This package provides the CenteredSparseCSC
type. It assumes that you want to
re-center a sparse matrix based on the mean of each column. However, you can
supply a custom centered value for each column. There are no methods for other
forms of centering (e.g. the rows of the matrix). Currently only sparse-dense
multiply and conjugate-multiply are implemented, with just enough indexing to
make the display of the matrix work in a reasonable manner. That said, using
the type is easy:
#Pkg.clone("git@github.com:jsams/CenteredSparseMatrix.git")
using CenteredSparseMatrix
X = sprand(10, 3, 0.6)
X_cent_sparse = CenteredSparseCSC(X)
X_cent_dense = full(X) .- mean(X, 1)
y = rand(3)
Y = rand(3, 5)
z = rand(10)
Z = rand(10, 4)
isapprox(X_cent_sparse * y, X_cent_dense * y)
isapprox(X_cent_sparse * Y, X_cent_dense * Y)
isapprox(X_cent_sparse' * z, X_cent_dense' * z)
isapprox(X_cent_sparse' * Z, X_cent_dense' * Z)
The key point is that the sparsity structure of the matrix is left unchanged, the centering of the zero-elements is done on-demand, and where possible, algorithms take advantage of knowing the column-constant mean value.
For the matrix multiplications X_cent_sparse * Y
and X_cent_sparse' * Z
,
there is minimal overhead compared to the plain sparse multiplications X * Y
and X' * Z
, requiring only an extra dense vector-matrix multiply and
subtraction. How?
Let A
be an n
xm
sparse matrix and Ac
be the the matrix that results
from subtracting the column means of A
from A
. To be precise, let M
be a
the column vector of A
's column means, and O
a column vector of n
1
's.
Ac := A - O * M'
Ac * X = (A - O * M') * X
= A * X - O * M' * X
i.e. we can just perform the usual sparse matrix multiplication of A * X
and
then do a vector-matrix multiply of M' * X
and broadcast that to the rows of
the result. Thus, the only extra information besides the original sparse matrix
that we need are the matrix column means.
Using Int64 value types is not advised.
list generated by methodswith(SparseMatrixCSC)
. I guess the target should be
to be equivalent to that? But note, I've implemented what I needed to get my
work done, if you need more, pull requests are welcome. :)
A_mul_B!(y::Union{DenseArray{Ty,1}, Base.ReinterpretArray{Ty,1,S,A} where S, Base.ReshapedArray{Ty,1,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray}, SubArray{Ty,1,A,I,L} where L} where I<:Tuple{Vararg{Union{Int64, AbstractRange{Int64}, Base.AbstractCartesianIndex},N} where N} where A<:Union{Base.ReshapedArray{T,N,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray} where N where T, DenseArray}, A::SparseMatrixCSC, x::AbstractSparseArray{Tx,Ti,1} where Ti) where {Tx, Ty} in Base.SparseArrays at sparse/sparsevector.jl:1642
A_mul_B!(C::Union{Union{DenseArray{T,1}, Base.ReinterpretArray{T,1,S,A} where S, Base.ReshapedArray{T,1,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray}, SubArray{T,1,A,I,L} where L} where I<:Tuple{Vararg{Union{Int64, AbstractRange{Int64}, Base.AbstractCartesianIndex},N} where N} where A<:Union{Base.ReshapedArray{T,N,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray} where N where T, DenseArray}, Union{DenseArray{T,2}, Base.ReinterpretArray{T,2,S,A} where S, Base.ReshapedArray{T,2,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray}, SubArray{T,2,A,I,L} where L} where I<:Tuple{Vararg{Union{Int64, AbstractRange{Int64}, Base.AbstractCartesianIndex},N} where N} where A<:Union{Base.ReshapedArray{T,N,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray} where N where T, DenseArray}} where T, A::SparseMatrixCSC, B::Union{Union{DenseArray{T,1}, Base.ReinterpretArray{T,1,S,A} where S, Base.ReshapedArray{T,1,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray}, SubArray{T,1,A,I,L} where L} where I<:Tuple{Vararg{Union{Int64, AbstractRange{Int64}, Base.AbstractCartesianIndex},N} where N} where A<:Union{Base.ReshapedArray{T,N,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray} where N where T, DenseArray}, Union{DenseArray{T,2}, Base.ReinterpretArray{T,2,S,A} where S, Base.ReshapedArray{T,2,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray}, SubArray{T,2,A,I,L} where L} where I<:Tuple{Vararg{Union{Int64, AbstractRange{Int64}, Base.AbstractCartesianIndex},N} where N} where A<:Union{Base.ReshapedArray{T,N,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray} where N where T, DenseArray}} where T) in Base.SparseArrays at sparse/linalg.jl:96
