/// <summary>
/// Multiplies two Tnums together.
/// </summary>
public static Tnum operator * (Tnum tn1, Tnum tn2)
{
Tnum result = new Tnum();
foreach(KeyValuePair<DateTime,List<Hval>> slice in TimePointValues(tn1,tn2))
{
Hstate top = PrecedingState(slice.Value);
decimal val1 = Convert.ToDecimal(slice.Value [0].Val);
decimal val2 = Convert.ToDecimal(slice.Value [1].Val);
// Short circuit 1
if (val1 == 0 || val2 == 0)
{
result.AddState(slice.Key, new Hval(0));
}
else if (top != Hstate.Known) // Short circuit 2
{
result.AddState(slice.Key, new Hval(null,top));
}
else // Do the math
{
decimal prod = val1 * val2;
result.AddState(slice.Key, new Hval(prod));
}
}
return result.Lean;
}
/// <summary>
/// Returns the total elapsed days that a Tvar has a given value,
/// for each of a given set of intervals.
/// Example: meetsAnnualTest = var.ElapsedDaysPerInterval(theYear) > 183;
/// </summary>
public Tnum TotalElapsedDaysPer(Tnum period)
{
// If base Tnum is ever unknown during the time period, return
// the state with the proper precedence
Hstate baseState = PrecedenceForMissingTimePeriods(this);
Hstate periodState = PrecedenceForMissingTimePeriods(period);
Hstate top = PrecedingState(baseState, periodState);
if (top != Hstate.Known) return new Tnum(top);
Tnum result = new Tnum();
int count = period.IntervalValues.Count;
for (int i=0; i < count; i++)
{
DateTime spanEnd = Time.EndOf;
if (i < count-1)
{
spanEnd = period.IntervalValues.Keys[i+1];
}
TimeSpan time = this.TotalElapsedTime(period.IntervalValues.Keys[i], spanEnd);
// Add the state, but not if it's at the end of time
if (period.IntervalValues.Keys[i] < Time.EndOf)
{
result.AddState(period.IntervalValues.Keys[i], time.TotalDays);
}
}
return result.Lean;
}
public static Tnum IntervalsSince(Tdate startDate, Tdate endDate, IntervalType interval, int? startAt)
{
// Handle unknowns
Hstate top = PrecedingState(startDate.FirstValue, endDate.FirstValue);
if (top != Hstate.Known) return new Tnum(new Hval(null,top));
DateTime start = startDate.ToDateTime;
DateTime end = endDate.ToDateTime;
Tnum result = new Tnum();
if (start != Time.DawnOf)
{
result.AddState(Time.DawnOf,0);
}
DateTime indexDate = start;
int? indexNumber = startAt;
while (indexDate < end)
{
result.AddState(indexDate,Convert.ToDecimal(indexNumber));
indexNumber++;
indexDate = indexDate.AddInterval(interval, 1);
}
if (end < Time.EndOf) result.AddState(end, 0);
return result;
}
/// <summary>
/// Takes a Tnum representing some value per unit time, and sums or
/// accumulates it over a given type of time interval to obtain a
/// running total.
/// </summary>
/// <example>
/// Calculate lifetime accrued income, given a person's annual income:
///
/// AccruedIncome = AnnualIncome.RunningSummedIntervals(TheYear)
///
/// The time units cancel: [$/year] * [year] yields [$].
/// </example>
public Tnum RunningSummedIntervals(Tnum interval)
{
// TODO: Review how uncertainty is handled here:
// Handle unknowns
Hstate top = PrecedingState(this.FirstValue, interval.FirstValue);
if (top != Hstate.Known) return new Tnum(new Hval(null,top));
// If base Tnum is ever unknown during the time period, return
// the state with the proper precedence
Hstate baseState = PrecedenceForMissingTimePeriods(this);
if (baseState != Hstate.Known) return new Tnum(baseState);
// Start accumulating...
Tnum result = new Tnum(0);
decimal total = 0;
decimal previousVal = 0;
// Iterate through the intervals, totaling
for (int i=1; i < interval.TimeLine.Count-1; i++)
{
total += Convert.ToDecimal(this.ObjectAsOf(interval.TimeLine.Keys[i]).Val);
// Only add changepoint if value actually changes
if (total != previousVal)
{
result.AddState(interval.TimeLine.Keys[i+1], total);
}
// Set for next iteration
previousVal = total;
}
return result;
}
/// <summary>
/// Finds the Tset associated with a given Tnum value on a given date.
