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sparsevector.jl
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sparsevector.jl
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# This file is a part of Julia. License is MIT: https://julialang.org/license
### Common definitions
using Base.LinAlg: Adjoint, Transpose
import Base: scalarmax, scalarmin, sort, find, findnz
import Base.LinAlg: promote_to_array_type, promote_to_arrays_
### The SparseVector
### Types
"""
SparseVector{Tv,Ti<:Integer} <: AbstractSparseVector{Tv,Ti}
Vector type for storing sparse vectors.
"""
struct SparseVector{Tv,Ti<:Integer} <: AbstractSparseVector{Tv,Ti}
n::Int # Length of the sparse vector
nzind::Vector{Ti} # Indices of stored values
nzval::Vector{Tv} # Stored values, typically nonzeros
function SparseVector{Tv,Ti}(n::Integer, nzind::Vector{Ti}, nzval::Vector{Tv}) where {Tv,Ti<:Integer}
n >= 0 || throw(ArgumentError("The number of elements must be non-negative."))
length(nzind) == length(nzval) ||
throw(ArgumentError("index and value vectors must be the same length"))
new(convert(Int, n), nzind, nzval)
end
end
SparseVector(n::Integer, nzind::Vector{Ti}, nzval::Vector{Tv}) where {Tv,Ti} =
SparseVector{Tv,Ti}(n, nzind, nzval)
# Define an alias for a view of a whole column of a SparseMatrixCSC. Many methods can be written for the
# union of such a view and a SparseVector so we define an alias for such a union as well
const SparseColumnView{T} = SubArray{T,1,<:SparseMatrixCSC,Tuple{Base.Slice{Base.OneTo{Int}},Int},false}
const SparseVectorUnion{T} = Union{SparseVector{T}, SparseColumnView{T}}
### Basic properties
length(x::SparseVector) = x.n
size(x::SparseVector) = (x.n,)
nnz(x::SparseVector) = length(x.nzval)
count(f, x::SparseVector) = count(f, x.nzval) + f(zero(eltype(x)))*(length(x) - nnz(x))
nonzeros(x::SparseVector) = x.nzval
function nonzeros(x::SparseColumnView)
rowidx, colidx = parentindices(x)
A = parent(x)
@inbounds y = view(A.nzval, nzrange(A, colidx))
return y
end
nonzeroinds(x::SparseVector) = x.nzind
function nonzeroinds(x::SparseColumnView)
rowidx, colidx = parentindices(x)
A = parent(x)
@inbounds y = view(A.rowval, nzrange(A, colidx))
return y
end
## similar
#
# parent method for similar that preserves stored-entry structure (for when new and old dims match)
_sparsesimilar(S::SparseVector, ::Type{TvNew}, ::Type{TiNew}) where {TvNew,TiNew} =
SparseVector(S.n, copyto!(similar(S.nzind, TiNew), S.nzind), similar(S.nzval, TvNew))
# parent method for similar that preserves nothing (for when old and new dims differ, and new is 1d)
_sparsesimilar(S::SparseVector, ::Type{TvNew}, ::Type{TiNew}, dims::Dims{1}) where {TvNew,TiNew} =
SparseVector(dims..., similar(S.nzind, TiNew, 0), similar(S.nzval, TvNew, 0))
# parent method for similar that preserves storage space (for old and new dims differ, and new is 2d)
_sparsesimilar(S::SparseVector, ::Type{TvNew}, ::Type{TiNew}, dims::Dims{2}) where {TvNew,TiNew} =
SparseMatrixCSC(dims..., ones(TiNew, last(dims)+1), similar(S.nzind, TiNew), similar(S.nzval, TvNew))
# The following methods hook into the AbstractArray similar hierarchy. The first method
# covers similar(A[, Tv]) calls, which preserve stored-entry structure, and the latter
# methods cover similar(A[, Tv], shape...) calls, which preserve nothing if the dims
# specify a SparseVector result and storage space if the dims specify a SparseMatrixCSC result.
similar(S::SparseVector{<:Any,Ti}, ::Type{TvNew}) where {Ti,TvNew} =
_sparsesimilar(S, TvNew, Ti)
similar(S::SparseVector{<:Any,Ti}, ::Type{TvNew}, dims::Union{Dims{1},Dims{2}}) where {Ti,TvNew} =
_sparsesimilar(S, TvNew, Ti, dims)
