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Inputs: A, b, ω Output: φ Choose an initial guess φ to the solution repeat until convergence for i from 1 until n do set σ to 0 for j from 1 until n do if j ≠ i then set σ to σ + a ij φ j end if end (j-loop) set φ i to (1 − ω)φ i + ω(b i − σ) / a ii end (i-loop) check if convergence is reached end (repeat) Note
NumPy (pronounced / ˈ n ʌ m p aɪ / NUM-py) is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. [3]
Matrix multiplication is an example of a 2-rank function, because it operates on 2-dimensional objects (matrices). Collapse operators reduce the dimensionality of an input data array by one or more dimensions. For example, summing over elements collapses the input array by 1 dimension.
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.
is how one would use Fortran to create arrays from the even and odd entries of an array. Another common use of vectorized indices is a filtering operation. Consider a clipping operation of a sine wave where amplitudes larger than 0.5 are to be set to 0.5. Using S-Lang, this can be done by
A generator call can then be used in place of a list, or other structure whose elements will be iterated over. Whenever the for loop in the example requires the next item, the generator is called, and yields the next item. Generators don't have to be infinite like the prime-number example above.
Conversely, loop fusion (or loop jamming) is a compiler optimization and loop transformation which replaces multiple loops with a single one. [3] [2] Loop fusion does not always improve run-time speed. On some architectures, two loops may actually perform better than one loop because, for example, there is increased data locality within
Unlike other for loop constructs, however, foreach loops [1] usually maintain no explicit counter: they essentially say "do this to everything in this set", rather than "do this x times". This avoids potential off-by-one errors and makes code simpler to read.