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sparsematrix.jl
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sparsematrix.jl
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# This file is a part of Julia. License is MIT: http://julialang.org/license
# Compressed sparse columns data structure
# Assumes that no zeros are stored in the data structure
# Assumes that row values in rowval for each column are sorted
# issorted(rowval[colptr[i]:(colptr[i+1]-1)]) == true
immutable SparseMatrixCSC{Tv,Ti<:Integer} <: AbstractSparseMatrix{Tv,Ti}
m::Int # Number of rows
n::Int # Number of columns
colptr::Vector{Ti} # Column i is in colptr[i]:(colptr[i+1]-1)
rowval::Vector{Ti} # Row values of nonzeros
nzval::Vector{Tv} # Nonzero values
function SparseMatrixCSC(m::Integer, n::Integer, colptr::Vector{Ti}, rowval::Vector{Ti}, nzval::Vector{Tv})
m < 0 && throw(ArgumentError("number of rows (m) must be ≥ 0, got $m"))
n < 0 && throw(ArgumentError("number of columns (n) must be ≥ 0, got $n"))
new(Int(m), Int(n), colptr, rowval, nzval)
end
end
function SparseMatrixCSC(m::Integer, n::Integer, colptr::Vector, rowval::Vector, nzval::Vector)
Tv = eltype(nzval)
Ti = promote_type(eltype(colptr), eltype(rowval))
SparseMatrixCSC{Tv,Ti}(m, n, colptr, rowval, nzval)
end
size(S::SparseMatrixCSC) = (S.m, S.n)
"""
nnz(A)
Returns the number of stored (filled) elements in a sparse array.
"""
nnz(S::SparseMatrixCSC) = Int(S.colptr[end]-1)
countnz(S::SparseMatrixCSC) = countnz(S.nzval)
"""
nonzeros(A)
Return a vector of the structural nonzero values in sparse array `A`. This
includes zeros that are explicitly stored in the sparse array. The returned
vector points directly to the internal nonzero storage of `A`, and any
modifications to the returned vector will mutate `A` as well. See `rowvals(A)`
and `nzrange(A, col)`.
"""
nonzeros(S::SparseMatrixCSC) = S.nzval
"""
rowvals(A::SparseMatrixCSC)
Return a vector of the row indices of `A`. Any modifications to the returned
vector will mutate `A` as well. Providing access to how the row indices are
stored internally can be useful in conjunction with iterating over structural
nonzero values. See also `nonzeros(A)` and `nzrange(A, col)`.
"""
rowvals(S::SparseMatrixCSC) = S.rowval
"""
nzrange(A::SparseMatrixCSC, col)
Return the range of indices to the structural nonzero values of a sparse matrix
column. In conjunction with `nonzeros(A)` and `rowvals(A)`, this allows for
convenient iterating over a sparse matrix :
A = sparse(I,J,V)
rows = rowvals(A)
vals = nonzeros(A)
m, n = size(A)
for i = 1:n
for j in nzrange(A, i)
row = rows[j]
val = vals[j]
# perform sparse wizardry...
end
end
"""
nzrange(S::SparseMatrixCSC, col::Integer) = S.colptr[col]:(S.colptr[col+1]-1)
function Base.show(io::IO, ::MIME"text/plain", S::SparseMatrixCSC)
print(io, S.m, "×", S.n, " sparse matrix with ", nnz(S), " ", eltype(S), " nonzero entries")
if nnz(S) != 0
print(io, ":")
show(io, S)
end
end
function Base.show(io::IO, S::SparseMatrixCSC)
if nnz(S) == 0
return show(io, MIME("text/plain"), S)
end
limit::Bool = get(io, :limit, false)
if limit
rows = displaysize(io)[1]
half_screen_rows = div(rows - 8, 2)
else
half_screen_rows = typemax(Int)
end
pad = ndigits(max(S.m,S.n))
k = 0
sep = "\n\t"
io = IOContext(io)
if !haskey(io, :compact)
io = IOContext(io, :compact => true)
end
for col = 1:S.n, k = S.colptr[col] : (S.colptr[col+1]-1)
if k < half_screen_rows || k > nnz(S)-half_screen_rows
print(io, sep, '[', rpad(S.rowval[k], pad), ", ", lpad(col, pad), "] = ")
if isassigned(S.nzval, k)
Base.show(io, S.nzval[k])
else
print(io, Base.undef_ref_str)
end
elseif k == half_screen_rows
print(io, sep, '\u22ee')
end
k += 1
end
end
## Reinterpret and Reshape
function reinterpret{T,Tv,Ti}(::Type{T}, a::SparseMatrixCSC{Tv,Ti})
if sizeof(T) != sizeof(Tv)
throw(ArgumentError("SparseMatrixCSC reinterpret is only supported for element types of the same size"))
end
mA, nA = size(a)
colptr = copy(a.colptr)
rowval = copy(a.rowval)
nzval = reinterpret(T, a.nzval)
return SparseMatrixCSC(mA, nA, colptr, rowval, nzval)
end
function sparse_compute_reshaped_colptr_and_rowval{Ti}(colptrS::Vector{Ti}, rowvalS::Vector{Ti}, mS::Int, nS::Int, colptrA::Vector{Ti}, rowvalA::Vector{Ti}, mA::Int, nA::Int)
lrowvalA = length(rowvalA)
maxrowvalA = (lrowvalA > 0) ? maximum(rowvalA) : zero(Ti)
((length(colptrA) == (nA+1)) && (maximum(colptrA) <= (lrowvalA+1)) && (maxrowvalA <= mA)) || throw(BoundsError())
colptrS[1] = 1
colA = 1
colS = 1
ptr = 1
@inbounds while colA <= nA
offsetA = (colA - 1) * mA
while ptr <= colptrA[colA+1]-1
rowA = rowvalA[ptr]
i = offsetA + rowA - 1
colSn = div(i, mS) + 1
rowS = mod(i, mS) + 1
while colS < colSn
colptrS[colS+1] = ptr
colS += 1
end
rowvalS[ptr] = rowS
ptr += 1
end
colA += 1
end
@inbounds while colS <= nS
colptrS[colS+1] = ptr
colS += 1
end
end
function reinterpret{T,Tv,Ti,N}(::Type{T}, a::SparseMatrixCSC{Tv,Ti}, dims::NTuple{N,Int})
if sizeof(T) != sizeof(Tv)
throw(ArgumentError("SparseMatrixCSC reinterpret is only supported for element types of the same size"))
end
if prod(dims) != length(a)
throw(DimensionMismatch("new dimensions $(dims) must be consistent with array size $(length(a))"))
end
mS,nS = dims
mA,nA = size(a)
numnz = nnz(a)
colptr = Array{Ti}(nS+1)
rowval = similar(a.rowval)
nzval = reinterpret(T, a.nzval)
sparse_compute_reshaped_colptr_and_rowval(colptr, rowval, mS, nS, a.colptr, a.rowval, mA, nA)
return SparseMatrixCSC(mS, nS, colptr, rowval, nzval)
end
function copy{T,P<:SparseMatrixCSC}(ra::ReshapedArray{T,2,P})
mS,nS = size(ra)
a = parent(ra)
mA,nA = size(a)
numnz = nnz(a)
colptr = similar(a.colptr, nS+1)
rowval = similar(a.rowval)
nzval = copy(a.nzval)
sparse_compute_reshaped_colptr_and_rowval(colptr, rowval, mS, nS, a.colptr, a.rowval, mA, nA)
return SparseMatrixCSC(mS, nS, colptr, rowval, nzval)
end
## Constructors
copy(S::SparseMatrixCSC) =
SparseMatrixCSC(S.m, S.n, copy(S.colptr), copy(S.rowval), copy(S.nzval))
function copy!(A::SparseMatrixCSC, B::SparseMatrixCSC)
