efg's Reference Library: Delphi Engineering Mathematics

Function Name	Description	Source(s)
arccosh	Function ArcCosh(X: Extended): Extended; Input: X >= 1	math, TPmath1(fmath), Turbo (p. 143), AugMath
ArcCotH	function ArcCotH( const X: Extended): Extended;	Kylix math
ArcCscH	function ArcCscH( const X: Extended): Extended;	Kylix math
ArcSecH	function ArcSecH( const X: Extended): Extended;	Kylix math
arcsinh	Function ArcSinh(X: Extended): Extended;	math, TPmath1(fmath), Turbo (p. 143), AugMath
arctanh	Function ArcTanh(X: Extended): Extended; Input: \|X\| <= 1	math, TPmath1(fmath), AugMath
cosh	Function Cosh(X: Extended): Extended; cosh(x) = [exp(x) + exp(-x)]/2	math, TPmath1(fmath), Turbo (p. 143), AugMath
coth	coth = 1/tanh function CotH(const X: Extended): Extended;	Kylix math, AugMath
csch	csch = 1/sinh function CscH( const X: Extended): Extended;	Kylix math, AugMath
ESBArCosh, ESBArSinh, ESBARTanh ESBCosh ESBSinh ESBTanh	hypberbolic functions and inverse functions	ESBMaths
farg_ch, farg_sh, farg_th	arccosh, arcsinh, arctanh	mathlib2(hyper387)
fch, fsh, fth	cosh, sinh, tanh	mathlib2(hyper387)
sech	1/cosh function SecH( const X: Extended): Extended;	Kylix math, AugMath
sinh	Function Sinh(X: Extended): Extended; sinh(x) = [exp(x) - exp(-x)]/2	math, TPmath1(fmath), Turbo (p. 142), AugMath
tanh	Function Tanh(X: Extended): Extended; tanh(x) = sinh(x)/cosh(x)	math, TPmath1(fmath), Turbo (p. 143), AugMath

Function Name	Description	Source(s)
bessI bessI0 bessI1	modified Bessel function I of integer order modified Bessel function I₀ modified Bessel function I₁	recipes
bessJ bessJ0 bessJ1	Bessel function J of integer order Bessel function J₀ Bessel function J₁	recipes
bessj(x,n)	Bessel function of the first kind	mathe
bessK bessK0 bessK1	modified Bessel function K of integer order modified Bessel function K₀ modified Bessel function K₁	recipes
bessY bessY0 bessY1	modified Bessel function Y of integer order modified Bessel function Y₀ modified Bessel function Y₁	recipes
Beta	beta function	TPmath1(fmath), recipes
cel	complete elliptic integral	recipes(cel)
erf erfc	error function, complementary	recipes, TPmath1(fmath)
erfcc	error function, complementary, concise	recipes
gamma	gamma function	TPmath1(fmath), mathe, Turbo (p. 142)
gammp gammq gammln	gamma function gamma(z + 1) = z * gamma(z) = z! incomplete gamma function (gammp) incomplete, complement (gammq) logarithm of gamma function (gammln)	recipes
Gradient & Hessian	Gradient and Hessian of a function of several variables.	TPmath2 (hessian)
IBeta	incomplete beta function	TPmath1(fmath)
IGamma	incomplete gamma function	TPmath1(fmath)
JGamma	complemement of IGamma	TPmath1(fmath)
LnGamma	Log(\| Gamma(X) \|)	TPmath1(fmath), StatUnit(distr)
plgndr	Legendre polynomials, associated (spherical harmonics)	recipes
SgnGamma	Sign of gamma function	TPmath1(fmath)
sncndn	Jacobian elliptic functions	recipes

