You can read an overview of this Numerical Linear Algebra course in this blog post. The course was originally taught in the University of San Francisco MS in Analytics graduate program. Course lecture videos are available on YouTube (note that the notebook numbers and video numbers do not line up, since some notebooks took longer than 1 video to cover).

# 7. PageRank with Eigen Decompositions¶

### Two Handy Tricks¶

Here are two tools that we'll be using today, which are useful in general.

1. Psutil is a great way to check on your memory usage. This will be useful here since we are using a larger data set.

In [462]:
import psutil

In [447]:
process = psutil.Process(os.getpid())
t = process.memory_info()

In [449]:
t.vms, t.rss

Out[449]:
(19475513344, 17856520192)
In [450]:
def mem_usage():
process = psutil.Process(os.getpid())

In [451]:
mem_usage()

Out[451]:
0.13217061955758594

2. TQDM gives you progress bars.

In [364]:
from time import sleep

In [463]:
# Without TQDM
s = 0
for i in range(10):
s += i
sleep(0.2)
print(s)

45

In [465]:
# With TQDM
from tqdm import tqdm

s = 0
for i in tqdm(range(10)):
s += i
sleep(0.2)
print(s)

100%|██████████| 10/10 [00:02<00:00,  4.96it/s]
45


## Motivation¶

Review

• What is SVD?
• What are some applications of SVD?

An interesting use of SVD that I recently came across was as a step in the de-biasing of Word2Vec word embeddings, from Quantifying and Reducing Stereotypes in Word Embeddings(Bolukbasi, et al).

Word2Vec is a useful library released by Google that represents words as vectors. The similarity of vectors captures semantic meaning, and analogies can be found, such as Paris:France :: Tokyo: Japan.

(source: Vector Representations of Words)

However, these embeddings can implicitly encode bias, such as father:doctor :: mother:nurse and man:computer programmer :: woman:homemaker.

One approach for de-biasing the space involves using SVD to reduce the dimensionality (Bolukbasi paper).

#### Ways to think about SVD¶

• Data compression
• SVD trades a large number of features for a smaller set of better features
• All matrices are diagonal (if you use change of bases on the domain and range)

### Perspectives on SVD¶

We usually talk about SVD in terms of matrices, $$A = U \Sigma V^T$$ but we can also think about it in terms of vectors. SVD gives us sets of orthonormal vectors ${v_j}$ and ${u_j}$ such that $$A v_j = \sigma_j u_j$$

$\sigma_j$ are scalars, called singular values

Q: Does this remind you of anything?

Relationship between SVD and Eigen Decomposition: the left-singular vectors of A are the eigenvectors of $AA^T$. The right-singular vectors of A are the eigenvectors of $A^T A$. The non-zero singular values of A are the square roots of the eigenvalues of $A^T A$ (and $A A^T$).

SVD is a generalization of eigen decomposition. Not all matrices have eigen values, but ALL matrices have singular values.

Let's forget SVD for a bit and talk about how to find the eigenvalues of a symmetric positive definite matrix...

## Today: Eigen Decomposition¶

The best classical methods for computing the SVD are variants on methods for computing eigenvalues. In addition to their links to SVD, Eigen decompositions are useful on their own as well. Here are a few practical applications of eigen decomposition:

Check out the 3 Blue 1 Brown videos on Change of basis and Eigenvalues and eigenvectors

"Eigenvalues are a way to see into the heart of a matrix... All the difficulties of matrices are swept away" -Strang

Vocab: A Hermitian matrix is one that is equal to it's own conjugate transpose. In the case of real-valued matrices (which is all we are considering in this course), Hermitian means the same as Symmetric.

Relevant Theorems:

• If A is symmetric, then eigenvalues of A are real and $A = Q \Lambda Q^T$
• If A is triangular, then its eigenvalues are equal to its diagonal entries