/// </summary>
private static Hval AssociatedTset(List<Tuple<Tset,Tnum>> setFcnVals, Tnum val, DateTime asOfDate)
{
foreach(Tuple<Tset,Tnum> t in setFcnVals)
{
// Handle uncertainty
Hval s = t.Item2.AsOf(asOfDate).FirstValue;
Hval v = val.AsOf(asOfDate).FirstValue;
if (s.IsUncertain && v.IsUncertain) return new Hval(null); // Not hitting this for some reason...
if (s.IsUnstated && v.IsUnstated) return new Hval(null, Hstate.Unstated);
if (s.IsStub && v.IsStub) return new Hval(null, Hstate.Stub);
// Compare numeric values
if (t.Item2.AsOf(asOfDate) == val.AsOf(asOfDate))
{
// Tsets created in Combos() are eternal, so FirstValue is ok here
return t.Item1.FirstValue;
}
}
return new Hval(null, Hstate.Stub);
}
/// <summary>
/// Provides a running count of how many whole intervals a Tbool
/// has been continuously true.
/// </summary>
/// <remarks>
/// Example:
/// tb = <--FTFTTF-->
/// tb.ICT = <--010120-->
///
/// Use judiciously with TheDay and TheCalendarWeek, as they have thousands of time intervals.
/// </remarks>
public Tnum ContinuousElapsedIntervals(Tnum interval)
{
// If base Tnum is ever unknown during the time period, return
// the state with the proper precedence
Hstate baseState = PrecedenceForMissingTimePeriods(this);
if (baseState != Hstate.Known) return new Tnum(baseState);
int intervalCount = 0;
DateTime dateNextTrue = this.DateNextTrue(Time.DawnOf);
DateTime dateNextTrueIntervalEnds = this.NextChangeDate(dateNextTrue.AddTicks(1));
Tnum result = new Tnum(0);
// Iterate through the time intervals in the input Tnum
for (int i=0; i < interval.IntervalValues.Count-1; i++)
{
DateTime start = interval.IntervalValues.Keys[i];
DateTime end = interval.IntervalValues.Keys[i+1];
// If base Tbool is always true during the interval, increment the count
if (end <= dateNextTrueIntervalEnds)
{
if (start >= dateNextTrue)
{
intervalCount++;
result.AddState(end, intervalCount);
continue;
}
}
else
{
// Otherwise, skip to next true interval
intervalCount = 0;
result.AddState(end, intervalCount);
dateNextTrue = this.DateNextTrue(end);
dateNextTrueIntervalEnds = this.NextChangeDate(dateNextTrue.AddTicks(1));
}
}
return result;
}
/// <summary>
/// Finds the total of a Tnum, summed over the given intervals between two
/// dates (start and end).
/// </summary>
/// <example>
/// AnnualIncome2014 = MonthlyIncome.TotalSummedIntervals(TheMonth, 2014-01-01, 2014-12-31)
/// </example>
public Tnum TotalSummedIntervals(Tnum interval, Tdate start, Tdate end)
{
Tnum rsi = RunningSummedIntervals(interval);
return rsi.AsOf(end) - rsi.AsOf(start);
}
public static Tnum IntervalsUntil(Tdate startDate, Tdate endDate, IntervalType interval, int startAt)
{
// Handle unknowns
Hstate top = PrecedingState(startDate.FirstValue, endDate.FirstValue);
if (top != Hstate.Known) return new Tnum(new Hval(null,top));
DateTime start = startDate.ToDateTime;
DateTime end = endDate.ToDateTime;
Tnum result = new Tnum();
DateTime indexDate = end;
int indexNumber = startAt-1;
while (indexDate > start)
{
if (indexNumber != startAt-1)
{
result.AddState(indexDate,Convert.ToString(indexNumber));
}
indexNumber++;
indexDate = indexDate.SubtractInterval(interval);
}
result.AddState(Time.DawnOf, 0);
result.AddState(start,Convert.ToString(indexNumber));
result.AddState(end, 0);
return result;
}
/// <summary>
/// Maps a function to a timeline, starting on a given date.