Function Name(s)	Description	Source(s)
Complex Arithmetic Overview		Stockton
Complex Functions	CConvert, CSet, CStr, CAdd, CDiv, CMult, CSub, CNeg, CLn, CExp, CPwr, CCos, CSin, CTan, CSec, CCsc, CCot, CCosh, CSinh, CTanh, CSech, CCsch, CCoth, CAbs, CAbsSqr, CIntPower, CRealPower, CPower, CConjugate, CSqrt, CRoot, CI0, CJ0, CLnGamma, CGama, CDeFuzz, DeFuzz, SetFuzz, FixAngle	efg's: ComplexMathLibrary
Complex Functions:	cadd, csub, cmul, cdiv, cneg, ccong, crcp, ciz, c_iz, czero, cmod, cequal, carg, cexp, cln, csqrt, ccos, csin, ctg, carc_cos, carc_sin, carc_tg, cch, csh, cth, carg_ch, carg_sh, carg_th	mathlib2(pcomplex)
Complex Functions	RP, IP, Cmplx, PolarCmplx, cabs, arg, cc, ca, cs, cm, rc, cd, cr, PrSqrt, cExp, cLn, csin, ccos, ctan, ccosh, csinh, ctanh	EZmath Another Complex Library
Complex Library		UDDF MATH
Complex Unit	www.ibrtses.com/delphi/complexrec.html
C_LU_Decomp	LU decomposition	TPmath1 (matcomp)
C_LU_Solve	Solves system of equations	TPmath1 (matcomp)
Delphi 6 Complex functions	General: VarComplexCreate (with overloads), VarComplex, VarIsComplex, VarAsComplex, VarComplexSimplify, VarComplexAbsSqr, VarComplexAbs, VarComplexAngle, VarComplexConjugate, VarComplexInverse, VarComplexExp, VarComplexLn, VarComplexSqr, VarComplexSqrt, VarComplexTimesPosI, VarComplexTimesNegI, VarComplexPower Trig/Hyperbolic: VarComplexCos, VarComplexSin, VarComplexTan, VarComplexCot, VarComplexSec, VarComplexCsc, VarComplexArcCos, VarComplexArcSin, VarComplexArcTan, VarComplexArcCot, VarComplexArcSec, VarComplexArcCsc, VarComplexCosH, VarComplexSinH, VarComplexTanH, VarComplexCotH, VarComplexSecH, VarComplexCscH, VarComplexArcCosH, VarComplexArcSinH, VarComplexArcTanH, VarComplexArcCotH, VarComplexArcSecH, VarComplexArcCscH Conversion: VarComplexToPolar, VarComplexFromPolar Variables: ComplexNumberSymbol, ComplexNumberSymbolBeforeImaginary	VarCmplx (D6). Fnd the source in ..\Delphi6\Source\Rtl\Common)
Intel's Digital Signal Processing Library (ISPL)	See Digital Signal Processing.	ISPL
MMEMatrix	Very easy and fast complex matrix class. http://delphi.icm.edu.pl/ftp/d40free/MMEMatrix.zip
Plotting Complex Functions	www.ibrtses.com/delphi/complexplot.html

Function Name	Description	Source(s)
Add_Matrix	add matrices A and B to give matrix C	Turbo (p. 146)
balanc	balance a nonsymmetric matrix	recipes
Determinant and Matrix Inverse		TPMath2 (DetInv)
Eigenvectors and Eigenvalues	Symmetric Matrix, General Square Matrix, Real Eigenvalue & EigenMatrix	TPMath2(EigenSym), TPMath2(EigenVal), TPMath2(EigenVec)
eigsrt	eigenvectors, sorts into order by eigenvalue	recipes
elmhes	reduce a general matrix to Hessenberg form	recipes
Extentia	Exentia is an open-source library for Delphi designed to perform computations on vectors of 32-bit floating point data elements using the Intel SSE, AMD 3D Now! and Intel x87 instruction sets. www.tommesani.com/Exentia.html Dr. Chris Rorden created a very basic project based on this software. It uses QueryPerformanceCounter to measure the performance benefit for using SIMD calls. www.psychology.nottingham.ac.uk/staff/cr1/simd.html
Gauss Elimination	www.optimalcode.com/exgauss.htm
Gaussian Reduction	www.ibrtses.com/delphi/dequ.html
GaussJ	Gauss-Jordan matrix inversion Download Turbo Pascal 5.5from the Borland Community Museum: http://community.borland.com/museum, and look for the HILB.PAS file.	mathe, recipes(gaussj)
hqr	eigenvalues of a Hessenberg matrix	recipes
Invert_Matrix	add matrices A and B to give matrix C	Turbo (p. 147-148)
Jacobi, EigenVals, EigenVect	Eigenvalues and Eigenvectors	TPMath1 (Eigen)
Linear Equations	Gauss-Jordan Elimination LU decomposition Singular value decomposition	TPMath2(SysEq) TPMath2(SysEqLU) TPMath2(SysEqSVD)
Linear Equations, Complex Coefficients		TPMath2(SysEqC)
lubksb ludcmp	linear equation solution, LU decomposition (ludcmp) and backsubstitution (lubksb)	recipes
Matrices		TPMath1 (Matrices)
Matrices, Complex Elements		TPMath1 (MatComp)
Matrix	Shareware Product by SDL (Software Development Lohninger) www.lohninger.com/matrix.html
Matrix Math Toolkit	Commerical Product from Engineering Objects International www.engineeringobjects.com/ MatrixMathToolkitv4.htm
Matrix Operations	Dynamic Types: TDynFloatMatrix TDynLWordMatrix TDynLIntMatrix MatrixIsRectangular, MatrixDimensions, MatrixIsSquare, MatricesSameDimensions, AddMatrices, AddToMatrix, SubtractMatrices, SubtractFromMatrix, MultiplyMatrixByConst, MultiplyMatrixByConst2, MultiplyMatrices, TransposeMatrix, GrandMean	ESBMaths
mprove	linear equation solution, iterative improvement	recipes
Mult_Matrix	add matrices A and B to give matrix C	Turbo (p. 147)
svbksb	singular value backsubstitution	recipes
svdcmp	singular value decomposition of a matrix	recipes
TVector	Vector component www.lohninger.com/vector.html
toeplz	solve Toeplitz systems	recipes
tred2	Householder reduction of a real, symmetric matrix	recipes
tqli	eigensolution of a symmetric tridiagonal matrix	recipes
tridag	solution of tridiagonal systems	recipes
vander	Vandermonde systems	recipes
Vector	Vectors is a class library for Object Pascal (Delphi 1, 3-5 and Free Pascal v.0.99.15 and higher), which implements vectors (dynamically sized arrays) based on different Object Pascal's simple types, including all integer and real types, booleans, pointers and strings. These vectors resemble TList class type from Delphi VCL, but in addition to the common operations like insert and delete they offer wide range of operations depending on type of vector elements - sorting, searching, arithmetic vector operations for number-type vectors, logical operations for boolean vectors and so on. The library also implements a range of derivative and additional classes - sparse vectors, matrixes, queues, stacks, dictionaries, streams	Vectors.zip from DSP
Vector Operations	Dynamic types: TDynFloatArray TDynLWordArray TDynLIntArray SquareAll, InverseAll, Log10All, LinearTransform, AddVectors, SubVectors, MultVectors, DotProduct	ESBMaths

