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Results with Julia v1.2.0
Testing was successful.
Last evaluation was ago and took 2 minutes, 11 seconds.
Resolving package versions...
Installed TensorToolbox ─ v1.0.1
Updating `~/.julia/environments/v1.2/Project.toml`
[9c690861] + TensorToolbox v1.0.1
Updating `~/.julia/environments/v1.2/Manifest.toml`
[9c690861] + TensorToolbox v1.0.1
[2a0f44e3] + Base64
[8ba89e20] + Distributed
[b77e0a4c] + InteractiveUtils
[8f399da3] + Libdl
[37e2e46d] + LinearAlgebra
[56ddb016] + Logging
[d6f4376e] + Markdown
[9a3f8284] + Random
[9e88b42a] + Serialization
[6462fe0b] + Sockets
[8dfed614] + Test
Testing TensorToolbox
Status `/tmp/jl_0ktnzL/Manifest.toml`
[9c690861] TensorToolbox v1.0.1
[2a0f44e3] Base64 [`@stdlib/Base64`]
[8ba89e20] Distributed [`@stdlib/Distributed`]
[b77e0a4c] InteractiveUtils [`@stdlib/InteractiveUtils`]
[8f399da3] Libdl [`@stdlib/Libdl`]
[37e2e46d] LinearAlgebra [`@stdlib/LinearAlgebra`]
[56ddb016] Logging [`@stdlib/Logging`]
[d6f4376e] Markdown [`@stdlib/Markdown`]
[9a3f8284] Random [`@stdlib/Random`]
[9e88b42a] Serialization [`@stdlib/Serialization`]
[6462fe0b] Sockets [`@stdlib/Sockets`]
[8dfed614] Test [`@stdlib/Test`]
**** Testing tensor.jl
**Test tensor X of size: (20, 10, 50, 5)
...Testing functions matten and tenmat (by mode).
Size of 1-mode matricization: [20, 2500]
Check if it folds back correctly: true
Size of 2-mode matricization: [10, 5000]
Check if it folds back correctly: true
Size of 3-mode matricization: [50, 1000]
Check if it folds back correctly: true
Size of 4-mode matricization: [5, 10000]
Check if it folds back correctly: true
...Testing functions matten and tenmat (by rows and columns).
Size of R=[2, 1] and C=[4, 3] matricization: [200, 250]
Check if it folds back correctly: true
...Testing function ttm.
Created 4 matrices with 5 rows and appropriate number of columns.
Size of tensor Y=ttm(X,M): (5, 5, 5, 5)
Multiplication error: 1.0614966277205394e-11
...Testing function ttv.
Multiplying a tensor X by a vector v in mode 2.
Size of tensor Y=ttv(X,v): (3, 2)
...Testing function krontm.
Created two tensors X and Y of order 3 and sizes (5, 4, 3) and (2, 5, 4).
Multiplying tkron(X,Y) by random matrix in mode 3.
Multiplication error: 1.4291399519651272e-14
Multiplying tkron(X,Y) by random matrices in modes [3, 2].
Multiplication error: 1.1463352458670898e-13
Multiplying tkron(X,Y) by random matrices in all modes.
Multiplication error: 6.48036789554587e-13
...Testing function mkrontv.
Multiplying mode-1 matricized tkron(X,Y) by a random vector.
Multiplication error: 3.056159864571351e-14
Multiplication error: 3.394700931633811e-15
...Testing function mttkrp.
Multiplying mode-1 matricized tensor X by Khatri-Rao product of matrices.
Multiplication error: 0.0
...Testing function dropdims.
Tensor X of size :(5, 4, 1, 3, 6, 1) squeezed to size :(5, 4, 3, 6).
...Testing contraction (contract).
Error: 0.0
****Testing ttensor.jl
...Test tensor X of size: (20, 10, 50, 5)
...Testing hosvd.
Creating exact decomposition with rank = size(X):
Results:
Type of output T: ttensor
Core tensor size: (20, 10, 50, 5)
Factor matrices sizes: (20, 20) (10, 10) (50, 50) (5, 5)
...Testing function full, i.e. n-mode multiplication (ttm): norm(full(T)-X) = 1.9199629166202601e-13
...Testing ttm for ttensor T and array of matrices A : norm(full(ttm(T,A))-ttm(full(T),A)) = 1.8622098354261415e-11
...Testing hosvd with smaller multilinear rank: [5, 5, 5, 5]
Results:
Type of output T: ttensor
Core tensor size: (5, 5, 5, 5)
Factor matrices sizes: (20, 5) (10, 5) (50, 5) (5, 5)
...Testing size of ttensor T : (20, 10, 50, 5)
...Testing ndims of ttensor T : 4
...Testing nrank of ttensor T for mode 1: 5
...Testing mrank of ttensor T: (5, 5, 5, 5)
...Testing functions matten and tenmat (by mode).
...Testing hosvd for tensor with noise.
For ttensor T, X=full(T) tensor of size (60, 50, 40) and rank [5, 5, 5] , N noise tensor and S=hosvd(X+N,[5, 5, 5]).
Error( norm(T-S) ): 0.014335549136667212. Noise norm: 0.17301045307868618.