# If the two matrices have the same length then all the
# elements in A will be overwritten.
if length(A) == length(B)
resize!(A.nzval, length(B.nzval))
resize!(A.rowval, length(B.rowval))
if size(A) == size(B)
# Simple case: we can simply copy the internal fields of B to A.
copy!(A.colptr, B.colptr)
copy!(A.rowval, B.rowval)
else
# This is like a "reshape B into A".
sparse_compute_reshaped_colptr_and_rowval(A.colptr, A.rowval, A.m, A.n, B.colptr, B.rowval, B.m, B.n)
end
else
length(A) >= length(B) || throw(BoundsError())
lB = length(B)
nnzA = nnz(A)
nnzB = nnz(B)
# Up to which col, row, and ptr in rowval/nzval will A be overwritten?
lastmodcolA = div(lB - 1, A.m) + 1
lastmodrowA = mod(lB - 1, A.m) + 1
lastmodptrA = A.colptr[lastmodcolA]
while lastmodptrA < A.colptr[lastmodcolA+1] && A.rowval[lastmodptrA] <= lastmodrowA
lastmodptrA += 1
end
lastmodptrA -= 1
if lastmodptrA >= nnzB
# A will have fewer non-zero elements; unmodified elements are kept at the end.
deleteat!(A.rowval, nnzB+1:lastmodptrA)
deleteat!(A.nzval, nnzB+1:lastmodptrA)
else
# A will have more non-zero elements; unmodified elements are kept at the end.
resize!(A.rowval, nnzB + nnzA - lastmodptrA)
resize!(A.nzval, nnzB + nnzA - lastmodptrA)
copy!(A.rowval, nnzB+1, A.rowval, lastmodptrA+1, nnzA-lastmodptrA)
copy!(A.nzval, nnzB+1, A.nzval, lastmodptrA+1, nnzA-lastmodptrA)
end
# Adjust colptr accordingly.
@inbounds for i in 2:length(A.colptr)
A.colptr[i] += nnzB - lastmodptrA
end
sparse_compute_reshaped_colptr_and_rowval(A.colptr, A.rowval, A.m, lastmodcolA-1, B.colptr, B.rowval, B.m, B.n)
end
copy!(A.nzval, B.nzval)
return A
end
similar(S::SparseMatrixCSC, Tv::Type=eltype(S)) = SparseMatrixCSC(S.m, S.n, copy(S.colptr), copy(S.rowval), Array{Tv}(length(S.nzval)))
similar{Tv,Ti,TvNew,TiNew}(S::SparseMatrixCSC{Tv,Ti}, ::Type{TvNew}, ::Type{TiNew}) = SparseMatrixCSC(S.m, S.n, convert(Array{TiNew},S.colptr), convert(Array{TiNew}, S.rowval), Array{TvNew}(length(S.nzval)))
@inline similar{Tv}(S::SparseMatrixCSC, ::Type{Tv}, d::Dims) = spzeros(Tv, d...)
function convert{Tv,Ti,TvS,TiS}(::Type{SparseMatrixCSC{Tv,Ti}}, S::SparseMatrixCSC{TvS,TiS})
if Tv == TvS && Ti == TiS
return S
else
return SparseMatrixCSC(S.m, S.n,
convert(Vector{Ti},S.colptr),
convert(Vector{Ti},S.rowval),
convert(Vector{Tv},S.nzval))
end
end
function convert{Tv,TvS,TiS}(::Type{SparseMatrixCSC{Tv}}, S::SparseMatrixCSC{TvS,TiS})
if Tv == TvS
return S
else
return SparseMatrixCSC(S.m, S.n,
S.colptr,
S.rowval,
convert(Vector{Tv},S.nzval))
end
end
function convert{Tv,Ti}(::Type{SparseMatrixCSC{Tv,Ti}}, M::AbstractMatrix)
m, n = size(M)
(I, J, V) = findnz(M)
return sparse_IJ_sorted!(convert(Vector{Ti},I),
convert(Vector{Ti},J),
convert(Vector{Tv},V),
m, n)
end
convert{T}(::Type{AbstractMatrix{T}}, A::SparseMatrixCSC) = convert(SparseMatrixCSC{T}, A)
convert(::Type{Matrix}, S::SparseMatrixCSC) = full(S)
convert(::Type{SparseMatrixCSC}, M::Matrix) = sparse(M)
"""
full(S)
Convert a sparse matrix or vector `S` into a dense matrix or vector.