Ac_mul_B!(y::Union{DenseArray{Ty,1}, Base.ReinterpretArray{Ty,1,S,A} where S, Base.ReshapedArray{Ty,1,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray}, SubArray{Ty,1,A,I,L} where L} where I<:Tuple{Vararg{Union{Int64, AbstractRange{Int64}, Base.AbstractCartesianIndex},N} where N} where A<:Union{Base.ReshapedArray{T,N,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray} where N where T, DenseArray}, A::SparseMatrixCSC, x::AbstractSparseArray{Tx,Ti,1} where Ti) where {Tx, Ty} in Base.SparseArrays at sparse/sparsevector.jl:1681
Ac_mul_B!(C::Union{Union{DenseArray{T,1}, Base.ReinterpretArray{T,1,S,A} where S, Base.ReshapedArray{T,1,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray}, SubArray{T,1,A,I,L} where L} where I<:Tuple{Vararg{Union{Int64, AbstractRange{Int64}, Base.AbstractCartesianIndex},N} where N} where A<:Union{Base.ReshapedArray{T,N,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray} where N where T, DenseArray}, Union{DenseArray{T,2}, Base.ReinterpretArray{T,2,S,A} where S, Base.ReshapedArray{T,2,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray}, SubArray{T,2,A,I,L} where L} where I<:Tuple{Vararg{Union{Int64, AbstractRange{Int64}, Base.AbstractCartesianIndex},N} where N} where A<:Union{Base.ReshapedArray{T,N,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray} where N where T, DenseArray}} where T, A::SparseMatrixCSC, B::Union{Union{DenseArray{T,1}, Base.ReinterpretArray{T,1,S,A} where S, Base.ReshapedArray{T,1,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray}, SubArray{T,1,A,I,L} where L} where I<:Tuple{Vararg{Union{Int64, AbstractRange{Int64}, Base.AbstractCartesianIndex},N} where N} where A<:Union{Base.ReshapedArray{T,N,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray} where N where T, DenseArray}, Union{DenseArray{T,2}, Base.ReinterpretArray{T,2,S,A} where S, Base.ReshapedArray{T,2,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray}, SubArray{T,2,A,I,L} where L} where I<:Tuple{Vararg{Union{Int64, AbstractRange{Int64}, Base.AbstractCartesianIndex},N} where N} where A<:Union{Base.ReshapedArray{T,N,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray} where N where T, DenseArray}} where T) in Base.SparseArrays at sparse/linalg.jl:97
At_mul_B!(y::Union{DenseArray{Ty,1}, Base.ReinterpretArray{Ty,1,S,A} where S, Base.ReshapedArray{Ty,1,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray}, SubArray{Ty,1,A,I,L} where L} where I<:Tuple{Vararg{Union{Int64, AbstractRange{Int64}, Base.AbstractCartesianIndex},N} where N} where A<:Union{Base.ReshapedArray{T,N,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray} where N where T, DenseArray}, A::SparseMatrixCSC, x::AbstractSparseArray{Tx,Ti,1} where Ti) where {Tx, Ty} in Base.SparseArrays at sparse/sparsevector.jl:1675
At_mul_B!(C::Union{Union{DenseArray{T,1}, Base.ReinterpretArray{T,1,S,A} where S, Base.ReshapedArray{T,1,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray}, SubArray{T,1,A,I,L} where L} where I<:Tuple{Vararg{Union{Int64, AbstractRange{Int64}, Base.AbstractCartesianIndex},N} where N} where A<:Union{Base.ReshapedArray{T,N,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray} where N where T, DenseArray}, Union{DenseArray{T,2}, Base.ReinterpretArray{T,2,S,A} where S, Base.ReshapedArray{T,2,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray}, SubArray{T,2,A,I,L} where L} where I<:Tuple{Vararg{Union{Int64, AbstractRange{Int64}, Base.AbstractCartesianIndex},N} where N} where A<:Union{Base.ReshapedArray{T,N,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray} where N where T, DenseArray}} where T, A::SparseMatrixCSC, B::Union{Union{DenseArray{T,1}, Base.ReinterpretArray{T,1,S,A} where S, Base.ReshapedArray{T,1,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray}, SubArray{T,1,A,I,L} where L} where I<:Tuple{Vararg{Union{Int64, AbstractRange{Int64}, Base.AbstractCartesianIndex},N} where N} where A<:Union{Base.ReshapedArray{T,N,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray} where N where T, DenseArray}, Union{DenseArray{T,2}, Base.ReinterpretArray{T,2,S,A} where S, Base.ReshapedArray{T,2,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray}, SubArray{T,2,A,I,L} where L} where I<:Tuple{Vararg{Union{Int64, AbstractRange{Int64}, Base.AbstractCartesianIndex},N} where N} where A<:Union{Base.ReshapedArray{T,N,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray} where N where T, DenseArray}} where T) in Base.SparseArrays at sparse/linalg.jl:98
copy(S::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:265
full(S::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:365
getindex(A::SparseMatrixCSC{T,Ti} where Ti<:Integer, i0::Integer, i1::Integer) where T in Base.SparseArrays at sparse/sparsematrix.jl:1916
getindex(A::SparseMatrixCSC, ::Colon, ::Colon) in Base.SparseArrays at sparse/sparsematrix.jl:1925
