Re: [boost] [uBlas] [Tensor] multiprecision and FFT?

Am Do., 7. Jan. 2021 um 14:24 Uhr schrieb Janek Kozicki via Boost < boost@lists.boost.org>:

Cem Bassoy via Boost said: (by the date of Thu, 7 Jan 2021 12:43:47 +0100)

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Have a look @ https://godbolt.org/z/cMKc9T

wow, This is very good. Thank you.

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You can get the pointer (like for vector) to the underlying contiguous memory (you do not own the memory):

This is exactly what I need. FFT does in-place transform by modifying the memory.

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using format_t = boost::numeric::ublas::column_major;

FFT does its work on row_major format. You have this one so I assume that you also have the other one ;)

However I needed to write a custom memory allocator (also very crude):

https://gitlab.com/cosurgi/trunk/-/blob/addQuantumMechanics_FixEnum_FixRebas...

https://gitlab.com/cosurgi/trunk/-/blob/addQuantumMechanics_FixEnum_FixRebas...

Can I provide a custom allocator to tensor_t ?

Yes, you can. We work with *std::vector* as the underlying base type. template > class tensor Just specialize your tensor type with your own allocator. You can also provide your own base type instead of *std::vector* but it must model the sequential container concept. using other_tensor_t = tensor>; In fact maybe during past 5 years some better C++ interface for

libfftw appeared. I will have to check :) maybe even boost library has an FFT interface? :)

If not then I will need to refactor this crude FFTW3_Allocator memory allocator.

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using tensor_t = boost::numeric::ublas::tensor; auto A = tensor_t(shape{3,4,2},2);auto ap = A.data(); You can also use the standard c++ library for convenience: std::for_each(A.begin(), A.end(), [](auto& a){ ++a; }); If you do not want to use the Einstein-notation, you can as well use either

I'm definitely going to use the Einstein notation :)

Glad it helps. Please note that contractions are not optimized. For small dimensions, the runtime should be tolerable. For larger dimensions and rank, please let me know - we are working on fast tensor contractions (e.g. https://github.com/bassoy/ttv)

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the prod function: // C3(i,l1,l2) = A(i,j,k)*T1(l1,j)*T2(l2,k); q = 3u; tensor_t C3 = prod(prod(A,matrix_t(m+1,n[q-2],1),q-1),matrix_t(m+2,n[q-1],1),q);

"prod" uses internally a C-like interface which will not allocate memory at all.

ttm(m, p, c.data(), c.extents().data(), c.strides().data(), a.data(), a.extents().data(), a.strides().data(), bb, nb.data(), wb.data());

I have another question about indexing the tensor.

Can I have a custom index redirection? I mean, when I type code to access zero-th element of 1D array:

tensor[0] = ... ;

Yes, random access with read and write. You can access tensor data with a single index like *t[0] *or* t[(n*m*...*k)/2]*. You can also use multi-indices for convenience, e.g. *t.at http://t.at(5,2,4,6)*

I mean to access the element which is located exactly in the middle of the reserved memory region. This is because libfftw implementation is not compatible with other parts of the quantum dynamic time propagation algorithm. This incompatibility is possible because FT is intrinsically periodic. Currently I have to use this function shiftByHalf():

https://gitlab.com/cosurgi/trunk/-/blob/addQuantumMechanics_FixEnum_FixRebas...

Which shifts by half an N-dimensional table. So that libfftw sees the data which it will process correctly. And doing a single calculation step is rather slow because after doing FFT it has to be shifted back:

https://gitlab.com/cosurgi/trunk/-/blob/addQuantumMechanics_FixEnum_FixRebas...

this makes calcuations very slow. If I could use some kind of index redirection, that will make all iterators treat the data as being shifted by half:

I am not really sure if I understand what you mean by *index redirection*. You can always advance pointers and iterators of tensor.

* zero-th element: in the middle of reserved memory.

* half: at the end of reserved memory

* half+1: at the beginning of reserved memory

If I understand you correctly, you would like to create two valid ranges. Let t be a p-order tensor *t* and n, m, k be its dimensions, where p = n*m*...*k with n,m,...,k > 1 Then *[first0,last0)* with *auto first0 = std::advance(std::begin(t), p/2); *// auto first0 = t.begin()+p/2; *auto last0 = std::end(t);* should be your first valid range. Then *[first1,last1)* *auto first1 = std::begin(t);* *auto last1 = std::advance(std::begin(t), p/2-1);* should be your second valid rang.

then all other parts of my algorithm will not need to be modified, because they solely work with iterators.

If you need you can also work with iterators: *std::advance(std::begin(t),5)* as you are used with *std::vector* . Note (for simplified interface with the fft library you can the shifting and advancing using raw pointers of the tensor *std::advance(t.data(),5) *or simply *t.data()+5.*

(Also I need to check if it's now possible to tell FFT to treat data differently, it wasn't possible 5 years ago, then I wouldn't need all these complications with indexing)

Thank you, your code is very promising. Janek

Thanks. Hope I could help you.

-- # Janek Kozicki http://janek.kozicki.pl/

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