Parser Functions¶
General Functions¶
^
Power
%
Modulus Division
!
Factorial (of Integer)
ABS(X)
Absolute Value
CEIL(X)
Integer Above X
EXP(X)
Exponential
FLOOR(X)
Integer Below X
FRACTION(X)
Fractional Part of X
INTEGER(X)
Integer Part of X
LN(X)
Natural Logarithm
LOG(X)
Base 10 Logarithm
PI
3.14159265358979323846
RAND(N)
Random Integer Between 0 and N Inclusive
RANDOM
Random Number Between 0 and 1 Inclusive
ROUND(X)
Round X to Nearest Integer
SQRT(X)
Square Root of X
Conditional Expressions¶
IF(expr,n1,n2)
Evaluates to n1 if expr true, n2 if expr false
> .GT.
Greater
< .LT.
Less
>= .GE.
Greater or Equal
<= .LE.
Less or Equal
== .EQ.
Equal
<> .NE.
Not Equal
Trigonometric Functions¶
ACOS(X)
ArcCosine of X (radians)
ACOSH(X)
Hyperbolic ArcCosine
ASIN(X)
ArcSine of X (radians
ASINH(X)
Hyperbolic ArcSine
ATAN(X)
ArcTangent of X (radians)
ATAN2(X,Y)
ArcTangent of X/Y (radians)
ATANH(X)
Hyperbolic ArcTangent
COS(X)
Cosine of X radians
COSH(X)
Hyperbolic Cosine
COT(X)
Cotangent of X radians
COTH(X)
Hyperbolic Cotangent
CSC(X)
Cosecant of X radians
CSCH(X)
Hyperbolic Cosecant
DTOR(Deg)
Degrees to Radians
RTOD(Rad)
Radians to Degrees
SEC(X)
Secant of X radians
SECH(X)
Hyperbolic Secant
SIN(X)
Sine of X radians
SINH(X)
Hyperbolic Sine
TAN(X)
Tangent of X radians
TANH(X)
Hyperbolic Tangent
Statistical Functions¶
!
Factorial (of Integer)
B0(N)
Bernoulli Number B0(N)
BET(A,B)
Beta Function
ERF(X)
Error Function
ERFC(X)
Error Function, Complement
ERFP1(X)
Error Function + 1.0
ERFM1(X)
Error Function - 1.0
GAM(X)
Gamma Function
HYPM(A,B,X)
Hypergeometric M
HYPU(A,B,X)
Hypergeometric U
HYPF(A,B,C,X)
Hypergeometric F
IBETA(A,B,X)
Incomplete Beta Function
IGAM(A,X)
Incomplete Gamma
IGAMC(A,X)
Incomplete Gamma, Complement
LGNDR(L,M,X)
Legendre Polynomial PLM(X)
LNFAC(X)
Natural Logarithm Factorial
LNGAM(X)
Natural Logarithm Gamma
PFBI(K,N,P)
Binomial Probability (Probability >=K Occurrences in N trials, P=probability/trial)
PFCP(K,N)
Cumulative Poisson Probability (Probability 0 to K-1 Occurrences for Mean=N)
PFF(V1,V2,F)
F Probability (Probability Variance 1 >= Variance 2 for F=f-statistic, V1=DOF1,V2=DOF2)
PFST(T,V)
Student-t Probability (Probability t < Observed t for v=DOF)
PFX2(X2,V)
Chi-Squared Probability (Probability Observed C2 < C2 for v DOF)
PFX2C(X2,V)
Chi-Squared Complement Probability (Probability Observed C2 > C2 for v DOF)
PSI(X)
Psi (Digamma) Function
Bessel Functions¶
J0(X) J1(X) JN(N,X)
Integer Order J Bessel, orders 0, 1, N
Y0(X) Y1(X) YN(N,X)
Integer Order Y Bessel, orders 0, 1, N
I0(X) I1(X) IN(N,X)
Integer Order I Modified Bessel, orders 0, 1, N
I0EIX(X) I1EIX(X)
EXP(-X) * Integer Order I Modified Bessel, orders 0, 1
K0(X) K1(X) KN(N,X)
Integer Order K Modified Bessel, orders 0, 1, N
JNU(NU,X)
Fractional Order J Bessel
YNU(NU,X)
Fractional Order Y Bessel
INU(NU,X)
Fractional Order I Modified Bessel
KNU(NU,X)
Fractional Order K Modified Bessel
DJNU(NU,X)
Fractional Order J Bessel 1st Derivative
DYNU(NU,X)
Fractional Order Y Bessel 1st Derivative
DINU(NU,X)
Fractional Order I Modified Bessel 1st Derivative
DKNU(NU,X)
Fractional Order Modified K Bessel 1st Derivative
SPHJN(N,X)
Spherical Bessel j
SPHYN(N,X)
Spherical Bessel y
SPHIN(N,X)
Spherical Modified Bessel i
SPHKN(N,X)
Spherical Modified Bessel k
DSPHJN(N,X)
Spherical Bessel j 1st Derivative
DSPHYN(N,X)
Spherical Bessel y 1st Derivative
DSPHIN(N,X)
Spherical Modified Bessel i 1st Derivative
DSPHKN(N,X)
Spherical Modified Bessel k 1st Derivative
AIRYA(X)
Airy A Function
AIRYB(X)
Airy B Function
DAIRYA(X)
Airy A 1st Derivative
DAIRYB(X)
Airy B 1st Derivative
Integral, Derivative, and Summation Functions¶
DX(n)
1st Derivative of function Fn with respect to X, d(#Fn)/dX.
