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A plot of the smoothstep(x) and smootherstep(x) functions, using 0 as the left edge and 1 as the right edgeSmoothstep is a family of sigmoid-like interpolation and clamping functions commonly used in computer graphics, [1] [2] video game engines, [3] and machine learning.
SymPy is an open-source Python library for symbolic computation. It provides computer algebra capabilities either as a standalone application, as a library to other applications, or live on the web as SymPy Live [2] or SymPy Gamma. [3] SymPy is simple to install and to inspect because it is written entirely in Python with few dependencies.
IML++ is a C++ library for solving linear systems of equations, capable of dealing with dense, sparse, and distributed matrices. IT++ is a C++ library for linear algebra (matrices and vectors), signal processing and communications. Functionality similar to MATLAB and Octave. LAPACK++, a C++ wrapper library for LAPACK and BLAS
$3,150 (Commercial), $99 (Student Suite), $700 (Academic), $194 (Home) including price of MATLAB. Proprietary: Provides tools for solving and manipulating symbolic math expressions and performing variable-precision arithmetic. SymPy: Ondřej Čertík 2006 2007 1.13.2: 11 August 2024: Free modified BSD license: Python-based TI-Nspire CAS ...
UNITY is a programming language constructed by K. Mani Chandy and Jayadev Misra for their book Parallel Program Design: A Foundation. It is a theoretical language which focuses on what , instead of where , when or how .
The code in the previous section uses an unoptimized inner while loop for clarity. In the unoptimized version, one must perform five multiplications per iteration. To reduce the number of multiplications the following code for the inner while loop may be used instead:
The following MATLAB code will plot the root locus of the closed-loop transfer function as varies using the described manual method as well as the rlocus built-in function: % Manual method K_array = ( 0 : 0.1 : 220 ). ' ; % .' is a transpose.
The degree of , or in other words the number of nth primitive roots of unity, is (), where is Euler's totient function. The fact that Φ n {\displaystyle \Phi _{n}} is an irreducible polynomial of degree φ ( n ) {\displaystyle \varphi (n)} in the ring Z [ x ] {\displaystyle \mathbb {Z} [x]} is a nontrivial result due to Gauss . [ 4 ]