Class: Quasi::LowDiscrepancySequence

Inherits:
Object
  • Object
show all
Defined in:
lib/LowDiscrepancySequence.rb

Direct Known Subclasses

Halton, NX

Instance Method Summary collapse

Constructor Details

#initialize(dim) ⇒ LowDiscrepancySequence

Returns a new instance of LowDiscrepancySequence.



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# File 'lib/LowDiscrepancySequence.rb', line 13

def initialize(dim)
@dim = dim
@index = 1 
@x = NArray.float(dim)
@y = NArray.float(dim)
end

Instance Method Details

#L2_discrepancy(n, r) ⇒ Object 



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# File 'lib/LowDiscrepancySequence.rb', line 50

def L2_discrepancy(n, r)
a,b =1.0,1.0
for k in 0..@dim
   a/=2
   b/=3
end

sum_1,sum_2 =0.0,0.0

loops=0
for i in 0..n
  for j in i+1..n
    sum_1+=product(i,j,r)
  end
end

sum_1*=2

for i in 0..n
  sum_1+=product(i,i,r)
end

sum_1/=(n*n)

#second sum
for i in 0..n
  sum_2+=productSQ(i,r)
end

sum_2/=n 
sum_2*=(2.0*a)
return Math.sqrt(sum_1-sum_2+b)

end

#n_inverse(x) ⇒ Object 



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# File 'lib/LowDiscrepancySequence.rb', line 106

def n_inverse(x)
sqrt_two_PI=2.5066282746310

e_1 = -3.969683028665376e+01
e_2 =  2.209460984245205e+02
e_3 = -2.759285104469687e+02
e_4 =  1.383577518672690e+02
e_5 = -3.066479806614716e+01
e_6 =  2.506628277459239e+00

f_1 = -5.447609879822406e+01
f_2 =  1.615858368580409e+02
f_3 = -1.556989798598866e+02
f_4 =  6.680131188771972e+01
f_5 = -1.328068155288572e+01



g_1 = -7.784894002430293e-03
g_2 = -3.223964580411365e-01
g_3 = -2.400758277161838e+00
g_4 = -2.549732539343734e+00
g_5 =  4.374664141464968e+00
g_6 =  2.938163982698783e+00


h_1 =  7.784695709041462e-03
h_2 =  3.224671290700398e-01
h_3 =  2.445134137142996e+00
h_4 =  3.754408661907416e+00

x_l   = 0.02425
x_u  = 1.0 - x_l


#lower

if( x < x_l )
  z = Math.sqrt(-2.0*Math.log(x))
  z = (((((g_1*z+g_2)*z+g_3)*z+g_4)*z+g_5)*z+g_6) / ((((h_1*z+h_2)*z+h_3)*z+h_4)*z+1.0)
elsif( x <= x_u )
#central
  z = x - 0.5; r = z*z
  z = (((((e_1*r+e_2)*r+e_3)*r+e_4)*r+e_5)*r+e_6)*z / (((((f_1*r+f_2)*r+f_3)*r+f_4)*r+f_5)*r+1.0)

#upper
else 
  z = Math.sqrt(-2.0*Math.log(1.0-x))
  z = -(((((g_1*z+g_2)*z+g_3)*z+g_4)*z+g_5)*z+g_6) /  ((((h_1*z+h_2)*z+h_3)*z+h_4)*z+1.0)

end

return z


end

#nextPoint(r) ⇒ Object 



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# File 'lib/LowDiscrepancySequence.rb', line 24

def nextPoint(r)
x= nextPoint
for k in 0..@dim
  r[k] = x[k]
end
end

#nextQuasiNormalVector ⇒ Object

TRANSFORM UNIFORM -> MULTINORMAL need thi, maybe narray



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# File 'lib/LowDiscrepancySequence.rb', line 91

def nextQuasiNormalVector
x=nextPoint()
z = Array.new(@dim)
for k in 0..@dim-1
  z[k]=n_inverse(x[k].to_f);
end
return z
end

#product(i, j, r) ⇒ Object

L^2-DISCREPANCY



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# File 'lib/LowDiscrepancySequence.rb', line 33

def product(i,j,r)
f=1.0
for k in 0..@dim
  f*=1.0-[r[i][k],r[j][k]].max
end
return f
end

#productSQ(i, r) ⇒ Object 



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# File 'lib/LowDiscrepancySequence.rb', line 41

def productSQ( i, r)
   f=1.0 
     for k in 0..@dim
       f*=(1.0-r[i][k]*r[i][k])
     end
     return f
end

#projectionOut(i, j, nPoints) ⇒ Object 



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# File 'lib/LowDiscrepancySequence.rb', line 100

def projectionOut(i,j, nPoints)
  name=getName
  puts i,j
  puts nextPoint(x)
end

#restart ⇒ Object 



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# File 'lib/LowDiscrepancySequence.rb', line 20

def restart
@index =1
end