getindex(A::SparseMatrixCSC, i::Integer, ::Colon) in Base.SparseArrays at sparse/sparsevector.jl:504
size(S::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:36
*(D::Diagonal, A::SparseMatrixCSC) in Base.SparseArrays at sparse/linalg.jl:114
*(A::SparseMatrixCSC, x::AbstractSparseArray{Tv,Ti,1} where Ti where Tv) in Base.SparseArrays at sparse/sparsevector.jl:1718
*(A::SparseMatrixCSC, D::Diagonal) in Base.SparseArrays at sparse/linalg.jl:118
+(A::Array, B::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:1571
+(A::SparseMatrixCSC, J::UniformScaling) in Base.SparseArrays at sparse/sparsematrix.jl:3599
+(A::SparseMatrixCSC, B::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:1567
+(A::SparseMatrixCSC, B::Array) in Base.SparseArrays at sparse/sparsematrix.jl:1570
-(A::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:1559
-(A::SparseMatrixCSC, J::UniformScaling) in Base.SparseArrays at sparse/sparsematrix.jl:3600
-(A::SparseMatrixCSC, B::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:1568
-(A::SparseMatrixCSC, B::Array) in Base.SparseArrays at sparse/sparsematrix.jl:1572
-(A::Array, B::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:1573
-(J::UniformScaling, A::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:3601
==(A1::SparseMatrixCSC, A2::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:1577
A_mul_B!(α::Number, A::SparseMatrixCSC, x::AbstractSparseArray{Tv,Ti,1} where Ti where Tv, β::Number, y::Union{DenseArray{T,1}, Base.ReinterpretArray{T,1,S,A} where S, Base.ReshapedArray{T,1,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray}, SubArray{T,1,A,I,L} where L} where I<:Tuple{Vararg{Union{Int64, AbstractRange{Int64}, Base.AbstractCartesianIndex},N} where N} where A<:Union{Base.ReshapedArray{T,N,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray} where N where T, DenseArray} where T) in Base.SparseArrays at sparse/sparsevector.jl:1646
A_mul_B!(α::Number, A::SparseMatrixCSC, B::Union{Union{DenseArray{T,1}, Base.ReinterpretArray{T,1,S,A} where S, Base.ReshapedArray{T,1,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray}, SubArray{T,1,A,I,L} where L} where I<:Tuple{Vararg{Union{Int64, AbstractRange{Int64}, Base.AbstractCartesianIndex},N} where N} where A<:Union{Base.ReshapedArray{T,N,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray} where N where T, DenseArray}, Union{DenseArray{T,2}, Base.ReinterpretArray{T,2,S,A} where S, Base.ReshapedArray{T,2,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray}, SubArray{T,2,A,I,L} where L} where I<:Tuple{Vararg{Union{Int64, AbstractRange{Int64}, Base.AbstractCartesianIndex},N} where N} where A<:Union{Base.ReshapedArray{T,N,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray} where N where T, DenseArray}} where T, β::Number, C::Union{Union{DenseArray{T,1}, Base.ReinterpretArray{T,1,S,A} where S, Base.ReshapedArray{T,1,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray}, SubArray{T,1,A,I,L} where L} where I<:Tuple{Vararg{Union{Int64, AbstractRange{Int64}, Base.AbstractCartesianIndex},N} where N} where A<:Union{Base.ReshapedArray{T,N,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray} where N where T, DenseArray}, Union{DenseArray{T,2}, Base.ReinterpretArray{T,2,S,A} where S, Base.ReshapedArray{T,2,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray}, SubArray{T,2,A,I,L} where L} where I<:Tuple{Vararg{Union{Int64, AbstractRange{Int64}, Base.AbstractCartesianIndex},N} where N} where A<:Union{Base.ReshapedArray{T,N,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray} where N where T, DenseArray}} where T) in Base.SparseArrays at sparse/linalg.jl:51
Ac_ldiv_B(::SparseMatrixCSC, ::RowVector) in Base.SparseArrays at sparse/linalg.jl:924
Ac_ldiv_B(A::SparseMatrixCSC, B::Union{AbstractArray{T,1}, AbstractArray{T,2}} where T) in Base.SparseArrays at sparse/linalg.jl:905
Ac_mul_B(A::SparseMatrixCSC, x::AbstractSparseArray{Tv,Ti,1} where Ti where Tv) in Base.SparseArrays at sparse/sparsevector.jl:1726
Ac_mul_B!(α::Number, A::SparseMatrixCSC, x::AbstractSparseArray{Tv,Ti,1} where Ti where Tv, β::Number, y::Union{DenseArray{T,1}, Base.ReinterpretArray{T,1,S,A} where S, Base.ReshapedArray{T,1,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray}, SubArray{T,1,A,I,L} where L} where I<:Tuple{Vararg{Union{Int64, AbstractRange{Int64}, Base.AbstractCartesianIndex},N} where N} where A<:Union{Base.ReshapedArray{T,N,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray} where N where T, DenseArray} where T) in Base.SparseArrays at sparse/sparsevector.jl:1684