...Testing hosvd with eps_abs=1e-5 on function defined tensor X of size (20, 20, 20) and multlinear rank(13, 13, 13)
Results:
Type of output T: ttensor
Core tensor size: (7, 7, 7)
Factor matrices sizes: (20, 7) (20, 7) (20, 7)
...Testing hosvd with eps_rel=1e-5 on function defined tensor X of size (20, 20, 20)
Results:
Type of output T: ttensor
Core tensor size: (6, 6, 6)
Factor matrices sizes: (20, 6) (20, 6) (20, 6)
...Testing if factor matrices of ttensor T are orthogonal: true
...Recompress Tucker tensor T to smaller rank: [3, 3, 3]
Results:
Type of output T: ttensor
Core tensor size: (3, 3, 3)
Factor matrices sizes: (20, 3) (20, 3) (20, 3)
...Testing orthogonal flag and reorthogonalization for random ttensor S of size (4, 5, 2).
Has orthogonal factor matrices: false
After reorthogonalization: true
...Testing norm of ttensor T.
|norm(T) - norm(full(T))| = 0.0
...Testing scalar multiplication 3*T.
norm(full(3*T) - 3*full(T)) = 2.762916642284124e-14
...Creating two random ttensors X and Y of size (6, 8, 2, 5, 4).
...Testing addition.
norm(full(X+Y) - (full(X)+full(Y))) = 1.2030301882854682e-13
...Testing inner product.
|innerprod(X,Y) - innerprod(full(X),full(Y))| = 4.547473508864641e-13
...Testing Hadamard product.
norm(full(ewprod(X,Y)) - full(X).*full(Y)) = 7.788617354608023e-13
...Testing singular values of matricizations of Tucker Tensor.
Singular values of matricizations of random Tucker tensor of size (10, 9, 8), rank [3, 3, 3] and norm 95.56446250783841.
Mode-1 singular values error: 3.332740845837229e-14
Mode-2 singular values error: 3.256115871121665e-14
Mode-3 singular values error: 4.3366397107056194e-14
Singular values of matricizations of random Tucker tensor of size (20, 20, 20, 20), rank [5, 5, 5, 5] and norm 9140.088731326556.
Mode-1 singular values error: 5.8810279171564445e-12
Mode-2 singular values error: 3.183231456205249e-12
Mode-3 singular values error: 3.83176928752453e-12
Mode-4 singular values error: 2.2737367544323206e-12
...Testing function mhadtv.
...Creating two random ttensors X and Y of size (5, 4, 3).
Multiplying mode-1 matricized ewprod(X,Y) by a random vector.
Multiplication error: 7.03065769189946e-15
Multiplication error: 1.0400858617096978e-14
Multiplication error: 1.078814721512637e-12
...Testing function mttkrp.
Multiplying mode-1 matricized tensor X by Khatri-Rao product of matrices.
Multiplication error: 2.148324584118883e-15
...Testing cp_als on ttensor.
Test rank-1 ttensor T of size: (5, 4, 3)
norm(full(Tcp)-T) = 3.208599566768793e-16
****Testing ktensor.jl
**Test rank-1 tensor X of size: (5, 4, 3)
...Testing cp_als.
norm(full(Xcp)-X) = 6.226787440222654e-16
**Test ktensors X and Y of size: (4, 3, 2)
...Testing function ndims.
X is of order: 3
...Testing function ttensor and full.
...Testing scalar multiplication.
norm(full(3*X) - 3*full(X)) = 1.3797236336603623e-15
...Testing functions plus and minus.
norm(full(Z)-(full(X)+full(Y))) = 2.891945847262976e-16
norm(full(Z)-(full(X)-full(Y))) = 9.490824173852923e-16
...Testing function innerprod.
norm(innerprod(X,Y)-innerprod(full(X),full(Y))) = 1.3322676295501878e-15
...Testing function norm.
...Testing functions arrange and arrange!.
norm(full(X)-full(Z)) = 5.261019068567312e-16
...Testing functions normalize and normalize!.
norm(full(X)-full(Z)) = 5.567057530901541e-16
...Testing functions redistribute and redistribute!.
norm(full(X)-full(Z)) = 5.161361836466869e-16
...Testing functions fixsigns, fixsigns! and isequal.
norm(full(X)-full(Z)) = 0.0
...Testing functions ttm and ttv.
...Testing function tocell.
Is the output MatrixCell: true
...Testing function tenmat by mode 2.
...Testing function mttkrp.
Multiplying mode-1 matricized tensor X by Khatri-Rao product of matrices.
Multiplication error: 1.3229106320778743e-15
****Testing dimtree.jl
...Testing creating a dimtree.
...Testing function non (number-of-nodes).
...Created two dimtrees for tensor of order 5, with 9 nodes.
...Testing functions:
- height
- children
- sibling
- parent
- is_leaf
- is_left
- is_right
- count_leaves
- dims
- lvl
- nodes_on_lvl
- node2ind
- subnodes
- left_child_length
Testing truncation of tensor X of size (2, 2, 2, 2, 2) to htensor.
norm(full(H)-X) = 9.642055270146469e-14
norm(full(H)-X) = 9.324974611567615e-14
...Testing size of htensor H : (5, 4, 3, 2, 4, 2)
...Testing ndims of htensor H : 6
...Testing ttm for ttensor H and array of matrices A : norm(full(ttm(H,A))-ttm(full(H),A)) = 2.4814352024564893e-13
...Testing norm of htensor H.
|norm(H) - norm(full(H))| = 1.0658141036401503e-14
...Testing scalar multiplication 3*H.
norm(full(3*H) - 3*full(H)) = 2.0587825671115578e-14
Testing functions plus and minus for htensors H1 and H2.
norm(full(H1+H2) - (full(H1)+full(H2))) = 9.542429867210369e-16
norm(full(H1+H2) - (full(H1)+full(H2))) = 7.723163476444606e-16
...Testing inner product.
|innerprod(H1,H2) - innerprod(full(H1),full(H2))| = 7.105427357601002e-15
Testing function dropdims for squeezed tensor X and squeezed htensor Y.
norm(full(Y)-dropdims(X,dims=1)) = 4.9696627478973456e-15
norm(full(Y)-dropdims(X,dims=2)) = 6.329610183504276e-15
norm(full(Y)-dropdims(X,dims=3)) = 5.093587695826778e-15
norm(full(Y)-dropdims(X,dims=4)) = 4.558214466076628e-15
norm(full(Y)-dropdims(X,dims=5)) = 3.725704666073741e-15
...Testing reorthogonalization for random htensor H of size (4, 5, 2).
