=L, +) +B.computeBID() + +assert np.array_equal(H.D_values, expected_histogram) +assert pytest.approx(B.Op.d0, abs=1e-3) == d_0 +assert pytest.approx(B.Op.d1, abs=1e-3) == d_1 +assert pytest.approx(np.log(B.Op.KL), abs=1e-2) == logKL diff --git a/tox.ini b/tox.ini index cba964a9..00e38852 100644 --- a/tox.ini +++ b/tox.ini @@ -1,6 +1,6 @@ [tox] # isolated_build = True -envlist = black-check, isort-check, py3.7, py3.8, py3.9, py3.10, py3.11, py3.12 +envlist = black-check, isort-check, py3.8, py3.9, py3.10, py3.11, py3.12 # vulture, flake8, pylint, [tox:.package] @@ -30,9 +30,6 @@ commands = --cov-report=html \ --cov-report=term -[testenv:py3.7] -basepython = python3.7 - [testenv:py3.8] basepython = python3.8 @@ -81,14 +78,6 @@ deps = commands = flake8 dadapy/base.py dadapy/metric_comparisons.py dadapy/clustering.py dadapy/id_estimation.py dadapy/density_estimation.py dadapy/data.py tests -[testenv:py3.7-nb] -basepython = python3.7 -deps = - pytest>=6.2.5,<6.3.0 - nbmake>=1.2,<1.3 -commands: - pytest examples/notebook_on_intrinsicdim_densityest_clustering.ipynb examples/notebook_on_information_imbalance.ipynb --nbmake --nbmake-timeout=300 - [testenv:py3.8-nb] basepython = python3.8 deps =