DAGONET SOFTWARE
2904 La Veta Dr. NE
Albuquerque NM 87110
(505) 768-7649

Dagonet Software Catalog

FORMATS AVAILABLE:
IBM PC 5-1/4" (360k; by 1.2M special request)
KAYPRO 392K and other CP/M favorites (if known to UNIFORM)
MACINTOSH 3-1/2"
AMIGA 3-1/2"
IBM 3-1/2"

C Tools for Scientists and Engineers: (see the McGraw-Hill Book) Software for linear systems, eigenvalues, singular value decomposition (SVD) and least squares fitting, ordinary differential equations ( Runge-Kutta-Fehlberg for non-stiff and a stiff system solver), Newton Raphson nonlinear system solver, Muller's method for solving nonlinear equations and Jenkins-Traub root solver for polynomials (with complex arithmetic packages in C), B-Splines , Adaptive quadrature, Fast Fourier and Hartley Transforms, and a simple plotting package. $9.95

Artificial Intelligence with Ada (also McGraw-Hill) Ada programs for forward- and backward-chaining expert system shells, frames database, and Augmented Transition Network parser. Includes Ada packages for string manipulation, hash table managment, parsing and evaluating arithmetic expressions. $29.95

Code from "More C Tools" (Okay, so the titles not particularly original. Son of C Tools?) : Statistical function calculator ( student's t, Chi-Square, F distributions and their inverses, p to z scores and back, Kolmogorov-Smirnov statistic, etc.), conjugate gradient method, Gaussian quadrature, block matrix methods, Multigrid method (1-D and 2-D examples) for partial differential equations, random number generation and use, ANOVA (Analysis of Variance), Error, Fresnel, Plasma Dispersion, Complex Error Dawson's integral and repeated integrals of the error function, Bresenham line-draw, contour plotting, roman numerals, typewriter program. $14.95

C Mathematical Function Library: $29.95

C MATH LIBRARY CONTENTS

All the functions of Abramowitz & Stegun and more! (series) means function sums the defining series until error criterion satisfied. This may not be efficient or effective for large arguments. Functions grouped by category. Last item on line gives file containing the function. NOTE: Book comes with 3-1/2" diskette of all software, costs $49.95. There is no point in ordering the diskette if you will order the book.

BESSEL

bessel function J,Y,I,K  integer n complex z  mf1.c
bessel functions J,Y,I,K-table for n=0,1,...,ntop mf1.c
J0,J1,Y0,Y1,K0,K1,I0,I1, integer n=0,1 mf1.c
Ji,Jin,Jotn,Ki,Kin integral of J, J/t, K mf1.c
J Y K I arbitrary real order and argument abb.c
integrals of I0,Y0 abb.c
integrals of K0/t, Y0/t, (I0-1)/t, (1-J0)/t bessi.c
Struve & modified Struve H0,H1,L0,L1 mf1.c
Ai,Bi,Ai',Bi' Airy functions also J[1/3] etc. abb.c
IAi,IBi integrals of Ai(z),Ai(-z),Bi(z),Bi(-z) abb.c
J E Anger/Weber functions abb.c
integral of (J+iE) Anger/Weber function (series) iaw.c
s Lommel(series) mf1.c
S,U,V Lommel (series) ebznew.c
On Neumann polynomial ebznew.c
zeros of J,Y,J',Y' bessz.c
spherical bessel functions j,k,i,y (pos integer order; i any integer) spb.c
J and N of imaginary order,real arg.,called Wedge functions

ELLIPTIC

complete and incomplete elliptic integrals 1st,2nd kind te.c
incomplete 3rd kind e3.c
Jacobian elliptic sn,cn,dn amplitude am (real arg) all real m te.c
complex argument Jacobian elliptic functions cje.c
Weierstrass P and derivative P',sigma, zeta functions cje.c
logarithmic derivatives of theta functions cje.c
Jacobian (capital) theta te.c
Jacobian Zeta 	te.c
Heuman function	te.c
am amplitude given u,m (real) te.c
amc amplitude for complex u ct4.c
theta and Neville theta functions (real argument) te.c
theta(i=1,2,3,4) for complex q,v (series) ct4.c
nome q given m 0<=m<=1  ct4.c
m given nome q 0<=q<=1   ct4.c
elliptic modular function m=emf(q) m,q complex ct4.c
elliptic modular function for t complex q= exp(i pi t) ct4.c
elliptic integrals of 1st,2nd kind for complex arguments cef.c
inverse of Weierstrass P function invw.c