Has orthogonal factor matrices: false
After reorthogonalization: true
Testing hrank: [1, 2, 2, 2, 2]
****Testing TTtensor.jl
...Test core tensors G of sizes:
(1, 4, 3)
(3, 6, 4)
(4, 3, 1)
...Test size of TTtensor T: (4, 6, 3)
...Test ndims of TTtensor T: 3
...Test TTsvd of TTtensor T: (3, 4)
...Test addition:
...Test dot product:
...Test tensor X of size: (5, 4, 3, 2)
...Testing TTsvd.
Results:
Type of output T: TTtensor
...Testing function full, i.e. contracted product (conprod): norm(full(T)-X) = 4.543062356583449e-15
...Testing TTsvd with requested rank.
Created tensor x of size (6, 5, 6, 5), with TTrank = (4, 4, 4).
T1=TTsvd(X,reqrank=[4, 4, 4])
norm(X-full(T1)) = 8.129410518171415e-14
...Testing recompression.
S=TTsvd(T): norm(full(S)-X) = 6.062061714602967e-14
...Testing reorthogonalization - function reorth.
Test TT-tensor T of size: (6, 5, 4, 3) with flags T.lorth = false and T.rorth = false.
Performing (default) left orthogonalization: Tl=reorth(T).
Flags: Tl.lorth = true, Tl.rorth = false.
Performing right orthogonalization: Tr=reorth(T,"right").
Flags: Tr.lorth = false, Tr.rorth = true.
norm(Diagonal(ones(size(Gn, 1))) - Gn * Gn') = 2.7323095490488697e-16
norm(Diagonal(ones(size(Gn, 1))) - Gn * Gn') = 6.330441298195492e-16
...Testing reorthogonalization with overwriting - function reorth!.
Performing (default) left orthogonalization: reorth!(T)
Flags: T.lorth = true, T.rorth = false.
Performing right orthogonalization: reorth!(T,"right")
Flags: T.lorth = true, T.rorth = true.
...Testing TTsvd on TT-tensors.
Fixed precision problem with ϵ = 1.0e-8.
Created TT-tensor T of size (6, 5, 6, 5), with TTrank = (4, 4, 4), but its actual TT-rank is (2,2,2)
T1=TTsvd(T,ϵ)
TTrank(T1) = (2, 2, 2)
norm(full(T)-full(T1)) = 4.87629365764864e-14
Fixed rank problem with reqrank = [2, 2, 2].
Created TT-tensor T of size (6, 5, 4, 3), with TTrank = (6, 12, 3).
T1=TTsvd(T,reqrank=[2, 2, 2])
TTrank(T1) = (2, 2, 2)
... Testing contraction with vectors - function TTtv.
... Testing transformation of ktensor to TTtensor - function kten2TT.
Test ktensor T of size (5, 4, 3, 2), and k-rank = 3, transofrming to TTtensor Ttt.
norm(full(T)-full(Ttt)) = 0.0
... Testing contraction of full tensor to TTtensor - function contract.
... Testing element-wise product of two TTtensor - function ewprod.
Testing TensorToolbox tests passed
Results with Julia v1.3.0
Testing was successful.
Last evaluation was ago and took 2 minutes, 29 seconds.
Resolving package versions...
Installed TensorToolbox ─ v1.0.1
Updating `~/.julia/environments/v1.3/Project.toml`
[9c690861] + TensorToolbox v1.0.1
Updating `~/.julia/environments/v1.3/Manifest.toml`
[9c690861] + TensorToolbox v1.0.1
[2a0f44e3] + Base64
[8ba89e20] + Distributed
[b77e0a4c] + InteractiveUtils
[8f399da3] + Libdl
[37e2e46d] + LinearAlgebra
[56ddb016] + Logging
[d6f4376e] + Markdown
[9a3f8284] + Random
[9e88b42a] + Serialization
[6462fe0b] + Sockets
[8dfed614] + Test
Testing TensorToolbox
Status `/tmp/jl_IASp4H/Manifest.toml`
[9c690861] TensorToolbox v1.0.1
[2a0f44e3] Base64 [`@stdlib/Base64`]
[8ba89e20] Distributed [`@stdlib/Distributed`]
[b77e0a4c] InteractiveUtils [`@stdlib/InteractiveUtils`]
[8f399da3] Libdl [`@stdlib/Libdl`]
[37e2e46d] LinearAlgebra [`@stdlib/LinearAlgebra`]
[56ddb016] Logging [`@stdlib/Logging`]
[d6f4376e] Markdown [`@stdlib/Markdown`]
[9a3f8284] Random [`@stdlib/Random`]
[9e88b42a] Serialization [`@stdlib/Serialization`]
[6462fe0b] Sockets [`@stdlib/Sockets`]
[8dfed614] Test [`@stdlib/Test`]
**** Testing tensor.jl
**Test tensor X of size: (20, 10, 50, 5)
...Testing functions matten and tenmat (by mode).
