C............ ELEMENTARY AND SPECIAL FUNCTIONS (search also class L5)

C1.......... Integer-valued functions (e.g., floor, ceiling, factorial, binomial coefficient)

BINOM    Evaluate the binomial coefficient.

FAC         Evaluate the factorial of the argument.

C2.......... Powers, roots, reciprocals

CBRT     Evaluate the cube root.

CCBRT   Evaluate the complex cube root.

C3.......... Polynomials

C3a........ Orthogonal

INITS    Initialize the orthogonal series so the function value is the number of terms needed to insure the error is no larger than the requested accuracy.

C3a2...... Chebyshev, Legendre

CSEVL    Evaluate the N-term Chebyshev series.

C4.......... Elementary transcendental functions

C4a         Trigonometric, inverse trigonometric

CACOS    Evaluate the complex arc cosine.

CARG       Evaluate the argument of a complex number.

CASIN    Evaluate the complex arc sine.

CATAN    Evaluate the complex arc tangent.

CATAN2  Evaluate the complex arc tangent of a ratio.

CCOT       Evaluate the complex cotangent.

COSDG    Evaluate the cosine for the argument in degrees.

COT         Evaluate the cotangent.

SINDG    Evaluate the sine for the argument in degrees.

C4b........ Exponential, logarithmic

ALNREL  Evaluate the natural logarithm of one plus the argument.

CEXPRL  Evaluate the complex exponential function factored from first order.

CLNREL  Evaluate the principal value of the complex natural logarithm of one plus the argument.

CLOG10  Evaluate the principal value of the complex common logarithm.

EXPRL    Evaluate the exponential function factored from first order, (EXP(X) − 1.0)/X.

C4c........ Hyperbolic, inverse hyperbolic

ACOSH    Evaluate the arc hyperbolic cosine.

ASINH    Evaluate the arc hyperbolic sine.

ATANH    Evaluate the arc hyperbolic tangent.

CACOSH  Evaluate the complex arc hyperbolic cosine.

CASINH  Evaluate the complex arc hyperbolic sine.

CATANH  Evaluate the complex arc hyperbolic tangent.

CCOSH    Evaluate the complex hyperbolic cosine.

CSINH    Evaluate the complex hyperbolic sine.

CTAN       Evaluate the complex tangent.

CTANH    Evaluate the complex hyperbolic tangent.

C5.......... Exponential and logarithmic integrals

ALI         Evaluate the logarithmic integral.

CHI         Evaluate the hyperbolic cosine integral.

CI           Evaluate the cosine integral.

CIN         Evaluate a function closely related to the cosine integral.

CINH       Evaluate a function closely related to the hyperbolic cosine integral.

E1           Evaluate the exponential integral for arguments greater than zero and the Cauchy principal value of the integral for arguments less than zero.

EI           Evaluate the exponential integral for arguments greater than zero and the Cauchy principal value for arguments less than zero.

ENE         Evaluate the exponential integral of integer order for arguments greater than zero scaled by EXP(X).

SHI         Evaluate the hyperbolic sine integral.

SI           Evaluate the sine integral.

C7.......... Gamma

C7a........ Gamma, log gamma, reciprocal gamma

ALGAMS  Return the logarithm of the absolute value of the gamma function and the sign of gamma.

ALNGAM  Evaluate the logarithm of the absolute value of the gamma function.

CGAMMA  Evaluate the complex gamma function.

CGAMR    Evaluate the reciprocal complex gamma function.

CLNGAM  Evaluate the complex natural logarithm of the gamma function.

GAMMA    Evaluate the complete gamma function.

GAMR       Evaluate the reciprocal gamma function.

POCH       Evaluate a generalization of Pochhammer's symbol.

POCH1    Evaluate a generalization of Pochhammer's symbol starting from the first order.

C7b........ Beta, log beta

ALBETA  Evaluate the natural logarithm of the complete beta function for positive arguments.

BETA       Evaluate the complete beta function.

CBETA    Evaluate the complex complete beta function.

