jiahao

jiahao

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]

jiahao

#################################################################
# A simple implementation of TSQR (Tall and Skinny QR) in Julia #
# Jiahao Chen <jiahao@mit.edu>, 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

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

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jiahao

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

"""
estimate_coeffs

August, 2015
Anna C. Gilbert

input: xs = samples of signal
  	 Λ = list of (freq,coeff) pairs in current approx
  	 Ω = list of (freq,coeff) pairs found in this iteration
       k = length of short filter

jiahao

"""
Savitzky-Golay filter of window half-width M and degree N

M is the number of points before and after to interpolate, i.e. the full width
of the window is 2M+1
"""
immutable SavitzkyGolayFilter{M,N} end

@generated function Base.call{M,N,T}(::Type{SavitzkyGolayFilter{M,N}},
     data::AbstractVector{T})

jiahao

include("rankstability.jl")

info("Julia semantics")

axiomsused = Dict()
@axiom matmul Mat * Mat --> Mat
@axiom mattrans transpose(Mat) --> Mat
@axiom matdiv Mat / Mat --> Mat
@axiom matvec Mat * Vec --> Vec