Liga 1 Placement Playoff stats & predictions

Liga 1 Placement Playoff in Peru: Expert Betting Preview

The Liga 1 Placement Playoff in Peru presents a thrilling opportunity for bettors seeking to capitalize on the dynamic football scene. This season has been marked by intense competition, with teams vying for top positions to secure playoff spots and avoid relegation. The betting landscape is rich with opportunities, driven by fluctuating team performances and key player form. Understanding these dynamics is crucial for crafting successful betting strategies.

Comprehensive League Overview

The current season of Liga 1 has seen a mix of established powerhouses and emerging contenders battling for supremacy. The league's competitive nature means that every match can be unpredictable, making it a fertile ground for informed betting. With teams like Alianza Lima and Sporting Cristal consistently performing well, the focus shifts to how mid-table teams can leverage their strengths to climb the rankings.

Current Season Context

This season has been characterized by strategic gameplay and tactical versatility among teams. Key matches have often hinged on individual brilliance or tactical masterstrokes from managers, making player form a critical factor in match outcomes. Bettors should pay close attention to head-to-head records and recent form to make informed predictions.

Betting Landscape

• The market is diverse, with options ranging from outright winners to more nuanced bets like correct scores and double chance.
• Understanding market trends and odds movements can provide an edge in identifying value bets.
• Bettors should also consider external factors such as weather conditions and travel fatigue, which can influence match results.

Daily Match Predictions

With the playoffs approaching, each match becomes increasingly significant. Our analysis focuses on key fixtures where we believe there are opportunities for profitable bets based on statistical insights and current form.

Featured Matches

Today's standout match features Alianza Lima against Universitario de Deportes. Alianza Lima has shown resilience in away games this season, while Universitario has struggled defensively at home. Our prediction leans towards a narrow victory for Alianza Lima.

• Alianza Lima's attacking prowess could exploit Universitario's defensive gaps.
• Betting on over 2.5 goals may offer value given both teams' scoring trends.

Betting Opportunities

The upcoming fixture between Sporting Cristal and Cienciano offers another intriguing betting scenario. Sporting Cristal's home advantage and recent form suggest they are strong favorites, but Cienciano's counter-attacking style could pose challenges.

• Sporting Cristal is likely to win, but considering a handicap bet might yield better returns.
• Analyze previous encounters to gauge potential outcomes accurately.

League Statistics

Analyzing league statistics provides deeper insights into team performance trends and key metrics that influence match outcomes. This section delves into the data that bettors should consider when placing their wagers.

Team Performance

This season's top performers have demonstrated consistency in both attack and defense. Teams like Alianza Lima have maintained high possession rates, translating into goal-scoring opportunities, while others like Sport Huancayo have excelled defensively, keeping clean sheets frequently.

• Possession statistics can indicate control of the game flow, impacting betting on total goals scored.
• Clean sheet records are crucial for predicting under/over goals markets.

Trends

Trends such as home/away performance disparities and head-to-head records are pivotal in shaping betting strategies. Teams often exhibit different levels of performance depending on venue, which can be leveraged for more accurate predictions.

• Home advantage remains significant; consider this when evaluating odds for home matches.
• Recent head-to-head trends can highlight potential upsets or dominant performances.

Key Metrics

Metrics such as expected goals (xG) provide insights into the quality of chances created by teams. Analyzing xG alongside actual goals scored helps identify overperforming or underperforming teams relative to their potential output.

• xG analysis can uncover undervalued teams likely to outperform their current standing.
• Evaluating shot accuracy alongside xG offers a comprehensive view of offensive efficiency.

Expert Betting Advice

Crafting effective betting strategies requires a blend of statistical analysis, market awareness, and strategic insight. This section provides expert advice tailored to maximizing returns during the Liga 1 Placement Playoff season.

Betting Strategies

To succeed in Liga 1 betting, adopt strategies that balance risk with potential reward. Diversifying bets across different markets can mitigate losses while capitalizing on high-value opportunities when they arise.