# The following methods cover similar(A, Tv, Ti[, shape...]) calls, which specify the
# result's index type in addition to its entry type, and aren't covered by the hooks above.
# The calls without shape again preserve stored-entry structure, whereas those with
# one-dimensional shape preserve nothing, and those with two-dimensional shape
# preserve storage space.
similar(S::SparseVector, ::Type{TvNew}, ::Type{TiNew}) where{TvNew,TiNew} =
_sparsesimilar(S, TvNew, TiNew)
similar(S::SparseVector, ::Type{TvNew}, ::Type{TiNew}, dims::Union{Dims{1},Dims{2}}) where {TvNew,TiNew} =
_sparsesimilar(S, TvNew, TiNew, dims)
similar(S::SparseVector, ::Type{TvNew}, ::Type{TiNew}, m::Integer) where {TvNew,TiNew} =
_sparsesimilar(S, TvNew, TiNew, (m,))
similar(S::SparseVector, ::Type{TvNew}, ::Type{TiNew}, m::Integer, n::Integer) where {TvNew,TiNew} =
_sparsesimilar(S, TvNew, TiNew, (m, n))
### Construct empty sparse vector
spzeros(len::Integer) = spzeros(Float64, len)
spzeros(::Type{T}, len::Integer) where {T} = SparseVector(len, Int[], T[])
spzeros(::Type{Tv}, ::Type{Ti}, len::Integer) where {Tv,Ti<:Integer} = SparseVector(len, Ti[], Tv[])
LinAlg.fillstored!(x::SparseVector, y) = (fill!(x.nzval, y); x)
### Construction from lists of indices and values
function _sparsevector!(I::Vector{<:Integer}, V::Vector, len::Integer)
# pre-condition: no duplicate indices in I
if !isempty(I)
p = sortperm(I)
permute!(I, p)
permute!(V, p)
end
SparseVector(len, I, V)
end
function _sparsevector!(I::Vector{<:Integer}, V::Vector, len::Integer, combine::Function)
if !isempty(I)
p = sortperm(I)
permute!(I, p)
permute!(V, p)
m = length(I)
r = 1
l = 1 # length of processed part
i = I[r] # row-index of current element
# main loop
while r < m
r += 1
i2 = I[r]
if i2 == i # accumulate r-th to the l-th entry
V[l] = combine(V[l], V[r])
else # advance l, and move r-th to l-th
pv = V[l]
l += 1
i = i2
if l < r
I[l] = i; V[l] = V[r]
end
end
end
if l < m
resize!(I, l)
resize!(V, l)
end
end
SparseVector(len, I, V)
end
"""
sparsevec(I, V, [m, combine])
Create a sparse vector `S` of length `m` such that `S[I[k]] = V[k]`.
Duplicates are combined using the `combine` function, which defaults to
`+` if no `combine` argument is provided, unless the elements of `V` are Booleans
in which case `combine` defaults to `|`.
# Examples
```jldoctest
julia> II = [1, 3, 3, 5]; V = [0.1, 0.2, 0.3, 0.2];
julia> sparsevec(II, V)
5-element SparseVector{Float64,Int64} with 3 stored entries:
[1] = 0.1
[3] = 0.5
[5] = 0.2
julia> sparsevec(II, V, 8, -)
8-element SparseVector{Float64,Int64} with 3 stored entries:
[1] = 0.1
[3] = -0.1
[5] = 0.2
julia> sparsevec([1, 3, 1, 2, 2], [true, true, false, false, false])
3-element SparseVector{Bool,Int64} with 3 stored entries:
[1] = true
[2] = false
[3] = true
```
"""
function sparsevec(I::AbstractVector{<:Integer}, V::AbstractVector, combine::Function)
length(I) == length(V) ||
throw(ArgumentError("index and value vectors must be the same length"))
len = 0
for i in I
i >= 1 || error("Index must be positive.")
if i > len
len = i
end
end
_sparsevector!(collect(I), collect(V), len, combine)
end
function sparsevec(I::AbstractVector{<:Integer}, V::AbstractVector, len::Integer, combine::Function)
length(I) == length(V) ||
throw(ArgumentError("index and value vectors must be the same length"))
for i in I
1 <= i <= len || throw(ArgumentError("An index is out of bound."))
end
_sparsevector!(collect(I), collect(V), len, combine)
end
sparsevec(I::AbstractVector, V::Union{Number, AbstractVector}, args...) =
sparsevec(Vector{Int}(I), V, args...)
sparsevec(I::AbstractVector, V::Union{Number, AbstractVector}) =
sparsevec(I, V, +)
sparsevec(I::AbstractVector, V::Union{Number, AbstractVector}, len::Integer) =
sparsevec(I, V, len, +)
sparsevec(I::AbstractVector, V::Union{Bool, AbstractVector{Bool}}) =
sparsevec(I, V, |)
sparsevec(I::AbstractVector, V::Union{Bool, AbstractVector{Bool}}, len::Integer) =
sparsevec(I, V, len, |)
sparsevec(I::AbstractVector, v::Number, combine::Function) =
sparsevec(I, fill(v, length(I)), combine)
sparsevec(I::AbstractVector, v::Number, len::Integer, combine::Function) =
sparsevec(I, fill(v, length(I)), len, combine)
### Construction from dictionary
"""
sparsevec(d::Dict, [m])
Create a sparse vector of length `m` where the nonzero indices are keys from
the dictionary, and the nonzero values are the values from the dictionary.
