Linear interpolation with Variables in T-SQL - sql-server

Question

Input to my procedur
#time datetime -- Example: 27.07.2015 01:00
With some SELECT staments I get the following information
#prevTime datetime -- Example: 27.07.2015 00:00
#prevValue real -- Example: 1
#nextTime datetime -- Example: 27.07.2015 02:00
#nextValue real -- Example: 3
Now I want to calculate
#value real -- In this Example the result should be: 2
i want to use "linear interpolation", see here: https://en.wikipedia.org/wiki/Linear_interpolation
Can someone tell me, how this gets done best? (Can i just convert the datetime into real?)
EDIT:
My first Quick&Dirty Idea:
SET #value = #prevValue + ((#nextValue-#prevValue)/(CAST(#nextTime as real)-CAST(#prevTime as real))) * (CAST(#time as real)-CAST(#prevTime as real));
Don't work, because datetime -> real is not precise
My second Quick&Dirty Idea:
SET #value = #prevValue + ((#nextValue-#prevValue)/(DATEDIFF(second,#nextTime,GETDATE())-DATEDIFF(second,#prevTime,GETDATE()))) * (DATEDIFF(second,#time,GETDATE())-DATEDIFF(second,#prevTime,GETDATE()));
Work's, but i would be happy if someone told me a nicer way

Answer 1

I'd submitted such code previously to SQL Server central as a code example at http://www.sqlservercentral.com/Forums/Topic872361-392-1.aspx
The code in question is below and performs standard gauss-jordan elimination to reduce supplied data points to an equation, then extrapolates accordingly:
-- Point type
CREATE TYPE Point AS TABLE (XCoordinate FLOAT, YCoordinate FLOAT);
GO
-- Curve fitting coefficient type
CREATE TYPE Coefficient AS TABLE (Multiplier FLOAT, PowerOfX INT);
GO
/**
* Function: fn_CurveFitPoints
* Author: Steven James Gray [ steve#cobaltsoftware.net ]
* Date: 24th February, 2010
* Version: 1.0
* Description:
* Takes a series of points in a table variant in POINT (X float, Y float) format and
* computes the n-1 power series curve fit using the Gauss-Jordan elimination process.
* Return value is a series of Multiplier, Power elements that can be used for producing
* an estimated Y value for any X value.
*
* Please refer to fn_ExtrapolateYValue(#xvalue, #coefficients) for a simple implementation
* of how to use the output of this function.
**/
CREATE FUNCTION dbo.fn_CurveFitPoints
(
#PointsToCurveFit POINT readonly
)
RETURNS #Result TABLE (Multiplier FLOAT, PowerOfX INT)
AS
BEGIN
-- ==========================================================================================
-- Stage 1 - Convert #PointsToFit into a matrix
-- ==========================================================================================
DECLARE #Matrix TABLE (MatrixRow INT, MatrixColumn INT, MatrixValue FLOAT);
DECLARE #TotalPoints INT = (SELECT COUNT(1) FROM #PointsToCurveFit);
WITH NumberProjectionCTE(CurrentNumber)
AS
(
SELECT 1
UNION ALL
SELECT 1+CurrentNumber FROM NumberProjectionCTE WHERE CurrentNumber < #TotalPoints
) INSERT INTO #Matrix
SELECT
Sequence-1, -- Each point gets it's own row
PWR.CurrentNumber-1, -- Column per power of X
CASE
WHEN PWR.CurrentNumber = 1 -- 1st column is X^0 = 1 Always
THEN 1
ELSE POWER(XCoordinate,PWR.CurrentNumber-1) -- Raise nth column to power n-1.
END
FROM
NumberProjectionCTE PWR, -- Cross join numeric point data and column indexes
(SELECT
ROW_NUMBER() OVER (ORDER BY XCoordinate, YCoordinate) AS Sequence,
XCoordinate,
YCoordinate
FROM
#PointsToCurveFit
) ValueData;
/* Append Y values as nth column */
INSERT INTO #Matrix
SELECT
ROW_NUMBER() OVER (ORDER BY XCoordinate, YCoordinate) - 1 AS Sequence,
#TotalPoints,
YCoordinate
FROM
#PointsToCurveFit;
-- ==========================================================================================
-- Stage 2 - Compute row echelon form of matrix
-- ==========================================================================================
DECLARE #lead INT = 0, #index INT = 0, #current FLOAT;
DECLARE #Rows INT = (SELECT MAX(MatrixRow) FROM #Matrix);
DECLARE #Columns INT = (SELECT MAX(MatrixColumn) FROM #Matrix);
DECLARE #Solved INT -- 0=Unsolvable, 1 = Solved
DECLARE #R INT = 0
WHILE #R <= #Rows
BEGIN
IF #Columns <= #lead
BEGIN
-- Cannot solve this one
SET #Solved = 0;
BREAK;
END;
SET #index = #R;
-- Determine if any row swaps are needed.
WHILE (SELECT MatrixValue FROM #Matrix WHERE MatrixRow = #index AND MatrixColumn = #lead) = 0
BEGIN
SET #index = #index + 1;
IF #Rows = #index
BEGIN
SET #index = #R;
SET #lead = #lead + 1;
IF #Columns = #lead
BEGIN
-- Cannot solve
SET #Solved = 0;
BREAK;
END;
END;
END;
-- Move this row to the correct position if needed.
IF #index <> #R
BEGIN
-- Swap rows
UPDATE #Matrix
SET MatrixRow = CASE MatrixRow
WHEN #R THEN #index
WHEN #index THEN #R
END
WHERE MatrixRow IN (#index, #R);
END;
-- Divide this row by it's lead column value, so that this row's lead is 1 (this will actually multiply/increase the value if lead <0)
DECLARE #Divisor FLOAT = (SELECT MatrixValue FROM #Matrix WHERE MatrixRow = #R AND MatrixColumn = #lead);
If #Divisor <> 1
BEGIN
UPDATE #Matrix SET MatrixValue = MatrixValue / #Divisor WHERE MatrixRow = #R;
END;
-- Update other rows and divide them by the appropriate multiple of this row in order to zero the current lead column.
UPDATE I
SET
MatrixValue = I.MatrixValue - (M.MatrixValue * R.MatrixValue)
FROM
#Matrix I
INNER JOIN #Matrix M ON M.MatrixRow = I.MatrixRow AND M.MatrixColumn = #lead
INNER JOIN #Matrix R ON R.MatrixColumn = I.MatrixColumn AND R.MatrixRow = #R AND R.MatrixRow <> I.MatrixRow
SET #lead = #lead + 1;
-- Move to next
SET #R = #R + 1;
END;
-- If we didn't bomb out, we're solved.
IF #Solved IS NULL
BEGIN
SET #Solved = 1
END;
-- ==========================================================================================
-- Stage 3 - Produce coefficients list (The final colum when in REF)
-- ==========================================================================================
IF #Solved = 1
BEGIN
INSERT INTO #Result (Multiplier, PowerOfX)
SELECT
MatrixValue,
MatrixRow
FROM #Matrix
WHERE MatrixColumn = #Columns;
END;
RETURN;
END;
GO
CREATE FUNCTION dbo.fn_ExtrapolateYValue
(
#XValue FLOAT,
#Coefficients Coefficient readonly
)
RETURNS FLOAT
AS
BEGIN
RETURN (SELECT SUM(Multiplier * POWER(#XValue, PowerOfX)) FROM #Coefficients);
END
For example:
DECLARE #PointsToCurveFit Point
-- A few simple X/Y values
INSERT INTO #PointsToCurveFit SELECT 1 , 6
INSERT INTO #PointsToCurveFit SELECT 2 , 3
INSERT INTO #PointsToCurveFit SELECT 3 , 2
-- Calculate the curve fitting coefficients
DECLARE #Coefficients Coefficient
INSERT INTO #Coefficients SELECT * FROM dbo.fn_CurveFitPoints(#PointsToCurveFit);
-- Shows that y= 11x^0 + 6x + x^2
SELECT * FROM #Coefficients;
-- Show the values for X=-5 to 5
WITH NumberCTE(Number)
AS
(
SELECT -5
UNION ALL
SELECT 1 + Number FROM NumberCTE WHERE Number < 5
) SELECT
Number AS XValue,
dbo.fn_ExtrapolateYValue(Number, #Coefficients) AS YValue
FROM NumberCTE;
In the code specified, I extrapolate the function of the curve from -5 to +5 on the X axis range.

