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sparsevector.jl
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# This file is a part of Julia. License is MIT: http://julialang.org/license
### Common definitions
import Base: scalarmax, scalarmin, sort
### The SparseVector
### Types
immutable SparseVector{Tv,Ti<:Integer} <: AbstractSparseVector{Tv,Ti}
n::Int # the number of elements
nzind::Vector{Ti} # the indices of nonzeros
nzval::Vector{Tv} # the values of nonzeros
function SparseVector(n::Integer, nzind::Vector{Ti}, nzval::Vector{Tv})
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{Tv,Ti}(n::Integer, nzind::Vector{Ti}, nzval::Vector{Tv}) =
SparseVector{Tv,Ti}(n, nzind, nzval)
### Basic properties
length(x::SparseVector) = x.n
size(x::SparseVector) = (x.n,)
nnz(x::SparseVector) = length(x.nzval)
countnz(x::SparseVector) = countnz(x.nzval)
nonzeros(x::SparseVector) = x.nzval
nonzeroinds(x::SparseVector) = x.nzind
similar{T}(x::SparseVector, ::Type{T}, D::Dims) = spzeros(T, D...)
### Construct empty sparse vector
spzeros(len::Integer) = spzeros(Float64, len)
spzeros{T}(::Type{T}, len::Integer) = SparseVector(len, Int[], T[])
# Construction of same structure, but with all ones
spones{T}(x::SparseVector{T}) = SparseVector(x.n, copy(x.nzind), ones(T, length(x.nzval)))
### Construction from lists of indices and values
function _sparsevector!{Ti<:Integer}(I::Vector{Ti}, V::Vector, len::Integer)
# pre-condition: no duplicate indexes in I
if !isempty(I)
p = sortperm(I)
permute!(I, p)
permute!(V, p)
end
SparseVector(len, I, V)
end
function _sparsevector!{Tv,Ti<:Integer}(I::Vector{Ti}, V::Vector{Tv}, 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 `|`.
"""
function sparsevec{Tv,Ti<:Integer}(I::AbstractVector{Ti}, V::AbstractVector{Tv}, 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(Ti, I), collect(Tv, V), len, combine)
end
function sparsevec{Tv,Ti<:Integer}(I::AbstractVector{Ti}, V::AbstractVector{Tv}, len::Integer, combine::Function)
length(I) == length(V) ||
throw(ArgumentError("index and value vectors must be the same length"))
maxi = convert(Ti, len)
for i in I
1 <= i <= maxi || throw(ArgumentError("An index is out of bound."))
end
_sparsevector!(collect(Ti, I), collect(Tv, V), len, combine)
end
sparsevec{Ti<:Integer}(I::AbstractVector{Ti}, V::Union{Number, AbstractVector}) =
sparsevec(I, V, +)
sparsevec{Ti<:Integer}(I::AbstractVector{Ti}, V::Union{Number, AbstractVector},
len::Integer) =
sparsevec(I, V, len, +)
sparsevec{Ti<:Integer}(I::AbstractVector{Ti}, V::Union{Bool, AbstractVector{Bool}}) =
sparsevec(I, V, |)
sparsevec{Ti<:Integer}(I::AbstractVector{Ti}, V::Union{Bool, AbstractVector{Bool}},
len::Integer) =
sparsevec(I, V, len, |)
sparsevec{Ti<:Integer}(I::AbstractVector{Ti}, v::Number, combine::Function) =
sparsevec(I, fill(v, length(I)), combine)
sparsevec{Ti<:Integer}(I::AbstractVector{Ti}, 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.
