Tensor Toolbox手册.docx
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Tensor Toolbox手册.docx
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TensorToolbox手册
TensorToolboxfordense,sparse,anddecomposedn-wayarrays.
cp_als-ComputeaCPdecompositionofanytypeoftensor.
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'-Toleranceondifferenceinfit{1.0e-4}
'maxiters'-Maximumnumberofiterations{50}
'dimorder'-Ordertoloopthroughdimensions{1:
ndims(A)}
'init'-Initialguess[{'random'}|'nvecs'|cellarray]
'printitn'-Printfiteveryniterations;0fornoprinting{1}
[P,U0,out]=CP_ALS(...)alsoreturnsadditionaloutputthatcontainstheinputparameters.
Note:
The"fit"isdefinedas1-norm(X-full(P))/norm(X)andislooselytheproportionofthedatadescribedbytheCPmodel,i.e.,afitof1isperfect.
%Examples:
%X=sptenrand([543],10);
%P=cp_als(X,2);
%P=cp_als(X,2,'dimorder',[321]);
%P=cp_als(X,2,'dimorder',[321],'init','nvecs');
%U0={rand(5,2),rand(4,2),[]};%<--InitialguessforfactorsofP
%[P,U0,out]=cp_als(X,2,'dimorder',[321],'init',U0);
%P=cp_als(X,2,out.params);%<--Sameparamsaspreviousrun
交替泊松回归求张量X的非负CP分解
cp_apr-ComputenonnegativeCPwithalternatingPoissonregression.
M=CP_APR(X,R)computesanestimateofthebestrank-R
M=CP_APR(X,R,'param',value,...)specifiesoptionalparametersandvalues.Validparametersandtheirdefaultvaluesare:
'tol'-ToleranceontheinnerKKTviolation{1.0e-4}
'maxiters'-Maximumnumberofiterations{1000}
'maxinneriters'=Maximumnumberofinneriterations{10}
'init'-Initialguess[{'random'}|ktensor]
'epsilon'-parametertoavoiddividebyzero{100*eps}
'kappatol'-toleranceoncomplementaryslackness{100*eps}
'kappa'-offsettofixcomplementaryslackness{10*eps}
'printitn'-Printeverynouteriterations;0fornoprinting{1}
'printinneritn'-Printeveryninneriterations{0}
[M,M0]=CP_APR(...)alsoreturnstheinitialguess.
[M,M0,out]=CP_APR(...)alsoreturnsadditionaloutput.
out.kktViolations-maximumkktviolationperiteration
out.nInnerIters-numberofinneriterationsperiteration
out.nViolations-numberoffactormatricesneedingcomplementary
slacknessadjustmentperiteration
out.nTotalIters-totalnumberofinneriterations
乘数更新求非负CP分解
cp_nmu-ComputenonnegativeCPwithmultiplicativeupdates.
cp_opt-FitsaCPmodeltoatensorviaoptimization.
cp_wopt-FitsaweightedCPmodeltoatensorviaoptimization.
create_guess-CreatesinitialguessforCPorTuckerfitting.
create_problem-Createtestproblemsfortensorfactorizations.
export_data-Exporttensor-relateddatatoafile.
import_data-Importtensor-relateddatatoafile.
khatrirao-Khatri-Raoproductofmatrices.
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,...)computestheKhatri-Raoproductofmultiplematricesthathavethesamenumberofcolumns.
khatrirao(C)computestheKhatri-RaoproductofthematricesincellarrayC.
khatrirao(...,'r')computestheKhatri-Raoproductinreverseorder.
%Examples
A=rand(5,2);B=rand(3,2);C=rand(2,2);
khatrirao(A,B)%<--Khatri-RaoofAandB
khatrirao(B,A,'r')%<--samethingasabove
khatrirao({C,B,A})%<--passingacellarray
khatrirao({A,B,C},'r')%<--sameasabove
parafac_als-Deprecated.UseCP_ALSinstead.
sptendiag-Createsasparsetensorwithvonthediagonal.
