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Download as PDF; Printable version; In other projects ... The table shows a comparison of functional programming languages which compares various ... Python: No [73 ...
Folds can be regarded as consistently replacing the structural components of a data structure with functions and values. Lists, for example, are built up in many functional languages from two primitives: any list is either an empty list, commonly called nil ([]), or is constructed by prefixing an element in front of another list, creating what is called a cons node ( Cons(X1,Cons(X2,Cons ...
The following mathematical statements hold when A is a full rank square matrix: A^-1 *(A * x)==A^-1 * (b) (A^-1 * A)* x ==A^-1 * b (matrix-multiplication associativity) x = A^-1 * b. where == is the equivalence relational operator. The previous statements are also valid MATLAB expressions if the third one is executed before the others ...
Note how the use of A[i][j] with multi-step indexing as in C, as opposed to a neutral notation like A(i,j) as in Fortran, almost inevitably implies row-major order for syntactic reasons, so to speak, because it can be rewritten as (A[i])[j], and the A[i] row part can even be assigned to an intermediate variable that is then indexed in a separate expression.
In mathematics, low-rank approximation refers to the process of approximating a given matrix by a matrix of lower rank. More precisely, it is a minimization problem, in which the cost function measures the fit between a given matrix (the data) and an approximating matrix (the optimization variable), subject to a constraint that the approximating matrix has reduced rank.
However, not all persistent data structures are purely functional. [1]: 16 For example, a persistent array is a data-structure which is persistent and which is implemented using an array, thus is not purely functional. [citation needed] In the book Purely functional data structures, Okasaki compares destructive updates to master chef's knives.
Distance-matrix methods may produce either rooted or unrooted trees, depending on the algorithm used to calculate them. [4] Given n species, the input is an n × n distance matrix M where M ij is the mutation distance between species i and j. The aim is to output a tree of degree 3 which is consistent with the distance matrix.
For the ring R = Z[√−5], both the module R and its submodule M generated by 2 and 1 + √−5 are indecomposable. While R is not isomorphic to M, R ⊕ R is isomorphic to M ⊕ M; thus the images of the M summands give indecomposable submodules L 1, L 2 < R ⊕ R which give a different decomposition of R ⊕ R.