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MATLAB (an abbreviation of "MATrix LABoratory" [18]) is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms , creation of user interfaces , and interfacing with programs written in other languages.
FreeMat is a free open-source numerical computing environment and programming language, [1] similar to MATLAB and GNU Octave. [2] In addition to supporting many MATLAB functions and some IDL functionality, it features a codeless interface to external C, C++, and Fortran code, further parallel distributed algorithm development (via MPI), and has plotting and 3D visualization capabilities. [3]
Matrix-free conjugate gradient method has been applied in the non-linear elasto-plastic finite element solver. [7] Solving these equations requires the calculation of the Jacobian which is costly in terms of CPU time and storage. To avoid this expense, matrix-free methods are employed.
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The first step when using the direct stiffness method is to identify the individual elements which make up the structure. Once the elements are identified, the structure is disconnected at the nodes, the points which connect the different elements together.
The Robotics Toolbox for Python is a reimplementation of the Robotics Toolbox for MATLAB for Python 3. [ 7 ] [ 8 ] Its functionality is a superset of the Robotics Toolbox for MATLAB, the programming model is similar, and it supports additional methods to define a serial link manipulator including URDF and elementary transform sequences.
The straightforward multiplication of a matrix that is X × Y by a matrix that is Y × Z requires XYZ ordinary multiplications and X(Y − 1)Z ordinary additions. In this context, it is typical to use the number of ordinary multiplications as a measure of the runtime complexity. If A is a 10 × 30 matrix, B is a 30 × 5 matrix, and C is a 5 × ...
The definition of matrix multiplication is that if C = AB for an n × m matrix A and an m × p matrix B, then C is an n × p matrix with entries = =. From this, a simple algorithm can be constructed which loops over the indices i from 1 through n and j from 1 through p, computing the above using a nested loop: