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Off-by-one errors are common in using the C library because it is not consistent with respect to whether one needs to subtract 1 byte – functions like fgets() and strncpy will never write past the length given them (fgets() subtracts 1 itself, and only retrieves (length − 1) bytes), whereas others, like strncat will write past the length given them.
Since the secant method can carry out twice as many steps in the same time as Steffensen's method, [a] in practical use the secant method actually converges faster than Steffensen's method, when both algorithms succeed: The secant method achieves a factor of about (1.6) 2 ≈ 2.6 times as many digits for every two steps (two function ...
MATLAB (an abbreviation of "MATrix LABoratory" [22]) 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.
SageMath is designed partially as a free alternative to the general-purpose mathematics products Maple and MATLAB. It can be downloaded or used through a web site. SageMath comprises a variety of other free packages, with a common interface and language. SageMath is developed in Python.
More generally, there are d! possible orders for a given array, one for each permutation of dimensions (with row-major and column-order just 2 special cases), although the lists of stride values are not necessarily permutations of each other, e.g., in the 2-by-3 example above, the strides are (3,1) for row-major and (1,2) for column-major.
The indexing expression for a 1-based index would then be ′ +. Hence, the efficiency benefit at run time of zero-based indexing is not inherent, but is an artifact of the decision to represent an array with the address of its first element rather than the address of the fictitious zeroth element.
Thus, if we have a vector containing elements (2, 5, 7, 3, 8, 6, 4, 1), and we want to create an array slice from the 3rd to the 6th items, we get (7, 3, 8, 6). In programming languages that use a 0-based indexing scheme, the slice would be from index 2 to 5. Reducing the range of any index to a single value effectively eliminates that index.
We consider estimating the density of the Gaussian mixture (4π) −1 exp(− 1 ⁄ 2 (x 1 2 + x 2 2)) + (4π) −1 exp(− 1 ⁄ 2 ((x 1 - 3.5) 2 + x 2 2)), from 500 randomly generated points. We employ the Matlab routine for 2-dimensional data. The routine is an automatic bandwidth selection method specifically designed for a second order ...