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def plot_karyotype_summary(haploid_coverage, chromosomes, chrom_length, output_dir, bed_filename, bed_file_sep=',', binsize=1000000, ...
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import os import bisect def create_percentile_rasters( raster_path, output_path, units_short, units_long, start_value, percentile_list, aoi_shape_path): """Creates a percentile (quartile) raster based on the raster_dataset. An attribute table is also constructed for the raster_dataset that...
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import torch def probs_to_mu_sigma(probs): """Calculate mean and covariance matrix for each channel of probs tensor of keypoint probabilites [N, C, H, W] mean calculated on a grid of scale [-1, 1] Parameters ---------- probs : torch.Tensor tensor of shape [N, C, H, W] where each chann...
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def fetch_biomart_genes_mm9(): """Fetches mm9 genes from Ensembl via biomart.""" return _fetch_genes_biomart( host='http://may2012.archive.ensembl.org', gene_name_attr='external_gene_id')
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def tweet_words(tweet): """Return the words in a tweet.""" return extract_words(tweet_text(tweet))
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def meter_statistics(meter_id,api_endpoint,token,meter_list,web,**kwargs): """ Get the statistics for the specified meter. Args: meter_id(string): The meter name. api_endpoint(string): The api endpoint for the ceilometer service. token(string): X-Auth-token. meter_list(list): T...
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from typing import Union from typing import Tuple def parse_image_size(image_size: Union[Text, int, Tuple[int, int]]): """Parse the image size and return (height, width). Args: image_size: A integer, a tuple (H, W), or a string with HxW format. Returns: A tuple of integer (height, width). ...
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def find_last_match(view, what, start, end, flags=0): """Find last occurrence of `what` between `start`, `end`. """ match = view.find(what, start, flags) new_match = None while match: new_match = view.find(what, match.end(), flags) if new_match and new_match.end() <= end: ...
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def convert_metrics_per_batch_to_per_sample(metrics, target_masks): """ Args: metrics: list of len(num_batches), each element: list of len(num_metrics), each element: (num_active_in_batch,) metric per element target_masks: list of len(num_batches), each element: (batch_size, seq_len, feat_dim) b...
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import asyncio async def get_series(database, series_id): """Get a series.""" series_query = """ select series.id, series.played, series_metadata.name, rounds.tournament_id, tournaments.id as tournament_id, tournaments.name as tournament_name, events.id as event_id, events.name as event_name ...
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def n_mpjpe(predicted, target): """ Normalized MPJPE (scale only), adapted from: https://github.com/hrhodin/UnsupervisedGeometryAwareRepresentationLearning/blob/master/losses/poses.py """ assert predicted.shape == target.shape norm_predicted = np.mean(np.sum(predicted**2, axis=2, keepdims=T...
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import math def calc_distance(p1, p2): """ calculates a distance on a 2d euclidean space, between two points""" dist = math.sqrt((p2[0] - p1[0]) ** 2 + (p2[1] - p1[1]) ** 2) return dist
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def rgb2ycbcr(img, range=255., only_y=True): """same as matlab rgb2ycbcr, please use bgr2ycbcr when using cv2.imread img: shape=[h, w, 3] range: the data range only_y: only return Y channel """ in_img_type = img.dtype img.astype(np.float32) range_scale = 255. / range img *= range_sca...
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def _create_xctest_bundle(name, actions, binary): """Creates an `.xctest` bundle that contains the given binary. Args: name: The name of the target being built, which will be used as the basename of the bundle (followed by the .xctest bundle extension). actions: The context's action...
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def doFile(path_, *args, **kwargs): """Execute a given file from path with arguments.""" result, reason = loadfile(path_) if result: data = result(*args, **kwargs) if data: return data[1] error(data[1]) error(reason)
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from pretty import pretty from pprint import pformat def pformat(obj, verbose=False): """ Prettyprint an object. Either use the `pretty` library or the builtin `pprint`. """ try: return pretty(obj, verbose=verbose) except ImportError: return pformat(obj)
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def reanalyze_function(*args): """ reanalyze_function(func_t pfn, ea_t ea1=0, ea_t ea2=BADADDR, bool analyze_parents=False) reanalyze_function(func_t pfn, ea_t ea1=0, ea_t ea2=BADADDR) reanalyze_function(func_t pfn, ea_t ea1=0) reanalyze_function(func_t pfn) """ return _idaapi.reanalyze_function...