"""
function sparsevec{Tv,Ti<:Integer}(dict::Associative{Ti,Tv})
m = length(dict)
nzind = Array{Ti}(m)
nzval = Array{Tv}(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{Tv,Ti<:Integer}(dict::Associative{Ti,Tv}, len::Integer)
m = length(dict)
nzind = Array{Ti}(m)
nzval = Array{Tv}(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!{Tv,Ti<:Integer}(x::SparseVector{Tv,Ti}, v::Tv, i::Ti)
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
if v == 0
deleteat!(nzind, k)
deleteat!(nzval, k)
else
nzval[k] = v
end
else # i not found
if v != 0
insert!(nzind, k, i)
insert!(nzval, k, v)
end
end
x
end
setindex!{Tv, Ti<:Integer}(x::SparseVector{Tv,Ti}, v, i::Integer) =
setindex!(x, convert(Tv, v), convert(Ti, i))
### Conversion
# convert SparseMatrixCSC to SparseVector
function convert{Tv,Ti<:Integer}(::Type{SparseVector{Tv,Ti}}, s::SparseMatrixCSC{Tv,Ti})
size(s, 2) == 1 || throw(ArgumentError("The input argument must have a single-column."))
SparseVector(s.m, s.rowval, s.nzval)
end
convert{Tv,Ti}(::Type{SparseVector{Tv}}, s::SparseMatrixCSC{Tv,Ti}) =
convert(SparseVector{Tv,Ti}, s)
convert{Tv,Ti}(::Type{SparseVector}, s::SparseMatrixCSC{Tv,Ti}) =
convert(SparseVector{Tv,Ti}, s)
# convert Vector to SparseVector
"""
sparsevec(A)
Convert a vector `A` into a sparse vector of length `m`.
"""
sparsevec{T}(a::AbstractVector{T}) = convert(SparseVector{T, Int}, a)
sparsevec(a::AbstractArray) = sparsevec(vec(a))
sparsevec(a::AbstractSparseArray) = vec(a)
sparse(a::AbstractVector) = sparsevec(a)
function _dense2sparsevec{Tv,Ti}(s::AbstractArray{Tv}, initcap::Ti)
# pre-condition: initcap > 0; the initcap determines the index type
n = length(s)
cap = initcap
nzind = Array{Ti}(cap)
nzval = Array{Tv}(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
convert{Tv,Ti}(::Type{SparseVector{Tv,Ti}}, s::AbstractVector{Tv}) =
_dense2sparsevec(s, convert(Ti, max(8, div(length(s), 8))))
convert{Tv}(::Type{SparseVector{Tv}}, s::AbstractVector{Tv}) =
convert(SparseVector{Tv,Int}, s)
convert{Tv}(::Type{SparseVector}, s::AbstractVector{Tv}) =
convert(SparseVector{Tv,Int}, s)
# convert between different types of SparseVector
convert{Tv,Ti,TvS,TiS}(::Type{SparseVector{Tv,Ti}}, s::SparseVector{TvS,TiS}) =
SparseVector{Tv,Ti}(s.n, convert(Vector{Ti}, s.nzind), convert(Vector{Tv}, s.nzval))
convert{Tv,TvS,TiS}(::Type{SparseVector{Tv}}, s::SparseVector{TvS,TiS}) =
SparseVector{Tv,TiS}(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)
copy!(A.nzind, nnzB+1, A.nzind, lastmodindA+1, nnzA-lastmodindA)
copy!(A.nzval, nnzB+1, A.nzval, lastmodindA+1, nnzA-lastmodindA)
end
end
end
function copy!(A::SparseVector, B::SparseVector)
prep_sparsevec_copy_dest!(A, length(B), nnz(B))
copy!(A.nzind, B.nzind)
copy!(A.nzval, B.nzval)
return A
end
function copy!(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
copy!(A.nzval, B.nzval)
return A
end
copy!{TvB, TiB}(A::SparseMatrixCSC, B::SparseVector{TvB,TiB}) =
copy!(A, SparseMatrixCSC{TvB,TiB}(B.n, 1, TiB[1, length(B.nzind)+1], B.nzind, B.nzval))
### Rand Construction
sprand{T}(n::Integer, p::AbstractFloat, rfn::Function, ::Type{T}) = sprand(GLOBAL_RNG, n, p, rfn, T)
