# Higher order SVD in Julia like Numpy?

**URL:** <https://discourse.julialang.org/t/higher-order-svd-in-julia-like-numpy/85025>\
**Category:** General Usage\
**Tags:** linearalgebra\
**Created:** [July 30, 2022, 10:54am UTC](https://discourse.julialang.org/t/higher-order-svd-in-julia-like-numpy/85025 "2022-07-30T10:54:25Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![cocoa1231](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/cocoa1231/32/22215_2.png) [@cocoa1231](https://discourse.julialang.org/u/cocoa1231)\
**Post date:** [July 30, 2022, 10:54am UTC](https://discourse.julialang.org/t/higher-order-svd-in-julia-like-numpy/85025/1 "2022-07-30T10:54:26Z")

</div>

Hello all

I was wondering if there is any way to do higher order SVD in Julia using `LinearAlgebra.jl` like you can using [numpy.linalg.svd](https://numpy.org/doc/stable/reference/generated/numpy.linalg.svd.html) or should I just use PyCall? I tried with `LinearAlgebra.svd` but it didn’t work out and I couldn’t find in the docs how to do it -

```julia
julia> A = randn(3, 5, 2)
3×5×2 Array{Float64, 3}:
[:, :, 1] =
  1.69017 0.539516 -0.436762 -0.882562 2.28308
 -0.180177 0.122244 -0.760002 -0.805284 1.15463
  0.218088 0.524262 1.12136 -2.33447 -0.706637

[:, :, 2] =
  0.850423 -1.12059 0.30392 -1.32743 -0.394143
  0.296605 0.766331 -0.25429 0.0635182 0.0745694
 -0.568156 -1.4385 0.0120621 1.66298 1.0844

julia> svd(A)
ERROR: MethodError: no method matching svd(::Array{Float64, 3})
Closest candidates are:
  svd(::StridedVecOrMat{T}; full, alg) where T<:Union{Float16, ComplexF16} at ~/.julia/juliaup/julia-1.8.0-rc3+0.x64/share/julia/stdlib/v1.8/LinearAlgebra/src/svd.jl:181
  svd(::StridedMatrix{T}, ::StridedMatrix{T}) where T<:Union{Float32, Float64, ComplexF32, ComplexF64} at ~/.julia/juliaup/julia-1.8.0-rc3+0.x64/share/julia/stdlib/v1.8/LinearAlgebra/src/svd.jl:407
  svd(::StridedVecOrMat{T}; full, alg) where T at ~/.julia/juliaup/julia-1.8.0-rc3+0.x64/share/julia/stdlib/v1.8/LinearAlgebra/src/svd.jl:178
  ...
Stacktrace:
 [1] top-level scope
   @ REPL[4]:1

```

Same thing in python -

```python
In [1]: import numpy as np

In [2]: A = np.random.randn(3, 5, 2)

In [3]: np.linalg.svd(A)
Out[3]: 
(array([[[-0.6037455 , 0.58416878, 0.2178343 , -0.36421969,
           0.33783197],
         [ 0.32082226, -0.42888505, 0.1985067 , -0.49056635,
           0.65808088],
         [ 0.25303468, 0.13119474, 0.92420027, 0.16216266,
          -0.19575117],
         [-0.4705167 , -0.38054641, 0.15731977, 0.655918 ,
           0.42287178],
         [ 0.49714378, 0.55926453, -0.18506123, 0.41250882,
           0.48544831]],
 
        [[-0.53278136, 0.63028902, -0.24075323, 0.4968516 ,
          -0.11855861],
         [-0.5110045 , -0.19041643, -0.59981223, -0.58222151,
           0.06212399],
         [-0.67157959, -0.32594425, 0.66462678, 0.00804075,
          -0.0307863 ],
         [-0.03712789, -0.67049536, -0.37229753, 0.63951442,
           0.03838423],
         [-0.05119373, 0.10331337, 0.04392 , 0.07150708,
           0.98977943]],
 
        [[-0.50891794, 0.66685684, 0.31052877, -0.10016269,
           0.43571069],
         [-0.41478297, -0.66256106, -0.02431718, -0.43413115,
           0.44710934],
         [ 0.11320181, -0.25154376, 0.9476955 , 0.07824908,
          -0.14021911],
         [-0.44217126, -0.22985906, -0.06724939, 0.86055279,
           0.08109132],
         [ 0.60052273, -0.01433001, 0.018202 , 0.2341443 ,
           0.76420693]]]),
 array([[2.27220514, 0.61766628],
        [3.57499854, 1.38367195],
        [2.60157849, 2.01610413]]),
 array([[[0.42173425, -0.90671948],
         [-0.90671948, -0.42173425]],
 
        [[0.60493221, -0.79627697],
         [0.79627697, 0.60493221]],
 
        [[0.63651737, -0.77126237],
         [0.77126237, 0.63651737]]]))

```

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<div class="post-metadata">

**Author:** ![maxkapur](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/maxkapur/32/21208_2.png) [@maxkapur](https://discourse.julialang.org/u/maxkapur)\
**Post date:** [July 30, 2022, 12:01pm UTC](https://discourse.julialang.org/t/higher-order-svd-in-julia-like-numpy/85025/2 "2022-07-30T12:01:39Z")

</div>

To be clear, this is just iterating the normal SVD for matrices over each slice of the array, right, not a generalization of SVD for higher-order tensors?

---

<div class="post-metadata">

**Author:** ![cocoa1231](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/cocoa1231/32/22215_2.png) [@cocoa1231](https://discourse.julialang.org/u/cocoa1231)\
**Post date:** [July 30, 2022, 12:07pm UTC](https://discourse.julialang.org/t/higher-order-svd-in-julia-like-numpy/85025/3 "2022-07-30T12:07:41Z")

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I need a generalization of SVD to higher order tensors. I apologize if I’m missing something, I am just starting to learn about higher order SVD and tensor networks, so I was unsure what `numpy.linalg.svd` was doing. I found [ITensors.jl](https://github.com/ITensor/ITensors.jl/) which seems to be doing what I require. It seems I got confused and just now realised `numpy.linalg.svd` was doing the iterative approach rather than a generalized SVD of higher-order tensors.