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{ ------------------------------------------------------------------
Floating point type (Default = Double)
------------------------------------------------------------------ }
{$IFDEF SINGLEREAL}
type Float = Single;
{$ELSE}
{$IFDEF EXTENDEDREAL}
type Float = Extended;
{$ELSE}
{$DEFINE DOUBLEREAL}
type Float = Double;
{$ENDIF}
{$ENDIF}
{ ------------------------------------------------------------------
Mathematical constants
------------------------------------------------------------------ }
const
Pi = 3.14159265358979323846; { Pi }
Ln2 = 0.69314718055994530942; { Ln(2) }
Ln10 = 2.30258509299404568402; { Ln(10) }
LnPi = 1.14472988584940017414; { Ln(Pi) }
InvLn2 = 1.44269504088896340736; { 1/Ln(2) }
InvLn10 = 0.43429448190325182765; { 1/Ln(10) }
TwoPi = 6.28318530717958647693; { 2*Pi }
PiDiv2 = 1.57079632679489661923; { Pi/2 }
SqrtPi = 1.77245385090551602730; { Sqrt(Pi) }
Sqrt2Pi = 2.50662827463100050242; { Sqrt(2*Pi) }
InvSqrt2Pi = 0.39894228040143267794; { 1/Sqrt(2*Pi) }
LnSqrt2Pi = 0.91893853320467274178; { Ln(Sqrt(2*Pi)) }
Ln2PiDiv2 = 0.91893853320467274178; { Ln(2*Pi)/2 }
Sqrt2 = 1.41421356237309504880; { Sqrt(2) }
Sqrt2Div2 = 0.70710678118654752440; { Sqrt(2)/2 }
Gold = 1.61803398874989484821; { Golden Mean = (1 + Sqrt(5))/2 }
CGold = 0.38196601125010515179; { 2 - GOLD }
{ ------------------------------------------------------------------
Machine-dependent constants
------------------------------------------------------------------ }
{$IFDEF SINGLEREAL}
const
MachEp = 1.192093E-7; { Floating point precision: 2^(-23) }
MaxNum = 3.402823E+38; { Max. floating point number: 2^128 }
MinNum = 1.175495E-38; { Min. floating point number: 2^(-126) }
MaxLog = 88.72283; { Max. argument for Exp = Ln(MaxNum) }
MinLog = -87.33655; { Min. argument for Exp = Ln(MinNum) }
MaxFac = 33; { Max. argument for Factorial }
MaxGam = 34.648; { Max. argument for Gamma }
MaxLgm = 1.0383E+36; { Max. argument for LnGamma }
{$ENDIF}
{$IFDEF DOUBLEREAL}
const
MachEp = 2.220446049250313E-16; { 2^(-52) }
MaxNum = 1.797693134862315E+308; { 2^1024 }
MinNum = 2.225073858507202E-308; { 2^(-1022) }
MaxLog = 709.7827128933840;
MinLog = -708.3964185322641;
MaxFac = 170;
MaxGam = 171.624376956302;
MaxLgm = 2.556348E+305;
{$ENDIF}
{$IFDEF EXTENDEDREAL}
const
MachEp = 1.08420217248550444E-19; { 2^(-63) }
MaxNum = 5.9486574767861588254E+4931; { 2^16383 }
MinNum = 6.7242062862241870125E-4932; { 2^(-16381) }
MaxLog = 11355.830259113584004;
MinLog = -11354.443964752464114;
MaxFac = 1754;
MaxGam = 1755.455;
MaxLgm = 1.04848146839019521E+4928;
{$ENDIF}
{ ------------------------------------------------------------------
Error codes for mathematical functions
------------------------------------------------------------------ }
const
FOk = 0; { No error }
FDomain = - 1; { Argument domain error }
FSing = - 2; { Function singularity }
FOverflow = - 3; { Overflow range error }
FUnderflow = - 4; { Underflow range error }
FTLoss = - 5; { Total loss of precision }
FPLoss = - 6; { Partial loss of precision }
{ ------------------------------------------------------------------
Error codes for matrix computations
------------------------------------------------------------------ }
const
MatOk = 0; { No error }
MatNonConv = -1; { Non-convergence }
MatSing = -2; { Quasi-singular matrix }
MatErrDim = -3; { Non-compatible dimensions }
MatNotPD = -4; { Matrix not positive definite }
{ ------------------------------------------------------------------
Error codes for optimization and nonlinear equations
------------------------------------------------------------------ }
const
OptOk = 0; { No error }
OptNonConv = -1; { Non-convergence }
OptSing = -2; { Quasi-singular hessian matrix }
OptBigLambda = -5; { Too high Marquardt parameter }
{ ------------------------------------------------------------------
Error codes for nonlinear regression
------------------------------------------------------------------ }
const
NLMaxPar = -6; { Max. number of parameters exceeded }
{ ------------------------------------------------------------------
Complex numbers
------------------------------------------------------------------ }
type Complex = record
X, Y : Float;
end;
{ ------------------------------------------------------------------
Vectors and matrices.
