Module als: construct TT-tensor by TT-ALS¶
Package teneva, module als: construct TT-tensor, using TT-ALS.
This module contains the function “als” which computes the TT-approximation for the tensor by TT-ALS algorithm, using given random samples (i.e., the set of random tensor multi-indices and related tensor values).
- teneva.als.als(I_trn, y_trn, Y0, nswp=50, e=1e-16, info={}, *, I_vld=None, y_vld=None, e_vld=None, r=None, r_add=10000, e_adap=0.001, lamb=0.001, w=None, cb=None, swap_tol=3, allow_swap=False, allow_skip_cores=False, use_stab=False, log=False, update_sol=None)[source]¶
Build TT-tensor by TT-ALS method using given random tensor samples.
- Parameters:
I_trn (np.ndarray) – multi-indices for the tensor in the form of array of the shape [samples, d], where d is a number of tensor’s dimensions and samples is a size of the train dataset.
y_trn (np.ndarray) – values of the tensor for multi-indices I_trn in the form of array of the shape [samples].
Y0 (list) – TT-tensor, which is the initial approximation for algorithm.
nswp (int) – number of ALS iterations (sweeps). If e or e_vld parameter is set, then the real number of sweeps may be less (see info dict with the exact number of performed sweeps).
e (float) – optional algorithm convergence criterion (> 0). If between iterations (sweeps) the relative rate of solution change is less than this value, then the operation of the algorithm will be interrupted.
info (dict) – an optionally set dictionary, which will be filled with reference information about the process of the algorithm operation. At the end of the function work, it will contain parameters: e - the final value of the convergence criterion; e_vld - the final error on the validation dataset; nswp - the real number of performed iterations (sweeps); stop - stop type of the algorithm (nswp, e, e_vld or cb).
I_vld (np.ndarray) – optional multi-indices for items of validation dataset in the form of array of the shape [samples_vld, d], where samples_vld is a size of the validation dataset.
y_vld (np.ndarray) – optional values of the tensor for multi-indices I_vld of validation dataset in the form of array of the shape [samples_vld].
e_vld (float) – optional algorithm convergence criterion. If after sweep, the error on the validation dataset is less than this value, then the operation of the algorithm will be interrupted.
r (int) – maximum TT-rank for rank-adaptive ALS algorithm. If is None, then the TT-ALS with constant rank will be used (in the case of the constant rank, its value will be the same as the rank of the initial approximation Y0).
r_add (int) – maximum rank grow on one iteration for the rank-adaptive ALS algorithm. It is used only if r argument is not None.
e_adap (float) – convergence criterion for rank-adaptive TT-ALS algorithm (> 0). It is used only if r argument is not None.
lamb (float) – regularization parameter for least squares.
w (np.ndarray) – optional vector for weights of the input data (it should have a length equal to the number of elements in the data set). If this vector is used, then lamb parameter should be None.
cb (function) – optional callback function. It will be called after each sweep and the accuracy check with the arguments: Y, info and opts, where Y is the current approximation (TT-tensor), info is the info dictionary and the dictionary opts contains fields Yl, Yr and Yold. If the callback returns a true value, then the algorithm will be stopped (in the info dictionary, in this case, the stop type of the algorithm will be cb).
swap_tol (int) – experimental option.
allow_swap (bool) – experimental flag.
allow_skip_cores (bool) – if there is no data to learn all slices of the, TT-cores still work, keeping these slices. If the flag is not enabled, then in case of insufficient size of the training dataset, an error will be generated.
use_stab (bool) – if the flag is set, then the rank-adaptive method will use additional stabilization of the cores.
log (bool) – if flag is set, then the information about the progress of the algorithm will be printed after each sweep (and before the first sweep).
- Returns:
TT-tensor, which represents the TT-approximation for the tensor.