"""
full
function full{Tv}(S::SparseMatrixCSC{Tv})
# Handle cases where zero(Tv) is not defined but the array is dense.
# (Should we really worry about this?)
A = length(S) == nnz(S) ? Array{Tv}(S.m, S.n) : zeros(Tv, S.m, S.n)
for col = 1 : S.n, k = S.colptr[col] : (S.colptr[col+1]-1)
A[S.rowval[k], col] = S.nzval[k]
end
return A
end
float(S::SparseMatrixCSC) = SparseMatrixCSC(S.m, S.n, copy(S.colptr), copy(S.rowval), float(copy(S.nzval)))
complex(S::SparseMatrixCSC) = SparseMatrixCSC(S.m, S.n, copy(S.colptr), copy(S.rowval), complex(copy(S.nzval)))
complex(A::SparseMatrixCSC, B::SparseMatrixCSC) = A + im*B
# Construct a sparse vector
# Note that unlike `vec` for arrays, this does not share data
vec(S::SparseMatrixCSC) = S[:]
"""
sparse(A)
Convert an AbstractMatrix `A` into a sparse matrix.
"""
sparse{Tv}(A::AbstractMatrix{Tv}) = convert(SparseMatrixCSC{Tv,Int}, A)
sparse(S::SparseMatrixCSC) = copy(S)
sparse_IJ_sorted!(I,J,V,m,n) = sparse_IJ_sorted!(I,J,V,m,n,+)
sparse_IJ_sorted!(I,J,V::AbstractVector{Bool},m,n) = sparse_IJ_sorted!(I,J,V,m,n,|)
function sparse_IJ_sorted!{Ti<:Integer}(I::AbstractVector{Ti}, J::AbstractVector{Ti},
V::AbstractVector,
m::Integer, n::Integer, combine::Function)
m = m < 0 ? 0 : m
n = n < 0 ? 0 : n
if isempty(V); return spzeros(eltype(V),Ti,m,n); end
cols = zeros(Ti, n+1)
cols[1] = 1 # For cumsum purposes
cols[J[1] + 1] = 1
lastdup = 1
ndups = 0
I_lastdup = I[1]
J_lastdup = J[1]
L = length(I)
@inbounds for k=2:L
if I[k] == I_lastdup && J[k] == J_lastdup
V[lastdup] = combine(V[lastdup], V[k])
ndups += 1
else
cols[J[k] + 1] += 1
lastdup = k-ndups
I_lastdup = I[k]
J_lastdup = J[k]
if ndups != 0
I[lastdup] = I_lastdup
V[lastdup] = V[k]
end
end
end
colptr = cumsum(cols)
# Allow up to 20% slack
if ndups > 0.2*L
numnz = L-ndups
deleteat!(I, (numnz+1):L)
deleteat!(V, (numnz+1):length(V))
end
return SparseMatrixCSC(m, n, colptr, I, V)
end
"""
sparse(I, J, V,[ m, n, combine])
Create a sparse matrix `S` of dimensions `m x n` such that `S[I[k], J[k]] = V[k]`. The
`combine` function is used to combine duplicates. If `m` and `n` are not specified, they
are set to `maximum(I)` and `maximum(J)` respectively. If the `combine` function is not
supplied, `combine` defaults to `+` unless the elements of `V` are Booleans in which case
`combine` defaults to `|`. All elements of `I` must satisfy `1 <= I[k] <= m`, and all
elements of `J` must satisfy `1 <= J[k] <= n`. Numerical zeros in (`I`, `J`, `V`) are
retained as structural nonzeros; to drop numerical zeros, use `dropzeros!`.
For additional documentation and an expert driver, see `Base.SparseArrays.sparse!`.
"""
function sparse{Tv,Ti<:Integer}(I::AbstractVector{Ti}, J::AbstractVector{Ti}, V::AbstractVector{Tv}, m::Integer, n::Integer, combine)
coolen = length(I)
if length(J) != coolen || length(V) != coolen
throw(ArgumentError(string("the first three arguments' lengths must match, ",
"length(I) (=$(length(I))) == length(J) (= $(length(J))) == length(V) (= ",
"$(length(V)))")))
end
if m == 0 || n == 0 || coolen == 0
if coolen != 0
if n == 0
throw(ArgumentError("column indices J[k] must satisfy 1 <= J[k] <= n"))
elseif m == 0
throw(ArgumentError("row indices I[k] must satisfy 1 <= I[k] <= m"))
end
end
SparseMatrixCSC(m, n, ones(Ti, n+1), Vector{Ti}(), Vector{Tv}())
else
# Allocate storage for CSR form
csrrowptr = Vector{Ti}(m+1)
csrcolval = Vector{Ti}(coolen)
csrnzval = Vector{Tv}(coolen)
# Allocate storage for the CSC form's column pointers and a necessary workspace
csccolptr = Vector{Ti}(n+1)
klasttouch = Vector{Ti}(n)
# Allocate empty arrays for the CSC form's row and nonzero value arrays
# The parent method called below automagically resizes these arrays
cscrowval = Vector{Ti}()
cscnzval = Vector{Tv}()
sparse!(I, J, V, m, n, combine, klasttouch,
csrrowptr, csrcolval, csrnzval,
csccolptr, cscrowval, cscnzval )
end
end
"""
sparse!{Tv,Ti<:Integer}(
I::AbstractVector{Ti}, J::AbstractVector{Ti}, V::AbstractVector{Tv},
m::Integer, n::Integer, combine, klasttouch::Vector{Ti},
csrrowptr::Vector{Ti}, csrcolval::Vector{Ti}, csrnzval::Vector{Tv},
[csccolptr::Vector{Ti}], [cscrowval::Vector{Ti}, cscnzval::Vector{Tv}] )
Parent of and expert driver for `sparse`; see `sparse` for basic usage. This method
allows the user to provide preallocated storage for `sparse`'s intermediate objects and
result as described below. This capability enables more efficient successive construction
of `SparseMatrixCSC`s from coordinate representations, and also enables extraction of an
unsorted-column representation of the result's transpose at no additional cost.
This method consists of three major steps: (1) Counting-sort the provided coordinate
representation into an unsorted-row CSR form including repeated entries. (2) Sweep through
the CSR form, simultaneously calculating the desired CSC form's column-pointer array,
detecting repeated entries, and repacking the CSR form with repeated entries combined;
this stage yields an unsorted-row CSR form with no repeated entries. (3) Counting-sort the
preceding CSR form into a fully-sorted CSC form with no repeated entries.
Input arrays `csrrowptr`, `csrcolval`, and `csrnzval` constitute storage for the
intermediate CSR forms and require `length(csrrowptr) >= m + 1`,
`length(csrcolval) >= length(I)`, and `length(csrnzval >= length(I))`. Input
array `klasttouch`, workspace for the second stage, requires `length(klasttouch) >= n`.
