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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.
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]
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
However, a generator is an object with persistent state, which can repeatedly enter and leave the same scope. 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.
For example, software libraries for linear algebra, such as BLAS, typically provide options to specify that certain matrices are to be interpreted in transposed order to avoid data movement. However, there remain a number of circumstances in which it is necessary or desirable to physically reorder a matrix in memory to its transposed ordering.
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.
In numerical linear algebra, the Arnoldi iteration is an eigenvalue algorithm and an important example of an iterative method.Arnoldi finds an approximation to the eigenvalues and eigenvectors of general (possibly non-Hermitian) matrices by constructing an orthonormal basis of the Krylov subspace, which makes it particularly useful when dealing with large sparse matrices.