DX2(n)
2nd Derivative of function Fn with respect to X, d2(#Fn)/dX2.
DY(n)
1st Derivative of function Fn with respect to Y, d(#Fn)/dY.
DY2(n)
2nd Derivative of function Fn with respect to Y, d2(#Fn)/dX2.
DXY(n)
Derivative of function Fn with respect to X and Y, d(#Fn)/dXdY.
Derivative Examples:
F1=GAUSSX(A0,A1,A2) F2=LORY(A0,A3,A4) Z=DX(F1)*DY(F2) F1=GAUSSX(A0,A1,A2)*LORY(1,A3,A4) Z=DXY(F1)
AI(n,st,end)AIP(n,st,end,prec)
Automated Integration of Fn from st to end with $ as variable of integration; supports infinite limits and undefined bounds; AI() seeks 1E-8 precision, AIP() seeks prec fractional convergence. The AI() and AIP() functions first attempt to achieve the target precision with a successive step Gaussian Quadrature procedure. If this is unsuccessful, a Romberg procedure with a maximum of 131K-177K steps follows.
QI(n,st,end)QIP(n,st,end,prec)
Gaussian Quadrature Integration of Fn from st to end with $ as variable of integration; supports infinite limits and undefined bounds; QI() seeks 1E-8 precision, QIP() seeks prec fractional convergence.
Integration Example:
F1=GAUSS$(A0,A1,A2) F2=LOR$(1,A3,A4) F3=QIP(F1,-INF,X,1e-5) F4=QIP(F2,-INF,Y,1e-5) Z=F3*F4
INF -INF
Infinite Limits for Integration functions. You should always use the INF constant rather than some arbitrarily large number.
DQIP(n, ost, oend, ist, iend, prec)
Gaussian Quadrature Double Integration of Fn from st to end with $ as outer variable of integration ranging from ost to oend and with $$ as the inner variable of integration ranging from ist to iend; supports infinite limits and undefined bounds; seeks prec fractional convergence.
Double Integration Example:
F1=A0*EXP(-0.5*(($-A1)/A2)^2)*1/(1+(($$-A3)/A4)^2) Z=DQIP(F1,-INF,X,-INF,Y,1E-5)
SUM(n,st,end,inc)
Sums Fn with index $ going from st to end with increment inc
SER(n,st,inc,lim)
Sums Fn with index $ beginning at st, incrementing with inc, until iteration’s fractional contribution lim
PROD(n,st,end,inc)
Multiplies Fn with index $ going from st to end with increment inc
XYZ Data Table Constants and Functions¶
XMIN
Minimum X
XMAX
Maximum X
XRANGE
Maximum X - Minimum X
XMN
or XMEAN
Mean of X Values
XSTD
Standard deviation of X values
XATYMIN
X of X,Y,Z point having minimum Y
XATYMAX
X of X,Y,Z point having maximum Y
XATZMIN
X of X,Y,Z point having minimum Z
XATZMAX
X of X,Y,Z point having maximum Z
XATXYMIN
X of X,Y,Z point having minimum XY vector length
XATXYMAX
X of X,Y,Z point having maximum XY vector length
XATXYZMIN
X of X,Y,Z point having minimum XYZ vector length
XATXYZMAX
X of X,Y,Z point having maximum XYZ vector length
XATXMAXYMIN
X of X,Y,Z point nearest maximum X, minimum Y
XATXMNYMIN
X of X,Y,Z point nearest X mean, minimum Y
XATXMINYMIN
X of X,Y,Z point nearest minimum X, minimum Y
XATXMAXYMN
X of X,Y,Z point nearest maximum X, Y mean
XATXMNYMN
X of X,Y,Z point nearest X mean, Y mean
XATXMINYMN
X of X,Y,Z point nearest minimum X, Y mean
XATXMAXYMAX
X of X,Y,Z point nearest maximum X, maximum Y
XATXMNYMAX
X of X,Y,Z point nearest X mean, maximum Y
XATXMINYMAX
X of X,Y,Z point nearest minimum X, maximum Y
YMIN
Minimum Y
YMAX
Maximum Y
YRANGE
Maximum Y - Minimum Y
YMN
or YMEAN
Mean of Y Values
YSTD
Standard deviation of Y values
YATXMIN