## DBpedia Dataset¶

Let's start with the Power Method, which finds one eigenvector. What good is just one eigenvector? you may be wondering. This is actually the basis for PageRank (read The $25,000,000,000 Eigenvector: the Linear Algebra Behind Google for more info) Instead of trying to rank the importance of all websites on the internet, we are going to use a dataset of Wikipedia links from DBpedia. DBpedia provides structured Wikipedia data available in 125 languages. "The full DBpedia data set features 38 million labels and abstracts in 125 different languages, 25.2 million links to images and 29.8 million links to external web pages; 80.9 million links to Wikipedia categories, and 41.2 million links to YAGO categories" --about DBpedia Today's lesson is inspired by this SciKit Learn Example ### Imports¶ In [361]: import os, numpy as np, pickle from bz2 import BZ2File from datetime import datetime from pprint import pprint from time import time from tqdm import tqdm_notebook from scipy import sparse from sklearn.decomposition import randomized_svd from sklearn.externals.joblib import Memory from urllib.request import urlopen  ### Downloading the data¶ The data we have are: • redirects: URLs that redirect to other URLs • links: which pages link to which other pages Note: this takes a while In [367]: PATH = 'data/dbpedia/' URL_BASE = 'http://downloads.dbpedia.org/3.5.1/en/' filenames = ["redirects_en.nt.bz2", "page_links_en.nt.bz2"] for filename in filenames: if not os.path.exists(PATH+filename): print("Downloading '%s', please wait..." % filename) open(PATH+filename, 'wb').write(urlopen(URL_BASE+filename).read())  In [368]: redirects_filename = PATH+filenames[0] page_links_filename = PATH+filenames[1]  ### Graph Adjacency Matrix¶ We will construct a graph adjacency matrix, of which pages point to which. The power$A^2$will give you how many ways there are to get from one page to another in 2 steps. You can see a more detailed example, as applied to airline travel, worked out in these notes. We want to keep track of which pages point to which pages. We will store this in a square matrix, with a$1$in position$(r, c)$indicating that the topic in row$r$points to the topic in column$c$You can read more about graphs here. ### Data Format¶ One line of the file looks like: • <http://dbpedia.org/resource/AfghanistanHistory> <http://dbpedia.org/property/redirect> <http://dbpedia.org/resource/History_of_Afghanistan> . In the below slice, the plus 1, -1 are to remove the <> In [369]: DBPEDIA_RESOURCE_PREFIX_LEN = len("http://dbpedia.org/resource/") SLICE = slice(DBPEDIA_RESOURCE_PREFIX_LEN + 1, -1)  In [370]: def get_lines(filename): return (line.split() for line in BZ2File(filename))  Loop through redirections and create dictionary of source to final destination In [371]: def get_redirect(targ, redirects): seen = set() while True: transitive_targ = targ targ = redirects.get(targ) if targ is None or targ in seen: break seen.add(targ) return transitive_targ  In [372]: def get_redirects(redirects_filename): redirects={} lines = get_lines(redirects_filename) return {src[SLICE]:get_redirect(targ[SLICE], redirects) for src,_,targ,_ in tqdm_notebook(lines, leave=False)}  In [373]: redirects = get_redirects(redirects_filename)  In [374]: mem_usage()  Out[374]: 13.766303744 In [375]: def add_item(lst, redirects, index_map, item): k = item[SLICE] lst.append(index_map.setdefault(redirects.get(k, k), len(index_map)))  In [376]: limit=119077682 #5000000  In [377]: # Computing the integer index map index_map = dict() # links->IDs lines = get_lines(page_links_filename) source, destination, data = [],[],[] for l, split in tqdm_notebook(enumerate(lines), total=limit): if l >= limit: break add_item(source, redirects, index_map, split[0]) add_item(destination, redirects, index_map, split[2]) data.append(1)  In [379]: n=len(data); n  Out[379]: 119077682 ### Looking at our data¶ The below steps are just to illustrate what info is in our data and how it is structured. They are not efficient. Let's see what type of items are in index_map: In [425]: index_map.popitem()  Out[425]: (b'1940_Cincinnati_Reds_Team_Issue', 9991173) Let's look at one item in our index map: 1940_Cincinnati_Reds_Team_Issue has index$9991173$. This only shows up once in the destination list: In [427]: [i for i,x in enumerate(source) if x == 9991173]  Out[427]: [119077649] In [428]: source[119077649], destination[119077649]  Out[428]: (9991173, 9991050) Now, we want to check which page is the source (has index$9991050$). Note: usually you should not access a dictionary by searching for its values. This is inefficient and not how dictionaries are intended to be used. In [429]: for page_name, index in index_map.items(): if index == 9991050: print(page_name)  b'W711-2'  We can see on Wikipedia that the Cincinati Red Teams Issue has redirected to W711-2: In [431]: test_inds = [i for i,x in enumerate(source) if x == 9991050]  In [466]: len(test_inds)  Out[466]: 47 In [433]: test_inds[:5]  Out[433]: [119076756, 119076757, 119076758, 119076759, 119076760] In [434]: test_dests = [destination[i] for i in test_inds]  Now, we want to check which page is the source (has index 9991174): In [435]: for page_name, index in index_map.items(): if index in test_dests: print(page_name)  b'Baseball' b'Ohio' b'Cincinnati' b'Flash_Thompson' b'1940' b'1938' b'Lonny_Frey' b'Cincinnati_Reds' b'Ernie_Lombardi' b'Baseball_card' b'James_Wilson' b'Trading_card' b'Detroit_Tigers' b'Baseball_culture' b'Frank_McCormick' b'Bucky_Walters' b'1940_World_Series' b'Billy_Werber' b'Ival_Goodman' b'Harry_Craft' b'Paul_Derringer' b'Johnny_Vander_Meer' b'Cigarette_card' b'Eddie_Joost' b'Myron_McCormick' b'Beckett_Media' b'Icarus_affair' b'Ephemera' b'Sports_card' b'James_Turner' b'Jimmy_Ripple' b'Lewis_Riggs' b'The_American_Card_Catalog' b'Rookie_card' b'Willard_Hershberger' b'Elmer_Riddle' b'Joseph_Beggs' b'Witt_Guise' b'Milburn_Shoffner'  We can see that the items in the list appear in the wikipedia page: (Source: Wikipedia) ### Create Matrix¶ Below we create a sparse matrix using Scipy's COO format, and that convert it to CSR. Questions: What are COO and CSR? Why would we create it with COO and then convert it right away? In [341]: X = sparse.coo_matrix((data, (destination,source)), shape=(n,n), dtype=np.float32) X = X.tocsr()  In [347]: del(data,destination, source)  In [342]: X  Out[342]: <119077682x119077682 sparse matrix of type '<class 'numpy.float32'>' with 93985520 stored elements in Compressed Sparse Row format> In [343]: names = {i: name for name, i in index_map.items()}  In [349]: mem_usage()  Out[349]: 12.903882752 ### Save matrix so we don't have to recompute¶ In [350]: pickle.dump(X, open(PATH+'X.pkl', 'wb')) pickle.dump(index_map, open(PATH+'index_map.pkl', 'wb'))  In [316]: X = pickle.load(open(PATH+'X.pkl', 'rb')) index_map = pickle.load(open(PATH+'index_map.pkl', 'rb'))  In [317]: names = {i: name for name, i in index_map.items()}  In [351]: X  Out[351]: <119077682x119077682 sparse matrix of type '<class 'numpy.float32'>' with 93985520 stored elements in Compressed Sparse Row format> ## Power method¶ ### Motivation¶ An$n \times n$matrix$A$is diagonalizable if it has$n$linearly independent eigenvectors$v_1,\, \ldots v_n$. Then any$w$can be expressed$w = \sum_{j=1}^n c_j v_j $, for some scalars$c_j$. Exercise: Show that $$A^k w = \sum_{j=1}^n c_j \lambda_j^k v_j$$ Question: How will this behave for large$k$? This is inspiration for the power method. ### Code¶ In [281]: def show_ex(v): print(', '.join(names[i].decode() for i in np.abs(v.squeeze()).argsort()[-1:-10:-1]))  In [453]: ?np.squeeze  How to normalize a sparse matrix: In [336]: S = sparse.csr_matrix(np.array([[1,2],[3,4]])) Sr = S.sum(axis=0).A1; Sr  Out[336]: array([4, 6], dtype=int64) In [337]: S.indices  Out[337]: array([0, 1, 0, 1], dtype=int32) In [338]: S.data  Out[338]: array([1, 2, 3, 4], dtype=int64) In [339]: S.data / np.take(Sr, S.indices)  Out[339]: array([ 0.25 , 0.33333, 0.75 , 0.66667]) In [328]: def power_method(A, max_iter=100): n = A.shape[1] A = np.copy(A) A.data /= np.take(A.sum(axis=0).A1, A.indices) scores = np.ones(n, dtype=np.float32) * np.sqrt(A.sum()/(n*n)) # initial guess for i in range(max_iter): scores = A @ scores nrm = np.linalg.norm(scores) scores /= nrm print(nrm) return scores  Question: Why normalize the scores on each iteration? In [345]: scores = power_method(X, max_iter=10)  0.621209 0.856139 1.02793 1.02029 1.02645 1.02504 1.02364 1.02126 1.019 1.01679  In [346]: show_ex(scores)  Living_people, Year_of_birth_missing_%28living_people%29, United_States, United_Kingdom, Race_and_ethnicity_in_the_United_States_Census, France, Year_of_birth_missing, World_War_II, Germany  In [ ]:   In [327]: mem_usage()  Out[327]: 11.692331008 ### Comments¶ Many advanced eigenvalue algorithms that are used in practice are variations on the power method. In Lesson 3: Background Removal, we used Facebook's fast randomized pca/svd library, fbpca. Check out the source code for the pca method we used. It uses the power method! Further Study • Check out Google Page Rank, Power Iteration and the Second EigenValue of the Google Matrix for animations of the distribution as it converges. • The convergence rate of the power method is the ratio of the largest eigenvalue to the 2nd largest eigenvalue. It can be speeded up by adding shifts. To find eigenvalues other than the largest, a method called deflation can be used. See Chapter 12.1 of Greenbaum & Chartier for more details. • Krylov Subspaces: In the Power Iteration, notice that we multiply by our matrix A each time, effectively calculating $$Ab,\,A^2b,\,A^3b,\,A^4b\, \ldots$$ The matrix with those vectors as columns is called the Krylov matrix, and the space spanned by those vectors is the Krylov subspace. Keep this in mind for later. ### Compare to SVD¶ In [27]: %time U, s, V = randomized_svd(X, 3, n_iter=3)  CPU times: user 8min 40s, sys: 1min 20s, total: 10min 1s Wall time: 5min 56s  In [28]: mem_usage()  Out[28]: 28.353073152 In [30]: # Top wikipedia pages according to principal singular vectors show_ex(U.T[0])  List_of_World_War_II_air_aces, List_of_animated_feature-length_films, List_of_animated_feature_films:2000s, International_Swimming_Hall_of_Fame, List_of_museum_ships, List_of_linguists, List_of_television_programs_by_episode_count, List_of_game_show_hosts, List_of_astronomers  In [31]: show_ex(U.T[1])  List_of_former_United_States_senators, List_of_United_States_Representatives_from_New_York, List_of_United_States_Representatives_from_Pennsylvania, Members_of_the_110th_United_States_Congress, List_of_Justices_of_the_Ohio_Supreme_Court, Congressional_endorsements_for_the_2008_United_States_presidential_election, List_of_United_States_Representatives_in_the_110th_Congress_by_seniority, List_of_Members_of_the_United_States_House_of_Representatives_in_the_103rd_Congress_by_seniority, List_of_United_States_Representatives_in_the_111th_Congress_by_seniority  In [32]: show_ex(V[0])  United_States, Japan, United_Kingdom, Germany, Race_and_ethnicity_in_the_United_States_Census, France, United_States_Army_Air_Forces, Australia, Canada  In [33]: show_ex(V[1])  Democratic_Party_%28United_States%29, Republican_Party_%28United_States%29, Democratic-Republican_Party, United_States, Whig_Party_%28United_States%29, Federalist_Party, National_Republican_Party, Catholic_Church, Jacksonian_democracy  Exercise: Normalize the data in various ways. Don't overwrite the adjacency matrix, but instead create a new one. See how your results differ. Eigen Decomposition vs SVD: • SVD involves 2 bases, eigen decomposition involves 1 basis • SVD bases are orthonormal, eigen basis generally not orthogonal • All matrices have an SVD, not all matrices (not even all square) have an eigen decomposition ## QR Algorithm¶ We used the power method to find the eigenvector corresponding to the largest eigenvalue of our matrix of Wikipedia links. This eigenvector gave us the relative importance of each Wikipedia page (like a simplified PageRank). Next, let's look at a method for finding all eigenvalues of a symmetric, positive definite matrix. This method includes 2 fundamental algorithms in numerical linear algebra, and is a basis for many more complex methods. The Second Eigenvalue of the Google Matrix: has "implications for the convergence rate of the standard PageRank algorithm as the web scales, for the stability of PageRank to perturbations to the link structure of the web, for the detection of Google spammers, and for the design of algorithms to speed up PageRank". ### Avoiding Confusion: QR Algorithm vs QR Decomposition¶ The QR algorithm uses something called the QR decomposition. Both are important, so don't get them confused. The QR decomposition decomposes a matrix$A = QR$into a set of orthonormal columns$Q$and a triangular matrix$R$. We will look at several ways to calculate the QR decomposition in a future lesson. For now, just know that it is giving us an orthogonal matrix and a triangular matrix. ### Linear Algebra¶ Two matrices$A$and$B$are similar if there exists a non-singular matrix$X$such that $$B = X^{-1}AX$$ Watch this: Change of Basis Theorem: If$X$is non-singular, then$A$and$X^{-1}AX$have the same eigenvalues. #### More Linear Algebra¶ A Schur factorization of a matrix$A$is a factorization: $$A = Q T Q^*$$ where$Q$is unitary and$T$is upper-triangular. Question: What can you say about the eigenvalues of$A$? Theorem: Every square matrix has a Schur factorization. #### Other resources¶ See Lecture 24 for proofs of above theorems (and more!) ### Algorithm¶ The most basic version of the QR algorithm: for k=1,2,... Q, R = A A = R @ Q  Under suitable assumptions, this algorithm converges to the Schur form of A! #### Why it works¶ Written again, only with subscripts:$A_0 = A$for$k=1,2,\ldots\quad Q_k$,$R_k$=$A_{k-1}\quad A_k$=$R_k Q_k$We can think of this as constructing sequences of$A_k$,$Q_k$, and$R_k$. $$A_k = Q_k \, R_k$$$$Q_k^{-1} \, A_k = R_k$$ Thus, $$R_k Q_k = Q_k^{-1} \, A_k \, Q_k$$$$A_k = Q_k^{-1} Q_2^{-1} Q_1^{-1} A Q_1 Q_2 \dots Q_k$$ Trefethen proves the following on page 216-217: $$A^k = Q_1 Q_2 \dots Q_k R_k R_{k-1}\dots R_1$$ Key: The QR algorithm constructs orthonormal bases for successive powers$A^k$. And remember the close relationship between powers of A and the eigen decomposition. To learn more, read up on Rayleigh quotients. #### Pure QR¶ In [467]: n = 6 A = np.random.rand(n,n) AT = A @ A.T  In [474]: def pure_qr(A, max_iter=50000): Ak = np.copy(A) n = A.shape[0] QQ = np.eye(n) for k in range(max_iter): Q, R = np.linalg.qr(Ak) Ak = R @ Q QQ = QQ @ Q if k % 100 == 0: print(Ak) print("\n") return Ak, QQ  #### Pure QR¶ In [475]: Ak, Q = pure_qr(A)  [[ 2.65646 0.21386 0.16765 0.75256 0.61251 0.93518] [ 0.52744 0.47579 0.17052 -0.41086 -0.21182 -0.01876] [ 0.29923 0.06964 0.11173 0.1879 -0.29101 0.60032] [ 0.2274 0.46162 -0.26654 0.08899 0.24631 0.26447] [-0.06093 0.02892 0.34162 0.07533 0.02393 -0.05456] [-0.06025 0.02694 -0.11675 -0.00927 -0.11939 -0.00767]] [[ 2.78023 0.52642 0.0395 -0.11135 0.1569 1.15184] [ 0. 0.18624 -0.297 -0.07256 -0.04537 0.27907] [ 0. 0.69328 0.34105 -0.12198 0.11029 0.0992 ] [-0. -0.0494 -0.02057 0.09461 0.59466 0.09115] [-0. 0.00008 -0.02659 -0.40372 0.06542 0.38612] [-0. 0. 0. 0. -0. -0.11832]] [[ 2.78023 -0.12185 -0.51401 0.17625 -0.07467 1.15184] [ 0. 0.2117 -0.70351 0.09974 -0.02986 0.00172] [ 0. 0.28284 0.32635 -0.0847 -0.08488 -0.29104] [-0. -0.00068 -0.00088 -0.01282 0.54836 0.13447] [-0. 0. -0.00102 -0.45718 0.16208 -0.37726] [-0. 0. 0. 0. -0. -0.11832]] [[ 2.78023 -0.33997 0.4049 0.17949 0.06291 1.15184] [ 0. 0.48719 -0.48788 -0.05831 -0.12286 -0.23486] [ 0. 0.49874 0.05104 -0.07191 0.03638 0.17261] [ 0. 0.00002 0. 0.02128 0.41958 0.3531 ] [ 0. -0. 0.00002 -0.58571 0.1278 -0.18838] [ 0. 0. 0. -0. 0. -0.11832]] [[ 2.78023 0.35761 0.38941 0.07462 0.17493 1.15184] [ 0. 0.0597 -0.55441 -0.0681 -0.04456 0.14084] [ 0. 0.43221 0.47853 -0.06068 0.12117 0.25519] [-0. -0. -0. 0.16206 0.45708 0.37724] [-0. 0. -0. -0.54821 -0.01298 0.1336 ] [ 0. 0. 0. 0. -0. -0.11832]] [[ 2.78023 0.06853 -0.52424 0.05224 -0.18287 1.15184] [ 0. 0.36572 -0.6889 0.07864 -0.09263 0.105 ] [ 0. 0.29772 0.17251 -0.09836 -0.02347 -0.27191] [ 0. -0. -0. 0.13719 0.57888 -0.20884] [ 0. 0. -0. -0.42642 0.01189 -0.34139] [ 0. 0. 0. 0. -0. -0.11832]] [[ 2.78023 -0.52782 0.03045 -0.14389 -0.12436 1.15184] [ 0. 0.25091 -0.27593 0.08994 -0.06581 -0.28672] [ 0. 0.7107 0.28732 0.10154 0.04751 -0.05245] [ 0. -0. -0. 0.0297 -0.59054 -0.01234] [ 0. -0. 0. 0.41475 0.11938 -0.40001] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.1533 0.50599 0.18983 0.01158 1.15184] [ 0. 0.18627 -0.69511 -0.0991 -0.00189 0.01621] [ 0. 0.29151 0.35196 0.05638 -0.10949 0.29102] [ 0. -0. -0. -0.02207 -0.48261 0.25246] [ 0. -0. 0. 0.52268 0.17116 0.31053] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.29683 -0.43751 -0.13852 0.13032 1.15184] [ 0. 0.48375 -0.53231 -0.01164 0.13482 0.216 ] [ 0. 0.45431 0.05448 -0.07972 -0.01795 -0.19571] [ 0. -0. 0. 0.10042 -0.40743 -0.39915] [ 0. -0. 0. 0.59786 0.04867 -0.02893] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.39373 -0.35284 0.00838 -0.19 1.15184] [ 0. 0.05184 -0.51278 0.05752 -0.0564 -0.16496] [ 0. 0.47384 0.48639 0.09426 0.09806 -0.24031] [ 0. -0. -0. 0.17043 -0.52593 0.30622] [ 0. -0. 0. 0.47936 -0.02134 -0.25766] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.0355 0.52751 0.10215 0.16042 1.15184] [ 0. 0.34047 -0.69946 -0.09606 -0.06944 -0.08773] [ 0. 0.28717 0.19776 0.09382 -0.04624 0.27796] [ 0. -0. -0. 0.08542 -0.60072 -0.10298] [ 0. -0. 0. 0.40458 0.06367 0.38672] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.51706 -0.11032 -0.17442 -0.07581 1.15184] [ 0. 0.31706 -0.2805 -0.08235 0.0863 0.29136] [ 0. 0.70612 0.22117 -0.09973 -0.02853 0.00826] [ 0. -0. -0. -0.01235 -0.5494 -0.13103] [ 0. -0. 0. 0.45589 0.16144 -0.37814] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.18529 -0.49517 -0.18006 0.06123 1.15184] [ 0. 0.16123 -0.68291 -0.09155 0.0279 -0.03476] [ 0. 0.30371 0.377 0.01655 -0.12472 -0.2894 ] [ 0. 0. 0. 0.01974 -0.42059 -0.35131] [ 0. 0. -0. 0.5847 0.12935 -0.19168] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.25477 0.46327 -0.07615 0.17427 1.15184] [ 0. 0.47278 -0.57146 -0.03461 -0.12937 -0.19683] [ 0. 0.41516 0.06545 0.08395 -0.00278 0.21498] [ 0. -0. 0. 0.16125 -0.45555 -0.3784 ] [ 0. -0. 0. 0.54974 -0.01216 0.13028] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.42908 0.30889 0.05099 0.18322 1.15184] [ 0. 0.05265 -0.46631 0.04976 -0.06424 0.18962] [ 0. 0.52032 0.48558 0.11539 0.07122 0.22136] [ 0. 0. 0. 0.13823 -0.57801 -0.21116] [ 0. 0. -0. 0.42728 0.01086 0.33995] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.00334 -0.52869 -0.14306 -0.12531 1.15184] [ 0. 0.3149 -0.7066 -0.10679 -0.04392 0.07066] [ 0. 0.28002 0.22333 0.08372 -0.06816 -0.28278] [ 0. 0. 0. 0.03087 -0.59113 -0.00969] [ 0. 0. -0. 0.41416 0.11821 -0.40008] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.49486 0.18611 0.18973 0.01317 1.15184] [ 0. 0.37763 -0.30407 -0.06365 0.1086 -0.28934] [ 0. 0.68255 0.1606 -0.09511 -0.00985 0.03524] [ 0. 0. 0. -0.02239 -0.48423 0.24985] [ 0. 0. -0. 0.52107 0.17148 0.31262] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.21799 0.48167 -0.13976 0.12898 1.15184] [ 0. 0.13689 -0.66682 0.07458 -0.05442 0.05403] [ 0. 0.31981 0.40134 0.03053 0.12464 0.28642] [ 0. 0. 0. 0.09859 -0.40695 -0.39886] [ 0. 0. -0. 0.59834 0.0505 -0.03275] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.21427 -0.48333 -0.00984 0.18993 1.15184] [ 0. 0.45651 -0.60498 0.07108 0.11122 0.17774] [ 0. 0.38164 0.08172 -0.08395 0.02278 -0.23101] [ 0. -0. 0. 0.17077 -0.52445 -0.30819] [ 0. -0. 0. 0.48084 -0.02169 0.2553 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.46223 -0.25664 0.10111 0.16108 1.15184] [ 0. 0.06482 -0.41681 -0.04447 0.07111 -0.21419] [ 0. 0.56981 0.47341 -0.12657 -0.04398 -0.19769] [ 0. 0. 0. 0.08669 -0.60057 -0.10548] [ 0. 0. -0. 0.40472 0.0624 0.38605] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.02821 0.52795 0.17386 0.07707 1.15184] [ 0. 0.28917 -0.71053 -0.11126 -0.01551 -0.05366] [ 0. 0.27609 0.24906 0.06641 -0.08922 0.28649] [ 0. -0. -0. -0.01166 -0.55066 0.12827] [ 0. -0. 0. 0.45463 0.16075 0.37909] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.46334 -0.25463 0.18062 -0.05954 1.15184] [ 0. 0.42654 -0.3423 0.03075 -0.12716 0.28138] [ 0. 0.64432 0.11169 0.0883 -0.00883 -0.07605] [ 0. 0. 0. 0.01821 -0.42163 0.3495 ] [ 0. 0. -0. 0.58366 0.13087 0.19495] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.25153 -0.46503 0.07768 -0.17359 1.15184] [ 0. 0.11372 -0.64641 0.05247 -0.07193 -0.07417] [ 0. 0.34021 0.42451 0.0736 0.10791 -0.28188] [ 0. -0. -0. 0.16041 -0.45403 0.37953] [ 0. -0. 0. 0.55126 -0.01132 -0.12694] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.17551 0.49872 -0.04973 -0.18356 1.15184] [ 0. 0.43663 -0.63305 0.0961 0.08709 -0.15898] [ 0. 0.35358 0.1016 -0.08053 0.04103 0.2443 ] [ 0. 0. -0. 0.13926 -0.57713 0.21349] [ 0. 0. -0. 0.42816 0.00983 -0.3385 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.49117 0.19565 -0.14223 -0.12625 1.15184] [ 0. 0.0908 -0.36765 -0.03961 0.07922 0.23763] [ 0. 0.61897 0.44743 -0.12984 -0.01694 0.16879] [ 0. -0. -0. 0.03205 -0.5917 -0.00704] [ 0. -0. 0. 0.41359 0.11704 -0.40014] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.05938 -0.52535 -0.18961 -0.01475 1.15184] [ 0. 0.26338 -0.71138 -0.10793 0.01612 0.03662] [ 0. 0.27524 0.27485 0.03935 -0.10739 -0.28917] [ 0. 0. 0. -0.02269 -0.48584 -0.24724] [ 0. 0. -0. 0.51945 0.17177 -0.31469] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.42532 0.31405 -0.14099 0.12764 1.15184] [ 0. 0.46081 -0.3892 -0.01295 -0.1334 -0.26875] [ 0. 0.59743 0.07742 0.07957 -0.02634 0.11283] [ 0. -0. -0. 0.09675 -0.40651 -0.39852] [ 0. -0. 0. 0.59879 0.05233 -0.03657] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.28599 0.44467 0.0113 -0.18985 1.15184] [ 0. 0.0924 -0.62121 -0.03168 0.07992 0.09528] [ 0. 0.36541 0.44583 -0.1049 -0.0812 0.27546] [ 0. -0. -0. 0.1711 -0.52297 0.31015] [ 0. -0. 0. 0.48232 -0.02201 -0.25291] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.13845 -0.51025 -0.10006 -0.16173 1.15184] [ 0. 0.41438 -0.65605 -0.11185 -0.06046 0.14063] [ 0. 0.33057 0.12385 0.07387 -0.05803 -0.2553 ] [ 0. 0. 0. 0.08796 -0.6004 0.10798] [ 0. 0. -0. 0.40489 0.06113 -0.38536] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.5134 -0.12629 -0.1733 -0.07834 1.15184] [ 0. 0.13174 -0.32385 0.0319 -0.08965 -0.25857] [ 0. 0.66277 0.40649 0.12582 -0.01014 -0.13453] [ 0. -0. -0. -0.01095 -0.55191 -0.12551] [ 0. -0. 0. 0.45338 0.16004 -0.38001] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.09043 0.52091 -0.18117 0.05785 1.15184] [ 0. 0.2376 -0.70917 0.09396 -0.04876 -0.01941] [ 0. 0.27745 0.30063 -0.00151 0.11739 0.29083] [ 0. 0. 0. 0.01671 -0.4227 -0.34767] [ 0. 0. -0. 0.58259 0.13238 -0.19821] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.38356 -0.36387 0.07921 -0.1729 1.15184] [ 0. 0.4804 -0.43903 -0.05633 -0.12341 0.25287] [ 0. 0.54759 0.05783 0.07018 -0.04075 -0.14496] [ 0. 0. -0. 0.15953 -0.45252 0.38064] [ 0. 0. -0. 0.55277 -0.01045 -0.12358] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.32133 -0.41985 0.04847 0.1839 1.15184] [ 0. 0.07395 -0.59076 -0.01536 0.0819 -0.11744] [ 0. 0.39586 0.46428 -0.12416 -0.05129 -0.26677] [ 0. 0. 0. 0.14027 -0.57624 -0.21581] [ 0. 0. -0. 0.42905 0.00881 0.33703] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.10295 0.51858 -0.14139 -0.12719 1.15184] [ 0. 0.39062 -0.67448 0.12025 0.03188 -0.1227 ] [ 0. 0.31214 0.14761 -0.06308 0.07439 0.26439] [ 0. 0. 0. 0.03323 -0.59225 -0.00439] [ 0. 0. -0. 0.41304 0.11586 -0.40018] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.52631 0.05017 -0.18948 -0.01632 1.15184] [ 0. 0.18641 -0.29145 -0.0171 0.10162 0.27541] [ 0. 0.69517 0.35182 -0.11404 0.03696 0.09543] [ 0. -0. -0. -0.02295 -0.48746 -0.24462] [ 0. -0. 0. 0.51783 0.17204 -0.31674] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.12158 -0.51453 -0.14221 0.12628 1.15184] [ 0. 0.21193 -0.70383 -0.06881 0.076 0.0019 ] [ 0. 0.2828 0.3263 -0.04211 -0.11272 -0.29147] [ 0. 0. 0. 0.09491 -0.4061 -0.39816] [ 0. 0. -0. 0.59919 0.05418 -0.04039] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.34032 0.4046 0.01277 -0.18975 1.15184] [ 0. 0.48718 -0.4875 0.09008 0.10189 -0.23501] [ 0. 0.49912 0.05105 -0.06166 0.05188 0.17241] [ 0. 0. -0. 0.1714 -0.52147 0.3121 ] [ 0. 0. -0. 0.48382 -0.02232 -0.25051] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.35731 0.38968 0.09901 0.16238 1.15184] [ 0. 0.0598 -0.55473 0.0032 -0.08133 0.14065] [ 0. 0.43189 0.47843 0.13388 0.02096 0.2553 ] [ 0. 0. 0. 0.08922 -0.60022 -0.11048] [ 0. 0. -0. 0.40507 0.05986 0.38465] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.06881 -0.5242 -0.17273 -0.07959 1.15184] [ 0. 0.36593 -0.6888 -0.12153 -0.0007 0.10514] [ 0. 0.29783 0.1723 0.04626 -0.08989 -0.27185] [ 0. 0. 0. -0.01023 -0.55314 -0.12275] [ 0. 0. -0. 0.45215 0.15932 -0.38091] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.52786 0.02978 0.1817 -0.05616 1.15184] [ 0. 0.25036 -0.27597 0.00829 0.11107 -0.28665] [ 0. 0.71065 0.28787 -0.09408 0.06109 -0.05281] [ 0. 0. 0. 0.01523 -0.42379 0.34581] [ 0. 0. -0. 