Enumerate: returns a straight forward enumerator over all values.All these methods optionallyĪccept a Zeros enumeration to control whether zero-values may be skipped or not. That can be used to iterate through all elements. matrix // overwrite a sub-matrix with the content of another matrix: m. init 6 4 ( fun i j -> float ( 10 * i + j ) ) m. In F# we can also use its slicing syntax: let m = DenseMatrix. To overwrite those elements with the provided data. M.SubMatrix( 1, 2, 1, 2) // įor each of these methods there is also a variant prefixed with Set that can be used We can also get entire column or row vectors, or a new matrix from parts of an existing one. For example, an in-place version of the code above: m.Multiply(v, v) // v. Provided theĭimensions match, most also allow one of the arguments to be passed as result, These methods also have an overload that accepts the result data structure as last argument,Īllowing to avoid allocating new structures for every single operation. The equivalent code fromĪbove when using instance methods: var v 2 = m.Multiply(v) anspose.īut even the operators have equivalent methods. Or in F# as functions in the Matrix module, e.g. let m = matrix ] let v = vector let v' = m * v let m' = m + 2.0 * m Arithmetic Instance MethodsĪll other operations are covered by methods, like Transpose and Conjugate, ArithmeticsĪll the common arithmetic operators like +, -, *, / and % are provided,īetween matrices, vectors and scalars. Or using any other of all the available functions. random 3 4 ( ContinuousUniform ( - 2.0, 4.0 ) ) let m7b = DenseMatrix. randomStandard 3 4 // random matrix with a uniform and one with a Gamma distribution: let m7a = DenseMatrix. ofColumnSeq x // random matrix with standard distribution: let m6 = DenseMatrix. init 3 ( fun r -> float ( 100 * r + c ) ) ) let m5 = DenseMatrix. identity 4 // dense 3x4 matrix created from a sequence of sequence-columns let x = Seq. init 3 4 ( fun i j -> float ( i + j ) ) // diagonal 4x4 identity matrix of single precision let m4 = DiagonalMatrix. zero 3 4 // dense 3x4 matrix initialized by a function let m3 = DenseMatrix. (usually the type is inferred, but not for zero matrices) let m2 = DenseMatrix. In F# we can use the builders just like in C#, but we can also use the F# modules: let m1 = matrix ] let v1 = vector // dense 3x4 matrix filled with zeros. Directly bind to an existing array without copying (note: no "Of") double x = existing. They support both single and double precision, real and complex floating point numbers.Ī_ doi: 10.1016/j.NET Numerics includes rich types for matrices and vectors. "Matrix differential calculus with applications in the multivariate linear model and its diagnostics". ^ Liu, Shuangzhe Leiva, Victor Zhuang, Dan Ma, Tiefeng Figueroa-Zúñiga, Jorge I.Matrix differential calculus with applications in statistics and econometrics. ^ Magnus, Jan Neudecker, Heinz (2019).Hands-on Matrix Algebra Using R: Active and Motivated Learning with Applications. "Simultaneous Reduction and Vec Stacking". "The R package 'sn': The Skew-Normal and Related Distributions such as the Skew-t". "Typing Linear Algebra: A Biproduct-oriented Approach". It is also used in local sensitivity and statistical diagnostics. Vectorization is used in matrix calculus and its applications in establishing e.g., moments of random vectors and matrices, asymptotics, as well as Jacobian and Hessian matrices. In R, function vec() of package 'ks' allows vectorization and function vech() implemented in both packages 'ks' and 'sn' allows half-vectorization. In Python NumPy arrays implement the flatten method, while in R the desired effect can be achieved via the c() or as.vector() functions. GNU Octave also allows vectorization and half-vectorization with vec(A) and vech(A) respectively. In Matlab/ GNU Octave a matrix A can be vectorized by A(:). Programming languages that implement matrices may have easy means for vectorization. There exist unique matrices transforming the half-vectorization of a matrix to its vectorization and vice versa called, respectively, the duplication matrix and the elimination matrix.
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