Size of 1-mode matricization: [20, 2500]
Check if it folds back correctly: true
Size of 2-mode matricization: [10, 5000]
Check if it folds back correctly: true
Size of 3-mode matricization: [50, 1000]
Check if it folds back correctly: true
Size of 4-mode matricization: [5, 10000]
Check if it folds back correctly: true
...Testing functions matten and tenmat (by rows and columns).
Size of R=[2, 1] and C=[4, 3] matricization: [200, 250]
Check if it folds back correctly: true
...Testing function ttm.
Created 4 matrices with 5 rows and appropriate number of columns.
Size of tensor Y=ttm(X,M): (5, 5, 5, 5)
Multiplication error: 7.500747052839271e-12
...Testing function ttv.
Multiplying a tensor X by a vector v in mode 2.
Size of tensor Y=ttv(X,v): (3, 2)
...Testing function krontm.
Created two tensors X and Y of order 3 and sizes (5, 4, 3) and (2, 5, 4).
Multiplying tkron(X,Y) by random matrix in mode 3.
Multiplication error: 1.2537928466057885e-14
Multiplying tkron(X,Y) by random matrices in modes [3, 2].
Multiplication error: 1.0280257558663545e-13
Multiplying tkron(X,Y) by random matrices in all modes.
Multiplication error: 6.528008669476721e-13
...Testing function mkrontv.
Multiplying mode-1 matricized tkron(X,Y) by a random vector.
Multiplication error: 2.218668981299174e-14
Multiplication error: 1.9641850382783467e-15
...Testing function mttkrp.
Multiplying mode-1 matricized tensor X by Khatri-Rao product of matrices.
Multiplication error: 0.0
...Testing function dropdims.
Tensor X of size :(5, 4, 1, 3, 6, 1) squeezed to size :(5, 4, 3, 6).
...Testing contraction (contract).
Error: 0.0
****Testing ttensor.jl
...Test tensor X of size: (20, 10, 50, 5)
...Testing hosvd.
Creating exact decomposition with rank = size(X):
Results:
Type of output T: ttensor
Core tensor size: (20, 10, 50, 5)
Factor matrices sizes: (20, 20) (10, 10) (50, 50) (5, 5)
...Testing function full, i.e. n-mode multiplication (ttm): norm(full(T)-X) = 1.849123653746041e-13
...Testing ttm for ttensor T and array of matrices A : norm(full(ttm(T,A))-ttm(full(T),A)) = 1.0982407434979288e-11
...Testing hosvd with smaller multilinear rank: [5, 5, 5, 5]
Results:
Type of output T: ttensor
Core tensor size: (5, 5, 5, 5)
Factor matrices sizes: (20, 5) (10, 5) (50, 5) (5, 5)
...Testing size of ttensor T : (20, 10, 50, 5)
...Testing ndims of ttensor T : 4
...Testing nrank of ttensor T for mode 1: 5
...Testing mrank of ttensor T: (5, 5, 5, 5)
...Testing functions matten and tenmat (by mode).
...Testing hosvd for tensor with noise.
For ttensor T, X=full(T) tensor of size (60, 50, 40) and rank [5, 5, 5] , N noise tensor and S=hosvd(X+N,[5, 5, 5]).
Error( norm(T-S) ): 0.014065007996964037. Noise norm: 0.17336643891832393.
...Testing hosvd with eps_abs=1e-5 on function defined tensor X of size (20, 20, 20) and multlinear rank(13, 13, 13)
Results:
Type of output T: ttensor
Core tensor size: (7, 7, 7)
Factor matrices sizes: (20, 7) (20, 7) (20, 7)
...Testing hosvd with eps_rel=1e-5 on function defined tensor X of size (20, 20, 20)
Results:
Type of output T: ttensor
Core tensor size: (6, 6, 6)
Factor matrices sizes: (20, 6) (20, 6) (20, 6)
...Testing if factor matrices of ttensor T are orthogonal: true
...Recompress Tucker tensor T to smaller rank: [3, 3, 3]
Results:
Type of output T: ttensor
Core tensor size: (3, 3, 3)
Factor matrices sizes: (20, 3) (20, 3) (20, 3)
...Testing orthogonal flag and reorthogonalization for random ttensor S of size (4, 5, 2).
Has orthogonal factor matrices: false
After reorthogonalization: true
...Testing norm of ttensor T.
|norm(T) - norm(full(T))| = 0.0
...Testing scalar multiplication 3*T.
norm(full(3*T) - 3*full(T)) = 2.762916642284124e-14
...Creating two random ttensors X and Y of size (6, 8, 2, 5, 4).
...Testing addition.
norm(full(X+Y) - (full(X)+full(Y))) = 2.9371417615883824e-13
...Testing inner product.
|innerprod(X,Y) - innerprod(full(X),full(Y))| = 0.0
...Testing Hadamard product.
norm(full(ewprod(X,Y)) - full(X).*full(Y)) = 4.6026466328654125e-12
...Testing singular values of matricizations of Tucker Tensor.
Singular values of matricizations of random Tucker tensor of size (10, 9, 8), rank [3, 3, 3] and norm 155.44992332458497.
Mode-1 singular values error: 5.955433342649105e-14
Mode-2 singular values error: 7.553172887309252e-14
Mode-3 singular values error: 5.1728291973635394e-14
Singular values of matricizations of random Tucker tensor of size (20, 20, 20, 20), rank [5, 5, 5, 5] and norm 10211.191977110153.