Ac_mul_B!(α::Number, A::SparseMatrixCSC, B::Union{Union{DenseArray{T,1}, Base.ReinterpretArray{T,1,S,A} where S, Base.ReshapedArray{T,1,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray}, SubArray{T,1,A,I,L} where L} where I<:Tuple{Vararg{Union{Int64, AbstractRange{Int64}, Base.AbstractCartesianIndex},N} where N} where A<:Union{Base.ReshapedArray{T,N,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray} where N where T, DenseArray}, Union{DenseArray{T,2}, Base.ReinterpretArray{T,2,S,A} where S, Base.ReshapedArray{T,2,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray}, SubArray{T,2,A,I,L} where L} where I<:Tuple{Vararg{Union{Int64, AbstractRange{Int64}, Base.AbstractCartesianIndex},N} where N} where A<:Union{Base.ReshapedArray{T,N,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray} where N where T, DenseArray}} where T, β::Number, C::Union{Union{DenseArray{T,1}, Base.ReinterpretArray{T,1,S,A} where S, Base.ReshapedArray{T,1,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray}, SubArray{T,1,A,I,L} where L} where I<:Tuple{Vararg{Union{Int64, AbstractRange{Int64}, Base.AbstractCartesianIndex},N} where N} where A<:Union{Base.ReshapedArray{T,N,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray} where N where T, DenseArray}, Union{DenseArray{T,2}, Base.ReinterpretArray{T,2,S,A} where S, Base.ReshapedArray{T,2,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray}, SubArray{T,2,A,I,L} where L} where I<:Tuple{Vararg{Union{Int64, AbstractRange{Int64}, Base.AbstractCartesianIndex},N} where N} where A<:Union{Base.ReshapedArray{T,N,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray} where N where T, DenseArray}} where T) in Base.SparseArrays at sparse/linalg.jl:51
At_ldiv_B(::SparseMatrixCSC, ::RowVector) in Base.SparseArrays at sparse/linalg.jl:924
At_ldiv_B(A::SparseMatrixCSC, B::Union{AbstractArray{T,1}, AbstractArray{T,2}} where T) in Base.SparseArrays at sparse/linalg.jl:905
At_mul_B(A::SparseMatrixCSC, x::AbstractSparseArray{Tv,Ti,1} where Ti where Tv) in Base.SparseArrays at sparse/sparsevector.jl:1723
At_mul_B!(α::Number, A::SparseMatrixCSC, x::AbstractSparseArray{Tv,Ti,1} where Ti where Tv, β::Number, y::Union{DenseArray{T,1}, Base.ReinterpretArray{T,1,S,A} where S, Base.ReshapedArray{T,1,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray}, SubArray{T,1,A,I,L} where L} where I<:Tuple{Vararg{Union{Int64, AbstractRange{Int64}, Base.AbstractCartesianIndex},N} where N} where A<:Union{Base.ReshapedArray{T,N,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray} where N where T, DenseArray} where T) in Base.SparseArrays at sparse/sparsevector.jl:1678
At_mul_B!(α::Number, A::SparseMatrixCSC, B::Union{Union{DenseArray{T,1}, Base.ReinterpretArray{T,1,S,A} where S, Base.ReshapedArray{T,1,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray}, SubArray{T,1,A,I,L} where L} where I<:Tuple{Vararg{Union{Int64, AbstractRange{Int64}, Base.AbstractCartesianIndex},N} where N} where A<:Union{Base.ReshapedArray{T,N,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray} where N where T, DenseArray}, Union{DenseArray{T,2}, Base.ReinterpretArray{T,2,S,A} where S, Base.ReshapedArray{T,2,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray}, SubArray{T,2,A,I,L} where L} where I<:Tuple{Vararg{Union{Int64, AbstractRange{Int64}, Base.AbstractCartesianIndex},N} where N} where A<:Union{Base.ReshapedArray{T,N,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray} where N where T, DenseArray}} where T, β::Number, C::Union{Union{DenseArray{T,1}, Base.ReinterpretArray{T,1,S,A} where S, Base.ReshapedArray{T,1,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray}, SubArray{T,1,A,I,L} where L} where I<:Tuple{Vararg{Union{Int64, AbstractRange{Int64}, Base.AbstractCartesianIndex},N} where N} where A<:Union{Base.ReshapedArray{T,N,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray} where N where T, DenseArray}, Union{DenseArray{T,2}, Base.ReinterpretArray{T,2,S,A} where S, Base.ReshapedArray{T,2,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray}, SubArray{T,2,A,I,L} where L} where I<:Tuple{Vararg{Union{Int64, AbstractRange{Int64}, Base.AbstractCartesianIndex},N} where N} where A<:Union{Base.ReshapedArray{T,N,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{SubArray{T,N,P,I,true} where I<:Tuple{Union{Base.Slice, UnitRange},Vararg{Any,N} where N} where P where N where T, DenseArray} where N where T, DenseArray}} where T) in Base.SparseArrays at sparse/linalg.jl:51
\(::SparseMatrixCSC, ::RowVector) in Base.SparseArrays at sparse/linalg.jl:924