function sprand{T}(r::AbstractRNG, n::Integer, p::AbstractFloat, rfn::Function, ::Type{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{T}(r::AbstractRNG, ::Type{T}, n::Integer, p::AbstractFloat) = 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{T}(::Type{T}, n::Integer, p::AbstractFloat) = 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::UnitRange, 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[r1:r2] - first(I) + 1, x.nzval[r1:r2])
end
# In the general case, we piggy back upon SparseMatrixCSC's optimized solution
@inline function getindex{Tv,Ti}(A::SparseMatrixCSC{Tv,Ti}, 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]
getindex{Tv,Ti}(A::SparseMatrixCSC{Tv,Ti}, i::Integer, J::AbstractVector{Bool}) = A[i, find(J)]
function Base.getindex{Tv,Ti}(A::SparseMatrixCSC{Tv,Ti}, i::Integer, J::AbstractVector)
checkbounds(A, i, J)
nJ = length(J)
colptrA = A.colptr; rowvalA = A.rowval; nzvalA = A.nzval
nzinds = Array{Ti}(0)
nzvals = Array{Tv}(0)
# adapted from SparseMatrixCSC's sorted_bsearch_A
ptrI = 1
@inbounds for j = 1:nJ
col = J[j]
rowI = i
ptrA = colptrA[col]
stopA = 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{Tv}(A::SparseMatrixCSC{Tv}, I::AbstractVector{Bool}) = _logical_index(A, I) # Ambiguities
getindex{Tv}(A::SparseMatrixCSC{Tv}, I::AbstractArray{Bool}) = _logical_index(A, I)
function _logical_index{Tv}(A::SparseMatrixCSC{Tv}, I::AbstractArray{Bool})
checkbounds(A, I)
n = sum(I)
nnzB = min(n, nnz(A))
colptrA = A.colptr; rowvalA = A.rowval; nzvalA = A.nzval
rowvalB = Array{Int}(nnzB)
nzvalB = Array{Tv}(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 Range
getindex(A::SparseMatrixCSC, ::Colon) = A[1:end]
function getindex{Tv}(A::SparseMatrixCSC{Tv}, I::UnitRange)
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 = Array{Int}(nnzB)
nzvalB = Array{Tv}(nnzB)
rowstart,colstart = ind2sub(szA, first(I))
rowend,colend = 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] = 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{Tv}(A::SparseMatrixCSC{Tv}, I::AbstractVector)
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 = Array{Int}(nnzB)
nzvalB = Array{Tv}(nnzB)
idxB = 1
for i in 1:n
((I[i] < 1) | (I[i] > nA)) && throw(BoundsError(A, I))
row,col = 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
### Generic functions operating on AbstractSparseVector
### getindex
function _spgetindex{Tv,Ti}(m::Int, nzind::AbstractVector{Ti}, nzval::AbstractVector{Tv}, i::Integer)
ii = searchsortedfirst(nzind, convert(Ti, i))
(ii <= m && nzind[ii] == i) ? nzval[ii] : zero(Tv)
end
function getindex{Tv}(x::AbstractSparseVector{Tv}, i::Integer)
checkbounds(x, i)
_spgetindex(nnz(x), nonzeroinds(x), nonzeros(x), i)
end
function getindex{Tv,Ti}(x::AbstractSparseVector{Tv,Ti}, I::UnitRange)
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 = Array{Ti}(mr)
rval = Array{Tv}(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{Tv,Ti}(x::AbstractSparseVector{Tv,Ti}, I::AbstractVector{Bool}) = x[find(I)]
getindex{Tv,Ti}(x::AbstractSparseVector{Tv,Ti}, I::AbstractArray{Bool}) = x[find(I)]
@inline function getindex{Tv,Ti}(x::AbstractSparseVector{Tv,Ti}, I::AbstractVector)
# SparseMatrixCSC has a nicely optimized routine for this; punt
S = SparseMatrixCSC(x.n, 1, [1,length(x.nzind)+1], x.nzind, x.nzval)
S[I, 1]
end
function getindex{Tv,Ti}(x::AbstractSparseVector{Tv,Ti}, I::AbstractArray)
