julia-common 0.4.7-6 / usr / share / julia / base / linalg.jl

# 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__()
    try
        Base.check_blas()
        if Base.blas_vendor() == :mkl
            ccall((:MKL_Set_Interface_Layer, Base.libblas_name), Void, (Cint,), USE_BLAS64 ? 1 : 0)
        end
    catch ex
        Base.showerror_nostdio(ex,
            "WARNING: Error during initialization of module LinAlg")
    end
end

end # module LinAlg