0.5815 0.13386 0.20144] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.15304 0.50607 -0.08074 0.17219 1.15184] [ 0. 0.18648 -0.6952 0.03825 -0.09147 0.01606] [ 0. 0.29142 0.35175 0.08101 0.09272 0.29103] [ 0. 0. 0. 0.15863 -0.45102 -0.38172] [ 0. 0. -0. 0.55427 -0.00955 0.1202 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.29718 -0.43727 -0.04721 -0.18423 1.15184] [ 0. 0.48381 -0.53197 -0.11247 -0.07526 0.21616] [ 0. 0.45466 0.05442 0.05413 -0.06119 -0.19553] [ 0. 0. -0. 0.14128 -0.57533 0.21812] [ 0. 0. -0. 0.42996 0.00781 -0.33554] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.39344 -0.35318 0.14055 0.12812 1.15184] [ 0. 0.05187 -0.51315 0.00659 0.08029 -0.16476] [ 0. 0.47347 0.48636 -0.13567 0.00965 -0.24044] [ 0. 0. 0. 0.03442 -0.59279 0.00175] [ 0. 0. -0. 0.4125 0.11467 0.4002 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.03577 0.52749 0.18934 0.01789 1.15184] [ 0. 0.34068 -0.69939 -0.1138 0.03323 -0.08788] [ 0. 0.28724 0.19755 0.02106 -0.10242 0.27791] [ 0. -0. -0. -0.02319 -0.48908 0.24199] [ 0. -0. 0. 0.51622 0.17228 0.31875] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.5172 -0.10967 -0.14341 0.12491 1.15184] [ 0. 0.31653 -0.28038 0.04262 0.11135 0.29135] [ 0. 0.70624 0.2217 -0.06857 0.07793 0.00862] [ 0. -0. -0. 0.09305 -0.40572 -0.39775] [ 0. -0. 0. 0.59957 0.05604 -0.04421] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.18503 -0.49527 -0.01424 0.18965 1.15184] [ 0. 0.16143 -0.68303 -0.01015 0.09519 -0.0346 ] [ 0. 0.3036 0.3768 -0.10826 -0.06406 -0.28941] [ 0. 0. 0. 0.17168 -0.51997 -0.31403] [ 0. 0. -0. 0.48532 -0.0226 0.24808] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.25511 0.46308 0.09796 0.16302 1.15184] [ 0. 0.4729 -0.57116 -0.12554 -0.04666 -0.19698] [ 0. 0.41546 0.06533 0.04626 -0.07008 0.21484] [ 0. -0. -0. 0.09049 -0.60002 -0.11297] [ 0. -0. 0. 0.40527 0.0586 0.38392] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.4288 0.30928 -0.17215 -0.08084 1.15184] [ 0. 0.0526 -0.46671 0.01637 0.07958 0.18942] [ 0. 0.51992 0.48563 -0.12923 0.0411 0.22154] [ 0. -0. -0. -0.00949 -0.55436 -0.12 ] [ 0. -0. 0. 0.45093 0.15858 -0.38179] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.0036 -0.52869 0.18221 -0.05447 1.15184] [ 0. 0.31511 -0.70655 0.094 -0.06711 0.0708 ] [ 0. 0.28007 0.22312 0.01322 0.10712 -0.28275] [ 0. -0. -0. 0.01378 -0.42491 0.34392] [ 0. -0. 0. 0.58038 0.13531 0.20465] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.49508 0.18551 -0.08227 0.17147 1.15184] [ 0. 0.37717 -0.30381 -0.07749 -0.09914 -0.28938] [ 0. 0.68281 0.16106 0.04417 -0.08488 0.03489] [ 0. -0. -0. 0.1577 -0.44953 -0.38277] [ 0. -0. 0. 0.55576 -0.00862 0.11681] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.21772 0.48179 0.04594 0.18455 1.15184] [ 0. 0.13709 -0.66697 -0.01194 -0.09157 0.05387] [ 0. 0.31966 0.40114 0.12396 0.03308 0.28645] [ 0. 0. 0. 0.14227 -0.5744 -0.22042] [ 0. 0. -0. 0.43089 0.00681 0.33402] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.2146 -0.48319 -0.1397 -0.12905 1.15184] [ 0. 0.45666 -0.60473 -0.13098 -0.01645 0.1779 ] [ 0. 0.38189 0.08157 0.0361 -0.07911 -0.23089] [ 0. 0. 0. 0.03561 -0.59331 0.0009 ] [ 0. 0. -0. 0.41198 0.11347 -0.4002 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.46197 -0.25711 -0.18919 -0.01945 1.15184] [ 0. 0.06467 -0.41722 -0.02879 -0.07874 -0.21399] [ 0. 0.5694 0.47356 0.11253 -0.07277 -0.19791] [ 0. -0. -0. -0.0234 -0.49069 -0.23935] [ 0. -0. 0. 0.5146 0.17249 -0.32073] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.02795 0.52796 0.1446 -0.12353 1.15184] [ 0. 0.28938 -0.71051 -0.06202 0.0937 -0.0538 ] [ 0. 0.27611 0.24885 -0.05182 -0.09838 0.28647] [ 0. -0. -0. 0.09118 -0.40539 0.39731] [ 0. -0. 0. 0.5999 0.0579 0.04803] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.46363 -0.25411 0.01571 -0.18953 1.15184] [ 0. 0.4262 -0.34194 -0.10508 -0.07786 0.28147] [ 0. 0.64468 0.11203 0.02623 -0.08483 -0.07573] [ 0. 0. -0. 0.17194 -0.51845 0.31595] [ 0. 0. -0. 0.48684 -0.02285 -0.24563] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.25125 -0.46518 -0.0969 -0.16365 1.15184] [ 0. 0.1139 -0.6466 -0.02852 -0.08437 -0.074 ] [ 0. 0.34003 0.42433 0.13059 0.00215 -0.28193] [ 0. -0. -0. 0.09175 -0.59981 0.11546] [ 0. -0. 0. 0.40549 0.05734 -0.38318] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.17582 0.49861 -0.17156 -0.08208 1.15184] [ 0. 0.43681 -0.63284 0.12872 -0.01606 -0.15914] [ 0. 0.35379 0.10142 -0.02137 0.08779 0.2442 ] [ 0. 0. 0. -0.00874 -0.55557 -0.11724] [ 0. 0. -0. 0.44972 0.15782 -0.38264] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.49095 0.19619 0.18271 -0.05278 1.15184] [ 0. 0.09052 -0.36805 -0.04589 -0.07569 0.23745] [ 0. 0.61858 0.44771 0.08364 -0.10079 0.16905] [ 0. 0. 0. 0.01234 -0.42605 0.342 ] [ 0. 0. -0. 0.57924 0.13674 0.20783] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.05913 -0.52538 -0.08379 0.17073 1.15184] [ 0. 0.26359 -0.71139 -0.02488 0.10628 0.03676] [ 0. 0.27524 0.27464 -0.08525 -0.0762 -0.28915] [ 0. 0. 0. 0.15674 -0.44806 -0.3838 ] [ 0. 0. -0. 0.55723 -0.00766 0.11339] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.42565 0.3136 0.04466 0.18486 1.15184] [ 0. 0.46059 -0.38879 -0.12336 -0.05234 -0.26887] [ 0. 0.59783 0.07764 0.0148 -0.08254 0.11255] [ 0. -0. 0. 0.14326 -0.57346 -0.22273] [ 0. -0. 0. 0.43183 0.00583 0.33249] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.28571 0.44486 0.13885 0.12997 1.15184] [ 0. 0.09256 -0.62144 -0.04133 -0.07541 0.0951 ] [ 0. 0.36518 0.44567 0.12946 -0.02889 0.27552] [ 0. 0. 0. 0.03681 -0.59382 -0.00353] [ 0. 0. -0. 0.41147 0.11228 0.40018] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.13875 -0.51017 0.18902 0.021 1.15184] [ 0. 0.41457 -0.65588 0.11658 -0.0508 0.14078] [ 0. 0.33074 0.12366 0.00017 0.09391 -0.25522] [ 0. -0. -0. -0.02358 -0.4923 0.2367 ] [ 0. -0. 0. 0.51299 0.17267 0.32269] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.51325 -0.12689 -0.14578 0.12213 1.15184] [ 0. 0.13134 -0.32418 -0.06697 -0.06751 -0.25841] [ 0. 0.66245 0.40688 0.04539 -0.11784 -0.13483] [ 0. -0. -0. 0.08931 -0.40509 -0.39683] [ 0. -0. 0. 0.60021 0.05977 -0.05184] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.09017 0.52095 0.01719 -0.1894 1.15184] [ 0. 0.23781 -0.7092 0.00841 0.10555 -0.01955] [ 0. 0.27742 0.30042 -0.10755 -0.04702 0.29082] [ 0. -0. -0. 0.17218 -0.51693 0.31786] [ 0. -0. 0. 0.48836 -0.02309 -0.24315] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.38392 -0.3635 0.09583 0.16427 1.15184] [ 0. 0.48029 -0.43862 0.13335 0.02486 0.25301] [ 0. 0.548 0.05794 -0.00692 0.08087 -0.14472] [ 0. -0. 0. 0.09301 -0.59957 -0.11794] [ 0. -0. 0. 0.40572 0.05608 0.38242] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.32103 -0.42007 0.17097 0.08331 1.15184] [ 0. 0.07408 -0.59104 0.05211 0.06505 -0.11726] [ 0. 0.39559 0.46415 -0.11986 0.06063 -0.26685] [ 0. 0. 0. -0.00797 -0.55676 0.11449] [ 0. 0. -0. 0.44853 0.15705 0.38347] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.10324 0.51852 0.18319 -0.05108 1.15184] [ 0. 0.39082 -0.67435 -0.0914 0.08443 -0.12285] [ 0. 0.31227 0.14741 -0.02899 -0.0931 0.26432] [ 0. -0. -0. 0.01093 -0.42721 0.34006] [ 0. -0. 0. 0.57808 0.13815 0.21099] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.52625 0.05082 -0.08532 0.16997 1.15184] [ 0. 0.18591 -0.29166 0.08808 0.05336 0.27529] [ 0. 0.69497 0.35232 -0.00778 0.11968 0.09577] [ 0. -0. -0. 0.15575 -0.4466 -0.3848 ] [ 0. -0. 0. 0.55869 -0.00667 0.10996] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.12132 -0.51459 0.04338 0.18517 1.15184] [ 0. 0.21214 -0.70388 0.03415 0.0967 0.00204] [ 0. 0.28274 0.32609 -0.11915 -0.01656 -0.29147] [ 0. 0. 0. 0.14423 -0.5725 -0.22502] [ 0. 0. -0. 0.43279 0.00486 0.33095] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.34068 0.4043 -0.13799 -0.13088 1.15184] [ 0. 0.48717 -0.48711 0.13592 -0.00445 -0.23517] [ 0. 0.49951 0.05106 0.00074 0.08058 0.1722 ] [ 0. 0. 0. 0.03801 -0.59431 0.00617] [ 0. 0. -0. 0.41098 0.11107 -0.40015] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.35701 0.38996 -0.18884 -0.02255 1.15184] [ 0. 0.05989 -0.55505 0.06203 0.05273 0.14045] [ 0. 0.43157 0.47834 -0.09919 0.09232 0.2554 ] [ 0. -0. -0. -0.02374 -0.49391 -0.23405] [ 0. -0. 0. 0.51138 0.17283 -0.32462] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.06908 -0.52417 0.14695 -0.12073 1.15184] [ 0. 0.36613 -0.6887 0.0536 -0.1091 0.10529] [ 0. 0.29793 0.1721 0.06074 0.08077 -0.27179] [ 0. -0. -0. 0.08744 -0.40482 0.39631] [ 0. -0. 0. 0.60047 0.06165 0.05565] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.5279 0.02911 -0.01868 0.18926 1.15184] [ 0. 0.24981 -0.27602 -0.10557 -0.03528 -0.28658] [ 0. 0.7106 0.28842 -0.01997 -0.11045 -0.05317] [ 0. -0. -0. 0.17239 -0.5154 -0.31976] [ 0. -0. 0. 0.48989 -0.0233 0.24066] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.15278 0.50615 -0.09476 -0.16489 1.15184] [ 0. 0.18668 -0.69528 0.05306 0.08378 0.01591] [ 0. 0.29134 0.35154 -0.12239 0.01324 0.29104] [ 0. -0. -0. 0.09427 -0.59933 0.12043] [ 0. -0. 0. 0.40597 0.05482 -0.38165] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.29754 -0.43703 -0.17036 -0.08453 1.15184] [ 0. 0.48387 -0.53162 -0.13043 0.03612 0.21632] [ 0. 0.455 0.05436 -0.01111 -0.08092 -0.19536] [ 0. 0. 0. -0.00718 -0.55794 -0.11174] [ 0. 0. -0. 0.44735 0.15627 -0.38428] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.39314 -0.35351 -0.18366 0.04939 1.15184] [ 0. 0.05191 -0.51351 -0.07124 -0.0376 -0.16455] [ 0. 0.47311 0.48632 0.0649 -0.11953 -0.24058] [ 0. -0. -0. 0.00955 -0.4284 -0.3381 ] [ 0. -0. 0. 0.57689 0.13954 -0.21412] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.03604 0.52747 0.08683 -0.1692 1.15184] [ 0. 0.34089 -0.69931 -0.01131 0.11804 -0.08802] [ 0. 0.28731 0.19734 -0.08731 -0.05748 0.27787] [ 0. -0. -0. 0.15474 -0.44516 0.38577] [ 0. -0. 0. 0.56014 -0.00565 -0.10651] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.51734 -0.10903 -0.04209 -0.18547 1.15184] [ 0. 0.316 -0.28026 -0.11821 -0.01508 0.29134] [ 0. 0.70636 0.22223 -0.03631 -0.09732 0.00898] [ 0. 0. 0. 0.14519 -0.57153 0.22731] [ 0. 0. -0. 0.43376 0.00389 -0.32938] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.18476 -0.49537 0.13712 0.13178 1.15184] [ 0. 0.16164 -0.68314 0.06698 0.06844 -0.03445] [ 0. 0.30348 0.37659 -0.11831 0.04269 -0.28943] [ 0. 0. 0. 0.03922 -0.59478 -0.0088 ] [ 0. 0. -0. 0.41051 0.10986 0.4001 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.25545 0.46289 -0.18865 -0.0241 1.15184] [ 0. 0.47301 -0.57086 0.11438 -0.0697 -0.19714] [ 0. 0.41576 0.06522 0.02643 0.07968 0.21469] [ 0. 0. 0. -0.02387 -0.49552 -0.23139] [ 0. 0. -0. 0.50977 0.17296 -0.32652] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.42851 0.30968 0.1481 -0.11931 1.15184] [ 0. 0.05255 -0.46711 -0.07872 -0.02004 0.18921] [ 0. 0.51952 0.48568 0.01962 -0.13418 0.22171] [ 0. 0. 0. 0.08555 -0.40459 0.39576] [ 0. 0. -0. 0.6007 0.06353 0.05946] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.00387 -0.52869 -0.02016 0.18911 1.15184] [ 0. 0.31532 -0.70651 0.02563 0.11264 0.07094] [ 0. 0.28012 0.22291 -0.1039 -0.02914 -0.28271] [ 0. 0. 0. 0.17258 -0.51386 -0.32164] [ 0. 0. -0. 0.49143 -0.02349 0.23814] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.49531 0.18491 -0.09369 -0.1655 1.15184] [ 0. 0.37671 -0.30355 0.12559 -0.00703 -0.28942] [ 0. 0.68307 0.16152 0.04456 0.08475 0.03454] [ 0. 0. 0. 0.09552 -0.59906 0.1229 ] [ 0. 0. -0. 0.40623 0.05356 -0.38086] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.21744 0.48192 -0.16976 -0.08575 1.15184] [ 0. 0.13729 -0.66712 0.0772 0.05072 0.05371] [ 0. 0.31951 0.40094 -0.10597 0.07229 0.28648] [ 0. -0. -0. -0.00638 -0.5591 -0.10898] [ 0. -0. 0. 0.44619 0.15547 -0.38507] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.21493 -0.48304 0.18411 -0.04769 1.15184] [ 0. 0.45681 -0.60448 0.08465 -0.10131 0.17806] [ 0. 0.38215 0.08142 0.04707 0.07309 -0.23077] [ 0. -0. -0. 0.00819 -0.42961 0.33611] [ 0. -0. 0. 0.57568 0.1409 0.21723] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.46171 -0.25757 0.08835 -0.16841 1.15184] [ 0. 0.06452 -0.41764 0.08378 0.0024 -0.21379] [ 0. 0.56899 0.47371 0.02583 0.13152 -0.19812] [ 0. 0. 0. 0.15369 -0.44373 0.38671] [ 0. 0. -0. 0.56157 -0.00461 -0.10304] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.02769 0.52798 -0.0408 -0.18575 1.15184] [ 0. 0.28959 -0.71049 0.05347 0.09885 -0.05394] [ 0. 0.27613 0.24864 -0.11116 -0.00061 0.28644] [ 0. -0. -0. 0.14614 -0.57054 0.2296 ] [ 0. -0. 0. 0.43475 0.00294 -0.32779] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.46392 -0.25357 0.13626 0.13268 1.15184] [ 0. 0.42585 -0.34158 0.12687 -0.03165 0.28155] [ 0. 0.64504 0.11238 0.04892 0.07416 -0.07541] [ 0. -0. -0. 0.04044 -0.59524 -0.01143] [ 0. -0. 0. 0.41006 0.10865 0.40004] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.25097 -0.46534 0.18845 0.02563 1.15184] [ 0. 0.11409 -0.64678 0.0839 0.02996 -0.07383] [ 0. 0.33984 0.42414 -0.0827 0.10106 -0.28197] [ 0. 0. 0. -0.02397 -0.49713 0.22872] [ 0. 0. -0. 0.50817 0.17306 0.3284 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.17613 0.4985 -0.14925 0.11788 1.15184] [ 0. 0.43698 -0.63263 0.04223 -0.12267 -0.15929] [ 0. 0.354 0.10125 0.06943 0.05777 0.2441 ] [ 0. 0. 0. 0.08366 -0.4044 -0.39517] [ 0. 0. -0. 0.6009 0.06542 -0.06326] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.49074 0.19672 -0.02165 0.18895 1.15184] [ 0. 0.09025 -0.36844 0.08746 -0.01333 0.23726] [ 0. 0.61819 0.44798 0.0609 0.11599 0.16931] [ 0. -0. -0. 0.17274 -0.51232 -0.3235 ] [ 0. -0. 0. 0.49298 -0.02365 0.2356 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.05887 -0.52541 0.09261 0.16611 1.15184] [ 0. 0.2638 -0.71139 0.07324 0.08097 0.0369 ] [ 0. 0.27523 0.27443 -0.11115 0.02671 -0.28913] [ 0. 0. 0. 0.09677 -0.59878 -0.12538] [ 0. 0. -0. 0.40651 0.05231 0.38005] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.42598 0.31315 0.16914 0.08696 1.15184] [ 0. 0.46037 -0.38839 -0.12016 0.05927 -0.26899] [ 0. 0.59824 0.07786 -0.05295 -0.06506 0.11226] [ 0. -0. -0. -0.00557 -0.56025 0.10623] [ 0. -0. 0. 0.44504 0.15466 0.38584] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.28542 0.44504 -0.18454 0.04599 1.15184] [ 0. 0.09273 -0.62167 0.08579 0.00617 0.09493] [ 0. 0.36495 0.4455 -0.046 0.1244 0.27558] [ 0. -0. -0. 0.00686 -0.43085 -0.33409] [ 0. -0. 0. 0.57444 0.14223 -0.22032] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.13905 -0.51009 -0.08986 0.16761 1.15184] [ 0. 0.41476 -0.65571 0.0038 0.12713 0.14093] [ 0. 0.33091 0.12347 -0.08722 -0.03472 -0.25514] [ 0. 0. 0. 0.15262 -0.44231 -0.38762] [ 0. 0. -0. 0.56298 -0.00353 0.09956] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.5131 -0.12749 0.03951 0.18603 1.15184] [ 0. 0.13095 -0.3245 -0.09093 0.02761 -0.25826] [ 0. 0.66212 0.40728 -0.0829 -0.09532 -0.13514] [ 0. -0. -0. 0.14708 -0.56953 -0.23187] [ 0. -0. 0. 0.43576 0.002 0.32618] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.08992 0.521 -0.13538 -0.13357 1.15184] [ 0. 0.23803 -0.70923 0.08692 0.06051 -0.0197 ] [ 0. 0.27739 0.3002 -0.10458 0.05324 0.29081] [ 0. -0. -0. 0.04165 -0.59567 0.01405] [ 0. -0. 0. 0.40962 0.10743 -0.39995] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.38427 -0.36313 -0.18823 -0.02716 1.15184] [ 0. 0.48019 -0.43821 -0.10237 0.089 0.25315] [ 0. 0.54841 0.05804 -0.05911 -0.05564 -0.14447] [ 0. 0. 0. -0.02405 -0.49873 -0.22605] [ 0. 0. -0. 0.50656 0.17314 -0.33025] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.32074 -0.4203 -0.15037 0.11644 1.15184] [ 0. 0.07422 -0.59131 -0.08139 0.01803 -0.11707] [ 0. 0.39531 0.46401 -0.00138 -0.1343 -0.26693] [ 0. -0. -0. 0.08177 -0.40424 -0.39454] [ 0. -0. 0. 0.60105 0.06732 -0.06706] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.10353 0.51847 -0.02314 0.18877 1.15184] [ 0. 0.39102 -0.67421 -0.04293 -0.11681 -0.123 ] [ 0. 0.31241 0.14721 0.09707 0.0089 0.26425] [ 0. 0. 0. 0.17288 -0.51076 -0.32535] [ 0. 0. -0. 0.49453 -0.02379 0.23303] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.52619 0.05147 0.09153 0.16671 1.15184] [ 0. 0.18541 -0.29186 0.09381 -0.04232 0.27517] [ 0. 0.69476 0.35282 0.09424 0.07428 0.09611] [ 0. -0. -0. 0.09802 -0.59848 -0.12785] [ 0. -0. 0. 0.40681 0.05106 0.37923] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.12106 -0.51465 0.16852 0.08816 1.15184] [ 0. 0.21235 -0.70394 0.09556 0.03729 0.00219] [ 0. 0.28268 0.32588 -0.09035 0.07939 -0.29147] [ 0. 0. 0. -0.00474 -0.56138 0.10349] [ 0. 0. -0. 0.44391 0.15383 0.38659] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.34104 0.404 0.18495 -0.0443 1.15184] [ 0. 0.48716 -0.48673 -0.07033 0.1164 -0.23532] [ 0. 0.4999 0.05107 -0.06801 -0.04322 0.172 ] [ 0. -0. -0. 0.00555 -0.4321 0.33206] [ 0. -0. 0. 0.57319 0.14354 0.22338] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.35671 0.39023 -0.09137 0.1668 1.15184] [ 0. 0.05998 -0.55537 0.07202 -0.03798 0.14026] [ 0. 0.43125 0.47825 0.0487 0.12644 0.25551] [ 0. -0. -0. 0.15152 -0.44091 -0.3885 ] [ 0. -0. 0. 0.56438 -0.00243 0.09605] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.06936 -0.52413 -0.03821 -0.1863 1.15184] [ 0. 0.36634 -0.68859 -0.07154 -0.09831 0.10543] [ 0. 0.29803 0.17189 0.09974 -0.01609 -0.27174] [ 0. -0. -0. 0.14801 -0.56851 0.23415] [ 0. -0. 0. 0.43678 0.00108 -0.32455] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.52793 0.02845 0.1345 0.13445 1.15184] [ 0. 0.24926 -0.27607 -0.0941 0.05933 -0.28652] [ 0. 0.71055 0.28897 -0.09819 -0.05452 -0.05353] [ 0. -0. -0. 0.04288 -0.5961 -0.01667] [ 0. -0. 0. 0.40919 0.10621 0.39985] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.15252 0.50622 0.18801 0.02868 1.15184] [ 0. 0.18689 -0.69537 -0.09862 -0.01068 0.01576] [ 0. 0.29125 0.35134 0.06588 -0.10396 0.29105] [ 0. 0. 0. -0.0241 -0.50032 0.22337] [ 0. 0. -0. 0.50497 0.17319 0.33207] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.29789 -0.43679 0.15149 -0.11498 1.15184] [ 0. 0.48393 -0.53127 0.02561 -0.1329 0.21648] [ 0. 0.45535 0.0543 0.07744 0.02593 -0.19518] [ 0. -0. -0. 0.07988 -0.40412 0.39388] [ 0. -0. 0. 0.60117 0.06921 0.07086] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.39284 -0.35383 -0.02464 0.18858 1.15184] [ 0. 0.05194 -0.51388 -0.06193 0.05152 -0.16435] [ 0. 0.47275 0.48629 -0.08566 -0.10565 -0.24072] [ 0. -0. -0. 0.173 -0.5092 -0.32719] [ 0. -0. 0. 0.49609 -0.02391 0.23045] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.03631 0.52745 -0.09044 -0.1673 1.15184] [ 0. 0.3411 -0.69924 0.09101 0.07606 -0.08816] [ 0. 0.28738 0.19713 -0.09674 0.03954 0.27782] [ 0. -0. -0. 0.09927 -0.59817 0.13032] [ 0. -0. 0. 0.40712 0.04982 -0.37839] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.51747 -0.10838 0.16789 0.08935 1.15184] [ 0. 0.31546 -0.28015 0.08854 -0.07966 0.29133] [ 0. 0.70648 0.22277 0.0975 0.03602 0.00935] [ 0. -0. -0. -0.0039 -0.5625 0.10074] [ 0. -0. 0. 0.44279 0.15299 0.38731] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.18449 -0.49547 -0.18535 0.0426 1.15184] [ 0. 0.16184 -0.68326 -0.09396 0.01864 -0.03429] [ 0. 0.30337 0.37639 0.029 -0.12236 -0.28945] [ 0. -0. -0. 0.00427 -0.43338 -0.33 ] [ 0. -0. 0. 0.57191 0.14482 -0.22641] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.25579 0.4627 0.09288 -0.16596 1.15184] [ 0. 0.47312 -0.57056 0.02194 0.13215 -0.1973 ] [ 0. 0.41606 0.06511 -0.08377 -0.00517 0.21455] [ 0. -0. 0. 0.15039 -0.43953 0.38935] [ 0. -0. 0. 0.56576 -0.0013 -0.09254] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.42823 0.31007 0.0369 0.18657 1.15184] [ 0. 0.0525 -0.4675 0.0542 -0.06049 0.18901] [ 0. 0.51912 0.48573 0.10978 0.07962 0.22189] [ 0. -0. -0. 0.14893 -0.56748 -0.23641] [ 0. -0. 0. 0.43781 0.00016 0.32291] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.00413 -0.52868 -0.13362 -0.13533 1.15184] [ 0. 0.31553 -0.70646 -0.10347 -0.05144 0.07108] [ 0. 0.28016 0.2227 0.08828 -0.062 -0.28268] [ 0. -0. -0. 0.0441 -0.5965 0.01929] [ 0. -0. 0. 0.40879 0.10498 -0.39973] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.49553 0.18431 0.18777 0.0302 1.15184] [ 0. 0.37625 -0.30329 -0.07284 0.10249 -0.28946] [ 0. 0.68334 0.16198 -0.0941 -0.01801 0.03419] [ 0. -0. -0. -0.02413 -0.50192 0.22068] [ 0. -0. 0. 0.50338 0.17321 0.33386] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.21717 0.48204 -0.15259 0.11352 1.15184] [ 0. 0.13748 -0.66727 0.07987 -0.04646 0.05355] [ 0. 0.31936 0.40075 0.01734 0.12708 0.28651] [ 0. -0. -0. 0.07798 -0.40403 -0.39318] [ 0. -0. 0. 0.60126 0.07111 -0.07464] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.21525 -0.4829 -0.02614 0.18838 1.15184] [ 0. 0.45696 -0.60422 0.06142 0.11689 0.17821] [ 0. 0.3824 0.08127 -0.08548 0.01571 -0.23065] [ 0. 0. -0. 0.17309 -0.50763 -0.32901] [ 0. 0. -0. 0.49766 -0.024 0.22784] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.46145 -0.25804 -0.08935 -0.16789 1.15184] [ 0. 0.06436 -0.41805 0.04906 -0.06791 -0.21359] [ 0. 0.56857 0.47387 0.12326 0.0527 -0.19834] [ 0. 0. 0. 0.10051 -0.59784 0.13278] [ 0. 0. -0. 0.40745 0.04857 -0.37753] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.02743 0.52799 0.16725 0.09054 1.15184] [ 0. 0.28981 -0.71047 -0.1098 -0.02411 -0.05408] [ 0. 0.27615 0.24842 0.07307 -0.08374 0.28641] [ 0. 0. 0. -0.00304 -0.56361 0.098 ] [ 0. 0. -0. 0.44168 0.15213 0.38802] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.46421 -0.25304 -0.18573 0.0409 1.15184] [ 0. 0.4255 -0.34123 -0.04319 0.12338 0.28164] [ 0. 0.6454 0.11273 -0.08889 0.00025 -0.07508] [ 0. 0. 0. 0.00301 -0.43468 -0.32791] [ 0. 0. -0. 0.57061 0.14607 -0.22942] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.25069 -0.46549 -0.09438 0.16511 1.15184] [ 0. 0.11427 -0.64697 -0.05918 0.06663 -0.07366] [ 0. 0.33965 0.42396 -0.06274 -0.1145 -0.28201] [ 0. -0. -0. 0.14923 -0.43816 -0.39018] [ 0. -0. 0. 0.56713 -0.00014 0.089 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.17645 0.49839 0.03559 0.18682 1.15184] [ 0. 0.43716 -0.63241 -0.08934 -0.0941 -0.15944] [ 0. 0.35421 0.10107 0.08325 -0.03494 0.244 ] [ 0. 0. -0. 0.14983 -0.56643 -0.23867] [ 0. 0. -0. 0.43886 -0.00074 0.32124] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.49052 0.19726 0.13273 0.1362 1.15184] [ 0. 0.08997 -0.36883 0.04481 -0.07623 0.23707] [ 0. 0.61779 0.44826 0.12842 0.02603 0.16957] [ 0. -0. -0. 0.04533 -0.59689 -0.0219 ] [ 0. -0. 0. 0.4084 0.10375 0.3996 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.05861 -0.52544 -0.18752 -0.03171 1.15184] [ 0. 0.26401 -0.7114 -0.10901 0.00651 0.03705] [ 0. 0.27523 0.27422 0.04867 -0.10341 -0.28911] [ 0. -0. -0. -0.02412 -0.5035 -0.21798] [ 0. -0. 0. 0.50179 0.17321 -0.33562] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.42632 0.3127 0.15367 -0.11205 1.15184] [ 0. 0.46015 -0.38798 -0.00094 0.13396 -0.26911] [ 0. 0.59864 0.07808 -0.08191 0.01822 0.11198] [ 0. -0. -0. 0.07608 -0.40399 0.39244] [ 0. -0. 0. 0.60131 0.07301 0.07843] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.28513 0.44522 0.02764 -0.18816 1.15184] [ 0. 0.0929 -0.6219 -0.03827 0.07706 0.09475] [ 0. 0.36473 0.44533 -0.09758 -0.0898 0.27565] [ 0. 0. 0. 0.17316 -0.50606 0.33082] [ 0. 0. -0. 0.49923 -0.02407 -0.2252 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.13935 -0.51001 0.08825 0.16847 1.15184] [ 0. 0.41495 -0.65554 0.10738 0.0682 0.14108] [ 0. 0.33108 0.12328 -0.07764 0.05272 -0.25506] [ 0. 0. 0. 0.10175 -0.59749 -0.13524] [ 0. 0. -0. 0.4078 0.04733 0.37665] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.51295 -0.1281 0.16661 0.09172 1.15184] [ 0. 0.13055 -0.32482 -0.0384 0.08686 -0.2581 ] [ 0. 0.6618 0.40768 -0.12637 0.00053 -0.13544] [ 0. -0. -0. -0.00218 -0.5647 0.09525] [ 0. -0. 0. 0.44059 0.15126 0.3887 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.08966 0.52104 0.1861 -0.03921 1.15184] [ 0. 0.23824 -0.70926 -0.09843 0.03916 -0.01984] [ 0. 0.27736 0.29999 0.01325 -0.11658 0.2908 ] [ 0. 0. 0. 0.00179 -0.43599 0.3258 ] [ 0. 0. -0. 0.5693 0.1473 0.2324 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.38462 -0.36275 -0.09587 0.16425 1.15184] [ 0. 0.48008 -0.4378 0.0441 0.12826 0.25329] [ 0. 0.54882 0.05815 -0.07373 0.03401 -0.14422] [ 0. 0. -0. 0.14805 -0.43682 -0.39097] [ 0. 0. -0. 0.56847 0.00104 0.08545] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.32045 -0.42052 0.03428 0.18707 1.15184] [ 0. 0.07436 -0.59158 -0.02132 0.08061 -0.11688] [ 0. 0.39504 0.46387 -0.11992 -0.06046 -0.26701] [ 0. -0. -0. 0.15072 -0.56536 -0.24093] [ 0. -0. 0. 0.43993 -0.00163 0.31955] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.10382 0.51841 0.13184 0.13707 1.15184] [ 0. 0.39122 -0.67408 -0.11775 -0.04036 -0.12314] [ 0. 0.31254 0.14701 0.06809 -0.06971 0.26418] [ 0. 0. 0. 0.04657 -0.59727 -0.02451] [ 0. 0. -0. 0.40802 0.10252 0.39945] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.52613 0.05211 -0.18726 -0.03321 1.15184] [ 0. 0.18492 -0.29207 -0.02569 0.09958 0.27505] [ 0. 0.69455 0.35331 -0.11698 0.02697 0.09645] [ 0. 0. 0. -0.0241 -0.50509 -0.21529] [ 0. 0. -0. 0.50021 0.17319 -0.33736] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.1208 -0.51471 -0.15474 0.11056 1.15184] [ 0. 0.21256 -0.704 -0.0764 0.06849 0.00234] [ 0. 0.28262 0.32567 -0.03009 -0.11643 -0.29147] [ 0. -0. -0. 0.07418 -0.40397 -0.39167] [ 0. -0. 0. 0.60132 0.07491 -0.0822 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.3414 0.4037 0.02915 -0.18794 1.15184] [ 0. 0.48715 -0.48634 0.08109 0.10918 -0.23547] [ 0. 0.50028 0.05108 -0.06571 0.04664 0.17179] [ 0. -0. 0. 0.1732 -0.50448 0.33261] [ 0. -0. 0. 