World Cup Women U17 Group E stats & predictions

MATCHDAY 1

Equipo A vs Equipo B:

En un encuentro lleno de emoción, Equipo A demostró su solidez defensiva al contener los ataques del rápido Equipo B. El partido terminó en un empate, lo que dejó abiertas las posibilidades para futuros enfrentamientos.

Equipo C vs Equipo D:

Equipo C mostró su capacidad para adaptarse y controlar el ritmo del partido. A pesar de la resistencia del joven Equipo D, lograron llevarse la victoria con un marcador ajustado.

MATCHDAY 2

Equipo B vs Equipo C:

Un duelo espectacular donde ambos equipos mostraron su mejor fútbol. El partido fue muy parejo, pero al final, Equipo B logró salir victorioso gracias a una jugada maestra en los últimos minutos.

Equipo D vs Equipo A:

Aunque Equipo D jugó con valentía, no pudo superar la táctica defensiva de Equipo A. El partido terminó sin goles, pero dejó claro que Equipo D tiene mucho potencial para mejorar.

Táctica Defensiva de Equipo A

Equipo A se enfoca en una sólida línea defensiva que dificulta la penetración del rival. Utilizan una formación 4-4-2 que les permite cubrir bien las bandas y proteger el área central.

Táctica Ofensiva de Equipo B

Con un estilo de juego ofensivo, Equipo B busca controlar el balón y crear oportunidades de gol constantemente. Su formación 4-3-3 les permite tener presencia en todo el campo.

Equilibrio Táctico de Equipo C

Equipo C combina una defensa sólida con ataques rápidos. Su formación 4-2-3-1 les permite tener jugadores creativos en ataque mientras mantienen una buena estructura defensiva.