Optional input arrays `csccolptr`, `cscrowval`, and `cscnzval` constitute storage for the
returned CSC form `S`. `csccolptr` requires `length(csccolptr) >= n + 1`. If necessary,
`cscrowval` and `cscnzval` are automatically resized to satisfy
`length(cscrowval) >= nnz(S)` and `length(cscnzval) >= nnz(S)`; hence, if `nnz(S)` is
unknown at the outset, passing in empty vectors of the appropriate type (`Vector{Ti}()`
and `Vector{Tv}()` respectively) suffices, or calling the `sparse!` method
neglecting `cscrowval` and `cscnzval`.
On return, `csrrowptr`, `csrcolval`, and `csrnzval` contain an unsorted-column
representation of the result's transpose.
You may reuse the input arrays' storage (`I`, `J`, `V`) for the output arrays
(`csccolptr`, `cscrowval`, `cscnzval`). For example, you may call
`sparse!(I, J, V, csrrowptr, csrcolval, csrnzval, I, J, V)`.
For the sake of efficiency, this method performs no argument checking beyond
`1 <= I[k] <= m` and `1 <= J[k] <= n`. Use with care. Testing with `--check-bounds=yes`
is wise.
This method runs in `O(m, n, length(I))` time. The HALFPERM algorithm described in
F. Gustavson, "Two fast algorithms for sparse matrices: multiplication and permuted
transposition," ACM TOMS 4(3), 250-269 (1978) inspired this method's use of a pair of
counting sorts.
"""
function sparse!{Tv,Ti<:Integer}(I::AbstractVector{Ti}, J::AbstractVector{Ti},
V::AbstractVector{Tv}, m::Integer, n::Integer, combine, klasttouch::Vector{Ti},
csrrowptr::Vector{Ti}, csrcolval::Vector{Ti}, csrnzval::Vector{Tv},
csccolptr::Vector{Ti}, cscrowval::Vector{Ti}, cscnzval::Vector{Tv} )
# Compute the CSR form's row counts and store them shifted forward by one in csrrowptr
fill!(csrrowptr, 0)
coolen = length(I)
@inbounds for k in 1:coolen
Ik = I[k]
if 1 > Ik || m < Ik
throw(ArgumentError("row indices I[k] must satisfy 1 <= I[k] <= m"))
end
csrrowptr[Ik+1] += 1
end
# Compute the CSR form's rowptrs and store them shifted forward by one in csrrowptr
countsum = 1
csrrowptr[1] = 1
@inbounds for i in 2:(m+1)
overwritten = csrrowptr[i]
csrrowptr[i] = countsum
countsum += overwritten
end
# Counting-sort the column and nonzero values from J and V into csrcolval and csrnzval
# Tracking write positions in csrrowptr corrects the row pointers
@inbounds for k in 1:coolen
Ik, Jk = I[k], J[k]
if 1 > Jk || n < Jk
throw(ArgumentError("column indices J[k] must satisfy 1 <= J[k] <= n"))
end
csrk = csrrowptr[Ik+1]
csrrowptr[Ik+1] = csrk+1
csrcolval[csrk] = Jk
csrnzval[csrk] = V[k]
end
# This completes the unsorted-row, has-repeats CSR form's construction
# Sweep through the CSR form, simultaneously (1) caculating the CSC form's column
# counts and storing them shifted forward by one in csccolptr; (2) detecting repeated
# entries; and (3) repacking the CSR form with the repeated entries combined.
#
# Minimizing extraneous communication and nonlocality of reference, primarily by using
# only a single auxiliary array in this step, is the key to this method's performance.
fill!(csccolptr, 0)
fill!(klasttouch, 0)
writek = 1
newcsrrowptri = 1
origcsrrowptri = 1
origcsrrowptrip1 = csrrowptr[2]
@inbounds for i in 1:m
for readk in origcsrrowptri:(origcsrrowptrip1-1)
j = csrcolval[readk]
if klasttouch[j] < newcsrrowptri
klasttouch[j] = writek
if writek != readk
csrcolval[writek] = j
csrnzval[writek] = csrnzval[readk]
end
writek += 1
csccolptr[j+1] += 1
else
klt = klasttouch[j]
csrnzval[klt] = combine(csrnzval[klt], csrnzval[readk])
end
end
newcsrrowptri = writek
origcsrrowptri = origcsrrowptrip1
origcsrrowptrip1 != writek && (csrrowptr[i+1] = writek)
i < m && (origcsrrowptrip1 = csrrowptr[i+2])
end
# Compute the CSC form's colptrs and store them shifted forward by one in csccolptr
countsum = 1
csccolptr[1] = 1
@inbounds for j in 2:(n+1)
overwritten = csccolptr[j]
csccolptr[j] = countsum
countsum += overwritten
end
# Now knowing the CSC form's entry count, resize cscrowval and cscnzval if necessary
cscnnz = countsum - 1
length(cscrowval) < cscnnz && resize!(cscrowval, cscnnz)
length(cscnzval) < cscnnz && resize!(cscnzval, cscnnz)
