Advanced Math UDF

[scintilla4evr]

I started writing this UDF a while ago, so I decided to share it here.

This is an UDF full of advanced mathematical functions. It allows to work with primes, create number sequences, interpolate, calculate values of functions like Riemann zeta.

Full list of functions:

Spoiler

BooleAnd
BooleOr
BooleNot
BooleEqual
BooleXor
Combination
CombinationR
Variation
VariationR
BellCurve
ParabolaCurve
CubicCurve
QuarticCurve
FoliumCurve
CissoidCurve
ConchoidCurve
SemicubicalParabolaCurve
SerpentineCurve
ContinuedFraction
Cosh
Coth
Csch
Sech
Sinh
Tanh
ACosh
ACoth
ACsch
ASech
ASinh
ATanh
LinearInterpolation
CosineInterpolation
CubicInterpolation
LogN
Log10
Log2
Logit
ArithmeticMean
HeinzMean
LogMean
HeronianMean
StolarskyMean
Sinc
BernoulliStirling
Gd
AGd
GaussLegendrePi
BitEqual
Factor
Divisors
GCD
LCM
Factorial
FactorialN
Superfactorial
Newton
Pi
Tau
Sigma
EulerTotient
Versin
Exsec
RisingFactorial
FallingFactorial
IsCoprime
IsPrime
IsPrime2
ListPrimes
ListPrimes2
NthPrime
NRoot
Cbrt
Stirling1
Stirling2
Bell
Bernoulli
Catalan
Carol
Cullen
AiryAi
AiryBi
BesselJ0
BesselJ1
BesselJn
BesselY0
BesselY1
BesselYn
Erf
Erfc
FourierSquareWave
FourierSawtoothWave
FourierTriangleWave
Gamma
Digamma
Beta
Sign
SawtoothWave
SquareWave
TriangleWave
RiemannZeta
RiemannXi
DirichletEta
HurwitzZeta
DirichletLambda
TriangularNum
HexagonalNum
Cot
Sec
Csc
ACot
ASec
ACsc

Added with 1.1:
Differential
Point
RotatePoint
AngleBetweenPoints
CoinFlip
DieRoll
CalculateProbability
NormalDistribution
ArcsineDistribution
BetaDistribution
DiracDelta

Added with 1.2:
Determinant
MultiplyArrayByMatrix
DistanceBetweenPoints
Vector
VectorAdd
VectorSubtract
VectorMultiplyScalar
VectorDivideScalar
VectorNegate
VectorApplyOp
VectorDotProduct
VectorCross
VectorLength
VectorNormalize
VectorAngleBetween
VectorReflect
VectorTransmit
EulerRotateX
EulerRotateY
EulerRotateZ
Complex
ComplexReal
ComplexImag
ComplexNegate
ComplexAbs
ComplexArg
ComplexConj
ComplexAdd
ComplexSubtract
ComplexMultiply
ComplexDivide
ComplexExp
ComplexLog
ComplexPow
Quaternion
QuaternionGetVector
QuaternionFromScalarVectorPair
QuaternionConj
QuaternionNorm
QuaternionAdd
QuaternionSubtract
QuaternionMultiply
QuaternionInvert
QuaternionDivide
QuaternionRotateVector

Added with 1.3:
PolygonalNum
NSimplexNum
Fibonacci
Lucas
LucasLehmer
IsPrimeLucas
IsMersennePrime
IsPrime3
ListPrimes3
Lychrel
Integral
Pascal
IsPrimeAKS
IsPrime1
Differential2
Limit
Solve
IdentityMatrix
TransposeMatrix

Added with version 1.3.1:
Trigamma

Added with version 1.4:
SolveDiff
FresnelC
FresnelS
Clausen
IncompleteGamma
Variance
StandardDeviation
NormalDistributonPDF
GeneticIteration
GeneticCrossPairs

Added with version 1.5:
Graph
GraphAddPoint
GraphAddLink
GraphMarkPoint
GraphGetMark
GraphMarkAll
GraphGetConnections
GraphGetPathLength
GraphFindPathDijkstra

Added with version 1.6:
VectorDistance
ATan2
AlphaMaxBetaMin
Triangle
TriangleGetAngles
LevenshteinDistance