构造稀疏均匀分布随机张量
sptenrand-Sparseuniformlydistributedrandomtensor.
R=sptenrand(sz,density)createsarandomsparsetensorofthespecifiedszwithapproximatelydensity*prod(sz)nonzeroentries.
R=sptanrand(sz,nz)createsarandomsparsetensorofthe
specifiedszwithapproximatelynznonzeroentries.
%Example:
R=sptenrand([542],12);
sshopm-Shiftedpowermethodforfindingarealeigenpairofarealtensor.
sshopmc-Shiftedpowermethodforreal/complexeigenpairofarealtensor.
tendiag-Createsatensorwithvonthediagonal.
teneye-Createidentitytensorofspecifiedsize.
tenones-Onestensor.
tenrand-Uniformlydistributedpseudo-randomtensor.
tenzeros-Createzerostensor.
HOOI算法做张量Tucker分解
tucker_als-Higher-orderorthogonaliteration.
T=TUCKER_ALS(X,R)computesthebestrank-(R1,R2,..,Rn)approximationoftensorX,accordingtothespecifieddimensionsinvectorR.TheinputXcanbeatensor,sptensor,ktensor,orttensor.TheresultreturnedinTisattensor.
T=TUCKER_ALS(X,R,'param',value,...)specifiesoptionalparametersandvalues.Validparametersandtheirdefaultvaluesare:
'tol'-Toleranceondifferenceinfit{1.0e-4}
'maxiters'-Maximumnumberofiterations{50}
'dimorder'-Ordertoloopthroughdimensions{1:
ndims(A)}
'init'-Initialguess[{'random'}|'nvecs'|cellarray]
'printitn'-Printfiteveryniterations{1}
[T,U0]=TUCKER_ALS(...)alsoreturnstheinitialguess.
%Examples:
%X=sptenrand([543],10);
%T=tucker_als(X,2);%<--bestrank(2,2,2)approximation
%T=tucker_als(X,[221]);%<--bestrank(2,2,1)approximation
%T=tucker_als(X,2,'dimorder',[321]);
%T=tucker_als(X,2,'dimorder',[321],'init','nvecs');
%U0={rand(5,2),rand(4,2),[]};%<--InitialguessforfactorsofT
%T=tucker_als(X,2,'dimorder',[321],'init',U0);
@TENSOR
and-LogicalAND(&)fortensors.
collapse-Collapsetensoralongspecifieddimensions.
contract-Contracttensoralongtwodimensions(arraytrace).
ctranspose-isnotdefinedfortensors.
disp-Commandwindowdisplayofatensor.
display-Commandwindowdisplayofatensor.
double-Converttensortodoublearray.
end-Lastindexofindexingexpressionfortensor.
eq-Equal(==)fortensors.
find-Findsubscriptsofnonzeroelementsinatensor.
full-Converttoa(dense)tensor.
ge-Greaterthanorequal(>=)fortensors.
gt-Greaterthan(>)fortensors.
innerprod-Efficientinnerproductwithatensor.
isequal-fortensors.
issymmetric-VerifythatatensorXissymmetricinspecifiedmodes.
ldivide-Leftarraydividefortensor.
le-Lessthanorequal(<=)fortensor.
lt-Lessthan(<)fortensor.
minus-Binarysubtraction(-)fortensors.
mldivide-Slashleftdivisionfortensors.
mrdivide-Slashrightdivisionfortensors.
mtimes-tensor-scalarmultiplication.
mttkrp-MatricizedtensortimesKhatri-Raoproductfortensor.
张量阶数ndims-Returnthenumberofdimensionsofatensor.
ne-Notequal(~=)fortensors.
nnz-Numberofnonzerosfortensors.
