lib: -X/--exchange now supports indirect price chains (#131)
Adds fgl as a dependency.
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@ -354,12 +354,12 @@ postingApplyValuation :: [PriceDirective] -> M.Map CommoditySymbol AmountStyle -
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postingApplyValuation prices styles periodend today ismultiperiod p v =
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postingApplyValuation prices styles periodend today ismultiperiod p v =
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case v of
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case v of
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AtCost Nothing -> postingToCost styles p
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AtCost Nothing -> postingToCost styles p
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AtCost mc -> postingValueAtDate prices mc periodend $ postingToCost styles p
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AtCost mc -> postingValueAtDate prices styles mc periodend $ postingToCost styles p
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AtEnd mc -> postingValueAtDate prices mc periodend p
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AtEnd mc -> postingValueAtDate prices styles mc periodend p
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AtNow mc -> postingValueAtDate prices mc today p
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AtNow mc -> postingValueAtDate prices styles mc today p
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AtDefault mc | ismultiperiod -> postingValueAtDate prices mc periodend p
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AtDefault mc | ismultiperiod -> postingValueAtDate prices styles mc periodend p
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AtDefault mc -> postingValueAtDate prices mc today p
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AtDefault mc -> postingValueAtDate prices styles mc today p
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AtDate d mc -> postingValueAtDate prices mc d p
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AtDate d mc -> postingValueAtDate prices styles mc d p
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-- | Convert this posting's amount to cost, and apply the appropriate amount styles.
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-- | Convert this posting's amount to cost, and apply the appropriate amount styles.
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postingToCost :: M.Map CommoditySymbol AmountStyle -> Posting -> Posting
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postingToCost :: M.Map CommoditySymbol AmountStyle -> Posting -> Posting
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@ -370,8 +370,8 @@ postingToCost styles p@Posting{pamount=a} = p{pamount=mixedAmountToCost styles a
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-- using the given market prices.
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-- using the given market prices.
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-- When market prices available on that date are not sufficient to
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-- When market prices available on that date are not sufficient to
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-- calculate the value, amounts are left unchanged.
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-- calculate the value, amounts are left unchanged.
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postingValueAtDate :: [PriceDirective] -> Maybe CommoditySymbol -> Day -> Posting -> Posting
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postingValueAtDate :: [PriceDirective] -> M.Map CommoditySymbol AmountStyle -> Maybe CommoditySymbol -> Day -> Posting -> Posting
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postingValueAtDate prices mc d p = postingTransformAmount (mixedAmountValueAtDate prices mc d) p
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postingValueAtDate prices styles mc d p = postingTransformAmount (mixedAmountValueAtDate prices styles mc d) p
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-- | Apply a transform function to this posting's amount.
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-- | Apply a transform function to this posting's amount.
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postingTransformAmount :: (MixedAmount -> MixedAmount) -> Posting -> Posting
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postingTransformAmount :: (MixedAmount -> MixedAmount) -> Posting -> Posting
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@ -1,7 +1,7 @@
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{-|
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{-|
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Find historical market prices (exchange rates) between commodities,
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Convert amounts to some related value in various ways. This involves
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convert amounts to value in various ways.
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looking up historical market prices (exchange rates) between commodities.
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-}
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-}
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@ -11,8 +11,7 @@ convert amounts to value in various ways.