0.50081 -0.02411 -0.22255] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.35642 0.3905 0.08715 0.16904 1.15184] [ 0. 0.06008 -0.55569 0.00871 -0.08097 0.14006] [ 0. 0.43093 0.47815 0.13206 0.0303 0.25562] [ 0. -0. -0. 0.10299 -0.59713 -0.1377 ] [ 0. -0. 0. 0.40816 0.0461 0.37576] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.06964 -0.52409 0.16596 0.09289 1.15184] [ 0. 0.36655 -0.68849 0.12118 0.01009 0.10557] [ 0. 0.29813 0.17168 -0.05297 0.086 -0.27168] [ 0. 0. 0. -0.00129 -0.56577 0.09251] [ 0. 0. -0. 0.43952 0.15038 0.38936] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.52797 0.02778 0.18645 -0.03751 1.15184] [ 0. 0.24872 -0.27612 -0.0026 0.11115 -0.28645] [ 0. 0.7105 0.28951 -0.09978 0.05169 -0.05389] [ 0. -0. -0. 0.00058 -0.43733 0.32367] [ 0. -0. 0. 0.56796 0.1485 0.23536] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.15225 0.5063 -0.09737 0.16337 1.15184] [ 0. 0.1871 -0.69545 0.04699 -0.08739 0.01561] [ 0. 0.29117 0.35113 0.07153 0.10014 0.29106] [ 0. -0. -0. 0.14683 -0.43549 -0.39173] [ 0. -0. 0. 0.5698 0.00225 0.08189] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.29824 -0.43655 -0.03296 -0.1873 1.15184] [ 0. 0.48399 -0.53093 -0.10652 -0.08352 0.21663] [ 0. 0.4557 0.05424 0.0584 -0.05707 -0.19501] [ 0. -0. 0. 0.1516 -0.56428 0.24317] [ 0. -0. 0. 0.44101 -0.00251 -0.31785] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.39255 -0.35416 -0.13094 -0.13793 1.15184] [ 0. 0.05198 -0.51424 -0.00112 -0.08055 -0.16415] [ 0. 0.47238 0.48625 0.13601 -0.00004 -0.24086] [ 0. 0. 0. 0.04781 -0.59763 0.02712] [ 0. 0. -0. 0.40767 0.10128 -0.39928] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.03658 0.52743 0.18699 0.03471 1.15184] [ 0. 0.34131 -0.69917 -0.11636 0.02309 -0.0883 ] [ 0. 0.28746 0.19692 0.02993 -0.1001 0.27778] [ 0. 0. 0. -0.02405 -0.50666 0.21258] [ 0. 0. -0. 0.49863 0.17313 0.33907] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.51761 -0.10773 0.1558 -0.10907 1.15184] [ 0. 0.31493 -0.28003 -0.03091 -0.11496 0.29131] [ 0. 0.70659 0.2233 0.0763 -0.07068 0.00971] [ 0. -0. -0. 0.07228 -0.404 0.39086] [ 0. -0. 0. 0.60129 0.07681 0.08597] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.18423 -0.49557 -0.03066 0.1877 1.15184] [ 0. 0.16204 -0.68337 -0.01822 0.09407 -0.03414] [ 0. 0.30325 0.37618 -0.10232 -0.07307 -0.28947] [ 0. -0. -0. 0.17321 -0.5029 -0.33439] [ 0. -0. 0. 0.50239 -0.02413 0.21987] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.25613 0.46251 -0.08604 -0.16961 1.15184] [ 0. 0.47324 -0.57026 0.12199 0.05538 -0.19746] [ 0. 0.41636 0.06499 -0.05089 0.06671 0.2144 ] [ 0. -0. 0. 0.10422 -0.59675 0.14015] [ 0. -0. 0. 0.40854 0.04486 -0.37485] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.42794 0.31047 -0.1653 -0.09405 1.15184] [ 0. 0.05245 -0.4679 0.01046 0.08053 0.1888 ] [ 0. 0.51872 0.48578 -0.13202 0.03109 0.22206] [ 0. 0. 0. -0.0004 -0.56683 -0.08977] [ 0. 0. -0. 0.43846 0.14949 -0.39 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.00439 -0.52868 -0.18678 0.03582 1.15184] [ 0. 0.31575 -0.70641 -0.10028 0.05745 0.07122] [ 0. 0.28021 0.22248 -0.0025 -0.10782 -0.28264] [ 0. -0. -0. -0.00059 -0.43868 -0.32152] [ 0. -0. 0. 0.56661 0.14968 -0.23829] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.49576 0.18371 0.09886 -0.16247 1.15184] [ 0. 0.37579 -0.30303 0.06747 0.10604 -0.2895 ] [ 0. 0.68359 0.16244 -0.05212 0.08047 0.03384] [ 0. -0. -0. 0.1456 -0.43418 0.39246] [ 0. -0. 0. 0.57111 0.00349 -0.07831] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.2169 0.48216 0.03163 0.18753 1.15184] [ 0. 0.13768 -0.66742 -0.00508 -0.09229 0.05338] [ 0. 0.31921 0.40055 0.12105 0.04234 0.28654] [ 0. -0. -0. 0.15246 -0.56319 -0.24541] [ 0. -0. 0. 0.4421 -0.00337 0.31612] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.21558 -0.48275 -0.13004 -0.13878 1.15184] [ 0. 0.45711 -0.60397 -0.12954 -0.02569 0.17837] [ 0. 0.38266 0.08112 0.04145 -0.07636 -0.23053] [ 0. -0. -0. 0.04905 -0.59797 0.02973] [ 0. -0. 0. 0.40733 0.10004 -0.39909] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.46119 -0.2585 0.18671 0.0362 1.15184] [ 0. 0.06421 -0.41846 0.02203 0.0808 -0.21339] [ 0. 0.56816 0.47402 -0.11849 0.06272 -0.19856] [ 0. -0. -0. -0.02397 -0.50823 0.20987] [ 0. -0. 0. 0.49706 0.17306 0.34075] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.02717 0.528 0.15684 -0.10756 1.15184] [ 0. 0.29002 -0.71045 -0.07151 0.08677 -0.05422] [ 0. 0.27617 0.24821 -0.04124 -0.10318 0.28639] [ 0. 0. 0. 0.07038 -0.40406 0.39001] [ 0. 0. -0. 0.60123 0.0787 0.08972] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.4645 -0.25251 0.03217 -0.18744 1.15184] [ 0. 0.42516 -0.34087 -0.09802 -0.08644 0.28172] [ 0. 0.64575 0.11307 0.03318 -0.08252 -0.07476] [ 0. -0. 0. 0.17321 -0.50131 0.33615] [ 0. -0. 0. 0.50398 -0.02412 -0.21717] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.25041 -0.46564 0.08493 0.17017 1.15184] [ 0. 0.11446 -0.64716 0.02264 0.08622 -0.07349] [ 0. 0.33947 0.42377 -0.13006 -0.01134 -0.28206] [ 0. -0. -0. 0.10545 -0.59635 -0.1426 ] [ 0. -0. 0. 0.40894 0.04363 0.37393] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.17676 0.49828 -0.16464 -0.09521 1.15184] [ 0. 0.43733 -0.6322 0.12963 -0.00613 -0.1596 ] [ 0. 0.35442 0.1009 -0.02791 0.08584 0.2439 ] [ 0. -0. -0. 0.00051 -0.56788 -0.08704] [ 0. -0. 0. 0.43742 0.14858 -0.39062] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.49031 0.1978 0.1871 -0.03412 1.15184] [ 0. 0.0897 -0.36922 -0.03835 -0.07962 0.23689] [ 0. 0.6174 0.44853 0.09323 -0.09212 0.16983] [ 0. -0. -0. -0.00174 -0.44006 0.31935] [ 0. -0. 0. 0.56524 0.15082 0.24119] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.05836 -0.52547 -0.10034 0.16156 1.15184] [ 0. 0.26423 -0.7114 -0.0352 0.10341 0.03719] [ 0. 0.27522 0.274 -0.07731 -0.08414 -0.28909] [ 0. -0. -0. 0.14433 -0.43289 -0.39316] [ 0. -0. 0. 0.5724 0.00476 0.07471] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.42665 0.31224 -0.0303 -0.18775 1.15184] [ 0. 0.45992 -0.38757 0.11903 0.06142 -0.26923] [ 0. 0.59905 0.07831 -0.02073 0.08135 0.11169] [ 0. -0. 0. 0.15331 -0.56208 0.24765] [ 0. -0. 0. 0.44321 -0.00422 -0.31437] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.28484 0.44541 -0.12913 -0.13962 1.15184] [ 0. 0.09306 -0.62213 0.03605 0.07815 0.09457] [ 0. 0.3645 0.44517 -0.13113 0.01965 0.27571] [ 0. 0. 0. 0.05029 -0.59829 0.03233] [ 0. 0. -0. 0.407 0.0988 -0.39889] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.13965 -0.50992 0.18641 0.03768 1.15184] [ 0. 0.41514 -0.65537 0.12063 -0.04042 0.14123] [ 0. 0.33125 0.12308 -0.00794 0.09348 -0.25497] [ 0. 0. 0. -0.02387 -0.5098 0.20716] [ 0. 0. -0. 0.49549 0.17296 0.34241] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.5128 -0.1287 0.15787 -0.10605 1.15184] [ 0. 0.13016 -0.32515 0.05967 0.07381 -0.25794] [ 0. 0.66147 0.40807 -0.05737 0.11265 -0.13574] [ 0. -0. -0. 0.06849 -0.40416 0.38913] [ 0. -0. 0. 0.60113 0.0806 0.09347] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.08941 0.52109 0.03368 -0.18718 1.15184] [ 0. 0.23845 -0.70929 -0.00069 0.10596 -0.01998] [ 0. 0.27733 0.29978 -0.10303 -0.05608 0.29079] [ 0. 0. 0. 0.17317 -0.49971 0.33789] [ 0. 0. -0. 0.50558 -0.02408 -0.21445] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.38497 -0.36238 -0.08381 -0.17072 1.15184] [ 0. 0.47997 -0.43739 -0.13126 -0.03412 0.25343] [ 0. 0.54923 0.05826 0.01232 -0.08027 -0.14398] [ 0. -0. 0. 0.10668 -0.59594 0.14505] [ 0. -0. 0. 0.40935 0.04241 -0.37299] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.32015 -0.42075 0.16397 0.09636 1.15184] [ 0. 0.0745 -0.59185 0.04715 0.0688 -0.1167 ] [ 0. 0.39477 0.46373 -0.12411 0.05127 -0.2671 ] [ 0. -0. -0. 0.00143 -0.56891 0.0843 ] [ 0. -0. 0. 0.43639 0.14766 0.39122] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.1041 0.51835 -0.1874 0.03243 1.15184] [ 0. 0.39142 -0.67394 0.09938 -0.07498 -0.12329] [ 0. 0.31268 0.14681 0.01966 0.09541 0.26412] [ 0. -0. -0. -0.00285 -0.44144 -0.31716] [ 0. -0. 0. 0.56385 0.15194 -0.24407] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.52606 0.05276 0.10182 -0.16063 1.15184] [ 0. 0.18442 -0.29228 -0.0824 -0.06143 0.27494] [ 0. 0.69434 0.35381 0.01936 -0.11854 0.09679] [ 0. -0. -0. 0.14304 -0.43162 0.39383] [ 0. -0. 0. 0.57367 0.00605 -0.0711 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.12054 -0.51478 0.02897 0.18796 1.15184] [ 0. 0.21277 -0.70406 0.02677 0.09908 0.00248] [ 0. 0.28257 0.32546 -0.11748 -0.02556 -0.29146] [ 0. -0. -0. 0.15415 -0.56095 -0.24988] [ 0. -0. 0. 0.44434 -0.00506 0.31261] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.34176 0.4034 0.12822 0.14046 1.15184] [ 0. 0.48714 -0.48595 -0.1359 -0.00512 -0.23562] [ 0. 0.50067 0.05109 0.00469 -0.08044 0.17158] [ 0. 0. 0. 0.05154 -0.5986 -0.03492] [ 0. 0. -0. 0.40669 0.09755 0.39867] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.35612 0.39077 0.18611 0.03916 1.15184] [ 0. 0.06017 -0.55601 -0.05737 -0.05781 0.13987] [ 0. 0.43061 0.47805 0.10683 -0.08332 0.25572] [ 0. -0. -0. -0.02374 -0.51136 0.20444] [ 0. -0. 0. 0.49393 0.17283 0.34404] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.06991 -0.52406 0.15888 -0.10452 1.15184] [ 0. 0.36675 -0.68839 0.06474 -0.10296 0.10572] [ 0. 0.29824 0.17148 0.05197 0.08657 -0.27163] [ 0. 0. 0. 0.06659 -0.40429 0.38821] [ 0. 0. -0. 0.601 0.08249 0.09721] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.528 0.02712 0.0352 -0.1869 1.15184] [ 0. 0.24817 -0.27617 0.10203 0.04398 -0.28638] [ 0. 0.71045 0.29006 0.0106 0.11194 -0.05425] [ 0. -0. -0. 0.17311 -0.49812 0.33962] [ 0. -0. 0. 0.50718 -0.02402 -0.2117 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.15199 0.50638 -0.08269 -0.17127 1.15184] [ 0. 0.18731 -0.69554 0.04711 0.08736 0.01546] [ 0. 0.29109 0.35092 -0.12295 0.00456 0.29106] [ 0. 0. 0. 0.1079 -0.59551 0.14749] [ 0. 0. -0. 0.40978 0.04119 -0.37203] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.29859 -0.43631 -0.16329 -0.0975 1.15184] [ 0. 0.48405 -0.53058 -0.13283 0.02608 0.21679] [ 0. 0.45604 0.05418 -0.00512 -0.08148 -0.19483] [ 0. -0. -0. 0.00236 -0.56992 -0.08157] [ 0. -0. 0. 0.43537 0.14673 -0.3918 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.39225 -0.35449 -0.18768 0.03074 1.15184] [ 0. 0.05201 -0.5146 -0.06731 -0.04427 -0.16395] [ 0. 0.47202 0.48622 0.07638 -0.11254 -0.24099] [ 0. 0. 0. -0.00395 -0.44285 -0.31495] [ 0. 0. -0. 0.56244 0.15303 -0.24692] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.03685 0.52741 -0.10329 0.15969 1.15184] [ 0. 0.34152 -0.69909 0.02291 -0.11642 -0.08844] [ 0. 0.28753 0.19671 0.08117 0.06573 0.27773] [ 0. -0. -0. 0.14172 -0.43037 -0.39447] [ 0. -0. 0. 0.57492 0.00736 0.06748] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.51774 -0.10708 -0.02763 -0.18816 1.15184] [ 0. 0.3144 -0.27992 -0.11658 -0.02379 0.2913 ] [ 0. 0.70671 0.22383 -0.02911 -0.09992 0.01008] [ 0. -0. -0. 0.15497 -0.55981 0.2521 ] [ 0. -0. 0. 0.44548 -0.00588 -0.31082] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.18396 -0.49566 -0.1273 -0.14129 1.15184] [ 0. 0.16225 -0.68349 -0.06208 -0.07302 -0.03398] [ 0. 0.30313 0.37598 0.12097 -0.0342 -0.28949] [ 0. 0. 0. 0.05279 -0.59889 0.03752] [ 0. 0. -0. 0.4064 0.0963 -0.39844] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.25648 0.46232 -0.18579 -0.04062 1.15184] [ 0. 0.47335 -0.56996 0.12004 -0.05953 -0.19762] [ 0. 0.41666 0.06488 0.01958 0.08156 0.21426] [ 0. -0. -0. -0.02359 -0.51291 -0.20172] [ 0. -0. 0. 0.49238 0.17268 -0.34564] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.42766 0.31086 -0.15988 0.10299 1.15184] [ 0. 0.05241 -0.4683 0.07625 0.02788 0.1886 ] [ 0. 0.51832 0.48582 -0.03348 0.13144 0.22223] [ 0. 0. 0. 0.0647 -0.40447 -0.38726] [ 0. 0. -0. 0.60083 0.08439 -0.10094] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.00466 -0.52868 0.03671 -0.1866 1.15184] [ 0. 0.31596 -0.70637 -0.01578 -0.11452 0.07136] [ 0. 0.28025 0.22227 0.10091 0.03799 -0.2826 ] [ 0. 0. 0. 0.17302 -0.49651 0.34133] [ 0. 0. -0. 0.50878 -0.02394 -0.20893] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.49598 0.18311 0.08156 0.1718 1.15184] [ 0. 0.37533 -0.30277 -0.12563 -0.00169 -0.28955] [ 0. 0.68385 0.1629 -0.03881 -0.08773 0.03348] [ 0. 0. 0. 0.10911 -0.59506 -0.14993] [ 0. 0. -0. 0.41023 0.03997 0.37105] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.21663 0.48228 -0.16261 -0.09863 1.15184] [ 0. 0.13788 -0.66756 0.07323 0.05644 0.05322] [ 0. 0.31906 0.40035 -0.11112 0.06397 0.28657] [ 0. 0. 0. 0.0033 -0.57092 -0.07884] [ 0. 0. -0. 0.43437 0.14578 -0.39236] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.21591 -0.48261 -0.18795 0.02905 1.15184] [ 0. 0.45726 -0.60371 -0.09428 0.0925 0.17853] [ 0. 0.38291 0.08097 -0.03972 -0.07724 -0.2304 ] [ 0. -0. -0. -0.00501 -0.44427 -0.31271] [ 0. -0. 0. 0.56102 0.1541 -0.24974] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.46093 -0.25897 -0.10476 0.15873 1.15184] [ 0. 0.06406 -0.41887 -0.08308 -0.01036 -0.21319] [ 0. 0.56775 0.47417 -0.0128 -0.13348 -0.19877] [ 0. 0. 0. 0.14038 -0.42915 -0.39507] [ 0. 0. -0. 0.57614 0.00871 0.06384] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.02691 0.52802 -0.02629 -0.18836 1.15184] [ 0. 0.29023 -0.71043 0.04581 0.10271 -0.05436] [ 0. 0.27619 0.248 -0.11072 -0.00908 0.28636] [ 0. 0. 0. 0.15578 -0.55866 0.25431] [ 0. 0. -0. 0.44663 -0.00669 -0.30901] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.46479 -0.25198 -0.12638 -0.14212 1.15184] [ 0. 0.42481 -0.34051 -0.12866 0.02273 0.28181] [ 0. 0.64611 0.11342 -0.04391 -0.0774 -0.07444] [ 0. -0. -0. 0.05404 -0.59916 0.04011] [ 0. -0. 0. 0.40613 0.09504 -0.39818] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.25013 -0.46579 0.18547 0.04209 1.15184] [ 0. 0.11464 -0.64734 0.0811 0.03704 -0.07332] [ 0. 0.33928 0.42359 -0.09111 0.09347 -0.2821 ] [ 0. -0. -0. -0.02342 -0.51445 0.19899] [ 0. -0. 0. 0.49084 0.17251 0.34722] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.17707 0.49817 -0.16086 0.10145 1.15184] [ 0. 0.43751 -0.63199 0.05483 -0.11765 -0.15975] [ 0. 0.35463 0.10072 0.06304 0.06456 0.2438 ] [ 0. -0. -0. 0.06281 -0.40467 -0.38627] [ 0. -0. 0. 0.60062 0.08627 -0.10466] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.49009 0.19833 0.03824 -0.1863 1.15184] [ 0. 0.08943 -0.36962 -0.08813 0.00596 0.2367 ] [ 0. 0.61701 0.4488 -0.05072 -0.12089 0.17009] [ 0. -0. -0. 0.17291 -0.49491 0.34302] [ 0. -0. 0. 0.51038 -0.02382 -0.20614] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.0581 -0.5255 0.08043 0.17234 1.15184] [ 0. 0.26444 -0.71141 0.0674 0.086 0.03733] [ 0. 0.27522 0.27379 -0.11269 0.01878 -0.28908] [ 0. -0. -0. 0.11033 -0.5946 -0.15237] [ 0. -0. 0. 0.41069 0.03876 0.37006] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.42698 0.31179 -0.16192 -0.09976 1.15184] [ 0. 0.4597 -0.38717 0.12423 -0.05003 -0.26935] [ 0. 0.59945 0.07853 0.04816 0.0688 0.1114 ] [ 0. -0. -0. 0.00426 -0.5719 -0.07611] [ 0. -0. 0. 0.43339 0.14483 -0.39289] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.28455 0.44559 0.1882 -0.02736 1.15184] [ 0. 0.09323 -0.62235 -0.08486 -0.01446 0.09439] [ 0. 0.36427 0.445 0.05801 -0.11922 0.27577] [ 0. -0. -0. -0.00604 -0.44571 0.31046] [ 0. -0. 0. 0.55958 0.15513 0.25253] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.13995 -0.50984 -0.10622 0.15776 1.15184] [ 0. 0.41534 -0.6552 -0.00882 0.12694 0.14138] [ 0. 0.33143 0.12289 -0.08331 -0.04307 -0.25489] [ 0. -0. -0. 0.13901 -0.42795 -0.39565] [ 0. -0. 0. 0.57735 0.01008 0.06019] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.51265 -0.1293 0.02494 0.18854 1.15184] [ 0. 0.12976 -0.32548 -0.09254 0.02082 -0.25778] [ 0. 0.66115 0.40847 -0.07557 -0.1014 -0.13604] [ 0. 0. 0. 0.15657 -0.55749 -0.25651] [ 0. 0. -0. 0.4478 -0.00748 0.30718] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.08915 0.52113 0.12546 0.14293 1.15184] [ 0. 0.23866 -0.70932 -0.08252 -0.06652 -0.02013] [ 0. 0.2773 0.29957 0.10801 -0.04571 0.29078] [ 0. -0. 0. 0.0553 -0.59942 -0.0427 ] [ 0. 0. 0. 0.40587 0.09379 0.39792] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.38533 -0.362 -0.18513 -0.04354 1.15184] [ 0. 0.47986 -0.43698 -0.10961 0.07987 0.25357] [ 0. 0.54965 0.05837 -0.05433 -0.06037 -0.14373] [ 0. 0. 0. -0.02322 -0.51599 -0.19626] [ 0. 0. 0. 0.48931 0.17231 -0.34877] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.31986 -0.42097 0.16183 -0.0999 1.15184] [ 0. 0.07463 -0.59213 0.08287 -0.00961 -0.11651] [ 0. 0.3945 0.4636 -0.01264 0.13368 -0.26718] [ 0. 0. 0. 0.06093 -0.40492 0.38525] [ 0. 0. 0. 0.60037 0.08815 0.10837] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.10439 0.51829 -0.03976 0.18598 1.15184] [ 0. 0.39162 -0.67381 -0.03259 -0.12018 -0.12344] [ 0. 0.31282 0.14661 0.09585 0.01726 0.26405] [ 0. 0. 0. 0.17277 -0.4933 -0.3447 ] [ 0. 0. 0. 0.51199 -0.02368 0.20333] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.526 0.05341 0.0793 0.17286 1.15184] [ 0. 0.18393 -0.29249 0.09628 -0.03577 0.27482] [ 0. 0.69414 0.3543 0.08901 0.08073 0.09713] [ 0. 0. -0. 0.11153 -0.59412 -0.1548 ] [ 0. 0. -0. 0.41117 0.03755 0.36905] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.12029 -0.51484 0.16122 0.10088 1.15184] [ 0. 0.21298 -0.70411 0.09255 0.04444 0.00263] [ 0. 0.28251 0.32525 -0.09606 0.07226 -0.29146] [ 0. 0. 0. 0.00523 -0.57287 0.07339] [ 0. 0. 0. 0.43242 0.14386 0.39341] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.34211 0.40309 0.18844 -0.02568 1.15184] [ 0. 0.48712 -0.48557 -0.08139 0.10896 -0.23578] [ 0. 0.50106 0.05111 -0.06359 -0.04948 0.17137] [ 0. 0. -0. -0.00705 -0.44716 0.30819] [ 0. 0. -0. 0.55813 0.15614 0.2553 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.35582 0.39105 -0.10767 0.15677 1.15184] [ 0. 0.06027 -0.55633 0.07539 -0.03085 0.13967] [ 0. 0.43029 0.47796 0.03592 0.13063 0.25583] [ 0. 0. -0. 0.13762 -0.42677 -0.39619] [ 0. 0. -0. 0.57853 0.01147 0.05653] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.07019 -0.52402 0.02358 0.18871 1.15184] [ 0. 0.36696 -0.68828 0.06382 0.10357 0.10586] [ 0. 0.29834 0.17127 -0.10059 0.00844 -0.27157] [ 0. 0. 0. 0.15735 -0.55631 -0.25871] [ 0. 0. 0. 0.44899 -0.00826 0.30533] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.52804 0.02645 0.12452 0.14375 1.15184] [ 0. 0.24762 -0.27623 -0.09775 0.05267 -0.28631] [ 0. 0.7104 0.29061 -0.0944 -0.06122 -0.05461] [ 0. 0. -0. 0.05656 -0.59966 -0.04528] [ 0. 0. -0. 0.40563 0.09253 0.39763] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.15173 0.50646 0.18479 0.04499 1.15184] [ 0. 0.18752 -0.69562 -0.09743 -0.01909 0.01531] [ 0. 0.291 0.35071 0.07456 -0.09784 0.29107] [ 0. 0. 0. -0.023 -0.51751 0.19353] [ 0. 0. 0. 0.48778 0.17209 0.35029] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.29895 -0.43607 -0.16278 0.09834 1.15184] [ 0. 0.48411 -0.53023 -0.03932 0.12954 0.21695] [ 0. 0.45639 0.05412 -0.07436 -0.03366 -0.19466] [ 0. 0. 0. 0.05906 -0.4052 -0.38419] [ 0. 0. 0. 0.60009 0.09003 -0.11207] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.39195 -0.35482 0.04128 -0.18565 1.15184] [ 0. 0.05205 -0.51497 0.06607 -0.04611 -0.16375] [ 0. 0.47166 0.48618 0.07611 0.11272 -0.24113] [ 0. 0. 0. 0.1726 -0.49169 0.34636] [ 0. 0. 0. 0.5136 -0.02352 -0.20049] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.03712 0.5274 -0.07816 -0.17338 1.15184] [ 0. 0.34173 -0.69902 0.08545 0.08236 -0.08858] [ 0. 0.28761 0.1965 -0.0992 0.0326 0.27769] [ 0. 0. -0. 0.11273 -0.59363 0.15722] [ 0. 0. -0. 0.41166 0.03635 -0.36802] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.51788 -0.10643 -0.16052 -0.10199 1.15184] [ 0. 0.31386 -0.2798 -0.09405 0.07278 0.29129] [ 0. 0.70682 0.22437 -0.09479 -0.04314 0.01044] [ 0. 0. 0. 0.0062 -0.57382 -0.07067] [ 0. 0. 0. 0.43147 0.14288 -0.39391] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.18369 -0.49576 -0.18866 0.024 1.15184] [ 0. 0.16245 -0.6836 -0.09541 0.00942 -0.03382] [ 0. 0.30302 0.37578 0.04084 -0.11886 -0.28951] [ 0. 0. -0. -0.00803 -0.44862 -0.3059 ] [ 0. 0. -0. 0.55667 0.15711 -0.25804] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.25682 0.46214 -0.10912 0.15576 1.15184] [ 0. 0.47346 -0.56966 -0.0087 -0.13372 -0.19777] [ 0. 0.41697 0.06476 0.0828 0.01329 0.21411] [ 0. 0. 0. 0.1362 -0.42561 -0.39669] [ 0. 0. 0. 0.57968 0.01289 0.05285] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.42737 0.31125 -0.02222 -0.18888 1.15184] [ 0. 0.05236 -0.4687 -0.05847 0.05632 0.1884 ] [ 0. 0.51792 0.48587 -0.10339 -0.0878 0.22241] [ 0. 0. 0. 0.15811 -0.55511 0.2609 ] [ 0. 0. 0. 0.45018 -0.00903 -0.30346] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.00492 -0.52868 0.12359 0.14455 1.15184] [ 0. 0.31617 -0.70632 0.09965 0.05863 0.0715 ] [ 0. 0.2803 0.22206 -0.09235 0.05561 -0.28257] [ 0. 0. 0. 0.05782 -0.59989 -0.04786] [ 0. 0. 0. 0.4054 0.09127 0.39733] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.4962 0.18251 0.18443 0.04642 1.15184] [ 0. 0.37487 -0.30251 -0.08114 0.09586 -0.28959] [ 0. 0.68411 0.16336 -0.09247 -0.02578 0.03313] [ 0. 0. -0. -0.02276 -0.51903 0.19079] [ 0. 0. -0. 0.48626 0.17184 0.35179] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.21635 0.48241 0.16372 -0.09677 1.15184] [ 0. 0.13807 -0.66771 -0.08433 0.03798 0.05306] [ 0. 0.31891 0.40016 -0.00397 -0.12814 0.28661] [ 0. 0. 0. 0.05719 -0.40551 0.38309] [ 0. 0. 0. 0.59978 0.0919 0.11575] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.21624 -0.48246 -0.04281 0.1853 1.15184] [ 0. 0.45741 -0.60346 0.05095 0.12188 0.17868] [ 0. 0.38317 0.08082 -0.08643 0.00828 -0.23028] [ 0. 0. 0. 0.17241 -0.49007 -0.348 ] [ 0. 0. 0. 0.51522 -0.02332 0.19763] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.46067 -0.25943 0.07701 0.17389 1.15184] [ 0. 0.06391 -0.41929 -0.05347 0.06438 -0.21299] [ 0. 0.56734 0.47432 -0.1193 -0.06125 -0.19898] [ 0. 0. -0. 0.11393 -0.59312 -0.15965] [ 0. 0. -0. 0.41218 0.03516 0.36698] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.02665 0.52803 -0.15981 -0.1031 1.15184] [ 0. 0.29044 -0.71041 0.10774 0.03235 -0.0545 ] [ 0. 0.27621 0.24779 -0.07912 0.07794 0.28633] [ 0. 0. -0. 0.00719 -0.57476 -0.06795] [ 0. 0. -0. 0.43054 0.14189 -0.39439] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.46508 -0.25145 0.18887 -0.02232 1.15184] [ 0. 0.42445 -0.34016 0.05489 -0.11853 0.28189] [ 0. 0.64647 0.11377 0.08867 0.00814 -0.07412] [ 0. 0. -0. -0.00897 -0.4501 0.30359] [ 0. 0. -0. 0.55519 0.15806 0.26075] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.24985 -0.46594 -0.11056 0.15474 1.15184] [ 0. 0.11483 -0.64753 -0.06551 0.06053 -0.07315] [ 0. 0.33909 0.4234 -0.05098 -0.12014 -0.28215] [ 0. 0. -0. 0.13476 -0.42448 -0.39717] [ 0. 0. -0. 0.58081 0.01433 0.04916] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.17739 0.49805 -0.02086 -0.18903 1.15184] [ 0. 0.43768 -0.63178 0.08186 0.10075 -0.1599 ] [ 0. 0.35484 0.10055 -0.08558 0.02851 0.2437 ] [ 0. 0. -0. 0.15886 -0.5539 0.26309] [ 0. 0. -0. 0.45139 -0.00977 -0.30157] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.48987 0.19887 0.12265 0.14535 1.15184] [ 0. 0.08916 -0.37001 0.04973 -0.07295 0.23652] [ 0. 0.61661 0.44907 0.12639 0.03491 0.17035] [ 0. 0. -0. 0.05908 -0.6001 -0.05044] [ 0. 0. -0. 0.40519 0.09 0.39701] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.05785 -0.52553 0.18406 0.04786 1.15184] [ 0. 0.26465 -0.71141 0.10925 0.00282 0.03747] [ 0. 0.27521 0.27358 -0.0573 0.0988 -0.28906] [ 0. 0. 0. -0.02249 -0.52054 0.18805] [ 0. 0. 0. 0.48475 0.17158 0.35327] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.42731 0.31134 -0.16464 0.09519 1.15184] [ 0. 0.45947 -0.38676 0.01482 -0.13308 -0.26946] [ 0. 0.59986 0.07876 0.08343 -0.00989 0.11112] [ 0. 0. 0. 0.05533 -0.40586 -0.38197] [ 0. 0. 0. 0.59943 0.09376 -0.11942] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.28427 0.44578 0.04434 -0.18494 1.15184] [ 0. 0.0934 -0.62258 -0.04483 0.07352 0.09421] [ 0. 0.36404 0.44483 -0.08925 -0.09802 0.27583] [ 0. 0. 0. 0.17219 -0.48846 0.34962] [ 0. 0. 0. 0.51683 -0.0231 -0.19475] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.14025 -0.50976 -0.07586 -0.1744 1.15184] [ 0. 0.41553 -0.65503 -0.10232 -0.07569 0.14153] [ 0. 0.3316 0.1227 0.08106 -0.04711 -0.25481] [ 0. 0. -0. 0.11512 -0.59259 0.16207] [ 0. 0. -0. 0.4127 0.03396 -0.36591] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.51249 -0.1299 0.1591 0.1042 1.15184] [ 0. 0.12937 -0.3258 -0.04449 0.0837 -0.25762] [ 0. 0.66082 0.40886 -0.1262 -0.00885 -0.13635] [ 0. 0. -0. 0.00819 -0.57568 0.06523] [ 0. 0. -0. 0.42961 0.1409 0.39485] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.08889 0.52117 -0.18906 0.02064 1.15184] [ 0. 0.23887 -0.70935 0.10186 -0.02942 -0.02027] [ 0. 0.27727 0.29935 -0.02455 0.11466 0.29077] [ 0. 0. -0. -0.00989 -0.45159 -0.30126] [ 0. 0. -0. 0.5537 0.15898 -0.26344] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.38568 -0.36163 0.112 -0.15371 1.15184] [ 0. 0.47975 -0.43657 -0.03113 -0.13199 0.25371] [ 0. 0.55006 0.05848 0.0767 -0.02676 -0.14348] [ 0. 0. -0. 0.13329 -0.42337 0.39761] [ 0. 0. -0. 0.58192 0.01579 -0.04547] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.31956 -0.42119 0.01949 0.18918 1.15184] [ 0. 0.07477 -0.5924 -0.02734 0.07884 -0.11632] [ 0. 0.39422 0.46346 -0.11486 -0.06952 -0.26726] [ 0. 0. -0. 0.15959 -0.55267 -0.26526] [ 0. 0. -0. 0.45262 -0.01051 0.29966] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.10468 0.51823 -0.1217 -0.14614 1.15184] [ 0. 0.39182 -0.67367 0.11468 0.04857 -0.12358] [ 0. 0.31295 0.14641 -0.07271 0.06474 0.26398] [ 0. 0. -0. 0.06035 -0.60029 0.05301] [ 0. 0. -0. 0.405 0.08874 -0.39667] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.52593 0.05406 -0.18369 -0.04928 1.15184] [ 0. 