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function normtypes(S) #For the first post, comparing vector outputs with naive definitions
  try
    R0 = typeof(abs(one(S))^0+abs(one(S))^0)
    R1 = typeof(abs(one(S))+abs(one(S)))
    Rp = typeof(sqrt(abs(one(S))^2+abs(one(S))^2))
    Ri = typeof(maximum(abs(one(S))))
    Ri2 = typeof(abs(one(S)))
    R0i = typeof(norm([one(S)], 0))
    R1i = typeof(norm([one(S)], 1))
    Rpi = typeof(norm([one(S)]))

jiahao

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jiahao

type BrokenArrowBidiagonal{T} <: AbstractMatrix{T}
    dv::Vector{T}
    av::Vector{T}
    ev::Vector{T}
end
Base.size(B::BrokenArrowBidiagonal) = (n=length(B.dv); (n, n))
function Base.size(B::BrokenArrowBidiagonal, n::Int)
    if n==1 || n==2
        return length(B.dv)
    else

jiahao

#################################################################
# A simple implementation of TSQR (Tall and Skinny QR) in Julia #
# Jiahao Chen <[email protected]>, 2015-08-03                      #
#################################################################
#
# TSQR is a communication-avoiding QR algorithm designed for
# distributed computation on tall, skinny matrices, which are
# typical of data matrices in Big Data applications.
#
# The primary reference is

jiahao

#function axpy!{T}(a::T, b::StridedVector{T}, c::StridedVector{T})
#    @simd for i=1:size(b, 1)
#        c[i] += a*b[i]
#    end
#end

mgs(A)=mgs!(copy(A))
function mgs!(Q) #Does not store R
    m, n = size(Q)
    Qc= [slice(Q,:,k) for k=1:n]

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.ipynb_checkpoints
*.ipynb

jiahao

import Base: +, -, ⋅, *, /, √, convert
export DoublelengthFloat

immutable DoublelengthFloat{T<:FloatingPoint} <: FloatingPoint
    head :: T
    tail :: T
end
DoublelengthFloat(x::FloatingPoint) = DoublelengthFloat(x, zero(x))
convert{T<:FloatingPoint}(::Type{DoublelengthFloat{T}}, x::T) = DoublelengthFloat(x)