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{-# LANGUAGE ScopedTypeVariables #-}
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{-# LANGUAGE ScopedTypeVariables #-}
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module Hledger.Data.Prices (
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module Hledger.Data.Prices (
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Prices
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amountValueAtDate
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,amountValueAtDate
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,amountApplyValuation
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,amountApplyValuation
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,mixedAmountValueAtDate
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,mixedAmountValueAtDate
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,mixedAmountApplyValuation
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,mixedAmountApplyValuation
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@ -22,8 +21,13 @@ module Hledger.Data.Prices (
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where
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where
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import Control.Applicative ((<|>))
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import Control.Applicative ((<|>))
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import Data.Decimal (roundTo)
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import Data.Function (on)
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import Data.Graph.Inductive (Gr, Node, NodeMap, mkMapGraph, mkNode, lab, out, suc, sp)
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import Data.List
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import Data.List
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import Data.List.Extra
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import qualified Data.Map as M
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import qualified Data.Map as M
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import Data.Maybe
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import qualified Data.Text as T
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import qualified Data.Text as T
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import Data.Time.Calendar (Day)
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import Data.Time.Calendar (Day)
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import Safe (headMay)
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import Safe (headMay)
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@ -34,9 +38,6 @@ import Hledger.Data.Amount
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import Hledger.Data.Dates (parsedate)
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import Hledger.Data.Dates (parsedate)
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d = parsedate
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-- amt c q = nullamt{acommodity=c, aquantity=q}
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tests_Prices = tests "Prices" [
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tests_Prices = tests "Prices" [
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tests_priceLookup
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tests_priceLookup
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]
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]
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@ -58,8 +59,8 @@ mixedAmountApplyValuation prices styles periodend today ismultiperiod v (Mixed a
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-- valuation date, using the given market prices.
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-- valuation date, using the given market prices.
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-- When market prices available on that date are not sufficient to
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-- When market prices available on that date are not sufficient to
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-- calculate the value, amounts are left unchanged.
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-- calculate the value, amounts are left unchanged.
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mixedAmountValueAtDate :: [PriceDirective] -> Maybe CommoditySymbol -> Day -> MixedAmount -> MixedAmount
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mixedAmountValueAtDate :: [PriceDirective] -> M.Map CommoditySymbol AmountStyle -> Maybe CommoditySymbol -> Day -> MixedAmount -> MixedAmount
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mixedAmountValueAtDate prices mc d (Mixed as) = Mixed $ map (amountValueAtDate prices mc d) as
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mixedAmountValueAtDate prices styles mc d (Mixed as) = Mixed $ map (amountValueAtDate prices styles mc d) as
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-- | Apply a specified valuation to this amount, using the provided
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-- | Apply a specified valuation to this amount, using the provided
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-- prices db, commodity styles, period-end/current dates,
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-- prices db, commodity styles, period-end/current dates,
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@ -68,12 +69,12 @@ amountApplyValuation :: [PriceDirective] -> M.Map CommoditySymbol AmountStyle ->
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amountApplyValuation prices styles periodend today ismultiperiod v a =
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amountApplyValuation prices styles periodend today ismultiperiod v a =
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case v of
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case v of
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AtCost Nothing -> amountToCost styles a
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AtCost Nothing -> amountToCost styles a
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AtCost mc -> amountValueAtDate prices mc periodend $ amountToCost styles a
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AtCost mc -> amountValueAtDate prices styles mc periodend $ amountToCost styles a
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AtEnd mc -> amountValueAtDate prices mc periodend a
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AtEnd mc -> amountValueAtDate prices styles mc periodend a
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AtNow mc -> amountValueAtDate prices mc today a
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AtNow mc -> amountValueAtDate prices styles mc today a
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AtDefault mc | ismultiperiod -> amountValueAtDate prices mc periodend a
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AtDefault mc | ismultiperiod -> amountValueAtDate prices styles mc periodend a
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AtDefault mc -> amountValueAtDate prices mc today a
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AtDefault mc -> amountValueAtDate prices styles mc today a
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AtDate d mc -> amountValueAtDate prices mc d a
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AtDate d mc -> amountValueAtDate prices styles mc d a
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-- | Find the market value of this amount in the given valuation
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-- | Find the market value of this amount in the given valuation
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-- commodity if any, otherwise the default valuation commodity, at the
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-- commodity if any, otherwise the default valuation commodity, at the
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@ -82,85 +83,183 @@ amountApplyValuation prices styles periodend today ismultiperiod v a =
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-- valuation date.)