# punt to SparseMatrixCSC
S = SparseMatrixCSC(x.n, 1, [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, x::AbstractSparseVector)
n = length(x)
nzind = nonzeroinds(x)
nzval = nonzeros(x)
xnnz = length(nzind)
if get(io, :multiline, false)
println(io, summary(x))
end
limit::Bool = get(io, :limit, false)
half_screen_rows = limit ? div(displaysize(io)[1] - 8, 2) : typemax(Int)
pad = ndigits(n)
sep = "\n\t"
io = IOContext(io, multiline=false)
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), "] = ")
Base.show(io, nzval[k])
println(io)
elseif k == half_screen_rows
println(io, " ", " "^pad, " \u22ee")
end
end
end
function summary(x::AbstractSparseVector)
string("Sparse vector of length ", length(x), " with ", length(nonzeros(x)),
" ", eltype(x), " nonzero entries:")
end
### Conversion to matrix
function convert{TvD,TiD,Tv,Ti}(::Type{SparseMatrixCSC{TvD,TiD}}, x::AbstractSparseVector{Tv,Ti})
n = length(x)
xnzind = nonzeroinds(x)
xnzval = nonzeros(x)
m = length(xnzind)
colptr = TiD[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(TiD, xnzind)
nzval = collect(TvD, xnzval)
SparseMatrixCSC(n, 1, colptr, rowval, nzval)
end
convert{TvD,Tv,Ti}(::Type{SparseMatrixCSC{TvD}}, x::AbstractSparseVector{Tv,Ti}) =
convert(SparseMatrixCSC{TvD,Ti}, x)
convert{Tv,Ti}(::Type{SparseMatrixCSC}, x::AbstractSparseVector{Tv,Ti}) =
convert(SparseMatrixCSC{Tv,Ti}, x)
### Array manipulation
function full{Tv}(x::AbstractSparseVector{Tv})
n = length(x)
n == 0 && return Array{Tv}(0)
nzind = nonzeroinds(x)
nzval = nonzeros(x)
r = zeros(Tv, n)
for i = 1:length(nzind)
r[nzind[i]] = nzval[i]
end
return r
end
vec(x::AbstractSparseVector) = x
copy(x::AbstractSparseVector) =
SparseVector(length(x), copy(nonzeroinds(x)), copy(nonzeros(x)))
function reinterpret{T,Tv}(::Type{T}, x::AbstractSparseVector{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{Tv<:AbstractFloat}(x::AbstractSparseVector{Tv}) = x
float(x::AbstractSparseVector) =
SparseVector(length(x), copy(nonzeroinds(x)), float(nonzeros(x)))
complex{Tv<:Complex}(x::AbstractSparseVector{Tv}) = x
complex(x::AbstractSparseVector) =
SparseVector(length(x), copy(nonzeroinds(x)), complex(nonzeros(x)))
### Concatenation
function hcat{Tv,Ti}(X::AbstractSparseVector{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 = Array{Ti}(n+1)
nzrow = Array{Ti}(tnnz)
nzval = Array{Tv}(tnnz)
roff = 1
@inbounds for j = 1:n
xj = X[j]
xnzind = nonzeroinds(xj)
xnzval = nonzeros(xj)
colptr[j] = roff
copy!(nzrow, roff, xnzind)
copy!(nzval, roff, xnzval)
roff += length(xnzind)
end
colptr[n+1] = roff
SparseMatrixCSC{Tv,Ti}(m, n, colptr, nzrow, nzval)
end
function vcat{Tv,Ti}(X::AbstractSparseVector{Tv,Ti}...)
# check sizes
n = length(X)
tnnz = 0
for j = 1:n
tnnz += nnz(X[j])
end
# construction
rnzind = Array{Ti}(tnnz)
rnzval = Array{Tv}(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
copy!(rnzval, ir+1, xnzval)
ir += xnnz
len += length(xj)
end
SparseVector(len, rnzind, rnzval)
end
hcat(Xin::Union{AbstractSparseVector, SparseMatrixCSC}...) = hcat(map(SparseMatrixCSC, Xin)...)
vcat(Xin::Union{AbstractSparseVector, SparseMatrixCSC}...) = vcat(map(SparseMatrixCSC, Xin)...)
hcat(Xin::Union{Vector, AbstractSparseVector}...) = hcat(map(sparse, Xin)...)
vcat(Xin::Union{Vector, AbstractSparseVector}...) = vcat(map(sparse, Xin)...)