CLBETA  Evaluate the complex logarithm of the complete beta function.

C7c........ Psi function

CPSI       Evaluate the logarithmic derivative of the gamma function for a complex argument.

PSI         Evaluates the derivative of the log gamma function.

C7d........ Polygamma functions

PSI1       Evaluates the second derivative of the log gamma function.

C7e........ Incomplete gamma

CHIDF    Evaluate the chi-squared distribution function.

CHIIN    Evaluate the inverse of the chi-squared distribution function.

GAMDF    Evaluate the gamma distribution function.

GAMI       Evaluate the incomplete gamma function.

GAMIC    Evaluate the complementary incomplete gamma function.

GAMIT    Evaluate the Tricomi form of the incomplete gamma function.

C7f......... Incomplete beta

BETAI    Evaluate the incomplete beta function ratio.

BETDF    Evaluate the beta probability distribution function.

BETIN    Evaluate the inverse of the beta distribution function.

C8.......... Error functions

C8a........ Error functions, their inverses, integrals, including the normal distribution function

ANORDF  Evaluate the standard normal (Gaussian) distribution function.

ANORIN  Evaluate the inverse of the standard normal (Gaussian) distribution function.

CERFE    Evaluate the complex scaled complemented error function.

ERF         Evaluate the error function.

ERFC       Evaluate the complementary error function.

ERFCE    Evaluate the exponentially scaled complementary error function.

ERFCI    Evaluate the inverse complementary error function.

ERFI       Evaluate the inverse error function.

C8b........ Fresnel integrals

FRESC    Evaluate the cosine Fresnel integral.

FRESS    Evaluate the sine Fresnel integral.

C8c........ Dawson's integral

DAWS       Evaluate Dawson function.

 

C10........ Bessel functions

C10a...... J, Y, H(1); H(2)

C10a1.... Real argument, integer order

BSJ0       Evaluate the Bessel function of the first kind of order zero.

BSJ1       Evaluate the Bessel function of the first kind of order one.

BSJNS    Evaluate a sequence of Bessel functions of the first kind with integer order and real arguments.

BSY0       Evaluate the Bessel function of the second kind of order zero.

BSY1       Evaluate the Bessel function of the second kind of order one.

C10a2.... Complex argument, integer order.

CBJNS    Evaluate a sequence of Bessel functions of the first kind with integer order and complex arguments.

C10a3.... Real argument, real order

BSJS       Evaluate a sequence of Bessel functions of the first kind with real order and real positive arguments.

BSYS       Evaluate a sequence of Bessel functions of the second kind with real nonnegative order and real positive arguments.

C10a4.... Complex argument, real order

CBJS       Evaluate a sequence of Bessel functions of the first kind with real order and complex arguments.

CBYS       Evaluate a sequence of Bessel functions of the second kind with real order and complex arguments.

C10b...... I, K

C10b1.... Real argument, integer order

BSI0       Evaluate the modified Bessel function of the first kind of order zero.

BSI0E    Evaluate the exponentially scaled modified Bessel function of the first kind of order zero.

BSI1       Evaluate the modified Bessel function of the first kind of order one.

BSI1E    Evaluate the exponentially scaled modified Bessel function of the first kind of order one.

BSINS    Evaluate a sequence of Modified Bessel functions of the first kind with integer order and real arguments.

BSK0       Evaluate the modified Bessel function of the second kind of order zero.

BSK0E    Evaluate the exponentially scaled modified Bessel function of the second kind of order zero.

BSK1       Evaluate the modified Bessel function of the second kind of order one.

BSK1E    Evaluate the exponentially scaled modified Bessel function of the second kind of order one.

C10b2.... Complex argument, integer order

CBINS    Evaluate a sequence of Modified Bessel functions of the first kind with integer order and complex arguments.

C10b3.... Real argument, real order

BSIES    Evaluate a sequence of exponentially scaled Modified Bessel functions of the first kind with nonnegative real order and real positive arguments.

BSIS       Evaluate a sequence of Modified Bessel functions of the first kind with real order and real positive arguments.

