diff options
Diffstat (limited to 'ot/lp/__init__.py')
| -rw-r--r-- | ot/lp/__init__.py | 52 |
1 files changed, 31 insertions, 21 deletions
diff --git a/ot/lp/__init__.py b/ot/lp/__init__.py index 8ec286b..17f1731 100644 --- a/ot/lp/__init__.py +++ b/ot/lp/__init__.py @@ -1,6 +1,9 @@ # -*- coding: utf-8 -*- """ Solvers for the original linear program OT problem + + + """ # Author: Remi Flamary <remi.flamary@unice.fr> @@ -39,26 +42,30 @@ def emd(a, b, M, numItermax=100000, log=False): - M is the metric cost matrix - a and b are the sample weights + .. warning:: + Note that the M matrix needs to be a C-order numpy.array in float64 + format. + Uses the algorithm proposed in [1]_ Parameters ---------- - a : (ns,) ndarray, float64 - Source histogram (uniform weigth if empty list) - b : (nt,) ndarray, float64 - Target histogram (uniform weigth if empty list) - M : (ns,nt) ndarray, float64 - loss matrix + a : (ns,) numpy.ndarray, float64 + Source histogram (uniform weight if empty list) + b : (nt,) numpy.ndarray, float64 + Target histogram (uniform weight if empty list) + M : (ns,nt) numpy.ndarray, float64 + Loss matrix (c-order array with type float64) numItermax : int, optional (default=100000) The maximum number of iterations before stopping the optimization algorithm if it has not converged. - log: boolean, optional (default=False) + log: bool, optional (default=False) If True, returns a dictionary containing the cost and dual variables. Otherwise returns only the optimal transportation matrix. Returns ------- - gamma: (ns x nt) ndarray + gamma: (ns x nt) numpy.ndarray Optimal transportation matrix for the given parameters log: dict If input log is true, a dictionary containing the cost and dual @@ -130,16 +137,20 @@ def emd2(a, b, M, processes=multiprocessing.cpu_count(), - M is the metric cost matrix - a and b are the sample weights + .. warning:: + Note that the M matrix needs to be a C-order numpy.array in float64 + format. + Uses the algorithm proposed in [1]_ Parameters ---------- - a : (ns,) ndarray, float64 - Source histogram (uniform weigth if empty list) - b : (nt,) ndarray, float64 - Target histogram (uniform weigth if empty list) - M : (ns,nt) ndarray, float64 - loss matrix + a : (ns,) numpy.ndarray, float64 + Source histogram (uniform weight if empty list) + b : (nt,) numpy.ndarray, float64 + Target histogram (uniform weight if empty list) + M : (ns,nt) numpy.ndarray, float64 + Loss matrix (c-order array with type float64) numItermax : int, optional (default=100000) The maximum number of iterations before stopping the optimization algorithm if it has not converged. @@ -153,7 +164,7 @@ def emd2(a, b, M, processes=multiprocessing.cpu_count(), ------- gamma: (ns x nt) ndarray Optimal transportation matrix for the given parameters - log: dict + log: dictnp If input log is true, a dictionary containing the cost and dual variables and exit status @@ -233,9 +244,9 @@ def free_support_barycenter(measures_locations, measures_weights, X_init, b=None Parameters ---------- - measures_locations : list of (k_i,d) np.ndarray + measures_locations : list of (k_i,d) numpy.ndarray The discrete support of a measure supported on k_i locations of a d-dimensional space (k_i can be different for each element of the list) - measures_weights : list of (k_i,) np.ndarray + measures_weights : list of (k_i,) numpy.ndarray Numpy arrays where each numpy array has k_i non-negatives values summing to one representing the weights of each discrete input measure X_init : (k,d) np.ndarray @@ -248,7 +259,7 @@ def free_support_barycenter(measures_locations, measures_weights, X_init, b=None numItermax : int, optional Max number of iterations stopThr : float, optional - Stop threshol on error (>0) + Stop threshold on error (>0) verbose : bool, optional Print information along iterations log : bool, optional @@ -533,14 +544,13 @@ def wasserstein_1d(x_a, x_b, a=None, b=None, p=1.): r"""Solves the p-Wasserstein distance problem between 1d measures and returns the distance - .. math:: - \gamma = arg\min_\gamma \left( \sum_i \sum_j \gamma_{ij} - |x_a[i] - x_b[j]|^p \\right)^{1/p} + \min_\gamma \left( \sum_i \sum_j \gamma_{ij} \|x_a[i] - x_b[j]\|^p \right)^{1/p} s.t. \gamma 1 = a, \gamma^T 1= b, \gamma\geq 0 + where : - x_a and x_b are the samples |