0.18343 -0.2927 -0.03377 0.09692 0.2747 ] [ 0. 0.69393 0.3548 -0.119 0.01711 0.09747] [ 0. 0. 0. -0.0222 -0.52205 -0.18531] [ 0. 0. 0. 0.48325 0.17129 -0.35471] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.12003 -0.5149 0.16555 -0.09361 1.15184] [ 0. 0.21319 -0.70417 0.08318 -0.06022 0.00277] [ 0. 0.28246 0.32504 0.01776 0.11886 -0.29146] [ 0. 0. 0. 0.05347 -0.40625 0.3808 ] [ 0. 0. 0. 0.59904 0.09561 0.12308] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.34247 0.40279 0.04587 -0.18457 1.15184] [ 0. 0.48711 -0.48518 0.07117 0.1159 -0.23593] [ 0. 0.50144 0.05112 -0.06944 0.04087 0.17116] [ 0. 0. -0. 0.17194 -0.48684 0.35122] [ 0. 0. -0. 0.51845 -0.02285 -0.19184] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.35552 0.39132 -0.07471 -0.17489 1.15184] [ 0. 0.06037 -0.55665 -0.01424 0.08022 0.13948] [ 0. 0.42997 0.47786 -0.12956 -0.03957 0.25594] [ 0. 0. 0. 0.11631 -0.59204 0.16448] [ 0. 0. 0. 0.41325 0.03278 -0.36484] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.07047 -0.52398 0.15838 0.10529 1.15184] [ 0. 0.36717 -0.68818 0.12015 0.01918 0.10601] [ 0. 0.29844 0.17106 -0.05919 0.08173 -0.27152] [ 0. 0. 0. 0.0092 -0.57658 0.06252] [ 0. 0. 0. 0.42871 0.13989 0.39529] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.52807 0.02579 0.18923 -0.01897 1.15184] [ 0. 0.24707 -0.27628 -0.01314 0.11019 -0.28624] [ 0. 0.71034 0.29116 -0.10444 0.04203 -0.05497] [ 0. 0. -0. -0.01078 -0.45309 0.29892] [ 0. 0. -0. 0.5522 0.15987 0.26609] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.15147 0.50654 -0.11343 0.15266 1.15184] [ 0. 0.18773 -0.69571 0.05551 -0.08235 0.01516] [ 0. 0.29092 0.3505 0.06109 0.10674 0.29108] [ 0. 0. -0. 0.1318 -0.42229 -0.39801] [ 0. 0. -0. 0.583 0.01728 0.04176] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.2993 -0.43583 0.01812 0.18932 1.15184] [ 0. 0.48417 -0.52988 0.09977 0.09151 0.21711] [ 0. 0.45674 0.05406 -0.06247 0.05252 -0.19448] [ 0. 0. 0. 0.16031 -0.55143 -0.26743] [ 0. 0. 0. 0.45386 -0.01122 0.29773] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.39166 -0.35515 0.12075 0.14693 1.15184] [ 0. 0.05208 -0.51533 -0.0043 0.08045 -0.16355] [ 0. 0.47129 0.48615 -0.13568 -0.00947 -0.24127] [ 0. 0. -0. 0.06162 -0.60047 -0.05558] [ 0. 0. -0. 0.40482 0.08747 0.39632] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.03739 0.52738 0.1833 0.0507 1.15184] [ 0. 0.34194 -0.69894 -0.11798 0.01313 -0.08873] [ 0. 0.28768 0.19629 0.03827 -0.09713 0.27764] [ 0. 0. 0. -0.02189 -0.52354 0.18256] [ 0. 0. 0. 0.48175 0.17098 0.35613] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.51801 -0.10578 -0.16644 0.09202 1.15184] [ 0. 0.31332 -0.27969 0.01892 0.11734 0.29127] [ 0. 0.70693 0.2249 -0.08326 0.06268 0.01081] [ 0. 0. 0. 0.05163 -0.40667 -0.3796 ] [ 0. 0. 0. 0.59862 0.09746 -0.12673] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.18343 -0.49586 0.0474 -0.18418 1.15184] [ 0. 0.16266 -0.68372 0.02645 -0.09218 -0.03367] [ 0. 0.30291 0.37557 0.09538 0.08182 -0.28952] [ 0. 0. 0. 0.17167 -0.48523 0.3528 ] [ 0. 0. 0. 0.52007 -0.02258 -0.18892] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.25716 0.46194 -0.07355 -0.17539 1.15184] [ 0. 0.47358 -0.56935 0.11779 0.06392 -0.19793] [ 0. 0.41727 0.06465 -0.05532 0.063 0.21396] [ 0. 0. -0. 0.11749 -0.59148 0.16689] [ 0. 0. -0. 0.41381 0.0316 -0.36374] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.42709 0.31164 0.15765 0.10637 1.15184] [ 0. 0.05232 -0.4691 -0.00466 -0.08103 0.18819] [ 0. 0.51752 0.48591 0.13399 -0.02116 0.22258] [ 0. 0. -0. 0.01022 -0.57747 0.05981] [ 0. 0. -0. 0.42782 0.13887 0.39571] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.00518 -0.52868 0.18939 -0.01729 1.15184] [ 0. 0.31638 -0.70627 0.10545 -0.04748 0.07164] [ 0. 0.28035 0.22185 -0.00795 0.10748 -0.28253] [ 0. 0. 0. -0.01165 -0.45461 0.29656] [ 0. 0. 0. 0.55068 0.16073 0.26872] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.49642 0.18191 0.11485 -0.15159 1.15184] [ 0. 0.3744 -0.30226 0.05657 0.11207 -0.28963] [ 0. 0.68437 0.16383 -0.05982 0.07517 0.03278] [ 0. 0. -0. 0.13029 -0.42123 0.39839] [ 0. 0. -0. 0.58406 0.01879 -0.03804] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.21608 0.48253 -0.01674 -0.18944 1.15184] [ 0. 0.13827 -0.66786 -0.00201 0.09249 0.0529 ] [ 0. 0.31876 0.39996 -0.11733 -0.0516 0.28663] [ 0. 0. 0. 0.16101 -0.55018 0.26959] [ 0. 0. 0. 0.45511 -0.01192 -0.29577] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.21656 -0.48231 -0.1198 -0.14771 1.15184] [ 0. 0.45756 -0.6032 -0.12747 -0.03472 0.17884] [ 0. 0.38342 0.08067 0.04653 -0.07328 -0.23016] [ 0. 0. -0. 0.06288 -0.60063 0.05815] [ 0. 0. -0. 0.40467 0.0862 -0.39595] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.46041 -0.2599 -0.1829 -0.05211 1.15184] [ 0. 0.06376 -0.4197 -0.01538 -0.08224 -0.21279] [ 0. 0.56692 0.47447 0.1234 -0.05255 -0.1992 ] [ 0. 0. 0. -0.02156 -0.52502 -0.17982] [ 0. 0. 0. 0.48027 0.17065 -0.35753] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.0264 0.52804 0.16731 -0.09042 1.15184] [ 0. 0.29066 -0.71039 -0.08021 0.07891 -0.05464] [ 0. 0.27623 0.24757 -0.03025 -0.10684 0.28631] [ 0. 0. 0. 0.0498 -0.40713 0.37837] [ 0. 0. 0. 0.59816 0.09929 0.13036] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.46537 -0.25091 -0.04894 0.18378 1.15184] [ 0. 0.4241 -0.3398 0.08996 0.09465 0.28198] [ 0. 0.64682 0.11413 -0.04018 0.07952 -0.07379] [ 0. 0. 0. 0.17136 -0.48361 -0.35437] [ 0. 0. 0. 0.52168 -0.02227 0.18597] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.24957 -0.46609 -0.07238 -0.17587 1.15184] [ 0. 0.11501 -0.64771 -0.01657 -0.08766 -0.07298] [ 0. 0.33891 0.42322 0.12887 0.02057 -0.28219] [ 0. 0. 0. 0.11866 -0.59091 0.1693 ] [ 0. 0. 0. 0.41439 0.03042 -0.36262] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.1777 0.49794 0.15692 0.10745 1.15184] [ 0. 0.43785 -0.63157 -0.12979 -0.00358 -0.16006] [ 0. 0.35506 0.10038 0.03411 -0.08348 0.2436 ] [ 0. 0. 0. 0.01125 -0.57834 0.0571 ] [ 0. 0. 0. 0.42695 0.13784 0.39611] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.48965 0.19941 0.18954 -0.01563 1.15184] [ 0. 0.08889 -0.3704 -0.0307 -0.08273 0.23633] [ 0. 0.61622 0.44934 0.10171 -0.08281 0.1706 ] [ 0. 0. -0. -0.01248 -0.45613 0.29418] [ 0. 0. -0. 0.54916 0.16156 0.27132] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.05759 -0.52555 0.11626 -0.15051 1.15184] [ 0. 0.26487 -0.71142 0.04544 -0.09942 0.03761] [ 0. 0.27521 0.27336 0.06841 0.09143 -0.28904] [ 0. 0. 0. 0.12876 -0.4202 0.39873] [ 0. 0. 0. 0.58509 0.02033 -0.03431] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.42764 0.31088 0.01536 0.18956 1.15184] [ 0. 0.45924 -0.38636 -0.11389 -0.07039 -0.26958] [ 0. 0.60026 0.07899 0.02673 -0.07968 0.11083] [ 0. 0. 0. 0.1617 -0.54891 -0.27174] [ 0. 0. 0. 0.45638 -0.01261 0.2938 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.28398 0.44596 -0.11884 -0.14848 1.15184] [ 0. 0.09356 -0.62281 0.03064 0.0805 0.09403] [ 0. 0.36382 0.44467 -0.13214 0.0104 0.27589] [ 0. 0. 0. 0.06415 -0.60077 0.06071] [ 0. 0. 0. 0.40452 0.08493 -0.39557] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.14055 -0.50968 0.1825 0.05351 1.15184] [ 0. 0.41572 -0.65485 0.12368 -0.0301 0.14168] [ 0. 0.33177 0.12251 -0.0157 0.09241 -0.25472] [ 0. 0. 0. -0.0212 -0.52649 0.17707] [ 0. 0. 0. 0.4788 0.17029 0.3589 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.51234 -0.1305 -0.16817 0.08882 1.15184] [ 0. 0.12898 -0.32613 -0.0518 -0.07931 -0.25746] [ 0. 0.66049 0.40925 0.06875 -0.10625 -0.13665] [ 0. 0. 0. 0.04797 -0.40762 -0.37711] [ 0. 0. 0. 0.59767 0.10111 -0.13397] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.08864 0.52122 0.05047 -0.18336 1.15184] [ 0. 0.23909 -0.70938 -0.01013 0.10556 -0.02041] [ 0. 0.27724 0.29914 -0.09755 -0.06501 0.29076] [ 0. 0. 0. 0.17103 -0.48199 0.35591] [ 0. 0. 0. 0.5233 -0.02194 -0.183 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.38603 -0.36125 0.07122 0.17635 1.15184] [ 0. 0.47964 -0.43616 0.1285 0.04332 0.25385] [ 0. 0.55047 0.05859 -0.01773 0.07929 -0.14324] [ 0. 0. 0. 0.11983 -0.59031 -0.17171] [ 0. 0. 0. 0.41498 0.02926 0.36149] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.31927 -0.42142 -0.15619 -0.10851 1.15184] [ 0. 0.07491 -0.59267 -0.04206 -0.07209 -0.11613] [ 0. 0.39395 0.46332 0.12755 -0.04186 -0.26734] [ 0. 0. 0. 0.01229 -0.5792 -0.05439] [ 0. 0. 0. 0.42609 0.1368 -0.39649] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.10497 0.51818 0.18967 -0.01396 1.15184] [ 0. 0.39202 -0.67354 -0.10622 0.06507 -0.12373] [ 0. 0.31309 0.14621 -0.01042 -0.09677 0.26391] [ 0. 0. 0. -0.01328 -0.45767 0.29179] [ 0. 0. 0. 0.54762 0.16237 0.2739 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.52586 0.0547 -0.11767 0.14941 1.15184] [ 0. 0.18294 -0.29291 0.07582 0.06908 0.27458] [ 0. 0.69371 0.35529 -0.03106 0.1162 0.0978 ] [ 0. 0. 0. 0.1272 -0.4192 -0.39903] [ 0. 0. 0. 0.58609 0.02188 0.03057] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.11977 -0.51496 0.01397 0.18967 1.15184] [ 0. 0.21341 -0.70422 0.019 0.10095 0.00292] [ 0. 0.2824 0.32482 -0.11506 -0.03464 -0.29146] [ 0. 0. -0. 0.16236 -0.54763 -0.27388] [ 0. 0. -0. 0.45766 -0.01328 0.2918 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.34283 0.40248 -0.11788 -0.14925 1.15184] [ 0. 0.48709 -0.48479 0.13522 0.01459 -0.23608] [ 0. 0.50183 0.05114 -0.01006 0.07994 0.17095] [ 0. 0. -0. 0.06543 -0.6009 0.06327] [ 0. 0. -0. 0.4044 0.08366 -0.39517] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.35522 0.39159 0.18208 0.05491 1.15184] [ 0. 0.06046 -0.55697 -0.05248 -0.06233 0.13928] [ 0. 0.42965 0.47777 0.11344 -0.07403 0.25604] [ 0. 0. -0. -0.02083 -0.52796 0.17431] [ 0. 0. -0. 0.47734 0.16991 0.36024] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.07075 -0.52395 -0.16901 0.0872 1.15184] [ 0. 0.36737 -0.68808 -0.07516 0.09571 0.10615] [ 0. 0.29855 0.17086 -0.04268 -0.09141 -0.27146] [ 0. 0. -0. 0.04616 -0.40814 -0.37581] [ 0. 0. -0. 0.59715 0.10293 -0.13757] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.5281 0.02512 0.05201 -0.18293 1.15184] [ 0. 0.24653 -0.27634 0.09762 0.05263 -0.28617] [ 0. 0.71028 0.2917 0.00076 0.11264 -0.05533] [ 0. 0. -0. 0.17067 -0.48037 0.35743] [ 0. 0. -0. 0.52492 -0.02158 -0.18001] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.15121 0.50662 -0.07004 -0.17682 1.15184] [ 0. 0.18794 -0.69579 0.04083 0.09056 0.01501] [ 0. 0.29083 0.35029 -0.12289 -0.00423 0.29109] [ 0. 0. 0. 0.12099 -0.5897 0.17411] [ 0. 0. 0. 0.41559 0.0281 -0.36034] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.29965 -0.43558 -0.15544 -0.10958 1.15184] [ 0. 0.48423 -0.52953 -0.13442 0.01615 0.21726] [ 0. 0.45709 0.054 0.00073 -0.08159 -0.19431] [ 0. 0. -0. 0.01334 -0.58004 -0.05169] [ 0. 0. -0. 0.42525 0.13575 -0.39685] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.39136 -0.35547 0.18978 -0.0123 1.15184] [ 0. 0.05212 -0.51569 0.06289 0.05036 -0.16334] [ 0. 0.47093 0.48611 -0.08682 0.10469 -0.24141] [ 0. 0. -0. -0.01406 -0.45921 0.28938] [ 0. 0. -0. 0.54608 0.16314 0.27644] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.03766 0.52736 -0.11906 0.1483 1.15184] [ 0. 0.34215 -0.69887 0.03457 -0.11359 -0.08887] [ 0. 0.28775 0.19608 0.07409 0.07351 0.2776 ] [ 0. 0. -0. 0.12563 -0.41823 -0.3993 ] [ 0. 0. -0. 0.58706 0.02346 0.02682] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.51814 -0.10513 0.01258 0.18977 1.15184] [ 0. 0.31279 -0.27958 0.11424 0.03261 0.29126] [ 0. 0.70704 0.22544 0.0215 0.10205 0.01117] [ 0. 0. 0. 0.16301 -0.54634 -0.27601] [ 0. 0. 0. 0.45895 -0.01393 0.28979] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.18316 -0.49596 0.11691 0.15001 1.15184] [ 0. 0.16286 -0.68383 0.05692 0.07722 -0.03351] [ 0. 0.30279 0.37537 -0.123 0.02561 -0.28954] [ 0. 0. -0. 0.0667 -0.60101 -0.06583] [ 0. 0. -0. 0.40429 0.08239 0.39475] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.2575 0.46175 0.18166 0.05629 1.15184] [ 0. 0.47369 -0.56905 -0.12464 0.04928 -0.19809] [ 0. 0.41757 0.06454 -0.01284 -0.08283 0.21382] [ 0. 0. 0. -0.02043 -0.52941 0.17156] [ 0. 0. 0. 0.47588 0.16952 0.36156] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.4268 0.31204 0.16984 -0.08558 1.15184] [ 0. 0.05227 -0.4695 -0.07302 -0.03541 0.18799] [ 0. 0.51713 0.48596 0.04693 -0.12728 0.22275] [ 0. 0. -0. 0.04436 -0.4087 0.37448] [ 0. 0. -0. 0.59659 0.10473 0.14116] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.00544 -0.52867 -0.05355 0.18249 1.15184] [ 0. 0.31659 -0.70623 0.00543 0.11555 0.07178] [ 0. 0.2804 0.22164 -0.09702 -0.04685 -0.2825 ] [ 0. 0. -0. 0.17028 -0.47876 -0.35893] [ 0. 0. -0. 0.52653 -0.02119 0.17699] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.49664 0.18131 0.06886 0.17728 1.15184] [ 0. 0.37394 -0.302 -0.12505 -0.01049 -0.28967] [ 0. 0.68462 0.16429 -0.03279 -0.09036 0.03243] [ 0. 0. 0. 0.12215 -0.58908 -0.1765 ] [ 0. 0. 0. 0.41622 0.02694 0.35918] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.21581 0.48265 0.15469 0.11063 1.15184] [ 0. 0.13847 -0.66801 -0.06896 -0.06171 0.05274] [ 0. 0.31861 0.39976 0.11552 -0.0555 0.28666] [ 0. 0. -0. 0.0144 -0.58087 0.04899] [ 0. 0. -0. 0.42442 0.13469 0.39719] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.21689 -0.48216 -0.18988 0.01064 1.15184] [ 0. 0.45771 -0.60294 -0.10276 0.08307 0.179 ] [ 0. 0.38368 0.08052 -0.03223 -0.08057 -0.23004] [ 0. 0. -0. -0.0148 -0.46077 -0.28696] [ 0. 0. -0. 0.54453 0.16389 -0.27896] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.46015 -0.26036 -0.12045 0.14717 1.15184] [ 0. 0.06362 -0.42011 -0.08158 -0.01841 -0.21258] [ 0. 0.56651 0.47461 0.00069 -0.13414 -0.19941] [ 0. 0. 0. 0.12403 -0.41728 -0.39953] [ 0. 0. 0. 0.58801 0.02506 0.02306] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.02614 0.52805 -0.01118 -0.18985 1.15184] [ 0. 0.29087 -0.71037 0.03763 0.10607 -0.05478] [ 0. 0.27625 0.24736 -0.10958 -0.01772 0.28628] [ 0. 0. 0. 0.16365 -0.54503 0.27814] [ 0. 0. 0. 0.46026 -0.01456 -0.28775] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.46565 -0.25038 0.11593 0.15076 1.15184] [ 0. 0.42375 -0.33944 0.12982 -0.01378 0.28206] [ 0. 0.64718 0.11448 0.03873 0.08029 -0.07347] [ 0. 0. 0. 0.06797 -0.6011 -0.06838] [ 0. 0. 0. 0.40419 0.08111 0.39431] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.24929 -0.46624 0.18123 0.05767 1.15184] [ 0. 0.1152 -0.6479 0.07785 0.04364 -0.07281] [ 0. 0.33872 0.42303 -0.09858 0.08548 -0.28223] [ 0. 0. -0. -0.02001 -0.53085 0.1688 ] [ 0. 0. -0. 0.47444 0.1691 0.36286] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.17801 0.49783 0.17065 -0.08396 1.15184] [ 0. 0.43803 -0.63135 -0.0668 0.11136 -0.16021] [ 0. 0.35527 0.1002 -0.05602 -0.07063 0.2435 ] [ 0. 0. 0. 0.04257 -0.4093 0.37311] [ 0. 0. 0. 0.59599 0.10652 0.14473] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.48944 0.19994 -0.05509 0.18203 1.15184] [ 0. 0.08862 -0.3708 0.08818 0.0017 0.23614] [ 0. 0.61583 0.44961 0.03976 0.12502 0.17086] [ 0. 0. 0. 0.16986 -0.47715 -0.36041] [ 0. 0. 0. 0.52814 -0.02078 0.17396] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.05733 -0.52558 -0.06768 -0.17773 1.15184] [ 0. 0.26508 -0.71142 -0.06113 -0.09066 0.03775] [ 0. 0.2752 0.27315 0.11366 -0.01066 -0.28902] [ 0. 0. 0. 0.12329 -0.58843 0.17889] [ 0. 0. 0. 0.41686 0.02579 -0.35799] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.42797 0.31043 -0.15394 -0.11168 1.15184] [ 0. 0.45901 -0.38595 0.12751 -0.04076 -0.2697 ] [ 0. 0.60067 0.07922 0.04325 0.0721 0.11054] [ 0. 0. -0. 0.01547 -0.58168 -0.04629] [ 0. 0. -0. 0.42361 0.13362 -0.39751] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.28369 0.44614 0.18997 -0.00899 1.15184] [ 0. 0.09373 -0.62303 -0.0832 -0.0224 0.09386] [ 0. 0.36359 0.4445 0.06913 -0.11307 0.27595] [ 0. 0. -0. -0.01552 -0.46233 0.28452] [ 0. 0. -0. 0.54296 0.1646 0.28144] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.14085 -0.50959 0.12183 -0.14603 1.15184] [ 0. 0.41591 -0.65468 0.02166 -0.12546 0.14183] [ 0. 0.33194 0.12232 0.0785 0.05117 -0.25464] [ 0. 0. 0. 0.12241 -0.41636 0.39973] [ 0. 0. 0. 0.58893 0.02667 -0.0193 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.51219 -0.1311 0.00978 0.18993 1.15184] [ 0. 0.12859 -0.32646 -0.09367 0.01373 -0.2573 ] [ 0. 0.66016 0.40964 -0.06755 -0.10707 -0.13695] [ 0. 0. 0. 0.16426 -0.54371 -0.28025] [ 0. 0. 0. 0.46158 -0.01518 0.28569] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.08838 0.52126 -0.11496 -0.15151 1.15184] [ 0. 0.2393 -0.70941 0.07774 0.07217 -0.02056] [ 0. 0.27721 0.29893 -0.11087 0.038 0.29075] [ 0. 0. 0. 0.06925 -0.60118 0.07093] [ 0. 0. 0. 0.40412 0.07984 -0.39386] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.38638 -0.36088 0.18078 0.05905 1.15184] [ 0. 0.47953 -0.43575 0.11583 -0.0705 0.25399] [ 0. 0.55088 0.0587 0.04937 0.06454 -0.14299] [ 0. 0. 0. -0.01957 -0.53228 0.16605] [ 0. 0. 0. 0.47301 0.16866 0.36413] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.31897 -0.42164 -0.17144 0.08233 1.15184] [ 0. 0.07505 -0.59294 -0.08348 0.00112 -0.11595] [ 0. 0.39368 0.46318 0.02645 -0.1316 -0.26742] [ 0. 0. 0. 0.0408 -0.40992 -0.37172] [ 0. 0. 0. 0.59537 0.10829 -0.14828] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.10525 0.51812 -0.05663 0.18156 1.15184] [ 0. 0.39222 -0.6734 -0.0216 -0.1227 -0.12387] [ 0. 0.31322 0.14601 0.09383 0.02576 0.26384] [ 0. 0. -0. 0.16942 -0.47554 -0.36187] [ 0. 0. -0. 0.52976 -0.02033 0.1709 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.5258 0.05535 -0.06649 -0.17818 1.15184] [ 0. 0.18245 -0.29312 -0.09832 0.02898 0.27446] [ 0. 0.6935 0.35578 -0.08325 -0.0869 0.09814] [ 0. 0. -0. 0.12444 -0.58777 0.18128] [ 0. 0. -0. 0.41752 0.02465 -0.35679] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.11951 -0.51502 0.15318 0.11272 1.15184] [ 0. 0.21362 -0.70428 0.0891 0.05117 0.00307] [ 0. 0.28234 0.32461 -0.10109 0.06491 -0.29146] [ 0. 0. -0. 0.01654 -0.58247 0.0436 ] [ 0. 0. -0. 0.42282 0.13254 0.39782] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.34319 0.40218 -0.19004 0.00734 1.15184] [ 0. 0.48708 -0.4844 0.09139 -0.10072 -0.23623] [ 0. 0.50222 0.05115 0.05876 0.05513 0.17074] [ 0. 0. -0. -0.0162 -0.4639 -0.28206] [ 0. 0. -0. 0.54139 0.16529 -0.2839 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.35492 0.39186 -0.12321 0.14488 1.15184] [ 0. 0.06056 -0.55729 0.07811 -0.02324 0.13909] [ 0. 0.42934 0.47767 0.02249 0.13357 0.25615] [ 0. 0. 0. 0.12078 -0.41548 -0.3999 ] [ 0. 0. 0. 0.58982 0.02831 0.01552] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.07102 -0.52391 0.00838 0.19 1.15184] [ 0. 0.36758 -0.68797 0.05547 0.10835 0.10629] [ 0. 0.29865 0.17065 -0.10086 0.00052 -0.2714 ] [ 0. 0. -0. 0.16486 -0.54238 -0.28236] [ 0. 0. -0. 0.46291 -0.01577 0.28361] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.52813 0.02446 0.11397 0.15225 1.15184] [ 0. 0.24598 -0.2764 -0.10092 0.04583 -0.2861 ] [ 0. 0.71023 0.29225 -0.09018 -0.06761 -0.05569] [ 0. 0. 0. 0.07052 -0.60124 -0.07348] [ 0. 0. 0. 0.40406 0.07856 0.3934 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.15095 0.50669 0.18033 0.06041 1.15184] [ 0. 0.18815 -0.69587 -0.0956 -0.0271 0.01486] [ 0. 0.29075 0.35008 0.0824 -0.09125 0.2911 ] [ 0. 0. -0. -0.01911 -0.5337 0.16329] [ 0. 0. -0. 0.47159 0.1682 0.36537] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.30001 -0.43534 -0.17222 0.08069 1.15184] [ 0. 0.48429 -0.52919 -0.05254 0.12479 0.21742] [ 0. 0.45744 0.05394 -0.07054 -0.04098 -0.19413] [ 0. 0. -0. 0.03904 -0.41058 -0.37029] [ 0. 0. -0. 0.59471 0.11005 -0.15181] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.39106 -0.3558 -0.05817 0.18107 1.15184] [ 0. 0.05216 -0.51606 -0.06986 0.04014 -0.16314] [ 0. 0.47057 0.48607 -0.0656 -0.11914 -0.24154] [ 0. 0. 0. 0.16894 -0.47393 -0.36331] [ 0. 0. 0. 0.53136 -0.01986 0.16782] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.03792 0.52734 -0.0653 -0.17862 1.15184] [ 0. 0.34236 -0.69879 0.07936 0.08834 -0.08901] [ 0. 0.28783 0.19587 -0.1012 0.02541 0.27755] [ 0. 0. 0. 0.12557 -0.5871 0.18366] [ 0. 0. 0. 0.41819 0.02352 -0.35557] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.51827 -0.10448 -0.15241 -0.11375 1.15184] [ 0. 0.31225 -0.27947 -0.0989 0.0657 0.29125] [ 0. 0.70715 0.22598 -0.09166 -0.04988 0.01154] [ 0. 0. -0. 0.01763 -0.58325 -0.04091] [ 0. 0. -0. 0.42204 0.13146 -0.3981 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.18289 -0.49606 0.1901 -0.0057 1.15184] [ 0. 0.16307 -0.68395 0.09596 -0.00036 -0.03336] [ 0. 0.30268 0.37516 -0.05196 0.11437 -0.28956] [ 0. 0. -0. -0.01686 -0.46547 0.2796 ] [ 0. 0. -0. 0.53982 0.16595 0.28633] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.25784 0.46156 0.12457 -0.14371 1.15184] [ 0. 0.4738 -0.56875 -0.00492 0.13395 -0.19825] [ 0. 0.41787 0.06443 -0.081 -0.02144 0.21367] [ 0. 0. 0. 0.11912 -0.41462 0.40003] [ 0. 0. 0. 0.59067 0.02996 -0.01175] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.42651 0.31243 -0.00697 -0.19005 1.15184] [ 0. 0.05223 -0.46989 -0.06254 0.0517 0.18778] [ 0. 0.51673 0.486 -0.09617 -0.09569 0.22292] [ 0. 0. -0. 0.16544 -0.54104 0.28446] [ 0. 0. -0. 0.46426 -0.01635 -0.2815 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.00571 -0.52867 -0.11299 -0.15298 1.15184] [ 0. 0.3168 -0.70618 -0.09537 -0.06551 0.07192] [ 0. 0.28044 0.22143 0.09593 -0.04899 -0.28246] [ 0. 0. 0. 0.0718 -0.60128 0.07602] [ 0. 0. 0. 0.40401 0.07729 -0.39291] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.49686 0.1807 -0.17987 -0.06177 1.15184] [ 0. 0.37348 -0.30175 0.08859 -0.08882 -0.2897 ] [ 0. 0.68487 0.16475 0.0903 0.03314 0.03208] [ 0. 0. -0. -0.01864 -0.53511 -0.16053] [ 0. 0. -0. 0.47018 0.16772 -0.36659] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.21553 0.48277 0.17298 -0.07905 1.15184] [ 0. 0.13867 -0.66816 -0.08786 0.02914 0.05257] [ 0. 0.31847 0.39956 0.00936 -0.1278 0.28669] [ 0. 0. -0. 0.03729 -0.41128 0.36883] [ 0. 0. -0. 0.59402 0.1118 0.15533] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.21722 -0.48202 0.05971 -0.18057 1.15184] [ 0. 0.45786 -0.60269 -0.03967 -0.12605 0.17915] [ 0. 0.38394 0.08037 0.08675 -0.00054 -0.22992] [ 0. 0. 0. 0.16844 -0.47232 0.36473] [ 0. 0. 0. 0.53297 -0.01935 -0.16472] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.45989 -0.26082 0.0641 0.17906 1.15184] [ 0. 0.06347 -0.42053 -0.05769 0.06051 -0.21238] [ 0. 0.5661 0.47476 -0.11468 -0.06963 -0.19963] [ 0. 0. 0. 0.1267 -0.58641 -0.18604] [ 0. 0. 0. 0.41888 0.02239 0.35433] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.02588 0.52807 0.15164 0.11478 1.15184] [ 0. 0.29108 -0.71035 -0.10514 -0.04022 -0.05492] [ 0. 0.27628 0.24715 0.08458 -0.07185 0.28625] [ 0. 0. -0. 0.01872 -0.58401 0.03822] [ 0. 0. -0. 0.42128 0.13037 0.39837] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.46594 -0.24985 0.19014 -0.00406 1.15184] [ 0. 0.4234 -0.33909 0.06573 -0.11276 0.28215] [ 0. 0.64753 0.11483 0.0877 0.01624 -0.07315] [ 0. 0. 0. -0.01749 -0.46706 0.27711] [ 0. 0. 0. 0.53823 0.16657 0.28873] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.24901 -0.46639 0.12592 -0.14252 1.15184] [ 0. 0.11539 -0.64808 0.07133 -0.05368 -0.07264] [ 0. 0.33854 0.42284 0.03846 0.12466 -0.28228] [ 0. 0. -0. 0.11745 -0.41379 0.40012] [ 0. 0. -0. 0.5915 0.03164 -0.00796] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.17833 0.49772 -0.00555 -0.1901 1.15184] [ 0. 0.4382 -0.63114 0.07364 0.10698 -0.16036] [ 0. 0.35548 0.10003 -0.08746 0.02172 0.2434 ] [ 0. 0. 0. 0.166 -0.53968 0.28655] [ 0. 0. 0. 0.46561 -0.01692 -0.27938] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.48922 0.20047 0.11199 0.15371 1.15184] [ 0. 0.08836 -0.37119 0.05439 -0.06936 0.23596] [ 0. 0.61543 0.44987 0.12377 0.04359 0.17112] [ 0. 0. 0. 0.07307 -0.60131 -0.07856] [ 0. 0. 0. 0.40398 0.07601 0.39241] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.05708 -0.52561 -0.1794 -0.06312 1.15184] [ 0. 0.26529 -0.71142 -0.10873 -0.01184 0.03789] [ 0. 0.2752 0.27294 0.06522 -0.09367 -0.289 ] [ 0. 0. 0. -0.01814 -0.53651 -0.15777] [ 0. 0. 0. 0.46879 0.16722 -0.36779] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.4283 0.30997 -0.17372 0.0774 1.15184] [ 0. 0.45879 -0.38555 0.02842 -0.13079 -0.26982] [ 0. 0.60107 0.07944 0.0841 -0.00151 0.11026] [ 0. 0. -0. 0.03556 -0.412 -0.36733] [ 0. 0. -0. 0.59329 0.11353 -0.15883] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.2834 0.44633 0.06125 -0.18005 1.15184] [ 0. 0.0939 -0.62326 -0.05128 0.06927 0.09368] [ 0. 0.36336 0.44433 -0.07991 -0.10571 0.27601] [ 0. 0. -0. 0.16791 -0.47072 0.36612] [ 0. 0. -0. 0.53457 -0.01882 -0.16159] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.14115 -0.50951 0.0629 0.17948 1.15184] [ 0. 0.4161 -0.65451 0.09665 0.0829 0.14198] [ 0. 0.33212 0.12213 -0.08412 0.0412 -0.25456] [ 0. 0. -0. 0.12782 -0.5857 -0.18841] [ 0. 0. -0. 0.41959 0.02127 0.35307] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.51203 -0.1317 0.15087 0.1158 1.15184] [ 0. 0.1282 -0.32679 -0.05019 0.0802 -0.25714] [ 0. 0.65983 0.41003 -0.12536 -0.01798 -0.13725] [ 0. 0. 0. 0.01982 -0.58475 0.03553] [ 0. 0. 0. 0.42054 0.12927 0.39862] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.08812 0.5213 -0.19017 0.00242 1.15184] [ 0. 0.23951 -0.70944 0.10426 -0.01969 -0.0207 ] [ 0. 0.27718 0.29872 -0.03527 0.11175 0.29074] [ 0. 0. 0. -0.01809 -0.46865 -0.27462] [ 0. 0. 0. 0.53665 0.16717 -0.29111] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.38674 -0.3605 -0.12727 0.14132 1.15184] [ 0. 0.47941 -0.43533 0.01756 0.13444 0.25413] [ 0. 0.55129 0.05882 -0.079 0.01909 -0.14274] [ 0. 