/// </summary>
// TODO: Get rid of Time.IntervalType
public static Tnum TemporalMap(Func<Tnum,Tnum> fcn, Tdate startDate, Tnum intervalCount, Time.IntervalType intervalType)
{
return fcn(Time.IntervalsSince(startDate, startDate.AddYears(intervalCount), intervalType));
}
/// <summary>
/// Implements Tset.OptimalSubset(Tnum fcn).
/// </summary>
private static Tset OptimalSubsetCore(Tset theSet, Func<Tset,Tnum> fcn)
{
Tset result = new Tset();
// For each time period in the Tset
for (int i=0; i < theSet.IntervalValues.Count; i++)
{
// Get some useful values
Hval thisSetVal = theSet.IntervalValues.Values[i];
DateTime start = theSet.IntervalValues.Keys[i];
// Handle uncertainty of theSet
if (!thisSetVal.IsKnown)
{
result.AddState(start, thisSetVal);
}
else
{
// Date parameters and set members of that time interval
List<Thing> mems = (List<Thing>)thisSetVal.Val;
DateTime end = Time.EndOf;
try {end = theSet.IntervalValues.Keys[i+1];} catch {}
// For each combination of set members, get the associated fcn val
List<Tuple<Tset,Tnum>> setFcnVals = new List<Tuple<Tset,Tnum>>();
Tnum maxVal = new Tnum(Decimal.MinValue);
foreach (Tset s in Combos(mems))
{
// Invoke the fcn for that subset
Tnum val = fcn(s);
// Save the result of the fcn and the associated Tset
setFcnVals.Add(Tuple.Create(s, val));
// Update the running maximum value
maxVal = Max(maxVal, val);
}
// Foreach changepoint in maxVal, find the associated Tset
for (int j=0; j < maxVal.IntervalValues.Count; j++)
{
DateTime mDate = maxVal.IntervalValues.Keys[j];
if (mDate >= start && mDate < end)
{
// Get the associated Tset
Hval outSet = AssociatedTset(setFcnVals, maxVal, mDate);
// Add the change point
result.AddState(mDate, outSet);
}
}
}
}
return result;
}
/// <summary>
/// Returns a Tbool in which the values are shifted in time relative to
/// the dates.
/// </summary>
public Tbool Shift(int offset, Tnum temporalPeriod)
{
return this.Shift<Tbool>(offset, temporalPeriod);
}
/// <summary>
/// Cosine
/// </summary>
public static Tnum Cos(Tnum tn)
{
return ApplyFcnToTimeline<Tnum>(x => CoreCos(x), tn);
}
/// <summary>
/// A raised to the B power
/// </summary>
public static Tnum Pow(Tnum tnA, Tnum tnB)
{
return(ApplyFcnToTimeline <Tnum>(x => CorePow(x), tnA, tnB));
}
/// <summary>
/// Adds a specified number of years to each DateTime in a Tdate.
/// Negative values are subtracted.
/// </summary>
public Tdate AddYears(Tnum days)
{
return ApplyFcnToTimeline<Tdate>(x => CoreAddYears(x), this, days);
}
/// <summary>
/// Returns a Tset in which the values are shifted in time relative to
/// the dates.
/// </summary>
public Tset Shift(int offset, Tnum temporalPeriod)
{
return this.Shift<Tset>(offset, temporalPeriod);
}
/// <summary>
/// Returns a Tdate in which the last value in a time period is the
/// final value.
/// </summary>
public Tdate PeriodEndVal(Tnum temporalPeriod)
{
return(this.PeriodEndVal <Tdate>(temporalPeriod).Lean);
}
/// <summary>
/// Returns true in the period during which a given date falls
/// Example: (2013-04-15).IsInPeriod(TheYear) is true for all of 2013, and otherwise false
/// </summary>
public Tbool IsInPeriod(Tnum interval)
{
// The event + 1 tick (temporal)
Tbool theEvent = Time.IsBetween(this, new Tdate(this.ToDateTime.AddTicks(1)));
// True during the interval when the event occurs
return theEvent.EverPer(interval);
}
/// <summary>
/// Returns a Tdate in which the values are shifted in time relative to
/// the dates.
