Module: NumRu::GAnalysis::LombScargle

Defined in:
lib/numru/ganalysis/lomb_scargle.rb

Class Method Summary collapse

Class Method Details

.derive_phase(t, f, dim, rank, mask = nil) ⇒ Object 



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# File 'lib/numru/ganalysis/lomb_scargle.rb', line 58

def derive_phase(t,f,dim,rank,mask=nil)
  multiple_f = !f.is_a?(Numeric)
  if multiple_f
    o2t = 4*Math::PI * f.newdim(0) * t.newdim(-1)  # 2 omega t
    mask = mask.newdim(-1) if mask
    nf = f.length
  else
    o2t = 4*Math::PI * f * t  # 2 omega t
  end
  with_miss = (mask && mask.count_false > 0)
  if dim >= 1
    o2t = o2t.newdim!( *([0]*dim) )
  end
  if dim < rank-1
    o2t = o2t.newdim!( *([dim+1]*(rank-1-dim)) )
  end
  if with_miss
    # sampling is not common for all grid points
    expander = NArray.float( *mask.shape )
    o2t += expander    # duplicates o2t for all grid points
    if multiple_f
      expander = NArray.byte(*([1]*rank+[nf])) # duplicates mask for all f
      mask += expander
    end
    o2t = NArrayMiss.to_nam(o2t,mask)
  end
  ph = 0.5* Misc::EMath::atan2( Misc::EMath.sin(o2t).sum(dim),
                               -Misc::EMath.cos(o2t).sum(dim)).newdim(dim)
  ot_ph = o2t*0.5 + ph  # omega*t + ph
  [ph, ot_ph]
end

.lomb_scargle(y, dim, t, f) ⇒ Object

Lomb-Scargle periodgram

ARGUMENTS

  • y [NArray or NArrayMiss] : data

  • dim [Integer] : the dimension to apply LS

  • t [1D NArray] : “time” (the coordinate values along dim)

  • f [Numric or 1D NArray] : frequency. If 1D NArray, the frequency dimension is added to the end of outputs

OUTPUTS

  • a : coef of cos

  • b : coef of sin (sqrt(a**2+b**2) is the amplitude)

  • reconst : reconstructed y (fitting result)

  • cos [NArray or NArrayMiss]: cos(2*pi*f*t + ph) (useful if you want to reconstruct for a part of f)

  • sin [NArray or NArrayMiss]: sin(2*pi*f*t + ph) (useful if you want to reconstruct for a part of f)

  • cc [NArray or NArrayMiss]: normarization factor sum(cos**2) (needed to derive power spectrum)

  • ss [NArray or NArrayMiss]: normarization factor sum(sin**2) (needed to derive power spectrum)

  • ph [NArray or NArrayMiss]: phase (for each f and, if with miss, for each grid point)



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# File 'lib/numru/ganalysis/lomb_scargle.rb', line 36

def lomb_scargle(y, dim, t, f)
  rank = y.rank
  if y.respond_to?(:get_mask)
    mask = y.get_mask
  else
    mask = nil
  end
  ph, ot_ph = derive_phase(t,f,dim,rank,mask)
  cos = Misc::EMath.cos( ot_ph )
  sin = Misc::EMath.sin( ot_ph )
  cc = (cos*cos).sum(dim)
  ss = (sin*sin).sum(dim)
  #p "%%%", (cos*sin).sum(dim), cc, ss
  if !f.is_a?(Numeric)
    y = y.newdim(-1)
  end
  a = (y*cos).sum(dim) / cc
  b = (y*sin).sum(dim) / ss
  reconst = (a.newdim(-2)*cos).sum(-1) + (b.newdim(-2)*sin).sum(-1)
  [a,b,reconst,cos,sin,cc,ss,ph]
end