TEST_VALUES
Sample Function Values

TEST_VALUES, a MATLAB library which returns a few selected values of various functions.

The intent of TEST_VALUES is to provide a means of making very simple tests for correctness of software designed to compute a variety of functions. The testing can be done automatically. The data provided is generally skimpy, and might not test the algorithm over a suitably wide range. It does, however, provide a small amount of reassurance that a given computation is (or is not) computing the appropriate quantity, and doing so reasonably accurately.

Licensing:

The computer code and data files made available on this web page are distributed under the GNU LGPL license.

Languages:

TEST_VALUES is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

CORDIC, a MATLAB library which use the CORDIC method to compute certain elementary functions.

FN, a MATLAB library which approximates elementary and special functions using Chebyshev polynomials, by Wayne Fullerton.

GSL, a C++ library which evaluates many special functions.

LEGENDRE_POLYNOMIAL, a MATLAB library which evaluates the Legendre polynomial and associated functions.

POLPAK, a MATLAB library which computes various mathematical functions; test values for many of these functions are available in TEST_VALUES.

PROB, a MATLAB library which computes various statistical functions; test values for many of these functions are available in TEST_VALUES.

SPECFUN, a FORTRAN77 library which computes various special functions, particularly Bessel functions.

STEAM, a FORTRAN90 library which computes various functions related to the physical properties of water; test values for many of these functions are available in TEST_VALUES.

test_values_test

Reference:

1. Milton Abramowitz, Irene Stegun,
   Handbook of Mathematical Functions,
   National Bureau of Standards, 1964,
   ISBN: 0-486-61272-4,
   LC: QA47.A34.
2. Lester Haar, John Gallagher, George Kell,
   NBS/NRC Steam Tables:
   Thermodynamic and Transport Properties and Computer Programs for Vapor and Liquid States of Water in SI Units,
   Hemisphere Publishing Corporation, Washington, 1984,
   ISBN: 0-89116-353-0,
   LC: TJ270.H3.
3. Allan McLeod,
   Algorithm 757: MISCFUN: A software package to compute uncommon special functions,
   ACM Transactions on Mathematical Software,
   Volume 22, Number 3, September 1996, pages 288-301.
4. Frank Powell,
   Statistical Tables for Sociology, Biology and Physical Sciences,
   Cambridge University Press, 1982,
   ISBN: 0521284732,
   LC: QA276.25.S73.
5. Eric Weisstein,
   CRC Concise Encyclopedia of Mathematics,
   CRC Press, 2002,
   Second edition,
   ISBN: 1584883472,
   LC: QA5.W45
6. Stephen Wolfram,
   The Mathematica Book,
   Fourth Edition,
   Cambridge University Press, 1999,
   ISBN: 0-521-64314-7,
   LC: QA76.95.W65.
7. Daniel Zwillinger, editor,
   CRC Standard Mathematical Tables and Formulae,
   30th Edition,
   CRC Press, 1996,
   ISBN: 0-8493-2479-3,
   LC: QA47.M315.
8. Daniel Zwillinger, Steven Kokoska,
   Standard Probability and Statistical Tables,
   CRC Press, 2000,
   ISBN: 1-58488-059-7,
   LC: QA273.3.Z95.

Source Code:

• abram0_values.m, returns selected values of the Abramowitz function of order 0.
• abram1_values.m, returns selected values of the Abramowitz function of order 1.
• abram2_values.m, returns selected values of the Abramowitz function of order 2.
• agm_values.m, returns selected values of the arithmetic geometric mean function.
• airy_ai_values.m, returns selected values of the Airy Ai function.
• airy_ai_int_values.m, returns selected values of the integral of the Airy Ai function.
• airy_ai_prime_values.m, returns selected values of the derivative of the Airy function Ai.
• airy_bi_values.m, returns selected values of the Airy Bi function.
• airy_bi_int_values.m, returns selected values of the integral of the Airy Bi function.
• airy_bi_prime_values.m, returns selected values of the derivative of the Airy function Bi.
• airy_cai_values.m, returns selected values of the Airy Ai function for complex argument.
• airy_cbi_values.m, returns selected values of the Airy Bi function for complex argument.
• airy_gi_values.m, returns selected values of the Airy Gi function.
• airy_hi_values.m, returns selected values of the Airy Hi function.
• arccos_values.m, returns selected values of the arc cosine function.
• arccosh_values.m, returns selected values of the hyperbolic arc cosine function.
• arcsin_values.m, returns selected values of the arc sine function.
• arcsinh_values.m, returns selected values of the hyperbolic arc sine function.
• arctan_values.m, returns selected values of the arc tangent function.
• arctan_int_values.m, returns selected values of the arctangent integral.
• arctan2_values.m, returns selected values of the arc tangent function of two arguments.
• arctanh_values.m, returns selected values of the hyperbolic arc tangent function.
• bei0_values.m, returns selected values of the Kelvin BEI function for NU = 0.
• bei1_values.m, returns selected values of the Kelvin BEI function for NU = 1.
• bell_values.m, returns selected values of the Bell numbers.
• ber0_values.m, returns selected values of the Kelvin BER function for NU = 0.
• ber1_values.m, returns selected values of the Kelvin BER function for NU = 1.
• bernoulli_number_values.m, returns selected values of the Bernoulli numbers.
• bernoulli_poly_values.m, returns selected values of the Bernoulli polynomials.
• bernstein_poly_01_values.m, returns selected values of the Bernstein polynomials.
• bessel_i0_values.m returns some values of the I0 Bessel function.
• bessel_i0_int_values.m returns some values of the integral of the I0 Bessel function.
• bessel_i0_spherical_values.m returns some values of the spherical Bessel function i0.
• bessel_i1_values.m returns some values of the I1 Bessel function.
• bessel_i1_spherical_values.m returns some values of the spherical Bessel function i1.
• bessel_in_values.m returns some values of the In Bessel function.
• bessel_ix_values.m returns some values of the In Bessel function for NONINTEGER order.
• bessel_j_spherical_values.m returns some values of the Spherical Bessel function j.
• bessel_j0_values.m returns some values of the J0 Bessel function.
• bessel_j0_int_values.m returns some values of the integral of the J0 Bessel function.
• bessel_j0_spherical_values.m returns some values of the Spherical Bessel function j0.
• bessel_j0_zerol_values.m returns some zeros of the Bessel function j0.
• bessel_j1_values.m returns some values of the J1 Bessel function.
• bessel_j1_spherical_values.m returns some values of the Spherical Bessel function j1.
• bessel_jn_values.m returns some values of the Jn Bessel function.
• bessel_jx_values.m returns some values of the Jn Bessel function for NONINTEGER order.
• bessel_k0_values.m returns some values of the K0 Bessel function.
• bessel_k0_int_values.m returns some values of the integral of the K0 Bessel function.
• bessel_k1_values.m returns some values of the K1 Bessel function.
• bessel_kn_values.m returns some values of the Kn Bessel function.
• bessel_kx_values.m returns some values of the Kn Bessel function for NONINTEGER order.
• bessel_y0_values.m returns some values of the Y0 Bessel function.
• bessel_y0_int_values.m returns some values of the integral of the Y0 Bessel function.
• bessel_y0_spherical_values.m returns some values of the Spherical Bessel function y0.
• bessel_y1_values.m returns some values of the Y1 Bessel function.
• bessel_y1_spherical_values.m returns some values of the Spherical Bessel function y1.
• bessel_yn_values.m returns some values of the Yn Bessel function.
• bessel_yx_values.m returns some values of the Yn Bessel function for NONINTEGER order.