/// </summary>
public Tdate Shift(int offset, Tnum temporalPeriod)
{
return(this.Shift <Tdate>(offset, temporalPeriod));
}
/// <summary>
/// ArcTan
/// </summary>
public static Tnum ArcTan(Tnum tn)
{
return(ApplyFcnToTimeline <Tnum>(x => CoreArcTan(x), tn));
}
/// <summary>
/// Cosine
/// </summary>
public static Tnum Cos(Tnum tn)
{
return(ApplyFcnToTimeline <Tnum>(x => CoreCos(x), tn));
}
/// <summary>
/// Logarithm of n to base b
/// </summary>
public static Tnum Log(Tnum b, Tnum n)
{
return(ApplyFcnToTimeline <Tnum>(x => CoreLog(x), b, n));
}
/// <summary>
/// Returns a Tset in which the last value in a time period is the
/// final value.
/// </summary>
public Tset PeriodEndVal(Tnum temporalPeriod)
{
return this.PeriodEndVal<Tset>(temporalPeriod).Lean;
}
/// <summary>
/// Logarithm of n to base b
/// </summary>
public static Tnum Log(Tnum b, Tnum n)
{
return ApplyFcnToTimeline<Tnum>(x => CoreLog(x), b, n);
}
/// <summary>
/// Square root
/// </summary>
public static Tnum Sqrt(Tnum tn)
{
return(ApplyFcnToTimeline <Tnum>(x => CoreSqrt(x), tn));
}
/// <summary>
/// ArcTan
/// </summary>
public static Tnum ArcTan(Tnum tn)
{
return ApplyFcnToTimeline<Tnum>(x => CoreArcTan(x), tn);
}
// ********************************************************************
// ROUNDING FUNCTIONS
// ********************************************************************
/// <summary>
/// Rounds a value to the nearest multiple of a given number. By default,
/// it rounds up in case of a tie.
/// </summary>
public Tnum RoundToNearest(Tnum multiple)
{
return RoundToNearest(multiple,false);
}
/// <summary>
/// Divides one Tnum by another.
/// </summary>
public static Tnum operator / (Tnum tn1, Tnum tn2)
{
Tnum result = new Tnum();
foreach(KeyValuePair<DateTime,List<Hval>> slice in TimePointValues(tn1,tn2))
{
Hstate top = PrecedingState(slice.Value);
decimal denominator = Convert.ToDecimal(slice.Value[1].Val);
if (denominator == 0) // Short circuit 1: Div-by-zero
{
result.AddState(slice.Key, new Hval(null));
}
else if (top != Hstate.Known) // Short circuit 2: Hstates
{
result.AddState(slice.Key, new Hval(null,top));
}
else // Do the math
{
decimal r = Convert.ToDecimal(slice.Value[0].Val) / denominator;
result.AddState(slice.Key, new Hval(r));
}
}
return result.Lean;
}
public Tnum RoundToNearest(Tnum multiple, Tbool breakTieByRoundingDown)
{
Tnum diff = this % multiple;
return Switch<Tnum>(() => diff > multiple / 2, () => this - diff + multiple,
()=> diff < multiple / 2 || breakTieByRoundingDown, ()=> this - diff,
() => true, () => this - diff + multiple);
}
/// <summary>
/// Rounds a value down to the next multiple of a given number.
/// </summary>
public Tnum RoundDown(Tnum multiple)
{
return(Switch <Tnum>(() => this % multiple != 0, () => this - (this % multiple),
() => true, () => this));
}
/// <summary>
/// Takes a Tnum representing some value per unit time, and accumulates it
/// over a given number of successive time intervals.
/// </summary>
/// <example>
/// Calculate income accumulated over a three month period, where the
/// person earned $3,000/month:
///
/// Income = MonthlyIncome.SlidingSummedIntervals(TheMonth, 3)
///
/// The time units cancel: [$/mo.] * [mo.] yields [$].
