diff --git a/data_loader/data_utils.py b/data_loader/data_utils.py index a90d335..a0ab2cf 100644 --- a/data_loader/data_utils.py +++ b/data_loader/data_utils.py @@ -9,22 +9,27 @@ class Dataset(object): - def __init__(self, data, stats): + def __init__(self, data, stats,type_normalize): self.__data = data - self.mean = stats['mean'] - self.std = stats['std'] + self.stats = stats + self.type_normalize = type_normalize + # self.mean = stats['mean'] + # self.std = stats['std'] def get_data(self, type): return self.__data[type] def get_stats(self): - return {'mean': self.mean, 'std': self.std} + return self.stats #{'mean': self.mean, 'std': self.std} + + def get_type(self): + return self.type_normalize #{'mean': self.mean, 'std': self.std} def get_len(self, type): return len(self.__data[type]) - def z_inverse(self, type): - return self.__data[type] * self.std + self.mean + # def z_inverse(self, type): + # return self.__data[type] * self.std + self.mean def seq_gen(len_seq, data_seq, offset, n_frame, n_route, day_slot, C_0=1): @@ -108,42 +113,102 @@ def data_gen(file_path, n_route, train_val_test_ratio, scalar, n_frame, day_slot try: data_seq = pd.read_csv(file_path, header=None) + data_seq_ori = pd.read_csv(file_path, header=None) + # data_seq = pd.read_csv(file_path, header=None) # .values # for column in list(data_seq.columns): - # #print(column) - # mean_val = data_seq[column].mean() - # data_seq[column].replace(0, mean_val, inplace=True) - data_seq = data_seq.values - - if scalar == 'min_max': # TODO: unify the covering range with zscore - my_matrix = np.array(data_seq) - scaler = MinMaxScaler() - scaler.fit(my_matrix) - data_seq = scaler.transform(my_matrix) + # # #print(column) + # mean_val = data_seq[column].mean() + # data_seq[column].replace(0, mean_val, inplace=True) + #data_seq = data_seq#.values + + # if scalar == 'min_max': # TODO: unify the covering range with zscore + # my_matrix = np.array(data_seq) + # scaler = MinMaxScaler() + # scaler.fit(my_matrix) + # data_seq = scaler.transform(my_matrix) # data_seq=data_seq[~(data_seq==0).all(axis=1), :] print(data_seq.shape) except FileNotFoundError: print(f'ERROR: input file was not found in {file_path}.') - + + n_sec_train = n_train - n_val length = len(data_seq) - n_frame + 1 train_len = int(n_train * length) + sec_train_len = int(n_sec_train * length) val_len = int(n_val * length) test_len = int(n_test * length) seq_train = data_seq[:train_len] + seq_test = data_seq[train_len:] - if scalar == 'z_score': - x_stats = {'mean': np.mean(seq_train), 'std': np.std(seq_train)} # TODO: fix the zscore - else: - x_stats = {'mean': 0, 'std': 1} + if scalar == 'min_max': # TODO: unify the covering range with zscore + my_matrix = np.array(seq_train) + all_matrix = np.array(data_seq) + scaler = MinMaxScaler() + scaler.fit(my_matrix) + seq_train = scaler.transform(my_matrix) - data_seq = z_score(data_seq, x_stats['mean'], x_stats['std']) + x_stats = [] + data_seq2 = pd.DataFrame(seq_train) + seq_test = pd.DataFrame(seq_test) - seq_train = seq_gen(train_len, data_seq, 0, n_frame, n_route, day_slot) - seq_val = seq_gen(val_len, data_seq, train_len, n_frame, n_route, day_slot) - seq_test = seq_gen(test_len, data_seq, train_len + val_len, n_frame, n_route, day_slot) + if scalar == 'z_score': + + #x_stats = {'mean': np.mean(seq_train), 'std': np.std(seq_train)} + + for column in list(data_seq2.columns): + #print(column) + stats = {} + data = np.array(data_seq2[column]) + stats = {'mean': np.mean(data), 'std': np.std(data)} + x_stats.append(stats) + #x_stats = {'mean': np.mean(seq_train), 'std': np.std(seq_train)} # TODO: fix the zscore + z_data = z_score(data_seq_ori.values, x_stats) + + x_stats = [] + + for column in list(seq_test.columns): + #print(column) + stats = {} + data = np.array(seq_test[column]) + stats = {'mean': np.mean(data), 'std': np.std(data)} + x_stats.append(stats) + + seq_test1 = z_score(data_seq.values, x_stats) + else: + for column in list(data_seq2.columns): + #print(column) + stats = {} + data = np.array(data_seq2[column]) + stats = {'mean': 0, 'std': 1} + x_stats.append(stats) + + #data_seq = data_seq.values + + + seq_train = seq_gen(train_len, z_data, 0, n_frame, n_route, day_slot) + #seq_train = seq_gen(train_len, seq_train, 0, n_frame, n_route, day_slot) + seq_val = seq_gen(val_len, z_data, sec_train_len, n_frame, n_route, day_slot) + seq_test = seq_gen(test_len, seq_test1, train_len , n_frame, n_route, day_slot) + data_seq = pd.read_csv(file_path, header=None).values + +# for column in list(data_seq.columns): +# mean_val = data_seq[column].mean() +# data_seq[column].replace(0, mean_val, inplace=True) + data_seq[np.where(data_seq == 0)] = np.nan + data_seq = pd.DataFrame(data_seq) + data_seq = data_seq.fillna(method='ffill', limit=len(data_seq)).fillna(method='bfill', limit=len(data_seq)) + data_seq = np.asarray(data_seq.values) + + + ori_train = seq_gen(train_len, data_seq, 0, n_frame, n_route, day_slot) + ori_val = seq_gen(val_len, data_seq, sec_train_len, n_frame, n_route, day_slot) + ori_test = seq_gen(test_len, data_seq, train_len , n_frame, n_route, day_slot) + + # seq_train = seq_gen(n_train, data_seq, 0, n_frame, n_route, day_slot) # seq_val = seq_gen(n_val, data_seq, n_train, n_frame, n_route, day_slot) # seq_test = seq_gen(n_test, data_seq, n_train + n_val, n_frame, n_route, day_slot) @@ -156,8 +221,12 @@ def data_gen(file_path, n_route, train_val_test_ratio, scalar, n_frame, day_slot # x_test = z_score(seq_test, x_stats['mean'], x_stats['std']) # # x_data = {'train': x_train, 'val': x_val, 'test': x_test} - x_data = {'train': seq_train, 'val': seq_val, 'test': seq_test} - dataset = Dataset(x_data, x_stats) + x_data = {'train': seq_train, 'val': seq_val, 'test': seq_test , 'ori_test': ori_test, 'ori_val': ori_val} + if scalar == 'z_score': + dataset = Dataset(x_data, x_stats,'z_score') + else: + dataset = Dataset(x_data, scaler,'min_max') + return dataset diff --git a/dataset/ECG_data.csv 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diff --git a/main.py b/main.py index 8d98b16..3e73389 100644 --- a/main.py +++ b/main.py @@ -36,7 +36,7 @@ parser.add_argument('--inf_mode', type=str, default='merge') parser.add_argument('--dataset', type=str, default='./dataset/ECG_data.csv') parser.add_argument('--output_dir', type=str, default='./output/ECG_data') -parser.add_argument('--scalar', type=str, default='min_max') +parser.add_argument('--scalar', type=str, default='z_score') parser.add_argument('--train', type=bool, default=True) parser.add_argument('--evaluate', type=bool, default=True) diff --git a/models/layers.py b/models/layers.py index d2259f0..ce8afa0 100644 --- a/models/layers.py +++ b/models/layers.py @@ -27,9 +27,10 @@ def gconv_fft_cnn_0221(x, theta, Ks, c_in, c_out, e): # x_tmp = tf.reshape(x,[-1,c_in]) # x_tmp = tf.reshape(tf.transpose(x, [0, 