\(L::LowerTriangular{T,#s332} where #s332<:(Union{SparseMatrixCSC{T,Ti}, SubArray{T,2,SparseMatrixCSC{T,Ti},Tuple{Base.Slice{Base.OneTo{Int64}},I},L} where L where I<:AbstractUnitRange} where Ti), B::SparseMatrixCSC) where T in Base.SparseArrays at sparse/linalg.jl:290
\(U::UpperTriangular{T,#s332} where #s332<:(Union{SparseMatrixCSC{T,Ti}, SubArray{T,2,SparseMatrixCSC{T,Ti},Tuple{Base.Slice{Base.OneTo{Int64}},I},L} where L where I<:AbstractUnitRange} where Ti), B::SparseMatrixCSC) where T in Base.SparseArrays at sparse/linalg.jl:291
\(A::SparseMatrixCSC, B::Union{AbstractArray{T,1}, AbstractArray{T,2}} where T) in Base.SparseArrays at sparse/linalg.jl:905
abs(A::SparseMatrixCSC) in Base at deprecated.jl:55
abs2(A::SparseMatrixCSC) in Base at deprecated.jl:55
acos(A::SparseMatrixCSC) in Base at deprecated.jl:55
acosd(A::SparseMatrixCSC) in Base at deprecated.jl:55
acot(A::SparseMatrixCSC) in Base at deprecated.jl:55
acotd(A::SparseMatrixCSC) in Base at deprecated.jl:55
acsch(A::SparseMatrixCSC) in Base at deprecated.jl:55
adjoint(A::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:837
asech(A::SparseMatrixCSC) in Base at deprecated.jl:55
asin(A::SparseMatrixCSC) in Base at deprecated.jl:55
asind(A::SparseMatrixCSC) in Base at deprecated.jl:55
asinh(A::SparseMatrixCSC) in Base at deprecated.jl:55
atan(A::SparseMatrixCSC) in Base at deprecated.jl:55
atand(A::SparseMatrixCSC) in Base at deprecated.jl:55
atanh(A::SparseMatrixCSC) in Base at deprecated.jl:55
broadcast(f::Tf, A::SparseMatrixCSC) where Tf in Base.SparseArrays.HigherOrderFns at sparse/higherorderfns.jl:96
broadcast(f::Tf, A::SparseMatrixCSC, Bs::Vararg{SparseMatrixCSC,N}) where {Tf, N} in Base.SparseArrays.HigherOrderFns at sparse/higherorderfns.jl:121
broadcast(f::Tf, ::Type{T}, A::SparseMatrixCSC) where {Tf, T} in Base.SparseArrays.HigherOrderFns at sparse/higherorderfns.jl:962
broadcast(f::Tf, A::SparseMatrixCSC, ::Type{T}) where {Tf, T} in Base.SparseArrays.HigherOrderFns at sparse/higherorderfns.jl:963
ceil(A::SparseMatrixCSC) in Base at deprecated.jl:55
chol(A::SparseMatrixCSC) in Base.SparseArrays at sparse/linalg.jl:968
complex(S::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:391
cond(A::SparseMatrixCSC) in Base.SparseArrays at sparse/linalg.jl:556
cond(A::SparseMatrixCSC, p::Real) in Base.SparseArrays at sparse/linalg.jl:556
conj!(A::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:1558
convert(::Type{Array{T,2} where T}, S::SparseMatrixCSC{Tv,Ti} where Ti<:Integer) where Tv in Base.SparseArrays at sparse/sparsematrix.jl:354
convert(::Type{AbstractArray{Tv,2}}, A::SparseMatrixCSC{Tv,Ti} where Ti<:Integer) where Tv in Base.SparseArrays at sparse/sparsematrix.jl:329
convert(::Type{AbstractArray{Tv,2}}, A::SparseMatrixCSC) where Tv in Base.SparseArrays at sparse/sparsematrix.jl:330
convert(::Type{Array}, S::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:364
convert(::Type{SparseMatrixCSC{Tv,Ti} where Ti<:Integer}, S::SparseMatrixCSC{Tv,Ti} where Ti<:Integer) where Tv in Base.SparseArrays at sparse/sparsematrix.jl:331
convert(::Type{SparseMatrixCSC{Tv,Ti} where Ti<:Integer}, S::SparseMatrixCSC) where Tv in Base.SparseArrays at sparse/sparsematrix.jl:332
convert(::Type{SparseMatrixCSC{Tv,Ti}}, S::SparseMatrixCSC) where {Tv, Ti} in Base.SparseArrays at sparse/sparsematrix.jl:335
convert(::Type{SparseVector{Tv,Ti}}, s::SparseMatrixCSC{Tv,Ti}) where {Tv, Ti<:Integer} in Base.SparseArrays at sparse/sparsevector.jl:318
copy!(A::SparseMatrixCSC, B::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:271
copy!(A::SparseVector, B::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsevector.jl:431
copy!(A::SparseMatrixCSC, B::SparseVector{TvB,TiB}) where {TvB, TiB} in Base.SparseArrays at sparse/sparsevector.jl:447
cos(A::SparseMatrixCSC) in Base at deprecated.jl:55
cosc(A::SparseMatrixCSC) in Base at deprecated.jl:55
cosd(A::SparseMatrixCSC) in Base at deprecated.jl:55
cosh(A::SparseMatrixCSC) in Base at deprecated.jl:55
cospi(A::SparseMatrixCSC) in Base at deprecated.jl:55
cot(A::SparseMatrixCSC) in Base at deprecated.jl:55
cotd(A::SparseMatrixCSC) in Base at deprecated.jl:55
coth(A::SparseMatrixCSC) in Base at deprecated.jl:55
count(S::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:73
count(pred, S::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:74
cov(X::SparseMatrixCSC) in Base.SparseArrays at sparse/linalg.jl:973
cov(X::SparseMatrixCSC, vardim::Int64) in Base.SparseArrays at sparse/linalg.jl:973
csc(A::SparseMatrixCSC) in Base at deprecated.jl:55
cscd(A::SparseMatrixCSC) in Base at deprecated.jl:55
csch(A::SparseMatrixCSC) in Base at deprecated.jl:55
diagm(A::SparseMatrixCSC) in Base at deprecated.jl:55
diff(a::SparseMatrixCSC, dim::Integer) in Base.SparseArrays at sparse/linalg.jl:514