Function Name/Category	Math Description	Source(s)
adaptive FIR filter using LMS algorithm		ISPL
BDSPP	The Basic Delphi signal processing package (BDSPP). The package represents FFT Properties 3.5 in parts. It includes key components on which FFT Properties 3.5 are based. The vast majority of the functionality offered by FFT Properties is available from these VCL components. www.teemach.com/FFTProp
convlv	convolution or deconvolution of data using FFT	recipes
correl	correlation or autocorrelation of data using FFT	recipes
cosft	fast cosine transform	recipes
dsxfft	Simple Fast Fourier Transformation Component. FFT and inverse FFT. http://delphi.icm.edu.pl/ftp/d20free/dsxfft.zip	Delphi Super Page
evlmem	power spectral estimation using maximum entropy coefficients	recipes
FFT Unit for Delphi	FFT and inverse FFT routines for any number of samples (but if the number of samples is an exact power of 2, the faster power-of-2 FFT algorithm is used). Can be used for real and complex signals. FFFT (Fractional FFT) routines can provide any range of spectral lines (Zoom FFT). Many data windows (Parzen, Welch, Hann, Hamming, Blackman, FlatTop, ...). The source code of the FFT unit is available. www.aho.ch/fft
FFT using TFastFourier component	Fast Fourier Transform www.lohninger.com/fourier.html
fftprop2	Educational software for understanding the FFT properties. www.teemach.com/FFTProp
finite impulse response (FIR) filter (many routines)		ISPL
fixrts	reflect roots of a polynomial into unit circle	recipes
four1	FFT in one dimension	recipes
Fourier Analysis, FFTs		TPmath1(fourier) DatabaseFTP: Select "7Object Pascal" followed by "FFT_1.ZIP"
fourn	FFT in multidimensions	recipes
infinite impulse response (IIR) filter (many routines)		ISPL
Intel Signal Processing Library	Intel Signal Processing Library V4.1 Delphi interface patch and examples http://home.t-online.de/home/Robert.Rossmair/nsp.htm	ISPL
memcof	evaluate maximum entropy coefficients	recipes
miscellaneous signal processing functions	Examples: Permute vector into binary bit-reversed order, uniform distribution, normal distribution, NSP tone generator, other tone functions, triangle functions, vector addition and multiplication, scalar and vector functions, autocorrelation, crosscorrelation, vector arithmetic and algebraic functions	ISPL
nspXConv where X is s, c, d, z, sd, cs, dz, zd, w	finite, linear convolution of two sequences	ISPL
nspXConv2D, for X=s, d, w	finite, linear convolution of two 2D signals	ISPL
nspvReal, nspvImag	Real and Imaginary part of Complex Vector	ISPL
nspvbMag, nspvbPhas	Magnitude and phase of Complex Vector	ISPL
predic	linear prediction using maximum entropy coefficients	recipes
realft	FFT of single real function	recipes
Signal Processing Package	www.dewresearch.com/products/SPP_index.htm
sinft	fast sine transform	recipes
Single frequency DFT (Goertzel algorithm)		ISPL
spctrm	power spectrum estimation using FFT	recipes
TFastFourier	Can transform data sets of up to 32k samples in both directions and provides several of the most important windowing functions (such as Hamming, Blackman, Cosine Square, Triangle, and others). www.lohninger.com/fourier.html
twofft	FFT of two real functions	recipes

Source

Description/Location

AugMath

Augmented Math (what Borland left out)
www.engineeringobjects.com/AugMathUnit.htm

ESBMaths

ESB Consultancy
Developers of Mathematical & Statistical
Software and Delphi Software.

ESBMaths is a collection of Integer and Floating Point Routines for Delphi. Includes probability and statistical related routines

Freeware ESBMaths with Source. www.esbconsult.com

EZMath

DSP

Delphi Super Page (not to be confused with Digital Signal Processing):
http://delphi.icm.edu.pl

ISPL

Delphi interface for the Intel Signal Processing Library (5430 lines, 872 procedures and functions exported by NSP.DLL): http://home.t-online.de/home/Robert.Rossmair/nsp.htm

Intel Signal Processing Library:
http://developer.intel.com/vtune/perflibst/spl

math

Borland's Delphi math unit

mathe

Scientific Subroutine Library

mathlib2

ftp://ftp.coriolis.com/Downloads/mathlib2.zip

recipes

Numerical Recipes Pascal shareware version, ftp://garbo.uwasa.fi/pc/turbopas/nrpas13.zip
(On-line FORTRAN/C Books: www.nr.com.)

StatUnit

www.math.ku.dk/ims/software/index.html

TPmath1
TPmath2

TP Math

Jean DeBord's TPMath
www.unilim.fr/pages_perso/jean.debord/tpmath/tpmath.htm

Turbo

Turbo Algorithms (C, Pascal, Basic, Prolog)
Keith Weiskamp, Namir Shamas, Ron Pronk
John Wiley, 1989 (Out of Print)

UDDF Math

Unofficial Delphi Developers FAQ: www.gnomehome.demon.nl/uddf/pages/math.htm (linki broken 30 July 2000)

Category	Math Description	Source(s)
bsstep	integrate ODEs, Bulirsch-Stoer step	recipes
mmid	integrate ODEs by modified midipoint method	recipes
odeint	integrate ODEs with accuracy monitoring	recipes
rk4	integrate one step of ODEs, fourth-order Runge-Kutta	recipes
rkdumb	integrate ODEs by fourth-order Runge-Kutta	recipes
shoot	solve two-point boundary value problem by shooting	recipes
shootf	solve two-point boundary value problem by shooting to a fitting point	recipes
solvde	two-point boundary value problem, solve by relaxation	recipes
sor	elliptic PDE solved by successive overrelation method	recipes