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def categorical_sample_logits(logits): """ Samples (symbolically) from categorical distribution, where logits is a NxK matrix specifying N categorical distributions with K categories specifically, exp(logits) / sum( exp(logits), axis=1 ) is the probabilities of the different classes Cleverly ...
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def mass(d, r): """ computes the right hand side of the differential equation of mass continuity """ return 4 * pi * d * r * r
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def bord(u): """ éxécution de bord("undébutuntructrucundébut") i suffix estPréfixe 23 ndébutuntructrucundébut False 22 débutuntructrucundébut False 21 ébutuntructrucundébut False 20 butuntructrucundébut False 19 utuntructrucundébut False 18 tuntructrucundé...
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def is_unique_n_bit_vector(string: str) -> bool: """ Similiar to the dict solution, it just uses a bit vector instead of a dict or array. """ vector = 0 for letter in string: if vector & 1 << ord(letter): return False vector |= 1 << ord(letter) return True
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def seq2msk(isq): """ Convert seqhis into mskhis OpticksPhoton.h uses a mask but seq use the index for bit-bevity:: 3 enum 4 { 5 CERENKOV = 0x1 << 0, 6 SCINTILLATION = 0x1 << 1, 7 MISS = 0x1 << 2, 8 BU...
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def split(ich): """ Split a multi-component InChI into InChIs for each of its components. (fix this for /s [which should be removed in split/join operations] and /m, which is joined as /m0110.. with no separators) :param ich: InChI string :type ich: str :rtype: tuple(str)...
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def crtb_cb(client, crtb): """Wait for the crtb to have the userId populated""" def cb(): c = client.reload(crtb) return c.userId is not None return cb
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def create_network(network_input, n_alphabets): """ create the structure of the neural network """ model = Sequential() model.add(LSTM(512,input_shape=(network_input.shape[1], network_input.shape[2]),return_sequences=True)) model.add(Dropout(0.3)) model.add(Bidirectional(LSTM(512, return_sequences=T...
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def create_derivative_graph(f, xrange, n): """Takes a function as an input with a specific interval xrange, then creates a list with the ouput y-points for the nth derivative of f. :param f: Input function that we wish to take the derivative of. :type f: lambda :param xrange: The interval on wh...
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def _matching_not_matching(on, **kwargs): """ Change the text for matching/not matching """ text = "matching" if not on else "not matching" classname = "colour-off" if not on else "colour-on" return text, classname
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import os def prepare_testenv(config=None, template=None, args=None): """ prepare an engine-ready environment for a test This utility method is used to provide an `RelengEngine` instance ready for execution on an interim working directory. Args: config (optional): dictionary of options t...
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def sample(model, x, steps, temperature=1.0, sample=False, top_k=None): """ take a conditioning sequence of indices in x (of shape (b,t)) and predict the next token in the sequence, feeding the predictions back into the model each time. Clearly the sampling has quadratic complexity unlike an RNN that is...
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def vstack(arg_list): """Wrapper on vstack to ensure list argument. """ return Vstack(*arg_list)
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import json def metadata_to_list(metadata): """Transform a metadata dictionary retrieved from Cassandra to a list of tuples. If metadata items are lists they are split into multiple pairs in the result list :param metadata: dict""" res = [] for k, v in metadata.iteritems(): try: ...
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def GetSetUpAndResponse(): """ This method is called by an API acting as a client while performing the PSI protocol. This method initialises a server object. (This API acts as server) This method uses the PSI Request ID given by the calling API to identify the corresponding node list from the server di...
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from typing import Optional from typing import Union import torch from pathlib import Path import json def load_separator( model_str_or_path: str = "umxhq", niter: int = 1, residual: bool = False, slicq_wiener: bool = False, wiener_win_len: Optional[int] = 300, device: Union[str, torch.device]...
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def IntermediateParticleConst_get_decorator_type_name(): """IntermediateParticleConst_get_decorator_type_name() -> std::string""" return _RMF.IntermediateParticleConst_get_decorator_type_name()
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def multiply_add_plain_with_delta(ct, pt, context_data): """Add plaintext to ciphertext. Args: ct (Ciphertext): ct is pre-computed carrier polynomial where we can add pt data. pt (Plaintext): A plaintext representation of integer data to be encrypted. context (Context): Context for extr...
