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Other Extensions

Apart from ITensor extension, FuzzifiED also provides other extensions, viz. HDF5 extension, KrylovKit extension, CUDA extension and SparseArrays extension.

HDF5 Extension

The HDF5 extension supports writing the types Confs, Basis, Terms, Operator, OpMat{ComplexF64} and OpMat{Float64} into HDF5 files and reading them from groups and subgroups in HDF5 format. This extension requires the packages HDF5. To use this extension, include at the heading 

using HDF5

A typical file operation process looks like

f = h5open(file_name, "cw")
# include the file name as a string 
# Modes : "cw" for write and "r" for read
...
close(f)

To write, include in the middle 

write(f, group_name :: String, cfs :: Confs)
write(f, group_name :: String, bs  :: Basis)
write(f, group_name :: String, tms :: Terms)
write(f, group_name :: String, op  :: Operator)
write(f, group_name :: String, mat :: OpMat{ComplexF64})
write(f, group_name :: String, mat :: OpMat{Float64})

To read, include in the middle 

cfs = read(f, group_name :: String, Confs)
bs  = read(f, group_name :: String, Basis)
tms = read(f, group_name :: String, Terms)
op  = read(f, group_name :: String, Operator)
mat = read(f, group_name :: String, OpMat{ComplexF64})
mat = read(f, group_name :: String, OpMat{Float64})

SparseArrays Extension

The SparseArrays extension supports the conversion between OpMat in FuzzifiED and the SparseMatrixCSC format. This extension requires the packages SparseArrays. To use this extension, include at the heading 

using SparseArrays
SparseArrays.SparseMatrixCSC — Method
SparseMatrixCSC(mat :: OpMat{ComplexF64}) :: SparseMatrixCSC{Int64,ComplexF64}
SparseMatrixCSC(mat :: OpMat{Float64}) :: SparseMatrixCSC{Int64,Float64}

converts the OpMat objects to a SparseMatrixCSC object in the SparseArrays package.

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FuzzifiED.OpMat — Method
OpMat(matcsc :: SparseMatrixCSC{Int64,ComplexF64}) :: OpMat{ComplexF64}
OpMat(matcsc :: SparseMatrixCSC{Int64,Float64}) :: OpMat{Float64}

converts the SparseMatrixCSC object in the SparseArrays package to an OpMat objects.

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KrylovKit Extension

The KrylovKit extension supports an interface diagonalising the sparse matrix using the KrylovKit pakage in Julia. This extension requires the packages KrylovKit. To use this extension, include at the heading 

using KrylovKit

Besides Arpack in Fortran, we also provide an interface calling KrylovKit in Julia.

FuzzifiED.GetEigensystemKrylov — Method
GetEigensystemKrylov(mat :: OpMat{ComplexF64}, nst :: Int64 ; initvec :: Vector{ComplexF64}, num_th :: Int64, disp_std :: Bool, kwargs...) :: Tuple{Vector{ComplexF64}, Matrix{ComplexF64}}
GetEigensystemKrylov(mat :: OpMat{Float64}, nst :: Int64 ; initvec :: Vector{Float64}, num_th :: Int64, disp_std :: Bool, kwargs...) :: Tuple{Vector{Float64}, Matrix{Float64}}

This method calls the eigsolve from Julia KrylovKit.jl package instead of Arpack from Fortran to calculate the lowest eigenstates of sparse matrix. The performance should be similar. For an example, refer to ising_spectrum_krylov.jl.

Arguments

  • mat :: OpMat{ComplexF64} or mat :: OpMat{Float64} is the matrix.
  • nst :: Int64 is the number of eigenstates to be calculated.
  • tol :: Float64 is the tolerence for the KrylovKit process. The default value is 1E-8.
  • ncv :: Int64 is the maximum dimension of the Krylov subspace. The default value is max(2 * nst, nst + 10). If krylovdim is also given, ncv will not be used.
  • initvec :: Vector{ComplexF64} or initvec :: Vector{Float64} is the initial vector. Facultative, a random initialisation by default.
  • num_th :: Int64, the number of threads. Facultative, NumThreads by default.
  • disp_std :: Bool, whether or not the log shall be displayed. Facultative, !SilentStd by default.
  • kwargs... is the options that will directly sent into eigsolve, see its documentation for detail.

Output

  • A length-nst array that has the same type as mat recording the eigenvalues, and
  • A dimd×nst matrix that has the same type as mat where every column records an eigenstate.
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Modified Version of KrylovKit

We have forked KrylovKit and made some modifications to better suit our need. To install the modified packages, please use 

using Pkg 
Pkg.add(url="https://github.com/FuzzifiED/KrylovKit.jl.git")

We add an algorithm LockedLanczos. It is a hard-locking (deflated) variant of the Lanczos algorithm that is useful when large number of eigenvectors (e. g. in the order of 1000) are required, for use in eigsolve with a real symmetric or complex Hermitian linear operator. Whenever a Ritz pair has converged to within a tolerence, it is locked, i. e. removed from the active Krylov subspace, but retained in the set against which every subsequent Krylov vector is orthogonalized.

CUDA Extension

The CUDA extension supports the conversion between OpMat in FuzzifiED and the CuSparseMatrixCSC in CUDA.CUSPARSE as well as the acceleration of diagonalisation on GPU. This extension requires the packages CUDA, KrylovKit and SparseArrays. To use this extension, include at the heading 

using CUDA, KrylovKit, SparseArrays
CUDA.CUSPARSE.CuSparseMatrixCSC — Method
CUSPARSE.CuSparseMatrixCSC(mat :: OpMat{ComplexF64})
CUSPARSE.CuSparseMatrixCSC(mat :: OpMat{Float64})

converts the OpMat objects to a CuSparseMatrixCSC object in the CUDA.CUSPARSE package.

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FuzzifiED.GetEigensystemCuda — Method
GetEigensystemCuda(mat :: OpMat{ComplexF64}, nst :: Int64 ; initvec :: Vector{ComplexF64}, num_th :: Int64, disp_std :: Bool, kwargs...) :: Tuple{Vector{ComplexF64}, CuArray{ComplexF64, 2, CUDA.DeviceMemory}}
GetEigensystemCuda(mat :: OpMat{Float64}, nst :: Int64 ; initvec :: Vector{Float64}, num_th :: Int64, disp_std :: Bool, kwargs...) :: Tuple{Vector{Float64}, CuArray{Float64, 2, CUDA.DeviceMemory}}

This method uses Julia KrylovKit package to calculate the lowest eigenstates of sparse matrix. The sparse matrix multiplication is realised by CUDA.CUSPARSE. For an example, refer to ising_spectrum_cuda.jl.

Arguments

  • mat :: OpMat{ComplexF64} or mat :: OpMat{Float64} is the matrix.
  • nst :: Int64 is the number of eigenstates to be calculated.
  • tol :: Float64 is the tolerence for the KrylovKit process. The default value is 1E-8.
  • ncv :: Int64 is the maximum dimension of the Krylov subspace. The default value is max(2 * nst, nst + 10). If krylovdim is also given, ncv will not be used.
  • initvec is the initial vector. Facultative, a random initialisation CUDA.rand(T, mat.dimd) by default.
  • disp_std :: Bool, whether or not the log shall be displayed. Facultative, !SilentStd by default.
  • kwargs... is the options that will directly sent into eigsolve, see its documentation for detail.

Output

  • A length-nst array that has the same type as mat recording the eigenvalues, and
  • A dimd×nst matrix that has the same type as mat where every column records an eigenstate.
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