Tensor Toolbox手册.docx

Tensor Toolbox for dense, sparse, and decomposed n-way arrays.cp_als - Compute a CP decomposition of any type of tensor.ALS交替最小二乘法求张量CP分解 P = CP_ALS(X,R)计算张量X秩为R的最佳近似CP分解，P=P.lambda, P.U P = CP_ALS(X,R,param,value,.)选择参数设置 tol - Tolerance on difference in fit 1.0e-4 maxiters - Maximum number of iterations 50 dimorder - Order to loop through dimensions 1:ndims(A) init - Initial guess random|nvecs|cell array printitn - Print fit every n iterations; 0 for no printing 1 P,U0,out = CP_ALS(.) also returns additional output that contains the input parameters.Note: The fit is defined as 1 - norm(X-full(P)/norm(X) and is loosely the proportion of the data described by the CP model, i.e., a fit of 1 is perfect.% Examples:% X = sptenrand(5 4 3, 10);% P = cp_als(X,2);% P = cp_als(X,2,dimorder,3 2 1);% P = cp_als(X,2,dimorder,3 2 1,init,nvecs);% U0 = rand(5,2),rand(4,2),; %- Initial guess for factors of P% P,U0,out = cp_als(X,2,dimorder,3 2 1,init,U0);% P = cp_als(X,2,out.params); %- Same params as previous run交替泊松回归求张量X的非负CP分解cp_apr - Compute nonnegative CP with alternating Poisson regression. M = CP_APR(X, R) computes an estimate of the best rank-R M = CP_APR(X, R, param, value, .) specifies optional parameters and values. Valid parameters and their default values are: tol - Tolerance on the inner KKT violation 1.0e-4 maxiters - Maximum number of iterations 1000 maxinneriters = Maximum number of inner iterations 10 init - Initial guess random|ktensor epsilon - parameter to avoid divide by zero 100*eps kappatol - tolerance on complementary slackness 100*eps kappa - offset to fix complementary slackness 10*eps printitn - Print every n outer iterations; 0 for no printing 1 printinneritn - Print every n inner iterations 0 M,M0 = CP_APR(.) also returns the initial guess. M,M0,out = CP_APR(.) also returns additional output. out.kktViolations - maximum kkt violation per iteration out.nInnerIters - number of inner iterations per iteration out.nViolations - number of factor matrices needing complementary slackness adjustment per iteration out.nTotalIters - total number of inner iterations乘数更新求非负CP分解cp_nmu - Compute nonnegative CP with multiplicative updates.cp_opt - Fits a CP model to a tensor via optimization. cp_wopt - Fits a weighted CP model to a tensor via optimization. create_guess - Creates initial guess for CP or Tucker fitting. create_problem - Create test problems for tensor factorizations. export_data - Export tensor-related data to a file. import_data - Import tensor-related data to a file.khatrirao - Khatri-Rao product of matrices. Y=khatrirao(A,B) 计算具有相同列数的矩阵A和B的khatri-rao积 KRON(A(:,1),B(:,1) . KRON(A(:,n),B(:,n) khatrirao(A1,A2,.) computes the Khatri-Rao product of multiple matrices that have the same number of columns. khatrirao(C) computes the Khatri-Rao product of the matrices in cell array C. khatrirao(.,r) computes the Khatri-Rao product in reverse order.% Examples A = rand(5,2); B = rand(3,2); C = rand(2,2); khatrirao(A,B) %- Khatri-Rao of A and B khatrirao(B,A,r) %- same thing as above khatrirao(C,B,A) %- passing a cell array khatrirao(A,B,C,r) %- same as above parafac_als - Deprecated. Use CP_ALS instead. sptendiag - Creates a sparse tensor with v on the diagonal.构造稀疏均匀分布随机张量 sptenrand - Sparse uniformly distributed random tensor. R=sptenrand(sz,density) creates a random sparse tensor of the specified sz with approximately density*prod(sz) nonzero entries. R = sptanrand(sz,nz) creates a random sparse tensor of the specified sz with approximately nz nonzero entries.