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def ginput(n=1, timeout=30, debug=False): """ Simple functional call for physicists. This will wait for n clicks from the user and return a list of the coordinates of each click. """ x = GaelInput() return x(n, timeout, debug)
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import json from datetime import datetime def retrieve_form_data(form, submission_type="solution"): """Quick utility function that groups together the processing of request data. Allows for easier handling of exceptions Takes request object as argument On Success, returns hashmap of processed data...other...
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import os def existing_file(fname): """ Check if the file exists. If not raise an error Parameters ---------- fname: string file name to parse Returns ------- fname : string """ if os.path.isfile(fname): return fname else: msg = "The file '{}' does...
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def keep_english_for_spacy_nn(df): """This function takes the DataFrame for songs and keep songs with english as main language for english version of spacy neural network for word processing""" #Keep only english for spacy NN English preprocessing words #Network for other languages like fre...
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def make_dealer_cards_more_fun(deck, dealer): """ to make dealercards more fun to make dealer win this game more. :param dealercards: dealercards :return: none maybe has a lot of memory work will arise. """ dealercards = card_sorting_dealer(dealer) count = 0 if jokbo(dealercards) =...
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import os import configparser import logging def subinit1_initpaths_config_log(): """ Initializes the paths (stored in global __PATHS): 1 Finds the project location 2 Reads config.ini 3 Reads the paths defined in config.ini 4 Checks that the paths exist """ # ----------------------------------------------...
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def data(request): """Returns available albums from the database. Can be optionally filtered by year. This is called from templates/albums/album/index.html when the year input is changed. """ year = request.GET.get('year') if year: try: year = int(year) except (ValueErro...
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from typing import Tuple def yaw_to_quaternion3d(yaw: float) -> Tuple[float,float,float,float]: """ Args: - yaw: rotation about the z-axis Returns: - qx,qy,qz,qw: quaternion coefficients """ qx,qy,qz,qw = Rotation.from_euler('z', yaw).as_quat() return qx,qy,qz,qw
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def parse_coap_response_code(response_code): """ Parse the binary code from CoAP response and return the response code as a float. See also https://tools.ietf.org/html/rfc7252#section-5.9 for response code definitions. :rtype float """ response_code_class = response_code // 32 response_code...
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from functools import reduce def modified_partial_sum_product( sum_op, prod_op, factors, eliminate=frozenset(), plate_to_step=dict() ): """ Generalization of the tensor variable elimination algorithm of :func:`funsor.sum_product.partial_sum_product` to handle markov dimensions in addition to plate...
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def load_scicar_cell_lines(test=False): """Download sci-CAR cell lines data from GEO.""" if test: adata = load_scicar_cell_lines(test=False) adata = subset_joint_data(adata) return adata return load_scicar( rna_url, rna_cells_url, rna_genes_url, atac_u...
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def binary_search(sorted_list, item): """ Implements a Binary Search, O(log n). If item is is list, returns amount of steps. If item not in list, returns None. """ steps = 0 start = 0 end = len(sorted_list) while start < end: steps += 1 mid = (start + end) // 2 ...
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from typing import List import os def _process_split( pipeline, *, filename_template: naming.ShardedFileTemplate, out_dir: utils.ReadWritePath, file_infos: List[naming.FilenameInfo], ): """Process a single split.""" beam = lazy_imports_lib.lazy_imports.apache_beam # Use unpack syntax on set...
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def _scale_by(number, should_fail=False): """ A helper function that creates a scaling policy and scales by the given number, if the number is not zero. Otherwise, just triggers convergence. :param int number: The number to scale by. :param bool should_fail: Whether or not the policy execution sho...
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import traceback def selectgender(value): """格式化为是/否 :param value:M/F, :return: 男/女 """ absent = {"M": u'男', "F": u'女'} try: if value: return absent[value] return "" except: traceback.print_exc()
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def Clifford_twirl_channel_one_qubit(K, rho, sys=1, dim=[2]): """ Twirls the given channel with Kraus operators in K by the one-qubit Clifford group on the given subsystem (specified by sys). """ n = int(np.log2(np.sum([d for d in dim]))) C1 = eye(2**n) C2 = Rx_i(sys, np.pi, n) C3 = Rx...
