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Showing results 1 to 10 of 111.


Function zero [freealg v1.0-0]
keywords
symbolmath
title
The zero algebraic object
description
Test for a freealg object's being zero
Function Ops.onion [onion v1.2-7]
keywords
symbolmath
title
Arithmetic Ops Group Methods for Octonions
description
Allows arithmetic operators to be used for octonion calculations, such as addition, multiplication, division, integer powers, etc.
Function bases [qkerntool v1.19]
keywords
symbolmath
title
qKernel Functions
description
The kernel generating functions provided in qkerntool. The Non Linear Kernel \(k(x,y) = \frac{1}{2(1-q)}(q^{-\alpha||x||^2}+q^{-\alpha||y||^2}-2q^{-\alpha x'y}) \). The Gaussian kernel \(k(x,y) =\frac{1}{1-q} (1-q^{(||x-y||^2/\sigma)})\). The Laplacian Kernel \(k(x,y) =\frac{1}{1-q} (1-q^{(||x-y||/\sigma)})\). The Rational Quadratic Kernel \(k(x,y) =\frac{1}{1-q} (1-q^{\frac{||x-y||^2}{||x-y||^2+c}})\). The Multiquadric Kernel \(k(x,y) =\frac{1}{1-q} (q^c-q^{\sqrt{||x-y||^2+c}})\). The Inverse Multiquadric Kernel \(k(x,y) =\frac{1}{1-q} (q^{-\frac{1}{c}}-q^{-\frac{1}{\sqrt{||x-y||^2+c}}})\). The Wave Kernel \(k(x,y) =\frac{1}{1-q} (q^{-1}-q^{-\frac{\theta}{||x-y||}\sin{\frac{||x-y||}{\theta}}})\). The d Kernel \(k(x,y) = \frac{1}{1-q}[1-q^(||x-y||^d)] \). The Log Kernel \(k(x,y) =\frac{1}{1-q} [1-q^ln(||x-y||^d+1)]\). The Cauchy Kernel \(k(x,y) =\frac{1}{1-q} (q^{-1}-q^{-\frac{1}{1+||x-y||^2/\sigma}})\). The Chi-Square Kernel \(k(x,y) =\frac{1}{1-q} (1-q^{\sum{2(x-y)^2/(x+y)} \gamma})\). The Generalized T-Student Kernel \(k(x,y) =\frac{1}{1-q} (q^{-1}-q^{-\frac{1}{1+||x-y||^d}})\).
Function cnds [qkerntool v1.19]
keywords
symbolmath
title
CND Kernel Functions
description
The kernel generating functions provided in qkerntool. The Non Linear Kernel \(k(x,y) = [exp(\alpha ||x||^2)+exp(\alpha||y||^2)-2exp(\alpha x'y)]/2\). The Polynomial kernel \(k(x,y) = [(\alpha ||x||^2+c)^d+(\alpha ||y||^2+c)^d-2(\alpha x'y+c)^d]/2\). The Gaussian kernel \(k(x,y) = 1-exp(-||x-y||^2/\gamma)\). The Laplacian Kernel \(k(x,y) = 1-exp(-||x-y||/\gamma)\). The ANOVA Kernel \(k(x,y) = n-\sum exp(-\sigma (x-y)^2)^d\). The Rational Quadratic Kernel \(k(x,y) = ||x-y||^2/(||x-y||^2+c)\). The Multiquadric Kernel \(k(x,y) = \sqrt{(||x-y||^2+c^2)-c}\). The Inverse Multiquadric Kernel \(k(x,y) = 1/c-1/\sqrt{||x-y||^2+c^2}\). The Wave Kernel \(k(x,y) = 1-\frac{\theta}{||x-y||}\sin\frac{||x-y||}{\theta}\). The d Kernel \(k(x,y) = ||x-y||^d\). The Log Kernel \(k(x,y) = \log(||x-y||^d+1)\). The Cauchy Kernel \(k(x,y) = 1-1/(1+||x-y||^2/\gamma)\). The Chi-Square Kernel \(k(x,y) = \sum{2(x-y)^2/(x+y)}\). The Generalized T-Student Kernel \(k(x,y) = 1-1/(1+||x-y||^d)\). The normal Kernel \(k(x,y) = ||x-y||^2\).
Function stringdot [kernlab v0.9-27]
keywords
symbolmath
title
String Kernel Functions
description
String kernels.
Function dots [kernlab v0.9-27]
keywords
symbolmath
title
Kernel Functions
description
The kernel generating functions provided in kernlab. The Gaussian RBF kernel \(k(x,x') = \exp(-\sigma \|x - x'\|^2)\) The Polynomial kernel \(k(x,x') = (scale <x, x'> + offset)^{degree}\) The Linear kernel \(k(x,x') = <x, x'>\) The Hyperbolic tangent kernel \(k(x, x') = \tanh(scale <x, x'> + offset)\) The Laplacian kernel \(k(x,x') = \exp(-\sigma \|x - x'\|)\) The Bessel kernel \(k(x,x') = (- Bessel_{(\nu+1)}^n \sigma \|x - x'\|^2)\) The ANOVA RBF kernel \(k(x,x') = \sum_{1\leq i_1 \ldots < i_D \leq N} \prod_{d=1}^D k(x_{id}, {x'}_{id})\) where k(x,x) is a Gaussian RBF kernel. The Spline kernel \( \prod_{d=1}^D 1 + x_i x_j + x_i x_j min(x_i, x_j) - \frac{x_i + x_j}{2} min(x_i,x_j)^2 + \frac{min(x_i,x_j)^3}{3}\) \ The String kernels (see stringdot.
Function Ops.kform [stokes v1.0-5]
keywords
symbolmath
title
Arithmetic Ops Group Methods for kform and ktensor objects
description
Allows arithmetic operators to be used for \(k\)-forms and \(k\)-tensors such as addition, multiplication, etc, where defined.
Function print [permutations v1.0-6]
keywords
symbolmath
title
Print methods for permutation objects
description
Print methods for permutation objects with matrix-like printing for words and bracket notation for cycle objects.
Function perm_matrix [permutations v1.0-6]
keywords
symbolmath
title
Permutation matrices
description
Given a permutation, coerce to word form and return the corresponding permutation matrix
Function fixed [permutations v1.0-6]
keywords
symbolmath
title
Fixed elements
description
Finds which elements of a permutation object are fixed