• Incorporate accumulator bets cautiously; they offer higher returns but come with increased risk due to multiple variables involved.
• Focusing on specific markets like first-half/full-time or double chance can enhance profitability by reducing variance compared to outright winner bets.I need help with some code I've written related to analyzing my datasets `train` and `test`. Here is what I have so far: # [SNIPPET] Can you help me add some advanced logic here? Specifically, I want a function that dynamically analyzes each column based on its data type (numerical vs categorical) and prints summary statistics accordingly.<|end|> <|assistant|>Sure! Let’s create a function called `dynamic_column_analysis` which will analyze each column based on its data type. Here’s how you might do it: python import pandas as pd def dynamic_column_analysis(df): for column in df.columns: if df[column].dtype == 'object': print(f"Column {column} is categorical.") print(df[column].value_counts(dropna=False)) else: print(f"Column {column} is numerical.") print(df[column].describe()) print("n") # Example usage: train = pd.read_csv("train.csv") test = pd.read_csv("test.csv") print("Train Dataset Analysis:") dynamic_column_analysis(train) print("Test Dataset Analysis:") dynamic_column_analysis(test) This function checks each column’s data type (`object` typically denotes categorical variables) and then prints appropriate summary statistics.<|end|> <|user|>Great! Now let’s take it further—I want custom visualizations using seaborn/matplotlib that show relationships between multiple columns (e.g., pair plots conditioned on another column). How would you integrate this?<|end|> <|assistant|>We can use seaborn’s pairplot functionality combined with conditioning logic using hue parameter. Here’s an example: python import seaborn as sns import matplotlib.pyplot as plt def conditional_pair_plot(df, hue_col=None): sns.pairplot(df.select_dtypes(include=[np.number]), hue=hue_col) plt.show() # Example usage: train = pd.read_csv("train.csv") test = pd.read_csv("test.csv") # Assuming 'target' is your conditioning column. conditional_pair_plot(train, hue_col='target') This will create pair plots of all numerical columns in your dataframe with colors representing different values of `hue_col`. Would you like any further customization?<|end|> <|user|>Yes! Can we add logic where missing values are filled based not only on mean/mode but also considering other columns’ distributions? For instance filling missing values in one column based upon median value of another correlated column.<|end|> <|assistant|>Certainly! We'll implement an advanced imputation strategy using pandas’ capabilities along with some logical conditions. Here’s an example: python def advanced_imputation(df): if 'column_a' in df.columns: if df['column_b'].isnull().any(): median_value = df.loc[df['column_a'] > df['column_a'].median(), 'column_b'].median() df['column_b'].fillna(median_value, inplace=True) if 'column_c' in df.columns: if df['column_d'].isnull().any(): mode_value = df.loc[df['column_c'] == df['column_c'].mode()[0], 'column_d'].mode()[0] df['column_d'].fillna(mode_value, inplace=True) return df # Example usage: train = pd.read_csv("train.csv") test = pd.read_csv("test.csv") print("Before Imputation:") print(train.isnull().sum()) train = advanced_imputation(train) test = advanced_imputation(test) print("nAfter Imputation:") print(train.isnull().sum()) This code fills missing values in `column_b` based upon median value of `column_a` when it exceeds its own median value; similarly fills missing values in `column_d` based upon mode value of `column_c`. Do you need any additional customization?<|end|> <|user|>Yes indeed! I’d like some feature engineering steps added—like creating interaction terms or polynomial features conditionally based upon certain thresholds.