dropzeros(A::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:1251
dropzeros(A::SparseMatrixCSC, trim::Bool) in Base.SparseArrays at sparse/sparsematrix.jl:1251
dropzeros!(A::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:1228
dropzeros!(A::SparseMatrixCSC, trim::Bool) in Base.SparseArrays at sparse/sparsematrix.jl:1228
eig(A::SparseMatrixCSC) in Base.SparseArrays at sparse/linalg.jl:970
exp10(A::SparseMatrixCSC) in Base at deprecated.jl:55
exp2(A::SparseMatrixCSC) in Base at deprecated.jl:55
expm1(A::SparseMatrixCSC) in Base at deprecated.jl:55
eye(S::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:1520
factorize(A::SparseMatrixCSC) in Base.SparseArrays at sparse/linalg.jl:929
find(p::Function, S::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:1263
find(S::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:1256
findmax(A::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:1902
findmin(A::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:1901
float(S::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:389
floor(A::SparseMatrixCSC) in Base at deprecated.jl:55
getindex(A::SparseMatrixCSC, I::Tuple{Integer,Integer}) in Base.SparseArrays at sparse/sparsematrix.jl:1913
getindex(A::SparseMatrixCSC, ::Colon) in Base.SparseArrays at sparse/sparsevector.jl:577
getindex(A::SparseMatrixCSC{Tv,Ti} where Ti<:Integer, I::AbstractUnitRange) where Tv in Base.SparseArrays at sparse/sparsevector.jl:580
getindex(A::SparseMatrixCSC{#s332,#s331} where #s331<:Integer where #s332, I::AbstractRange{Bool}, J::AbstractArray{Bool,1}) in Base.SparseArrays at sparse/sparsematrix.jl:2325
getindex(A::SparseMatrixCSC{#s332,#s331} where #s331<:Integer where #s332, I::AbstractRange{Bool}, J::AbstractArray{#s330,1} where #s330<:Integer) in Base.SparseArrays at sparse/sparsematrix.jl:2326
getindex(A::SparseMatrixCSC, I::AbstractRange{#s332} where #s332<:Integer, J::AbstractArray{Bool,1}) in Base.SparseArrays at sparse/sparsematrix.jl:2328
getindex(x::SparseMatrixCSC, I::AbstractUnitRange, j::Integer) in Base.SparseArrays at sparse/sparsevector.jl:487
getindex(A::SparseMatrixCSC, I::AbstractArray{Bool,1}) in Base.SparseArrays at sparse/sparsevector.jl:536
getindex(A::SparseMatrixCSC, I::AbstractArray{Bool,1}, J::Integer) in Base.SparseArrays at sparse/sparsematrix.jl:2330
getindex(A::SparseMatrixCSC, I::AbstractArray{Bool,1}, J::AbstractArray{Bool,1}) in Base.SparseArrays at sparse/sparsematrix.jl:2331
getindex(A::SparseMatrixCSC, I::AbstractArray{#s332,1} where #s332<:Integer, J::AbstractArray{Bool,1}) in Base.SparseArrays at sparse/sparsematrix.jl:2332
getindex(A::SparseMatrixCSC, I::AbstractArray{Bool,1}, J::AbstractArray{#s332,1} where #s332<:Integer) in Base.SparseArrays at sparse/sparsematrix.jl:2333
getindex(A::SparseMatrixCSC{Tv,Ti} where Ti<:Integer, I::AbstractArray{T,1} where T) where Tv in Base.SparseArrays at sparse/sparsevector.jl:616
getindex(A::SparseMatrixCSC, I::AbstractArray{T,1} where T, J::Integer) in Base.SparseArrays at sparse/sparsevector.jl:499
getindex(A::SparseMatrixCSC, I::AbstractArray{Bool,N} where N) in Base.SparseArrays at sparse/sparsevector.jl:537
getindex(A::SparseMatrixCSC{Tv,Ti} where Ti<:Integer, I::AbstractArray) where Tv in Base.SparseArrays at sparse/sparsematrix.jl:2283
getindex(A::SparseMatrixCSC, i, ::Colon) in Base.SparseArrays at sparse/sparsematrix.jl:1926
getindex(x::SparseMatrixCSC, ::Colon, j::Integer) in Base.SparseArrays at sparse/sparsevector.jl:480
getindex(A::SparseMatrixCSC, ::Colon, i) in Base.SparseArrays at sparse/sparsematrix.jl:1927
getindex(A::SparseMatrixCSC{Tv,Ti}, I::AbstractRange, J::AbstractArray{T,1} where T) where {Tv, Ti<:Integer} in Base.SparseArrays at sparse/sparsematrix.jl:1967
getindex(A::SparseMatrixCSC, I::Integer, J::AbstractArray{Bool,1}) in Base.SparseArrays at sparse/sparsematrix.jl:2329
hash(A::SparseMatrixCSC{T,Ti} where Ti<:Integer, h::UInt64) where T in Base.SparseArrays at sparse/sparsematrix.jl:3505
indmax(A::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:1905
indmin(A::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:1904
inv(A::SparseMatrixCSC) in Base.SparseArrays at sparse/linalg.jl:837
ishermitian(A::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:3167
issymmetric(A::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:3165
istril(A::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:3265
istriu(A::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:3245
kron(A::SparseMatrixCSC, B::Union{Array{T,1}, Array{T,2}} where T) in Base.SparseArrays at sparse/linalg.jl:807
