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For example, to perform an element by element sum of two arrays, a and b to produce a third c, it is only necessary to write c = a + b In addition to support for vectorized arithmetic and relational operations, these languages also vectorize common mathematical functions such as sine.
The arrays are heterogeneous: a single array can have keys of different types. PHP's associative arrays can be used to represent trees, lists, stacks, queues, and other common data structures not built into PHP. An associative array can be declared using the following syntax:
The literature on programming languages contains an abundance of informal claims about their relative expressive power, but there is no framework for formalizing such statements nor for deriving interesting consequences. [52] This table provides two measures of expressiveness from two different sources.
PHP >= 7.3 [87] Toolkit-independent Yes Push-pull Yes Table and row data gateway or Doctrine Unit tests, PHP Unit or other independent Yes ACL-based Yes APC, Database, File, Memcache, Zend Platform: Yes Yes ? ? Laravel: PHP >= 8.0 [88] Any Yes Push Yes Eloquent: PHPUnit: Yes Yes Yes APC, Database, File, Memcache, Redis: Yes Yes Yes Yes Li3 ...
List comprehension is a syntactic construct available in some programming languages for creating a list based on existing lists. It follows the form of the mathematical set-builder notation (set comprehension) as distinct from the use of map and filter functions.
C++ template library; binds to optimized BLAS such as the Intel MKL; Includes matrix decompositions, non-linear solvers, and machine learning tooling Eigen: Benoît Jacob C++ 2008 3.4.0 / 08.2021 Free MPL2: Eigen is a C++ template library for linear algebra: matrices, vectors, numerical solvers, and related algorithms. Fastor [5]
Typically, two representations are present, one for integers fitting the native word size minus any tag bit (SmallInteger) and one supporting arbitrary sized integers (LargeInteger). Arithmetic operations support polymorphic arguments and return the result in the most appropriate compact representation.
Both MATLAB and GNU Octave natively support linear algebra operations such as matrix multiplication, matrix inversion, and the numerical solution of system of linear equations, even using the Moore–Penrose pseudoinverse. [7] [8] The Nial example of the inner product of two arrays can be implemented using the native matrix multiplication operator.