% Example: R = sptenrand(5 4 2,12); sshopm - Shifted power method for finding a real eigenpair of a real tensor. sshopmc - Shifted power method for real/complex eigenpair of a real tensor. tendiag - Creates a tensor with v on the diagonal. teneye - Create identity tensor of specified size. tenones - Ones tensor. tenrand - Uniformly distributed pseudo-random tensor. tenzeros - Create zeros tensor.HOOI算法做张量Tucker分解 tucker_als - Higher-order orthogonal iteration. T=TUCKER_ALS(X,R) computes the best rank-(R1,R2,.,Rn) approximation of tensor X, according to the specified dimensions in vector R. The input X can be a tensor, sptensor, ktensor, or ttensor. The result returned in T is a ttensor. T=TUCKER_ALS(X,R,param,value,.) specifies optional parameters and values. Valid parameters and their default values are: tol - Tolerance on difference in fit 1.0e-4 maxiters - Maximum number of iterations 50 dimorder - Order to loop through dimensions 1:ndims(A) init - Initial guess random|nvecs|cell array printitn - Print fit every n iterations 1T,U0 = TUCKER_ALS(.) also returns the initial guess.% Examples:% X = sptenrand(5 4 3, 10);% T = tucker_als(X,2); %- best rank(2,2,2) approximation % T = tucker_als(X,2 2 1); %- best rank(2,2,1) approximation % T = tucker_als(X,2,dimorder,3 2 1);% T = tucker_als(X,2,dimorder,3 2 1,init,nvecs);% U0 = rand(5,2),rand(4,2),; %=) for tensors. gt - Greater than () for tensors. innerprod - Efficient inner product with a tensor. isequal - for tensors. issymmetric - Verify that a tensor X is symmetric in specified modes. ldivide - Left array divide for tensor. le - Less than or equal (=) for tensor. lt - Less than () for tensor. minus - Binary subtraction (-) for tensors. mldivide - Slash left division for tensors. mrdivide - Slash right division for tensors. mtimes - tensor-scalar multiplication. mttkrp - Matricized tensor times Khatri-Rao product for tensor.张量阶数ndims - Return the number of dimensions of a tensor. ne - Not equal (=) for tensors. nnz - Number of nonzeros for tensors. 张量F范数norm - Frobenius norm of a tensor. not - Logical NOT () for tensors. nvecs - Compute the leading mode-n vectors for a tensor. or - Logical OR (|) for tensors. permute - Permute tensor dimensions. plus - Binary addition (+) for tensors. power - Elementwise power (.) operator for a tensor. rdivide - Right array divide for tensors. reshape - Change tensor size. scale - Scale along specified dimensions of tensor. size - Tensor dimensions. squeeze - Remove singleton dimensions from a tensor. subsasgn - Subscripted assignment for a tensor. subsref - Subscripted reference for tensors. symmetrize - Symmetrize a tensor X in specified modes. tenfun - Apply a function to each element in a tensor. tensor - Create tensor.张量Hadamard积（.*）times - Array multiplication for tensors.张量装置 transpose - is not defined on tensors.张量d维度乘积ttm - Tensor times matrix. Y = TTM(X,A,N) computes the n-mode product of tensor X with a matrix A; i.e., X x_N A. The integer N specifies the dimension (or mode) of X along which A should be multiplied. If size(A) =J,I, then X must have size(X,N) = I. The result will be the same order and size as X except that size(Y,N) = J. Y = TTM(X,A,B,C,.) computes the n-mode product of tensor X with a sequence of matrices in the cell array. The n-mode products are computed sequentially along all dimensions (or modes) of X. The cell array contains ndims(X) matrices. Y = TTM(X,A,B,C,.,DIMS) computes the sequence tensor-matrix products along the dimensions specified by DIMS. Y = TTM(.,t) performs the same computations as above except the matrices are transposed.