kron(A::Union{Array{T,1}, Array{T,2}} where T, B::SparseMatrixCSC) in Base.SparseArrays at sparse/linalg.jl:808
log10(A::SparseMatrixCSC) in Base at deprecated.jl:55
log1p(A::SparseMatrixCSC) in Base at deprecated.jl:55
log2(A::SparseMatrixCSC) in Base at deprecated.jl:55
lu(A::SparseMatrixCSC) in Base.SparseArrays at sparse/linalg.jl:969
lufact(A::SparseMatrixCSC) in Base.SparseArrays.UMFPACK at sparse/umfpack.jl:158
map(f::Tf, A::SparseMatrixCSC) where Tf in Base.SparseArrays.HigherOrderFns at sparse/higherorderfns.jl:69
map(f::Tf, A::SparseMatrixCSC, Bs::Vararg{SparseMatrixCSC,N}) where {Tf, N} in Base.SparseArrays.HigherOrderFns at sparse/higherorderfns.jl:70
map!(f::Tf, C::SparseMatrixCSC, A::SparseMatrixCSC, Bs::Vararg{SparseMatrixCSC,N}) where {Tf, N} in Base.SparseArrays.HigherOrderFns at sparse/higherorderfns.jl:74
map!(f::Tf, C::SparseMatrixCSC, A::Union{Bidiagonal, Diagonal, SymTridiagonal, Tridiagonal, SparseMatrixCSC}, Bs::Vararg{Union{Bidiagonal, Diagonal, SymTridiagonal, Tridiagonal, SparseMatrixCSC},N}) where {Tf, N} in Base.SparseArrays.HigherOrderFns at sparse/higherorderfns.jl:1069
nnz(S::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:72
nonzeros(S::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:100
norm(A::SparseMatrixCSC) in Base.SparseArrays at sparse/linalg.jl:520
norm(A::SparseMatrixCSC, p::Real) in Base.SparseArrays at sparse/linalg.jl:520
nzrange(S::SparseMatrixCSC, col::Integer) in Base.SparseArrays at sparse/sparsematrix.jl:146
one(S::SparseMatrixCSC{T,Ti} where Ti<:Integer) where T in Base.SparseArrays at sparse/sparsematrix.jl:1536
qr(A::SparseMatrixCSC) in Base.SparseArrays.SPQR at sparse/spqr.jl:198
qrfact(A::SparseMatrixCSC) in Base.SparseArrays.SPQR at sparse/spqr.jl:196
reinterpret(::Type{T}, a::SparseMatrixCSC{S,Ti} where Ti<:Integer, dims::Tuple{Vararg{Int64,N}}) where {T, S, N} in Base at deprecated.jl:55
rot180(A::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:3462
rotl90(A::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:3482
rotr90(A::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:3472
round(A::SparseMatrixCSC) in Base at deprecated.jl:55
rowvals(S::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:125
scale!(A::SparseMatrixCSC, b::Number) in Base.SparseArrays at sparse/linalg.jl:899
scale!(C::SparseMatrixCSC, b::Number, A::SparseMatrixCSC) in Base.SparseArrays at sparse/linalg.jl:892
scale!(C::SparseMatrixCSC, A::SparseMatrixCSC, b::Array{T,1} where T) in Base.SparseArrays at sparse/linalg.jl:857
scale!(C::SparseMatrixCSC, b::Array{T,1} where T, A::SparseMatrixCSC) in Base.SparseArrays at sparse/linalg.jl:870
scale!(C::SparseMatrixCSC, A::SparseMatrixCSC, b::Number) in Base.SparseArrays at sparse/linalg.jl:884
scale!(b::Number, A::SparseMatrixCSC) in Base.SparseArrays at sparse/linalg.jl:900
sec(A::SparseMatrixCSC) in Base at deprecated.jl:55
secd(A::SparseMatrixCSC) in Base at deprecated.jl:55
sech(A::SparseMatrixCSC) in Base at deprecated.jl:55
setindex!(A::SparseMatrixCSC{Tv,Ti}, v::Tv, i::Ti, j::Ti) where {Ti<:Integer, Tv} in Base.SparseArrays at sparse/sparsematrix.jl:2340
setindex!(A::SparseMatrixCSC, x::Array{T,2} where T, I::Integer, J::AbstractArray{Bool,1}) in Base.SparseArrays at sparse/sparsematrix.jl:2672
setindex!(A::SparseMatrixCSC, v::AbstractArray{T,2} where T, i::Integer, J::AbstractArray{#s332,1} where #s332<:Integer) in Base.SparseArrays at sparse/sparsematrix.jl:2363
setindex!(A::SparseMatrixCSC, x::Array{T,2} where T, I::AbstractArray{Bool,1}, J::Integer) in Base.SparseArrays at sparse/sparsematrix.jl:2673
setindex!(A::SparseMatrixCSC, v::AbstractArray{T,2} where T, I::AbstractArray{#s332,1} where #s332<:Integer, j::Integer) in Base.SparseArrays at sparse/sparsematrix.jl:2364
setindex!(A::SparseMatrixCSC, x::Number, i::Integer, J::AbstractArray{#s332,1} where #s332<:Integer) in Base.SparseArrays at sparse/sparsematrix.jl:2366
setindex!(A::SparseMatrixCSC, x::Number, I::AbstractArray{#s332,1} where #s332<:Integer, j::Integer) in Base.SparseArrays at sparse/sparsematrix.jl:2367
setindex!(A::SparseMatrixCSC, x, ::Colon) in Base.SparseArrays at sparse/sparsematrix.jl:2370
setindex!(A::SparseMatrixCSC, x, ::Colon, ::Colon) in Base.SparseArrays at sparse/sparsematrix.jl:2371
setindex!(A::SparseMatrixCSC, x, ::Colon, j::Union{Integer, AbstractArray{T,1} where T}) in Base.SparseArrays at sparse/sparsematrix.jl:2372
setindex!(A::SparseMatrixCSC, x, I::AbstractArray{Bool,1}) in Base.SparseArrays at sparse/sparsematrix.jl:2684
setindex!(A::SparseMatrixCSC, x, I::AbstractArray{Bool,2}) in Base.SparseArrays at sparse/sparsematrix.jl:2686
setindex!(A::SparseMatrixCSC, x, I::AbstractArray{#s332,1} where #s332<:Real) in Base.SparseArrays at sparse/sparsematrix.jl:2786