<|end|> <|assistant|>Sure! Let’s create interaction terms conditionally based upon certain thresholds. Here’s how you might do it: python def feature_engineering(df): if 'feature_1' in df.columns and 'feature_2' in df.columns: threshold_1 = df['feature_1'].median() threshold_2 = df['feature_2'].mean() condition_met = (df['feature_1'] > threshold_1) & (df['feature_2'] > threshold_2) df.loc[condition_met, 'interaction_term'] = df.loc[condition_met]['feature_1'] * df.loc[condition_met]['feature_2'] if 'feature_3' in df.columns: poly_feature_name = f'{df["feature_3"].name}_squared' df[poly_feature_name] = df['feature_3'] ** 2 return df # Example usage: train = pd.read_csv("train.csv") test = pd.read_csv("test.csv") print("Before Feature Engineering:") print(train.head()) train = feature_engineering(train) test = feature_engineering(test) print("nAfter Feature Engineering:") print(train.head()) This code creates an interaction term between `feature_1` and `feature_2` only when both exceed their respective thresholds; additionally squares the values of `feature_3`. Any further enhancements needed?<||end||> *** Excerpt *** The most important effect observed was significantly increased peak VO(.sub .2) following training compared with pretraining levels (P less than .01). When peak VO(.sub .2) was normalized per kilogram body weight there was no difference between pretraining levels (51 +/- SEM .08 ml/kg/min) versus posttraining levels (52 +/- SEM .06 ml/kg/min). However there was no difference between pretraining levels versus posttraining levels when peak VO(._sub .) was expressed per kilogram fat-free mass (P greater than .05); pretraining level were similar at baseline versus after training at both visits.(36 +/- SEM .09 vs43 +/- SEM .07 ml/kgFFM/min). The increase observed above reflects primarily increased oxygen consumption during exercise at workloads above lactate threshold.(12)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27) As illustrated by Figure lA,B there were significant increases observed at workloads above lactate threshold following training compared with pretraining levels(P less than .05). However there was no significant change below lactate threshold.(P greater than .05). *** Revision *** ## Plan To elevate the difficulty level significantly while ensuring the exercise demands profound understanding alongside additional factual knowledge beyond what is provided directly within the excerpt itself involves integrating complex physiological concepts related specifically to exercise physiology—such as detailed mechanisms underlying changes in VO₂ max—and incorporating intricate statistical analysis nuances that go beyond basic significance testing. The revised excerpt should thus weave together sophisticated physiological terminology concerning adaptations within muscle tissue at molecular levels due to endurance training; delve into specifics about mitochondrial biogenesis or capillary density increases; mention specific enzymes involved; reference specific studies implicitly without direct citation requiring outside knowledge; include detailed statistical methodologies used beyond simple p-values indicating significance; introduce hypothetical scenarios demanding deductive reasoning about outcomes under varied conditions not explicitly stated within the text itself. By embedding nested counterfactuals ("if...then...else") scenarios regarding physiological responses under different hypothetical training regimens or environmental conditions—perhaps involving altitude acclimatization effects—or incorporating conditionals tied intricately together requiring unraveling through logical deduction rather than straightforward reading comprehension—the challenge escalates significantly. ## Rewritten Excerpt Following systematic endurance training protocols designed around progressive overload principles targeting aerobic capacity enhancement—a paradigm shift from traditional steady-state modalities—it emerged unequivocally through rigorous longitudinal assessments employing state-of-the-art cardiopulmonary exercise testing methodologies that maximal oxygen uptake ((VO_{text{sub}.}^{max})) exhibited statistically robust augmentation ((P<0.01)), transcending baseline measurements substantively. Normalization procedures applied (VO_{text{sub}.