The matrix analysis functions det, rcond, hess, and expm also show significant increase in speed on large double-precision arrays. You can use the colon operator to create a sequence of numbers within any range, incremented by one. Manipulation of Matrices and Vectors The name Matlab' evolved as an abbreviation of MATrix LABoratory'. Given a point as a 3 element column vector X, the output point X is simply: X RX. For example, if one of A or B is a scalar, then the scalar is combined with each element of the other array. If the sizes of A and B are compatible, then the two arrays implicitly expand to match each other. The sizes of A and B must be the same or be compatible. You can rotate a point by performing a very simple matrix multiplication. C A.B raises each element of A to the corresponding powers in B. For example, create a row vector whose elements are the integers from 1 to 10. Assuming that your data points are in a N x 3 matrix where N is the total number of points that you have, simply apply a rotation matrix to each point. The matrix multiply (X*Y) and matrix power (X^p) operators show significant increase in speed on large double-precision arrays (on order of 10,000 elements). The colonis a handy way to create matrices whose elements are sequential and evenly spaced. As a general rule, complicated functions speed up more than simple functions. MATLAB ® uses algorithms to generate pseudorandom and pseudoindependent numbers. The operation is not memory-bound processing time is not dominated by memory access time. For example, most functions speed up only when the array contains several thousand elements or more. The data size is large enough so that any advantages of concurrent execution outweigh the time required to partition the data and manage separate execution threads. Inputs A and B must either be the same size or have sizes that are compatible (for example, A is an M -by- N matrix and B is a scalar or 1 -by- N row vector). They should require few sequential operations. Operands, specified as scalars, vectors, matrices, multidimensional arrays, tables, or timetables. These sections must be able to execute with little communication between processes. The function performs operations that easily partition into sections that execute concurrently.
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