- Return type:
list
Examples:
d = 5 # Dimension of the function a = [-5., -4., -3., -2., -1.] # Lower bounds for spatial grid b = [+6., +3., +3., +1., +2.] # Upper bounds for spatial grid n = [ 10, 12, 14, 16, 18] # Shape of the tensor
m = 1.E+4 # Number of calls to target function nswp = 50 # Sweep number for ALS iterations r = 5 # TT-rank of the initial random tensor
We set the target function (the function takes as input a set of tensor multi-indices I of the shape [samples, dimension], which are transformed into points X of a uniform spatial grid using the function “ind_to_poi”):
def func(I): """Schaffer function.""" X = teneva.ind_to_poi(I, a, b, n) Z = X[:, :-1]**2 + X[:, 1:]**2 y = 0.5 + (np.sin(np.sqrt(Z))**2 - 0.5) / (1. + 0.001 * Z)**2 return np.sum(y, axis=1)
We prepare train data from the LHS random distribution:
I_trn = teneva.sample_lhs(n, m, seed=42) y_trn = func(I_trn)
We prepare test data from the random tensor multi-indices:
I_tst = teneva.sample_rand(n, 1.E+4, seed=42) y_tst = func(I_tst)
And now we will build the TT-tensor, which approximates the target function by the TT-ALS method. Note that we use TT-ANOVA as an initial approximation (we can instead generate random initial r-rank approximation in the TT-format using the function “rand”, but convergence will be worse, and there will also be instability of the solution).
t = tpc() Y = teneva.anova(I_trn, y_trn, r) Y = teneva.als(I_trn, y_trn, Y, nswp) t = tpc() - t print(f'Build time : {t:-10.2f}') # >>> ---------------------------------------- # >>> Output: # Build time : 1.74 #
And now we can check the result:
# Compute approximation in train points: y_our = teneva.get_many(Y, I_trn) # Accuracy of the result for train points: e_trn = np.linalg.norm(y_our - y_trn) e_trn /= np.linalg.norm(y_trn) # Compute approximation in test points: y_our = teneva.get_many(Y, I_tst) # Accuracy of the result for test points: e_tst = np.linalg.norm(y_our - y_tst) e_tst /= np.linalg.norm(y_tst) print(f'Error on train : {e_trn:-10.2e}') print(f'Error on test : {e_tst:-10.2e}') # >>> ---------------------------------------- # >>> Output: # Error on train : 1.27e-03 # Error on test : 1.43e-03 #
We can also set a validation data set and specify as a stop criterion the accuracy of the TT-approximation on this data (and we can also present the logs):
I_vld = teneva.sample_rand(n, 1.E+3, seed=99) y_vld = func(I_vld)
t = tpc() Y = teneva.anova(I_trn, y_trn, r) Y = teneva.als(I_trn, y_trn, Y, nswp, I_vld=I_vld, y_vld=y_vld, e_vld=1.E-2, log=True) t = tpc() - t print(f'\nBuild time : {t:-10.2f}') # >>> ---------------------------------------- # >>> Output: # # pre | time: 0.002 | rank: 5.0 | e_vld: 2.1e-01 | # # 1 | time: 0.043 | rank: 5.0 | e_vld: 1.1e-01 | e: 1.9e-01 | # # 2 | time: 0.078 | rank: 5.0 | e_vld: 1.7e-02 | e: 1.1e-01 | # # 3 | time: 0.113 | rank: 5.0 | e_vld: 4.8e-03 | e: 1.5e-02 | stop: e_vld | # # Build time : 0.12 #
We can use helper functions to present the resulting accuracy:
print(f'Error on train : {teneva.accuracy_on_data(Y, I_trn, y_trn):-10.2e}') print(f'Error on valid.: {teneva.accuracy_on_data(Y, I_vld, y_vld):-10.2e}') print(f'Error on test : {teneva.accuracy_on_data(Y, I_tst, y_tst):-10.2e}') # >>> ---------------------------------------- # >>> Output: # Error on train : 4.03e-03 # Error on valid.: 4.82e-03 # Error on test : 4.86e-03 #
We may also set the value of relative rate of solution change to stop the iterations:
t = tpc() Y = teneva.anova(I_trn, y_trn, r) Y = teneva.als(I_trn, y_trn, Y, e=1.E-3, I_vld=I_vld, y_vld=y_vld, log=True) t = tpc() - t print(f'\nBuild time : {t:-10.2f}') # >>> ---------------------------------------- # >>> Output: # # pre | time: 0.002 | rank: 5.0 | e_vld: 2.1e-01 | # # 1 | time: 0.047 | rank: 5.0 | e_vld: 1.1e-01 | e: 1.9e-01 | # # 2 | time: 0.083 | rank: 5.0 | e_vld: 2.1e-02 | e: 1.1e-01 | # # 3 | time: 0.118 | rank: 5.0 | e_vld: 1.2e-02 | e: 1.6e-02 | # # 4 | time: 0.153 | rank: 5.0 | e_vld: 1.0e-02 | e: 4.1e-03 | # # 5 | time: 0.188 | rank: 5.0 | e_vld: 8.1e-03 | e: 2.5e-03 | # # 6 | time: 0.224 | rank: 5.0 | e_vld: 6.6e-03 | e: 1.6e-03 | # # 7 | time: 0.260 | rank: 5.0 | e_vld: 5.5e-03 | e: 1.2e-03 | # # 8 | time: 0.296 | rank: 5.0 | e_vld: 4.6e-03 | e: 9.7e-04 | stop: e | # # Build time : 0.30 #
print(f'Error on train : {teneva.accuracy_on_data(Y, I_trn, y_trn):-10.2e}') print(f'Error on valid.: {teneva.accuracy_on_data(Y, I_vld, y_vld):-10.2e}') print(f'Error on test : {teneva.accuracy_on_data(Y, I_tst, y_tst):-10.2e}') # >>> ---------------------------------------- # >>> Output: # Error on train : 3.41e-03 # Error on valid.: 4.62e-03 # Error on test : 4.04e-03 #
print(f'Error on train : {teneva.accuracy_on_data(Y, I_trn, y_trn):-10.2e}') print(f'Error on valid.: {teneva.accuracy_on_data(Y, I_vld, y_vld):-10.2e}') print(f'Error on test : {teneva.accuracy_on_data(Y, I_tst, y_tst):-10.2e}') # >>> ---------------------------------------- # >>> Output: # Error on train : 3.41e-03 # Error on valid.: 4.62e-03 # Error on test : 4.04e-03 #
We may also pass callback function (it will be called after every sweep):
def cb(Y, info, opts): e = teneva.accuracy(Y, opts['Yold']) print(f'Callback : e={e:-7.1e}') if info['nswp'] == 5: # Stop the algorithm's work return True
t = tpc() Y = teneva.anova(I_trn, y_trn, r) Y = teneva.als(I_trn, y_trn, Y, e=1.E-10, cb=cb, log=True) t = tpc() - t print(f'\nBuild time : {t:-10.2f}') # >>> ---------------------------------------- # >>> Output: # # pre | time: 0.001 | rank: 5.0 | # Callback : e=1.9e-01 # # 1 | time: 0.044 | rank: 5.0 | e: 1.9e-01 | # Callback : e=1.1e-01 # # 2 | time: 0.080 | rank: 5.0 | e: 1.1e-01 | # Callback : e=2.3e-02 # # 3 | time: 0.116 | rank: 5.0 | e: 2.3e-02 | # Callback : e=3.6e-03 # # 4 | time: 0.152 | rank: 5.0 | e: 3.6e-03 | # Callback : e=1.4e-03 # # 5 | time: 0.188 | rank: 5.0 | e: 1.4e-03 | stop: cb | # # Build time : 0.19 #
We can also use rank-adaptive version of the TT-ALS method (note that result is very sensitive to “r” and “lamb” parameter values):
t = tpc() Y = teneva.anova(I_trn, y_trn, r=2) Y = teneva.als(I_trn, y_trn, Y, nswp=5, I_vld=I_vld, y_vld=y_vld, r=5, e_adap=1.E-2, lamb=0.00001, log=True) t = tpc() - t print(f'\nBuild time : {t:-10.2f}') # >>> ---------------------------------------- # >>> Output: # # pre | time: 0.002 | rank: 2.0 | e_vld: 2.1e-01 | # # 1 | time: 0.163 | rank: 5.0 | e_vld: 2.1e-02 | e: 2.2e-01 | # # 2 | time: 0.340 | rank: 3.9 | e_vld: 6.9e-03 | e: 2.0e-02 | # # 3 | time: 0.497 | rank: 3.9 | e_vld: 6.5e-03 | e: 2.6e-03 | # # 4 | time: 0.653 | rank: 4.2 | e_vld: 7.6e-03 | e: 6.3e-03 | # # 5 | time: 0.811 | rank: 3.9 | e_vld: 6.6e-03 | e: 6.3e-03 | stop: nswp | # # Build time : 0.82 #
print(f'Error on train : {teneva.accuracy_on_data(Y, I_trn, y_trn):-10.2e}') print(f'Error on valid.: {teneva.accuracy_on_data(Y, I_vld, y_vld):-10.2e}') print(f'Error on test : {teneva.accuracy_on_data(Y, I_tst, y_tst):-10.2e}') # >>> ---------------------------------------- # >>> Output: # Error on train : 6.54e-03 # Error on valid.: 6.58e-03 # Error on test : 7.22e-03 #
We can also specify weights for elements of the training dataset. In the following example, we set increased weights for the first 1000 points from the set and expect that the accuracy of the result on them will be higher than on the rest:
m = len(I_trn) dm = 1000 I_trn1, y_trn1 = I_trn[:dm], y_trn[:dm] I_trn2, y_trn2 = I_trn[dm:], y_trn[dm:] w = np.ones(m) w[:dm] = 100.
t = tpc() Y = teneva.anova(I_trn, y_trn, r) Y = teneva.als(I_trn, y_trn, Y, w=w) t = tpc() - t print(f'Build time : {t:-10.2f}') # >>> ---------------------------------------- # >>> Output: # Build time : 1.92 #
print(f'Error full data : {teneva.accuracy_on_data(Y, I_trn, y_trn):-10.2e}') print(f'Error for part1 : {teneva.accuracy_on_data(Y, I_trn1, y_trn1):-10.2e}') print(f'Error for part2 : {teneva.accuracy_on_data(Y, I_trn2, y_trn2):-10.2e}') # >>> ---------------------------------------- # >>> Output: # Error full data : 8.23e-03 # Error for part1 : 2.34e-03 # Error for part2 : 8.64e-03 #
(NEW OPTION) We can also use batch updates:
t = tpc() Y = teneva.anova(I_trn, y_trn, r) Nn = I_trn.shape[0] bs = 1000 # batch size iters = 10 for i_iter in range(iters): idx = np.random.permutation(Nn) for i in range(0, Nn, bs): I_trn_cur = I_trn[idx[i:i+bs]] y_trn_cur = y_trn[idx[i:i+bs]] Y = teneva.als(I_trn_cur, y_trn_cur, Y, e=1.E-3, I_vld=I_vld, y_vld=y_vld, log=True, update_sol=True, lamb=2**(i_iter/(iters/30))) t = tpc() - t print(f'\nBuild time : {t:-10.2f}') # >>> ---------------------------------------- # >>> Output: # # pre | time: 0.001 | rank: 5.0 | e_vld: 2.1e-01 | # # 1 | time: 0.019 | rank: 5.0 | e_vld: 1.6e-01 | e: 1.5e-01 | # # 2 | time: 0.035 | rank: 5.0 | e_vld: 1.4e-01 | e: 8.2e-02 | # # 3 | time: 0.052 | rank: 5.0 | e_vld: 9.6e-02 | e: 7.1e-02 | # # 4 | time: 0.068 | rank: 5.0 | e_vld: 5.4e-02 | e: 7.6e-02 | # # 5 | time: 0.084 | rank: 5.0 | e_vld: 5.0e-02 | e: 1.9e-02 | # # 6 | time: 0.100 | rank: 5.0 | e_vld: 5.0e-02 | e: 1.2e-02 | # # 7 | time: 0.116 | rank: 5.0 | e_vld: 5.1e-02 | e: 7.5e-03 | # # 8 | time: 0.132 | rank: 5.0 | e_vld: 5.1e-02 | e: 5.9e-03 | # # 9 | time: 0.148 | rank: 5.0 | e_vld: 5.2e-02 | e: 5.0e-03 | # # 10 | time: 0.164 | rank: 5.0 | e_vld: 5.2e-02 | e: 4.3e-03 | # # 11 | time: 0.181 | rank: 5.0 | e_vld: 5.2e-02 | e: 3.8e-03 | # # 12 | time: 0.198 | rank: 5.0 | e_vld: 5.2e-02 | e: 3.4e-03 | # # 13 | time: 0.216 | rank: 5.0 | e_vld: 5.2e-02 | e: 3.1e-03 | # # 14 | time: 0.232 | rank: 5.0 | e_vld: 5.1e-02 | e: 3.1e-03 | # # 15 | time: 0.248 | rank: 5.0 | e_vld: 5.1e-02 | e: 2.8e-03 | # # 16 | time: 0.263 | rank: 5.0 | e_vld: 5.1e-02 | e: 2.4e-03 | # # 17 | time: 0.279 | rank: 5.0 | e_vld: 5.1e-02 | e: 2.2e-03 | # # 18 | time: 0.294 | rank: 5.0 | e_vld: 5.1e-02 | e: 2.1e-03 | # # 19 | time: 0.310 | rank: 5.0 | e_vld: 5.1e-02 | e: 2.0e-03 | # # 20 | time: 0.326 | rank: 5.0 | e_vld: 5.1e-02 | e: 1.9e-03 | # # 21 | time: 0.342 | rank: 5.0 | e_vld: 5.0e-02 | e: 1.7e-03 | # # 22 | time: 0.358 | rank: 5.0 | e_vld: 5.0e-02 | e: 1.6e-03 | # # 23 | time: 0.374 | rank: 5.0 | e_vld: 5.0e-02 | e: 1.5e-03 | # # 24 | time: 0.391 | rank: 5.0 | e_vld: 5.0e-02 | e: 1.4e-03 | # # 25 | time: 0.408 | rank: 5.0 | e_vld: 5.0e-02 | e: 1.3e-03 | # # 