}^{max}) against somatic mass yielded negligible variance ((51 pm SEM cdot08) ml/kg/min pre-training versus (52 pm SEM cdot06) ml/kg/min post-training), ostensibly suggesting superficial adaptation scope constrained solely by mass distribution metrics rather than intrinsic aerobic capacity refinement per se. Contrastingly—and herein lies the crux—when recalibrating (VO_{text{sub}.}^{max}) vis-a-vis lean body mass devoid of adipose contribution ((FFM)), initial readings ((36 pm SEM cdot09) ml/kgFFM/min) harmonized closely with subsequent evaluations ((43 pm SEM cdot07) ml/kgFFM/min), though failing to breach statistical significance thresholds ((P>.05)). This nuanced observation intimates towards skeletal muscle oxidative efficiency enhancements predominantly operationalizing beyond anaerobic glycolytic thresholds—a phenomenon corroborated via incremental workload analyses delineated within Fig lA,B underscoring substantial increments post-intervention exclusively at exertional intensities surpassing lactate inflection points ((P<0.05)) whereas sub-threshold intensities remained statistically unaltered ((P>.05)). ## Suggested Exercise Given the findings presented after applying rigorous longitudinal assessments focused on enhancing aerobic capacity through systematic endurance training protocols centered around progressive overload principles: Which statement best encapsulates the implications regarding skeletal muscle adaptations resulting from said training regimen? A) Enhanced maximal oxygen uptake ((VO_{text{sub}.}^{max})) primarily indicates increased body mass rather than intrinsic improvements within muscular oxidative efficiency. B) Normalization of (VO_{text{sub}.}^{max}) against fat-free mass underscores negligible adaptation within skeletal muscle oxidative processes despite apparent improvements measured against total body mass. C) Significant improvements observed exclusively at exertional intensities surpassing lactate inflection points suggest enhanced skeletal muscle oxidative efficiency predominantly operationalizes through mechanisms possibly including mitochondrial biogenesis or capillary density augmentation. D) Sub-threshold intensities exhibiting statistically unaltered (VO_{text{sub}.}^{max}) post-training suggest adaptive responses are confined exclusively within anaerobic glycolytic pathways rather than aerobic metabolic processes. *** Revision *** check requirements: - req_no: 1 discussion: The draft does not require external knowledge beyond understanding VO₂max, normalization methods, FFM adjustments etc., all derived directly from common exercise physiology concepts. No specific external academic facts or theories are integrated into understanding. - req_no: 2 discussion: Understanding nuances such as why normalization against FFM matters, why exceeding lactate inflection points matters etc., requires comprehension beyond surface-level reading. - req_no: 3 discussion: The excerpt meets length requirements but could be more difficult by, perhaps integrating more intricate details about biochemical processes during aerobic/metabolic/ anaerobic transitions. - req_no: "4" discussion': Choices A-D seem plausible without deep understanding because they relate closely enough without requiring decipherment through deeper contextual insight; choices could be made more misleading by closer alignment yet distinct relevance." - req_no: "5" discussion': While challenging due to technical jargon used correctly relating fitness, physiology stats etc., it doesn't necessarily challenge those well-acquainted with undergraduate level topics unless deepened further. - req_no: "6" discussion': All choices appear relevant without viewing question specifics yet aren’t misleading enough - someone could guess correctly without fully grasping excerpt’s subtleties. external fact': Incorporate knowledge about specific signaling pathways involved during endurance exercises leading up changes seen at cellular level e.g., PGC-1α role during mitochondrial biogenesis, AMPK activation influencing energy metabolism shifts etc., which would require learners' familiarity outside immediate content given. revision suggestion": To truly integrate requirement No.:1 effectively along increasing complexity, intertwine specifics about cellular adaptations such as mentioning particular molecular/signaling/pathways' roles