# Examples
```jldoctest
julia> sparsevec(Dict(1 => 3, 2 => 2))
2-element SparseVector{Int64,Int64} with 2 stored entries:
[1] = 3
[2] = 2
```
"""
function sparsevec(dict::AbstractDict{Ti,Tv}) where {Tv,Ti<:Integer}
m = length(dict)
nzind = Vector{Ti}(uninitialized, m)
nzval = Vector{Tv}(uninitialized, m)
cnt = 0
len = zero(Ti)
for (k, v) in dict
k >= 1 || throw(ArgumentError("index must be positive."))
if k > len
len = k
end
cnt += 1
@inbounds nzind[cnt] = k
@inbounds nzval[cnt] = v
end
resize!(nzind, cnt)
resize!(nzval, cnt)
_sparsevector!(nzind, nzval, len)
end
function sparsevec(dict::AbstractDict{Ti,Tv}, len::Integer) where {Tv,Ti<:Integer}
m = length(dict)
nzind = Vector{Ti}(uninitialized, m)
nzval = Vector{Tv}(uninitialized, m)
cnt = 0
maxk = convert(Ti, len)
for (k, v) in dict
1 <= k <= maxk || throw(ArgumentError("an index (key) is out of bound."))
cnt += 1
@inbounds nzind[cnt] = k
@inbounds nzval[cnt] = v
end
resize!(nzind, cnt)
resize!(nzval, cnt)
_sparsevector!(nzind, nzval, len)
end
### Element access
function setindex!(x::SparseVector{Tv,Ti}, v::Tv, i::Ti) where {Tv,Ti<:Integer}
checkbounds(x, i)
nzind = nonzeroinds(x)
nzval = nonzeros(x)
m = length(nzind)
k = searchsortedfirst(nzind, i)
if 1 <= k <= m && nzind[k] == i # i found
nzval[k] = v
else # i not found
if v != 0
insert!(nzind, k, i)
insert!(nzval, k, v)
end
end
x
end
setindex!(x::SparseVector{Tv,Ti}, v, i::Integer) where {Tv,Ti<:Integer} =
setindex!(x, convert(Tv, v), convert(Ti, i))
### dropstored!
"""
dropstored!(x::SparseVector, i::Integer)
Drop entry `x[i]` from `x` if `x[i]` is stored and otherwise do nothing.
# Examples
```jldoctest
julia> x = sparsevec([1, 3], [1.0, 2.0])
3-element SparseVector{Float64,Int64} with 2 stored entries:
[1] = 1.0
[3] = 2.0
julia> Base.SparseArrays.dropstored!(x, 3)
3-element SparseVector{Float64,Int64} with 1 stored entry:
[1] = 1.0
julia> Base.SparseArrays.dropstored!(x, 2)
3-element SparseVector{Float64,Int64} with 1 stored entry:
[1] = 1.0
```
"""
function dropstored!(x::SparseVector, i::Integer)
if !(1 <= i <= x.n)
throw(BoundsError(x, i))
end
searchk = searchsortedfirst(x.nzind, i)
if searchk <= length(x.nzind) && x.nzind[searchk] == i
# Entry x[i] is stored. Drop and return.
deleteat!(x.nzind, searchk)
deleteat!(x.nzval, searchk)
end
return x
end
# TODO: Implement linear collection indexing methods for dropstored! ?
# TODO: Implement logical indexing methods for dropstored! ?
### Conversion
# convert SparseMatrixCSC to SparseVector
function SparseVector{Tv,Ti}(s::SparseMatrixCSC{Tv,Ti}) where {Tv,Ti<:Integer}
size(s, 2) == 1 || throw(ArgumentError("The input argument must have a single-column."))
SparseVector(s.m, s.rowval, s.nzval)
end
SparseVector{Tv}(s::SparseMatrixCSC{Tv,Ti}) where {Tv,Ti} = SparseVector{Tv,Ti}(s)
SparseVector(s::SparseMatrixCSC{Tv,Ti}) where {Tv,Ti} = SparseVector{Tv,Ti}(s)
# convert Vector to SparseVector
"""
sparsevec(A)
Convert a vector `A` into a sparse vector of length `m`.