# Finally counting-sort the row and nonzero values from the CSR form into cscrowval and
# cscnzval. Tracking write positions in csccolptr corrects the column pointers.
@inbounds for i in 1:m
for csrk in csrrowptr[i]:(csrrowptr[i+1]-1)
j = csrcolval[csrk]
x = csrnzval[csrk]
csck = csccolptr[j+1]
csccolptr[j+1] = csck+1
cscrowval[csck] = i
cscnzval[csck] = x
end
end
SparseMatrixCSC(m, n, csccolptr, cscrowval, cscnzval)
end
function sparse!{Tv,Ti<:Integer}(I::AbstractVector{Ti}, J::AbstractVector{Ti},
V::AbstractVector{Tv}, m::Integer, n::Integer, combine, klasttouch::Vector{Ti},
csrrowptr::Vector{Ti}, csrcolval::Vector{Ti}, csrnzval::Vector{Tv},
csccolptr::Vector{Ti} )
sparse!(I, J, V, m, n, combine, klasttouch,
csrrowptr, csrcolval, csrnzval,
csccolptr, Vector{Ti}(), Vector{Tv}() )
end
function sparse!{Tv,Ti<:Integer}(I::AbstractVector{Ti}, J::AbstractVector{Ti},
V::AbstractVector{Tv}, m::Integer, n::Integer, combine, klasttouch::Vector{Ti},
csrrowptr::Vector{Ti}, csrcolval::Vector{Ti}, csrnzval::Vector{Tv} )
sparse!(I, J, V, m, n, combine, klasttouch,
csrrowptr, csrcolval, csrnzval,
Vector{Ti}(n+1), Vector{Ti}(), Vector{Tv}() )
end
dimlub(I) = isempty(I) ? 0 : Int(maximum(I)) #least upper bound on required sparse matrix dimension
sparse(I,J,v::Number) = sparse(I, J, fill(v,length(I)))
sparse(I,J,V::AbstractVector) = sparse(I, J, V, dimlub(I), dimlub(J))
sparse(I,J,v::Number,m,n) = sparse(I, J, fill(v,length(I)), Int(m), Int(n))
sparse(I,J,V::AbstractVector,m,n) = sparse(I, J, V, Int(m), Int(n), +)
sparse(I,J,V::AbstractVector{Bool},m,n) = sparse(I, J, V, Int(m), Int(n), |)
sparse(I,J,v::Number,m,n,combine::Function) = sparse(I, J, fill(v,length(I)), Int(m), Int(n), combine)
function sparse(T::SymTridiagonal)
m = length(T.dv)
return sparse([1:m;2:m;1:m-1],[1:m;1:m-1;2:m],[T.dv;T.ev;T.ev], Int(m), Int(m))
end
function sparse(T::Tridiagonal)
m = length(T.d)
return sparse([1:m;2:m;1:m-1],[1:m;1:m-1;2:m],[T.d;T.dl;T.du], Int(m), Int(m))
end
function sparse(B::Bidiagonal)
m = length(B.dv)
B.isupper || return sparse([1:m;2:m],[1:m;1:m-1],[B.dv;B.ev], Int(m), Int(m)) # lower bidiagonal
return sparse([1:m;1:m-1],[1:m;2:m],[B.dv;B.ev], Int(m), Int(m)) # upper bidiagonal
end
## Transposition and permutation methods
"""
halfperm!{Tv,Ti,Tq<:Integer}(X::SparseMatrixCSC{Tv,Ti}, A::SparseMatrixCSC{Tv,Ti},
q::AbstractVector{Tq}, f::Function = identity)
Column-permute and transpose `A`, simultaneously applying `f` to each entry of `A`, storing
the result `(f(A)Q)^T` (`map(f, transpose(A[:,q]))`) in `X`.
`X`'s dimensions must match those of `transpose(A)` (`X.m == A.n` and `X.n == A.m`), and `X`
must have enough storage to accommodate all allocated entries in `A` (`length(X.rowval) >= nnz(A)`
and `length(X.nzval) >= nnz(A)`). Column-permutation `q`'s length must match `A`'s column
count (`length(q) == A.n`).
This method is the parent of several methods performing transposition and permutation
operations on `SparseMatrixCSC`s. As this method performs no argument checking, prefer
the safer child methods (`[c]transpose[!]`, `permute[!]`) to direct use.
This method implements the `HALFPERM` algorithm described in F. Gustavson, "Two fast
algorithms for sparse matrices: multiplication and permuted transposition," ACM TOMS 4(3),
250-269 (1978). The algorithm runs in `O(A.m, A.n, nnz(A))` time and requires no space
beyond that passed in.
"""
function halfperm!{Tv,Ti,Tq<:Integer}(X::SparseMatrixCSC{Tv,Ti}, A::SparseMatrixCSC{Tv,Ti},
q::AbstractVector{Tq}, f::Function = identity)
_computecolptrs_halfperm!(X, A)
_distributevals_halfperm!(X, A, q, f)
return X
end
"""
Helper method for `halfperm!`. Computes `transpose(A[:,q])`'s column pointers, storing them
shifted one position forward in `X.colptr`; `_distributevals_halfperm!` fixes this shift.
"""
function _computecolptrs_halfperm!{Tv,Ti}(X::SparseMatrixCSC{Tv,Ti}, A::SparseMatrixCSC{Tv,Ti})
# Compute `transpose(A[:,q])`'s column counts. Store shifted forward one position in X.colptr.
fill!(X.colptr, 0)
@inbounds for k in 1:nnz(A)
X.colptr[A.rowval[k] + 1] += 1
end
# Compute `transpose(A[:,q])`'s column pointers. Store shifted forward one position in X.colptr.
X.colptr[1] = 1
countsum = 1
@inbounds for k in 2:(A.m + 1)
overwritten = X.colptr[k]
X.colptr[k] = countsum
countsum += overwritten
end
end
"""
Helper method for `halfperm!`. With `transpose(A[:,q])`'s column pointers shifted one
position forward in `X.colptr`, computes `map(f, transpose(A[:,q]))` by appropriately
distributing `A.rowval` and `f`-transformed `A.nzval` into `X.rowval` and `X.nzval`
respectively. Simultaneously fixes the one-position-forward shift in `X.colptr`.