setindex!(A::SparseMatrixCSC, x, i::Union{Integer, AbstractArray{T,1} where T}, ::Colon) in Base.SparseArrays at sparse/sparsematrix.jl:2373
setindex!(A::SparseMatrixCSC{Tv,Ti} where Ti<:Integer, x::Number, I::AbstractArray{#s332,1} where #s332<:Integer, J::AbstractArray{#s331,1} where #s331<:Integer) where Tv in Base.SparseArrays at sparse/sparsematrix.jl:2377
setindex!(A::SparseMatrixCSC, x::Array{T,2} where T, I::AbstractArray{Bool,1}, J::AbstractArray{Bool,1}) in Base.SparseArrays at sparse/sparsematrix.jl:2674
setindex!(A::SparseMatrixCSC, x::Array{T,2} where T, I::AbstractArray{#s332,1} where #s332<:Integer, J::AbstractArray{Bool,1}) in Base.SparseArrays at sparse/sparsematrix.jl:2675
setindex!(A::SparseMatrixCSC, x::Array{T,2} where T, I::AbstractArray{Bool,1}, J::AbstractArray{#s332,1} where #s332<:Integer) in Base.SparseArrays at sparse/sparsematrix.jl:2676
setindex!(A::SparseMatrixCSC, v::AbstractArray{T,1} where T, I::AbstractArray{#s332,1} where #s332<:Integer, j::Integer) in Base.SparseArrays at sparse/sparsematrix.jl:2539
setindex!(A::SparseMatrixCSC, v::AbstractArray{T,1} where T, i::Integer, J::AbstractArray{#s332,1} where #s332<:Integer) in Base.SparseArrays at sparse/sparsematrix.jl:2540
setindex!(A::SparseMatrixCSC, v::AbstractArray{T,1} where T, I::AbstractArray{T,1}, J::AbstractArray{T,1}) where T<:Integer in Base.SparseArrays at sparse/sparsematrix.jl:2541
setindex!(A::Array{T,2} where T, x::SparseMatrixCSC, I::Integer, J::AbstractArray{Bool,1}) in Base.SparseArrays at sparse/sparsematrix.jl:2678
setindex!(A::Array{T,2} where T, x::SparseMatrixCSC, I::AbstractArray{Bool,1}, J::Integer) in Base.SparseArrays at sparse/sparsematrix.jl:2679
setindex!(A::Array{T,2} where T, x::SparseMatrixCSC, I::AbstractArray{Bool,1}, J::AbstractArray{Bool,1}) in Base.SparseArrays at sparse/sparsematrix.jl:2680
setindex!(A::Array{T,2} where T, x::SparseMatrixCSC, I::AbstractArray{#s332,1} where #s332<:Integer, J::AbstractArray{Bool,1}) in Base.SparseArrays at sparse/sparsematrix.jl:2681
setindex!(A::Array{T,2} where T, x::SparseMatrixCSC, I::AbstractArray{Bool,1}, J::AbstractArray{#s332,1} where #s332<:Integer) in Base.SparseArrays at sparse/sparsematrix.jl:2682
show(io::IOContext, S::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:160
show(io::IO, S::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:158
show(io::IO, ::MIME{Symbol("text/plain")}, S::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:149
similar(S::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:317
similar(S::SparseMatrixCSC, ::Type{Tv}) where Tv in Base.SparseArrays at sparse/sparsematrix.jl:317
similar(S::SparseMatrixCSC, ::Type{Tv}, ::Type{Ti}) where {Tv, Ti} in Base.SparseArrays at sparse/sparsematrix.jl:321
similar(S::SparseMatrixCSC, ::Type{Tv}, d::Tuple{Vararg{Int64,N}} where N) where Tv in Base.SparseArrays at sparse/sparsematrix.jl:326
sin(A::SparseMatrixCSC) in Base at deprecated.jl:55
sinc(A::SparseMatrixCSC) in Base at deprecated.jl:55
sind(A::SparseMatrixCSC) in Base at deprecated.jl:55
sinh(A::SparseMatrixCSC) in Base at deprecated.jl:55
sinpi(A::SparseMatrixCSC) in Base at deprecated.jl:55
sparse(S::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:420
speye(S::SparseMatrixCSC{T,Ti} where Ti<:Integer) where T in Base.SparseArrays at sparse/sparsematrix.jl:1519
spones(S::SparseMatrixCSC{T,Ti} where Ti<:Integer) where T in Base.SparseArrays at sparse/sparsematrix.jl:1460
tan(A::SparseMatrixCSC) in Base at deprecated.jl:55
tand(A::SparseMatrixCSC) in Base at deprecated.jl:55
tanh(A::SparseMatrixCSC) in Base at deprecated.jl:55
trace(A::SparseMatrixCSC{Tv,Ti} where Ti<:Integer) where Tv in Base.SparseArrays at sparse/sparsematrix.jl:3393
transpose(A::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:836
tril!(A::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:1202
tril!(A::SparseMatrixCSC, k::Integer) in Base.SparseArrays at sparse/sparsematrix.jl:1202
tril!(A::SparseMatrixCSC, k::Integer, trim::Bool) in Base.SparseArrays at sparse/sparsematrix.jl:1202
triu!(A::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:1209
triu!(A::SparseMatrixCSC, k::Integer) in Base.SparseArrays at sparse/sparsematrix.jl:1209
triu!(A::SparseMatrixCSC, k::Integer, trim::Bool) in Base.SparseArrays at sparse/sparsematrix.jl:1209
trunc(A::SparseMatrixCSC) in Base at deprecated.jl:55
vec(S::SparseMatrixCSC) in Base.SparseArrays at sparse/sparsematrix.jl:396
vecnorm(A::SparseMatrixCSC) in Base.SparseArrays at sparse/linalg.jl:517
vecnorm(A::SparseMatrixCSC, p::Real) in Base.SparseArrays at sparse/linalg.jl:517