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-- valuation date.)
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-- If the market prices available on that date are not sufficient to
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-- If the market prices available on that date are not sufficient to
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-- calculate this value, the amount is left unchanged.
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-- calculate this value, the amount is left unchanged.
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amountValueAtDate :: [PriceDirective] -> Maybe CommoditySymbol -> Day -> Amount -> Amount
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amountValueAtDate :: [PriceDirective] -> M.Map CommoditySymbol AmountStyle -> Maybe CommoditySymbol -> Day -> Amount -> Amount
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amountValueAtDate pricedirectives mc d a =
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amountValueAtDate pricedirectives styles mto d a =
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case priceLookup pricedirectives d mc (acommodity a) of
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case priceLookup pricedirectives d (acommodity a) mto of
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Just v -> v{aquantity=aquantity v * aquantity a}
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Nothing -> a
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Nothing -> a
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Just (comm, rate) -> styleAmount styles $ amount{acommodity=comm, aquantity=rate * aquantity a}
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------------------------------------------------------------------------------
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------------------------------------------------------------------------------
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-- Market price lookup, naive version
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-- Market price lookup
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tests_priceLookup =
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let
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d = parsedate
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a q c = amount{acommodity=c, aquantity=q}
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p date from q to = PriceDirective{pddate=d date, pdcommodity=from, pdamount=a q to}
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ps1 = [
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p "2000/01/01" "A" 10 "B"
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,p "2000/01/01" "B" 10 "C"
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,p "2000/01/01" "C" 10 "D"
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,p "2000/01/01" "E" 2 "D"
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,p "2001/01/01" "A" 11 "B"
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]
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in tests "priceLookup" [
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priceLookup ps1 (d "1999/01/01") "A" Nothing `is` Nothing
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,priceLookup ps1 (d "2000/01/01") "A" Nothing `is` Just ("B",10)
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,priceLookup ps1 (d "2000/01/01") "B" (Just "A") `is` Just ("A",0.1)
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,priceLookup ps1 (d "2000/01/01") "A" (Just "E") `is` Just ("E",500)
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]
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-- | Given a list of price directives in parse order, find the market
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-- | Given a list of price directives in parse order, find the market
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-- value at the given date of one unit of a given commodity, in a
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-- value at the given date of one unit of a given source commodity, in
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-- different specified valuation commodity, defaulting to the
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-- a different specified valuation commodity, or a default valuation
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-- commodity of the most recent applicable price.
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-- commodity.
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-- This might be slow if there are many price declarations.
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--
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--
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-- When the valuation commodity is specified, this looks for, in order:
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-- When the valuation commodity is specified, this looks for, in order:
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--
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--
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-- - a direct price, giving the exchange rate from source commodity to
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-- - a price declaration giving the exchange rate from source
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-- valuation commodity.
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-- commodity to valuation commodity ("declared price").
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--
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--
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-- - a reverse direct price, giving the exchange rate from valuation
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-- - a price declaration from valuation to source commodity, which
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-- commodity to source commodity, which is inverted.
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-- gets inverted ("reverse price").
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--
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--
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-- - (TODO: the shortest chain of prices leading from source commodity
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-- - the shortest chain of prices (declared or reverse) leading from
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-- to valuation commodity, which is collapsed into a single
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-- source commodity to valuation commodity, which gets collapsed
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-- synthetic exchange rate.)
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-- into a single synthetic exchange rate ("indirect price").
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--
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--
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-- When the valuation commodity is not specified, this looks for the
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-- When the valuation commodity is not specified, this looks for the
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-- latest applicable market price, and converts to the commodity
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-- latest applicable market price, and converts to the commodity
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-- mentioned in that price. Note when valuing amounts over multiple
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-- mentioned in that price (default valuation commodity).
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-- periods, this default valuation commodity may vary, since it
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-- depends on the presence and parse order of market price
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-- declarations in each period.