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def unpack_batch(batch, use_cuda=False): """ Unpack a batch from the data loader. """ input_ids = batch[0] input_mask = batch[1] segment_ids = batch[2] boundary_ids = batch[3] pos_ids = batch[4] rel_ids = batch[5] knowledge_feature = batch[6] bio_ids = batch[1] # knowledge_adjoin...
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def truncate(text: str, length: int = 255, end: str = "...") -> str: """Truncate text. Parameters --------- text : str length : int, default 255 Max text length. end : str, default "..." The characters that come at the end of the text. Returns ------- truncated text...
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from sys import path import logging def create_logger(log_dir, log_file, level="info"): """ Function used to create logger object based on log directory and log file name """ handler = RotatingFileHandler(filename=path.join(log_dir, log_file), mode='a', maxBytes=5...
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def gaussian_slice(x, sigma, mu): """ return a slice of x in which the gaussian is significant exp(-0.5 * ((x - mu) / sigma) ** 2) < given_threshold """ r = sigma * sp.sqrt(-2.0 * sp.log(small_thr)) x_lo = bisect_left(x, mu - r) x_hi = bisect_right(x, mu + r) return slice(x_lo, x_hi)
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def preview(delivery_id): """ 打印预览 :param delivery_id: :return: """ delivery_info = get_delivery_row_by_id(delivery_id) # 检查资源是否存在 if not delivery_info: abort(404) # 检查资源是否删除 if delivery_info.status_delete == STATUS_DEL_OK: abort(410) delivery_print_date = ti...
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import requests def request_with_json(json_payload): """ Load interpolations from the interp service into the DB """ test_response = requests.post(INTERP_URL, json=json_payload) test_response_json = test_response.json() return test_response_json
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def correlation(df, rowvar=False): """ Calculate column-wise Pearson correlations using ``numpy.ma.corrcoef`` Input data is masked to ignore NaNs when calculating correlations. Data is returned as a Pandas ``DataFrame`` of column_n x column_n dimensions, with column index copied to both axes. ...
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def cost_zpk_fit(zpk_args, f, x, error_func=kontrol.core.math.log_mse, error_func_kwargs={}): """The cost function for fitting a frequency series with zero-pole-gain. Parameters ---------- zpk_args: array A 1-D list of zeros, poles, and gain. Zeros and ...
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def getTrainPredictions(img,subImgSize,model): """Makes a prediction for an image. Takes an input of any size, crops it to specified size, makes predictions for each cropped window, and stitches output together. Parameters ---------- img : np.array (n x m x 3) Image to be transformed ...
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def use_bcbio_variation_recall(algs): """Processing uses bcbio-variation-recall. Avoids core requirement if not used. """ for alg in algs: jointcaller = alg.get("jointcaller", []) if not isinstance(jointcaller, (tuple, list)): jointcaller = [jointcaller] for caller in joi...
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from typing import Mapping def _sa_model_info(Model: type, types: AttributeType) -> Mapping[str, AttributeInfo]: """ Get the full information about the model This function gets a full, cachable, information about the model's `types` attributes, once. sa_model_info() can then filter it the way it likes, w...
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def bll6_models(estimators, cv_search={}, transform_search={}): """ Provides good defaults for transform_search to models() Args: estimators: list of estimators as accepted by models() transform_search: optional LeadTransform arguments to override the defaults """ cvd = dict( ...
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def bgColor(col): """ Return a background color for a given column title """ # Auto-generated columns if col in ColumnList._COLUMNS_GEN: return BG_GEN # KiCad protected columns elif col in ColumnList._COLUMNS_PROTECTED: return BG_KICAD # Additional user columns else: ...
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def merge_hedge_positions(df, hedge): """ 将一个表中的多条记录进行合并,然后对冲 :param self: :param df: :return: """ # 临时使用,主要是因为i1709.与i1709一类在分组时会出问题,i1709.是由api中查询得到 if df.empty: return df df['Symbol'] = df['InstrumentID'] # 合并 df = df.groupby(by=['Symbol', 'InstrumentID', 'HedgeFla...
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import numpy def BackwardSubTri(U,y): """ usage: x = BackwardSubTri(U,y) Row-oriented backward substitution to solve the upper-triangular, 'tridiagonal' linear system U x = y This function does not ensure that U has the correct nonzero structure. It does, however, attempt to catch ...
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def discrete_model(parents, lookup_table): """ Create CausalAssignmentModel based on a lookup table. Lookup_table maps inputs values to weigths of the output values The actual output values are sampled from a discrete distribution of integers with probability proportional to the weights. Looku...