"""
function _distributevals_halfperm!{Tv,Ti,Tq<:Integer}(X::SparseMatrixCSC{Tv,Ti},
A::SparseMatrixCSC{Tv,Ti}, q::AbstractVector{Tq}, f::Function)
@inbounds for Xi in 1:A.n
Aj = q[Xi]
for Ak in nzrange(A, Aj)
Ai = A.rowval[Ak]
Xk = X.colptr[Ai + 1]
X.rowval[Xk] = Xi
X.nzval[Xk] = f(A.nzval[Ak])
X.colptr[Ai + 1] += 1
end
end
return # kill potential type instability
end
function ftranspose!{Tv,Ti}(X::SparseMatrixCSC{Tv,Ti}, A::SparseMatrixCSC{Tv,Ti}, f::Function)
# Check compatibility of source argument A and destination argument X
if X.n != A.m
throw(DimensionMismatch(string("destination argument `X`'s column count, ",
"`X.n (= $(X.n))`, must match source argument `A`'s row count, `A.m (= $(A.m))`")))
elseif X.m != A.n
throw(DimensionMismatch(string("destination argument `X`'s row count,
`X.m (= $(X.m))`, must match source argument `A`'s column count, `A.n (= $(A.n))`")))
elseif length(X.rowval) < nnz(A)
throw(ArgumentError(string("the length of destination argument `X`'s `rowval` ",
"array, `length(X.rowval) (= $(length(X.rowval)))`, must be greater than or ",
"equal to source argument `A`'s allocated entry count, `nnz(A) (= $(nnz(A)))`")))
elseif length(X.nzval) < nnz(A)
throw(ArgumentError(string("the length of destination argument `X`'s `nzval` ",
"array, `length(X.nzval) (= $(length(X.nzval)))`, must be greater than or ",
"equal to source argument `A`'s allocated entry count, `nnz(A) (= $(nnz(A)))`")))
end
halfperm!(X, A, 1:A.n, f)
end
transpose!{Tv,Ti}(X::SparseMatrixCSC{Tv,Ti}, A::SparseMatrixCSC{Tv,Ti}) = ftranspose!(X, A, identity)
ctranspose!{Tv,Ti}(X::SparseMatrixCSC{Tv,Ti}, A::SparseMatrixCSC{Tv,Ti}) = ftranspose!(X, A, conj)
function ftranspose{Tv,Ti}(A::SparseMatrixCSC{Tv,Ti}, f::Function)
X = SparseMatrixCSC(A.n, A.m, Vector{Ti}(A.m+1), Vector{Ti}(nnz(A)), Vector{Tv}(nnz(A)))
halfperm!(X, A, 1:A.n, f)
end
transpose{Tv,Ti}(A::SparseMatrixCSC{Tv,Ti}) = ftranspose(A, identity)
ctranspose{Tv,Ti}(A::SparseMatrixCSC{Tv,Ti}) = ftranspose(A, conj)
"""
unchecked_noalias_permute!{Tv,Ti,Tp<:Integer,Tq<:Integer}(X::SparseMatrixCSC{Tv,Ti},
A::SparseMatrixCSC{Tv,Ti}, p::AbstractVector{Tp}, q::AbstractVector{Tq},
C::SparseMatrixCSC{Tv,Ti})
See [`permute!`](:func:`Base.SparseArrays.permute!`) for basic usage. Parent of `permute[!]`
methods operating on `SparseMatrixCSC`s that assume none of `X`, `A`, and `C` alias each
other. As this method performs no argument checking, prefer the safer child methods
(`permute[!]`) to direct use.
This method consists of two major steps: (1) Column-permute (`Q`,`I[:,q]`) and transpose `A`
to generate intermediate result `(AQ)^T` (`transpose(A[:,q])`) in `C`. (2) Column-permute
(`P^T`, I[:,p]) and transpose intermediate result `(AQ)^T` to generate result
`((AQ)^T P^T)^T = PAQ` (`A[p,q]`) in `X`.
The first step is a call to `halfperm!`, and the second is a variant on `halfperm!` that
avoids an unnecessary length-`nnz(A)` array-sweep and associated recomputation of column
pointers. See [`halfperm!`](:func:Base.SparseArrays.halfperm!) for additional algorithmic
information.
See also: [`unchecked_aliasing_permute!`](:func:`Base.SparseArrays.unchecked_aliasing_permute!`)
"""
function unchecked_noalias_permute!{Tv,Ti,Tp<:Integer,Tq<:Integer}(X::SparseMatrixCSC{Tv,Ti},
A::SparseMatrixCSC{Tv,Ti}, p::AbstractVector{Tp}, q::AbstractVector{Tq},
C::SparseMatrixCSC{Tv,Ti})
halfperm!(C, A, q)
_computecolptrs_permute!(X, A, q, X.colptr)
_distributevals_halfperm!(X, C, p, identity)
return X
end
"""
unchecked_aliasing_permute!{Tv,Ti,Tp<:Integer,Tq<:Integer}(
A::SparseMatrixCSC{Tv,Ti}, p::AbstractVector{Tp}, q::AbstractVector{Tq},
C::SparseMatrixCSC{Tv,Ti}, workcolptr::Vector{Ti})
See [`permute!`](:func:`Base.SparseArrays.permute!`) for basic usage. Parent of `permute!`
methods operating on `SparseMatrixCSC`s where the source and destination matrices are the
same. See [`unchecked_noalias_permute!`](:func:`Base.SparseArrays.unchecked_noalias_permute`)
for additional information; these methods are identical but for this method's requirement of
the additional `workcolptr`, `length(workcolptr) >= A.n + 1`, which enables efficient
handling of the source-destination aliasing.
"""
function unchecked_aliasing_permute!{Tv,Ti,Tp<:Integer,Tq<:Integer}(
A::SparseMatrixCSC{Tv,Ti}, p::AbstractVector{Tp}, q::AbstractVector{Tq},
C::SparseMatrixCSC{Tv,Ti}, workcolptr::Vector{Ti})
halfperm!(C, A, q)
_computecolptrs_permute!(A, A, q, workcolptr)
_distributevals_halfperm!(A, C, p, identity)
return A
end
"""
Helper method for `unchecked_noalias_permute!` and `unchecked_aliasing_permute!`.
Computes `PAQ`'s column pointers, storing them shifted one position forward in `X.colptr`;
`_distributevals_halfperm!` fixes this shift. Saves some work relative to
`_computecolptrs_halfperm!` as described in `uncheckednoalias_permute!`'s documentation.
"""
function _computecolptrs_permute!{Tv,Ti,Tq<:Integer}(X::SparseMatrixCSC{Tv,Ti},
A::SparseMatrixCSC{Tv,Ti}, q::AbstractVector{Tq}, workcolptr::Vector{Ti})
# Compute `A[p,q]`'s column counts. Store shifted forward one position in workcolptr.
@inbounds for k in 1:A.n
workcolptr[k+1] = A.colptr[q[k] + 1] - A.colptr[q[k]]
end
# Compute `A[p,q]`'s column pointers. Store shifted forward one position in X.colptr.
X.colptr[1] = 1
countsum = 1
@inbounds for k in 2:(X.n + 1)
overwritten = workcolptr[k]
X.colptr[k] = countsum
countsum += overwritten
end
end
"""
Helper method for `permute` and `permute!` methods operating on `SparseMatrixCSC`s.
Checks compatibility of source argument `A`, row-permutation argument `p`, and
column-permutation argument `q`.