• beta_values.m returns some values of the Beta function.
• beta_cdf_values.m returns some values of the Beta CDF.
• beta_inc_values.m returns some values of the incomplete Beta function.
• beta_log_values.m returns some values of the logarithm of the Beta function.
• beta_noncentral_cdf_values.m returns some values of the noncentral incomplete Beta function.
• beta_pdf_values.m returns some values of the Beta PDF.
• binomial_values.m returns some values of the binomial coefficients.
• binomial_cdf_values.m returns some values of the binomial CDF.
• binomial_pdf_values.m returns some values of the binomial PDF.
• bivariate_normal_cdf_values.m returns some values of the bivariate normal CDF.
• c8_log_values.m returns some values of the logarithm of a complex value.
• catalan_values.m returns some values of the Catalan numbers.
• cauchy_cdf_values.m returns some values of the Cauchy CDF.
• cbrt_values.m returns some values of the cube root function.
• cheby_t_poly_values.m returns values of the Chebyshev polynomial T(n,x).
• cheby_t01_poly_values.m returns values of the shifted Chebyshev polynomial T01(n,x).
• cheby_u_poly_values.m returns values of the Chebyshev polynomial U(n,x).
• cheby_u01_poly_values.m returns values of the shifted Chebyshev polynomial U01(n,x).
• cheby_v_poly_values.m returns values of the Chebyshev polynomial V(n,x).
• cheby_v01_poly_values.m returns values of the shifted Chebyshev polynomial V01(n,x).
• cheby_w_poly_values.m returns values of the Chebyshev polynomial W(n,x).
• cheby_w01_poly_values.m returns values of the shifted Chebyshev polynomial W01(n,x).
• chi_values.m returns some values of the hyperbolic cosine integral function.
• chi_square_cdf_values.m returns some values of the Chi-Square CDF.
• chi_square_noncentral_cdf_values.m returns some values of the noncentral Chi-Square CDF.
• chi_square_pdf_values.m returns some values of the Chi-Square PDF.
• ci_values.m returns some values of the cosine integral function.
• cin_values.m returns some values of the alternate cosine integral function.
• cinh_values.m returns some values of the alternate hyperbolic cosine integral function.
• clausen_values.m returns some values of Clausen's integral function.
• clebsch_gordan_values.m returns some values of the Clebsch-Gordan coefficients.
• collatz_count_values.m returns some values of the length of the Collatz sequence.
• cos_values.m returns some values of the cosine function.
• cos_degree_values.m returns some values of the cosine function for arguments in degrees.
• cos_power_int_values.m returns some values of the integral of the N-th power of the cosine function;
• cosh_values.m returns some values of the hyperbolic cosine function.
• cot_values.m returns some values of the cotangent function.
• cp_values.m returns some values of the specific heat at constant pressure.
• dawson_values.m returns some values of Dawson's integral.
• debye1_values.m returns some values of the Debye1 function of order 1.
• debye2_values.m returns some values of the Debye1 function of order 2.
• debye3_values.m returns some values of the Debye1 function of order 3.
• debye4_values.m returns some values of the Debye1 function of order 4.
• dedekind_sum_values.m returns some values of the Dedekind sum.
• dielectric_values.m returns some values of the static dielectric constant.
• dilogarithm_values.m returns some values of the dilogarithm function.
• e1_values.m returns some values of the exponential integral function E1(X).
• ei_values.m returns some values of the exponential integral function EI(X).
• elliptic_ea_values.m returns values of the complete elliptic integral E(A).
• elliptic_ek_values.m returns values of the complete elliptic integral E(K).
• elliptic_em_values.m returns values of the complete elliptic integral E(M).
• elliptic_fa_values.m returns values of the complete elliptic integral F(A).
• elliptic_fk_values.m returns values of the complete elliptic integral F(K).
• elliptic_fm_values.m returns values of the complete elliptic integral F(M).
• elliptic_inc_ea_values.m returns values of the incomplete elliptic integral E(PHI,A).
• elliptic_inc_ek_values.m returns values of the incomplete elliptic integral E(PHI,K).
• elliptic_inc_em_values.m returns values of the incomplete elliptic integral E(PHI,M).
• elliptic_inc_fa_values.m returns values of the incomplete elliptic integral F(PHI,A).
• elliptic_inc_fk_values.m returns values of the incomplete elliptic integral F(PHI,K).
• elliptic_inc_fm_values.m returns values of the incomplete elliptic integral F(PHI,M).