0. -0. 0.11576 -0.41299 -0.40018] [ 0. 0. -0. 0.5923 0.03333 0.00417] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.31868 -0.42186 0.00413 0.19014 1.15184] [ 0. 0.07519 -0.59321 -0.0334 0.07653 -0.11576] [ 0. 0.39341 0.46304 -0.10894 -0.07841 -0.2675 ] [ 0. 0. 0. 0.16655 -0.53831 -0.28862] [ 0. 0. 0. 0.46698 -0.01746 0.27723] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.10554 0.51806 -0.111 -0.15443 1.15184] [ 0. 0.39242 -0.67326 0.11106 0.0565 -0.12402] [ 0. 0.31336 0.14581 -0.07694 0.0595 0.26377] [ 0. 0. 0. 0.07435 -0.60132 0.08109] [ 0. 0. 0. 0.40397 0.07474 -0.3919 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.52573 0.056 0.17892 0.06446 1.15184] [ 0. 0.18195 -0.29334 0.04131 -0.09374 0.27433] [ 0. 0.69329 0.35628 0.12017 -0.00745 0.09848] [ 0. 0. 0. -0.01762 -0.53789 0.15501] [ 0. 0. 0. 0.4674 0.16671 0.36896] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.11925 -0.51508 0.17445 -0.07575 1.15184] [ 0. 0.21383 -0.70433 0.08902 -0.05135 0.00321] [ 0. 0.28229 0.3244 0.00534 0.11999 -0.29146] [ 0. 0. -0. 0.03385 -0.41276 0.36581] [ 0. 0. -0. 0.59253 0.11524 0.16231] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.34355 0.40187 -0.06279 0.17952 1.15184] [ 0. 0.48706 -0.48401 -0.06031 -0.12191 -0.23638] [ 0. 0.50261 0.05117 0.07277 -0.03459 0.17053] [ 0. 0. -0. 0.16735 -0.46913 -0.3675 ] [ 0. 0. -0. 0.53616 -0.01826 0.15845] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.35463 0.39213 -0.06169 -0.1799 1.15184] [ 0. 0.06066 -0.5576 -0.01979 0.07907 0.13889] [ 0. 0.42902 0.47757 -0.12635 -0.04878 0.25626] [ 0. 0. -0. 0.12893 -0.58498 0.19078] [ 0. 0. -0. 0.42032 0.02016 -0.3518 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.0713 -0.52387 -0.15008 -0.11681 1.15184] [ 0. 0.36778 -0.68787 -0.11849 -0.02797 0.10644] [ 0. 0.29876 0.17045 0.06493 -0.07714 -0.27135] [ 0. 0. 0. 0.02093 -0.58548 -0.03285] [ 0. 0. 0. 0.41981 0.12816 -0.39885] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.52816 0.02379 0.19018 -0.00079 1.15184] [ 0. 0.24544 -0.27646 -0.0232 0.10831 -0.28603] [ 0. 0.71017 0.29279 -0.10807 0.03226 -0.05605] [ 0. 0. 0. -0.01866 -0.47024 0.27211] [ 0. 0. 0. 0.53505 0.16774 0.29345] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.15069 0.50677 -0.1286 0.14011 1.15184] [ 0. 0.18835 -0.69596 0.06365 -0.07634 0.01471] [ 0. 0.29067 0.34987 0.04982 0.11237 0.2911 ] [ 0. 0. 0. 0.11405 -0.41223 -0.4002 ] [ 0. 0. 0. 0.59306 0.03504 0.00037] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.30036 -0.4351 0.00271 0.19016 1.15184] [ 0. 0.48435 -0.52884 0.09218 0.09918 0.21758] [ 0. 0.45779 0.05388 -0.06629 0.04752 -0.19395] [ 0. 0. -0. 0.16707 -0.53693 -0.29069] [ 0. 0. -0. 0.46836 -0.01798 0.27506] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.39077 -0.35613 -0.11 -0.15514 1.15184] [ 0. 0.0522 -0.51642 0.00967 -0.07999 -0.16294] [ 0. 0.47021 0.48603 0.13468 0.0189 -0.24168] [ 0. 0. -0. 0.07563 -0.60131 0.08363] [ 0. 0. -0. 0.40398 0.07346 -0.39136] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.03819 0.52732 0.17844 0.0658 1.15184] [ 0. 0.34256 -0.69872 -0.11873 0.00339 -0.08915] [ 0. 0.2879 0.19566 0.04605 -0.09359 0.27751] [ 0. 0. -0. -0.01708 -0.53926 0.15225] [ 0. 0. -0. 0.46603 0.16617 0.37011] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.5184 -0.10383 -0.17516 0.07409 1.15184] [ 0. 0.31172 -0.27937 0.00687 0.11848 0.29123] [ 0. 0.70726 0.22651 -0.08934 0.05406 0.01191] [ 0. 0. -0. 0.03215 -0.41354 -0.36425] [ 0. 0. -0. 0.59175 0.11694 -0.16577] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.18263 -0.49616 -0.06433 0.17897 1.15184] [ 0. 0.16327 -0.68406 -0.03477 0.08947 -0.0332 ] [ 0. 0.30256 0.37496 -0.08741 -0.09019 -0.28958] [ 0. 0. 0. 0.16676 -0.46754 -0.36884] [ 0. 0. 0. 0.53775 -0.01767 0.15529] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.25819 0.46137 0.06047 0.18031 1.15184] [ 0. 0.47391 -0.56844 -0.11291 -0.07226 -0.19841] [ 0. 0.41818 0.06432 0.05954 -0.05893 0.21352] [ 0. 0. -0. 0.13003 -0.58424 -0.19315] [ 0. 0. -0. 0.42106 0.01905 0.3505 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.42623 0.31282 0.1493 0.11781 1.15184] [ 0. 0.05219 -0.47029 0.00101 -0.08113 0.18758] [ 0. 0.51633 0.48604 0.1352 -0.01135 0.2231 ] [ 0. 0. 0. 0.02205 -0.58619 0.03017] [ 0. 0. 0. 0.4191 0.12704 0.39906] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.00597 -0.52867 -0.19018 -0.00084 1.15184] [ 0. 0.31702 -0.70613 -0.10953 0.03737 0.07206] [ 0. 0.28049 0.22121 0.01799 -0.10617 -0.28243] [ 0. 0. 0. -0.0192 -0.47184 -0.26959] [ 0. 0. 0. 0.53345 0.16828 -0.29577] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.49708 0.1801 -0.12993 0.13888 1.15184] [ 0. 0.37301 -0.3015 -0.0449 -0.11708 -0.28974] [ 0. 0.68513 0.16522 0.06712 -0.06899 0.03173] [ 0. 0. -0. 0.11232 -0.41149 -0.40018] [ 0. 0. -0. 0.5938 0.03676 -0.00343] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.21526 0.48289 0.00128 0.19018 1.15184] [ 0. 0.13886 -0.6683 0.00934 -0.09213 0.05241] [ 0. 0.31832 0.39937 0.11276 0.06082 0.28672] [ 0. 0. 0. 0.16757 -0.53553 -0.29275] [ 0. 0. 0. 0.46976 -0.01849 0.27287] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.21755 -0.48187 0.10899 0.15585 1.15184] [ 0. 0.45801 -0.60243 0.12478 0.04356 0.17931] [ 0. 0.38419 0.08022 -0.05137 0.06987 -0.2298 ] [ 0. 0. -0. 0.0769 -0.60129 -0.08616] [ 0. 0. -0. 0.404 0.07218 0.39082] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.45963 -0.26128 0.17794 0.06713 1.15184] [ 0. 0.06332 -0.42094 0.00888 0.0831 -0.21218] [ 0. 0.56568 0.4749 -0.12731 0.04237 -0.19984] [ 0. 0. 0. -0.01653 -0.54062 0.14949] [ 0. 0. 0. 0.46467 0.16561 0.37123] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.02562 0.52808 0.17585 -0.07243 1.15184] [ 0. 0.29129 -0.71033 -0.088 0.07025 -0.05506] [ 0. 0.2763 0.24694 -0.01904 -0.10931 0.28623] [ 0. 0. -0. 0.03047 -0.41436 0.36267] [ 0. 0. -0. 0.59093 0.11862 0.16921] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.46623 -0.24931 0.06587 -0.17841 1.15184] [ 0. 0.42304 -0.33874 -0.0809 -0.10237 0.28223] [ 0. 0.64789 0.11519 0.04714 -0.07577 -0.07282] [ 0. 0. 0. 0.16614 -0.46595 0.37017] [ 0. 0. 0. 0.53934 -0.01705 -0.1521 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.24873 -0.46654 -0.05926 -0.18072 1.15184] [ 0. 0.11557 -0.64827 -0.01031 -0.0887 -0.07247] [ 0. 0.33835 0.42266 0.12699 0.02983 -0.28232] [ 0. 0. -0. 0.13113 -0.58348 0.19551] [ 0. 0. -0. 0.42181 0.01796 -0.34919] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.17864 0.49761 -0.1485 -0.11881 1.15184] [ 0. 0.43838 -0.63093 0.12924 0.01306 -0.16052] [ 0. 0.35569 0.09985 -0.03997 0.08074 0.24329] [ 0. 0. 0. 0.02317 -0.58689 -0.0275 ] [ 0. 0. 0. 0.4184 0.12591 -0.39925] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.489 0.20101 0.19017 0.00246 1.15184] [ 0. 0.08809 -0.37159 -0.02305 -0.08503 0.23577] [ 0. 0.61504 0.45014 0.10905 -0.07305 0.17138] [ 0. 0. 0. -0.01971 -0.47344 0.26706] [ 0. 0. 0. 0.53185 0.16879 0.29806] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.05682 -0.52564 0.13124 -0.13764 1.15184] [ 0. 0.2655 -0.71143 0.05543 -0.09432 0.03803] [ 0. 0.2752 0.27273 0.05864 0.09789 -0.28898] [ 0. 0. -0. 0.11058 -0.41079 0.40013] [ 0. 0. -0. 0.5945 0.0385 0.00724] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.42863 0.30951 -0.00015 0.19018 1.15184] [ 0. 0.45856 -0.38515 -0.10787 -0.0792 -0.26993] [ 0. 0.60148 0.07967 0.0328 -0.07749 0.10997] [ 0. 0. -0. 0.16806 -0.53413 -0.29479] [ 0. 0. -0. 0.47116 -0.01897 0.27066] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.28312 0.44651 0.10798 0.15655 1.15184] [ 0. 0.09406 -0.62348 -0.0251 -0.08247 0.0935 ] [ 0. 0.36314 0.44416 0.1325 -0.00113 0.27607] [ 0. 0. 0. 0.07818 -0.60125 -0.08868] [ 0. 0. 0. 0.40404 0.07091 0.39025] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.14145 -0.50943 0.17744 0.06844 1.15184] [ 0. 0.41629 -0.65433 0.12579 -0.01992 0.14213] [ 0. 0.33229 0.12194 -0.02308 0.09075 -0.25447] [ 0. 0. -0. -0.01595 -0.54197 0.14673] [ 0. 0. -0. 0.46332 0.16504 0.37233] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.51188 -0.1323 0.17653 -0.07077 1.15184] [ 0. 0.12781 -0.32712 0.04351 0.08394 -0.25698] [ 0. 0.6595 0.41042 -0.07932 0.09878 -0.13755] [ 0. 0. 0. 0.02881 -0.41521 0.36105] [ 0. 0. 0. 0.59008 0.12028 0.17263] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.08787 0.52135 -0.06741 0.17783 1.15184] [ 0. 0.23972 -0.70947 0.01983 -0.10426 -0.02084] [ 0. 0.27716 0.2985 0.09107 0.0737 0.29073] [ 0. 0. 0. 0.16549 -0.46438 -0.37147] [ 0. 0. 0. 0.54092 -0.0164 0.14889] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.38709 -0.36012 -0.05803 -0.18111 1.15184] [ 0. 0.4793 -0.43492 -0.12503 -0.05243 0.25427] [ 0. 0.5517 0.05893 0.02315 -0.07792 -0.14249] [ 0. 0. 0. 0.13222 -0.58271 0.19786] [ 0. 0. 0. 0.42258 0.01687 -0.34786] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.31838 -0.42208 0.1477 0.1198 1.15184] [ 0. 0.07533 -0.59348 0.03687 0.07494 -0.11558] [ 0. 0.39314 0.4629 -0.13023 0.03244 -0.26758] [ 0. 0. 0. 0.02431 -0.58757 0.02482] [ 0. 0. 0. 0.41772 0.12478 0.39943] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.10583 0.518 -0.19014 -0.00408 1.15184] [ 0. 0.39262 -0.67312 0.1119 -0.05487 -0.12417] [ 0. 0.3135 0.14561 0.00139 0.09723 0.2637 ] [ 0. 0. 0. -0.02019 -0.47505 -0.26452] [ 0. 0. 0. 0.53024 0.16928 -0.30032] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.52566 0.05664 -0.13255 0.13638 1.15184] [ 0. 0.18146 -0.29355 0.06839 0.07617 0.27421] [ 0. 0.69307 0.35677 -0.04271 0.11263 0.09882] [ 0. 0. -0. 0.10883 -0.41012 -0.40005] [ 0. 0. -0. 0.59517 0.04026 -0.01105] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.119 -0.51514 0.00159 -0.19018 1.15184] [ 0. 0.21404 -0.70439 -0.01085 -0.10223 0.00336] [ 0. 0.28223 0.32419 0.11182 0.04378 -0.29146] [ 0. 0. -0. 0.16852 -0.53271 0.29683] [ 0. 0. -0. 0.47258 -0.01944 -0.26842] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.3439 0.40156 -0.10697 -0.15725 1.15184] [ 0. 0.48705 -0.48363 0.13388 0.02396 -0.23654] [ 0. 0.503 0.05118 -0.01536 0.07909 0.17032] [ 0. 0. 0. 0.07945 -0.6012 0.0912 ] [ 0. 0. 0. 0.4041 0.06963 -0.38967] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.35433 0.3924 0.17693 0.06976 1.15184] [ 0. 0.06076 -0.55792 -0.04743 -0.06631 0.1387 ] [ 0. 0.4287 0.47747 0.11906 -0.06456 0.25636] [ 0. 0. 0. -0.01536 -0.54331 0.14397] [ 0. 0. 0. 0.46198 0.16445 0.37341] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.07158 -0.52383 -0.17719 0.0691 1.15184] [ 0. 0.36799 -0.68776 -0.08469 0.0875 0.10658] [ 0. 0.29886 0.17024 -0.03305 -0.09523 -0.27129] [ 0. 0. 0. 0.02717 -0.41609 -0.35941] [ 0. 0. 0. 0.5892 0.12192 -0.17603] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.52819 0.02313 -0.06895 0.17724 1.15184] [ 0. 0.24489 -0.27652 -0.09229 -0.06113 -0.28596] [ 0. 0.71011 0.29334 0.00946 -0.11245 -0.05641] [ 0. 0. -0. 0.16481 -0.4628 -0.37275] [ 0. 0. -0. 0.54249 -0.01573 0.14567] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.15043 0.50685 -0.05681 -0.1815 1.15184] [ 0. 0.18856 -0.69604 0.03423 0.09334 0.01456] [ 0. 0.29058 0.34967 -0.12219 -0.01314 0.29111] [ 0. 0. -0. 0.1333 -0.58192 0.20021] [ 0. 0. -0. 0.42337 0.01579 -0.34652] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.30071 -0.43485 0.1469 0.12079 1.15184] [ 0. 0.48441 -0.52849 0.13527 -0.00635 0.21774] [ 0. 0.45814 0.05382 -0.00645 0.0813 -0.19378] [ 0. 0. -0. 0.02544 -0.58823 0.02215] [ 0. 0. -0. 0.41706 0.12364 0.39959] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.39047 -0.35645 -0.1901 -0.00569 1.15184] [ 0. 0.05224 -0.51678 -0.05809 -0.05583 -0.16274] [ 0. 0.46984 0.48599 0.09618 -0.09615 -0.24181] [ 0. 0. -0. -0.02064 -0.47666 -0.26196] [ 0. 0. -0. 0.52863 0.16973 -0.30255] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.03846 0.5273 0.13384 -0.13511 1.15184] [ 0. 0.34277 -0.69864 -0.04609 0.1095 -0.08929] [ 0. 0.28798 0.19546 -0.06611 -0.08065 0.27746] [ 0. 0. -0. 0.10706 -0.40948 0.39992] [ 0. 0. -0. 0.59581 0.04203 0.01486] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.51853 -0.10318 0.00303 -0.19016 1.15184] [ 0. 0.31118 -0.27926 -0.11113 -0.04148 0.29122] [ 0. 0.70736 0.22705 -0.01348 -0.10362 0.01227] [ 0. 0. 0. 0.16897 -0.53128 0.29886] [ 0. 0. 0. 0.47401 -0.01988 -0.26617] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.18236 -0.49625 -0.10595 -0.15794 1.15184] [ 0. 0.16348 -0.68417 -0.05149 -0.08105 -0.03305] [ 0. 0.30245 0.37475 0.12443 -0.01693 -0.2896 ] [ 0. 0. -0. 0.08073 -0.60112 0.09372] [ 0. 0. -0. 0.40417 0.06836 -0.38907] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.25853 0.46118 0.17641 0.07106 1.15184] [ 0. 0.47402 -0.56814 -0.12826 0.03903 -0.19857] [ 0. 0.41848 0.06421 -0.00626 -0.08351 0.21338] [ 0. 0. -0. -0.01475 -0.54463 0.1412 ] [ 0. 0. -0. 0.46066 0.16384 0.37446] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.42594 0.31321 -0.17783 0.06742 1.15184] [ 0. 0.05215 -0.47069 0.0691 0.04249 0.18737] [ 0. 0.51594 0.48608 -0.05975 0.12181 0.22327] [ 0. 0. -0. 0.02554 -0.417 -0.35773] [ 0. 0. -0. 0.58829 0.12354 -0.17941] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.00623 -0.52866 -0.07049 0.17664 1.15184] [ 0. 0.31723 -0.70609 -0.00533 0.11563 0.0722 ] [ 0. 0.28054 0.221 -0.09219 -0.0556 -0.28239] [ 0. 0. 0. 0.16411 -0.46124 -0.374 ] [ 0. 0. 0. 0.54405 -0.01502 0.14242] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.4973 0.1795 0.05557 0.18188 1.15184] [ 0. 0.37254 -0.30124 -0.12384 -0.01936 -0.28978] [ 0. 0.68538 0.16569 -0.02648 -0.09261 0.03138] [ 0. 0. -0. 0.13437 -0.58112 -0.20256] [ 0. 0. -0. 0.42418 0.01472 0.34515] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.21499 0.48302 0.14609 0.12177 1.15184] [ 0. 0.13906 -0.66845 -0.06441 -0.06656 0.05225] [ 0. 0.31817 0.39917 0.1192 -0.04692 0.28675] [ 0. 0. 0. 0.02659 -0.58888 0.01949] [ 0. 0. 0. 0.41641 0.1225 0.39972] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.21788 -0.48172 0.19004 0.00729 1.15184] [ 0. 0.45816 -0.60217 0.11007 -0.07319 0.17947] [ 0. 0.38445 0.08007 0.02472 0.0831 -0.22967] [ 0. 0. -0. -0.02107 -0.47827 0.2594 ] [ 0. 0. -0. 0.52702 0.17016 0.30475] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.45936 -0.26174 -0.13513 0.13383 1.15184] [ 0. 0.06318 -0.42135 -0.07927 -0.0264 -0.21198] [ 0. 0.56527 0.47505 0.01441 -0.13342 -0.20005] [ 0. 0. -0. 0.10527 -0.40888 -0.39976] [ 0. 0. -0. 0.59641 0.04381 -0.01868] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.02536 0.52809 -0.00448 0.19013 1.15184] [ 0. 0.29151 -0.7103 -0.02894 -0.10884 -0.0552 ] [ 0. 0.27632 0.24672 0.10771 0.02652 0.2862 ] [ 0. 0. 0. 0.16939 -0.52985 -0.30087] [ 0. 0. 0. 0.47545 -0.02031 0.26389] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.46651 -0.24877 0.10492 0.15862 1.15184] [ 0. 0.42269 -0.33838 0.13036 -0.0048 0.28232] [ 0. 0.64824 0.11554 0.03338 0.08282 -0.0725 ] [ 0. 0. -0. 0.082 -0.60104 -0.09624] [ 0. 0. -0. 0.40426 0.06709 0.38846] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.24845 -0.46669 -0.17588 -0.07236 1.15184] [ 0. 0.11576 -0.64845 -0.07419 -0.04974 -0.0723 ] [ 0. 0.33817 0.42247 0.10513 -0.07719 -0.28237] [ 0. 0. -0. -0.01412 -0.54594 -0.13844] [ 0. 0. -0. 0.45935 0.16321 -0.37549] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.17896 0.49749 -0.17846 0.06575 1.15184] [ 0. 0.43855 -0.63071 0.07793 -0.10394 -0.16067] [ 0. 0.35591 0.09968 0.04852 0.07588 0.24319] [ 0. 0. 0. 0.02394 -0.41794 -0.35603] [ 0. 0. 0. 0.58735 0.12515 -0.18277] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.48878 0.20154 0.07203 -0.17602 1.15184] [ 0. 0.08782 -0.37198 -0.08753 -0.0096 0.23558] [ 0. 0.61464 0.4504 -0.02807 -0.12825 0.17163] [ 0. 0. 0. 0.16337 -0.45968 0.37523] [ 0. 0. 0. 0.54561 -0.01428 -0.13915] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.05656 -0.52567 0.05434 0.18226 1.15184] [ 0. 0.26572 -0.71143 0.05442 0.09493 0.03817] [ 0. 0.27519 0.27251 -0.11406 0.00236 -0.28896] [ 0. 0. 0. 0.13543 -0.58029 -0.2049 ] [ 0. 0. 0. 0.425 0.01366 0.34377] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.42896 0.30905 0.14528 0.12274 1.15184] [ 0. 0.45832 -0.38474 -0.13005 0.03148 -0.27005] [ 0. 0.60188 0.07991 -0.03822 -0.075 0.10968] [ 0. 0. -0. 0.02774 -0.58951 0.01682] [ 0. 0. -0. 0.41578 0.12134 0.39985] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.28283 0.44669 0.18997 0.00889 1.15184] [ 0. 0.09423 -0.62371 -0.08088 -0.02991 0.09332] [ 0. 0.36291 0.444 0.07929 -0.10614 0.27613] [ 0. 0. 0. -0.02147 -0.47988 0.25682] [ 0. 0. 0. 0.52541 0.17055 0.30692] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.14175 -0.50934 -0.1364 0.13253 1.15184] [ 0. 0.41647 -0.65416 -0.03449 0.12262 0.14228] [ 0. 0.33246 0.12175 -0.07279 -0.05886 -0.25439] [ 0. 0. 0. 0.10348 -0.40831 -0.39957] [ 0. 0. 0. 0.59698 0.04561 -0.02249] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.51173 -0.1329 0.00592 -0.19009 1.15184] [ 0. 0.12742 -0.32745 0.09428 -0.00635 -0.25682] [ 0. 0.65917 0.41081 0.05882 0.11225 -0.13785] [ 0. 0. 0. 0.1698 -0.5284 0.30287] [ 0. 0. 0. 0.47689 -0.02071 -0.26159] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.08761 0.52139 -0.10389 -0.1593 1.15184] [ 0. 0.23994 -0.7095 0.07258 0.07747 -0.02098] [ 0. 0.27713 0.29829 -0.11319 0.03014 0.29072] [ 0. 0. -0. 0.08327 -0.60093 0.09875] [ 0. 0. -0. 0.40436 0.06581 -0.38782] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.38744 -0.35974 0.17534 0.07365 1.15184] [ 0. 0.47919 -0.43451 0.12108 -0.06098 0.25441] [ 0. 0.55211 0.05904 0.04428 0.06819 -0.14224] [ 0. 0. -0. -0.01348 -0.54724 0.13568] [ 0. 0. -0. 0.45805 0.16256 0.3765 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.31809 -0.42231 0.17907 -0.06407 1.15184] [ 0. 0.07547 -0.59375 0.08322 0.00729 -0.11539] [ 0. 0.39287 0.46276 -0.03981 0.12816 -0.26766] [ 0. 0. 0. 0.02236 -0.4189 0.3543 ] [ 0. 0. 0. 0.58639 0.12673 0.1861 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.10612 0.51794 -0.07356 0.17538 1.15184] [ 0. 0.39282 -0.67299 -0.01003 -0.12425 -0.12431] [ 0. 0.31364 0.14541 0.09095 0.03432 0.26364] [ 0. 0. 0. 0.16261 -0.45814 -0.37643] [ 0. 0. 0. 0.54716 -0.01352 0.13587] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.52559 0.05729 -0.05309 -0.18262 1.15184] [ 0. 0.18097 -0.29377 -0.09992 0.02195 0.27409] [ 0. 0.69286 0.35726 -0.07695 -0.09275 0.09915] [ 0. 0. 0. 0.13648 -0.57946 0.20724] [ 0. 0. 0. 0.42583 0.01261 -0.34236] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.11874 -0.51519 0.14446 0.1237 1.15184] [ 0. 0.21425 -0.70445 0.08524 0.05751 0.0035 ] [ 0. 0.28218 0.32398 -0.10547 0.05737 -0.29145] [ 0. 0. 0. 0.0289 -0.59013 0.01416] [ 0. 0. 0. 0.41516 0.12018 0.39995] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.34426 0.40126 0.18989 0.01049 1.15184] [ 0. 0.48703 -0.48324 -0.10028 0.09188 -0.23669] [ 0. 0.50339 0.0512 -0.0536 -0.06014 0.17011] [ 0. 0. -0. -0.02184 -0.4815 0.25423] [ 0. 0. -0. 0.52379 0.17092 0.30907] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.35403 0.39267 -0.13766 0.13122 1.15184] [ 0. 0.06086 -0.55824 0.08009 -0.01527 0.1385 ] [ 0. 0.42839 0.47737 0.00861 0.13516 0.25647] [ 0. 0. -0. 0.10167 -0.40777 -0.39933] [ 0. 0. -0. 0.59752 0.04742 -0.02631] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.07186 -0.52379 0.00738 -0.19004 1.15184] [ 0. 0.3682 -0.68766 -0.04648 -0.11258 0.10672] [ 0. 0.29897 0.17003 0.10048 0.00765 -0.27123] [ 0. 0. -0. 0.17018 -0.52694 0.30486] [ 0. 0. -0. 0.47835 -0.02109 -0.25926] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.52822 0.02246 0.10286 0.15997 1.15184] [ 0. 0.24434 -0.27658 -0.1036 0.03882 -0.28589] [ 0. 0.71005 0.29389 -0.08554 -0.07371 -0.05677] [ 0. 0. -0. 0.08455 -0.60081 -0.10126] [ 0. 0. -0. 0.40448 0.06454 0.38718] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.15016 0.50693 -0.1748 -0.07493 1.15184] [ 0. 0.18877 -0.69612 0.09321 0.03468 0.01441] [ 0. 0.2905 0.34946 -0.08943 0.08427 0.29112] [ 0. 0. -0. -0.01281 -0.54852 -0.13292] [ 0. 0. -0. 0.45677 0.1619 -0.37748] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.30107 -0.43461 -0.17966 0.06238 1.15184] [ 0. 0.48446 -0.52814 -0.06505 0.11878 0.21789] [ 0. 0.45849 0.05377 -0.06607 -0.04779 -0.1936 ] [ 0. 0. 0. 0.0208 -0.4199 -0.35253] [ 0. 0. 0. 0.5854 0.12829 -0.18942] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.39017 -0.35678 -0.0751 0.17473 1.15184] [ 0. 0.05227 -0.51714 -0.07322 0.03364 -0.16254] [ 0. 0.46948 0.48595 -0.05418 -0.12474 -0.24195] [ 0. 0. -0. 0.16181 -0.4566 -0.37761] [ 0. 0. -0. 0.54869 -0.01273 0.13256] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.03873 0.52728 0.05185 0.18298 1.15184] [ 0. 0.34298 -0.69857 -0.07274 -0.09397 -0.08943] [ 0. 0.28805 0.19525 0.10269 -0.01796 0.27742] [ 0. 0. 0. 0.13752 -0.57861 -0.20957] [ 0. 0. 0. 0.42669 0.01157 0.34094] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.51866 -0.10253 -0.14363 -0.12466 1.15184] [ 0. 0.31064 -0.27916 -0.10314 0.05846 0.2912 ] [ 0. 0.70747 0.22759 -0.08813 -0.05627 0.01264] [ 0. 0. 0. 0.03007 -0.59073 -0.01151] [ 0. 0. 0. 0.41457 0.11902 -0.40003] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.1821 -0.49635 0.1898 0.01208 1.15184] [ 0. 0.16368 -0.68429 0.09567 0.00843 -0.03289] [ 0. 0.30234 0.37455 -0.06226 0.10903 -0.28961] [ 0. 0. 0. -0.02218 -0.48312 0.25164] [ 0. 0. 0. 0.52217 0.17126 0.31119] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.25887 0.46099 -0.13891 0.1299 1.15184] [ 0. 0.47414 -0.56784 0.01872 -0.13277 -0.19872] [ 0. 0.41879 0.06409 0.07836 0.02949 0.21323] [ 0. 0. 0. 0.09985 -0.40727 -0.39906] [ 0. 0. 0. 0.59802 0.04924 -0.03013] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.42565 0.3136 0.00883 -0.18998 1.15184] [ 0. 0.0521 -0.47108 -0.06638 0.04661 0.18717] [ 0. 0.51554 0.48612 -0.08808 -0.10321 0.22344] [ 0. 0. 0. 0.17054 -0.52547 0.30684] [ 0. 0. 0. 0.47982 -0.02145 -0.25692] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.0065 -0.52866 -0.10182 -0.16063 1.15184] [ 0. 0.31744 -0.70604 -0.09062 -0.07206 0.07234] [ 0. 0.28059 0.22079 0.09903 -0.04216 -0.28235] [ 0. 0. -0. 0.08582 -0.60067 0.10377] [ 0. 0. -0. 0.40462 0.06327 -0.38651] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.49752 0.17889 0.17425 0.0762 1.15184] [ 0. 0.37208 -0.30099 -0.0952 0.08146 -0.28982] [ 0. 0.68563 0.16615 -0.08765 -0.04008 0.03102] [ 0. 0. -0. -0.01213 -0.5498 0.13016] [ 0. 0. -0. 0.4555 0.16122 0.37844] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.21472 0.48314 0.18024 -0.0607 1.15184] [ 0. 0.13926 -0.6686 -0.09045 0.02009 0.05209] [ 0. 0.31803 0.39897 0.0224 -0.12611 0.28678] [ 0. 0. 0. 0.01926 -0.42092 0.35075] [ 0. 0. 0. 0.58437 0.12983 0.19271] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.21821 -0.48157 0.07663 -0.17406 1.15184] [ 0. 0.4583 -0.60191 -0.02766 -0.12927 0.17962] [ 0. 0.38471 0.07993 0.08635 0.00746 -0.22955] [ 0. 0. -0. 0.16099 -0.45507 0.37876] [ 0. 0. -0. 0.55022 -0.0119 -0.12923] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.4591 -0.2622 -0.05059 -0.18333 1.15184] [ 0. 0.06304 -0.42176 0.0617 -0.05629 -0.21178] [ 0. 0.56486 0.47519 0.10937 0.0778 -0.20026] [ 0. 0. 0. 0.13855 -0.57774 0.2119 ] [ 0. 0. 0. 0.42755 0.01053 -0.3395 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.0251 0.5281 0.1428 0.12561 1.15184] [ 0. 0.29172 -0.71028 -0.10203 -0.04774 -0.05534] [ 0. 0.27634 0.24651 0.08948 -0.06551 0.28617] [ 0. 0. 0. 0.03124 -0.59131 0.00885] [ 0. 0. 0. 0.41398 0.11784 0.4001 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.4668 -0.24824 -0.18969 -0.01366 1.15184] [ 0. 0.42233 -0.33803 -0.07564 0.10623 0.2824 ] [ 0. 0.64859 0.1159 -0.08607 -0.02397 -0.07217] [ 0. 0. 0. -0.02249 -0.48473 -0.24903] [ 0. 0. 0. 0.52056 0.17158 -0.31328] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.24817 -0.46683 0.14015 -0.12856 1.15184] [ 0. 0.11594 -0.64864 0.07651 -0.04615 -0.07213] [ 0. 0.33799 0.42229 0.02534 0.12792 -0.28241] [ 0. 0. 0. 0.09801 -0.40681 0.39876] [ 0. 0. 0. 0.59849 0.05107 0.03395] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.17927 0.49738 -0.0103 0.1899 1.15184] [ 0. 0.43872 -0.6305 -0.06464 -0.11271 -0.16082] [ 0. 0.35612 0.09951 0.08884 -0.01458 0.24309] [ 0. 0. 0. 0.17088 -0.52399 -0.30881] [ 0. 0. 0. 0.4813 -0.02179 0.25455] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.48856 0.20207 0.10078 0.16129 1.15184] [ 0. 0.08756 -0.37238 0.05879 -0.06549 0.2354 ] [ 0. 0.61425 0.45067 0.12055 0.05207 0.17189] [ 0. 0. -0. 0.08709 -0.60052 -0.10627] [ 0. 0. -0. 0.40477 0.062 0.38583] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.05631 -0.52569 0.17369 0.07747 1.15184] [ 0. 0.26593 -0.71143 0.10751 0.02049 0.03831] [ 0. 0.27519 0.2723 -0.07245 0.0881 -0.28895] [ 0. 0. 0. -0.01144 -0.55105 0.1274 ] [ 0. 0. 0. 0.45424 0.16053 0.37938] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.42929 0.3086 0.1808 -0.05901 1.15184] [ 0. 0.45809 -0.38434 -0.04153 0.12717 -0.27017] [ 0. 0.60228 0.08014 -0.08393 -0.00679 0.10939] [ 0. 0. -0. 0.01774 -0.42196 0.34893] [ 0. 0. -0. 0.58333 0.13135 0.19598] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.28254 0.44687 0.07817 -0.17338 1.15184] [ 0. 0.0944 -0.62393 -0.05753 0.06427 0.09315] [ 0. 0.36269 0.44383 -0.06956 -0.11274 0.27619] [ 0. 0. 0. 0.16014 -0.45355 0.37988] [ 0. 0. 0. 0.55174 -0.01105 -0.12589] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.14205 -0.50926 -0.04934 -0.18367 1.15184] [ 0. 0.41666 -0.65399 -0.09036 -0.08982 0.14243] [ 0. 0.33264 0.12157 0.0868 -0.03497 -0.2543 ] [ 0. 0. -0. 0.13958 -0.57685 0.21422] [ 0. 0. -0. 0.42844 0.00951 -0.33804] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.51157 -0.13349 -0.14197 -0.12655 1.15184] [ 0. 