1, 3, 2]), [-1, n]) - real_kernel = tf.multiply(theta, kernel) + #real_kernel = tf.multiply(theta, kernel) +theta + real_kernel = tf.matmul(theta, kernel) #+theta x_mul = tf.matmul(x_tmp, real_kernel) - x_gconv = tf.reshape(x_mul, [-1, n, c_out]) + x_gconv = tf.transpose(tf.reshape(x_mul, [-1, c_out, n_route]),[0,2,1]) # x_mul = x_tmp * ker -> [batch_size*c_in, Ks*n_route] -> [batch_size, c_in, Ks, n_route] # x_mul = tf.reshape(tf.matmul(x_tmp, kernel), [-1, time_step, c_in, n_route]) # x_mul = tf.transpose(x_mul, [0, 1, 3, 2]) @@ -293,7 +294,8 @@ def fc(x, type='fore'): tf.add_to_collection(name='weight_decay', value=tf.nn.l2_loss(wt)) bt = tf.get_variable(name='bt_' + type, initializer=tf.zeros([channel_temp]), dtype=tf.float32) hidden = tf.sigmoid(tf.add(tf.matmul(x_tmp, wt), bt)) - out = tf.nn.softmax(hidden) + #out = tf.nn.softmax(hidden) + out = tf.nn.sigmoid(hidden) outputs = tf.reshape(out, [-1, time_step_temp, route_temp, channel_temp]) return outputs @@ -430,15 +432,24 @@ def stemGNN_block(x, Ks, Kt, channels, scope, keep_prob, e, v, l1, flag=0, act_f GF = graph_fft(x, v, True) x = GF - x = tf.spectral.fft(tf.cast(x, dtype=tf.complex64)) + #x = tf.reshape(tf.transpose(x, [0, 2, 3, 1]), [-1, T]) + #x = tf.spectral.fft(tf.cast(x, dtype=tf.complex64)) x = tf.real(x) x_imag = tf.imag(x) + + #x = tf.transpose(tf.reshape(x,[-1,n,c_in,T]),[0,3,1,2]) + #x_imag = tf.transpose(tf.reshape(x_imag,[-1,n,c_in,T]),[0,3,1,2]) # c_in = c_t _, time_step_temp, route_temp, channel_temp = x.get_shape().as_list() x = temporal_conv_layer(x, Kt, c_si, c_t, 'GLU') x_imag = temporal_conv_layer_imag(x_imag, Kt, c_si, c_t, 'GLU') - _, T, n, _ = x.get_shape().as_list() + _, T, n, cc = x.get_shape().as_list() + #x = tf.reshape(tf.transpose(x, [0, 2, 3, 1]), [-1, T]) + #x_imag = tf.reshape(tf.transpose(x_imag, [0, 2, 3, 1]), [-1, T]) x = tf.to_float(tf.spectral.ifft((tf.complex(x, x_imag)))) + #x = tf.transpose(tf.reshape(x,[-1,n,cc,T]),[0,3,1,2]) + + #x = tf.reshape(x,[-1,n,c_in]) # g_conv _, _, _, c_fft = x.get_shape().as_list() diff --git a/models/tester.py b/models/tester.py index 9d4ee80..a162ff9 100644 --- a/models/tester.py +++ b/models/tester.py @@ -1,41 +1,42 @@ from data_loader.data_utils import gen_batch -from utils.math_utils import evaluation +from utils.math_utils import evaluation,z_inverse from os.path import join as pjoin import tensorflow as tf import numpy as np import time import pandas as pd +from utils.math_utils import z_score,z_inverse tf.disable_eager_execution() -def z_score(x, mean, std): - ''' - Z-score normalization function: $z = (X - \mu) / \sigma $, - where z is the z-score, X is the value of the element, - $\mu$ is the population mean, and $\sigma$ is the standard deviation. - :param x: np.ndarray, input array to be normalized. - :param mean: float, the value of mean. - :param std: float, the value of standard deviation. - :return: np.ndarray, z-score normalized array. - ''' - # return x - return (x - mean) / std +# def z_score(x, mean, std): +# ''' +# Z-score normalization function: $z = (X - \mu) / \sigma $, +# where z is the z-score, X is the value of the element, +# $\mu$ is the population mean, and $\sigma$ is the standard deviation. +# :param x: np.ndarray, input array to be normalized. +# :param mean: float, the value of mean. +# :param std: float, the value of standard deviation. +# :return: np.ndarray, z-score normalized array. +# ''' +# # return