------------------------------------------------------------------ }
const { Maximal array size }
{$IFDEF _16BIT}
MaxSize = 65536; { 64 kilobytes : 2^16 }
{$ELSE}
MaxSize = 2147483648; { 2 gigabytes : 2^31 }
{$ENDIF}
FltSize = SizeOf(Float);
CompSize = SizeOf(Complex);
IntSize = SizeOf(Integer);
BoolSize = SizeOf(Boolean);
StrSize = SizeOf(String);
PtrSize = SizeOf(Pointer);
MAX_FLT = Trunc(MaxSize / FltSize) - 2;
MAX_COMP = Trunc(MaxSize / CompSize) - 2;
MAX_INT = Trunc(MaxSize / IntSize) - 2;
MAX_BOOL = Trunc(MaxSize / BoolSize) - 2;
MAX_STR = Trunc(MaxSize / StrSize) - 2;
MAX_VEC = Trunc(MaxSize / PtrSize) - 2;
type
TVector = array[0..MAX_FLT] of Float;
TIntVector = array[0..MAX_INT] of Integer;
TCompVector = array[0..MAX_COMP] of Complex;
TBoolVector = array[0..MAX_BOOL] of Boolean;
TStrVector = array[0..MAX_STR] of String;
PVector = ^TVector;
PIntVector = ^TIntVector;
PBoolVector = ^TBoolVector;
PCompVector = ^TCompVector;
PStrVector = ^TStrVector;
type
XTMatrix = array[0..MAX_VEC] of PVector;
TIntMatrix = array[0..MAX_VEC] of PIntVector;
TBoolMatrix = array[0..MAX_VEC] of PBoolVector;
TCompMatrix = array[0..MAX_VEC] of PCompVector;
TStrMatrix = array[0..MAX_VEC] of PStrVector;
PMatrix = ^XTMatrix;
PIntMatrix = ^TIntMatrix;
PBoolMatrix = ^TBoolMatrix;
PCompMatrix = ^TCompMatrix;
PStrMatrix = ^TStrMatrix;
{ ------------------------------------------------------------------
Functional types
------------------------------------------------------------------ }
{ Function of one variable }
type TFunc = function(X : Float) : Float;
{ Function of several variables }
type TFuncNVar = function(X : PVector) : Float;
{ Nonlinear equation system }
type TEquations = procedure(X, F : PVector);
{ Differential equation system }
type TDiffEqs = procedure(X : Float; Y, Yp : PVector);
{ Jacobian }
type TJacobian = procedure(X : PVector; D : PMatrix);
{ Gradient }
type TGradient = procedure(X, G : PVector);
{ Hessian and Gradient }
type THessGrad = procedure(X, G : PVector; H : PMatrix);
{ ------------------------------------------------------------------
Random number generators
------------------------------------------------------------------ }
type RNG_Type =
(RNG_MWC, { Multiply-With-Carry }
RNG_MT, { Mersenne Twister }
RNG_UVAG); { Universal Virtual Array Generator }
{ ------------------------------------------------------------------
Statistics
------------------------------------------------------------------ }
type StatClass = record { Statistical class }
Inf : Float; { Lower bound }
Sup : Float; { Upper bound }
N : Integer; { Number of values }
F : Float; { Frequency }
D : Float; { Density }
end;
const
MAX_CLS = 1000; { Max. number of statistical classes }
type
TStatClassVector = array[0..MAX_CLS] of StatClass;
PStatClassVector = ^TStatClassVector;
{ ------------------------------------------------------------------
Curve fit
------------------------------------------------------------------ }
type
TRegTest = record { Test of regression }
Vr : Float; { Residual variance }
R2 : Float; { Coefficient of determination }
R2a : Float; { Adjusted coeff. of determination }
F : Float; { Variance ratio (explained/residual) }
Nu1, Nu2 : Integer; { Degrees of freedom }
end;
{ Optimization algorithms for nonlinear regression }
type
TOptAlgo = (
NL_MARQ, { Marquardt algorithm }
NL_SIMP, { Simplex algorithm }
NL_BFGS, { BFGS algorithm }
NL_SA, { Simulated annealing }
NL_GA); { Genetic algorithm }
{ Regression function }
type
TRegFunc = function(X : Float; B : PVector) : Float;
{ Procedure to compute the derivatives of the regression function
with respect to the regression parameters }
type
TDerivProc = procedure(X, Y : Float; B, D : PVector);
{ ------------------------------------------------------------------
Graphics
------------------------------------------------------------------ }
type
Str30 = String[30];
TScale = (LinScale, LogScale);
TGrid = (NoGrid, HorizGrid, VertiGrid, BothGrid);
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