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Updated juobs_linalg documentation with examples

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docs/build/assets/themeswap.js
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// Small function to quickly swap out themes. Gets put into the <head> tag..
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docs/build/index.html
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src/juobs_linalg.jl
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......@@ -13,45 +13,46 @@ end
=#
@doc raw"""
get_matrix(corr_diag::Vector{Array}, corr_upper::Vector{Array} )
get_matrix(diag::Vector{Array}, upper::Vector{Array} )
This method returns an array of dim `T` where each element is a symmetrix matrix of dimension n of `uwreal` correlators
at fixed time i=1..T. It takes as input:
`corr_diag`: vector of dimension n of correlators liying on the diagonal
This function allows the user to build an array of matrices, where each matrix is a symmetric matrix of correlators at a given timeslice.
It takes as input:
`corr_upper`: vector of correlators liying on the upper diagonal.
- `diag::Vector{Array}`: vector of correlators. Each correlator will constitute a diagonal element of the matrices A[i] where i runs over the timeslices, i.e.
`A[i][1,1] = diag[1], .... A[i][n,n] = diag[n]`
`Given n=length(diag)`, the matrices will have dimension n*n
- `upper::Vector{Array}`: vector of correlators liying on the upper diagonal position.
`A[i][1,2] = upper[1], .. , A[i][1,n] = upper[n-1], `
`A[i][2,3] = upper[n], .. , A[i][n-1,n] = upper[n(n-1)/2]`
Given n, `length(upper)=n(n-1)/2`
The method returns an array of symmetric matrices of dimension n for each timeslice
Each correlator is an vector of uwreal variables of dimension `T`.
Example:
```@example
for i in 1:n
a[i,i] = Vector{uwreal} # vector of uwreal variables of dimension T. They will constitute the diagonal elements of the matrices
for i in 1:n-1
for j in i+1:n
a[i,j] = Vector{uwreal} # vector of uwreal variables of dimension T. They will constitute the upper diagonal elements of the matrices. A matrix
of dimension n*n has n(n-1)/2 upper diagonal elements.
Assume n=4
diagonal = Vector{Array}()
push!(diagonal, a[1,1],a[2,2],a[3,3],a[4,4])
upsize = Vector{Array}()
push!(upsize, a[1,2], a[1,3], a[1,4], a[2,3], a[2,4], a[3,4])
array_of_matrices = get_matrix(diagonal, upsize)
Examples:
```@example
## load data
pp_data = read_mesons(path, "G5", "G5")
pa_data = read_mesons(path, "G5", "G0G5")
aa_data = read_mesons(path, "G0G5", "G0G5")
Julia> T-element Array{Array,1}
## create Corr struct
corr_pp = corr_obs.(pp_data)
corr_pa = corr_obs.(pa_data)
corr_aa = corr_obs.(aa_data) # array of correlators for different \mu_q combinations
size(array_of_matrices)
## set up matrices
corr_diag = [corr_pp[1], corr_aa[1]]
corr_upper = [corr_pa[1]]
Julia> (T,)
matrices = [corr_diag, corr_upper]
array_of_matrices[t] # t in 1:T
Julia> matrices[i]
pp[i] ap[i]
pa[i] aa[i]
Julia> 4*4 Array{uwreal,2}
## where i runs over the timeslices
```
"""
function get_matrix(corr_diag::Vector{Vector{uwreal}}, corr_upper::Vector{Vector{uwreal}})
......@@ -79,12 +80,41 @@ function get_matrix(corr_diag::Vector{Vector{uwreal}}, corr_upper::Vector{Vector
return res
end
get_matrix(corr_diag::Vector{Corr}, corr_upper::Vector{Corr}) = get_matrix(getfield.(corr_diag, :obs), getfield.(corr_upper, :obs))
@doc raw"""
energies(evals::Vector{Array})
energies(evals::Vector{Array}; wpm::Union{Dict{Int64,Vector{Float64}},Dict{String,Vector{Float64}}, Nothing}=nothing)
This method computes the energy level from the eigenvalues according to:
``E_i(t) = \log(λ(t) / λ(t+1))``
Given a vector where each entry `evals[t]` is a `uwreal` array of eigenvalues, this method computes the effective energies of the first N states, where ```N=dim(evals[t])```.
The index `t` here runs from 1:T=lenght(evals), while the index `i` stands for the number of energy levels computed: i = length(evals[t])
It returns a vector array `eff_en` where each entry `eff_en[t]` contains the first N states energies as uwreal objects
where `i=1,..,n` with `n=length(evals[1])` and `t=1,..,T` total time slices.