Added with version 1.7:
Mandelbrot
WarpFactor
LorenzFactor
TimeDilation
LengthContraction
Mollify
BellCurveMollifier
LinearMollifier
ConstantMollifier
SharpMollifier

 

Changelog:

Spoiler

Version 1.7:

• Added Mandelbrot()
• Added WarpFactor()
• Fixed ComplexLog()
• Added physics constants (from physics.nist.gov)
• Added LorentzFactor(), TimeDilation(), LengthContraction() and RelativisticMomentum()
• Added Mollify(), BellCurveMollifier, LinearMollifier, ConstantMollifier and SharpMollifier
• Added NewtonianGravity()

Version 1.6:

• Added VectorDistance()
• Fixed RotatePoint()
• Point() and DistanceBetweenPoints() now call Vector() and VectorDistance() respectively
• Added ATan2()
• Added AlphaMaxBetaMin()
• Added Triangle() and TriangleGetAngles()
• Added LevenshteinDistance() using Wagner-Fischer algorithm
• Added an example of genetic algorithm

Version 1.5:

• Added graph functions
• Added GraphFindPathDijkstra() for finding the path in an undirected graph (example included)

Version 1.4:

• Added SolveDiff() for numerically solving differential equations
• Added Fresnel integrals (FresnelC and FresnelS)
• Added some statistical functions (more later)
• Added Clausen()
• Added IncompleteGamma()
• Added basic genetic algorithm functions (see Genetic.au3)
• Fixed issues with _Degree(), _Radian() and _MathCheckDiv()

Version 1.3.1:

• Reimplemented DLL functions in AutoIt
• Added Trigamma()

Version 1.3:

• Added polygonal and n-simplex numbers
• Added Fibonacci, Lucas and Lucas-Lehmer sequences
• Added IsPrime3(), faster alternative to both IsPrime1() and IsPrime2()
• Added IsPrimeAKS()
• Added IsMersennePrime()
• Added Lychrel()
• Added Integral()
• Added Pascal's triangle
• Renamed IsPrime() to IsPrime1()
• Added IdentityMatrix() and TransposeMatrix()
• Added Solve()
• Added new IsPrime()
• Renamed Differential() to Differential2()
• Added new Differential()

Version 1.2:

• Added matrices
• Added DistanceBetweenPoints()
• Added vectors
• Added Euler rotations
• Added complex numbers
• Added procedural events for probability calculations
• Corrected algorithm for differentials
• Added quaternions

Version 1.1:

• Added differentials
• Added probability calculation and some predefined events
• Added point functions
• Added examples for differentials and probability

Version 1.0:

• first version of the UDF

Download

Edited September 18, 2016 by scintilla4evr

[jchd]

Where does math.dll come from?

[scintilla4evr]

Where does math.dll come from?

I wrote it in C++ to make some calculations faster.

[mLipok]

added here:

https://www.autoitscript.com/wiki/User_Defined_Functions#Maths

[scintilla4evr]

New version!

Changes include:

• Complex numbers
• Quaternions
• Probability improvements
• And more!

 Math_UDF.zip

[RTFC]

Hi scintilla4evr,

First off, great to see more maths support for AutoIt being added. But I'm having a little trouble understanding your design choices. Only four functions (Bessel, error function, and two Gamma) actually use your tiny dll, which you say is for speed reasons. But any function involving trig would also benefit from being carried out directly on the FPU rather than in AutoIt, not to mention calculus, log, and iterative search algos like you use for primes all being faster when pre-compiled. So if you decide to provide a dedicated dll (which is definitely beneficial here), why not put everything in there? Alternatively, if you favour pure AutoIt for legibility and understanding, why not dispense with the dll altogether, especially since you now need an additional msvcr dll that is about 73 times bigger than your own dll? Incidentally, you can get rid of that dependency by compiling with runtime binary flag /MT instead of /MD (in MSVC, under Code Generation in Project properties, section C++). It would also help if you provide your dll source, but that is of course entirely up to you. But if I were to use your Bessel functions I would want to know how your algorithms actually work, since Bessel functions can be solved in several, rather different ways. It's just a thought.