Answer 2

I had this quest for enginering system, calucalting welding strength and here is how I solved it - clean and simple.
CREATE TABLE WeldStrengthReduction
(
[Temperature] numeric(18,4) NOT NULL ,
[Reduction] numeric(18,4) NOT NULL ,
);
GO
insert into WeldStrengthReduction (Temperature,Reduction)
values
(510,1),
(538,0.95),
(566,0.91),
(593,0.86),
(621,0.82),
(649,0.77),
(677,0.73),
(704,0.68),
(732,0.64),
(760,0.59),
(788,0.55),
(816,0.5);
Go
Create Function WSRF(#Tempreture Numeric(18,4) ) returns Numeric(18,4)
as
begin
declare
#X1 Numeric(18,4),
#X2 Numeric(18,4),
#X3 Numeric(18,4),
#Y1 Numeric(18,4),
#Y2 Numeric(18,4),
#Y3 Numeric(18,4),
#pointer int
set #X2 = #Tempreture
declare #Templist table (id int IDENTITY(1,1), temp numeric(18,4), red numeric(18,4))
insert into #Templist select Temperature,Reduction from WeldStrengthReduction order by Temperature
select top 1 #X3 = temp, #Y3 = red, #pointer = id from #Templist where temp >= #Tempreture
if #pointer = 1 return #Y3 -- if incomming tempereture is below lowest, return according to lowewst temp
if #pointer is null return null -- if incomming tempereture is above highest, return null
select #X1 = temp, #Y1 = red from #Templist where id = #pointer - 1
set #Y2 = ((#X2-#X1)*(#Y3-#Y1))/(#X3 - #X1) + #Y1
return #Y2
end;
Go
select WSRF(772);
select WSRF(300);
select WSRF(1200);