# This file is a part of Julia. License is MIT: http://julialang.org/license
module LinAlg
importall Base
importall ..Base.Operators
import Base: USE_BLAS64, size, copy, copy_transpose!, power_by_squaring,
print_matrix, transpose!, unsafe_getindex, unsafe_setindex!,
isapprox
export
# Modules
LAPACK,
BLAS,
# Types
SymTridiagonal,
Tridiagonal,
Bidiagonal,
Factorization,
BunchKaufman,
Cholesky,
CholeskyPivoted,
Eigen,
GeneralizedEigen,
GeneralizedSVD,
GeneralizedSchur,
Hessenberg,
LU,
LDLt,
QR,
QRPivoted,
Schur,
SVD,
Hermitian,
Symmetric,
LowerTriangular,
UpperTriangular,
Diagonal,
UniformScaling,
# Functions
axpy!,
bkfact,
bkfact!,
chol,
cholfact,
cholfact!,
cond,
condskeel,
copy!,
cross,
ctranspose,
det,
diag,
diagind,
diagm,
diff,
dot,
eig,
eigfact,
eigfact!,
eigmax,
eigmin,
eigs,
eigvals,
eigvals!,
eigvecs,
expm,
eye,
factorize,
givens,
gradient,
hessfact,
hessfact!,
isdiag,
ishermitian,
isposdef,
isposdef!,
issym,
istril,
istriu,
kron,
ldltfact!,
ldltfact,
linreg,
logabsdet,
logdet,
logm,
lu,
lufact,
lufact!,
lyap,
norm,
nullspace,
ordschur!,
ordschur,
peakflops,
pinv,
qr,
qrfact!,
qrfact,
rank,
scale,
scale!,
schur,
schurfact!,
schurfact,
sqrtm,
svd,
svdfact!,
svdfact,
svds,
svdvals!,
svdvals,
sylvester,
trace,
transpose,
tril,
triu,
tril!,
triu!,
vecdot,
vecnorm,
# Operators
\,
/,
A_ldiv_B!,
A_ldiv_Bc,
A_ldiv_Bt,
A_mul_B!,
A_mul_Bc,
A_mul_Bc!,
A_mul_Bt,
A_mul_Bt!,
A_rdiv_Bc,
A_rdiv_Bt,
Ac_ldiv_B,
Ac_ldiv_Bc,
Ac_mul_B,
Ac_mul_B!,
Ac_mul_Bc,
Ac_mul_Bc!,
Ac_rdiv_B,
Ac_rdiv_Bc,
At_ldiv_B,
At_ldiv_Bt,
At_mul_B,
At_mul_B!,
At_mul_Bt,
At_mul_Bt!,
At_rdiv_B,
At_rdiv_Bt,
# Constants
I
typealias BlasFloat Union{Float64,Float32,Complex128,Complex64}
typealias BlasReal Union{Float64,Float32}
typealias BlasComplex Union{Complex128,Complex64}
if USE_BLAS64
typealias BlasInt Int64
else
typealias BlasInt Int32
end
# Check that stride of matrix/vector is 1
function chkstride1(A...)
for a in A
stride(a,1)== 1 || error("matrix does not have contiguous columns")
end
end
# Check that matrix is square
function chksquare(A)
m,n = size(A)
m == n || throw(DimensionMismatch("matrix is not square"))
m
end
function chksquare(A...)
sizes = Int[]
for a in A
size(a,1)==size(a,2) || throw(DimensionMismatch("matrix is not square: dimensions are $(size(a))"))
push!(sizes, size(a,1))
end
return sizes
end
# Check that upper/lower (for special matrices) is correctly specified
macro chkuplo()
:((uplo=='U' || uplo=='L') || throw(ArgumentError("""invalid uplo = $uplo
Valid choices are 'U' (upper) or 'L' (lower).""")))
end
const CHARU = 'U'
const CHARL = 'L'
char_uplo(uplo::Symbol) = uplo == :U ? CHARU : (uplo == :L ? CHARL : throw(ArgumentError("uplo argument must be either :U or :L")))
copy_oftype{T,N}(A::AbstractArray{T,N}, ::Type{T}) = copy(A)
copy_oftype{T,N,S}(A::AbstractArray{T,N}, ::Type{S}) = convert(AbstractArray{S,N}, A)
include("linalg/exceptions.jl")
include("linalg/generic.jl")
include("linalg/blas.jl")
include("linalg/matmul.jl")
include("linalg/lapack.jl")
include("linalg/dense.jl")
include("linalg/tridiag.jl")
include("linalg/triangular.jl")
include("linalg/factorization.jl")
include("linalg/qr.jl")
include("linalg/eigen.jl")
include("linalg/svd.jl")
include("linalg/schur.jl")
include("linalg/cholesky.jl")
include("linalg/lu.jl")
include("linalg/bunchkaufman.jl")
include("linalg/symmetric.jl")
include("linalg/diagonal.jl")
include("linalg/bidiag.jl")
include("linalg/uniformscaling.jl")
include("linalg/givens.jl")
include("linalg/special.jl")
include("linalg/bitarray.jl")
include("linalg/ldlt.jl")
include("linalg/arpack.jl")
include("linalg/arnoldi.jl")
function __init__()
Base.check_blas()
if Base.blas_vendor() == :mkl
ccall((:MKL_Set_Interface_Layer, Base.libblas_name), Void, (Cint,), USE_BLAS64 ? 1 : 0)
end
end
end # module LinAlg