Search Results for "matrix"
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Showing 14 open source projects for "matrix"
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ExponentialUtilities.jl
Fast and differentiable implementations of matrix exponentials
ExponentialUtilities is a package of utility functions for matrix functions of exponential type, including functionality for the matrix exponential and phi-functions. These methods are more numerically stable, generic (thus support a wider range of number types), and faster than the matrix exponentiation tools in Julia's Base. The tools are used by the exponential integrators in OrdinaryDiffEq. -
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Rotations.jl
Julia implementations for different rotation parameterizations
...This package implements various 3D rotation parameterizations and defines conversions between them. At their heart, each rotation parameterization is a 3×3 unitary (orthogonal) matrix (based on the StaticArrays.jl package), and acts to rotate a 3-vector about the origin through matrix-vector multiplication. While the RotMatrix type is a dense representation of a 3×3 matrix, we also have sparse (or computed, rather) representations such as quaternions, angle-axis parameterizations, and Euler angles. All rotation types support one(R) to construct the identity rotation for the desired parameterization. -
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HCubature.jl
Pure-Julia multidimensional h-adaptive integration
...Because hcubature is written purely in Julia, the integrand f(x) can return any vector-like object (technically, any type supporting +, -, * real, and norm: a Banach space). You can integrate real, complex, and matrix-valued integrands, for example. Note that HCubature assumes that your function f(x) can be computed at arbitrary points in the integration domain. (This is the ideal way to do numerical integration.) If you instead have f(x) precomputed at a fixed set of points, such as a Cartesian grid, you will need to use some other method (e.g. ... -
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BlockArrays.jl
BlockArrays for Julia
...Secondly, it also implements two different types of block arrays that follow the AbstractBlockArray interface. The type BlockArray stores each block contiguously while the type PseudoBlockArray stores the full matrix contiguously. This means that BlockArray supports fast noncopying extraction and insertion of blocks while PseudoBlockArray supports fast access to the full matrix to use in for example a linear solver. -
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SymEngine.jl
Julia wrappers of SymEngine
Julia Wrappers for SymEngine, a fast symbolic manipulation library, written in C++. -
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Nemo.jl
Julia bindings for various mathematical libraries (including flint2)
Nemo is a computer algebra package for the Julia programming language. It aims to cover commutative algebra, number theory and group theory. Julia bindings for various mathematical libraries (including flint2) -
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AbstractAlgebra.jl
Generic abstract algebra functionality in pure Julia
AbstractAlgebra is a pure Julia package for computational abstract algebra. It grew out of the Nemo project and provides all of the abstract types and generic implementations that Nemo relies on. It was originally developed by William Hart, Tommy Hofmann, Fredrik Johansson and Claus Fieker with contributions from others. Current maintainers are Claus Fieker, Tommy Hofmann and Max Horn. -
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UMAP.jl
Uniform Manifold Approximation and Projection (UMAP) implementation
A pure Julia implementation of the Uniform Manifold Approximation and Projection dimension reduction algorithm. The umap function takes two arguments, X (a column-major matrix of shape (n_features, n_samples)), n_components (the number of dimensions in the output embedding), and various keyword arguments. -
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EvoTrees.jl
Boosted trees in Julia
A Julia implementation of boosted trees with CPU and GPU support. Efficient histogram-based algorithms with support for multiple loss functions, including various regressions, multi-classification and Gaussian max likelihood. -
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Tullio.jl
Tullio is a very flexible einsum macro
Tullio is a very flexible einsum macro. It understands many array operations written in index notation -- not just matrix multiplication and permutations, but also convolutions, stencils, scatter/gather, and broadcasting. Used by itself the macro writes ordinary nested loops much like Einsum.@einsum. One difference is that it can parse more expressions, and infer ranges for their indices. Another is that it will use multi-threading (via Threads.@spawn) and recursive tiling, on large enough arrays. -
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Reduce.jl
Symbolic parser for Julia language term rewriting using REDUCE algebra
REDUCE is a portable general-purpose computer algebra system. It is a system for doing scalar, vector and matrix algebra by computer, which also supports arbitrary precision numerical approximation and interfaces to gnuplot to provide graphics. It can be used interactively for simple calculations (as illustrated in the screenshot below) but also provides a full programming language, with a syntax similar to other modern programming languages. -
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ProxSDP.jl
Semidefinite programming optimization solver
ProxSDP is an open-source semidefinite programming (SDP) solver based on the paper "Exploiting Low-Rank Structure in Semidefinite Programming by Approximate Operator Splitting". The main advantage of ProxSDP over other state-of-the-art solvers is the ability to exploit the low-rank structure inherent to several SDP problems. -
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DiffEqOperators.jl
Linear operators for discretizations of differential equations
...Care is taken to give efficiency by avoiding unnecessary allocations, using purpose-built stencil compilers, allowing GPUs and parallelism, etc. Any operator can be concretized as an Array, a BandedMatrix or a sparse matrix. -
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ManifoldLearning
Package for manifold learning and nonlinear dimensionality reduction
A Julia package for manifold learning and nonlinear dimensionality reduction. Most of the methods use k-nearest neighbors method for constructing local subspace representation. By default, neighbors are computed from a distance matrix of a dataset. This is not an efficient method, especially, for large datasets.
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