0.12703 -0.32778 0.0555 -0.0764 -0.25666] [ 0. 0.65884 0.4112 0.1239 0.02685 -0.13815] [ 0. 0. 0. 0.03242 -0.59187 -0.0062 ] [ 0. 0. 0. 0.41342 0.11667 -0.40015] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.08736 0.52143 -0.18957 -0.01524 1.15184] [ 0. 0.24015 -0.70953 0.1057 -0.01008 -0.02113] [ 0. 0.2771 0.29808 -0.04534 0.10798 0.29071] [ 0. 0. -0. -0.02277 -0.48635 -0.24642] [ 0. 0. -0. 0.51894 0.17186 -0.31534] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.38779 -0.35936 -0.14137 0.12721 1.15184] [ 0. 0.47907 -0.4341 0.00362 0.13551 0.25455] [ 0. 0.55252 0.05916 -0.08055 0.01111 -0.14199] [ 0. 0. 0. 0.09617 -0.40637 -0.39841] [ 0. 0. 0. 0.59892 0.05291 -0.03777] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.3178 -0.42253 0.01176 -0.18982 1.15184] [ 0. 0.07561 -0.59402 0.03946 -0.07366 -0.1152 ] [ 0. 0.3926 0.46262 0.10209 0.08708 -0.26774] [ 0. 0. 0. 0.1712 -0.5225 0.31077] [ 0. 0. 0. 0.48279 -0.02211 -0.25216] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.1064 0.51788 -0.09973 -0.16193 1.15184] [ 0. 0.39302 -0.67285 0.1069 0.06417 -0.12446] [ 0. 0.31377 0.14521 -0.0808 0.05399 0.26357] [ 0. 0. -0. 0.08835 -0.60035 0.10877] [ 0. 0. -0. 0.40495 0.06073 -0.38514] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.52552 0.05793 0.17312 0.07873 1.15184] [ 0. 0.18048 -0.29398 0.04832 -0.09009 0.27397] [ 0. 0.69264 0.35775 0.12056 0.00196 0.09949] [ 0. 0. -0. -0.01073 -0.5523 0.12464] [ 0. 0. -0. 0.453 0.15981 0.38029] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.11848 -0.51525 0.18134 -0.05732 1.15184] [ 0. 0.21446 -0.7045 0.09386 -0.04206 0.00365] [ 0. 0.28212 0.32377 -0.00695 0.11984 -0.29145] [ 0. 0. 0. 0.01624 -0.42304 0.34709] [ 0. 0. 0. 0.58225 0.13284 0.19923] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.34462 0.40095 -0.0797 0.17268 1.15184] [ 0. 0.48701 -0.48285 -0.04856 -0.12705 -0.23684] [ 0. 0.50378 0.05122 0.07561 -0.0278 0.1699 ] [ 0. 0. 0. 0.15925 -0.45205 -0.38098] [ 0. 0. 0. 0.55324 -0.01017 0.12252] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.35373 0.39294 -0.04807 -0.18401 1.15184] [ 0. 0.06095 -0.55855 -0.02536 0.0775 0.13831] [ 0. 0.42807 0.47728 -0.12241 -0.05791 0.25657] [ 0. 0. 0. 0.14059 -0.57595 0.21653] [ 0. 0. 0. 0.42934 0.0085 -0.33656] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.07213 -0.52376 0.14113 0.12748 1.15184] [ 0. 0.3684 -0.68755 0.11624 0.03646 0.10687] [ 0. 0.29907 0.16983 -0.07022 0.07223 -0.27118] [ 0. 0. 0. 0.0336 -0.59242 0.00356] [ 0. 0. 0. 0.41287 0.11548 0.40018] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.52825 0.0218 0.18944 0.01681 1.15184] [ 0. 0.2438 -0.27664 -0.03271 0.10561 -0.28582] [ 0. 0.70998 0.29443 -0.11071 0.02252 -0.05713] [ 0. 0. -0. -0.02303 -0.48797 0.24379] [ 0. 0. -0. 0.51732 0.17212 0.31737] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.1499 0.507 0.14259 -0.12585 1.15184] [ 0. 0.18898 -0.69621 -0.07125 0.06942 0.01426] [ 0. 0.29042 0.34925 -0.03788 -0.11687 0.29113] [ 0. 0. 0. 0.09432 -0.40598 0.39803] [ 0. 0. 0. 0.59931 0.05476 0.04159] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.30142 -0.43436 -0.01323 0.18972 1.15184] [ 0. 0.48452 -0.52779 0.08372 0.10646 0.21805] [ 0. 0.45884 0.05371 -0.06984 0.04206 -0.19342] [ 0. 0. 0. 0.17149 -0.521 -0.31271] [ 0. 0. 0. 0.48429 -0.02241 0.24975] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.38987 -0.3571 0.09868 0.16258 1.15184] [ 0. 0.05231 -0.5175 -0.01501 0.07917 -0.16234] [ 0. 0.46912 0.48591 -0.13304 -0.02823 -0.24208] [ 0. 0. -0. 0.08962 -0.60016 -0.11126] [ 0. 0. -0. 0.40513 0.05947 0.38442] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.039 0.52726 -0.17255 -0.07998 1.15184] [ 0. 0.34319 -0.69849 0.1187 0.00606 -0.08958] [ 0. 0.28813 0.19504 -0.05327 0.08958 0.27737] [ 0. 0. -0. -0.01 -0.55353 -0.12189] [ 0. 0. -0. 0.45177 0.15909 -0.38119] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.51879 -0.10188 0.18186 -0.05563 1.15184] [ 0. 0.31011 -0.27905 0.00503 -0.11839 0.29118] [ 0. 0.70757 0.22812 0.09446 -0.04501 0.013 ] [ 0. 0. -0. 0.01477 -0.42414 0.34521] [ 0. 0. -0. 0.58115 0.13432 0.20245] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.18183 -0.49645 -0.08122 0.17197 1.15184] [ 0. 0.16389 -0.6844 -0.04307 0.08588 -0.03274] [ 0. 0.30222 0.37434 -0.07841 -0.09803 -0.28963] [ 0. 0. -0. 0.15834 -0.45055 -0.38205] [ 0. 0. -0. 0.55474 -0.00926 0.11914] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.25921 0.4608 -0.04681 -0.18433 1.15184] [ 0. 0.47425 -0.56753 0.10733 0.08039 -0.19888] [ 0. 0.41909 0.06398 -0.06355 0.05448 0.21308] [ 0. 0. -0. 0.14159 -0.57504 0.21884] [ 0. 0. -0. 0.43025 0.00749 -0.33506] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.42537 0.31399 0.14028 0.12841 1.15184] [ 0. 0.05206 -0.47148 0.00657 -0.08083 0.18697] [ 0. 0.51514 0.48617 0.13568 -0.00166 0.22361] [ 0. 0. -0. 0.03479 -0.59296 0.00091] [ 0. 0. -0. 0.41233 0.11429 0.4002 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.00676 -0.52866 -0.18929 -0.01838 1.15184] [ 0. 0.31765 -0.70599 -0.11255 0.02726 0.07248] [ 0. 0.28063 0.22058 0.02754 -0.10402 -0.28232] [ 0. 0. -0. -0.02326 -0.48958 -0.24116] [ 0. 0. -0. 0.51571 0.17235 -0.31938] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.49773 0.17829 0.14379 -0.12448 1.15184] [ 0. 0.37161 -0.30074 0.03264 0.12092 -0.28986] [ 0. 0.68588 0.16662 -0.07387 0.06201 0.03067] [ 0. 0. -0. 0.09246 -0.40561 0.39761] [ 0. 0. -0. 0.59968 0.05662 0.04541] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.21444 0.48326 0.0147 -0.18961 1.15184] [ 0. 0.13946 -0.66874 -0.01686 0.09113 0.05193] [ 0. 0.31788 0.39877 -0.10728 -0.06992 0.28681] [ 0. 0. 0. 0.17177 -0.51949 0.31464] [ 0. 0. 0. 0.4858 -0.02268 -0.24731] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.21853 -0.48142 -0.09762 -0.16321 1.15184] [ 0. 0.45845 -0.60166 -0.12148 -0.05219 0.17978] [ 0. 0.38497 0.07978 0.05597 -0.06614 -0.22943] [ 0. 0. -0. 0.09088 -0.59996 0.11375] [ 0. 0. -0. 0.40534 0.0582 -0.38369] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.45884 -0.26266 0.17196 0.08123 1.15184] [ 0. 0.06289 -0.42218 0.00255 0.08345 -0.21158] [ 0. 0.56445 0.47534 -0.1303 0.03224 -0.20048] [ 0. 0. -0. -0.00925 -0.55474 0.11913] [ 0. 0. -0. 0.45055 0.15834 0.38206] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.02484 0.52812 -0.18237 0.05394 1.15184] [ 0. 0.29193 -0.71026 0.09475 -0.06097 -0.05549] [ 0. 0.27636 0.2463 0.00782 0.1106 0.28615] [ 0. 0. -0. 0.01332 -0.42526 -0.34332] [ 0. 0. -0. 0.58003 0.13576 -0.20565] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.46709 -0.2477 -0.08275 0.17124 1.15184] [ 0. 0.42197 -0.33768 0.07085 0.10944 0.28248] [ 0. 0.64895 0.11626 -0.05398 0.07126 -0.07185] [ 0. 0. 0. 0.1574 -0.44907 -0.3831 ] [ 0. 0. 0. 0.55622 -0.00832 0.11574] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.24789 -0.46698 0.04554 0.18465 1.15184] [ 0. 0.11613 -0.64882 0.00385 0.08929 -0.07196] [ 0. 0.3378 0.4221 -0.12438 -0.03911 -0.28245] [ 0. 0. -0. 0.14258 -0.57411 -0.22115] [ 0. 0. -0. 0.43119 0.0065 0.33355] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.17958 0.49727 0.13943 0.12934 1.15184] [ 0. 0.4389 -0.63029 -0.12802 -0.02232 -0.16098] [ 0. 0.35634 0.09933 0.04552 -0.07764 0.24299] [ 0. 0. 0. 0.03599 -0.59347 -0.00173] [ 0. 0. 0. 0.41182 0.1131 0.4002 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.48834 0.20261 0.18913 0.01994 1.15184] [ 0. 0.0873 -0.37277 -0.01551 -0.08659 0.23521] [ 0. 0.61385 0.45093 0.11525 -0.063 0.17215] [ 0. 0. -0. -0.02346 -0.4912 0.23852] [ 0. 0. -0. 0.51409 0.17255 0.32135] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.05605 -0.52572 -0.14498 0.12309 1.15184] [ 0. 0.26614 -0.71144 -0.06496 0.08812 0.03846] [ 0. 0.27519 0.27209 -0.04812 -0.10338 -0.28893] [ 0. 0. -0. 0.0906 -0.40529 -0.39716] [ 0. 0. -0. 0.6 0.05849 -0.04923] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.42962 0.30814 -0.01618 0.18949 1.15184] [ 0. 0.45786 -0.38393 -0.10094 -0.08777 -0.27029] [ 0. 0.60269 0.08037 0.03889 -0.07473 0.1091 ] [ 0. 0. 0. 0.17202 -0.51798 -0.31655] [ 0. 0. 0. 0.48732 -0.02293 0.24485] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.28225 0.44705 0.09656 0.16385 1.15184] [ 0. 0.09457 -0.62416 -0.01942 -0.08407 0.09297] [ 0. 0.36246 0.44366 0.13221 0.00814 0.27625] [ 0. 0. -0. 0.09215 -0.59974 -0.11624] [ 0. 0. -0. 0.40556 0.05694 0.38295] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.14235 -0.50918 0.17137 0.08246 1.15184] [ 0. 0.41685 -0.65381 0.12704 -0.00991 0.14258] [ 0. 0.33281 0.12138 -0.03006 0.08859 -0.25422] [ 0. 0. 0. -0.0085 -0.55594 0.11638] [ 0. 0. 0. 0.44935 0.15758 0.3829 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.51141 -0.13409 0.18287 -0.05225 1.15184] [ 0. 0.12665 -0.32811 0.03496 0.08766 -0.25649] [ 0. 0.65851 0.41158 -0.08893 0.09041 -0.13845] [ 0. 0. -0. 0.0119 -0.42641 0.3414 ] [ 0. 0. -0. 0.57888 0.13719 0.20883] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.0871 0.52148 -0.08427 0.17049 1.15184] [ 0. 0.24036 -0.70955 0.02969 -0.10198 -0.02127] [ 0. 0.27707 0.29787 0.08357 0.08201 0.2907 ] [ 0. 0. -0. 0.15643 -0.4476 -0.38412] [ 0. 0. -0. 0.55769 -0.00735 0.11232] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.38815 -0.35898 0.04426 0.18496 1.15184] [ 0. 0.47895 -0.43369 0.12082 0.06146 0.25469] [ 0. 0.55293 0.05928 -0.02859 0.07614 -0.14174] [ 0. 0. 0. 0.14357 -0.57316 -0.22345] [ 0. 0. 0. 0.43213 0.00552 0.33201] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.3175 -0.42275 0.13858 0.13025 1.15184] [ 0. 0.07575 -0.59429 0.03159 0.07739 -0.11502] [ 0. 0.39233 0.46248 -0.13218 0.02302 -0.26782] [ 0. 0. -0. 0.03719 -0.59397 -0.00436] [ 0. 0. -0. 0.41132 0.1119 0.40018] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.10669 0.51782 0.18896 0.02149 1.15184] [ 0. 0.39322 -0.67271 -0.11648 0.04455 -0.12461] [ 0. 0.31391 0.14501 0.00734 -0.09687 0.2635 ] [ 0. 0. 0. -0.02364 -0.49281 0.23587] [ 0. 0. 0. 0.51248 0.17272 0.3233 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.52545 0.05858 0.14615 -0.12169 1.15184] [ 0. 0.17999 -0.2942 -0.0602 -0.08254 0.27385] [ 0. 0.69242 0.35824 0.0541 -0.10782 0.09983] [ 0. 0. -0. 0.08872 -0.405 0.39667] [ 0. 0. -0. 0.60029 0.06036 0.05304] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.11822 -0.51531 -0.01766 0.18936 1.15184] [ 0. 0.21467 -0.70455 0.00233 0.10286 0.00379] [ 0. 0.28207 0.32356 -0.10772 -0.05292 -0.29145] [ 0. 0. -0. 0.17224 -0.51645 -0.31846] [ 0. 0. -0. 0.48884 -0.02316 0.24237] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.34498 0.40064 -0.0955 -0.16447 1.15184] [ 0. 0.48699 -0.48246 0.13189 0.03322 -0.23699] [ 0. 0.50416 0.05124 -0.0206 0.07788 0.16968] [ 0. 0. -0. 0.0934 -0.5995 0.11872] [ 0. 0. -0. 0.40579 0.05568 -0.38218] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.35343 0.3932 -0.17078 -0.08369 1.15184] [ 0. 0.06105 -0.55887 0.04225 0.06976 0.13811] [ 0. 0.42775 0.47718 -0.12375 0.05499 0.25668] [ 0. 0. 0. -0.00772 -0.55713 -0.11362] [ 0. 0. 0. 0.44816 0.15681 -0.38373] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.07241 -0.52372 -0.18334 0.05055 1.15184] [ 0. 0.36861 -0.68745 -0.09318 0.07851 0.10701] [ 0. 0.29918 0.16962 -0.02325 -0.09799 -0.27112] [ 0. 0. -0. 0.0105 -0.42758 -0.33945] [ 0. 0. -0. 0.57771 0.13859 -0.21198] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.52828 0.02113 0.08579 -0.16973 1.15184] [ 0. 0.24325 -0.2767 0.08601 0.06937 -0.28575] [ 0. 0.70992 0.29498 -0.01999 0.11127 -0.05749] [ 0. 0. -0. 0.15544 -0.44615 0.3851 ] [ 0. 0. -0. 0.55915 -0.00635 -0.10888] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.14964 0.50708 -0.04298 -0.18526 1.15184] [ 0. 0.18919 -0.69629 0.02729 0.09569 0.01411] [ 0. 0.29033 0.34904 -0.12082 -0.02216 0.29113] [ 0. 0. 0. 0.14454 -0.5722 0.22574] [ 0. 0. 0. 0.4331 0.00455 -0.33045] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.30177 -0.43412 0.13772 0.13116 1.15184] [ 0. 0.48457 -0.52744 0.1354 0.00332 0.21821] [ 0. 0.45919 0.05366 -0.01202 0.08062 -0.19324] [ 0. 0. 0. 0.03839 -0.59446 -0.007 ] [ 0. 0. 0. 0.41083 0.11069 0.40014] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.38958 -0.35743 -0.18878 -0.02304 1.15184] [ 0. 0.05236 -0.51786 -0.05301 -0.06069 -0.16214] [ 0. 0.46876 0.48587 0.10444 -0.08711 -0.24222] [ 0. 0. 0. -0.02378 -0.49442 -0.23321] [ 0. 0. 0. 0.51087 0.17287 -0.32522] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.03927 0.52724 0.14732 -0.12028 1.15184] [ 0. 0.3434 -0.69842 -0.05727 0.10417 -0.08972] [ 0. 0.28821 0.19483 -0.05735 -0.08699 0.27732] [ 0. 0. 0. 0.08684 -0.40474 0.39614] [ 0. 0. 0. 0.60055 0.06224 0.05685] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.51892 -0.10123 -0.01914 0.18922 1.15184] [ 0. 0.30957 -0.27895 0.10719 0.05036 0.29117] [ 0. 0.70767 0.22866 0.00505 0.10458 0.01337] [ 0. 0. 0. 0.17245 -0.51492 -0.32035] [ 0. 0. 0. 0.49037 -0.02336 0.23987] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.18156 -0.49655 -0.09442 -0.16509 1.15184] [ 0. 0.16409 -0.68451 -0.04578 -0.08449 -0.03258] [ 0. 0.30211 0.37414 0.12525 -0.00816 -0.28965] [ 0. 0. 0. 0.09466 -0.59924 0.12121] [ 0. 0. 0. 0.40605 0.05442 -0.3814 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.25955 0.4606 -0.17017 -0.08491 1.15184] [ 0. 0.47436 -0.56723 0.13097 -0.02886 -0.19904] [ 0. 0.4194 0.06387 -0.00013 0.08368 0.21293] [ 0. 0. -0. -0.00693 -0.5583 -0.11087] [ 0. 0. -0. 0.44699 0.15602 -0.38454] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.42508 0.31437 0.1838 -0.04885 1.15184] [ 0. 0.05202 -0.47188 -0.06458 -0.04903 0.18676] [ 0. 0.51475 0.4862 0.07173 -0.11519 0.22378] [ 0. 0. -0. 0.00912 -0.42878 0.33748] [ 0. 0. -0. 0.57651 0.13997 0.2151 ] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.00702 -0.52865 -0.08731 0.16896 1.15184] [ 0. 0.31786 -0.70594 -0.01641 0.11466 0.07263] [ 0. 0.28068 0.22037 -0.08638 -0.06412 -0.28228] [ 0. 0. -0. 0.15441 -0.44471 -0.38606] [ 0. 0. -0. 0.56059 -0.00533 0.10542] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.49795 0.17768 0.04169 0.18556 1.15184] [ 0. 0.37114 -0.30049 -0.12196 -0.02831 -0.28989] [ 0. 0.68613 0.16709 -0.01986 -0.09445 0.03032] [ 0. 0. 0. 0.14549 -0.57122 -0.22803] [ 0. 0. 0. 0.43407 0.00359 0.32888] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.21417 0.48338 -0.13685 -0.13206 1.15184] [ 0. 0.13965 -0.66889 0.05961 0.07101 0.05176] [ 0. 0.31773 0.39858 -0.12219 0.03825 0.28684] [ 0. 0. 0. 0.0396 -0.59492 0.00963] [ 0. 0. 0. 0.41037 0.10948 -0.40008] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.21886 -0.48127 0.18859 0.02458 1.15184] [ 0. 0.4586 -0.6014 0.11625 -0.06303 0.17994] [ 0. 0.38523 0.07963 0.01729 0.08488 -0.22931] [ 0. 0. 0. -0.02391 -0.49603 0.23055] [ 0. 0. 0. 0.50927 0.17299 0.32712] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.45858 -0.26312 -0.14846 0.11886 1.15184] [ 0. 0.06275 -0.42259 -0.07613 -0.03421 -0.21138] [ 0. 0.56403 0.47548 0.02815 -0.13126 -0.20069] [ 0. 0. 0. 0.08496 -0.40453 -0.39558] [ 0. 0. 0. 0.60077 0.06413 -0.06066] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.02458 0.52813 -0.02063 0.18906 1.15184] [ 0. 0.29215 -0.71024 -0.01973 -0.11096 -0.05563] [ 0. 0.27639 0.24608 0.10504 0.03542 0.28612] [ 0. 0. -0. 0.17263 -0.51338 -0.32222] [ 0. 0. -0. 0.49191 -0.02354 0.23734] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.46737 -0.24716 -0.09335 -0.1657 1.15184] [ 0. 0.42161 -0.33733 -0.13027 -0.00421 0.28256] [ 0. 0.6493 0.11662 -0.02784 -0.085 -0.07152] [ 0. 0. -0. 0.09592 -0.59898 0.12368] [ 0. 0. -0. 0.40632 0.05317 -0.38061] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.24761 -0.46713 -0.16956 -0.08613 1.15184] [ 0. 0.11632 -0.649 -0.07019 -0.05537 -0.0718 ] [ 0. 0.33762 0.42191 0.11081 -0.06868 -0.28249] [ 0. 0. 0. -0.00613 -0.55946 -0.10812] [ 0. 0. 0. 0.44583 0.15521 -0.38532] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.1799 0.49715 0.18424 -0.04716 1.15184] [ 0. 0.43907 -0.63007 -0.08807 0.09558 -0.16113] [ 0. 0.35655 0.09916 -0.04067 -0.08026 0.24289] [ 0. 0. 0. 0.00777 -0.43 0.33548] [ 0. 0. 0. 0.57529 0.14132 0.21821] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.48812 0.20314 0.08883 -0.16816 1.15184] [ 0. 0.08704 -0.37317 -0.08613 -0.01765 0.23502] [ 0. 0.61346 0.45119 -0.01572 -0.13043 0.1724 ] [ 0. 0. -0. 0.15336 -0.44328 0.387 ] [ 0. 0. -0. 0.56201 -0.00427 -0.10195] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.05579 -0.52575 -0.0404 -0.18584 1.15184] [ 0. 0.26636 -0.71144 -0.04725 -0.09878 0.0386 ] [ 0. 0.27518 0.27187 0.11384 0.00613 -0.28891] [ 0. 0. 0. 0.14644 -0.57022 0.23031] [ 0. 0. 0. 0.43507 0.00265 -0.32729] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.42995 0.30768 0.13598 0.13296 1.15184] [ 0. 0.45762 -0.38353 -0.13189 0.0222 -0.2704 ] [ 0. 0.60309 0.08061 -0.0331 -0.0775 0.10882] [ 0. 0. 0. 0.04082 -0.59538 -0.01225] [ 0. 0. 0. 0.40992 0.10827 0.40001] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.28197 0.44723 0.18838 0.02611 1.15184] [ 0. 0.09474 -0.62438 -0.078 -0.03695 0.09279] [ 0. 0.36224 0.44349 0.08846 -0.09857 0.27631] [ 0. 0. -0. -0.024 -0.49763 0.22788] [ 0. 0. -0. 0.50766 0.17309 0.32898] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.14265 -0.50909 0.1496 -0.11743 1.15184] [ 0. 0.41704 -0.65364 0.0471 -0.11842 0.14273] [ 0. 0.33298 0.12119 0.06627 0.06599 -0.25414] [ 0. 0. 0. 0.08307 -0.40434 0.39497] [ 0. 0. 0. 0.60095 0.06602 0.06446] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.51126 -0.13469 0.02212 -0.18889 1.15184] [ 0. 0.12626 -0.32845 0.0943 0.00131 -0.25633] [ 0. 0.65818 0.41197 0.04936 0.11687 -0.13875] [ 0. 0. -0. 0.17279 -0.51183 0.32409] [ 0. 0. -0. 0.49346 -0.0237 -0.23479] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.08684 0.52152 -0.09227 -0.1663 1.15184] [ 0. 0.24057 -0.70958 0.06704 0.08242 -0.02141] [ 0. 0.27704 0.29766 -0.11495 0.02211 0.29069] [ 0. 0. 0. 0.09717 -0.59869 0.12616] [ 0. 0. 0. 0.4066 0.05192 -0.37979] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.3885 -0.3586 -0.16894 -0.08733 1.15184] [ 0. 0.47884 -0.43328 -0.12542 0.05138 0.25483] [ 0. 0.55335 0.05939 -0.03909 -0.07134 -0.14149] [ 0. 0. -0. -0.00531 -0.56061 -0.10537] [ 0. 0. -0. 0.44468 0.1544 -0.38608] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.31721 -0.42297 0.18467 -0.04546 1.15184] [ 0. 0.07589 -0.59456 0.08216 0.01549 -0.11483] [ 0. 0.39206 0.46234 -0.05251 0.12346 -0.2679 ] [ 0. 0. -0. 0.00644 -0.43124 0.33346] [ 0. 0. -0. 0.57405 0.14264 0.22128] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.10698 0.51776 -0.09034 0.16736 1.15184] [ 0. 0.39342 -0.67257 0.002 -0.12471 -0.12475] [ 0. 0.31405 0.14481 0.08717 0.04283 0.26343] [ 0. 0. -0. 0.15228 -0.44187 -0.3879 ] [ 0. 0. -0. 0.56342 -0.00319 0.09846] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.52537 0.05922 0.0391 0.18612 1.15184] [ 0. 0.1795 -0.29442 0.10104 -0.01467 0.27372] [ 0. 0.6922 0.35873 0.07007 0.09826 0.10016] [ 0. 0. 0. 0.14738 -0.56921 -0.23259] [ 0. 0. 0. 0.43608 0.00171 0.32567] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.11797 -0.51537 -0.13511 -0.13385 1.15184] [ 0. 0.21488 -0.70461 -0.08101 -0.06347 0.00394] [ 0. 0.28201 0.32335 0.10923 -0.04967 -0.29145] [ 0. 0. 0. 0.04204 -0.59581 0.01488] [ 0. 0. 0. 0.40948 0.10705 -0.39992] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 -0.34534 0.40033 -0.18816 -0.02764 1.15184] [ 0. 0.48697 -0.48207 0.10806 -0.0826 -0.23714] [ 0. 0.50455 0.05126 0.04823 0.06453 0.16947] [ 0. 0. -0. -0.02407 -0.49923 -0.2252 ] [ 0. 0. -0. 0.50606 0.17316 -0.33082] [ 0. 0. 0. 0. 0. -0.11832]] [[ 2.78023 0.35313 0.39347 -0.15072 0.11598 1.15184] [ 0. 0.06115 -0.55918 0.08127 -0.00705 0.13792] [ 0. 0.42744 0.47708 -0.0055 0.13529 0.25678] [ 0. 0. 0. 0.08118 -0.4042 -0.39434] [ 0. 0. 0. 0.60109 0.06791 -0.06826] [ 0. 0. 0. 0. 0. -0.11832]]  Let's compare to the eigenvalues: In [469]: np.linalg.eigvals(A)  Out[469]: array([ 2.78023+0.j , -0.11832+0.j , 0.26911+0.44246j, 0.26911-0.44246j, 0.07454+0.49287j, 0.07454-0.49287j]) Check that Q is orthogonal: In [476]: np.allclose(np.eye(n), Q @ Q.T), np.allclose(np.eye(n), Q.T @ Q)  Out[476]: (True, True) This is really really slow. #### Practical QR (QR with shifts)¶ Idea: Instead of factoring$A_k$as$Q_k R_k$, 1. Get the QR factorization $$A_k - s_k I = Q_k R_k$$ 2. Set $$A_{k+1} = R_k Q_k + s_k I$$ Choose$s_k$to approximate an eigenvalue of$A$. We'll use$s_k = A_k(m,m)$. The idea of adding shifts to speed up convergence shows up in many algorithms in numerical linear algebra (including the power method, inverse iteration, and Rayleigh quotient iteration). #### Homework: Add shifts to the QR algorithm¶ In [460]: #Exercise: Add shifts to the QR algorithm #Exercise: def practical_qr(A, iters=10): #Exercise: return Ak, Q  #### Practical QR¶ In [204]: Ak, Q = practical_qr(A, 10)  [ 5.16264 2.53603 0.31923 0.35315 0.97569 0.43615] [ 7.99381 0.05922 0.34478 0.29482 0.79026 0.29999] [ 8.00491 0.04358 0.89735 0.26386 0.26182 0.31135] [ 8.00493 0.13648 0.91881 0.14839 0.24313 0.33115] [ 8.00493 0.43377 0.62809 0.13429 0.24592 0.33589] [ 8.00493 0.81058 0.25128 0.13297 0.24722 0.3359 ] [ 8.00493 0.98945 0.07221 0.13292 0.24747 0.3359 ] [ 8.00493 1.0366 0.02497 0.13296 0.24751 0.3359 ] [ 8.00493 1.04688 0.01465 0.13299 0.24752 0.3359 ] [ 8.00493 1.04902 0.0125 0.13301 0.24753 0.3359 ]  Check that Q is orthogonal: In [201]: np.allclose(np.eye(n), Q @ Q.T), np.allclose(np.eye(n), Q.T @ Q)  Out[201]: (True, True) Let's compare to the eigenvalues: In [196]: np.linalg.eigvals(A)  Out[196]: array([ 2.68500+0.j , 0.19274+0.41647j, 0.19274-0.41647j, -0.35988+0.43753j, -0.35988-0.43753j, -0.18346+0.j ]) Problem: This is better than the unshifted version (which wasn't even guaranteed to converge), but is still really slow! In fact, it is$\mathcal{O}(n^4)$, which is awful. In the case of symmetric matrices, it's$\mathcal{O}(n^3)$However, if you start with a Hessenberg matrix (zeros below the first subdiagonal), it's faster:$\mathcal{O}(n^3)$, and$\mathcal{O}(n^2)$if symmetric. ## A Two-Phase Approach¶ In practice, a two phase approach is used to find eigenvalues: 1. Reduce the matrix to Hessenberg form (zeros below the first subdiagonal) 2. Iterative process that causes Hessenberg to converge to a triangular matrix. The eigenvalues of a triangular matrix are the values on the diagonal, so we are finished! (source: Trefethen, Lecture 25) In the case of a Hermitian matrix, this approach is even faster, since the intermediate step is also Hermitian (and a Hermitian Hessenberg is tridiagonal). (source: Trefethen, Lecture 25) Phase 1 reaches an exact solution in a finite number of steps, whereas Phase 2 theoretically never reaches the exact solution. We've already done step 2: the QR algorithm. Remember that it would be possible to just use the QR algorithm, but ridiculously slow. ## Arnoldi Iteration¶ We can use the Arnoldi iteration for phase 1 (and the QR algorithm for phase 2). #### Initializations¶ In [459]: import numpy as np n = 5 A0 = np.random.rand(n,n) #.astype(np.float64) A = A0 @ A0.T np.set_printoptions(precision=5, suppress=True)  ### Linear Algebra Review: Projections¶ When vector$\mathbf{b}$is projected onto a line$\mathbf{a}$, its projection$\mathbf{p}$is the part of$\mathbf{b}$along that line$\mathbf{a}$. Let's look at interactive graphic (3.4) for section 3.2.2: Projections of the Immersive Linear Algebra online book. (source: Immersive Math) And here is what it looks like to project a vector onto a plane: When vector$\mathbf{b}$is projected onto a line$\mathbf{a}$, its projection$\mathbf{p}$is the part of$\mathbf{b}$along that line$\mathbf{a}$. So$\mathbf{p}$is some multiple of$\mathbf{a}$. Let$\mathbf{p} = \hat{x}\mathbf{a}$where$\hat{x}$is a scalar. #### Orthogonality¶ The key to projection is orthogonality: The line from$\mathbf{b}$to$\mathbf{p}$(which can be written$\mathbf{b} - \hat{x}\mathbf{a}$) is perpendicular to$\mathbf{a}$. This means that $$\mathbf{a} \cdot (\mathbf{b} - \hat{x}\mathbf{a}) = 0$$ and so $$\hat{x} = \frac{\mathbf{a} \cdot \mathbf{b}}{\mathbf{a} \cdot \mathbf{a}}$$ ### The Algorithm¶ Motivation: We want orthonormal columns in$Q$and a Hessenberg$H$such that$A Q = Q H$. Thinking about it iteratively, $$A Q_n = Q_{n+1} H_n$$ where$Q_{n+1}$is$n\times n+1$and$H_n$is$n+1 \times n$. This creates a solvable recurrence relation. (source: Trefethen, Lecture 33) Pseudo-code for Arnoldi Algorithm Start with an arbitrary vector (normalized to have norm 1) for first col of Q for n=1,2,3... v = A @ nth col of Q for j=1,...n project v onto q_j, and subtract the projection off of v want to capture part of v that isn't already spanned by prev columns of Q store coefficients in H normalize v, and then make it the (n+1)th column of Q Notice that we are multiplying A by the previous vector in Q and removing the components that are not orthogonal to the existing columns of Q. Question: Repeated multiplications of A? Does this remind you of anything? #### Answer:¶ In [ ]: #Exercise Answer The *Power Method* involved iterative multiplications by A as well!  ### About how the Arnoldi Iteration works¶ • With the Arnoldi Iteration, we are finding an orthonormal basis for the Krylov subspace. The Krylov matrix $$K = \left[b \; Ab \; A^2b \; \dots \; A^{n-1}b \right]$$ has a QR factorization $$K = QR$$ and that is the same$Q$that is being found in the Arnoldi Iteration. Note that the Arnoldi Iteration does not explicity calculate$K$or$R\$.