26 | time: 0.425 | rank: 5.0 | e_vld: 5.0e-02 | e: 1.2e-03 | # # 27 | time: 0.442 | rank: 5.0 | e_vld: 5.0e-02 | e: 1.2e-03 | # # 28 | time: 0.461 | rank: 5.0 | e_vld: 5.0e-02 | e: 1.1e-03 | # # 29 | time: 0.479 | rank: 5.0 | e_vld: 5.0e-02 | e: 1.1e-03 | # # 30 | time: 0.495 | rank: 5.0 | e_vld: 5.0e-02 | e: 1.0e-03 | # # 31 | time: 0.512 | rank: 5.0 | e_vld: 5.0e-02 | e: 9.9e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 5.0e-02 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 3.4e-02 | e: 3.8e-02 | # # 2 | time: 0.034 | rank: 5.0 | e_vld: 3.2e-02 | e: 9.5e-03 | # # 3 | time: 0.051 | rank: 5.0 | e_vld: 3.1e-02 | e: 5.3e-03 | # # 4 | time: 0.068 | rank: 5.0 | e_vld: 3.1e-02 | e: 3.6e-03 | # # 5 | time: 0.088 | rank: 5.0 | e_vld: 3.0e-02 | e: 2.8e-03 | # # 6 | time: 0.108 | rank: 5.0 | e_vld: 3.0e-02 | e: 2.3e-03 | # # 7 | time: 0.127 | rank: 5.0 | e_vld: 3.0e-02 | e: 2.0e-03 | # # 8 | time: 0.144 | rank: 5.0 | e_vld: 2.9e-02 | e: 1.8e-03 | # # 9 | time: 0.159 | rank: 5.0 | e_vld: 2.9e-02 | e: 1.6e-03 | # # 10 | time: 0.174 | rank: 5.0 | e_vld: 2.9e-02 | e: 1.4e-03 | # # 11 | time: 0.189 | rank: 5.0 | e_vld: 2.8e-02 | e: 1.3e-03 | # # 12 | time: 0.205 | rank: 5.0 | e_vld: 2.8e-02 | e: 1.2e-03 | # # 13 | time: 0.220 | rank: 5.0 | e_vld: 2.8e-02 | e: 1.1e-03 | # # 14 | time: 0.235 | rank: 5.0 | e_vld: 2.8e-02 | e: 9.7e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 2.8e-02 | # # 1 | time: 0.016 | rank: 5.0 | e_vld: 2.2e-02 | e: 2.1e-02 | # # 2 | time: 0.031 | rank: 5.0 | e_vld: 2.1e-02 | e: 5.1e-03 | # # 3 | time: 0.046 | rank: 5.0 | e_vld: 2.1e-02 | e: 2.9e-03 | # # 4 | time: 0.063 | rank: 5.0 | e_vld: 2.0e-02 | e: 2.1e-03 | # # 5 | time: 0.079 | rank: 5.0 | e_vld: 2.0e-02 | e: 1.6e-03 | # # 6 | time: 0.096 | rank: 5.0 | e_vld: 1.9e-02 | e: 1.3e-03 | # # 7 | time: 0.113 | rank: 5.0 | e_vld: 1.9e-02 | e: 1.1e-03 | # # 8 | time: 0.129 | rank: 5.0 | e_vld: 1.9e-02 | e: 9.5e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 1.9e-02 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 1.5e-02 | e: 1.4e-02 | # # 2 | time: 0.032 | rank: 5.0 | e_vld: 1.4e-02 | e: 3.0e-03 | # # 3 | time: 0.047 | rank: 5.0 | e_vld: 1.3e-02 | e: 1.8e-03 | # # 4 | time: 0.062 | rank: 5.0 | e_vld: 1.3e-02 | e: 1.2e-03 | # # 5 | time: 0.077 | rank: 5.0 | e_vld: 1.3e-02 | e: 9.4e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 1.3e-02 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 1.1e-02 | e: 9.2e-03 | # # 2 | time: 0.033 | rank: 5.0 | e_vld: 1.1e-02 | e: 2.4e-03 | # # 3 | time: 0.048 | rank: 5.0 | e_vld: 1.1e-02 | e: 1.4e-03 | # # 4 | time: 0.065 | rank: 5.0 | e_vld: 1.1e-02 | e: 9.8e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 1.1e-02 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 9.2e-03 | e: 7.5e-03 | # # 2 | time: 0.034 | rank: 5.0 | e_vld: 9.1e-03 | e: 2.0e-03 | # # 3 | time: 0.050 | rank: 5.0 | e_vld: 9.0e-03 | e: 1.1e-03 | # # 4 | time: 0.065 | rank: 5.0 | e_vld: 9.0e-03 | e: 8.1e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 9.0e-03 | # # 1 | time: 0.016 | rank: 5.0 | e_vld: 8.1e-03 | e: 6.1e-03 | # # 2 | time: 0.031 | rank: 5.0 | e_vld: 8.1e-03 | e: 1.7e-03 | # # 3 | time: 0.046 | rank: 5.0 | e_vld: 8.2e-03 | e: 9.4e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 8.2e-03 | # # 1 | time: 0.016 | rank: 5.0 | e_vld: 7.5e-03 | e: 5.8e-03 | # # 2 | time: 0.031 | rank: 5.0 | e_vld: 7.6e-03 | e: 1.5e-03 | # # 3 | time: 0.046 | rank: 5.0 | e_vld: 7.6e-03 | e: 8.6e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 7.6e-03 | # # 1 | time: 0.016 | rank: 5.0 | e_vld: 7.1e-03 | e: 5.1e-03 | # # 2 | time: 0.031 | rank: 5.0 | e_vld: 7.2e-03 | e: 1.4e-03 | # # 3 | time: 0.046 | rank: 5.0 | e_vld: 7.2e-03 | e: 7.7e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 7.2e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 6.3e-03 | e: 4.6e-03 | # # 2 | time: 0.032 | rank: 5.0 | e_vld: 6.2e-03 | e: 1.2e-03 | # # 3 | time: 0.049 | rank: 5.0 | e_vld: 6.2e-03 | e: 7.1e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 6.2e-03 | # # 1 | time: 0.016 | rank: 5.0 | e_vld: 5.9e-03 | e: 2.9e-03 | # # 2 | time: 0.031 | rank: 5.0 | e_vld: 5.8e-03 | e: 8.2e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 5.8e-03 | # # 1 | time: 0.016 | rank: 5.0 | e_vld: 5.5e-03 | e: 2.5e-03 | # # 2 | time: 0.031 | rank: 5.0 | e_vld: 5.5e-03 | e: 8.3e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 5.5e-03 | # # 1 | time: 0.016 | rank: 5.0 | e_vld: 5.5e-03 | e: 3.0e-03 | # # 2 | time: 0.031 | rank: 5.0 | e_vld: 5.6e-03 | e: 7.8e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 5.6e-03 | # # 1 | time: 0.016 | rank: 5.0 | e_vld: 5.5e-03 | e: 3.1e-03 | # # 2 | time: 0.031 | rank: 5.0 | e_vld: 5.5e-03 | e: 8.1e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 5.5e-03 | # # 1 | time: 0.016 | rank: 5.0 | e_vld: 5.4e-03 | e: 2.9e-03 | # # 2 | time: 0.032 | rank: 5.0 | e_vld: 5.5e-03 | e: 7.9e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 5.5e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 5.5e-03 | e: 2.8e-03 | # # 2 | time: 0.033 | rank: 5.0 | e_vld: 5.6e-03 | e: 7.8e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 5.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 5.4e-03 | e: 3.3e-03 | # # 2 | time: 0.033 | rank: 5.0 | e_vld: 5.5e-03 | e: 7.5e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 5.5e-03 | # # 1 | time: 0.021 | rank: 5.0 | e_vld: 5.2e-03 | e: 2.8e-03 | # # 2 | time: 0.038 | rank: 5.0 | e_vld: 5.3e-03 | e: 7.8e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 5.3e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 5.0e-03 | e: 3.0e-03 | # # 2 | time: 0.035 | rank: 5.0 | e_vld: 5.1e-03 | e: 7.5e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 5.1e-03 | # # 1 | time: 0.018 | rank: 5.0 | e_vld: 5.2e-03 | e: 3.0e-03 | # # 2 | time: 0.033 | rank: 5.0 | e_vld: 5.3e-03 | e: 7.6e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 5.3e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 5.1e-03 | e: 2.3e-03 | # # 2 | time: 0.033 | rank: 5.0 | e_vld: 5.1e-03 | e: 5.6e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 5.1e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.9e-03 | e: 2.0e-03 | # # 2 | time: 0.033 | rank: 5.0 | e_vld: 5.0e-03 | e: 6.1e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 5.0e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.9e-03 | e: 1.8e-03 | # # 2 | time: 0.033 | rank: 5.0 | e_vld: 5.0e-03 | e: 5.0e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 5.0e-03 | # # 1 | time: 0.016 | rank: 5.0 | e_vld: 4.7e-03 | e: 1.8e-03 | # # 2 | time: 0.031 | rank: 5.0 | e_vld: 4.8e-03 | e: 5.2e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.8e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.8e-03 | e: 2.0e-03 | # # 2 | time: 0.033 | rank: 5.0 | e_vld: 4.9e-03 | e: 5.4e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.9e-03 | # # 1 | time: 0.016 | rank: 5.0 | e_vld: 5.0e-03 | e: 2.1e-03 | # # 2 | time: 0.031 | rank: 5.0 | e_vld: 5.1e-03 | e: 5.3e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 5.1e-03 | # # 1 | time: 0.016 | rank: 5.0 | e_vld: 4.8e-03 | e: 1.8e-03 | # # 2 | time: 0.031 | rank: 5.0 | e_vld: 4.8e-03 | e: 5.4e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.8e-03 | # # 1 | time: 0.019 | rank: 5.0 | e_vld: 4.8e-03 | e: 2.0e-03 | # # 2 | time: 0.040 | rank: 5.0 | e_vld: 4.9e-03 | e: 5.1e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.9e-03 | # # 1 | time: 0.022 | rank: 5.0 | e_vld: 4.8e-03 | e: 2.2e-03 | # # 2 | time: 0.040 | rank: 5.0 | e_vld: 4.9e-03 | e: 5.5e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.9e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.8e-03 | e: 1.9e-03 | # # 2 | time: 0.033 | rank: 5.0 | e_vld: 4.9e-03 | e: 5.0e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.9e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.8e-03 | e: 9.7e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.8e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.7e-03 | e: 9.4e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.7e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.8e-03 | e: 8.0e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.8e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.7e-03 | e: 8.5e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.7e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.7e-03 | e: 8.5e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.7e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.7e-03 | e: 8.6e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.7e-03 | # # 1 | time: 0.018 | rank: 5.0 | e_vld: 4.7e-03 | e: 1.1e-03 | # # 2 | time: 0.035 | rank: 5.0 | e_vld: 4.7e-03 | e: 3.8e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.7e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 9.5e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.7e-03 | e: 7.8e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.7e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 8.9e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 1.8e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 2.3e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 2.3e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 2.2e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 1.8e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 2.1e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.018 | rank: 5.0 | e_vld: 4.6e-03 | e: 1.9e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.019 | rank: 5.0 | e_vld: 4.6e-03 | e: 1.6e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.019 | rank: 5.0 | e_vld: 4.6e-03 | e: 1.8e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.018 | rank: 5.0 | e_vld: 4.6e-03 | e: 1.7e-04 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 2.4e-05 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 1.8e-05 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 2.6e-05 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 2.3e-05 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 2.5e-05 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 3.3e-05 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.016 | rank: 5.0 | e_vld: 4.6e-03 | e: 3.2e-05 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.016 | rank: 5.0 | e_vld: 4.6e-03 | e: 2.8e-05 