x +# return (x - mean) / std -def z_inverse(x, mean, std): - ''' - The inverse of function z_score(). - :param x: np.ndarray, input to be recovered. - :param mean: float, the value of mean. - :param std: float, the value of standard deviation. - :return: np.ndarray, z-score inverse array. - ''' +# def z_inverse(x, mean, std): +# ''' +# The inverse of function z_score(). +# :param x: np.ndarray, input to be recovered. +# :param mean: float, the value of mean. +# :param std: float, the value of standard deviation. +# :return: np.ndarray, z-score inverse array. +# ''' - # return x +# # return x - return x * std + mean +# return x * std + mean def multi_pred(sess, y_pred, seq, batch_size, n_his, n_pred, step_idx, dynamic_batch=True): @@ -90,6 +91,13 @@ def model_inference(sess, pred, inputs, batch_size, n_his, n_pred, step_idx, min raise ValueError(f'ERROR: the value of n_pred "{n_pred}" exceeds the length limit.') y_val, len_val, x_temp = multi_pred(sess, pred, x_val, batch_size, n_his, n_pred, step_idx) + y_val = y_val.transpose((2, 0, 1, 3)) + s1,s2,s3,s4 = y_val.shape + y_val = y_val.reshape(s1,-1) + y_val = z_inverse(y_val,x_stats) + y_val = y_val.reshape(s1,s2,s3,s4) + y_val = y_val.transpose((1, 2, 0, 3)) + x_val = inputs.get_data('ori_val') evl_val = evaluation(x_val[0:len_val, step_idx + n_his, :, :], y_val, x_stats) # chks: indicator that reflects the relationship of values between evl_val and min_va_val. @@ -98,6 +106,13 @@ def model_inference(sess, pred, inputs, batch_size, n_his, n_pred, step_idx, min if sum(chks): min_va_val[chks] = evl_val[chks] y_pred, len_pred, x_temp = multi_pred(sess, pred, x_test, batch_size, n_his, n_pred, step_idx) + y_pred = y_pred.transpose((2, 0, 1, 3)) + s1,s2,s3,s4 = y_pred.shape + y_pred = y_pred.reshape(s1,-1) + y_pred = z_inverse(y_pred,x_stats) + y_pred = y_pred.reshape(s1,s2,s3,s4) + y_pred = y_pred.transpose((1, 2, 0, 3)) + x_test = inputs.get_data('ori_test') evl_pred = evaluation(x_test[0:len_pred, step_idx + n_his, :, :], y_pred, x_stats) min_val = evl_pred return min_va_val, min_val @@ -116,16 +131,21 @@ def model_test(inputs, batch_size, n_his, n_pred, inf_mode, load_path): start_time = time.time() model_path = tf.train.get_checkpoint_state(load_path).model_checkpoint_path + #with tf.device('/cpu:0'): test_graph = tf.Graph() with test_graph.as_default(): - saver = tf.train.import_meta_graph(pjoin(f'{model_path}.meta')) + + with tf.device('/cpu:0'): + saver = tf.train.import_meta_graph(pjoin(f'{model_path}.meta')) with tf.Session(graph=test_graph) as test_sess: - saver.restore(test_sess, tf.train.latest_checkpoint(load_path)) - print(f'>> Loading saved model from {model_path} ...') - - pred = test_graph.get_collection('y_pred') + + with tf.device('/cpu:0'): + saver.restore(test_sess, tf.train.latest_checkpoint(load_path)) + print(f'>> Loading saved model from {model_path} ...') + #with tf.device('/cpu:0'): + pred = test_graph.get_collection('y_pred') if inf_mode == 'sep': # for inference mode 'sep', the type of step index is int. @@ -133,13 +153,23 @@ def model_test(inputs, batch_size, n_his, n_pred, inf_mode, load_path): tmp_idx = [step_idx] elif inf_mode == 'merge': # for inference mode 'merge', the type of step index is np.ndarray. - step_idx = tmp_idx = np.arange(3, n_pred + 1, 3) - 1 + step_idx = tmp_idx = np.arange(1, n_pred+1, 1) - 1 else: raise ValueError(f'ERROR: test mode "{inf_mode}" is not