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--
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--
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-- If no applicable market price or chain of prices can be found, or
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-- Note when calling this repeatedly for different periods, the
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-- if the source commodity and the valuation commodity are the same,
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-- default valuation commodity can vary, since it depends on the
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-- this returns Nothing.
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-- presence and parse order of market price declarations in each
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-- period.
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--
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--
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priceLookup :: [PriceDirective] -> Day -> Maybe CommoditySymbol -> CommoditySymbol -> Maybe Amount
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-- This returns the valuation commodity that was specified or
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priceLookup pricedirectives d mto from
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-- inferred, and the quantity of it that one unit of the source
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-- commodity is worth. Or if no applicable market price or chain of
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| otherwise = mdirectprice <|> mreverseprice
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-- prices can be found, or the source commodity and the valuation
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-- commodity are the same, returns Nothing.
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--
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-- A 'Prices' database (price graphs) is built each time this is
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-- called, which is probably wasteful when looking up multiple prices
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-- on the same day; it could be built at a higher level, or memoised.
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--
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priceLookup :: [PriceDirective] -> Day -> CommoditySymbol -> Maybe CommoditySymbol -> Maybe (CommoditySymbol, Quantity)
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priceLookup pricedirectives d from mto =
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let
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-- build a graph of the commodity exchange rates in effect on this day
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Prices{prNodemap=m, prDeclaredPrices=g, prWithReversePrices=gr} = pricesAtDate pricedirectives d
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fromnode = node m from
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-- if to is unspecified, try to find a default valuation commodity based on available prices
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mto' = mto <|> mdefaultto
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where
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where
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dbgprice lbl =
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-- the default valuation commodity, if we could find one.
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dbg4With ( ((lbl++" for "++T.unpack from++" at "++show d++": ") ++)
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-- XXX how to choose ? Take lowest sorted ?
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. maybe "none" showAmount )
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-- Take first, hoping current order is useful ? <-
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-- Keep parse order in label and take latest parsed ?
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mdefaultto = headMay (suc g fromnode) >>= lab g
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in
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case mto' of
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Nothing -> Nothing
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Just to | to==from -> Nothing
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Just to ->
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-- We have a commodity to convert to. Find the most direct price available,
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-- and return it as an amount.
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case
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-- These seem unnecessary, and we can avoid building one of the graphs
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-- mdeclaredprice <|> mreverseprice <|>
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mindirectprice of
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Nothing -> Nothing
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Just q -> Just (to, q)
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where
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tonode = node m to
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-- mdeclaredprice :: Maybe Quantity =
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-- dbg ("declared market price "++T.unpack from++"->"++T.unpack to) $
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-- nodesEdgeLabel g (fromnode,tonode)
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-- mreverseprice :: Maybe Quantity =
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-- dbg ("reverse market price "++T.unpack from++"->"++T.unpack to) $
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-- ((1 /) <$> nodesEdgeLabel g (tonode,fromnode))
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mindirectprice :: Maybe Quantity =
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-- Find the shortest path, if any, between from and to.
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-- This time use gr which includes both declared and reverse prices.
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case sp fromnode tonode gr :: Maybe [Node] of
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Nothing -> Nothing
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Just nodes ->
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dbg ("market price "++intercalate "->" (map T.unpack comms)) $
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Just $ product $ pathEdgeLabels gr nodes -- convert to a single exchange rate
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where comms = catMaybes $ map (lab g) nodes
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latestfirst = reverse $ sortOn pddate pricedirectives -- sortOn will preserve parse order within the same date I think
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-- log a message and a Maybe Quantity, hiding Just/Nothing and limiting decimal places
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dbg msg = dbg4With (((msg++": ")++) . maybe "" (show . roundTo 3))
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-- Key to commodity symbols:
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-- | Convert a list of market price directives in parse order to
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-- from - commodity we are converting from (looking up a price for)
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-- a database of market prices in effect on a given day,
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-- mto - commodity we want to convert to, or Nothing meaning use default
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-- allowing efficient lookup of exchange rates between commodity pairs.