• elliptic_inc_pia_values.m returns values of the incomplete elliptic integral Pi(PHI,N,A).
• elliptic_inc_pik_values.m returns values of the incomplete elliptic integral Pi(PHI,vN,K).
• elliptic_inc_pim_values.m returns values of the incomplete elliptic integral Pi(PHI,N,M).
• elliptic_pia_values.m returns values of the complete elliptic integral Pi(N,A).
• elliptic_pik_values.m returns values of the complete elliptic integral Pi(N,K).
• elliptic_pim_values.m returns values of the complete elliptic integral Pi(N,M).
• erf_values.m returns some values of the ERF or "error" function.
• erfc_values.m returns some values of the ERFC or "complementary error" function.
• euler_number_values.m returns some values of the Euler numbers.
• euler_poly_values.m returns some values of the Euler polynomials.
• exp_values.m returns some values of the exponential function.
• exp3_int_values.m returns some values of the EXP3 integral function.
• exponential_01_pdf_values.m returns some values of the standard exponential PDF.
• exponential_cdf_values.m returns some values of the exponential CDF.
• exponential_pdf_values.m returns some values of the exponential PDF.
• extreme_values_cdf_values.m returns some values of the extreme_values CDF.
• f_cdf_values.m returns some values of the F CDF.
• f_noncentral_cdf_values.m returns some values of the noncentral F CDF.
• fresnel_cos_values.m returns some values of the Fresnel cosine integral function.
• fresnel_sin_values.m returns some values of the Fresnel sine integral function.
• frobenius_number_data_values.m returns some data values for the general Frobenius number problem.
• frobenius_number_order_values.m returns some order values for the general Frobenius number problem.
• frobenius_number_order2_values.m returns some values of the Frobenius number of order2.
• gamma_values.m, returns selected values of the Gamma function.
• gamma_01_pdf_values.m, returns selected values of the standard Gamma PDF.
• gamma_cdf_values.m, returns selected values of the Gamma CDF.
• gamma_inc_values.m, returns selected values of the incomplete Gamma function.
• gamma_inc_p_values.m, returns selected values of the incomplete Gamma P function.
• gamma_inc_q_values.m, returns selected values of the incomplete Gamma Q function.
• gamma_inc_tricomi_values.m, returns selected values of Tricomi's incomplete Gamma function.
• gamma_log_values.m returns some values of the logarithm of the Gamma function.
• gamma_pdf_values.m, returns selected values of a Gamma PDF.
• gegenbauer_poly_values.m returns some values of the Gegenbauer polynomials.
• geometric_cdf_values.m returns some values of the geometric CDF.
• goodwin_values.m returns some values of the Goodwin function.
• gud_values.m returns some values of the Gudermannian function.
• hermite_function_values.m returns some values of the Hermite function Hf(n,x).
• hermite_poly_phys_values.m returns some values of the physicist's Hermite polynomial H(n,x).
• hermite_poly_prob_values.m returns some values of the probabilist's Hermite polynomial He(n,x).
• hyper_1f1_values.m returns some values of the hypergeometric 1F1 function.
• hyper_2f1_values.m returns some values of the hypergeometric 2F1 function.
• hypergeometric_cdf_values.m returns some values of the hypergeometric CDF.
• hypergeometric_pdf_values.m returns some values of the hypergeometric PDF.
• hypergeometric_u_values.m returns some values of the hypergeometric function U(a,b,x).
• i0ml0_values.m returns some values of the I0ML0 function.
• i1ml1_values.m returns some values of the I1ML1 function.
• i4_factorial_values.m returns values of the factorial function.
• i4_factorial2_values.m returns values of the double factorial function.
• i4_fall_values.m returns values of the integer falling factorial function.
• i4_rise_values.m returns values of the integer rising factorial function.
• int_values.m returns some values of the "int" function.
• inverse_chi_square_pdf_values.m returns some values of the inverse chi square PDF.
• inverse_gamma_pdf_values.m returns some values of the inverse gamma PDF.
• jacobi_cn_values.m returns some values of the Jacobi elliptic function CN(U,M).
• jacobi_dn_values.m returns some values of the Jacobi elliptic function DN(U,M).
• jacobi_poly_values.m returns some values of the Jacobi polynomial.
• jacobi_sn_values.m returns some values of the Jacobi elliptic function SN(U,M).
• jed_ce_values.m returns some values of the Julian Ephemeris Date and the corresponding Common Era year/month/day/fraction date.
• jed_mjd_values.m returns some values of the Julian Ephemeris Date and the corresponding Modified Julian Day count.