• Intuition: K contains good information about the largest eigenvalues of A, and the QR factorization reveals this information by peeling off one approximate eigenvector at a time.

The Arnoldi Iteration is two things:

1. the basis of many of the iterative algorithms of numerical linear algebra
2. a technique for finding eigenvalues of nonhermitian matrices (Trefethen, page 257)

How Arnoldi Locates Eigenvalues

1. Carry out Arnoldi iteration
2. Periodically calculate the eigenvalues (called Arnoldi estimates or Ritz values) of the Hessenberg H, using the QR algorithm
3. Check at whether these values are converging. If they are, they're probably eigenvalues of A.

### Implementation¶

In [246]:
# Decompose square matrix A @ Q ~= Q @ H
def arnoldi(A):
m, n = A.shape
assert(n <= m)

# Hessenberg matrix
H = np.zeros([n+1,n]) #, dtype=np.float64)
# Orthonormal columns
Q = np.zeros([m,n+1]) #, dtype=np.float64)
# 1st col of Q is a random column with unit norm
b = np.random.rand(m)
Q[:,0] = b / np.linalg.norm(b)
for j in range(n):
v = A @ Q[:,j]
for i in range(j+1):
#This comes from the formula for projection of v onto q.
#Since columns q are orthonormal, q dot q = 1
H[i,j] = np.dot(Q[:,i], v)
v = v - (H[i,j] * Q[:,i])
H[j+1,j] = np.linalg.norm(v)
Q[:,j+1] = v / H[j+1,j]

# printing this to see convergence, would be slow to use in practice
print(np.linalg.norm(A @ Q[:,:-1] - Q @ H))
return Q[:,:-1], H[:-1,:]

In [86]:
Q, H = arnoldi(A)

8.59112969133
4.45398729097
0.935693639985
3.36613943339
0.817740180293


Check that H is tri-diagonal:

In [70]:
H

Out[70]:
array([[ 5.62746,  4.05085, -0.     ,  0.     , -0.     ],
[ 4.05085,  3.07109,  0.33036,  0.     , -0.     ],
[ 0.     ,  0.33036,  0.98297,  0.11172, -0.     ],
[ 0.     ,  0.     ,  0.11172,  0.29777,  0.07923],
[ 0.     ,  0.     ,  0.     ,  0.07923,  0.06034]])

#### Exercise¶

Write code to confirm that:

1. AQ = QH
2. Q is orthonormal

In [71]:
#Exercise:
np.allclose(A @ Q, Q @ H)

Out[71]:
True
In [456]:
#Exercise:
np.allclose(np.eye(len(Q)), Q.T @ Q)

Out[456]:
True

#### General Case:¶

General Matrix: Now we can do this on our general matrix A (not symmetric). In this case, we are getting a Hessenberg instead of a Tri-diagonal

In [74]:
Q0, H0 = arnoldi(A0)

1.44287067354
1.06234006889
0.689291414367
0.918098818651
4.7124490411e-16


Check that H is Hessenberg:

In [76]:
H0

Out[76]:
array([[ 1.67416,  0.83233, -0.39284,  0.10833,  0.63853],
[ 1.64571,  1.16678, -0.54779,  0.50529,  0.28515],
[ 0.     ,  0.16654, -0.22314,  0.08577, -0.02334],
[ 0.     ,  0.     ,  0.79017,  0.11732,  0.58978],
[ 0.     ,  0.     ,  0.     ,  0.43238, -0.07413]])
In [77]:
np.allclose(A0 @ Q0, Q0 @ H0)

Out[77]:
True
In [78]:
np.allclose(np.eye(len(Q0)), Q0.T @ Q0), np.allclose(np.eye(len(Q0)), Q0 @ Q0.T)

Out[78]:
(True, True)

## Putting it all together¶

In [215]:
def eigen(A, max_iter=20):
Q, H = arnoldi(A)
Ak, QQ = practical_qr(H, max_iter)
U = Q @ QQ
D = np.diag(Ak)
return U, D

In [213]:
n = 10
A0 = np.random.rand(n,n)
A = A0 @ A0.T

In [242]:
U, D = eigen(A, 40)

14.897422908
1.57451192745
1.4820012435
0.668164424736
0.438450319682
0.674050723258
1.19470880942
0.217103444634
0.105443975462
3.8162597576e-15
[ 27.34799   1.22613   1.29671   0.70253   0.49651   0.56779   0.60974
0.70123   0.19209   0.04905]
[ 27.34981   1.85544   1.04793   0.49607   0.44505   0.7106    1.00724
0.07293   0.16058   0.04411]
[ 27.34981   2.01074   0.96045   0.54926   0.61117   0.8972    0.53424
0.19564   0.03712   0.04414]
[ 27.34981   2.04342   0.94444   0.61517   0.89717   0.80888   0.25402
0.19737   0.03535   0.04414]
[ 27.34981   2.04998   0.94362   0.72142   1.04674   0.58643   0.21495
0.19735   0.03534   0.04414]
[ 27.34981   2.05129   0.94496   0.90506   0.95536   0.49632   0.21015
0.19732   0.03534   0.04414]
[ 27.34981   2.05156   0.94657   1.09452   0.79382   0.46723   0.20948
0.1973    0.03534   0.04414]
[ 27.34981   2.05161   0.94863   1.1919    0.70539   0.45628   0.20939
0.19728   0.03534   0.04414]
[ 27.34981   2.05162   0.95178   1.22253   0.67616   0.45174   0.20939
0.19727   0.03534   0.04414]
[ 27.34981   2.05162   0.95697   1.22715   0.66828   0.44981   0.2094
0.19725   0.03534   0.04414]
[ 27.34981   2.05162   0.96563   1.22124   0.66635   0.44899   0.20941
0.19724   0.03534   0.04414]
[ 27.34981   2.05162   0.97969   1.20796   0.66592   0.44864   0.20942
0.19723   0.03534   0.04414]
[ 27.34981   2.05162   1.00135   1.18652   0.66585   0.44849   0.20943
0.19722   0.03534   0.04414]
[ 27.34981   2.05162   1.03207   1.15586   0.66584   0.44843   0.20943
0.19722   0.03534   0.04414]
[ 27.34981   2.05162   1.07082   1.11714   0.66584   0.4484    0.20944
0.19721   0.03534   0.04414]
[ 27.34981   2.05162   1.11307   1.07489   0.66585   0.44839   0.20944
0.1972    0.03534   0.04414]
[ 27.34981   2.05162   1.15241   1.03556   0.66585   0.44839   0.20945
0.1972    0.03534   0.04414]
[ 27.34981   2.05162   1.18401   1.00396   0.66585   0.44839   0.20945
0.1972    0.03534   0.04414]
[ 27.34981   2.05162   1.20652   0.98145   0.66585   0.44839   0.20946
0.19719   0.03534   0.04414]
[ 27.34981   2.05162   1.22121   0.96676   0.66585   0.44839   0.20946
0.19719   0.03534   0.04414]
[ 27.34981   2.05162   1.23026   0.95771   0.66585   0.44839   0.20946
0.19719   0.03534   0.04414]
[ 27.34981   2.05162   1.23563   0.95234   0.66585   0.44839   0.20946
0.19718   0.03534   0.04414]
[ 27.34981   2.05162   1.23876   0.94921   0.66585   0.44839   0.20947
0.19718   0.03534   0.04414]
[ 27.34981   2.05162   1.24056   0.94741   0.66585   0.44839   0.20947
0.19718   0.03534   0.04414]
[ 27.34981   2.05162   1.24158   0.94639   0.66585   0.44839   0.20947
0.19718   0.03534   0.04414]
[ 27.34981   2.05162   1.24216   0.94581   0.66585   0.44839   0.20947
0.19718   0.03534   0.04414]
[ 27.34981   2.05162   1.24249   0.94548   0.66585   0.44839   0.20947
0.19718   0.03534   0.04414]
[ 27.34981   2.05162   1.24268   0.94529   0.66585   0.44839   0.20947
0.19718   0.03534   0.04414]
[ 27.34981   2.05162   1.24278   0.94519   0.66585   0.44839   0.20947
0.19718   0.03534   0.04414]
[ 27.34981   2.05162   1.24284   0.94513   0.66585   0.44839   0.20947
0.19718   0.03534   0.04414]
[ 27.34981   2.05162   1.24288   0.94509   0.66585   0.44839   0.20947
0.19718   0.03534   0.04414]
[ 27.34981   2.05162   1.2429    0.94507   0.66585   0.44839   0.20947
0.19717   0.03534   0.04414]
[ 27.34981   2.05162   1.24291   0.94506   0.66585   0.44839   0.20947
0.19717   0.03534   0.04414]
[ 27.34981   2.05162   1.24291   0.94506   0.66585   0.44839   0.20947
0.19717   0.03534   0.04414]
[ 27.34981   2.05162   1.24292   0.94505   0.66585   0.44839   0.20947
0.19717   0.03534   0.04414]
[ 27.34981   2.05162   1.24292   0.94505   0.66585   0.44839   0.20947
0.19717   0.03534   0.04414]
[ 27.34981   2.05162   1.24292   0.94505   0.66585   0.44839   0.20948
0.19717   0.03534   0.04414]
[ 27.34981   2.05162   1.24292   0.94505   0.66585   0.44839   0.20948
0.19717   0.03534   0.04414]
[ 27.34981   2.05162   1.24292   0.94505   0.66585   0.44839   0.20948
0.19717   0.03534   0.04414]
[ 27.34981   2.05162   1.24292   0.94505   0.66585   0.44839   0.20948
0.19717   0.03534   0.04414]

In [240]:
D

Out[240]:
array([ 5.10503,  0.58805,  0.49071, -0.65174, -0.60231, -0.37664,
-0.13165,  0.0778 , -0.10469, -0.29771])
In [241]:
np.linalg.eigvals(A)

Out[241]:
array([ 27.34981,   2.05162,   1.24292,   0.94505,   0.66585,   0.44839,
0.20948,   0.19717,   0.04414,   0.03534])
In [236]:
np.linalg.norm(U @ np.diag(D) @ U.T - A)

Out[236]:
0.0008321887107978883
In [237]:
np.allclose(U @ np.diag(D) @ U.T, A, atol=1e-3)

Out[237]:
True

Let's find some eigenvalues!

from Nonsymmetric Eigenvalue Problems chapter:

Note that "direct" methods must still iterate, since finding eigenvalues is mathematically equivalent to finding zeros of polynomials, for which no noniterative methods can exist. We call a method direct if experience shows that it (nearly) never fails to converge in a fixed number of iterations.

Iterative methods typically provide approximations only to a subset of the eigenvalues and eigenvectors and are usually run only long enough to get a few adequately accurate eigenvalues rather than a large number

our ultimate algorithm: the shifted Hessenberg QR algorithm

### Coming Up¶

We will be coding our own QR decomposition (two different ways!) in the future, but first we are going to see another way that the QR decomposition can be used: to calculate linear regression.

## End¶

### Miscellaneous Notes¶

Symmetric matrices come up naturally:

• distance matrices