 

[scintilla4evr]

Version 1.3:

• Added polygonal and n-simplex numbers
• Added Fibonacci, Lucas and Lucas-Lehmer sequences
• Added IsPrime3(), faster alternative to both IsPrime1() and IsPrime2()
• Added IsPrimeAKS()
• Added IsMersennePrime()
• Added Lychrel()
• Added Integral()
• Added Pascal's triangle
• Renamed IsPrime() to IsPrime1()
• Added IdentityMatrix() and TransposeMatrix()
• Added Solve()
• Added new IsPrime()
• Renamed Differential() to Differential2()
• Added new Differential()

And RFTC, I will follow your advice and try to reimplement these functions in AutoIt and get rid of the DLLs. Thanks for the advice!

Advanced Math UDF

[RTFC]

That's great, scintilla4evr!

[scintilla4evr]

Version 1.3.1:

• The DLLs are now gone. Forever.
• Added Trigamma()

Advanced Math UDF

[scintilla4evr]

Version 1.4:

• Added SolveDiff() for numerically solving differential equations
• Added Fresnel integrals (FresnelC and FresnelS)
• Added some statistical functions (more later)
• Added Clausen()
• Added IncompleteGamma()
• Added basic genetic algorithm functions (see Genetic.au3)
• Fixed issues with _Degree(), _Radian() and _MathCheckDiv()

I'll try to make an example of a genetic algorithm and include it in the next version.

Advanced Math UDF

Edited May 3, 2016 by scintilla4evr

[scintilla4evr]

Version 1.5:

• Added graph functions
• Added GraphFindPathDijkstra() for finding the path in an undirected graph (example included)

Advanced Math UDF

PS. No example for a genetic algorithm yet. Sorry! Will you forgive me?

[TNV]

That's greate! Thanks!

[scintilla4evr]

1.6:

• Added VectorDistance()
• Fixed RotatePoint()
• Point() and DistanceBetweenPoints() now call Vector() and VectorDistance() respectively
• Added ATan2()
• Added AlphaMaxBetaMin()
• Added Triangle() and TriangleGetAngles()
• Added LevenshteinDistance() using Wagner-Fischer algorithm
• Added an example of genetic algorithm (finally!)

Advanced Math UDF

[innovationresolver]

Very nice update ! 

Really cool UDF. 

Thanks !

[scintilla4evr]

1.7:

• Added Mandelbrot()
• Added WarpFactor()
• Fixed ComplexLog()
• Added physics constants (from physics.nist.gov)
• Added LorentzFactor(), TimeDilation(), LengthContraction() and RelativisticMomentum()
• Added Mollify(), BellCurveMollifier, LinearMollifier, ConstantMollifier and SharpMollifier
• Added NewtonianGravity()

Advanced Math UDF

[Andreik]

I tried to understand how your UDF work but I failed. There are so many warning and errors thrown to console. I saw many functions defined like this one:

Func __Pascal(ByRef $aRet)
    Local $ret[UBound($arr)+1]
    Local $i

    For $i = 0 To UBound($arr)
        $v1 = ($i > 0) ? $arr[$i-1] : 1
        $v2 = ($i < UBound($arr)) ? $arr[$i] : 1
        $ret[$i] = $v1+$v2
    Next

    Return $ret
EndFunc

whici might be fine using global variables but doesn't looks good since every function might be stand alone and code easy to debug. With your last UDF version, I tried to run Mollify example and my console cry out.