# Examples
```jldoctest
julia> sparsevec([1.0, 2.0, 0.0, 0.0, 3.0, 0.0])
6-element SparseVector{Float64,Int64} with 3 stored entries:
[1] = 1.0
[2] = 2.0
[5] = 3.0
```
"""
sparsevec(a::AbstractVector{T}) where {T} = SparseVector{T, Int}(a)
sparsevec(a::AbstractArray) = sparsevec(vec(a))
sparsevec(a::AbstractSparseArray) = vec(a)
sparsevec(a::AbstractSparseVector) = vec(a)
sparse(a::AbstractVector) = sparsevec(a)
function _dense2sparsevec(s::AbstractArray{Tv}, initcap::Ti) where {Tv,Ti}
# pre-condition: initcap > 0; the initcap determines the index type
n = length(s)
cap = initcap
nzind = Vector{Ti}(uninitialized, cap)
nzval = Vector{Tv}(uninitialized, cap)
c = 0
@inbounds for i = 1:n
v = s[i]
if v != 0
if c >= cap
cap *= 2
resize!(nzind, cap)
resize!(nzval, cap)
end
c += 1
nzind[c] = i
nzval[c] = v
end
end
if c < cap
resize!(nzind, c)
resize!(nzval, c)
end
SparseVector(n, nzind, nzval)
end
SparseVector{Tv,Ti}(s::AbstractVector{Tv}) where {Tv,Ti} =
_dense2sparsevec(s, convert(Ti, max(8, div(length(s), 8))))
SparseVector{Tv}(s::AbstractVector{Tv}) where {Tv} = SparseVector{Tv,Int}(s)
SparseVector(s::AbstractVector{Tv}) where {Tv} = SparseVector{Tv,Int}(s)
# convert between different types of SparseVector
SparseVector{Tv}(s::SparseVector{Tv}) where {Tv} = s
SparseVector{Tv,Ti}(s::SparseVector{Tv,Ti}) where {Tv,Ti} = s
SparseVector{Tv,Ti}(s::SparseVector) where {Tv,Ti} =
SparseVector{Tv,Ti}(s.n, convert(Vector{Ti}, s.nzind), convert(Vector{Tv}, s.nzval))
SparseVector{Tv}(s::SparseVector{<:Any,Ti}) where {Tv,Ti} =
SparseVector{Tv,Ti}(s.n, s.nzind, convert(Vector{Tv}, s.nzval))
### copying
function prep_sparsevec_copy_dest!(A::SparseVector, lB, nnzB)
lA = length(A)
lA >= lB || throw(BoundsError())
# If the two vectors have the same length then all the elements in A will be overwritten.
if length(A) == lB
resize!(A.nzval, nnzB)
resize!(A.nzind, nnzB)
else
nnzA = nnz(A)
lastmodindA = searchsortedlast(A.nzind, lB)
if lastmodindA >= nnzB
# A will have fewer non-zero elements; unmodified elements are kept at the end.
deleteat!(A.nzind, nnzB+1:lastmodindA)
deleteat!(A.nzval, nnzB+1:lastmodindA)
else
# A will have more non-zero elements; unmodified elements are kept at the end.
resize!(A.nzind, nnzB + nnzA - lastmodindA)
resize!(A.nzval, nnzB + nnzA - lastmodindA)
copyto!(A.nzind, nnzB+1, A.nzind, lastmodindA+1, nnzA-lastmodindA)
copyto!(A.nzval, nnzB+1, A.nzval, lastmodindA+1, nnzA-lastmodindA)
end
end
end
function copyto!(A::SparseVector, B::SparseVector)
prep_sparsevec_copy_dest!(A, length(B), nnz(B))
copyto!(A.nzind, B.nzind)
copyto!(A.nzval, B.nzval)
return A
end
function copyto!(A::SparseVector, B::SparseMatrixCSC)
prep_sparsevec_copy_dest!(A, length(B), nnz(B))
ptr = 1
@assert length(A.nzind) >= length(B.rowval)
maximum(B.colptr)-1 <= length(B.rowval) || throw(BoundsError())
@inbounds for col=1:length(B.colptr)-1
offsetA = (col - 1) * B.m
while ptr <= B.colptr[col+1]-1
A.nzind[ptr] = B.rowval[ptr] + offsetA
ptr += 1
end
end
copyto!(A.nzval, B.nzval)
return A
end
copyto!(A::SparseMatrixCSC, B::SparseVector{TvB,TiB}) where {TvB,TiB} =
copyto!(A, SparseMatrixCSC{TvB,TiB}(B.n, 1, TiB[1, length(B.nzind)+1], B.nzind, B.nzval))
### Rand Construction
sprand(n::Integer, p::AbstractFloat, rfn::Function, ::Type{T}) where {T} = sprand(GLOBAL_RNG, n, p, rfn, T)
function sprand(r::AbstractRNG, n::Integer, p::AbstractFloat, rfn::Function, ::Type{T}) where T
I = randsubseq(r, 1:convert(Int, n), p)
V = rfn(r, T, length(I))
SparseVector(n, I, V)
end
sprand(n::Integer, p::AbstractFloat, rfn::Function) = sprand(GLOBAL_RNG, n, p, rfn)
function sprand(r::AbstractRNG, n::Integer, p::AbstractFloat, rfn::Function)