Juventud y Energía de Equipo D

Aunque menos experimentado, Equipo D utiliza su juventud a favor con ataques veloz[0]: # -*- coding: utf-8 -*- [1]: import numpy as np [2]: from . import _array_ops [3]: from . import _array_utils [4]: from . import _binned_statistic_dd [5]: from . import _histogram_base [6]: from . import _ndpolybase [7]: from ._wraps import wrap_subroutine [8]: __all__ = ['histogram', 'histogramdd', 'binned_statistic', [9]: 'binned_statistic_2d', 'binned_statistic_dd', [10]: 'gaussian_kde', 'scoreatpercentile', 'scoreatpercentile_from_sequence'] [11]: class histogram(_histogram_base.HistogramBase): [12]: """ [13]: Compute the histogram of a set of data. [14]: Histograms provide a visualization of data distribution. [15]: They are also useful for quantization and for [16]: comparing two probability distributions. [17]: Parameters [18]: ---------- [19]: x : array_like or tuple of array_like [20]: Input data. The histogram is computed over the flattened array [21]: by default. [22]: If `x` is a sequence of arrays then a multi-dimensional histogram [23]: is computed over all the data combined. [24]: bins : int or sequence or str or `~astropy.units.Quantity`, optional [25]: If `bins` is an int, it defines the number of equal-width bins in the [26]: given range (10, by default). If `bins` is a sequence, [27]: it defines the bin edges, including the rightmost edge, [28]: allowing for non-uniform bin widths. [29]: Alternatively, if `x` contains multidimensional samples, [30]: `bins` can be a string or `~astropy.units.Quantity` object to be passed to [31]: `numpy.histogram_bin_edges` (e.g., ``'auto'``, ``'fd'``, ``'sturges'``, [32]: ``'doane'``, ``'scott'``, ``'rice'``, ``'sqrt'``, or ``'auto'``) [33]: specifying the method used to calculate the optimal bin width, [34]: or an array of bin edges manually specifying the bins. [35]: range : array_like or str or `~astropy.units.Quantity`, optional [36]: The lower and upper range of the bins. [37]: (`min(data)`, `max(data)`), by default. [38]: If provided as a string or Quantity object, [39]: this is passed to `numpy.histogram_bin_edges`. [40]: density : bool, optional [41]: If ``False`` (default) the result will contain the number of samples in each bin. [42]: If ``True``, the result is the value of the probability *density* function at the bin, [43]: normalized such that *integral(hist[x], dx) == 1*. [44]: Returns [45]: ------- [46]: hist : ndarray or tuple of ndarray [47]: The values of the histogram. See `density` for a description of how these values are normalized. """ class histogramdd(_binned_statistic_dd.BinnedStatisticDD): """ Parameters x : array_like An n x m array containing n data points in m dimensions Alternatively an m-length list of n arrays can be passed; in this case only In this case each row will represent a d-dimensional point and each array in the list represents one dimension This option is provided for convenience so that multiple datasets can be easily input as arguments (e.g., hist = scipy.stats.histogramdd(x=[X,Y,Z])) bins : int or sequence or str or `~astropy.units.Quantity`, optional Number of bins for each dimension Defaults to 10 bins for each dimension If int If bins is an int then it specifies the number of bins for each dimension. If bins is a string or Quantity object then it specifies how to calculate bin width. If sequence If bins is a sequence then it should be a length-D sequence where D is the number of dimensions and each element specifies the bin edges for that dimension. The first element specifies the bin edges for x[:,0], and so on until x[:,-1] which uses bins[-1]. Each element can either be an int giving the number of bins for that dimension, or it can be a 1-D array giving the bin edges for that dimension directly. Note that when passing an array to specify bin edges you do not need to pass N+1 elements where N is your largest data value because histogramdd does not assume your first and last bins include your minimum and maximum values respectively; see documentation on numpy.histogramdd for more information. Examples The following examples all produce 10x20x15 bins in 3-D: >>> histogramdd([X,Y,Z],bins=10) >>> histogramdd([X,Y,Z],bins=(10,20,15)) >>> histogramdd([X,Y,Z],bins=(10,[0,.5,1,.51,.6,...15],15)) >>> histogramdd([X,Y,Z],bins='auto') >>> histogramdd([X,Y,Z],bins='fd') range : array_like or str or `~astropy.units.Quantity`, optional The lower and upper range of the bins Defaults to (min(X), max(X)) in each dimension Note that if range is not specified either using range or through edges[i][0] and edges[i][-1], then automatic determination of range might not work for some inputs: see documentation on numpy.histogramdd normed : bool, optional Whether to return probabilities instead of counts weights : array_like An n-element array of values w_i weighing each sample density : bool If False (default), returns counts; if True returns probability densities spacial_dims : int copy : bool old_behavior : bool blocksize : int return_edges : bool _pp_args : dict ***** Tag Data ***** ID: 1 description: Class definition for histogram with complex parameters and detailed docstring. start line: 11 end line: 44 dependencies: - type: Class name: _histogram_base.HistogramBase start line: 5 end line: 5 context description: This snippet defines a class 'histogram' that extends '_histogram_base.HistogramBase'. It includes parameters with various options such as handling multidimensional arrays, different types for 'bins', and options like 'density'. The docstring provides detailed information about these parameters and their possible values. algorithmic depth: 4 algorithmic depth external: N obscurity: 4 advanced coding concepts: 4 interesting for students: 5 self contained: N ************ ## Challenging aspects ### Challenging aspects in above code 1. **Handling Multidimensional Arrays**: The provided snippet allows input data to be either flattened arrays or sequences of arrays representing multidimensional samples. Handling such inputs requires careful consideration to ensure correct binning across dimensions. 2. **Flexible Bin Specification**: The `bins` parameter can be an integer (defining equal-width bins), a sequence (defining specific bin edges), or a string/Quantity object indicating different methods for computing optimal bin width using `numpy.histogram_bin_edges`. This flexibility necessitates robust handling to accommodate various input formats seamlessly. 3. **Range Parameter**: The `range` parameter can be specified as an array-like object defining lower and upper bounds or as a string/Quantity object passed to `numpy.histogram_bin_edges`. Properly interpreting and applying these different types requires careful parsing and validation logic. 4. **Density Option**: The `density` parameter changes how histogram values are normalized—either as raw counts or probability densities. Implementing this feature requires correctly adjusting computations based on this boolean flag. 5. **Inheritance from Base Class**: Extending `_histogram_base.HistogramBase` implies leveraging functionality from this base class while potentially overriding certain methods to accommodate additional features specific to this implementation. ### Extension 1. **Dynamic Bin Adjustment**: Extend functionality to dynamically adjust bin widths based on data distribution characteristics during runtime. 2. **Weighted Histograms**: Introduce support for weighted histograms where each sample has an associated weight influencing its contribution to histogram counts. 3. **Custom Bin Functions**: Allow users to define custom functions for determining bin edges beyond standard methods like `'auto'`, `'fd'`, etc. 4. **Multi-threaded Computation**: Although generic multi-thread safety isn't suggested here due to its broad applicability, implementing specific parallel computation strategies tailored to handle large datasets efficiently could add complexity. 5. **Handling Streaming Data**: Adapt the histogram computation to handle streaming data where new samples continuously arrive and require updating existing histograms without recomputing from scratch. ## Exercise ### Problem Statement: You are tasked with enhancing the given [SNIPPET] by introducing additional features while maintaining its core functionalities: 1. **Dynamic Bin Adjustment**: Implement dynamic adjustment of bin widths based on data distribution characteristics during runtime. 2. **Weighted Histograms**: Add support for weighted histograms where each sample has an associated weight influencing its contribution to histogram counts. 3. **Custom Bin Functions**: Allow users to define custom functions for determining bin edges beyond standard methods like `'auto'`, `'fd'`, etc. ### Requirements: - Extend the existing [SNIPPET] code without breaking existing functionalities. - Implement dynamic bin adjustment that recalculates optimal bin widths based on real-time data analysis. - Add support for weighted histograms with an additional