### math functions
### Unary Map
# zero-preserving functions (z->z, nz->nz)
for op in [:-, :abs, :abs2, :conj]
@eval begin
$(op)(x::AbstractSparseVector) =
SparseVector(length(x), copy(nonzeroinds(x)), $(op)(nonzeros(x)))
end
end
# functions f, such that
# f(x) can be zero or non-zero when x != 0
# f(x) = 0 when x == 0
#
macro unarymap_nz2z_z2z(op, TF)
esc(quote
function $(op){Tv<:$(TF),Ti<:Integer}(x::AbstractSparseVector{Tv,Ti})
R = typeof($(op)(zero(Tv)))
xnzind = nonzeroinds(x)
xnzval = nonzeros(x)
m = length(xnzind)
ynzind = Array{Ti}(m)
ynzval = Array{R}(m)
ir = 0
@inbounds for j = 1:m
i = xnzind[j]
v = $(op)(xnzval[j])
if v != zero(v)
ir += 1
ynzind[ir] = i
ynzval[ir] = v
end
end
resize!(ynzind, ir)
resize!(ynzval, ir)
SparseVector(length(x), ynzind, ynzval)
end
end)
end
real{T<:Real}(x::AbstractSparseVector{T}) = x
@unarymap_nz2z_z2z real Complex
imag{Tv<:Real,Ti<:Integer}(x::AbstractSparseVector{Tv,Ti}) = SparseVector(length(x), Ti[], Tv[])
@unarymap_nz2z_z2z imag Complex
for op in [:floor, :ceil, :trunc, :round]
@eval @unarymap_nz2z_z2z $(op) Real
end
for op in [:log1p, :expm1,
:sin, :tan, :sinpi, :sind, :tand,
:asin, :atan, :asind, :atand,
:sinh, :tanh, :asinh, :atanh]
@eval @unarymap_nz2z_z2z $(op) Number
end
# function that does not preserve zeros
macro unarymap_z2nz(op, TF)
esc(quote
function $(op){Tv<:$(TF),Ti<:Integer}(x::AbstractSparseVector{Tv,Ti})
v0 = $(op)(zero(Tv))
R = typeof(v0)
xnzind = nonzeroinds(x)
xnzval = nonzeros(x)
n = length(x)
m = length(xnzind)
y = fill(v0, n)
@inbounds for j = 1:m
y[xnzind[j]] = $(op)(xnzval[j])
end
y
end
end)
end
for op in [:exp, :exp2, :exp10, :log, :log2, :log10,
:cos, :csc, :cot, :sec, :cospi,
:cosd, :cscd, :cotd, :secd,
:acos, :acot, :acosd, :acotd,
:cosh, :csch, :coth, :sech,
:acsch, :asech]
@eval @unarymap_z2nz $(op) Number
end
### Binary Map
# mode:
# 0: f(nz, nz) -> nz, f(z, nz) -> z, f(nz, z) -> z
# 1: f(nz, nz) -> z/nz, f(z, nz) -> nz, f(nz, z) -> nz
# 2: f(nz, nz) -> z/nz, f(z, nz) -> z/nz, f(nz, z) -> z/nz
function _binarymap{Tx,Ty}(f::Function,
x::AbstractSparseVector{Tx},
y::AbstractSparseVector{Ty},
mode::Int)
0 <= mode <= 2 || throw(ArgumentError("Incorrect mode $mode."))