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import base64 import json import tempfile import traceback def retrieve(datafile, provider): """ Retrieve a file from the remote provider :param datafile: :param provider: :return: the path to a temporary file containing the data, or None """ r = _connect(provider) try: data =...
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def edf_parse_message(EDFFILE): """Return message info.""" message = edf_get_event_data(EDFFILE).contents time = message.sttime message = string_at(byref(message.message[0]), message.message.contents.len + 1)[2:] message = message.decode('UTF-8') return (time, message)
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from typing import Dict import logging def read_abbrevs_and_add_to_db(abbrevs_path: str, db: Connection) -> Dict[str, int]: """Add abbreviations from `abbrevs_path` to `idx` and `defns`.""" with open(abbrevs_path, 'rt') as ab: abbrevs = read_abbrevs(ab) abbrev_nid = ...
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def is_encrypted(input_file: str) -> bool: """Checks if the inputted file is encrypted using PyPDF4 library""" with open(input_file, 'rb') as pdf_file: pdf_reader = PdfFileReader(pdf_file, strict=False) return pdf_reader.isEncrypted
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def get_parameter_by_name(device, name): """ Find the given device's parameter that belongs to the given name """ for i in device.parameters: if i.original_name == name: return i return
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from typing import Optional import requests def LogPrint(email: str, fileName: str, materialType: str, printWeight: float, printPurpose: str, msdNumber: Optional[str], paymentOwed: bool) -> bool: """Logs a print. Returns if the task was successful. :param email: Email of the user exporting the print. :pa...
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def is_requirement(line): """ Return True if the requirement line is a package requirement; that is, it is not blank, a comment, or editable. """ # Remove whitespace at the start/end of the line line = line.strip() # Skip blank lines, comments, and editable installs return not ( ...
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def read_pose_txt(pose_txt): """ Read the pose txt file and return a 4x4 rigid transformation. """ with open(pose_txt, "r") as f: lines = f.readlines() pose = np.zeros((4, 4)) for line_idx, line in enumerate(lines): items = line.split(" ") for i in range(4...
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def get_futures(race_ids=list(range(1, 13000))): """Get Futures for all BikeReg race pages with given race_ids.""" session = FuturesSession(max_workers=8) return [session.get(f'https://results.bikereg.com/race/{race_id}') for race_id in race_ids if race_id not in BAD_IDS]
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def sum_of_proper_divisors(number: int): """ Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n). :param number: :return: """ divisors = [] for n in range(1, number): if number % n == 0: divisors.append(n) retu...
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def coddington_meridional(p, q, theta): """ return radius of curvature """ f = p * q / (p + q) R = 2 * f / np.sin(theta) return R
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def read_analysis_file(timestamp=None, filepath=None, data_dict=None, file_id=None, ana_file=None, close_file=True, mode='r'): """ Creates a data_dict from an AnalysisResults file as generated by analysis_v3 :param timestamp: str with a measurement timestamp :param filepath: (str)...
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def get_player_macro_econ_df(rpl: sc2reader.resources.Replay, pid: int) -> pd.DataFrame: """This function organises the records of a player's major macroeconomic performance indicators. The function uses a player's PlayerStatsEvents contained in a Replay object to compose a...
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import re def get_seconds_from_duration(time_str: str) -> int: """ This function will convert the TM1 time to seconds :param time_str: P0DT00H01M43S :return: int """ pattern = re.compile('\w(\d+)\w\w(\d+)\w(\d+)\w(\d+)\w') matches = pattern.search(time_str) d, h, m, s = matches.groups(...
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def get_protecteds(object: Object) -> Dictionary: """Gets the protected namespaces of an object.""" return object.__protecteds__
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def pah2area(_position, angle, height, shape): """Calculates area from position, angle, height depending on shape.""" if shape == "PseudoVoigt": fwhm = np.tan(angle) * height area = (height * (fwhm * np.sqrt(np.pi / ln2)) / (1 + np.sqrt(1 / (np.pi * ln2)))) return area ...
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from typing import Callable import os import logging def caching_query_s3( s3_url: str, query_fun: Callable, force_query=False, df_save_fun: Callable = lambda df, loc: df.to_pickle(loc, compression="gzip"), df_load_fun: Callable = lambda loc: pd.read_pickle(loc, compression="gzip"), ): """ ...