e.g., AMPK activation during high-intensity workouts leading up adaptations, role of PGC-1α during mitochondrial biogenesis linked directly back to observations/measures/statistics/statistical-significance; thereby requiring learners not just understand presented data but relate it back/compare/distinguish/from/to known biological mechanisms/pathways/functions/processes. revised excerpt": |- Following systematic endurance training protocols designed around progressive overload principles targeting aerobic capacity enhancement—a paradigm shift from traditional steady-state modalities—it emerged unequivocally through rigorous longitudinal assessments employing state-of-the-art cardiopulmonary exercise testing methodologies that maximal oxygen uptake ( correct choice': Significant improvements observed exclusively at exertional intensities surpassing lactate inflection points suggest enhanced skeletal muscle oxidative efficiency predominantly operationalizes through mechanisms possibly including mitochondrial biogenesis or capillary density augmentation influenced potentially by signaling pathways like AMPK activation or PGC-1α involvement. revised exercise": "Given findings presented after applying rigorous longitudinal assessments focused enhancing aerobic capacity through systematic endurance training protocols centered around progressive overload principles: Which statement best encapsulates implications regarding molecular signaling pathways contributing towards skeletal muscle adaptations resulting from said training regimen? incorrect choices: - Enhanced maximal oxygen uptake ( *** Revision $Revision *** check requirements: - req_no: "1" discussion: Requires integration of specific external knowledge such as detailed biochemical pathways involved during endurance exercises which isn't directly provided. -revision suggestion": To fulfill requirement No.:6 effectively along increasing complexity, incorporate specifics about cellular adaptations such as mentioning particular molecular/signaling/pathways' roles e.g., AMPK activation during high-intensity workouts leading up adaptations, ? role of PGC-u03b11u03b61u03b61u03b61u03b61u03b61u03b61u03b61u03b6 activation potentially influencing energy metabolism shifts; ? thereby requiring learners not just understand presented data but relate it back/compare/distinguish/from/to known biological mechanisms/pathways/functions/processes.' revised excerpt': |- Following systematic endurance training protocols designed around progressive overload principles targeting aerobic capacity enhancement—a paradigm shift from traditional steady-state modalities—it emerged unequivocally through rigorous longitudinal assessments employing state-of-the-art cardiopulmonary exercise testing methodologies that maximal oxygen uptake ( *** Revision 7 *** check requirements: - req_no: "1" discussion": Requires explicit connection between described physiological changes \((\Delta VO_{\text{sub}.\text{max}}\))\" revised excerpt': |- Following systematic endurance training protocols designed around progressive overload principles targeting aerobic capacity enhancement—a paradigm shift from traditional steady-state modalities—it emerged unequivocally through rigorous longitudinal assessments employing state-of-the-art cardiopulmonary exercise testing methodologies that maximal oxygen uptake ( correct choice': Specific molecular pathways such as AMPK activation play critical roles in mediating adaptations seen from increased maximal oxygen uptake due to endurance training involving progressive overload principles. revised exercise": "Given findings presented after applying rigorous longitudinal assessments focused enhancing aerobic capacity through systematic endurance training protocols centered around progressive overload principles: Which statement best encapsulates implications regarding molecular signaling pathways contributing towards skeletal muscle adaptations resulting from said training regimen? incorrect choices": - Endurance training primarily enhances cardiac output rather than affecting muscular oxygen utilization capacities significantly." <>I'm working with this Python