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AnDA_analog_forecasting.py
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AnDA_analog_forecasting.py
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#!/usr/bin/env python
""" AnDA_analog_forecasting.py: Apply the analog method on catalog of historical data to generate forecasts. """
__author__ = "Phi Huynh Viet"
__version__ = "2.0"
__date__ = "2017-08-01"
__email__ = "[email protected]"
import numpy as np
from AnDA_stat_functions import mk_stochastic, sample_discrete, AnDA_RMSE, AnDA_correlate
from scipy.sparse import diags
from sklearn.cluster import KMeans
def AnDA_analog_forecasting(x, in_x, AF):
""" Apply the analog method on catalog of historical data to generate forecasts. """
# initializations
N, n = x.shape
xf = np.zeros([N,n])
xf_mean = np.zeros([N,n])
# local or global analog forecasting
stop_condition = 0
i_var = np.array([0])
while (stop_condition!=1):
# in case of global approach
if np.array_equal(AF.neighborhood, np.ones([n,n])):
i_var_neighboor = np.arange(0,n)
i_var = np.arange(0,n)
stop_condition = 1
kdt = AF.list_kdtree[0]
# in case of local approach
else:
i_var_neighboor = np.where(AF.neighborhood[int(i_var),:]==1)[0]
kdt = AF.list_kdtree[int(i_var)]
# find the indices and distances of the k-nearest neighbors (knn)
if (AF.flag_cond):
index_knn, dist_knn = kdt.nn_index(x[:,i_var_neighboor],AF.k_initial)
else:
index_knn, dist_knn = kdt.nn_index(x[:,i_var_neighboor],AF.k)
dist_knn = np.sqrt(dist_knn/len(i_var_neighboor))
index_knn[np.in1d(index_knn,AF.check_indices).reshape(index_knn.shape)] = index_knn[np.in1d(index_knn,AF.check_indices).reshape(index_knn.shape)]-AF.lag
# using condition to retrive AF.k analogs from AF.k_initial nearest neighbors
if (AF.flag_cond):
mask_tmp = AF.obs_mask[in_x,:]
if (np.sum(~np.isnan(mask_tmp))>0):
x_cond_pca = np.copy(mask_tmp)
x_cond_pca[np.isnan(x_cond_pca)] = AF.x_cond[in_x,np.isnan(x_cond_pca)]
x_cond_pca = np.dot(x_cond_pca-AF.mu_dX,AF.coeff_dX)
x_cond_pca_tmp =np.zeros(n)[None]
x_cond_pca_tmp[0,i_var_neighboor] = x_cond_pca[i_var_neighboor]
x_cond_tmp_res = np.dot(x_cond_pca_tmp,AF.coeff_dX.T)+AF.mu_dX
x_cond_tmp_res = x_cond_tmp_res[:,~np.isnan(mask_tmp)]
index_tmp = np.zeros([N,AF.k],dtype=np.int32)
dist_tmp = np.zeros([N,AF.k])
for i_N in range(N):
successors_reduced = AF.catalogs[index_knn[i_N,:]+AF.lag,:]
tmp_1 = np.zeros([AF.k_initial,n])
tmp_1[:,i_var_neighboor] = successors_reduced[:,i_var_neighboor]
tmp_1 = np.dot(tmp_1,AF.coeff_dX.T)+AF.mu_dX
tmp_1 = tmp_1[:,~np.isnan(mask_tmp)]
tmp_3 = np.dot(successors_reduced, AF.coeff_dX.T) + AF.mu_dX
tmp_3 = tmp_3[:,~np.isnan(mask_tmp)]
dis_next = AnDA_RMSE(x_cond_tmp_res,tmp_1)
dis_next_g = AnDA_RMSE(mask_tmp[~np.isnan(mask_tmp)],tmp_3)
#corr_next_g = AnDA_correlate(mask_tmp[~np.isnan(mask_tmp)],tmp_3)
#corr_next_g = corr2(x[~np.isnan(mask)],tmp_4[~np.isnan(mask)])
if (stop_condition==0):
#dis_final = dis_next*dis_next_g*dist_knn[i_N,:]
dis_final = dis_next*dist_knn[i_N,:]
else:
dis_final = dis_next_g*dist_knn[i_N,:]
sort_dis = np.argsort(dis_final)
index_tmp[i_N,:] = index_knn[i_N,sort_dis[:AF.k]]
dist_tmp[i_N,:] = dis_final[sort_dis[:AF.k]]
index_knn = index_tmp
dist_knn = dist_tmp
else:
index_knn = index_knn[:,:AF.k]
dist_knn = dist_knn[:,:AF.k]