"""
function _checkargs_sourcecompatperms_permute!{Tv,Ti,Tp<:Integer,Tq<:Integer}(
A::SparseMatrixCSC{Tv,Ti}, p::AbstractVector{Tp}, q::AbstractVector{Tq})
if length(q) != A.n
throw(DimensionMismatch(string("the length of column-permutation argument `q`, ",
"`length(q) (= $(length(q)))`, must match source argument `A`'s column ",
"count, `A.n (= $(A.n))`")))
elseif length(p) != A.m
throw(DimensionMismatch(string("the length of row-permutation argument `p`, ",
"`length(p) (= $(length(p)))`, must match source argument `A`'s row count, ",
"`A.m (= $(A.m))`")))
end
end
"""
Helper method for `permute` and `permute!` methods operating on `SparseMatrixCSC`s.
Checks whether row- and column- permutation arguments `p` and `q` are valid permutations.
"""
function _checkargs_permutationsvalid_permute!{Ti<:Integer,Tp<:Integer,Tq<:Integer}(
p::AbstractVector{Tp}, pcheckspace::Vector{Ti},
q::AbstractVector{Tq}, qcheckspace::Vector{Ti})
if !_ispermutationvalid_permute!(p, pcheckspace)
throw(ArgumentError("row-permutation argument `p` must be a valid permutation"))
elseif !_ispermutationvalid_permute!(q, qcheckspace)
throw(ArgumentError("column-permutation argument `q` must be a valid permutation"))
end
end
function _ispermutationvalid_permute!{Ti<:Integer,Tp<:Integer}(perm::AbstractVector{Tp},
checkspace::Vector{Ti})
n = length(perm)
checkspace[1:n] = 0
for k in perm
(0 < k <= n) && ((checkspace[k] $= 1) == 1) || return false
end
return true
end
"""
Helper method for `permute` and `permute!` methods operating on `SparseMatrixCSC`s.
Checks compatibility of source argument `A` and destination argument `X`.
"""
function _checkargs_sourcecompatdest_permute!{Tv,Ti}(A::SparseMatrixCSC{Tv,Ti},
X::SparseMatrixCSC{Tv,Ti})
if X.m != A.m
throw(DimensionMismatch(string("destination argument `X`'s row count, ",
"`X.m (= $(X.m))`, must match source argument `A`'s row count, `A.m (= $(A.m))`")))
elseif X.n != A.n
throw(DimensionMismatch(string("destination argument `X`'s column count, ",
"`X.n (= $(X.n))`, must match source argument `A`'s column count, `A.n (= $(A.n))`")))
elseif length(X.rowval) < nnz(A)
throw(ArgumentError(string("the length of destination argument `X`'s `rowval` ",
"array, `length(X.rowval) (= $(length(X.rowval)))`, must be greater than or ",
"equal to source argument `A`'s allocated entry count, `nnz(A) (= $(nnz(A)))`")))
elseif length(X.nzval) < nnz(A)
throw(ArgumentError(string("the length of destination argument `X`'s `nzval` ",
"array, `length(X.nzval) (= $(length(X.nzval)))`, must be greater than or ",
"equal to source argument `A`'s allocated entry count, `nnz(A) (= $(nnz(A)))`")))
end
end
"""
Helper method for `permute` and `permute!` methods operating on `SparseMatrixCSC`s.
Checks compatibility of source argument `A` and intermediate result argument `C`.
"""
function _checkargs_sourcecompatworkmat_permute!{Tv,Ti}(A::SparseMatrixCSC{Tv,Ti},
C::SparseMatrixCSC{Tv,Ti})
if C.n != A.m
throw(DimensionMismatch(string("intermediate result argument `C`'s column count, ",
"`C.n (= $(C.n))`, must match source argument `A`'s row count, `A.m (= $(A.m))`")))
elseif C.m != A.n
throw(DimensionMismatch(string("intermediate result argument `C`'s row count, ",
"`C.m (= $(C.m))`, must match source argument `A`'s column count, `A.n (= $(A.n))`")))
elseif length(C.rowval) < nnz(A)
throw(ArgumentError(string("the length of intermediate result argument `C`'s ",
"`rowval` array, `length(C.rowval) (= $(length(C.rowval)))`, must be greater than ",
"or equal to source argument `A`'s allocated entry count, `nnz(A) (= $(nnz(A)))`")))
elseif length(C.nzval) < nnz(A)
throw(ArgumentError(string("the length of intermediate result argument `C`'s ",
"`rowval` array, `length(C.nzval) (= $(length(C.nzval)))`, must be greater than ",
"or equal to source argument `A`'s allocated entry count, `nnz(A)` (= $(nnz(A)))")))
end
end
"""
Helper method for `permute` and `permute!` methods operating on `SparseMatrixCSC`s.
Checks compatibility of source argument `A` and workspace argument `workcolptr`.
"""
function _checkargs_sourcecompatworkcolptr_permute!{Tv,Ti}(A::SparseMatrixCSC{Tv,Ti},
workcolptr::Vector{Ti})
if length(workcolptr) <= A.n
throw(DimensionMismatch(string("argument `workcolptr`'s length, ",
"`length(workcolptr) (= $(length(workcolptr)))`, must exceed source argument ",
"`A`'s column count, `A.n (= $(A.n))`")))
end
end
"""
permute!{Tv,Ti,Tp<:Integer,Tq<:Integer}(X::SparseMatrixCSC{Tv,Ti}, A::SparseMatrixCSC{Tv,Ti},
p::AbstractVector{Tp}, q::AbstractVector{Tq}[, C::SparseMatrixCSC{Tv,Ti}])
Bilaterally permute `A`, storing result `PAQ` (`A[p,q]`) in `X`. Stores intermediate result
`(AQ)^T` (`transpose(A[:,q])`) in optional argument `C` if present. Requires that none of
`X`, `A`, and, if present, `C` alias each other; to store result `PAQ` back into `A`, use
the following method lacking `X`:
permute!{Tv,Ti,Tp<:Integer,Tq<:Integer}(A::SparseMatrixCSC{Tv,Ti}, p::AbstractVector{Tp},
q::AbstractVector{Tq}[, C::SparseMatrixCSC{Tv,Ti}[, workcolptr::Vector{Ti}]])
`X`'s dimensions must match those of `A` (`X.m == A.m` and `X.n == A.n`), and `X` must
have enough storage to accommodate all allocated entries in `A` (`length(X.rowval) >= nnz(A)`
and `length(X.nzval) >= nnz(A)`). Column-permutation `q`'s length must match `A`'s column
count (`length(q) == A.n`). Row-permutation `p`'s length must match `A`'s row count
(`length(p) == A.m`).