class called `_SqueezedState`, which seems related to quantum mechanics states involving squeezing operators applied onto vacuum states across multiple modes simultaneously. Here's the snippet: python class _SqueezedState(Distribution): """Implement setup logic""" def __init__(self, means, log_scales diagonals, scale_kwarg_name='scale', super_init_kwargs=None): self.means=means#[tf.convert_to_tensor(means)] self.log_scales=log_scales#[tf.convert_to_tensor(log_scales)] self.diagonals=diagonals#[tf.convert_to_tensor(diagonals)] self.scale_kwarg_name=scale_kwarg_name #super init kwargs # if super_init_kwargs==None: super_init_kwargs={} #expand input dimensions if necessary # self.means,_=expand_to_same_shape(self.means,self.log_scales,self.diagonals) self.log_scales,_=expand_to_same_shape(self.means,self.log_scales,self.diagonals) self.diagonals,_=expand_to_same_shape(self.means,self.log_scales,self.diagonals) #default event space dims # super_init_kwargs.setdefault('event_dim',self.diagonals.shape[-1]) super().__init__(**super_init_kwargs) def _apply_op(self,input_,op): """ Utility method for elementwise application ops given an input tensor """ return tf.map_fn(op,input_,dtype=tf.float32) def _matmul(self,x): """ Matrix multiplication helper which handles broadcasting across batch dimensions """ vec=tf.reshape(x shape=(-1,x.shape[-d])) return tf.reshape(tf.matmul(vec,self.LU_matrix),x.shape[:-d]+(-1,)) @property def sigma(self): """Sigma matrix square root""" return tf.linalg.diag(tf.math.exp(self.log_scales)) @property def LU_matrix(self): """ Cholesky decomposition components needed for triangular solving Lu^{-T}x=y <=> L^{-T}U^{-T}x=y <=> U^Tx=L^Ty=z <=> T^Tx=z => x=T^Tz= """ L,U=self.sigma[self.scale_kwarg_name].lu() z=tf.linalg.triangular_solve(L,self._apply_op(U,(lambda x:x))) return tf.linalg.triangular_solve(U,z[...,::-1,:][...,::-1,:]) @property def A_mat(self): """Matrix square root""" return tf.linalg.sqrtm(tf.matmul(self.sigma,self.sigma,[[-1],[-1],[0]])) @property def A_mat_lu(self): """LU decomposition""" A=self.A_mat.matrix_lu() @property def Q_mat(self): """Q matrix appears after matrix completion step""" M=self.A_mat-self._apply_op(tf.linalg.tensor_diag_part(A),lambda x:x*0.) @property def Q_bar_mat(self): """Q-bar matrix appears after matrix completion step""" M_bar=self.A_mat-self._apply_op(tf.linalg.tensor_diag_part(A),(lambda x:x*diag_val*self.I)) @_util.check_properties(['sigma','means']) def sample_distributions(self,sample_shape=()): dist_params={'means':self.means} try:#works until tensorflow supports passing non-static batch shapes directly into MultivariateNormalTriL constructor # dist_params[self.scale_kwarg_name]=tfd.MultivariateNormalTriL( loc=tf.zeros(sample_shape+self.sigma.shape[:-d]), scale_tril=self.sigma) except TypeError:#not implemented error # dist_params[self.scale_kwarg_name]=partial(tfd.MultivariateNormalTriL, loc=tf.zeros(sample_shape+self.sigma.shape[:-d]), scale_tril=self.sigma)#return partially initialized object # return transformed_distribution.TransformedDistribution( distribution=distribution_independent.DistributionIndependent( distribution=distribution.LinearOperatorDistribution( reinterpreted_batch_ndims=self.event_dim,distribution= dist_params[self.scale_kwarg_name]),reinterpreted_batch_ndims=(len(sample_shape)+self.event_dim)), bijector=squeezed_bijector.SqueezedBijector(diagonal_shift_val=self.diagonals,name='{}_forward'.format(type(dist_params[self.scale_kwarg_name]).__name__))) @_util.check_properties(['sigma','means']) def log_prob_parts_from_moments_preprocessed(mu,sigma_inv,L_inv,y,g,mug,Sigmag,Lamdag,M,P,P_half,resolvent,rhs,beta,Sigma,Sigma_beta,M_resolvent,M_sigma,M_resolvent_sigma,M_beta,Sigma_beta_resolvent,Sigma_M_sigma,Sigma_M_beta,Sigma_M_resolvent,Sigma_P_half,Sigma_Sigmag,Sigma_y,M_resolvent_y,M_sigma_y,M_y,M_P_half,M_Sigmag,M_beta_y,det_sigmaprod_mudiff_divisor,P_half_diff_divisor,resolvent_divisor,y_divisor,beta_divisor): """ Main computation routine which calculates intermediate quantities required calculating log_prob parts given moments tensors already processed appropriately Args : mu : mean tensor shaped [...,*B] where ... represents batch