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-- pfrom - commodity that this market price converts from
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pricesAtDate :: [PriceDirective] -> Day -> Prices
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-- pto - commodity that this market price converts to
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pricesAtDate pricedirectives d = Prices{
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prNodemap = m
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,prDeclaredPrices = g
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,prWithReversePrices = gr
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}
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where
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-- get the latest (before d) declared price for each commodity pair
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latestdeclaredprices :: [MarketPrice] =
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dbg4 "latestdeclaredprices" $
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nubSortBy (compare `on` (\(MarketPrice{..})->(mpfrom,mpto))) $ -- keep only the first (ie newest and latest parsed) price for each pair
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map snd $ -- discard the parse order label
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sortBy (flip compare `on` (\(parseorder,mp)->(mpdate mp,parseorder))) $ -- sort with newest dates and latest parse order first
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zip [1..] $ -- label with parse order
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map priceDirectiveToMarketPrice $
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filter ((<=d).pddate) pricedirectives -- consider only price declarations up to the valuation date
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-- and the latest declared or reverse price for each commodity pair
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latestdeclaredandreverseprices =
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latestdeclaredprices `union` map marketPriceReverse latestdeclaredprices
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-- XXX hopefully this prioritises the declared prices, test
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allcomms = sort $ map mpfrom latestdeclaredandreverseprices
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(g :: PriceGraph, m :: NodeMap CommoditySymbol) = mkMapGraph
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(dbg5 "g nodelabels" allcomms) -- this must include all nodes mentioned in edges
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(dbg5 "g edges" [(mpfrom, mpto, mprate) | MarketPrice{..} <- latestdeclaredprices])
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(gr, _) = mkMapGraph
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(dbg5 "gr nodelabels" allcomms) -- this must include all nodes mentioned in edges
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(dbg5 "gr edges" [(mpfrom, mpto, mprate) | MarketPrice{..} <- latestdeclaredandreverseprices])
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-- prPriceDirectives is sorted by date then parse order, reversed. So the
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priceDirectiveToMarketPrice :: PriceDirective -> MarketPrice
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-- first price on or before the valuation date is the effective one.
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priceDirectiveToMarketPrice PriceDirective{..} =
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MarketPrice{ mpdate = pddate
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, mpfrom = pdcommodity
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, mpto = acommodity pdamount
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, mprate = aquantity pdamount
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}
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mdirectprice =
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marketPriceReverse :: MarketPrice -> MarketPrice
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dbgprice "direct market price" $
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marketPriceReverse mp@MarketPrice{..} = mp{mpfrom=mpto, mpto=mpfrom, mprate=1/mprate}
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headMay [pdamount | PriceDirective{pddate, pdcommodity=pfrom, pdamount} <- latestfirst
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, let pto = acommodity pdamount
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------------------------------------------------------------------------------
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, pddate <= d
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-- fgl helpers
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, pfrom == from
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, maybe True (== pto) mto
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-- | Look up an existing node by its label in the given NodeMap.
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]
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-- (If the node does not exist, a new one will be generated, but not
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mreverseprice =
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-- persisted in the nodemap.)
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dbgprice "reverse market price" $
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node :: Ord a => NodeMap a -> a -> Node
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headMay [ priceamt
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node m = fst . fst . mkNode m
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| PriceDirective{pddate, pdcommodity=pfrom, pdamount} <- latestfirst
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, let pto = acommodity pdamount
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-- | Convert a valid path from the given graph to the corresponding
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, pddate <= d
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-- edge labels. When there are multiple edges between two nodes, the
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, pto == from
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-- lowest-sorting label is used.