% Examples% X = tensor(rand(5,3,4,2);% A = rand(4,5); B = rand(4,3); C = rand(3,4); D = rand(3,2);% Y = ttm(X, A, 1) %- computes X times A in mode-1% Y = ttm(X, A,B,C,D, 1) %- same as above% Y = ttm(X, A, 1, t) %- same as above% Y = ttm(X, A,B,C,D, 1 2 3 4) %- 4-way multiply% Y = ttm(X, D,C,B,A, 4 3 2 1) %- same as above% Y = ttm(X, A,B,C,D) %- same as above% Y = ttm(X, A,B,C,D, t) %- same as above% Y = ttm(X, C,D, 3 4) %- X times C in mode-3 & D in mode-4% Y = ttm(X, A,B,C,D, 3 4) %- same as above% Y = ttm(X, A,B,D, 1 2 4) %- 3-way multiply% Y = ttm(X, A,B,C,D, 1 2 4) %- same as above% Y = ttm(X, A,B,D, -3) %- same as above% Y = ttm(X, A,B,C,D, -3) %- same as above ttsv - Tensor times same vector in multiple modes.张量与张量的乘积（用于计算外积、内积、缩并）ttt - Tensor mulitplication (tensor times tensor).张量的外积 TTT(X,Y) computes the outer product of tensors X and Y.张量的缩并或者内积 TTT(X,Y,XDIMS,YDIMS) computes the contracted product of tensors X and Y in the dimensions specified by the row vectors XDIMS and YDIMS. The sizes of the dimensions specified by XDIMS and YDIMS must match; that is, size(X,XDIMS) must equal size(Y,YDIMS). 张量的缩并或者内积 TTT(X,Y,DIMS) computes the inner product of tensors X and Y in the dimensions specified by the vector DIMS. The sizes of the dimensions specified by DIMS must match; that is, size(X,DIMS) must equal size(Y,DIMS). % Examples% X = tensor(rand(4,2,3);% Y = tensor(rand(3,4,2);% Z = ttt(X,Y) %- outer product of X and Y% Z = ttt(X,X,1:3) %- inner product of X with itself% Z = ttt(X,Y,1 2 3,2 3 1) %- inner product of X & Y% Z = ttt(X,Y,1 3,2 1) %- product of X & Y along specified dims张量与向量乘积 ttv - Tensor times vector. Y = TTV(X,A,N) computes the product of tensor X with a (column) vector A. The integer N specifies the dimension in X along which A is multiplied. If size(A) = I,1, then X must have size(X,N) = I. Note that ndims(Y) = ndims(X) - 1 because the N-th dimension is removed. Y = TTV(X,A,B,C,.) computes the product of tensor X with a sequence of vectors in the cell array. The products are computed sequentially along all dimensions (or modes) of X. The cell array contains ndims(X) vectors. Y = TTV(X,A,B,C,.,DIMS) computes the sequence of tensor-vector products along the dimensions specified by DIMS.% Examples% X = tensor(rand(5,3,4,2);% A = rand(5,1); B = rand(3,1); C = rand(4,1); D = rand(2,1);% Y = ttv(X, A, 1) %- X times A in mode 1% Y = ttv(X, A,B,C,D, 1) %- same as above% Y = ttv(X, A,B,C,D, 1 2 3 4) %- All-mode multiply% Y = ttv(X, D,C,B,A, 4 3 2 1) %- same as above% Y = ttv(X, A,B,C,D) %- same as above% Y = ttv(X, C,D, 3 4) %- X times C in mode-3 & D in mode-4% Y = ttv(X, A,B,C,D, 3 4) %- same as above% Y = ttv(X, A,B,D, 1 2 4) %- 3-way mutplication% Y = ttv(X, A,B,C,D, 1 2 4) %- same as above% Y = ttv(X, A,B,D, -3) %- same as above% Y = ttv(X, A,B,C,D, -3) %- same as above uminus - Unary minus (-) for tensors. uplus - Unary plus (+) for tensors. xor - Logical EXCLUSIVE OR for tensors.SPTENSOR and - Logical AND (&) for sptensors. collapse - Collapse sparse tensor along specified dimensions. contract - Contract sparse tensor along two dimensions (array trace). ctranspose - is not defined for sparse tensors. disp - Command window display of a sparse tensor. display - Command window display of a sparse tensor. divide - Divide an SPTENSOR by a nonnegative KTENSOR. double - Converts a sparse tensor to a dense multidimensional array. elemfun - Manipulate the nonzero elements of a sparse tensor. end - Last index of indexing expression for sparse tensor. eq - Equal (=) for sptensors. find - Find subscripts of nonzero elements in a sparse tensor. full - Convert a sparse tensor to a (dense) tensor. ge - Greater than or equal for sptensors. gt - Greater than for sptensors. innerprod - Efficient inner product with a sparse tensor. isequal - for sptensors. ldivide - Array right division for sparse tensors. le - Less than or equal for sptensors. lt - Less than for sptensors. minus - Binary subtraction for sparse tensors. mldivide - Slash left division for sparse tensors. mrdivide - Slash right division for sparse tensors. 