`C`'s dimensions must match those of `transpose(A)` (`C.m == A.n` and `C.n == A.m`), and `C`
must have enough storage to accommodate all allocated entries in `A` (`length(C.rowval)` >= nnz(A)`
and `length(C.nzval) >= nnz(A)`).
For additional (algorithmic) information, and for versions of these methods that forgo
argument checking, see (unexported) parent methods [`unchecked_noalias_permute!`](:func:`Base.SparseArrays.unchecked_noalias_permute!`)
and [`unchecked_aliasing_permute!`](:func:`Base.SparseArrays.unchecked_aliasing_permute!`).
See also: [`permute`](:func:`Base.SparseArrays.permute`)
"""
function permute!{Tv,Ti,Tp<:Integer,Tq<:Integer}(X::SparseMatrixCSC{Tv,Ti},
A::SparseMatrixCSC{Tv,Ti}, p::AbstractVector{Tp}, q::AbstractVector{Tq})
_checkargs_sourcecompatdest_permute!(A, X)
_checkargs_sourcecompatperms_permute!(A, p, q)
C = SparseMatrixCSC(A.n, A.m, Vector{Ti}(A.m + 1), Vector{Ti}(nnz(A)), Vector{Tv}(nnz(A)))
_checkargs_permutationsvalid_permute!(p, C.colptr, q, X.colptr)
unchecked_noalias_permute!(X, A, p, q, C)
end
function permute!{Tv,Ti,Tp<:Integer,Tq<:Integer}(X::SparseMatrixCSC{Tv,Ti},
A::SparseMatrixCSC{Tv,Ti}, p::AbstractVector{Tp}, q::AbstractVector{Tq},
C::SparseMatrixCSC{Tv,Ti})
_checkargs_sourcecompatdest_permute!(A, X)
_checkargs_sourcecompatperms_permute!(A, p, q)
_checkargs_sourcecompatworkmat_permute!(A, C)
_checkargs_permutationsvalid_permute!(p, C.colptr, q, X.colptr)
unchecked_noalias_permute!(X, A, p, q, C)
end
function permute!{Tv,Ti,Tp<:Integer,Tq<:Integer}(A::SparseMatrixCSC{Tv,Ti},
p::AbstractVector{Tp}, q::AbstractVector{Tq})
_checkargs_sourcecompatperms_permute!(A, p, q)
C = SparseMatrixCSC(A.n, A.m, Vector{Ti}(A.m + 1), Vector{Ti}(nnz(A)), Vector{Tv}(nnz(A)))
workcolptr = Vector{Ti}(A.n + 1)
_checkargs_permutationsvalid_permute!(p, C.colptr, q, workcolptr)
unchecked_aliasing_permute!(A, p, q, C, workcolptr)
end
function permute!{Tv,Ti,Tp<:Integer,Tq<:Integer}(A::SparseMatrixCSC{Tv,Ti},
p::AbstractVector{Tp}, q::AbstractVector{Tq}, C::SparseMatrixCSC{Tv,Ti})
_checkargs_sourcecompatperms_permute!(A, p, q)
_checkargs_sourcecompatworkmat_permute!(A, C)
workcolptr = Vector{Ti}(A.n + 1)
_checkargs_permutationsvalid_permute!(p, C.colptr, q, workcolptr)
unchecked_aliasing_permute!(A, p, q, C, workcolptr)
end
function permute!{Tv,Ti,Tp<:Integer,Tq<:Integer}(A::SparseMatrixCSC{Tv,Ti},
p::AbstractVector{Tp}, q::AbstractVector{Tq}, C::SparseMatrixCSC{Tv,Ti},
workcolptr::Vector{Ti})
_checkargs_sourcecompatperms_permute!(A, p, q)
_checkargs_sourcecompatworkmat_permute!(A, C)
_checkargs_sourcecompatworkcolptr_permute!(A, workcolptr)
_checkargs_permutationsvalid_permute!(p, C.colptr, q, workcolptr)
unchecked_aliasing_permute!(A, p, q, C, workcolptr)
end
"""
permute{Tv,Ti,Tp<:Integer,Tq<:Integer}(A::SparseMatrixCSC{Tv,Ti}, p::AbstractVector{Tp},
q::AbstractVector{Tq})
Bilaterally permute `A`, returning `PAQ` (`A[p,q]`). Column-permutation `q`'s length must
match `A`'s column count (`length(q) == A.n`). Row-permutation `p`'s length must match `A`'s
row count (`length(p) == A.m`).
For expert drivers and additional information, see [`permute!`](:func:`Base.SparseArrays.permute!`).
"""
function permute{Tv,Ti,Tp<:Integer,Tq<:Integer}(A::SparseMatrixCSC{Tv,Ti},
p::AbstractVector{Tp}, q::AbstractVector{Tq})
_checkargs_sourcecompatperms_permute!(A, p, q)
X = SparseMatrixCSC(A.m, A.n, Vector{Ti}(A.n + 1), Vector{Ti}(nnz(A)), Vector{Tv}(nnz(A)))
C = SparseMatrixCSC(A.n, A.m, Vector{Ti}(A.m + 1), Vector{Ti}(nnz(A)), Vector{Tv}(nnz(A)))
_checkargs_permutationsvalid_permute!(p, C.colptr, q, X.colptr)
unchecked_noalias_permute!(X, A, p, q, C)
end
## fkeep! and children tril!, triu!, droptol!, dropzeros[!]
"""
fkeep!(A::AbstractSparseArray, f, trim::Bool = true)
Keep elements of `A` for which test `f` returns `true`. `f`'s signature should be
f(i::Integer, [j::Integer,] x) -> Bool
where `i` and `j` are an element's row and column indices and `x` is the element's
value. This method makes a single sweep
through `A`, requiring `O(A.n, nnz(A))`-time for matrices and `O(nnz(A))`-time for vectors
and no space beyond that passed in. If `trim` is `true`, this method trims `A.rowval` or `A.nzind` and
`A.nzval` to length `nnz(A)` after dropping elements.
"""
function fkeep!(A::SparseMatrixCSC, f, trim::Bool = true)
An = A.n
Acolptr = A.colptr
Arowval = A.rowval
Anzval = A.nzval
# Sweep through columns, rewriting kept elements in their new positions
# and updating the column pointers accordingly as we go.