Mode-1 singular values error: 4.50176909753812e-12
Mode-2 singular values error: 4.725873098056247e-12
Mode-3 singular values error: 6.6523802335394945e-12
Mode-4 singular values error: 7.458411103860602e-12
...Testing function mhadtv.
...Creating two random ttensors X and Y of size (5, 4, 3).
Multiplying mode-1 matricized ewprod(X,Y) by a random vector.
Multiplication error: 1.2121276483828486e-14
Multiplication error: 1.461072060248201e-14
Multiplication error: 1.844566752377881e-12
...Testing function mttkrp.
Multiplying mode-1 matricized tensor X by Khatri-Rao product of matrices.
Multiplication error: 1.1890203701269815e-14
...Testing cp_als on ttensor.
Test rank-1 ttensor T of size: (5, 4, 3)
norm(full(Tcp)-T) = 4.416364168247873e-17
****Testing ktensor.jl
**Test rank-1 tensor X of size: (5, 4, 3)
...Testing cp_als.
norm(full(Xcp)-X) = 2.4595479356938113e-16
**Test ktensors X and Y of size: (4, 3, 2)
...Testing function ndims.
X is of order: 3
...Testing function ttensor and full.
...Testing scalar multiplication.
norm(full(3*X) - 3*full(X)) = 5.324442579404919e-16
...Testing functions plus and minus.
norm(full(Z)-(full(X)+full(Y))) = 5.889482005950448e-16
norm(full(Z)-(full(X)-full(Y))) = 1.0344538778264393e-15
...Testing function innerprod.
norm(innerprod(X,Y)-innerprod(full(X),full(Y))) = 6.661338147750939e-16
...Testing function norm.
...Testing functions arrange and arrange!.
norm(full(X)-full(Z)) = 4.783309287441108e-16
...Testing functions normalize and normalize!.
norm(full(X)-full(Z)) = 3.764949453935611e-16
...Testing functions redistribute and redistribute!.
norm(full(X)-full(Z)) = 5.043960206559463e-16
...Testing functions fixsigns, fixsigns! and isequal.
norm(full(X)-full(Z)) = 0.0
...Testing functions ttm and ttv.
...Testing function tocell.
Is the output MatrixCell: true
...Testing function tenmat by mode 2.
...Testing function mttkrp.
Multiplying mode-1 matricized tensor X by Khatri-Rao product of matrices.
Multiplication error: 1.160399051051184e-15
****Testing dimtree.jl
...Testing creating a dimtree.
...Testing function non (number-of-nodes).
...Created two dimtrees for tensor of order 5, with 9 nodes.
...Testing functions:
- height
- children
- sibling
- parent
- is_leaf
- is_left
- is_right
- count_leaves
- dims
- lvl
- nodes_on_lvl
- node2ind
- subnodes
- left_child_length
Testing truncation of tensor X of size (2, 2, 2, 2, 2) to htensor.
norm(full(H)-X) = 9.642055270146469e-14
norm(full(H)-X) = 9.324974611567615e-14
...Testing size of htensor H : (5, 4, 3, 2, 4, 2)
...Testing ndims of htensor H : 6
...Testing ttm for ttensor H and array of matrices A : norm(full(ttm(H,A))-ttm(full(H),A)) = 8.608619237455852e-13
...Testing norm of htensor H.
|norm(H) - norm(full(H))| = 1.0658141036401503e-14
...Testing scalar multiplication 3*H.
norm(full(3*H) - 3*full(H)) = 2.0492359422928584e-14
Testing functions plus and minus for htensors H1 and H2.
norm(full(H1+H2) - (full(H1)+full(H2))) = 1.1198953432285394e-15
norm(full(H1+H2) - (full(H1)+full(H2))) = 7.15757921555296e-16
...Testing inner product.
|innerprod(H1,H2) - innerprod(full(H1),full(H2))| = 3.552713678800501e-15
Testing function dropdims for squeezed tensor X and squeezed htensor Y.
norm(full(Y)-dropdims(X,dims=1)) = 8.137497409638755e-15
norm(full(Y)-dropdims(X,dims=2)) = 3.5941327070641825e-15
norm(full(Y)-dropdims(X,dims=3)) = 5.095851118916444e-15
norm(full(Y)-dropdims(X,dims=4)) = 3.2669297017709956e-15
norm(full(Y)-dropdims(X,dims=5)) = 3.91167796714721e-15
...Testing reorthogonalization for random htensor H of size (4, 5, 2).
Has orthogonal factor matrices: false
After reorthogonalization: true
Testing hrank: [1, 2, 2, 2, 2]
****Testing TTtensor.jl
...Test core tensors G of sizes:
(1, 4, 3)
(3, 6, 4)
(4, 3, 1)
...Test size of TTtensor T: (4, 6, 3)
...Test ndims of TTtensor T: 3
...Test TTsvd of TTtensor T: (3, 4)
...Test addition:
...Test dot product:
...Test tensor X of size: (5, 4, 3, 2)
...Testing TTsvd.
Results:
Type of output T: TTtensor
...Testing function full, i.e. contracted product (conprod): norm(full(T)-X) = 3.928120341493524e-15
...Testing TTsvd with requested rank.
Created tensor x of size (6, 5, 6, 5), with TTrank = (4, 4, 4).
T1=TTsvd(X,reqrank=[4, 4, 4])
norm(X-full(T1)) = 1.9878151837212397e-13
...Testing recompression.
S=TTsvd(T): norm(full(S)-X) = 1.5131130179940105e-13
...Testing reorthogonalization - function reorth.
Test TT-tensor T of size: (6, 5, 4, 3) with flags T.lorth = false and T.rorth = false.