/// </example>
public Tnum SlidingSummedIntervals(Tnum interval, Tnum windowSize)
{
// TODO: Review how uncertainty is handled here:
// Handle unknowns
Hstate top = PrecedingState(this.FirstValue, interval.FirstValue, windowSize.FirstValue);
if (top != Hstate.Known) return new Tnum(new Hval(null,top));
// If base Tnum is ever unknown during the time period, return
// the state with the proper precedence
Hstate baseState = PrecedenceForMissingTimePeriods(this);
if (baseState != Hstate.Known) return new Tnum(baseState);
// Handle eternal values
if (this.IsEternal)
{
return this * windowSize;
}
// Start accumulating...
int num = windowSize.ToHardInt;
// Get first accumulated value
decimal firstVal = 0;
for (int j=0; j<num; j++)
{
// Don't walk off the end of the timeline
if (j < interval.TimeLine.Count)
{
firstVal += this.AsOf(interval.TimeLine.Keys [j]).ToHardDecimal;
}
}
Tnum result = new Tnum(firstVal);
// Iterate through the subsequent intervals
decimal previousVal = firstVal;
for (int i=1; i < interval.TimeLine.Count-num; i++)
{
// Take the value from the last iteration, and slide it the time window to the right,
// subtracting the left interval and adding the new right one.
decimal lastOldInterval = Convert.ToDecimal(this.ObjectAsOf(interval.TimeLine.Keys[i-1]).Val);
decimal nextNewInterval = Convert.ToDecimal(this.ObjectAsOf(interval.TimeLine.Keys[i+num-1]).Val);
decimal newVal = previousVal - lastOldInterval + nextNewInterval;
// Only add changepoint if value actually changes
if (newVal != previousVal)
{
// The value of an interval is counted after it has elapsed
result.AddState(interval.TimeLine.Keys[i+num], newVal);
}
// Set for next iteration
previousVal = newVal;
}
return result;
}
/// <summary>
/// Returns a Tbool in which the last value in a time period is the
/// final value.
/// </summary>
public Tbool PeriodEndVal(Tnum temporalPeriod)
{
return this.PeriodEndVal<Tbool>(temporalPeriod).Lean;
}
/// <summary>
/// Returns the total number of elapsed intervals between two dates.
/// </summary>
public Tnum TotalElapsedIntervals(Tnum interval, Tdate start, Tdate end)
{
Tnum rei = RunningElapsedIntervals(interval);
return rei.AsOf(end) - rei.AsOf(start);
}
//*********************************************************************
// TEMPORAL "RECURRENCE" FUNCTIONS
//*********************************************************************
/// <summary>
/// Loops (cycles) through numbers over time (e.g. 1 2 3 4 1 2 3 4 ...)
/// </summary>
public static Tnum Recurrence(Tdate startDate, Tdate endDate, IntervalType interval, int min, int max)
{
// Handle unknowns
Hstate top = PrecedingState(startDate.FirstValue, endDate.FirstValue);
if (top != Hstate.Known) return new Tnum(new Hval(null,top));
DateTime start = startDate.ToDateTime;
DateTime end = endDate.ToDateTime;
Tnum result = new Tnum();
if (start != Time.DawnOf)
{
result.AddState(Time.DawnOf, 0);
}
DateTime indexDate = start;
int indexNumber = min;
while (indexDate < end)
{
result.AddState(indexDate,Convert.ToString(indexNumber));
indexDate = indexDate.AddInterval(interval, 1);
// Reset sequence
indexNumber++;
if (indexNumber > max)
{
indexNumber = min;
}
}
result.AddState(end, 0);
return result;
}
/// <summary>
/// Finds the total of a Tnum, summed over the given intervals between two
/// dates (start and end).
/// </summary>
/// <example>
/// AnnualIncome2014 = MonthlyIncome.TotalSummedIntervals(TheMonth, 2014-01-01, 2014-12-31)
/// </example>
public Tnum TotalSummedIntervals(Tnum interval, Tdate start, Tdate end)
{
Tnum rsi = RunningSummedIntervals(interval);
return(rsi.AsOf(end) - rsi.AsOf(start));
}
// ********************************************************************
// ROUNDING FUNCTIONS
// ********************************************************************
/// <summary>
/// Rounds a value to the nearest multiple of a given number. By default,
/// it rounds up in case of a tie.
/// </summary>
public Tnum RoundToNearest(Tnum multiple)
{
return(RoundToNearest(multiple, false));
}
/// <summary>
/// Natural logarithm
/// </summary>
public static Tnum Log(Tnum tn)
{
return ApplyFcnToTimeline<Tnum>(x => CoreNatLog(x), tn);
}
/// <summary>
/// Rounds a value down to the next multiple of a given number.