Quote

>"C:\Program Files (x86)\AutoIt3\SciTE\..\AutoIt3.exe" "C:\Program Files (x86)\AutoIt3\SciTE\AutoIt3Wrapper\AutoIt3Wrapper.au3" /run /prod /ErrorStdOut /in "C:\advmathudf-au3-master\advmathudf-au3-master\Examples\Mollify.au3" /UserParams    
+>11:44:49 Starting AutoIt3Wrapper v.17.224.935.0 SciTE v.3.7.3.0   Keyboard:00000409  OS:WIN_10/  CPU:X64 OS:X64  Environment(Language:0409)  CodePage:0  utf8.auto.check:4
+>         SciTEDir => C:\Program Files (x86)\AutoIt3\SciTE   UserDir => C:\Users\...\AppData\Local\AutoIt v3\SciTE\AutoIt3Wrapper   SCITE_USERHOME => C:\...\AppData\Local\AutoIt v3\SciTE 
>Running AU3Check (3.3.14.5)  from:C:\Program Files (x86)\AutoIt3  input:C:\advmathudf-au3-master\advmathudf-au3-master\Examples\Mollify.au3
"C:\advmathudf-au3-master\advmathudf-au3-master\Math\Curves.au3"(42,26) : warning: $ret possibly not declared/created yet
    $ret[0] = Cos($theta)*$r
    ~~~~~~~~~~~~~~~~~~~~~~~~^
"C:\advmathudf-au3-master\advmathudf-au3-master\Math\Curves.au3"(51,16) : warning: $ret possibly not declared/created yet
    $ret[0] = $t^2
    ~~~~~~~~~~~~~~^
"C:\advmathudf-au3-master\advmathudf-au3-master\Math\Sequences.au3"(108,24) : warning: $arr: possibly used before declaration.
    Local $ret[UBound($arr)
    ~~~~~~~~~~~~~~~~~~~~~~^
"C:\advmathudf-au3-master\advmathudf-au3-master\Math\Special\Airy.au3"(332,12) : warning: $x: possibly used before declaration.
    ElseIf $x <=
    ~~~~~~~~~~^
"C:\advmathudf-au3-master\advmathudf-au3-master\Math\Special\Step.au3"(9,14) : warning: $t: possibly used before declaration.
    Return 2*($t/
    ~~~~~~~~~~~~^
"C:\advmathudf-au3-master\advmathudf-au3-master\Math\Special\TrigIntegrals.au3"(4,66) : warning: $__g_ADVMATHUDF_INTEGRALSTEP: possibly used before declaration.
    Return Integral(_SiIntegral, 0, $x, $__g_ADVMATHUDF_INTEGRALSTEP,
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~^
"C:\advmathudf-au3-master\advmathudf-au3-master\Math\Calculus\Integral.au3"(5,26) : warning: $Infinity: possibly used before declaration.
    If $vStart = -$Infinity And
    ~~~~~~~~~~~~~~~~~~~~~~~~^
"C:\advmathudf-au3-master\advmathudf-au3-master\Math\Graphs\Graph.au3"(38,28) : error: Statement cannot be just an expression.
        ($aGraph[0])[$i] = $iMark
        ~~~~~~~~~~~~~~~~~~~~~~~~~^
"C:\advmathudf-au3-master\advmathudf-au3-master\Math\Sequences.au3"(108,24) : error: $arr: undeclared global variable.
    Local $ret[UBound($arr)
    ~~~~~~~~~~~~~~~~~~~~~~^
"C:\advmathudf-au3-master\advmathudf-au3-master\Math\Special\Step.au3"(9,14) : error: $t: undeclared global variable.
    Return 2*($t/
    ~~~~~~~~~~~~^
"C:\advmathudf-au3-master\advmathudf-au3-master\Math\Calculus\Integral.au3"(5,26) : error: $Infinity: undeclared global variable.
    If $vStart = -$Infinity And
    ~~~~~~~~~~~~~~~~~~~~~~~~^
"C:\advmathudf-au3-master\advmathudf-au3-master\Math\Special\Gamma.au3"(9,40) : error: Gamma2(): undefined function.
        Return $Pi / (Sin($Pi*$x)*Gamma2(1-$x)
        ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~^
C:\advmathudf-au3-master\Examples\Mollify.au3 - 5 error(s), 7 warning(s)
!>11:44:50 AU3Check ended. Press F4 to jump to next error.rc:2
+>11:44:50 AutoIt3Wrapper Finished.
>Exit code: 2    Time: 1.902

This might be a very useful UDF but it should be rewrite in a better manner.

Edited June 8, 2018 by Andreik

[water]

When do you start

[Haselnuzz]

Hi,

this maybe an absolute stupid question, but how to proceed, once i have downloaded the udf-file?
What i have done so far, downloaded, extracted to D:\Test\Maths. Then pointed Sciteconfig to that folder as userincluded folder. That´s it. So, if i want to i.e. compute the GCD of two integers in a Form...well?...no clue...can you assist me?

Thanks,

 

Patrick