BSKES    Evaluate a sequence of exponentially scaled modified Bessel functions of the second kind of fractional order.

BSKS       Evaluate a sequence of modified Bessel functions of the second kind of fractional order.

C10b4.... Complex argument, real order

CBIS       Evaluate a sequence of Modified Bessel functions of the first kind with real order and complex arguments.

CBKS       Evaluate a sequence of Modified Bessel functions of the second kind with real order and complex arguments.

C10c...... Kelvin functions

AKEI0    Evaluate the Kelvin function of the second kind, kei, of order zero.

AKEI1    Evaluate the Kelvin function of the second kind, kei, of order one.

AKEIP0  Evaluates the derivative of the Kelvin function of the second kind, kei, of order zero.

AKER0    Evaluate the Kelvin function of the second kind, ker, of order zero.

AKER1    Evaluate the Kelvin function of the second kind, ker, of order one.

AKERP0  Evaluate the derivative of the Kelvin function of the second kind, ker, of order zero.

BEI0       Evaluate the Kelvin function of the first kind, bei, of order zero.

BEI1       Evaluate the Kelvin function of the first kind, bei, of order one.

BEIP0    Evaluate the derivative of the Kelvin function of the first kind, bei, of order zero.

BER0       Evaluate the Kelvin function of the first kind, ber, of order zero.

BER1       Evaluate the Kelvin function of the first kind, ber, of order one.

BERP0    Evaluate the derivative of the Kelvin function of the first kind, ber, of order zero.

C10d...... Airy and Scorer functions

AI           Evaluate the Airy function.

AID         Evaluate the derivative of the Airy function.

AIDE       Evaluate the exponentially scaled derivative of the Airy function.

AIE         Evaluate the exponentially scaled Airy function.

BI           Evaluate the Airy function of the second kind.

BID         Evaluate the derivative of the Airy function of the second kind.

BIDE       Evaluate the exponentially scaled derivative of the Airy function of the second kind.

BIE         Evaluate the exponentially scaled Airy function of the second kind.

C14........ Elliptic integrals

CEJCN    Evaluate the complex Jacobi elliptic integral cn(z, m).

CEJDN    Evaluate the complex Jacobi elliptic integral dn(z, m).

CEJSN    Evaluate the complex Jacobi elliptic function sn(z, m).

EJCN       Evaluate the Jacobi elliptic function cn(x, m).

EJDN       Evaluate the Jacobi elliptic function dn(x, m).

EJSN       Evaluate the Jacobi elliptic function sn(x, m).

ELE         Evaluate the complete elliptic integral of the second kind E(x).

ELK         Evaluate the complete elliptic integral of the kind K(x).

ELRC       Evaluate an elementary integral from which inverse circular functions, logarithms and inverse hyperbolic functions can be computed.

ELRD       Evaluate Carlson's incomplete elliptic integral of the second kind RD(X, Y, Z).

ELRF       Evaluate Carlson's incomplete elliptic integral of the first kind RF(X, Y, Z).

ELRJ       Evaluate Carlson's incomplete elliptic integral of the third kind RJ(X, Y, Z, RHO).

C15........ Weierstrass elliptic functions

CWPL       Evaluate the Weierstrass P-function in the lemniscat case for complex argument with unit period parallelogram.

CWPLD    Evaluate the first derivative of the Weierstrass P-function in the lemniscatic case for complex argum with unit period parallelogram.

CWPQ       Evaluate the Weierstrass P-function in the equianharmonic case for complex argument with unit period parallelogram.

CWPQD    Evaluate the first derivative of the Weierstrass P-function in the equianharmonic case for complex argument with unit period parallelogram.

C17........ Mathieu functions

MATCE    Evaluate a sequence of even, periodic, integer order, real Mathieu functions.

MATEE    Evaluate the eigenvalues for the periodic Mathieu functions.

MATSE    Evaluate a sequence of odd, periodic, integer order, real Mathieu functions.

C19........ Other special functions

SPENC    Evaluate a form of Spence's integral.