Y of X,Y,Z point having minimum X
YATXMAX
Y of X,Y,Z point having maximum X
YATZMIN
Y of X,Y,Z point having minimum Z
YATZMAX
Y of X,Y,Z point having maximum Z
YATXYMIN
Y of X,Y,Z point having minimum XY vector length
YATXYMAX
Y of X,Y,Z point having maximum XY vector length
YATXYZMIN
Y of X,Y,Z point having minimum XYZ vector length
YATXYZMAX
Y of X,Y,Z point having maximum XYZ vector length
YATXMAXYMIN
Y of X,Y,Z point nearest maximum X, minimum Y
YATXMNYMIN
Y of X,Y,Z point nearest X mean, minimum Y
YATXMINYMIN
Y of X,Y,Z point nearest minimum X, minimum Y
YATXMAXYMN
Y of X,Y,Z point nearest maximum X, Y mean
YATXMNYMN
Y of X,Y,Z point nearest X mean, Y mean
YATXMINYMN
Y of X,Y,Z point nearest minimum X, Y mean
YATXMAXYMAX
Y of X,Y,Z point nearest maximum X, maximum Y
YATXMNYMAX
Y of X,Y,Z point nearest X mean, maximum Y
YATXMINYMAX
Y of X,Y,Z point nearest minimum X, maximum Y
ZMIN
Minimum Z
ZMAX
Maximum Z
ZRANGE
Maximum Z - Minimum Z
ZMN
or ZMEAN
Mean of Z Values
ZSTD
Standard deviation of Z values
ZATXMIN
Z of X,Y,Z point having minimum X
ZATXMAX
Z of X,Y,Z point having maximum X
ZATYMIN
Z of X,Y,Z point having minimum Y
ZATYMAX
Z of X,Y,Z point having maximum Y
ZATXYMIN
Z of X,Y,Z point having minimum XY vector length
ZATXYMAX
Z of X,Y,Z point having maximum XY vector length
ZATXYZMIN
Z of X,Y,Z point having minimum XYZ vector length
ZATXYZMAX
Z of X,Y,Z point having maximum XYZ vector length
ZATXMAXYMIN
Z of X,Y,Z point nearest maximum X, minimum Y
ZATXMNYMIN
Z of X,Y,Z point nearest X mean, minimum Y
ZATXMINYMIN
Z of X,Y,Z point nearest minimum X, minimum Y
ZATXMAXYMN
Z of X,Y,Z point nearest maximum X, Y mean
ZATXMNYMN
Z of X,Y,Z point nearest X mean, Y mean
ZATXMINYMN
Z of X,Y,Z point nearest minimum X, Y mean
ZATXMAXYMAX
Z of X,Y,Z point nearest maximum X, maximum Y
ZATXMNYMAX
Z of X,Y,Z point nearest X mean, maximum Y
ZATXMINYMAX
Z of X,Y,Z point nearest minimum X, maximum Y
NOISE(P)
Random Uniform P% Z Noise. A calculation Z=Z+NOISE(10) would be used to add 10% uniform random noise to a data set.
GNOISE(P)
Random Gaussian P% Z Noise. A calculation Z=Z+GNOISE(10) would be used to add 10% Gaussian random noise to a data set.
Non-Linear Base Functions¶
The non-linear base functions are built-in functions that enable fast and easy construction of UDFs and View Functions.
These functions are available in X, Y, and variable of integration $ versions. An X suffix processes the X variable, the Y suffix processes the Y variable, and the $ suffix processes the variable of integration.
The following abbreviations are used:
AMPL
= Amplitude
CTR
= Center
WID
= Peak or Transition Width
RATE
= Time Constant Term
The functions are as follows with the suffix X, Y, or $ to replace the _ symbol:
GAUSS_(AMPL, CTR, WID)
Gaussian Peak
LOR_(AMPL,CTR,WID)
Lorentzian Peak
LOGNORM_(AMPL,CTR,WID)
Log Normal Peak
LOGISTIC_(AMPL,CTR,WID)
Logistic Peak
EXTRVAL_(AMPL,CTR,WID)
Extreme Value Peak
GCUM_(AMPL,CTR,WID)
Gaussian Cumulative
LORCUM_(AMPL,CTR,WID)
Lorentzian Cumulative
LNCUM_(AMPL,CTR,WID)
Log-Normal Cumulative
SIG_(AMPL,CTR,WID)
Sigmoid Transition
EXVCUM_(AMPL,CTR,WID)
Extreme-Value Cumulative
LDR_(AMPL,CTR,WID)
Logistic Dose Response Transition
EXP_(AMPL,RATE)
Single Exponential
POW_(BASE,EXP)
Power