张量与标量乘积mtimes - sptensor-scalar multiplication. mttkrp - Matricized tensor times Khatri-Rao product for sparse tensor. ndims - Number of dimensions of a sparse tensor. ne - Not equal (=) for sptensors. nnz - Number of nonzeros in sparse tensor. norm - Frobenius norm of a sparse tensor. not - Logical NOT () for sptensors. nvecs - Compute the leading mode-n vectors for a sparse tensor. ones - Replace nonzero elements of sparse tensor with ones. or - Logical OR (|) for sptensors. permute - Rearrange the dimensions of a sparse tensor. plus - Binary addition for sparse tensors. rdivide - Array right division for sparse tensors. reshape - Reshape sparse tensor. scale - Scale along specified dimensions for sparse tensors. size - Sparse tensor dimensions. spmatrix - Converts a two-way sparse tensor to sparse matrix. sptensor - Create a sparse tensor. squeeze - Remove singleton dimensions from a sparse tensor. subsasgn - Subscripted assignment for sparse tensor. subsref - Subscripted reference for a sparse tensor. times - Array multiplication for sparse tensors. transpose - is not defined on sparse tensors. ttm - Sparse tensor times matrix. ttt - Sparse tensor times sparse tensor. ttv - Sparse tensor times vector. uminus - Unary minus (-) for sptensor. uplus - Unary plus (+) for sptensor. xor - Logical XOR for sptensors.TTENSOR disp - Command window display of a ttensor. display - Command window display of a ttensor. double - Convert ttensor to double array. end - Last index of indexing expression for ttensor. full - Convert a ttensor to a (dense) tensor. innerprod - Efficient inner product with a ttensor. isequal - True if each component of two ttensors is numerically equal. mtimes - Implement scalar multiplication for a ttensor. mttkrp - Matricized tensor times Khatri-Rao product for ttensor. ndims - Return the number of dimensions for a ttensor. norm - Norm of a ttensor. nvecs - Compute the leading mode-n vectors for a ttensor. permute - Permute dimensions for a ttensor. size - Size of a ttensor. subsasgn - Subscripted reference for a ttensor. subsref - Subscripted reference for a ttensor. ttensor - Tensor stored as a Tucker operator (decomposed). ttm - Tensor times matrix for ttensor. ttv - Tensor times vector for ttensor. uminus - Unary minus for ttensor. uplus - Unary plus for ttensor.KTENSOR arrange - Arranges the rank-1 components of a ktensor. datadisp - Special display of a ktensor. disp - Command window display for a ktensor. display - Command window display for a ktensor. double - Convert a ktensor to a double array. end - Last index of indexing expression for ktensor. extract - Creates a new ktensor with only the specified components. fixsigns - Fix sign ambiguity of a ktensor. full - Convert a ktensor to a (dense) tensor. innerprod - Efficient inner product with a ktensor. isequal - True if each component of two ktensors is numerically equal. ktensor - Tensor stored as a Kruskal operator (decomposed). minus - Binary subtraction for ktensor. mtimes - Implement A*B (scalar multiply) for ktensor. mttkrp - Matricized tensor times Khatri-Rao product for ktensor. ncomponents - Number of components for a ktensor. ndims - Number of dimensions for a ktensor. norm - Frobenius norm of a ktensor. normalize - Normalizes the columns of the factor matrices. nvecs - Compute the leading mode-n vectors for a ktensor. permute - Permute dimensions of a ktensor. plus - Binary addition for ktensor. redistribute - Distribute lambda values to a specified mode. score - Checks if two ktensors match except for permutation. size - Size of ktensor. subsasgn - Subscripted assignement for ktensor. subsref - Subscripted reference for a ktensor. times - Element-wise multiplication for ktensor. tocell - Convert X to a