Last update: 08/09/2014
MTT
Matlab Tensor Tools is an easy-to-use library to work with tensors.
See also:
Presentation about Matrix and Tensor Tools for Computer Vision
http://www.slideshare.net/andrewssobral/matrix-and-tensor-tools-for-computer-vision
LRSLibrary: Low-Rank and Sparse Tools for Background Modeling and Subtraction in Videos
https://github.com/andrewssobral/lrslibrary
IMTSL: Incremental and Multi-feature Tensor Subspace Learning
https://github.com/andrewssobral/imtsl
Citation
If you use this code for your publications, please cite it as:
@misc{asobral2014,
author = "Sobral, Andrews",
title = "Matlab Tensor Tools",
year = "2014",
url = "https://github.com/andrewssobral/mtt/"
}
Demos
tensor_demo_operations.m - Basic operations
tensor_demo_hosvd_ihosvd.m - High-order singular value decomposition (Tucker decomposition)
tensor_demo_parafac_als.m - CP decomposition via ALS (Alternating Least-Squares)
tensor_demo_tucker_als.m - Tucker decomposition via ALS (Alternating Least-Squares)
tensor_demo_tsvd.m - t-SVD and inverse t-svd
tensor_demo_ntf.m - Non-Negative Tensor Factorization
tensor_demo_subtensors_ntf_hals.m - Low-rank approximation based Non-Negative Tensor(CP) factorization
tensor_demo_inclearn.m - Incremental tensor learning
Example of tensor operations
A = reshape(1:12,[2,2,3]);
B = reshape(1:12,[2,2,3]);
%% Basic operations
[A1,A2,A3] = tensor_matricization(A);
M22 = reshape(1:4,[2,2]);
M33 = reshape(1:9,[3,3]);
B1 = tensor_nmodeproduct(A,M22,1);
B2 = tensor_nmodeproduct(A,M22,2);
B3 = tensor_nmodeproduct(A,M33,3);
Au = tensor_unfold(A);
A_hat = tensor_fold(Au,size(A));
[A1_] = tensor_slices_frontal(A);
[A2_] = tensor_slices_lateral(A);
[A3_] = tensor_slices_horizontal(A);
[At1_] = tensor_fibers_column(A);
[At2_] = tensor_fibers_row(A);
[At3_] = tensor_fibers_tube(A);
Bt = tensor_transpose(B);
[C] = tensor_product(A,B);
%% HoSVD and iHoSVD decomposition
T = tensor(A);
[core,U] = tensor_hosvd(T);
[T_hat] = tensor_ihosvd(core,U);
%% t-SVD decomposition
[U,S,V] = tensor_t_svd(A);
[C] = tensor_product(U,S);
[A_hat] = tensor_product(C,tensor_transpose(V));
%% Tucker ALS decomposition
r = 10;
T_hat = tucker_als(T,[r r r]);
%% PARAFAC/CP ALS decomposition
T_hat = cp_als(T, r);
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题目背景 模板题，无背景 题目描述 给定 22 个多项式 F(x), G(x)F(x),G(x) ，请求出 F(x) * G(x)F(x)∗G(x) 。 系数对 pp 取模，且不保证 pp 可以分解成 p = a \cdot 2^k + 1p=a⋅2k+1 之形式。 输入输出格式 输入格式： 输入共 33 行。 第一行 33 个整数 n, m, pn,m,p ，分别表示 F(x), G(x)F
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前言 51nod1258真是道好题。。。 一道题，学会了3个东西：伯努利数，自然数幂和，MTT… 前置科技（其实学MTT的人估计都会。。。） CRT(中国剩余定理) NTT NTT算法的局限 众所周知，NTT是通过原根的性质来进行快速傅里叶变化 不过，同时也对其模数做出了要求，对于一个模数M，若 φ ( M ) \varphi(M) φ(M)中，2的次数较少（小于要转的序列长度）就不可做了 所以，
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任意模数FFT时记M为sqrt(mo) 将每个数a分为a/M,a%M后分别进行三次实数FFT const LL mo=1e9+7; const LL M=sqrt(mo); const LDB pi=acos(-1); LL cunt[511][511]; struct cp{ LDB r,i; }a1[511][1024],a2[511][1024],tmp[1024
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MTT：任意模数NTT 概述 有时我们用FFT处理的数据很大，而模数可以分解为\(a\cdot 2^k+1\)的形式。次数用FFT精度不够，用NTT又找不到足够大的模数，于是MTT就应运而生了。 MTT没有模数的限制，比NTT更加自由，应用广泛，可以用于任意模数或很大的数。 MTT MTT是基于NTT的，其思想很简单，就是做多次NTT，每次使用不同的素数，然后使用CRT合并解，在合并的过程中模最终
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题目链接：点击查看 题目大意：给出一个长度为 n n n 的多项式 F ( x ) F(x) F(x) 和一个长度为 m m m 的多项式 G ( x ) G(x) G(x)，求 F ( x ) ∗ G ( x ) F(x)*G(x) F(x)∗G(x)，模数任意，值域 1 e 9 1e9 1e9 题目分析：如果不取模的话极限情况下会达到 1 0 9 ∗ 1 0 9 ∗ 1 0 5 = 1 0 2