Performing (default) left orthogonalization: Tl=reorth(T).
Flags: Tl.lorth = true, Tl.rorth = false.
Performing right orthogonalization: Tr=reorth(T,"right").
Flags: Tr.lorth = false, Tr.rorth = true.
norm(Diagonal(ones(size(Gn, 1))) - Gn * Gn') = 5.980282050312834e-16
norm(Diagonal(ones(size(Gn, 1))) - Gn * Gn') = 5.078718441931913e-16
...Testing reorthogonalization with overwriting - function reorth!.
Performing (default) left orthogonalization: reorth!(T)
Flags: T.lorth = true, T.rorth = false.
Performing right orthogonalization: reorth!(T,"right")
Flags: T.lorth = true, T.rorth = true.
...Testing TTsvd on TT-tensors.
Fixed precision problem with ϵ = 1.0e-8.
Created TT-tensor T of size (6, 5, 6, 5), with TTrank = (4, 4, 4), but its actual TT-rank is (2,2,2)
T1=TTsvd(T,ϵ)
TTrank(T1) = (2, 2, 2)
norm(full(T)-full(T1)) = 8.862313134702342e-14
Fixed rank problem with reqrank = [2, 2, 2].
Created TT-tensor T of size (6, 5, 4, 3), with TTrank = (6, 12, 3).
T1=TTsvd(T,reqrank=[2, 2, 2])
TTrank(T1) = (2, 2, 2)
... Testing contraction with vectors - function TTtv.
... Testing transformation of ktensor to TTtensor - function kten2TT.
Test ktensor T of size (5, 4, 3, 2), and k-rank = 3, transofrming to TTtensor Ttt.
norm(full(T)-full(Ttt)) = 0.0
... Testing contraction of full tensor to TTtensor - function contract.
... Testing element-wise product of two TTtensor - function ewprod.
Testing TensorToolbox tests passed
Results with Julia v1.3.1-pre-7704df0a5a
Testing was successful.
Last evaluation was ago and took 2 minutes, 13 seconds.
Resolving package versions...
Installed TensorToolbox ─ v1.0.1
Updating `~/.julia/environments/v1.3/Project.toml`
[9c690861] + TensorToolbox v1.0.1
Updating `~/.julia/environments/v1.3/Manifest.toml`
[9c690861] + TensorToolbox v1.0.1
[2a0f44e3] + Base64
[8ba89e20] + Distributed
[b77e0a4c] + InteractiveUtils
[8f399da3] + Libdl
[37e2e46d] + LinearAlgebra
[56ddb016] + Logging
[d6f4376e] + Markdown
[9a3f8284] + Random
[9e88b42a] + Serialization
[6462fe0b] + Sockets
[8dfed614] + Test
Testing TensorToolbox
Status `/tmp/jl_hG05sw/Manifest.toml`
[9c690861] TensorToolbox v1.0.1
[2a0f44e3] Base64 [`@stdlib/Base64`]
[8ba89e20] Distributed [`@stdlib/Distributed`]
[b77e0a4c] InteractiveUtils [`@stdlib/InteractiveUtils`]
[8f399da3] Libdl [`@stdlib/Libdl`]
[37e2e46d] LinearAlgebra [`@stdlib/LinearAlgebra`]
[56ddb016] Logging [`@stdlib/Logging`]
[d6f4376e] Markdown [`@stdlib/Markdown`]
[9a3f8284] Random [`@stdlib/Random`]
[9e88b42a] Serialization [`@stdlib/Serialization`]
[6462fe0b] Sockets [`@stdlib/Sockets`]
[8dfed614] Test [`@stdlib/Test`]
**** Testing tensor.jl
**Test tensor X of size: (20, 10, 50, 5)
...Testing functions matten and tenmat (by mode).
Size of 1-mode matricization: [20, 2500]
Check if it folds back correctly: true
Size of 2-mode matricization: [10, 5000]
Check if it folds back correctly: true
Size of 3-mode matricization: [50, 1000]
Check if it folds back correctly: true
Size of 4-mode matricization: [5, 10000]
Check if it folds back correctly: true
...Testing functions matten and tenmat (by rows and columns).
Size of R=[2, 1] and C=[4, 3] matricization: [200, 250]
Check if it folds back correctly: true
...Testing function ttm.
Created 4 matrices with 5 rows and appropriate number of columns.
Size of tensor Y=ttm(X,M): (5, 5, 5, 5)
Multiplication error: 7.880556416068144e-12
...Testing function ttv.
Multiplying a tensor X by a vector v in mode 2.
Size of tensor Y=ttv(X,v): (3, 2)
...Testing function krontm.
Created two tensors X and Y of order 3 and sizes (5, 4, 3) and (2, 5, 4).
Multiplying tkron(X,Y) by random matrix in mode 3.
Multiplication error: 1.5430647611029857e-14
Multiplying tkron(X,Y) by random matrices in modes [3, 2].
Multiplication error: 1.2558619865777448e-13
Multiplying tkron(X,Y) by random matrices in all modes.
Multiplication error: 7.049966209938088e-13
...Testing function mkrontv.
Multiplying mode-1 matricized tkron(X,Y) by a random vector.
Multiplication error: 4.7265781317840344e-14
Multiplication error: 2.604295469441609e-15
...Testing function mttkrp.
Multiplying mode-1 matricized tensor X by Khatri-Rao product of matrices.
Multiplication error: 0.0
...Testing function dropdims.
Tensor X of size :(5, 4, 1, 3, 6, 1) squeezed to size :(5, 4, 3, 6).
...Testing contraction (contract).