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, maybe False (== pfrom) mto -- use reverse prices only when target commodity is explicitly specified
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pathEdgeLabels :: (Show b, Ord b) => Gr a b -> [Node] -> [b]
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, let PriceDirective{pdamount=priceamt} = undefined -- marketPriceInvert mp
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pathEdgeLabels g = map frommaybe . map (nodesEdgeLabel g) . pathEdges
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]
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where frommaybe = fromMaybe (error' "pathEdgeLabels: expected no Nothings here")
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tests_priceLookup = tests "priceLookup" [
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-- | Convert a path to node pairs representing the path's edges.
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priceLookup [] (d "2019-06-01") Nothing "" `is` Nothing
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pathEdges :: [Node] -> [(Node,Node)]
|
||||||
]
|
pathEdges p = [(f,t) | f:t:_ <- tails p]
|
||||||
|
|
||||||
|
-- | Get the label of a graph edge from one node to another.
|
||||||
|
-- When there are multiple such edges, the lowest-sorting label is used.
|
||||||
|
nodesEdgeLabel :: Ord b => Gr a b -> (Node, Node) -> Maybe b
|
||||||
|
nodesEdgeLabel g (from,to) = headMay $ sort [l | (_,t,l) <- out g from, t==to]
|
||||||
|
|
||||||
------------------------------------------------------------------------------
|
------------------------------------------------------------------------------
|
||||||
|
|||||||
@ -27,6 +27,7 @@ import Data.Data
|
|||||||
import Data.Decimal
|
import Data.Decimal
|
||||||
import Data.Default
|
import Data.Default
|
||||||
import Data.Functor (($>))
|
import Data.Functor (($>))
|
||||||
|
import Data.Graph.Inductive (Gr, NodeMap)
|
||||||
import Data.List (intercalate)
|
import Data.List (intercalate)
|
||||||
import Text.Blaze (ToMarkup(..))
|
import Text.Blaze (ToMarkup(..))
|
||||||
--XXX https://hackage.haskell.org/package/containers/docs/Data-Map.html
|
--XXX https://hackage.haskell.org/package/containers/docs/Data-Map.html
|
||||||
@ -445,15 +446,17 @@ data MarketPrice = MarketPrice {
|
|||||||
|
|
||||||
instance NFData MarketPrice
|
instance NFData MarketPrice
|
||||||
|
|
||||||
-- | A database of the exchange rates between commodity pairs at a given date,
|
-- | A graph whose node labels are commodities and edge labels are exchange rates.
|
||||||
-- organised as maps for efficient lookup.
|
type PriceGraph = Gr CommoditySymbol Quantity
|
||||||
|
|
||||||
|
-- | A snapshot of the known exchange rates between commodity pairs at a given date.
|
||||||
data Prices = Prices {
|
data Prices = Prices {
|
||||||
prDeclaredPrices ::
|
prNodemap :: NodeMap CommoditySymbol
|
||||||
M.Map CommoditySymbol -- from commodity A
|
,prDeclaredPrices :: PriceGraph -- ^ Explicitly declared market prices for commodity pairs.
|
||||||
(M.Map CommoditySymbol -- to commodity B
|
,prWithReversePrices :: PriceGraph -- ^ The above, plus derived reverse prices for any pairs which don't have a declared price.
|
||||||
Quantity) -- exchange rate from A to B (one A is worth this many B)
|
-- ,prWithIndirectPrices :: PriceGraph -- ^ The above, plus indirect prices found for any pairs which don't have a declared or reverse price.
|
||||||
-- ^ Explicitly declared market prices, as { FROMCOMM : { TOCOMM : RATE } }.
|
|
||||||
}
|
}
|
||||||
|
deriving (Show)
|
||||||
|
|
||||||
-- | What kind of value conversion should be done on amounts ?
|
-- | What kind of value conversion should be done on amounts ?