I = randsubseq(r, 1:convert(Int, n), p)
V = rfn(r, length(I))
SparseVector(n, I, V)
end
sprand(n::Integer, p::AbstractFloat) = sprand(GLOBAL_RNG, n, p, rand)
sprand(r::AbstractRNG, n::Integer, p::AbstractFloat) = sprand(r, n, p, rand)
sprand(r::AbstractRNG, ::Type{T}, n::Integer, p::AbstractFloat) where {T} = sprand(r, n, p, (r, i) -> rand(r, T, i))
sprand(r::AbstractRNG, ::Type{Bool}, n::Integer, p::AbstractFloat) = sprand(r, n, p, truebools)
sprand(::Type{T}, n::Integer, p::AbstractFloat) where {T} = sprand(GLOBAL_RNG, T, n, p)
sprandn(n::Integer, p::AbstractFloat) = sprand(GLOBAL_RNG, n, p, randn)
sprandn(r::AbstractRNG, n::Integer, p::AbstractFloat) = sprand(r, n, p, randn)
## Indexing into Matrices can return SparseVectors
# Column slices
function getindex(x::SparseMatrixCSC, ::Colon, j::Integer)
checkbounds(x, :, j)
r1 = convert(Int, x.colptr[j])
r2 = convert(Int, x.colptr[j+1]) - 1
SparseVector(x.m, x.rowval[r1:r2], x.nzval[r1:r2])
end
function getindex(x::SparseMatrixCSC, I::AbstractUnitRange, j::Integer)
checkbounds(x, I, j)
# Get the selected column
c1 = convert(Int, x.colptr[j])
c2 = convert(Int, x.colptr[j+1]) - 1
# Restrict to the selected rows
r1 = searchsortedfirst(x.rowval, first(I), c1, c2, Forward)
r2 = searchsortedlast(x.rowval, last(I), c1, c2, Forward)
SparseVector(length(I), [x.rowval[i] - first(I) + 1 for i = r1:r2], x.nzval[r1:r2])
end
# In the general case, we piggy back upon SparseMatrixCSC's optimized solution
@inline function getindex(A::SparseMatrixCSC, I::AbstractVector, J::Integer)
M = A[I, [J]]
SparseVector(M.m, M.rowval, M.nzval)
end
# Row slices
getindex(A::SparseMatrixCSC, i::Integer, ::Colon) = A[i, 1:end]
function Base.getindex(A::SparseMatrixCSC{Tv,Ti}, i::Integer, J::AbstractVector) where {Tv,Ti}
checkbounds(A, i, J)
nJ = length(J)
colptrA = A.colptr; rowvalA = A.rowval; nzvalA = A.nzval
nzinds = Vector{Ti}()
nzvals = Vector{Tv}()
# adapted from SparseMatrixCSC's sorted_bsearch_A
ptrI = 1
@inbounds for j = 1:nJ
col = J[j]
rowI = i
ptrA = Int(colptrA[col])
stopA = Int(colptrA[col+1]-1)
if ptrA <= stopA
if rowvalA[ptrA] <= rowI
ptrA = searchsortedfirst(rowvalA, rowI, ptrA, stopA, Base.Order.Forward)
if ptrA <= stopA && rowvalA[ptrA] == rowI
push!(nzinds, j)
push!(nzvals, nzvalA[ptrA])
end
end
ptrI += 1
end
end
return SparseVector(nJ, nzinds, nzvals)
end
# Logical and linear indexing into SparseMatrices
getindex(A::SparseMatrixCSC, I::AbstractVector{Bool}) = _logical_index(A, I) # Ambiguities
getindex(A::SparseMatrixCSC, I::AbstractArray{Bool}) = _logical_index(A, I)
function _logical_index(A::SparseMatrixCSC{Tv}, I::AbstractArray{Bool}) where Tv
checkbounds(A, I)
n = sum(I)
nnzB = min(n, nnz(A))
colptrA = A.colptr; rowvalA = A.rowval; nzvalA = A.nzval
rowvalB = Vector{Int}(uninitialized, nnzB)
nzvalB = Vector{Tv}(uninitialized, nnzB)
c = 1
rowB = 1
@inbounds for col in 1:A.n
r1 = colptrA[col]
r2 = colptrA[col+1]-1
for row in 1:A.m
if I[row, col]
while (r1 <= r2) && (rowvalA[r1] < row)
r1 += 1
end
if (r1 <= r2) && (rowvalA[r1] == row)
nzvalB[c] = nzvalA[r1]
rowvalB[c] = rowB
c += 1
end
rowB += 1
(rowB > n) && break
end
end
(rowB > n) && break
end
if nnzB > (c-1)
deleteat!(nzvalB, c:nnzB)
deleteat!(rowvalB, c:nnzB)
end
SparseVector(n, rowvalB, nzvalB)
end
# TODO: further optimizations are available for ::Colon and other types of AbstractRange
getindex(A::SparseMatrixCSC, ::Colon) = A[1:end]
function getindex(A::SparseMatrixCSC{Tv}, I::AbstractUnitRange) where Tv
checkbounds(A, I)
szA = size(A)
nA = szA[1]*szA[2]
colptrA = A.colptr
rowvalA = A.rowval
nzvalA = A.nzval
n = length(I)
nnzB = min(n, nnz(A))
rowvalB = Vector{Int}(uninitialized, nnzB)