Error: 0.0
****Testing ttensor.jl
...Test tensor X of size: (20, 10, 50, 5)
...Testing hosvd.
Creating exact decomposition with rank = size(X):
Results:
Type of output T: ttensor
Core tensor size: (20, 10, 50, 5)
Factor matrices sizes: (20, 20) (10, 10) (50, 50) (5, 5)
...Testing function full, i.e. n-mode multiplication (ttm): norm(full(T)-X) = 1.9338268534390268e-13
...Testing ttm for ttensor T and array of matrices A : norm(full(ttm(T,A))-ttm(full(T),A)) = 7.42628321588659e-12
...Testing hosvd with smaller multilinear rank: [5, 5, 5, 5]
Results:
Type of output T: ttensor
Core tensor size: (5, 5, 5, 5)
Factor matrices sizes: (20, 5) (10, 5) (50, 5) (5, 5)
...Testing size of ttensor T : (20, 10, 50, 5)
...Testing ndims of ttensor T : 4
...Testing nrank of ttensor T for mode 1: 5
...Testing mrank of ttensor T: (5, 5, 5, 5)
...Testing functions matten and tenmat (by mode).
...Testing hosvd for tensor with noise.
For ttensor T, X=full(T) tensor of size (60, 50, 40) and rank [5, 5, 5] , N noise tensor and S=hosvd(X+N,[5, 5, 5]).
Error( norm(T-S) ): 0.01327926101534265. Noise norm: 0.17334579558792046.
...Testing hosvd with eps_abs=1e-5 on function defined tensor X of size (20, 20, 20) and multlinear rank(13, 13, 13)
Results:
Type of output T: ttensor
Core tensor size: (7, 7, 7)
Factor matrices sizes: (20, 7) (20, 7) (20, 7)
...Testing hosvd with eps_rel=1e-5 on function defined tensor X of size (20, 20, 20)
Results:
Type of output T: ttensor
Core tensor size: (6, 6, 6)
Factor matrices sizes: (20, 6) (20, 6) (20, 6)
...Testing if factor matrices of ttensor T are orthogonal: true
...Recompress Tucker tensor T to smaller rank: [3, 3, 3]
Results:
Type of output T: ttensor
Core tensor size: (3, 3, 3)
Factor matrices sizes: (20, 3) (20, 3) (20, 3)
...Testing orthogonal flag and reorthogonalization for random ttensor S of size (4, 5, 2).
Has orthogonal factor matrices: false
After reorthogonalization: true
...Testing norm of ttensor T.
|norm(T) - norm(full(T))| = 0.0
...Testing scalar multiplication 3*T.
norm(full(3*T) - 3*full(T)) = 2.762916642284124e-14
...Creating two random ttensors X and Y of size (6, 8, 2, 5, 4).
...Testing addition.
norm(full(X+Y) - (full(X)+full(Y))) = 1.6157503885512517e-13
...Testing inner product.
|innerprod(X,Y) - innerprod(full(X),full(Y))| = 5.4569682106375694e-12
...Testing Hadamard product.
norm(full(ewprod(X,Y)) - full(X).*full(Y)) = 1.5130380436287428e-12
...Testing singular values of matricizations of Tucker Tensor.
Singular values of matricizations of random Tucker tensor of size (10, 9, 8), rank [3, 3, 3] and norm 87.68737589430809.
Mode-1 singular values error: 1.5888218580782548e-14
Mode-2 singular values error: 4.5496934130773415e-14
Mode-3 singular values error: 5.728578676879116e-14
Singular values of matricizations of random Tucker tensor of size (20, 20, 20, 20), rank [5, 5, 5, 5] and norm 8928.23388943427.
Mode-1 singular values error: 3.990391809289632e-12
Mode-2 singular values error: 5.1849175410968106e-12
Mode-3 singular values error: 2.651609927327309e-12
Mode-4 singular values error: 2.612324645514504e-12
...Testing function mhadtv.
...Creating two random ttensors X and Y of size (5, 4, 3).
Multiplying mode-1 matricized ewprod(X,Y) by a random vector.
Multiplication error: 2.9893669801409083e-16
Multiplication error: 2.1513704567906022e-15
Multiplication error: 2.871166393568923e-14
...Testing function mttkrp.
Multiplying mode-1 matricized tensor X by Khatri-Rao product of matrices.
Multiplication error: 3.195147797709499e-15
...Testing cp_als on ttensor.
Test rank-1 ttensor T of size: (5, 4, 3)
norm(full(Tcp)-T) = 4.769346574355995e-16
****Testing ktensor.jl
**Test rank-1 tensor X of size: (5, 4, 3)
...Testing cp_als.
norm(full(Xcp)-X) = 3.489856656915694e-16
**Test ktensors X and Y of size: (4, 3, 2)
...Testing function ndims.
X is of order: 3
...Testing function ttensor and full.
...Testing scalar multiplication.
norm(full(3*X) - 3*full(X)) = 9.305364597889227e-16
...Testing functions plus and minus.
norm(full(Z)-(full(X)+full(Y))) = 1.0254548988792393e-15
norm(full(Z)-(full(X)-full(Y))) = 7.97218214573518e-16
...Testing function innerprod.
norm(innerprod(X,Y)-innerprod(full(X),full(Y))) = 4.440892098500626e-16
...Testing function norm.
...Testing functions arrange and arrange!.
norm(full(X)-full(Z)) = 8.719845996599256e-16
...Testing functions normalize and normalize!.
norm(full(X)-full(Z)) = 6.365655192508265e-16
...Testing functions redistribute and redistribute!.
norm(full(X)-full(Z)) = 1.148088173416408e-15
...Testing functions fixsigns, fixsigns! and isequal.
norm(full(X)-full(Z)) = 0.0
...Testing functions ttm and ttv.
