Thread: *ANSWER* q5
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Old 05-06-2013, 05:18 PM
arcticblue arcticblue is offline
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Join Date: Apr 2013
Posts: 17
Default *ANSWER* q5

I got Q5 wrong and don't know where I've gone wrong. My code is below and I believe my partial derivatives are correct. I believe eta and the starting values are correct. I then loop through using the weights to calculate the new weights. The same weights are used for both partial derivatives and then both weights are updated at the end of the iteration. I then get the results at the bottom. I end up with iteration 17 being when the error drops below 10e-14 (which is the wrong number of iterations). To calculate the error I'm summing the square of the differences and then taking the sqrt. (Refer to print statement in code).

So can someone point out what I've done wrong, I'm sure it's obvious to someone who got the answer right but it's not to me. Alternatively if anyone has some code that works then please post it and I'll try and work out how mine is different.

Thank you.

Code:
def derWRTu(u,v):
    result = Decimal(2)*(Decimal.exp(v) + Decimal(2) * v * Decimal.exp(-u)) * (u * Decimal.exp(v) - Decimal(2)*v*Decimal.exp(-u))
    return result

def derWRTv(u,v):
    result = Decimal(2)*(u*Decimal.exp(v) - Decimal(2) * Decimal.exp(-u)) * (u * Decimal.exp(v) - Decimal(2)*v*Decimal.exp(-u))
    return result

eta = Decimal(0.1)
weight1 = Decimal(1.0)
weight2 = Decimal(1.0)

for i in range(1,20):
        temp1 = Decimal(weight1 - eta * derWRTu(weight1,weight2))
        temp2 = Decimal(weight2 - eta * derWRTv(weight1,weight2))
        print i, temp1, temp2, math.sqrt((temp1 - weight1)**2 + (temp2 - weight2)**2)
        weight1 = temp1
        weight2 = temp2
Results
iteration newWeight1 newWeight2 error

1 -0.369542993196839967955794109 0.2139205536245797574025398844 1.5791038301
2 0.0305206903512627734316713927 -0.5079340454438062055203607077 0.825302982601
3 0.1075231141989984274494072585 -0.1222102555735032213170381668 0.393334737025
4 0.06564482581488226125563096705 -0.0151665598769331032201461945 0.114944090002
5 0.04784117062171890279998341002 0.01848989922674513542330801974 0.038075285654
6 0.04499946309943379128005628962 0.02349925169679327305149255062 0.00575924594121
7 0.04475601902934555265991082578 0.02392429647039781800619960613 0.000489824534736
8 0.04473774604067714316407965262 0.02395617479661382948530576517 3.67441124156e-05
9 0.04473639081750715769541853207 0.02395853892224864452997465102 2.72501740502e-06
10 0.04473629039778214055992344406 0.02395871409914178947550918280 2.01918461425e-07
11 0.04473628295735141684956930350 0.02395872707857492077823017572 1.49608052512e-08
12 0.04473628240606795227909993835 0.02395872804025939239070240562 1.10849018094e-09
13 0.04473628236522174893968490660 0.02395872811151340584997873671 8.21312776066e-11
14 0.04473628236219533441993488016 0.02395872811679282384392635644 6.08534626789e-12
15 0.04473628236197109852827296072 0.02395872811718399134381489950 4.50881079752e-13
16 0.04473628236195448423608868001 0.02395872811721297408644352622 3.34070961782e-14
17 0.04473628236195325323465204219 0.02395872811721512150250060613 2.47522933467e-15
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