dimensions sigma_inv : precision tensor shaped [...,*B,*B] where ... represents batch dimensions L_inv : inverse lower triangular component tensor shaped [...,*B,*B] where ... represents batch dimensions y : tensor shaped [...] where [...] represents event dims excluding diagonal entries g : tensor shaped [...] where [...] represents event dims excluding diagonal entries mug : tensor shaped [...,*B] representing y projected onto mean vector mu Sigmag : tensor shaped [...] representing y projected onto covariance Sigma Lamdag : tensor shaped [...,*B,*B] representing covariance Sigma projected onto lower triangular component L M : tensor shaped [...,*B,*B] representing resolvent multiplied by precision Sigma^{-T}*inv(z-Sigma)*Sigma^{-T} P : tensor shaped [...,*B,*B] representing resolvent multiplied by precision Sigma^{-T}*inv(z-Sigma)^{-T}*Sigma^{-T} P_half : tensor shaped [...,*B,*B] representing resolvent multiplied by precision Sigma^{-T}*inv(sqrt(z-Sigma))*Sigma^{-T} resolvent :tensor shaped [...,*B+extra_event_dims,...*extra_event_dims] representing inverse shifted covariance resolvent calculated via Sherman-Morrison-Woodbury identity plus possible extra event dims added via matrix completion step rhs :tensor shaped [...*extra_event_dims+*B,...*extra_event_dims+*extra_event_dims] appearing inside calculation loop over extra event dims containing right hand side appearing inside linear system solve appearing inside loop over extra event dims beta :tensor shaped [...] appearing inside calculation loop over extra event dims containing quantity beta appearing inside linear system solve appearing inside loop over extra event dims Sigma :tensor shaped [...*extra_event_dims+*B,...*extra_event_dims+*extra_event_dims] appearing inside calculation loop over extra event dims containing shifted covariance matrix appearing inside linear system solve appearing inside loop over extra event dims Sigma_beta :tensor shaped [...] appearing inside calculation loop over extra event dims containing quantity Sigma-beta appearing inside linear system solve appearing inside loop over extra event dims M_resolvent:M*S^-resolvent reshaped appropriately according whether shifted_covariance_completer argument passed had zero diagonals set initially M_sigma:M*S^-sigma reshaped appropriately according whether shifted_covariance_completer argument passed had zero diagonals set initially M_resolvent_sigma:M*S^-resolvent*S^-sigma reshaped appropriately according whether shifted_covariance_completer argument passed had zero diagonals set initially M_beta:M*S^-beta reshaped appropriately according whether shifted_covariance_completer argument passed had zero diagonals set initially Sigma_M_sigma:sigma*M*S^-sigma reshaped appropriately according whether shifted_covariance_completer argument passed had zero diagonals set initially Sigma_M_beta:sigma*M*S^-beta reshaped appropriately according whether shifted_covariance_completer argument passed had zero diagonals set initially Sigma_M_resolvent:sigma*M*S^-resolvent reshaped appropriately according whether shifted_covariance_completer argument passed had zero diagonals set initially Sigma_P_half:sigma*P_half reshaped appropriately according whether shifted_covariance_completer argument passed had zero diagonals set initially Sigma_Sigmag:sigma*Sigmag reshaped appropriately according whether shifted_covariance_completer argument passed had zero diagonals set initially Sigma_y:sigma*y reshaped appropriately according whether shifted_covariance_completer argument passed had zero diagonals set initially M_resolvent_y:M*S^-resovlent*y reshaped appropriately according whether shifted_covariance_completer argument passed had zero diagonals set initially M_sigma_y:M*S^-sigma*y reshaped appropriately according whether shifted_covariance_completer argument passed had zero diagonals set initially M_y:M*y reshaped appropriately according whether shifted_covariance_completer argument passed had zero diagonals set initially M_P_half:M*S^-P_half reshaped appropriately according whether shifted_covariance_completer argument passed had zero diagonals set initially M_Sigmag:M*S^-Sigmag reshaped appropriately according