...Testing function tocell.
Is the output MatrixCell: true
...Testing function tenmat by mode 2.
...Testing function mttkrp.
Multiplying mode-1 matricized tensor X by Khatri-Rao product of matrices.
Multiplication error: 1.4359319616405837e-15
****Testing dimtree.jl
...Testing creating a dimtree.
...Testing function non (number-of-nodes).
...Created two dimtrees for tensor of order 5, with 9 nodes.
...Testing functions:
- height
- children
- sibling
- parent
- is_leaf
- is_left
- is_right
- count_leaves
- dims
- lvl
- nodes_on_lvl
- node2ind
- subnodes
- left_child_length
Testing truncation of tensor X of size (2, 2, 2, 2, 2) to htensor.
norm(full(H)-X) = 9.642055270146469e-14
norm(full(H)-X) = 9.324974611567615e-14
...Testing size of htensor H : (5, 4, 3, 2, 4, 2)
...Testing ndims of htensor H : 6
...Testing ttm for ttensor H and array of matrices A : norm(full(ttm(H,A))-ttm(full(H),A)) = 4.645398146103157e-13
...Testing norm of htensor H.
|norm(H) - norm(full(H))| = 7.105427357601002e-15
...Testing scalar multiplication 3*H.
norm(full(3*H) - 3*full(H)) = 1.997966270471449e-14
Testing functions plus and minus for htensors H1 and H2.
norm(full(H1+H2) - (full(H1)+full(H2))) = 1.1119563949618733e-15
norm(full(H1+H2) - (full(H1)+full(H2))) = 9.586791989626881e-16
...Testing inner product.
|innerprod(H1,H2) - innerprod(full(H1),full(H2))| = 7.105427357601002e-15
Testing function dropdims for squeezed tensor X and squeezed htensor Y.
norm(full(Y)-dropdims(X,dims=1)) = 1.1703970388398494e-14
norm(full(Y)-dropdims(X,dims=2)) = 3.546093878183873e-15
norm(full(Y)-dropdims(X,dims=3)) = 4.281201945101918e-15
norm(full(Y)-dropdims(X,dims=4)) = 5.625881274348526e-15
norm(full(Y)-dropdims(X,dims=5)) = 3.680623755400682e-15
...Testing reorthogonalization for random htensor H of size (4, 5, 2).
Has orthogonal factor matrices: false
After reorthogonalization: true
Testing hrank: [1, 2, 2, 2, 2]
****Testing TTtensor.jl
...Test core tensors G of sizes:
(1, 4, 3)
(3, 6, 4)
(4, 3, 1)
...Test size of TTtensor T: (4, 6, 3)
...Test ndims of TTtensor T: 3
...Test TTsvd of TTtensor T: (3, 4)
...Test addition:
...Test dot product:
...Test tensor X of size: (5, 4, 3, 2)
...Testing TTsvd.
Results:
Type of output T: TTtensor
...Testing function full, i.e. contracted product (conprod): norm(full(T)-X) = 1.5710058178838452e-14
...Testing TTsvd with requested rank.
Created tensor x of size (6, 5, 6, 5), with TTrank = (4, 4, 4).
T1=TTsvd(X,reqrank=[4, 4, 4])
norm(X-full(T1)) = 6.048791334916279e-13
...Testing recompression.
S=TTsvd(T): norm(full(S)-X) = 1.1237166315465522e-12
...Testing reorthogonalization - function reorth.
Test TT-tensor T of size: (6, 5, 4, 3) with flags T.lorth = false and T.rorth = false.
Performing (default) left orthogonalization: Tl=reorth(T).
Flags: Tl.lorth = true, Tl.rorth = false.
Performing right orthogonalization: Tr=reorth(T,"right").
Flags: Tr.lorth = false, Tr.rorth = true.
norm(Diagonal(ones(size(Gn, 1))) - Gn * Gn') = 6.61889713242203e-16
norm(Diagonal(ones(size(Gn, 1))) - Gn * Gn') = 6.893398677371794e-16
...Testing reorthogonalization with overwriting - function reorth!.
Performing (default) left orthogonalization: reorth!(T)
Flags: T.lorth = true, T.rorth = false.
Performing right orthogonalization: reorth!(T,"right")
Flags: T.lorth = true, T.rorth = true.
...Testing TTsvd on TT-tensors.
Fixed precision problem with ϵ = 1.0e-8.
Created TT-tensor T of size (6, 5, 6, 5), with TTrank = (4, 4, 4), but its actual TT-rank is (2,2,2)
T1=TTsvd(T,ϵ)
TTrank(T1) = (2, 2, 2)
norm(full(T)-full(T1)) = 1.2505365073821823e-13
Fixed rank problem with reqrank = [2, 2, 2].
Created TT-tensor T of size (6, 5, 4, 3), with TTrank = (6, 12, 3).
T1=TTsvd(T,reqrank=[2, 2, 2])
TTrank(T1) = (2, 2, 2)
... Testing contraction with vectors - function TTtv.
... Testing transformation of ktensor to TTtensor - function kten2TT.
Test ktensor T of size (5, 4, 3, 2), and k-rank = 3, transofrming to TTtensor Ttt.
norm(full(T)-full(Ttt)) = 0.0
... Testing contraction of full tensor to TTtensor - function contract.
... Testing element-wise product of two TTtensor - function ewprod.
Testing TensorToolbox tests passed