LEGENDRE FUNCTIONS & Spheroidal Wave Functions

Pl,m for integer l,m, abs(x)<1 (recurs from pm,m) leg1.c
Ql,m integer l,m  all valid x leg1.c
Pl0, Ql0  (m=0) all valid x leg1.c
pmunu qmunu for |1-x|<2, nonintegral mu,nu leg1.c
pli,qli for z=ix  x>0 leg1.c
legendrea x real or imaginary  leg2.c
qleg l,m x>1 leg2.c
qnu  q nu real,mu=0 x real any, or z=ix x>1.
leg1,2,3 Pnm, Qnm x>1. gaut.c
legendre1,2 P a,n(x) Pa+n,m(x) a real>0,x>1 gaut.c
Plm,Qlm for  z=ix x>0  leg2.c,leg3.c
conical P -.5-i*tau,n (x)  x>1. gaut.c
conicalt  as above but  of cos(theta) so  -1<x<=1 gaut.c
Mehler conical functions for -1<x<1 integer mu mehler.c
toroidal Q-.5+n,m (x) x>1. gaut.c
d coefficients for Prolate/Oblate Spheroidal Wave Functions in terms of 
	Legendre function expansions spherr.c
Angular  & Radial Spheroidal wave functions, joining factors spherr.c
Mathieu functions and their chracteristic values mathieu.c
legtable pn,m for n=m,m+1,...N  spherr.c
cq, cp: P, Q complex mu,nu, z cq.c cp.c

PLASMA DISPERSION FUNCTION & Relatives

plasma dispersion function mf2.c
complex error function mf2.c
error function mf2.c
fresnel integrals mf2.c
dawson's integral mf2.c
ritchie integral mf2.c
ierfc repeated integrals of complementary error function mf2.c,ierf.c

GAMMA,DIGAMMA,BETA

gamma,logarithm of gamma  statg.c
incomplete gamma statg.c
complex gamma cgamma.c
digamma (psi)derivative of gamma. two versions. digam.c
polygamma (1st and 2nd derivatives of digamma) digam.c
polygamma (series for higher derivatives) ebznew.c
incomplete beta statg.c

RIEMANN ZETA & Related Functions

Zeta	real arguments ebznew.c
Bernoulli numbers B[n] ebznew.c
Euler numbers E[n] ebznew.c
Spence (Dilogarithm) integral ebznew.c
Bernpoly: value of nth Bernoulli polynomial ebznew.c
Dilogarithm (rational approx.) dilog.c
polylogarithm (series) polylog.c
dilogarithm and trilogarithm trilog.c
Zeta of two arguments (Hurwitz) (series) ebznew.c
Capital Phi Lerch Transcendent(series) ebznew.c
Catalan beta. eta and lambda (series) ebznew.c
omega (sum of exp(-pi*x*n^2) for n=1 to infinity) (series) czeta.c
czeta  zeta for complex arguments (series+transfm.)  czeta.c

STIRLING & Related numbers

stirling numbers of first and second kinds stirl.c
Euler numbers of first kind stirl.c
Fibonacci numbers stirl.c

EXPONENTIAL INTEGRAL & Related Functions

alpha,  En, li (logarithmic integral)  mf1.c
beta integral mf1.c
complex argument En ( series |z|<.05 else cont. fraction) cei.c
Ei  eict.c
Ci,Si, E1	ei.c
iterated Ci,Si integral sii.c
Boehmer integral (generalized Fresnel), Si,Ci, Shi,Chi boehmer.c

INTEGRALS (see A&S Ch27; Ritchie, Dilogarithm, Polylogarithm above)

Sievert mf2.c
Debye ebznew.c
f[n] for n=1,2,3  f123.c
Clausen ebznew.c

HYPERGEOMETRIC & Relatives

M,W Kummer,Whittaker confluent hypergeometric function(series) mf1.c
U confluent hypergeometric function u.c
U,V,W  parabolic cylinder/Weber functions. W in cgamma.c U,V: mf1.c
2f1,1f2 hypergeometric (series) mf1.c
F,G Coulomb Wave Functions (former series;latter integral) cwf.c
chf.c confluent hypergeometric functions M, U for complex arith. chf.c
Gauss Hypergeometric function complex arith. f211.c f212c f213.c