It returns a vector array en where each entry en[i][t] contains the i-th states energy at time t
Examples:
```@example
## load data
pp_data = read_mesons(path, "G5", "G5")
pa_data = read_mesons(path, "G5", "G0G5")
aa_data = read_mesons(path, "G0G5", "G0G5")
## create Corr struct
corr_pp = corr_obs.(pp_data)
corr_pa = corr_obs.(pa_data)
corr_aa = corr_obs.(aa_data) # array of correlators for different \mu_q combinations
## set up matrices
corr_diag = [corr_pp[1], corr_aa[1]]
corr_upper = [corr_pa[1]]
matrices = [corr_diag, corr_upper]
## solve the GEVP
evals = getall_eigvals(matrices, 5) #where t_0=5
en = energies(evals)
Julia> en[i] # i-th state energy at each timeslice
```
"""
function energies(evals::Union{Vector{Vector{uwreal}},Array{Array{uwreal}} }; wpm::Union{Dict{Int64,Vector{Float64}},Dict{String,Vector{Float64}}, Nothing}=nothing)
time = length(evals)
......@@ -108,7 +138,7 @@ end
This function solves a GEVP problem, returning the eigenvalues, for a list of matrices, taking as generalised matrix the one
at index t0, i.e:
``C(t_i)v_i = λ_i C(t_0) v_i``, with i=1:lenght(a)
``C(t_i)v_i = λ_i C(t_0) v_i``, with i=1:lenght(a)
It takes as input:
......@@ -125,9 +155,28 @@ It returns:
where `res[i]` are the generalised eigenvalues of the i-th matrix of the input array.
Examples:
```@example
mat_array = get_matrix(diag, upper_diag)
evals = getall_eigvals(mat_array, 5)
```@example
## load data
pp_data = read_mesons(path, "G5", "G5")
pa_data = read_mesons(path, "G5", "G0G5")
aa_data = read_mesons(path, "G0G5", "G0G5")
## create Corr struct
corr_pp = corr_obs.(pp_data)
corr_pa = corr_obs.(pa_data)
corr_aa = corr_obs.(aa_data) # array of correlators for different \mu_q combinations
## set up matrices
corr_diag = [corr_pp[1], corr_aa[1]]
corr_upper = [corr_pa[1]]
matrices = [corr_diag, corr_upper]
## solve the GEVP
evals = getall_eigvals(matrices, 5) #where t_0=5
Julia>
```
"""
function getall_eigvals(a::Vector{Matrix}, t0::Int64; iter=30 )
......@@ -150,9 +199,19 @@ It takes as input:
- `b::Matrix{uwreal}` : a matrix of uwreal, optional
- `iter=30`: optional flag to set the iterations of the qr algorithm used to solve the eigenvalue problem
It returns:
- `res = Vector{uwreal}`: a vector where each elements is an eigenvalue
```@example
a = Matrix{uwreal}(nothing, n,n) ## n*n matrix of uwreal with nothing entries
b = Matrix{uwreal}(nothing, n,n) ## n*n matrix of uwreal with nothing entries
res = uweigvals(a) ##eigenvalues
res1 = uweigvals(a,b) ## generalised eigenvalues
```
"""
function uweigvals(a::Matrix{uwreal}; iter = 30)
n = size(a,1)
......@@ -176,7 +235,7 @@ end
This function solves a GEVP problem, returning the eigenvectors, for a list of matrices.
``C(t_i)v_i = λ_i C(t_i-\delta_t) v_i``, with i=1:lenght(a)
``C(t_i)v_i = λ_i C(t_i-\delta_t) v_i ``, with i=1:lenght(a)
Here `delta_t` is the time shift within the two matrices of the problem, and is kept fixed.
It takes as input:
......@@ -189,7 +248,7 @@ It takes as input:
It returns:
- `res` = Vector{Matrix{uwreal}}
- `res = Vector{Matrix{uwreal}}`
where each `res[i]` is a matrix with the eigenvectors as columns
Examples:
......@@ -203,7 +262,6 @@ function getall_eigvecs(a::Vector{Matrix}, delta_t; iter=30)
res = Vector{Matrix{uwreal}}(undef, n)
[res[i] = uweigvecs(a[i+delta_t], a[i]) for i=1:n]
return res
end
@doc raw"""
......@@ -219,9 +277,19 @@ It takes as input:
- `b::Matrix{uwreal}` : a matrix of uwreal, optional
- `iter=30` : the number of iterations of the qr algorithm used to extract the eigenvalues
It returns:
- `res = Matrix{uwreal}`: a matrix where each column is an eigenvector
Examples:
```@example
a = Matrix{uwreal}(nothing, n,n) ## n*n matrix of uwreal with nothing entries
b = Matrix{uwreal}(nothing, n,n) ## n*n matrix of uwreal with nothing entries
res = uweigvecs(a) ##eigenvectors in column
res1 = uweigvecs(a,b) ## generalised eigenvectors in column
```
"""
function uweigvecs(a::Matrix{uwreal}; iter = 30)
n = size(a,1)
......@@ -258,9 +326,22 @@ It takes as input:
- `b::Matrix{uwreal}` : a matrix of uwreal, optional
- `iter=30` : the number of iterations of the qr algorithm used to extract the eigenvalues
It returns:
- `evals = Vector{uwreal}`: a vector where each elements is an eigenvalue
- `evecs = Matrix{uwreal}`: a matrix where the i-th column is the eigenvector of the i-th eigenvalue
Examples:
```@example
a = Matrix{uwreal}(nothing, n,n) ## n*n matrix of uwreal with nothing entries
b = Matrix{uwreal}(nothing, n,n) ## n*n matrix of uwreal with nothing entries
eval, evec = uweigen(a)
eval1, evec1 = uweigvecs(a,b)
```
"""
function uweigen(a::Matrix{uwreal}; iter = 30)
return uweigvals(a, iter=iter), uweigvecs(a, iter=iter)
......
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