nzvalB = Vector{Tv}(uninitialized, nnzB)
rowstart,colstart = Base._ind2sub(szA, first(I))
rowend,colend = Base._ind2sub(szA, last(I))
idxB = 1
@inbounds for col in colstart:colend
minrow = (col == colstart ? rowstart : 1)
maxrow = (col == colend ? rowend : szA[1])
for r in colptrA[col]:(colptrA[col+1]-1)
rowA = rowvalA[r]
if minrow <= rowA <= maxrow
rowvalB[idxB] = Base._sub2ind(szA, rowA, col) - first(I) + 1
nzvalB[idxB] = nzvalA[r]
idxB += 1
end
end
end
if nnzB > (idxB-1)
deleteat!(nzvalB, idxB:nnzB)
deleteat!(rowvalB, idxB:nnzB)
end
SparseVector(n, rowvalB, nzvalB)
end
function getindex(A::SparseMatrixCSC{Tv,Ti}, I::AbstractVector) where {Tv,Ti}
szA = size(A)
nA = szA[1]*szA[2]
colptrA = A.colptr
rowvalA = A.rowval
nzvalA = A.nzval
n = length(I)
nnzB = min(n, nnz(A))
rowvalB = Vector{Ti}(uninitialized, nnzB)
nzvalB = Vector{Tv}(uninitialized, nnzB)
idxB = 1
for i in 1:n
((I[i] < 1) | (I[i] > nA)) && throw(BoundsError(A, I))
row,col = Base._ind2sub(szA, I[i])
for r in colptrA[col]:(colptrA[col+1]-1)
@inbounds if rowvalA[r] == row
if idxB <= nnzB
rowvalB[idxB] = i
nzvalB[idxB] = nzvalA[r]
idxB += 1
else # this can happen if there are repeated indices in I
push!(rowvalB, i)
push!(nzvalB, nzvalA[r])
end
break
end
end
end
if nnzB > (idxB-1)
deleteat!(nzvalB, idxB:nnzB)
deleteat!(rowvalB, idxB:nnzB)
end
SparseVector(n, rowvalB, nzvalB)
end
function find(x::SparseVector)
if !(eltype(x) <: Bool)
Base.depwarn("In the future `find(A)` will only work on boolean collections. Use `find(x->x!=0, A)` instead.", :find)
end
return find(x->x!=0, x)
end
function find(p::Function, x::SparseVector{<:Any,Ti}) where Ti
if p(zero(eltype(x)))
return invoke(find, Tuple{Function, Any}, p, x)
end
numnz = nnz(x)
I = Vector{Ti}(uninitialized, numnz)
nzind = x.nzind
nzval = x.nzval
count = 1
@inbounds for i = 1 : numnz
if p(nzval[i])
I[count] = nzind[i]
count += 1
end
end
count -= 1
if numnz != count
deleteat!(I, (count+1):numnz)
end
return I
end
function findnz(x::SparseVector{Tv,Ti}) where {Tv,Ti}
numnz = nnz(x)
I = Vector{Ti}(uninitialized, numnz)
V = Vector{Tv}(uninitialized, numnz)
nzind = x.nzind
nzval = x.nzval
count = 1
@inbounds for i = 1 : numnz
if nzval[i] != 0
I[count] = nzind[i]
V[count] = nzval[i]
count += 1
end
end
count -= 1
if numnz != count
deleteat!(I, (count+1):numnz)
deleteat!(V, (count+1):numnz)
end
return (I, V)
end
### Generic functions operating on AbstractSparseVector
### getindex
function _spgetindex(m::Int, nzind::AbstractVector{Ti}, nzval::AbstractVector{Tv}, i::Integer) where {Tv,Ti}
ii = searchsortedfirst(nzind, convert(Ti, i))
(ii <= m && nzind[ii] == i) ? nzval[ii] : zero(Tv)
end
function getindex(x::AbstractSparseVector, i::Integer)
checkbounds(x, i)
_spgetindex(nnz(x), nonzeroinds(x), nonzeros(x), i)
end
function getindex(x::AbstractSparseVector{Tv,Ti}, I::AbstractUnitRange) where {Tv,Ti}
checkbounds(x, I)
xlen = length(x)
i0 = first(I)
i1 = last(I)
xnzind = nonzeroinds(x)
xnzval = nonzeros(x)
m = length(xnzind)
# locate the first j0, s.t. xnzind[j0] >= i0
j0 = searchsortedfirst(xnzind, i0)
# locate the last j1, s.t. xnzind[j1] <= i1
j1 = searchsortedlast(xnzind, i1, j0, m, Forward)
# compute the number of non-zeros
jrgn = j0:j1
mr = length(jrgn)
rind = Vector{Ti}(uninitialized, mr)
rval = Vector{Tv}(uninitialized, mr)
if mr > 0
c = 0
for j in jrgn
c += 1
rind[c] = convert(Ti, xnzind[j] - i0 + 1)
rval[c] = xnzval[j]
end
end
SparseVector(length(I), rind, rval)
end
getindex(x::AbstractSparseVector, I::AbstractVector{Bool}) = x[find(I)]
getindex(x::AbstractSparseVector, I::AbstractArray{Bool}) = x[find(I)]
@inline function getindex(x::AbstractSparseVector{Tv,Ti}, I::AbstractVector) where {Tv,Ti}