• jed_rd_values.m returns some values of the Julian Ephemeris Date and the corresponding Reingold Dershowitz date.
• jed_weekday_values.m returns some values of the Julian Ephemeris Date and the day of the week.
• kei0_values.m, returns selected values of the Kelvin KEI function for NU = 0.
• kei1_values.m, returns selected values of the Kelvin KEI function for NU = 1.
• ker0_values.m, returns selected values of the Kelvin KER function for NU = 0.
• ker1_values.m, returns selected values of the Kelvin KER function for NU = 1.
• laguerre_associated_values.m returns values of associated Laguerre functions.
• laguerre_general_values.m returns values of generalized Laguerre functions.
• laguerre_polynomial_values.m returns some values of the Laguerre polynomial.
• lambert_w_values.m returns values of the Lambert W function.
• laplace_cdf_values.m returns values of the Laplace CDF.
• legendre_associated_values.m returns values of associated Legendre functions.
• legendre_associated_normalized_values.m returns values of the normalized associated Legendre functions.
• legendre_associated_normalized_sphere_values.m returns values of the normalized associated Legendre functions, normalized for the surface of the unit sphere.
• legendre_function_q_values.m returns values of the Legendre Q function.
• legendre_normalized_polynomial_values.m returns values of the normalized Legendre polynomials.
• legendre_polynomial_values.m returns values of the Legendre polynomials.
• legendre_shifted_polynomial_values.m returns values of the shifted Legendre polynomials.
• lerch_values.m returns values of the Lerch transcendent function.
• linear_system_values.m returns some linear systems.
• lobachevsky_values.m returns values of the Lobachevsky function.
• lobatto_polynomial_values.m returns values of the Lobatto polynomials.
• lobatto_polynomial_derivatives.m, returns values of the derivative of Lobatto polynomials.
• log10_values.m returns some values of the logarithm base 10 function.
• log_values.m returns some values of the natural logarithm function.
• log_normal_cdf_values.m returns values of the LogNormal CDF.
• log_series_cdf_values.m returns values of the LogSeries CDF.
• logarithmic_integral_values.m returns values of the logarithmic integral.
• logistic_cdf_values.m returns values of the logistic CDF.
• mertens_values.m returns some values of the Mertens function.
• mittag_leffler_ea_values.m returns some values of the Mittag-Leffler one parameter function.
• mittag_leffler_eab_values.m returns some values of the Mittag-Leffler two parameter function.
• moebius_values.m returns some values of the Moebius function.
• multinomial_pdf_sizes.m returns sizes of multinomial PDF data.
• multinomial_pdf_values.m returns values of multinomial PDF data.
• negative_binomial_cdf_values.m returns some values of the Negative Binomial CDF.
• nine_j_values.m returns some values of the Wigner 9J coefficients;
• normal_01_cdf_values.m returns values of the standard Normal CDF.
• normal_01_pdf_values.m returns values of the standard Normal PDF.
• normal_cdf_values.m returns some values of the Normal CDF.
• normal_pdf_values.m returns some values of the Normal PDF.
• omega_values.m returns some values of the OMEGA function.
• owen_values.m returns some values of Owen's T function.
• partition_count_values.m returns some values of the integer partition count.
• partition_distinct_count_values.m returns some values of Q(N).
• phi_values.m returns some values of the PHI function.
• pi_values.m returns some values of the PI function.
• poisson_cdf_values.m returns some values of the Poisson CDF.
• polylogarithm_values.m returns some values of the polylogarithm function.
• polyomino_chiral_count_values.m returns some values of the number of chiral polyominoes.
• polyomino_fixed_count_values.m returns some values of the number of fixed polyominoes.
• polyomino_free_count_values.m returns some values of the number of free polyominoes.
• prandtl_values.m returns some values of the Prandtl number.
• prime_values.m returns some values of the prime function.
• psat_values.m returns some values of the saturation pressure.
• psi_values.m returns some values of the Psi or Digamma function.
• r8_factorial_values.m returns values of the real factorial function.
• r8_factorial_log_values.m returns values of log(n!).
• r8_factorial2_values.m returns values of the double factorial function.
• r8_fall_values.m returns some values of the falling factorial function.
• r8_rise_values.m returns some values of the rising factorial function.
