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--- howtos:calibration:projecting_into_history [2009/12/01 13:51]
shona.weldon created
+++ howtos:calibration:projecting_into_history [2009/12/01 14:02] (current)
shona.weldon
@@ Line 8: / Line 8: @@
 <code>
-local ratioFamPerPer[cr,th] = familiesTot[cr,th] / CTotPop[cr,th]
+local ratioFamPerPer[cr,t19782006] = familiesTot[cr,t19782006] / CTotPop[cr,t19782006]
-local ratioFamPerPerPH[cr,t19101977] = lintrend (ratioFamPerPer[cr,th]; time=1910)
+local ratioFamPerPerPH[cr,t19101977] = lintrend (ratioFamPerPer[cr,t19782006]; time=1910)
-familiesPH[cr,t19101977] = extract (CEEFpop[cr,t18511990]; time:1910..1977) * ratioFamPerPerPH[cr,t19101977]
+familiesPH[cr,t19101977] = extract (CTotPopPH[cr,t18511990]; time:1910..1977) * ratioFamPerPerPH[cr,t19101977]
 </code>
 The main danger here is that your linear trend variable, ratioFamPerPerPH[cr,t19101977], goes negative
-===== log and exponential lintrend=====
-Another way to use lintrend and avoid the negatives it to use logarithm and exponential
-<code>
-local ratioFamPerPer[cr,th] = familiesTot[cr,th] / CTotPop[cr,th]
-local ratioFamPerPerPH[cr,t19101977] = exp (max (lintrend (loge (ratioFamPerPer[cr,th]); time=1910), 0))
-familiesPH[cr,t19101977] = extract (CEEFpop[cr,t18511990]; time:1910..1977) * ratioFamPerPerPH[cr,t19101977]
-</code>
 ===== Ratio with linint =====
-A safer way is to create an extra variable which is the ratio of the first year of pre-history to the first year of history and then linear interpret between these 2 points for the historic period.
+A safer way is to create an extra variable which is the ratio of the first year of pre-history (ratioFamPerPer1910to1978) to the first year of history and then linear interpret between these 2 points for the historic period.
 <code>
-local ratioFamPerPer[cr,th] = familiesTot[cr,th] / CTotPop[cr,th]
+! Build an object to hold the time from beginning of pre history to end of history and put in the part we know
-local ratioFamPerPerPHx[cr,t19101977] = changeseq (copyshape (ratioFamPerPer[cr,th]); dim=time, start=1910)
+local ratioFamPerPer[cr,t19782006] = familiesTot[cr,t19782006] / CTotPop[cr,t19782006]
-ratioFamPerPerPHx[cr,t19101977] = insert (ratioFamPerPer[cr,th]; time->time:1978)
+local ratioFamPerPerPHx[cr,t19101977] = changeseq (copyshape (ratioFamPerPer[cr,t19782006]); dim=time, start=1910)
-ratioFamPerPerPHx[cr,t19101977] = insert (extract (ratioFamPerPer[cr,th]; time:1978, shrink=on) * \
+ratioFamPerPerPHx[cr,t19101977] = insert (ratioFamPerPer[cr,t19782006]; time->time:1978)
+! Multiply the ratioFamPerPer1910to1978 agains against the first year of history and insert that as the first year of pre history
+ratioFamPerPerPHx[cr,t19101977] = insert (extract (ratioFamPerPer[cr,t19782006]; time:1978, shrink=on) * \
 	ratioFamPerPer1910to1978[cr]; time:1910)
+! Do Linear interpolation between these values
 local ratioFamPerPerPH[cr,t19101977]  = extract (linint (ratioFamPerPerPHx[cr,t19101977]); time:+0..1977)
+! Apply the ratio
 familiesPH[cr,t19101977] = extract (CEEFpop[cr,t18511990]; time:1910..1977) * ratioFamPerPerPH[cr,t19101977]
 </code>
 The main problem with this approach is that it is very flat over pre-history time
+===== log and exponential lintrend=====
+Another way is to use lintrend with logarithm and exponential
+<code>
+local ratioFamPerPer[cr,t19782006] = familiesTot[cr,t19782006] / CTotPop[cr,t19782006]
+local ratioFamPerPerPH[cr,t19101977] = exp (max (lintrend (loge (ratioFamPerPer[cr,t19782006]); time=1910), 0))
+familiesPH[cr,t19101977] = extract (CEEFpop[cr,t18511990]; time:1910..1977) * ratioFamPerPerPH[cr,t19101977]
+</code>

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