|
||||||
-- UI: --value=cost|end|now|DATE[,COMM]
|
-- UI: --value=cost|end|now|DATE[,COMM]
|
||||||
|
|||||||
@ -4,7 +4,7 @@ cabal-version: 1.12
|
|||||||
--
|
--
|
||||||
-- see: https://github.com/sol/hpack
|
-- see: https://github.com/sol/hpack
|
||||||
--
|
--
|
||||||
-- hash: ac2028674178919d87ff7e06ea16e97e245e92deeb60beb9689c083547cd1a44
|
-- hash: 89c2a4dadadc88418d53e5b39a17bcc9831b58cf46dbf77c4a5598f6db326cbc
|
||||||
|
|
||||||
name: hledger-lib
|
name: hledger-lib
|
||||||
version: 1.14.99
|
version: 1.14.99
|
||||||
@ -121,6 +121,7 @@ library
|
|||||||
, directory
|
, directory
|
||||||
, easytest >=0.2.1 && <0.3
|
, easytest >=0.2.1 && <0.3
|
||||||
, extra
|
, extra
|
||||||
|
, fgl >=5.5.3.0
|
||||||
, file-embed >=0.0.10
|
, file-embed >=0.0.10
|
||||||
, filepath
|
, filepath
|
||||||
, hashtables >=1.2.3.1
|
, hashtables >=1.2.3.1
|
||||||
@ -223,6 +224,7 @@ test-suite doctests
|
|||||||
, doctest >=0.16
|
, doctest >=0.16
|
||||||
, easytest >=0.2.1 && <0.3
|
, easytest >=0.2.1 && <0.3
|
||||||
, extra
|
, extra
|
||||||
|
, fgl >=5.5.3.0
|
||||||
, file-embed >=0.0.10
|
, file-embed >=0.0.10
|
||||||
, filepath
|
, filepath
|
||||||
, hashtables >=1.2.3.1
|
, hashtables >=1.2.3.1
|
||||||
@ -324,6 +326,7 @@ test-suite easytests
|
|||||||
, directory
|
, directory
|
||||||
, easytest >=0.2.1 && <0.3
|
, easytest >=0.2.1 && <0.3
|
||||||
, extra
|
, extra
|
||||||
|
, fgl >=5.5.3.0
|
||||||
, file-embed >=0.0.10
|
, file-embed >=0.0.10
|
||||||
, filepath
|
, filepath
|
||||||
, hashtables >=1.2.3.1
|
, hashtables >=1.2.3.1
|
||||||
|
|||||||
@ -55,6 +55,7 @@ dependencies:
|
|||||||
- deepseq
|
- deepseq
|
||||||
- directory
|
- directory
|
||||||
- easytest >= 0.2.1 && <0.3
|
- easytest >= 0.2.1 && <0.3
|
||||||
|
- fgl >=5.5.3.0
|
||||||
- file-embed >=0.0.10
|
- file-embed >=0.0.10
|
||||||
- filepath
|
- filepath
|
||||||
- hashtables >=1.2.3.1
|
- hashtables >=1.2.3.1
|
||||||
|
|||||||
@ -550,9 +550,11 @@ you want.
|
|||||||
|
|
||||||
To select a different valuation commodity: write the commodity symbol
|
To select a different valuation commodity: write the commodity symbol
|
||||||
after the valuation type, separated by a comma (eg: **`--value=now,EUR`**).
|
after the valuation type, separated by a comma (eg: **`--value=now,EUR`**).
|
||||||
Currently this will only use market prices leading directly from A to
|
This will use, in this preferred order:
|
||||||
B, or (after inverting them) prices from B to A;
|
|
||||||
it does not yet follow chains of market prices.
|
- declared prices (from source commodity to valuation commodity)
|
||||||
|
- reverse prices (declared prices from valuation to source commodity, inverted)
|
||||||
|
- indirect prices (prices calculated from the shortest chain of declared or reverse prices from source to valuation commodity).
|
||||||
|
|
||||||
#### --value examples
|
#### --value examples
|
||||||
|
|
||||||
|
|||||||
Loading…
Reference in New Issue
Block a user