/// </summary>
public Tnum RoundDown(Tnum multiple)
{
return Switch<Tnum>(() => this % multiple != 0, () => this - (this % multiple),
() => true, () => this);
}
/// <summary>
/// Natural logarithm
/// </summary>
public static Tnum Log(Tnum tn)
{
return(ApplyFcnToTimeline <Tnum>(x => CoreNatLog(x), tn));
}
/// <summary>
/// Provides a running count of how many intervals (years, days, etc.) a Tbool
/// has been true within some sliding window of time. At the end of that sliding
/// window, this function returns the amount of time that has elapsed within the
/// window during which the Tbool was true.
/// </summary>
/// <remarks>
/// Example: For a given Tbool, at any given point in time, for how many days during the
/// previous 3 days is the Tbool true?
///
/// tb = <FTTTFTTTFFFF>
/// tb.SEI(3, TheDay) = <001232223210>
/// </remarks>
public Tnum SlidingElapsedIntervals(Tnum interval, Tnum windowSize)
{
// If a Tbool is eternally true, return windowSize
if (this.IsTrue)
{
return windowSize;
}
// The number of true intervals in a sliding window of time equals
// the running count as of time1 minus the running count as of time0.
Tnum r = this.RunningElapsedIntervals(interval);
int size = Convert.ToInt32(windowSize.FirstValue.Val) * -1;
// Counts the current inerval
return r - r.Shift(size, interval);
}
/// <summary>
/// A raised to the B power
/// </summary>
public static Tnum Pow(Tnum tnA, Tnum tnB)
{
return ApplyFcnToTimeline<Tnum>(x => CorePow(x), tnA, tnB);
}
/// <summary>
/// Square root
/// </summary>
public static Tnum Sqrt(Tnum tn)
{
return ApplyFcnToTimeline<Tnum>(x => CoreSqrt(x), tn);
}
/// <summary>
/// Takes a Tnum representing some value per unit time, and accumulates it
/// over a given number of successive time intervals.
/// </summary>
/// <example>
/// Calculate income accumulated over a three month period, where the
/// person earned $3,000/month:
///
/// Income = MonthlyIncome.SlidingSummedIntervals(TheMonth, 3)
///
/// The time units cancel: [$/mo.] * [mo.] yields [$].
/// </example>
public Tnum SlidingSummedIntervals(Tnum interval, Tnum windowSize)
{
// TODO: Review how uncertainty is handled here:
// Handle unknowns
Hstate top = PrecedingState(this.FirstValue, interval.FirstValue, windowSize.FirstValue);
if (top != Hstate.Known)
{
return(new Tnum(new Hval(null, top)));
}
// If base Tnum is ever unknown during the time period, return
// the state with the proper precedence
Hstate baseState = PrecedenceForMissingTimePeriods(this);
if (baseState != Hstate.Known)
{
return(new Tnum(baseState));
}
// Handle eternal values
if (this.IsEternal)
{
return(this * windowSize);
}
// Start accumulating...
int num = windowSize.ToHardInt;
// Get first accumulated value
decimal firstVal = 0;
for (int j = 0; j < num; j++)
{
// Don't walk off the end of the timeline
if (j < interval.TimeLine.Count)
{
firstVal += this.AsOf(interval.TimeLine.Keys [j]).ToHardDecimal;
}
}
Tnum result = new Tnum(firstVal);
// Iterate through the subsequent intervals
decimal previousVal = firstVal;
for (int i = 1; i < interval.TimeLine.Count - num; i++)
{
// Take the value from the last iteration, and slide it the time window to the right,
// subtracting the left interval and adding the new right one.
decimal lastOldInterval = Convert.ToDecimal(this.ObjectAsOf(interval.TimeLine.Keys[i - 1]).Val);
decimal nextNewInterval = Convert.ToDecimal(this.ObjectAsOf(interval.TimeLine.Keys[i + num - 1]).Val);
decimal newVal = previousVal - lastOldInterval + nextNewInterval;
// Only add changepoint if value actually changes
if (newVal != previousVal)
{
// The value of an interval is counted after it has elapsed
result.AddState(interval.TimeLine.Keys[i + num], newVal);
}
// Set for next iteration
previousVal = newVal;
}
return(result);
}