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By default, a Pandas index is a series of integers ascending from 0, similar to the indices of Python arrays. However, indices can use any NumPy data type, including floating point, timestamps, or strings. [4]: 112 Pandas' syntax for mapping index values to relevant data is the same syntax Python uses to map dictionary keys to values.
Support for multi-dimensional arrays may also be provided by external libraries, which may even support arbitrary orderings, where each dimension has a stride value, and row-major or column-major are just two possible resulting interpretations. Row-major order is the default in NumPy [19] (for Python).
NumPy (pronounced / ˈ n ʌ m p aɪ / NUM-py) is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. [3]
For a (0,2) tensor, [1] twice contracting with the inverse metric tensor and contracting in different indices raises each index: =. Similarly, twice contracting with the metric tensor and contracting in different indices lowers each index:
The following list contains syntax examples of how to determine the dimensions (index of the first element, the last element or the size in elements). Some languages index from zero. Some index from one. Some carry no such restriction, or even allow indexing by any enumerated type, not only integers.
# imports from jax import jit import jax.numpy as jnp # define the cube function def cube (x): return x * x * x # generate data x = jnp. ones ((10000, 10000)) # create the jit version of the cube function jit_cube = jit (cube) # apply the cube and jit_cube functions to the same data for speed comparison cube (x) jit_cube (x)
The @ infix operator is intended to be used by libraries such as NumPy for matrix multiplication. [104] [105] The syntax :=, called the "walrus operator", was introduced in Python 3.8. It assigns values to variables as part of a larger expression. [106] In Python, == compares by value.
Youden's J statistic is = + = + with the two right-hand quantities being sensitivity and specificity.Thus the expanded formula is: = + + + The index was suggested by W. J. Youden in 1950 [1] as a way of summarising the performance of a diagnostic test; however, the formula was earlier published in Science by C. S. Pierce in 1884. [2]