R = typeof(f(zero(Tx), zero(Ty)))
n = length(x)
length(y) == n || throw(DimensionMismatch())
xnzind = nonzeroinds(x)
xnzval = nonzeros(x)
ynzind = nonzeroinds(y)
ynzval = nonzeros(y)
mx = length(xnzind)
my = length(ynzind)
cap = (mode == 0 ? min(mx, my) : mx + my)::Int
rind = Array{Int}(cap)
rval = Array{R}(cap)
ir = 0
ix = 1
iy = 1
ir = (
mode == 0 ? _binarymap_mode_0!(f, mx, my,
xnzind, xnzval, ynzind, ynzval, rind, rval) :
mode == 1 ? _binarymap_mode_1!(f, mx, my,
xnzind, xnzval, ynzind, ynzval, rind, rval) :
_binarymap_mode_2!(f, mx, my,
xnzind, xnzval, ynzind, ynzval, rind, rval)
)::Int
resize!(rind, ir)
resize!(rval, ir)
return SparseVector(n, rind, rval)
end
function _binarymap_mode_0!(f::Function, mx::Int, my::Int,
xnzind, xnzval, ynzind, ynzval, rind, rval)
# f(nz, nz) -> nz, f(z, nz) -> z, f(nz, z) -> z
ir = 0; ix = 1; iy = 1
@inbounds while ix <= mx && iy <= my
jx = xnzind[ix]
jy = ynzind[iy]
if jx == jy
v = f(xnzval[ix], ynzval[iy])
ir += 1; rind[ir] = jx; rval[ir] = v
ix += 1; iy += 1
elseif jx < jy
ix += 1
else
iy += 1
end
end
return ir
end
function _binarymap_mode_1!{Tx,Ty}(f::Function, mx::Int, my::Int,
xnzind, xnzval::AbstractVector{Tx},
ynzind, ynzval::AbstractVector{Ty},
rind, rval)
# f(nz, nz) -> z/nz, f(z, nz) -> nz, f(nz, z) -> nz
ir = 0; ix = 1; iy = 1
@inbounds while ix <= mx && iy <= my
jx = xnzind[ix]
jy = ynzind[iy]
if jx == jy
v = f(xnzval[ix], ynzval[iy])
if v != zero(v)
ir += 1; rind[ir] = jx; rval[ir] = v
end
ix += 1; iy += 1
elseif jx < jy
v = f(xnzval[ix], zero(Ty))
ir += 1; rind[ir] = jx; rval[ir] = v
ix += 1
else
v = f(zero(Tx), ynzval[iy])
ir += 1; rind[ir] = jy; rval[ir] = v
iy += 1
end
end
@inbounds while ix <= mx
v = f(xnzval[ix], zero(Ty))
ir += 1; rind[ir] = xnzind[ix]; rval[ir] = v
ix += 1
end
@inbounds while iy <= my
v = f(zero(Tx), ynzval[iy])
ir += 1; rind[ir] = ynzind[iy]; rval[ir] = v
iy += 1
end
return ir
end
function _binarymap_mode_2!{Tx,Ty}(f::Function, mx::Int, my::Int,
xnzind, xnzval::AbstractVector{Tx},
ynzind, ynzval::AbstractVector{Ty},
rind, rval)
# f(nz, nz) -> z/nz, f(z, nz) -> z/nz, f(nz, z) -> z/nz
ir = 0; ix = 1; iy = 1
@inbounds while ix <= mx && iy <= my
jx = xnzind[ix]
jy = ynzind[iy]
if jx == jy
v = f(xnzval[ix], ynzval[iy])
if v != zero(v)
ir += 1; rind[ir] = jx; rval[ir] = v
end
ix += 1; iy += 1
elseif jx < jy
v = f(xnzval[ix], zero(Ty))
if v != zero(v)
ir += 1; rind[ir] = jx; rval[ir] = v
end
ix += 1
else
v = f(zero(Tx), ynzval[iy])
if v != zero(v)
ir += 1; rind[ir] = jy; rval[ir] = v
end
iy += 1
end
end
@inbounds while ix <= mx
v = f(xnzval[ix], zero(Ty))
if v != zero(v)
ir += 1; rind[ir] = xnzind[ix]; rval[ir] = v
end
ix += 1
end
@inbounds while iy <= my
v = f(zero(Tx), ynzval[iy])
if v != zero(v)
ir += 1; rind[ir] = ynzind[iy]; rval[ir] = v
end
iy += 1
end
return ir
end