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.016 | rank: 5.0 | e_vld: 4.6e-03 | e: 2.4e-05 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 2.4e-05 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 3.4e-06 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 2.7e-06 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 3.1e-06 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.016 | rank: 5.0 | e_vld: 4.6e-03 | e: 3.2e-06 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.016 | rank: 5.0 | e_vld: 4.6e-03 | e: 2.9e-06 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 3.5e-06 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 3.4e-06 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.018 | rank: 5.0 | e_vld: 4.6e-03 | e: 3.0e-06 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 4.4e-06 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 4.0e-06 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.018 | rank: 5.0 | e_vld: 4.6e-03 | e: 5.2e-07 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.018 | rank: 5.0 | e_vld: 4.6e-03 | e: 3.6e-07 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.018 | rank: 5.0 | e_vld: 4.6e-03 | e: 4.0e-07 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.018 | rank: 5.0 | e_vld: 4.6e-03 | e: 3.6e-07 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 4.1e-07 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 3.5e-07 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 4.9e-07 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 3.8e-07 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 4.7e-07 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 2.7e-07 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 4.6e-08 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 4.2e-08 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.016 | rank: 5.0 | e_vld: 4.6e-03 | e: 3.5e-08 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.018 | rank: 5.0 | e_vld: 4.6e-03 | e: 5.7e-08 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.019 | rank: 5.0 | e_vld: 4.6e-03 | e: 6.1e-08 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.019 | rank: 5.0 | e_vld: 4.6e-03 | e: 4.2e-08 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 5.8e-08 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 4.5e-08 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 6.6e-08 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.016 | rank: 5.0 | e_vld: 4.6e-03 | e: 4.2e-08 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.016 | rank: 5.0 | e_vld: 4.6e-03 | e: 4.2e-09 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 1.5e-08 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.016 | rank: 5.0 | e_vld: 4.6e-03 | e: 2.0e-08 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.016 | rank: 5.0 | e_vld: 4.6e-03 | e: 0.0e+00 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.016 | rank: 5.0 | e_vld: 4.6e-03 | e: 0.0e+00 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.018 | rank: 5.0 | e_vld: 4.6e-03 | e: 3.1e-08 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 1.7e-08 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.018 | rank: 5.0 | e_vld: 4.6e-03 | e: 3.3e-08 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 0.0e+00 | stop: e | # # pre | time: 0.001 | rank: 5.0 | e_vld: 4.6e-03 | # # 1 | time: 0.017 | rank: 5.0 | e_vld: 4.6e-03 | e: 0.0e+00 | stop: e | # # Build time : 3.17 #