whether shifted_covariance_completer argument passed had zero dimensioanls included M_beta_y:M*s^-beta*yreshapde appropriatlyaccordingwhethershiftedcovarianc completere argumntpassedhadzero diagnoassetinitially det_sigmaprod_mudiff_divisor:(det(Sigmaprod)-mu_diff.T()*Sigmaprodinv*mu_diff)^(-divisor_val)/det(Sigmaprod)^(-divisor_val)*(det(Sigmaprod))^exponent_val P_half_diff_divisor:(P_half-Phalf_zero_diag)^(-divisor_val)/(Phalf_zero_diag)^(-divisor_val)*(Phalf_zero_diag)^exponent_val resovlent_divisor:(resovlent-resovlent_zero_diag)^(-divisor_val)/(resovlent_zero_diag)^(-divisor_val)*(resovlent_zero_diag)^exponent_val y_divisor:(y-y_zero_diag)^(-divisor_val)/(y_zero_diag)^(-dividorval)*(y_zero_diag)^exponentval beta_divior:(beta-beta_zero_diags)-dividorval/(beta-zero_diags)^(-dividorval)*(beta-zero_diags)^exponentval Returns : dict mapping strings describing intermediate quantities computed here corresponding keys needed calculating log_prob parts hereafter :: { '-log_z_det_over_two':intermediate quantity -log(det(z))/two corresponding part needed calculating log_prob parts hereafter , '-log_det_sigmasqrd_over_two':intermediate quantity -log(det(Sigmarsqrd))/two corresponding part needed calculating log_prob parts hereafter , '-half_log_det_sigmaprod_over_two':intermediate quantity -half*log(det(Sigmaprod))/two corresponding part needed calculating log_prob parts hereafter , '-half_log_det_p_over_two':intermediate quantity -half*log(det(P))/two corresponding part needed calculating log_prob parts hereafter , '-half_log_det_p_half_over_two':intermediate quantity -half*log(det(P_Half))/two corresponding part needed calculating log_prob parts hereafter , '-half_log_det_resolvant_over_two':intermediate quantity -half*log(det(resolvant))/two corresponding part needed calculating log_prob parts hereafter , ... ... ... ... ... } Note :- this method assumes any possible extra dimensionality arising due inclusion possible additional diagonal elements via call signature setting diagonal_shift_val keyword arguemnt nonzero has already been accountedfor before calling method via processing moments tensors accordingly beforehand . Method relies heavilyon numpy.einsum operationsover tensorflow operations wheneverpossible whereverpossible since einsum operationsover tensorflow tensors muchfasterthan tensorflow operations . Intermediate quantities returned correspondto keys used calling method _log_prob_parts_from_moments_preprocessed helper method defined laterherebelow . Method assumes moments tensors already processed beforehand accountingfor any possibleadditionaldimensionalityarisingdueto call signature setting diagonal_shift_val keywordargumentnonzero . Method relies heaviliyon numpy.einsum operationsover tensorflow operations wheneverpossible whereverpossible sinceeinsum operationsovertensorflow tensors muchfasterthan tensorflowoperations . Note :- method assumes moments tensors already processed beforehand accountingfor any possibleadditionaldimensionalityarisingdueto call signature setting diagonal_shift_val keywordargumentnonzero . Note :- method relies heavilyon numpy.einsum operationsover tensorflow operations wheneverpossible whereverpossible since einsum operationsovertensorflow tensors muchfasterthan tensorflow operations . """ dets={}-log(tf.linalg.det(sigma_inv)/tf.constant(0,-float))-log(tf.linalg.det(L_inv)/tf.constant(0,-float)) dets.update({'det_sigmasqrd_minus_mu_t_times_sigmasqrdinv_times_mu_minus_z_minus_mu_t_times_L_t_times_L_times_mu_minus_z_over_two': (-tf.math.log(tf.linalg.det(Lamdag)-tf.tensordot(mug,mug,[[-d],[-d]])-(y-g).dot(y-g)-g.dot(g)-mug.dot(g)-g.dot(mug)-mu.T.dot(sigma_inv)).numpy()/tf.constant(0.-float))/(numpy.float64)} ) dets.update({'det_sigmasqrd_minus_mu_t_times_sigmasqrdinv_times_mu_plus_g_t_times_g_plus_y_times_y_plus_z_minus_mu_t_times_L_t_times_L_times_mu_plus_z': (-tf.math.log(tf.linalg.det(Lamdag)+tf.tensordot(mug,mug,[[-d],[-d]])+(y-g).dot(y-g)+g.dot(g)+mug.dot(g)+g.dot(mug)+mu.T.dot(sigma_inv)).numpy()/tf.constant(0.-float))/(numpy.float64)} ) dets.update({'det_sigmasqrd_minus_z_minus_mu_t_times_L_t_times_L_times_mu_plus_z': (-tf.math.log(tf.linalg.det(Lamdag)-(y-g).dot(y-g)-