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def config(key, values, axis=None): """Class decorator to parameterize the Chainer configuration. This is a specialized form of `parameterize` decorator to parameterize the Chainer configuration. For all `time_*` functions and `setup` function in the class, this decorator wraps the function to be calle...
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import sys import logging def handle_switches(args, sysroot): """Fetch the targeted binary and determine how to attach gdb. Args: args: Parsed arguments. sysroot: Local sysroot path. Returns: (binary_file, attach_pid, run_cmd). Precisely one of attach_pid or run_cmd will ...
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def dot2states(dot): """Translate a dot-bracket string in a sequence of numerical states""" dot = dot.replace(".", "0") # Unpaired dot = dot.replace("(", "1") # Paired dot = dot.replace(")", "1") # Paired return np.array(list(dot), dtype=int)
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def mel_to_hz(mels, htk=False): """Convert mel bin numbers to frequencies Examples -------- >>> librosa.mel_to_hz(3) 200. >>> librosa.mel_to_hz([1,2,3,4,5]) array([ 66.667, 133.333, 200. , 266.667, 333.333]) Parameters ---------- mels : np.ndarray [shape=(n,)],...
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import numpy as np def load_images(images): """ Decodes batch of image bytes and returns a 4-D numpy array. """ batch = [] for image in images: img_np = readImage(image) batch.append(img_np) batch_images = np.concatenate(batch) logger.info('batch_images.shape:%s'%(str(bat...
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from bob.db.base.utils import null import sys def dumplist(args): """Dumps lists of files based on your criteria""" db = Database() objects = db.objects( protocol=args.protocol, purposes=args.purposes, groups=args.groups, kinds=args.kinds ) output = sys.stdout ...
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def stats_hook(): """ decorator to register a stats hook. :raises InvalidStatsHookTypeError: invalid stats hook type error. :returns: stats hook class. :rtype: type """ def decorator(cls): """ decorates the given class and registers an instance of it into available...
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def safe_infer(node, context=None): """Return the inferred value for the given node. Return None if inference failed or if there is some ambiguity (more than one node has been inferred). """ try: inferit = node.infer(context=context) value = next(inferit) except exceptions.Infer...
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import functools def catch_exception(func): """ Returns: object: """ @functools.wraps(func) def wrapper(*args, **kwargs): worker = kwargs['error_catcher'] try: return func(*args, **kwargs) except Exception as e: print('stdout:', worker.stdou...
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def RandomCrop(parent, new_shape, name=""): """\ Crop an image layer at a random location with size ``[height, width]``. :param parent: parent layer :param new_shape: [height, width] size :param name: name of the output layer :return: CropRandom layer """ return _eddl.RandomCrop(parent,...
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import subprocess def run_client(instance): """ Start a client process """ port = [1008, 8989, 9002][instance] cpu = ['(3,4)', '(5,6)', '(7,8)'][instance] # TODO: the following line is an example of code that is not suitable! # should switch to run_udp_app instead of this function ...
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import time def get_linear_sys(eqns, params): """Gets the linear system corresponding to the symbolic equations Note that this function only work for models where the left-hand side of the equations all contain only linear terms with respect to the given model parameters. For these linear cases, this...
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def slightly(membership: npt.ArrayLike) -> npt.ArrayLike: """ Applies the element-wise function fn(u) = u^(1/2). :param membership: Membership function to be modified. >>> from fuzzy_expert.operators import slightly >>> slightly([0, 0.25, 0.5, 0.75, 1]) array([0. , 0.16326531, 0.9969618...
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def int_max(int_a, int_b): """ max(a, b) """ if int_a > int_b: return int_a else: return int_b
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def extract_depth_map(frame): """ Extract front-view lidar camera projection for ground-truth depth maps """ (range_images, camera_projections, range_image_top_pose) = frame_utils.parse_range_image_and_camera_projection(frame) for c in frame.context.camera_calibrations: if dataset_pb2.CameraName.Name.Nam...
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from .functions import express def cross(vect1, vect2): """ Returns cross product of two vectors. Examples ======== >>> from sympy.vector import CoordSys3D >>> from sympy.vector.vector import cross >>> R = CoordSys3D('R') >>> v1 = R.i + R.j + R.k >>> v2 = R.x * R.i + R.y * R.j + ...
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