• rayleigh_values.m returns some values of the Rayleigh CDF.
• scaled_inverse_chi_square_pdf_values.m returns some values of the scaled inverse chi square PDF.
• secvir_values.m returns some values of the second virial coefficient.
• shi_values.m returns some values of the hyperbolic sine integral function.
• si_values.m returns some values of the sine integral function.
• sigma_values.m returns some values of the Sigma function.
• sin_values.m returns some values of the sine function.
• sin_degree_values.m returns some values of the sine function for arguments in degrees.
• sin_power_int_values.m returns some values of the integral of the N-th power of the sine function;
• sinh_values.m returns some values of the hyperbolic sine function.
• six_j_values.m returns some values of the Wigner 6J coefficients;
• sound_values_values.m returns some values of the speed of sound.
• sphere_unit_area_values.m returns some values of the area of the unit sphere in various dimensions.
• sphere_unit_volume_values.m returns some values of the volume of the unit sphere in various dimensions.
• spherical_harmonic_values.m returns some values of the spherical harmonic function.
• sqrt_values.m returns some values of the square root function.
• stirling1_values.m returns some values of the Stirling numbers of the first kind.
• stirling2_values.m returns some values of the Stirling numbers of the second kind.
• stromgen_values.m returns some values of the Stromgen integral function.
• struve_h0_values.m returns some values of the Struve H0 function.
• struve_h1_values.m returns some values of the Struve H1 function.
• struve_l0_values.m returns some values of the Struve L0 function.
• struve_l1_values.m returns some values of the Struve L1 function.
• student_cdf_values.m returns some values of the Student CDF.
• student_noncentral_cdf_values.m returns some values of the noncentral Student CDF.
• subfactorial_values.m returns values of the subfactorial function.
• surten_values.m returns some values of the surface tension.
• synch1_values.m returns some values of the synchrotron function 1.
• synch2_values.m returns some values of the synchrotron function 2.
• tan_values.m returns some values of the tangent function.
• tanh_values.m returns some values of the hyperbolic tangent function.
• tau_values.m returns some values of the Tau function.
• thercon_values.m returns some values of the thermal conductivity.
• three_j_values.m returns some values of the Wigner 3J coefficients;
• timestamp.m, prints the YMDHMS date as a timestamp.
• tran02_values.m returns some values of the transportation function of order 2.
• tran03_values.m returns some values of the transportation function of order 3.
• tran04_values.m returns some values of the transportation function of order 4.
• tran05_values.m returns some values of the transportation function of order 5.
• tran06_values.m returns some values of the transportation function of order 6.
• tran07_values.m returns some values of the transportation function of order 7.
• tran08_values.m returns some values of the transportation function of order 8.
• tran09_values.m returns some values of the transportation function of order 9.
• trigamma_values.m returns some values of the TriGamma function.
• truncated_normal_ab_cdf_values.m returns some values of the CDF of the truncated normal distribution.
• truncated_normal_ab_pdf_values.m returns some values of the PDF of the truncated normal distribution.
• truncated_normal_a_cdf_values.m returns some values of the CDF of the lower truncated normal distribution.
• truncated_normal_a_pdf_values.m returns some values of the PDF of the lower truncated normal distribution.
• truncated_normal_b_cdf_values.m returns some values of the CDF of the upper truncated normal distribution.
• truncated_normal_b_pdf_values.m returns some values of the PDF of the upper truncated normal distribution.
• tsat_values.m returns some values of the saturation temperature.
• van_der_corput_values.m returns some values of the van der Corput sequence.
• viscosity_values.m returns some values of the viscosity function.
• von_mises_cdf_values.m returns some values of the von Mises CDF.
• weekday_values.m returns some values of the day of the week for given Y/M/D dates in the Common Era Julian/Gregorian calendar.
• weibull_cdf_values.m returns some values of the Weibull CDF.
• wright_omega_values.m returns some values of the Wright Omega function.
• zeta_values.m returns some values of the Riemann Zeta function.
• zeta_m1_values.m returns some values of the Riemann Zeta Minus One function.