defined.') x_test, x_stats = inputs.get_data('test'), inputs.get_stats() y_test, len_test, y_all_data = multi_pred(test_sess, pred, x_test, batch_size, n_his, n_pred, step_idx) + y_test = y_test.transpose((2, 0, 1, 3)) + s1,s2,s3,s4 = y_test.shape + y_test = y_test.reshape(s1,-1) + #y_pred = z_inverse(y_pred,x_stats) + y_test = z_inverse(y_test,x_stats) + y_test = y_test.reshape(s1,s2,s3,s4) + y_test = y_test.transpose((1, 2, 0, 3)) + + x_test = inputs.get_data('ori_test') + evl = evaluation(x_test[0:len_test, step_idx + n_his, :, :], y_test, x_stats) # for i in range(0,len(x_test)): # y_pre = y_all_data[:,i,:,:] @@ -149,8 +179,17 @@ def model_test(inputs, batch_size, n_his, n_pred, inf_mode, load_path): # pd.DataFrame(np.squeeze(x_all)).to_csv('conv_x_'+str(i)+'.csv') # pd.DataFrame(np.squeeze(y_pre)).to_csv('conv_y_'+str(i)+'.csv') + amape=[] + amae=[] + armse=[] + + for ix in tmp_idx: - te = evl[ix - 2:ix + 1] + te = evl[ix*3:ix*3 + 3] print(f'Time Step {ix + 1}: MAPE {te[0]:7.3%}; MAE {te[1]:4.3f}; RMSE {te[2]:6.3f}.') + amape.append(te[0]) + amae.append(te[1]) + armse.append(te[2]) + print(f'Results: MAPE {np.mean(amape):7.3%}; MAE {np.mean(amae):4.3f}; RMSE {np.mean(armse):6.3f}.') print(f'Model Test Time {time.time() - start_time:.3f}s') print('Testing model finished!') diff --git a/models/trainer.py b/models/trainer.py index 7390f67..3ea60df 100644 --- a/models/trainer.py +++ b/models/trainer.py @@ -98,7 +98,7 @@ def model_train(inputs, blocks, args, tensorboard_summary_dir, model_dir): min_val = min_va_val = np.array([4e1, 1e5, 1e5]) elif inf_mode == 'merge': # for inference mode 'merge', the type of step index is np.ndarray. - step_idx = tmp_idx = np.arange(3, n_pred + 1, 3) - 1 + step_idx = tmp_idx = np.arange(1, n_pred+1, 1) - 1 min_val = min_va_val = np.array([4e1, 1e5, 1e5] * len(step_idx)) else: raise ValueError(f'ERROR: test mode "{inf_mode}" is not defined.') @@ -123,23 +123,40 @@ def model_train(inputs, blocks, args, tensorboard_summary_dir, model_dir): # pd.DataFrame(e_value_1).to_csv("e_value" + str(i) + ".csv") if not os.path.exists(model_dir): os.makedirs(model_dir) + + if (i + 1) % args.save == 0: start_time = time.time() - min_va_val, min_val = \ - model_inference(sess, pred, inputs, batch_size, n_his, n_pred, step_idx, min_va_val, min_val) - + + evl, min_val = \ + model_inference(sess, pred, inputs, batch_size, n_his, n_pred, step_idx, min_va_val, min_val) + + # for ix in tmp_idx: + # va, te = min_va_val[ix - 2:ix + 1], min_val[ix - 2:ix + 1] + # print(f'Time Step {ix + 1}: ' + # f'MAPE {va[0]:7.3%}, {te[0]:7.3%}; ' + # f'MAE {va[1]:4.3f}, {te[1]:4.3f}; ' + # f'RMSE {va[2]:6.3f}, {te[2]:6.3f}.') + amape=[] + amae=[] + armse=[] for ix in tmp_idx: - va, te = min_va_val[ix - 2:ix + 1], min_val[ix - 2:ix + 1] - print(f'Time Step {ix + 1}: ' - f'MAPE {va[0]:7.3%}, {te[0]:7.3%}; ' - f'MAE {va[1]:4.3f}, {te[1]:4.3f}; ' - f'RMSE {va[2]:6.3f}, {te[2]:6.3f}.') + te = evl[ix*3:ix*3 + 3] + amape.append(te[0]) + amae.append(te[1]) + armse.append(te[2]) + print(f'Time Step {ix + 1}: MAPE {te[0]:7.3%}; MAE {te[1]:4.3f}; RMSE {te[2]:6.3f}.') + + print(f'Results: MAPE {np.mean(amape):7.3%}; MAE {np.mean(amae):4.3f}; RMSE {np.mean(armse):6.3f}.') + print(f'Epoch {i:2d} Inference Time {time.time() - start_time:.3f}s') + + model_save(sess, global_steps, 'StemGNN', model_dir) - if va[0] < minimum_mape: - minimum_mape = va[0] + if evl[1] <= minimum_mape: + minimum_mape = evl[1] best_model_dir_name = pjoin(model_dir, 'best') if not os.path.exists(best_model_dir_name): os.makedirs(best_model_dir_name) diff --git a/utils/math_utils.py b/utils/math_utils.py index 2c205d6..9c58935 100644 --- a/utils/math_utils.py +++ b/utils/math_utils.py @@ -1,11 +1,23 @@ + + import numpy as np import math - -import pandas as pd from scipy.stats import pearsonr +import pandas as pd - -def z_score(x, mean, std): +# #def z_score(x, mean, std): +# ''' +# Z-score normalization function: $z = (X - \mu) / \sigma $, +# where z is the z-score, X is the value of the element, +# $\mu$ is the population mean, and $\sigma$ is the standard deviation. +# :param x: np.ndarray, input array to be normalized. +# :param mean: float, the value of mean. +# :param std: float, the value of standard deviation. +# :return: np.ndarray, z-score normalized array. +# ''' +# # return (x - mean) / std + +def z_score(x, x_stats): ''' Z-score normalization function: $z = (X - \mu) / \sigma $, where z is the z-score, X is the value of the element, @@ -14,16 +26,22 @@ def z_score(x, mean, std): :param mean: float, the value of mean. :param std: float, the value of standard deviation. :return: np.ndarray, z-score normalized array. + ''' - x = (x - mean) / std + + for i in range(0,len(x[0])): + x[:,i]=(x[:,i]-x_stats[i]['mean'])/x_stats[i]['std'] + x[np.where(x == 0)] = np.nan x = pd.DataFrame(x) x = x.fillna(method='ffill', limit=len(x)).fillna(method='bfill', limit=len(x)) x = np.asarray(x.values) + return x -def z_inverse(x, mean, std): + +def z_inverse(x, x_stats): ''' The inverse of function z_score(). :param x: np.ndarray, input to be recovered. @@ -31,7 +49,25 @@ def z_inverse(x, mean, std): :param std: float, the value of standard deviation. :return: np.ndarray, z-score inverse array. ''' - return x * std + mean + + for i in range(0,len(x)): + x[i,:]=(x[i,:]*x_stats[i]['std'])+ x_stats[i]['mean'] + + + + return x + +# def z_inverse(x, mean, std): +# ''' +# The inverse of function z_score(). +# :param x: np.ndarray, input to be recovered. +# :param mean: float, the value of mean. +# :param std: float, the value of standard deviation. +# :return: np.ndarray, z-score inverse array. +# ''' +# for i in range(0,len(x[0])): +# x[:,i]=(x[:,i]*x_stats[i]['std'])+ x_stats[i]['mean'] +# return x * std + mean def MAPE(v, v_): @@ -41,7 +77,7 @@ def MAPE(v, v_): :param v_: np.ndarray or int, prediction. :return: int, MAPE averages on all elements of input. ''' - return np.mean(np.abs((v_ - v) / v)) + return np.mean(np.abs(np.abs(v_ - v) / v)) def RMSE(v, v_): @@ -63,11 +99,9 @@ def MAE(v, v_): ''' return np.mean(np.abs(v_ - v)) - def rrse_(y_true, y_pred): return np.sqrt(np.sum((y_true - y_pred) ** 2) / np.sum((y_true - np.mean(y_true)) ** 2)) - def CORR(y_true, y_pred): y_true = np.array(y_true, 'float32') y_pred = np.array(y_pred, 'float32') @@ -95,14 +129,16 @@ def evaluation(y, y_, x_stats): ''' dim = len(y_.shape) - # print(y) - # print(y_) + #print(y) + #print(y_) + if dim == 3: # single_step case - v = z_inverse(y, x_stats['mean'], x_stats['std']) - v_ = z_inverse(y_, x_stats['mean'], x_stats['std']) + + v = y#z_inverse(np.squeeze(y), x_stats) + v_ = y_#z_inverse(y_, x_stats) return np.array([MAPE(v, v_), MAE(v, v_), RMSE(v, v_)]) - # return np.array([rrse_(v, v_), MAE(v, v_), CORR(v, v_)]) + #return np.array([rrse_(v, v_), MAE(v, v_), CORR(v, v_)]) else: # multi_step case tmp_list = []