ORTHOGONAL POLYNOMIALS (in orthop.c)

P Jacobi		
C Gegenbauer Ultraspherical  
T Chebyshev U shifted
L Generalized Laguerre
H Hermite
P Legendre

MISCELLANEOUS & AUXILLIARY ROUTINES USED BY ABOVE

solution of cubic,quartic equations (real coeff.) invw.c
complex arcsin,arccos. elem.c
complex sine and cosine cbess.c 
brent root finder for root x of f(x)=0 in interval a<x<b f(a)f(b)<0 brent.c
pochammer's symbol real x: orthop.c complex: f211.c
wigner (Clebsch-Gordon), wigner 3j, 6j, Racah coefficients  wigner.c
elem. trancendental functions elem.c
"exact" solutions of cubic,quartic,quadratic, complex coef. polyrt.c
powers and roots pr.c

STATISTICAL FUNCTIONS (statg.c)

student's t
chi-square
F distribution
Hotelling's T for n=2
various functions simply related to error function.
	(p and z score transformations, cummulative prob.)
noncentral versions of t,chi-square,F
inverses of t, chi-square, F, central and non-central versions.
	(i.e., given confidence return variable value).
Kolmogorv-Smirnov (one-sample)
Wilcoxon & Mann-Whitney sign test and 2 sample test
(note that various mathematical functions are to be found in
the C Tools and More C Tools diskettes, such as various
complex arithmetic functions (log, exponential, etc.))

C++ Code:

Math functions: Using the Pade (rational approximation) method
given in Spanier and Oldham, a number of functions are modeled
including:

Hurwitz zeta function (more robust method than Spanier and Oldnam!)
Lerch Phi
Generalized Hypergeometric Function,Meijer G function, MacRobert E.

Package for C++ for classes of vectors & matrices of complex
numbers with typical operations (multiplication, etc.).  NOT as
complete as that in, say, B. Eckel's book but better handling of
storage allocation (see forthcoming article in C User's Journal
for a discussion).

Arbitrary Precision Arithmetic & Number Theory ($9.95)

Contents: 1) a package of arbitrary precision routines for add,subtract, multiply, divide for integers, rationals, and reals. Conversion from rational to real, between type long and integers, and between real and type double (uses sscanf, only precision of type float achieved). Arbitrary precision integer arithmetic for: greatest common divisor (gcd) of m,n (also finds m',n' such that m'm+n'n=gcd), a^b mod c (or a^b when c=0) and a*b mod c, generating and testing large primes, generating RSA cryptosystem keys, encrypting & decrypting in RSA system, and converting between number systems of different bases. 2) a package to do basic number theory, using the above, including: Jacobi and Moebius symbols, Jordan J, Mangoldt Lambda, Liouville nu (count of prime divisors), prime factors, divisors, sigma (sum of kth powers of divisors, k>=0), and calculate the partition numbers p(n) and q(n) either by recurrence or asymptotically. For binary bases, shifts and modular square roots may be found. There are caveats (specfied below) on using the second package for factoring large numbers (greater than two hundred million) or determining the number of partitions for large numbers. The factoring is done "brute force." A more efficient method may be implemented in the future. A table of primes up to 16,384 is provided, which makes factoring realtively efficient up to numbers below 268 million, beyond which primes have to be generated and then used as candidate factors. Due to imprecisions in floating-point arithmetic, the asymptotic results for p and q may not be exact, although the formulae are in principle capable of exactly determining the (integer) p and q.

Also included are C++ routines for classes Integer, Rational, Real to permit writing code such as: Integer A,B,C,D; A=B*C+D; where A, etc. are arb. prec. integers. Various conversions are provided; a large integer may be written as a string, e.g.: "1234567890". The Rational and Real classes closely follow that of Integer, but have not been fully tested.

Sparse Matrix Package. ($19.95)

Includes linear system solvers using Generalized Minimum Residual Method (GMRES), minmum residual method (MRES) and the stabilized bi-conjugate gradient method (BiCSTAB) for general systems, and conjugate gradient method for symmetric positive-defininte systems. Chokesky (LDL*) decompostion for symmetric positive-definite matrices. LU decomposition for various matrices with fill control. Various preconditioning methods. In C. Also a good bibliography on these methods. Very useful for those starting research in this area. Note that preconditioning is still an art, not a science, so the user will have to experiment to find the best methods and preconditioners for his problem. This is a rapidly evolving field!