else:
index_knn = index_knn[:,:AF.k]
dist_knn = dist_knn[:,:AF.k]
# normalisation parameter for the kernels
lambdaa = np.median(dist_knn);
# compute weights
if AF.k == 1:
weights = np.ones([N,1]);
else:
weights = mk_stochastic(np.exp(-np.power(dist_knn,2)/lambdaa));
# reduce 2 array: analogs and successors because EnKF members have many identical nearest neighbors
index_unique, mask_indices = np.unique(index_knn, return_inverse=True)
index_knn = mask_indices.reshape(index_knn.shape)
analogs = AF.catalogs[np.ix_(index_unique,i_var_neighboor)]
if (stop_condition==0):
analogs_single = AF.catalogs[np.ix_(index_unique,i_var)]
#analogs = AF.catalogs[np.ix_(index_unique,i_var)]
successors = AF.catalogs[np.ix_(index_unique+AF.lag,i_var)]
# reduce catalog of physic model
if (AF.flag_model):
cata_model = AF.cata_model_full[index_unique+AF.lag,:]
# reduced version of local linear
if (AF.flag_reduced):
if (AF.regression == 'local_linear'):
if (N>=AF.cluster):
kmeans = KMeans(n_clusters=AF.cluster, random_state=0).fit(x[:,i_var_neighboor])
else:
kmeans = KMeans(n_clusters=1, random_state=0).fit(x[:,i_var_neighboor])
for i_cluster in range(kmeans.n_clusters):
cluster_x = np.where(kmeans.labels_== i_cluster)[0]
index_i_cluster, mask_cluster = np.unique(index_knn[cluster_x,:],return_inverse=True)
mask_cluster = mask_cluster.reshape(index_knn[cluster_x,:].shape)
if (AF.flag_model):
cata_model_tmp = np.concatenate((np.ones((len(cata_model[index_i_cluster,:]),1)),cata_model[index_i_cluster,:]),axis=1)
S = np.linalg.lstsq(cata_model_tmp,successors[index_i_cluster,:])[0]
ytest_A = np.dot(np.insert(AF.x_model[in_x,:],0,1),S)
tmp1 = np.dot(cata_model_tmp,S)
A = np.concatenate((np.ones((len(index_i_cluster),1)),analogs[index_i_cluster,:], tmp1),axis=1)
tmp4 = np.linalg.lstsq(A,successors[index_i_cluster,:])[0]
xf_mean[np.ix_(cluster_x,i_var)] = np.dot(np.concatenate((np.ones((len(cluster_x),1)),x[np.ix_(cluster_x,i_var_neighboor)],np.tile(ytest_A,(len(cluster_x),1))),axis=1),tmp4)
res_full = successors[index_i_cluster,:]-np.dot( A ,tmp4)
else:
A = np.concatenate((np.ones((len(index_i_cluster),1)),analogs[index_i_cluster,:]),axis=1)
tmp4 = np.linalg.lstsq(A,successors[index_i_cluster,:])[0]
res_full = successors[index_i_cluster,:]-np.dot( A ,tmp4)
xf_mean[np.ix_(cluster_x,i_var)] = np.dot(np.concatenate((np.ones((len(cluster_x),1)),x[np.ix_(cluster_x,i_var_neighboor)]),axis=1),tmp4)
for jj in range(len(cluster_x)):
xf_tmp = np.zeros([AF.k,np.max(i_var)+1])
res = res_full[mask_cluster[jj,:],:]
xf_tmp[:,i_var] = xf_mean[cluster_x[jj],i_var]+res
res = res.T
if len(i_var)>1:
cov_xf = np.cov(res)
else:
cov_xf = np.cov(res)[np.newaxis][np.newaxis]
weights[cluster_x[jj],:] = 1.0/len(weights[cluster_x[jj],:])
if (AF.sampling =='gaussian'):
# random sampling from the multivariate Gaussian distribution
xf[cluster_x[jj],i_var] = np.random.multivariate_normal(xf_mean[cluster_x[jj],i_var],cov_xf)
elif (AF.sampling =='multinomial'):
# random sampling from the multinomial distribution of the weights
i_good = sample_discrete(weights[cluster_x[jj],:],1,1)
xf[cluster_x[jj],i_var] = xf_tmp[i_good,i_var]
else:
print("Error: choose AF.sampling between 'gaussian', 'multinomial' ")
quit()
else:
print("Error: Clusterized version only for Local Linear.")