# SparseMatrixCSC has a nicely optimized routine for this; punt
S = SparseMatrixCSC(x.n, 1, Ti[1,length(x.nzind)+1], x.nzind, x.nzval)
S[I, 1]
end
function getindex(x::AbstractSparseVector{Tv,Ti}, I::AbstractArray) where {Tv,Ti}
# punt to SparseMatrixCSC
S = SparseMatrixCSC(x.n, 1, Ti[1,length(x.nzind)+1], x.nzind, x.nzval)
S[I]
end
getindex(x::AbstractSparseVector, ::Colon) = copy(x)
### show and friends
function show(io::IO, ::MIME"text/plain", x::AbstractSparseVector)
xnnz = length(nonzeros(x))
print(io, length(x), "-element ", typeof(x), " with ", xnnz,
" stored ", xnnz == 1 ? "entry" : "entries")
if xnnz != 0
println(io, ":")
show(io, x)
end
end
show(io::IO, x::AbstractSparseVector) = show(convert(IOContext, io), x)
function show(io::IOContext, x::AbstractSparseVector)
# TODO: make this a one-line form
n = length(x)
nzind = nonzeroinds(x)
nzval = nonzeros(x)
xnnz = length(nzind)
if length(nzind) == 0
return show(io, MIME("text/plain"), x)
end
limit::Bool = get(io, :limit, false)
half_screen_rows = limit ? div(displaysize(io)[1] - 8, 2) : typemax(Int)
pad = ndigits(n)
if !haskey(io, :compact)
io = IOContext(io, :compact => true)
end
for k = 1:length(nzind)
if k < half_screen_rows || k > xnnz - half_screen_rows
print(io, " ", '[', rpad(nzind[k], pad), "] = ")
if isassigned(nzval, Int(k))
show(io, nzval[k])
else
print(io, Base.undef_ref_str)
end
k != length(nzind) && println(io)
elseif k == half_screen_rows
println(io, " ", " "^pad, " \u22ee")
end
end
end
### Conversion to matrix
function SparseMatrixCSC{Tv,Ti}(x::AbstractSparseVector) where {Tv,Ti}
n = length(x)
xnzind = nonzeroinds(x)
xnzval = nonzeros(x)
m = length(xnzind)
colptr = Ti[1, m+1]
# Note that this *cannot* share data like normal array conversions, since
# modifying one would put the other in an inconsistent state
rowval = collect(Ti, xnzind)
nzval = collect(Tv, xnzval)
SparseMatrixCSC(n, 1, colptr, rowval, nzval)
end
SparseMatrixCSC{Tv}(x::AbstractSparseVector{<:Any,Ti}) where {Tv,Ti} = SparseMatrixCSC{Tv,Ti}(x)
SparseMatrixCSC(x::AbstractSparseVector{Tv,Ti}) where {Tv,Ti} = SparseMatrixCSC{Tv,Ti}(x)
function Vector(x::AbstractSparseVector{Tv}) where Tv
n = length(x)
n == 0 && return Vector{Tv}()
nzind = nonzeroinds(x)
nzval = nonzeros(x)
r = zeros(Tv, n)
for k in 1:nnz(x)
i = nzind[k]
v = nzval[k]
r[i] = v
end
return r
end
Array(x::AbstractSparseVector) = Vector(x)
### Array manipulation
vec(x::AbstractSparseVector) = x
copy(x::AbstractSparseVector) =
SparseVector(length(x), copy(nonzeroinds(x)), copy(nonzeros(x)))
function reinterpret(::Type{T}, x::AbstractSparseVector{Tv}) where {T,Tv}
sizeof(T) == sizeof(Tv) ||
throw(ArgumentError("reinterpret of sparse vectors only supports element types of the same size."))
SparseVector(length(x), copy(nonzeroinds(x)), reinterpret(T, nonzeros(x)))
end
float(x::AbstractSparseVector{<:AbstractFloat}) = x
float(x::AbstractSparseVector) =
SparseVector(length(x), copy(nonzeroinds(x)), float(nonzeros(x)))
complex(x::AbstractSparseVector{<:Complex}) = x
complex(x::AbstractSparseVector) =
SparseVector(length(x), copy(nonzeroinds(x)), complex(nonzeros(x)))
### Concatenation
# Without the first of these methods, horizontal concatenations of SparseVectors fall
# back to the horizontal concatenation method that ensures that combinations of
# sparse/special/dense matrix/vector types concatenate to SparseMatrixCSCs, instead
# of _absspvec_hcat below. The <:Integer qualifications are necessary for correct dispatch.
hcat(X::SparseVector{Tv,Ti}...) where {Tv,Ti<:Integer} = _absspvec_hcat(X...)
hcat(X::AbstractSparseVector{Tv,Ti}...) where {Tv,Ti<:Integer} = _absspvec_hcat(X...)