张量F范数norm-Frobeniusnormofatensor.
not-LogicalNOT(~)fortensors.
nvecs-Computetheleadingmode-nvectorsforatensor.
or-LogicalOR(|)fortensors.
permute-Permutetensordimensions.
plus-Binaryaddition(+)fortensors.
power-Elementwisepower(.^)operatorforatensor.
rdivide-Rightarraydividefortensors.
reshape-Changetensorsize.
scale-Scalealongspecifieddimensionsoftensor.
size-Tensordimensions.
squeeze-Removesingletondimensionsfromatensor.
subsasgn-Subscriptedassignmentforatensor.
subsref-Subscriptedreferencefortensors.
symmetrize-SymmetrizeatensorXinspecifiedmodes.
tenfun-Applyafunctiontoeachelementinatensor.
tensor-Createtensor.
张量Hadamard积(‘.*’)times-Arraymultiplicationfortensors.
张量装置transpose-isnotdefinedontensors.
张量d维度乘积ttm-Tensortimesmatrix.
Y=TTM(X,A,N)computesthen-modeproductoftensorXwithamatrixA;i.e.,Xx_NA.TheintegerNspecifiesthedimension(ormode)ofXalongwhichAshouldbemultiplied.
Ifsize(A)=[J,I],thenXmusthavesize(X,N)=I.TheresultwillbethesameorderandsizeasXexceptthatsize(Y,N)=J.
Y=TTM(X,{A,B,C,...})computesthen-modeproductoftensorXwithasequenceofmatricesinthecellarray.Then-modeproductsarecomputedsequentiallyalongalldimensions(ormodes)ofX.Thecellarraycontainsndims(X)matrices.
Y=TTM(X,{A,B,C,...},DIMS)computesthesequencetensor-matrixproductsalongthedimensionsspecifiedbyDIMS.
Y=TTM(...,'t')performsthesamecomputationsasaboveexceptthematricesaretransposed.
%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)%<--computesXtimesAinmode-1
%Y=ttm(X,{A,B,C,D},1)%<--sameasabove
%Y=ttm(X,A',1,'t')%<--sameasabove
%Y=ttm(X,{A,B,C,D},[1234])%<--4-waymultiply
%Y=ttm(X,{D,C,B,A},[4321])%<--sameasabove
%Y=ttm(X,{A,B,C,D})%<--sameasabove
%Y=ttm(X,{A',B',C',D'},'t')%<--sameasabove
%Y=ttm(X,{C,D},[34])%<--XtimesCinmode-3&Dinmode-4
%Y=ttm(X,{A,B,C,D},[34])%<--sameasabove
%Y=ttm(X,{A,B,D},[124])%<--3-waymultiply
%Y=ttm(X,{A,B,C,D},[124])%<--sameasabove
%Y=ttm(X,{A,B,D},-3)%<--sameasabove
%Y=ttm(X,{A,B,C,D},-3)%<--sameasabove
ttsv-Tensortimessamevectorinmultiplemodes.
张量与张量的乘积(用于计算外积、内积、缩并)
ttt-Tensormulitplication(tensortimestensor).
张量的外积TTT(X,Y)computestheouterproductoftensorsXandY.
张量的缩并或者内积TTT(X,Y,XDIMS,YDIMS)computesthecontractedproductoftensorsXandYinthedimensionsspecifiedbytherowvectorsXDIMSandYDIMS.ThesizesofthedimensionsspecifiedbyXDIMSandYDIMSmustmatch;thatis,size(X,XDIMS)mustequalsize(Y,YDIMS).
张量的缩并或者内积TTT(X,Y,DIMS)computestheinnerproductoftensorsXandYinthedimensionsspecifiedbythevectorDIMS.ThesizesofthedimensionsspecifiedbyDIMSmustmatch;thatis,size(X,DIMS)mustequalsize(Y,DIMS).
%Examples
%X=tensor(rand(4,2,3));
%Y=tensor(rand(3,4,2));
%Z=ttt(X,Y)%<--outerproductofXandY
%Z=ttt(X,X,1:
3)%<--innerproductofXwithitself
%Z=ttt(X,Y,[123],[231])%<--innerproductofX&Y
%Z=ttt(X,Y,[13]
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