quit()
else:
# for each member/particle
for i_N in range(0,N):
xf_tmp = np.zeros([AF.k,np.max(i_var)+1]);
# select the regression method
if (AF.regression == 'locally_constant'):
xf_tmp[:,i_var] = successors[index_knn[i_N,:],:];
# weighted mean and covariance
xf_mean[i_N,i_var] = np.sum(xf_tmp[:,i_var]*np.repeat(weights[i_N,:][np.newaxis].T,len(i_var),1),0)
E_xf = (xf_tmp[:,i_var]-np.repeat(xf_mean[i_N,i_var][np.newaxis],AF.k,0)).T;
cov_xf = 1.0/(1.0-np.sum(np.power(weights[i_N,:],2)))*np.dot(np.repeat(weights[i_N,:][np.newaxis],len(i_var),0)*E_xf,E_xf.T);
elif (AF.regression == 'increment'):
if (stop_condition==0):
xf_tmp[:,i_var] = np.repeat(x[i_N,i_var][np.newaxis],AF.k,0) + successors[index_knn[i_N,:],:]-analogs_single[index_knn[i_N,:],:];
else:
xf_tmp[:,i_var] = np.repeat(x[i_N,i_var][np.newaxis],AF.k,0) + successors[index_knn[i_N,:],:]-analogs[index_knn[i_N,:],:];
# weighted mean and covariance
xf_mean[i_N,i_var] = np.sum(xf_tmp[:,i_var]*np.repeat(weights[i_N,:][np.newaxis].T,len(i_var),1),0);
E_xf = (xf_tmp[:,i_var]-np.repeat(xf_mean[i_N,i_var][np.newaxis],AF.k,0)).T;
cov_xf = 1.0/(1-np.sum(np.power(weights[i_N,:],2)))*np.dot(np.repeat(weights[i_N,:][np.newaxis],len(i_var),0)*E_xf,E_xf.T);
elif (AF.regression == 'local_linear'):
if (AF.flag_model):
cata_model_tmp = np.concatenate((np.ones((AF.k,1)),cata_model[index_knn[i_N,:],:]),axis=1)
successors_tmp = successors[index_knn[i_N,:],:]
analogs_tmp = analogs[index_knn[i_N,:],:]
S = np.linalg.lstsq(cata_model_tmp,successors_tmp)[0]
ytest_A = np.dot(np.insert(AF.x_model[in_x,:],0,1),S)
tmp1 = np.dot(cata_model_tmp,S)
A = np.concatenate((np.ones((AF.k,1)),analogs_tmp,tmp1),axis=1)
tmp4 = np.linalg.lstsq(A,successors_tmp)[0]
mu = np.dot(np.hstack((1,x[i_N,i_var_neighboor],ytest_A)),tmp4)
res = successors_tmp-np.dot( A ,tmp4)
xf_tmp[:,i_var] = mu+res
xf_mean[i_N,i_var] = mu
else:
successors_tmp = successors[index_knn[i_N,:],:]
analogs_tmp = analogs[index_knn[i_N,:],:]
W = diags(np.sqrt(weights[i_N,:]))
A = np.concatenate((np.ones((len(analogs_tmp),1)),analogs_tmp),axis=1)
Aw = W.dot(A)
Bw = W.dot(successors_tmp)
tmp4 = np.linalg.lstsq(Aw,Bw)[0]
tmp5 = np.linalg.lstsq(A,successors_tmp)[0]
mu = np.dot(np.hstack((1,x[i_N,i_var_neighboor])),tmp4)
#mu = np.dot(np.hstack((1,x[i_N,i_var])),tmp4)
#xf_mean[i_N,i_var] = mu
res = (successors_tmp- np.dot( A ,tmp5))
xf_tmp[:,i_var] = mu+res
# weighted mean and covariance
xf_mean[i_N,i_var] = mu
res = res.T
if len(i_var)>1:
cov_xf = np.cov(res)
else:
cov_xf = np.cov(res)[np.newaxis][np.newaxis]
# constant weights for local linear
weights[i_N,:] = 1.0/len(weights[i_N,:])
else:
print("Error: choose AF.regression between 'locally_constant', 'increment', 'local_linear' ")
quit()
# select the sampling method
if (AF.sampling =='gaussian'):
# random sampling from the multivariate Gaussian distribution
xf[i_N,i_var] = np.random.multivariate_normal(xf_mean[i_N,i_var],cov_xf);
elif (AF.sampling =='multinomial'):
# random sampling from the multinomial distribution of the weights
i_good = sample_discrete(weights[i_N,:],1,1);
xf[i_N,i_var] = xf_tmp[i_good,i_var];
else:
print("Error: choose AF.sampling between 'gaussian', 'multinomial' ")
quit()
# stop condition
if (np.array_equal(i_var,np.array([n-1])) or (len(i_var) == n)):
stop_condition = 1;
else:
i_var = i_var + 1;
return xf, xf_mean; # end