function _absspvec_hcat(X::AbstractSparseVector{Tv,Ti}...) where {Tv,Ti}
# check sizes
n = length(X)
m = length(X[1])
tnnz = nnz(X[1])
for j = 2:n
length(X[j]) == m ||
throw(DimensionMismatch("Inconsistent column lengths."))
tnnz += nnz(X[j])
end
# construction
colptr = Vector{Ti}(uninitialized, n+1)
nzrow = Vector{Ti}(uninitialized, tnnz)
nzval = Vector{Tv}(uninitialized, tnnz)
roff = 1
@inbounds for j = 1:n
xj = X[j]
xnzind = nonzeroinds(xj)
xnzval = nonzeros(xj)
colptr[j] = roff
copyto!(nzrow, roff, xnzind)
copyto!(nzval, roff, xnzval)
roff += length(xnzind)
end
colptr[n+1] = roff
SparseMatrixCSC{Tv,Ti}(m, n, colptr, nzrow, nzval)
end
# Without the first of these methods, vertical concatenations of SparseVectors fall
# back to the vertical concatenation method that ensures that combinations of
# sparse/special/dense matrix/vector types concatenate to SparseMatrixCSCs, instead
# of _absspvec_vcat below. The <:Integer qualifications are necessary for correct dispatch.
vcat(X::SparseVector{Tv,Ti}...) where {Tv,Ti<:Integer} = _absspvec_vcat(X...)
vcat(X::AbstractSparseVector{Tv,Ti}...) where {Tv,Ti<:Integer} = _absspvec_vcat(X...)
function vcat(X::SparseVector...)
commeltype = promote_type(map(eltype, X)...)
commindtype = promote_type(map(indtype, X)...)
vcat(map(x -> SparseVector{commeltype,commindtype}(x), X)...)
end
function _absspvec_vcat(X::AbstractSparseVector{Tv,Ti}...) where {Tv,Ti}
# check sizes
n = length(X)
tnnz = 0
for j = 1:n
tnnz += nnz(X[j])
end
# construction
rnzind = Vector{Ti}(uninitialized, tnnz)
rnzval = Vector{Tv}(uninitialized, tnnz)
ir = 0
len = 0
@inbounds for j = 1:n
xj = X[j]
xnzind = nonzeroinds(xj)
xnzval = nonzeros(xj)
xnnz = length(xnzind)
for i = 1:xnnz
rnzind[ir + i] = xnzind[i] + len
end
copyto!(rnzval, ir+1, xnzval)
ir += xnnz
len += length(xj)
end
SparseVector(len, rnzind, rnzval)
end
hcat(Xin::Union{Vector, AbstractSparseVector}...) = hcat(map(sparse, Xin)...)
vcat(Xin::Union{Vector, AbstractSparseVector}...) = vcat(map(sparse, Xin)...)
# Without the following method, vertical concatenations of SparseVectors with Vectors
# fall back to the vertical concatenation method that ensures that combinations of
# sparse/special/dense matrix/vector types concatenate to SparseMatrixCSCs (because
# the vcat method immediately above is less specific, being defined in AbstractSparseVector
# rather than SparseVector).
vcat(X::Union{Vector,SparseVector}...) = vcat(map(sparse, X)...)
### Concatenation of un/annotated sparse/special/dense vectors/matrices
# TODO: These methods and definitions should be moved to a more appropriate location,
# particularly some future equivalent of base/linalg/special.jl dedicated to interactions
# between a broader set of matrix types.
# TODO: A definition similar to the third exists in base/linalg/bidiag.jl. These definitions
# should be consolidated in a more appropriate location, e.g. base/linalg/special.jl.
const _SparseArrays = Union{SparseVector, SparseMatrixCSC, RowVector{<:Any,<:SparseVector}, Adjoint{<:Any,<:SparseVector}, Transpose{<:Any,<:SparseVector}}
const _SpecialArrays = Union{Diagonal, Bidiagonal, Tridiagonal, SymTridiagonal}
const _SparseConcatArrays = Union{_SpecialArrays, _SparseArrays}
const _Symmetric_SparseConcatArrays{T,A<:_SparseConcatArrays} = Symmetric{T,A}
const _Hermitian_SparseConcatArrays{T,A<:_SparseConcatArrays} = Hermitian{T,A}
const _Triangular_SparseConcatArrays{T,A<:_SparseConcatArrays} = Base.LinAlg.AbstractTriangular{T,A}
const _Annotated_SparseConcatArrays = Union{_Triangular_SparseConcatArrays, _Symmetric_SparseConcatArrays, _Hermitian_SparseConcatArrays}
const _Symmetric_DenseArrays{T,A<:Matrix} = Symmetric{T,A}
const _Hermitian_DenseArrays{T,A<:Matrix} = Hermitian{T,A}
const _Triangular_DenseArrays{T,A<:Matrix} = Base.LinAlg.AbstractTriangular{T,A}