L............. STATISTICS, PROBABILITY

L5........... Function evaluation (search also class C)

L5a......... Univariate

L5a1....... Cumulative distribution functions, probability density functions

GCDF       Evaluate a general continuous cumulative distribution function given ordinates of the density.

L5a1b.... Beta, binomial

BETDF    Evaluate the beta probability distribution function.

BETNDF  Evaluate the noncentral beta cumulative distribution function.

BETNPR  Evaluate the noncentral beta probability distribution function.

BINDF    Evaluate the binomial distribution function.

BINPR    Evaluate the binomial probability function.

L5a1c..... Cauchy, chi-squared

CHIDF    Evaluate the chi-squared distribution function.

CSNDF    Evaluate the noncentral chi-squared distribution function.

CSNPR    Evaluate the noncentral chi-squared probability density function.

L5a1f..... F distribution

FDF         Evaluate the F distribution function.

FNDF       Evaluate the noncentral F cumulative distribution function (CDF).

FNPR       Evaluate the noncentral F probability density function.

L5a1g.... Gamma, general, geometric

GAMDF    Evaluate the gamma distribution function.

L5a1h.... Halfnormal, hypergeometric

HYPDF    Evaluate the hypergeometric distribution function.

HYPPR    Evaluate the hypergeometric probability function.

L5a1k..... Kendall F statistic, Kolmogorov-Smirnov

AKS1DF  Evaluate the distribution function of the one-sided Kolmogorov-Smirnov goodness of fit D+ or D− test statistic based on continuous data for one sample.

AKS2DF  Evaluate the distribution function of the Kolmogorov-Smirnov goodness of fit D test statistic based on continuous data for two samples.

L5a1n.... Negative binomial, normal

ANORDF  Evaluate the standard normal (Gaussian) distribution function.

L5a1p.... Pareto, Poisson

POIDF    Evaluate the Poisson distribution function.

POIPR    Evaluate the Poisson probability function.

L5a1t..... t distribution

TDF         Evaluate the Student's t distribution function.

TNPR       Evaluate the noncentral Student's t probability distribution function.

TNDF       Evaluate the noncentral Student's t distribution function.

L5a2....... Inverse cumulative distribution functions, sparsity functions

GCIN       Evaluate the inverse of a general continuous cumulative distribution function given ordinates of the density.

L5a2b.... Beta, binomial

BETIN    Evaluate the inverse of the beta distribution function.

BETNIN  Evaluate the inverse of the noncentral beta cumulative distribution function (CDF).

L5a2c..... Cauchy, chi-squared

CHIIN    Evaluate the inverse of the chi-squared distribution function.

L5a2f..... F distribution

FIN         Evaluate the inverse of the F distribution function.

FNIN       Evaluate the inverse of the F cumulative distribution function (CDF).

L5a2n.... Negative binomial, normal, normal scores

ANORIN  Evaluate the inverse of the standard normal (Gaussian) distribution function.

L5a2t..... t distribution

TIN         Evaluate the inverse of the Student's t distribution function.

L5b........ Multivariate

L5b1...... Cumulative distribution functions, probability density functions

L5b1n.... Normal

BNRDF    Evaluate the bivariate normal distribution function.

N............ DATA HANDLING

N1.......... Input, output

IFNAN    Check if a value is NaN (not a number).

N4.......... Storage management (e.g., stacks, heaps, trees)

IWKCIN  Initialize bookkeeping locations describing the character workspace stack.

IWKIN    Initialize bookkeeping locations describing the workspace stack.

R............ SERVICE ROUTINES

R1.......... Machine-dependent constants

AMACH    Retrieve single-precision machine constants.

DMACH    Retrieve double precision machine constants.

IFNAN    Check if a value is NaN (not a number).

IMACH    Retrieve integer machine constants.

UMACH    Set or retrieve input or output device unit numbers.

R3.......... Error handling

ERSET    Set error handler default print and stop actions.

IERCD    Retrieve the code for an informational error.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

http://www.vni.com/ PHONE: 713.784.3131 FAX:713.781.9260