TEST_VALUES
Sample Function Values

TEST_VALUES is a Python 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:

FN, a Python library which approximates elementary and special functions using Chebyshev polynomials; functions include Airy, Bessel I, Bessel J, Bessel K, Bessel Y, beta, confluent hypergeometric, cosine integral, Dawson's integral, digamma (psi), error, exponential integral, gamma, hyperbolic cosine integral, hyperbolic sine integral, incomplete gamma, log gamma, logarithmic integral, Pochhammer, psi, sine integral, Spence; by Wayne Fullerton.

Source Code:

• abram0_values.py, returns selected values of the Abramowitz function of order 0.
• abram1_values.py, returns selected values of the Abramowitz function of order 1.
• abram2_values.py, returns selected values of the Abramowitz function of order 2.
• agm_values.py, returns selected values of the arithmetic geometric mean function.
• airy_ai_values.py, returns selected values of the Airy Ai function.
• airy_ai_int_values.py, returns selected values of the integral of the Airy Ai function.
• airy_ai_prime_values.py, returns selected values of the derivative of the Airy function Ai.
• airy_bi_values.py, returns selected values of the Airy Bi function.
• airy_bi_int_values.py, returns selected values of the integral of the Airy Bi function.
• airy_bi_prime_values.py, returns selected values of the derivative of the Airy function Bi.
• airy_cai_values.py, returns selected values of the Airy Ai function for complex argument.
• airy_cbi_values.py, returns selected values of the Airy Bi function for complex argument.
• airy_gi_values.py, returns selected values of the Airy Gi function.
• airy_hi_values.py, returns selected values of the Airy Hi function.
• arccos_values.py, returns selected values of the arc cosine function.
• arccosh_values.py, returns selected values of the hyperbolic arc cosine function.
• arcsin_values.py, returns selected values of the arc sine function.
• arcsinh_values.py, returns selected values of the hyperbolic arc sine function.
• arctan_values.py, returns selected values of the arc tangent function.
• arctan_int_values.py, returns selected values of the arctangent integral.
• arctan2_values.py, returns selected values of the arc tangent function of two arguments.
• arctanh_values.py, returns selected values of the hyperbolic arc tangent function.
• bei0_values.py, returns selected values of the Kelvin BEI function for NU = 0.
• bei1_values.py, returns selected values of the Kelvin BEI function for NU = 1.
• bell_values.py, returns selected values of the Bell numbers.
• ber0_values.py, returns selected values of the Kelvin BER function for NU = 0.
• ber1_values.py, returns selected values of the Kelvin BER function for NU = 1.
• bernoulli_number_values.py, returns selected values of the Bernoulli numbers.
• bernoulli_poly_values.py, returns selected values of the Bernoulli polynomials.
• bernstein_poly_01_values.py, returns selected values of the Bernstein polynomials.
• bessel_i0_values.py returns some values of the I0 Bessel function.
• bessel_i0_int_values.py returns some values of the integral of the I0 Bessel function.
• bessel_i0_spherical_values.py returns some values of the spherical Bessel function i0.
• bessel_i1_values.py returns some values of the I1 Bessel function.
• bessel_i1_spherical_values.py returns some values of the spherical Bessel function i1.
• bessel_in_values.py returns some values of the In Bessel function.
• bessel_ix_values.py returns some values of the In Bessel function for NONINTEGER order.
• bessel_j_spherical_values.py returns some values of the Spherical Bessel function j.
• bessel_j0_values.py returns some values of the J0 Bessel function.
• bessel_j0_int_values.py returns some values of the integral of the J0 Bessel function.
• bessel_j0_spherical_values.py returns some values of the Spherical Bessel function j0.
• bessel_j0_zero_values.py returns some zeros of the Bessel function j0.
• bessel_j1_values.py returns some values of the J1 Bessel function.
• bessel_j1_spherical_values.py returns some values of the Spherical Bessel function j1.
• bessel_jn_values.py returns some values of the Jn Bessel function.
• bessel_jx_values.py returns some values of the Jn Bessel function for NONINTEGER order.
• bessel_k0_values.py returns some values of the K0 Bessel function.
• bessel_k0_int_values.py returns some values of the integral of the K0 Bessel function.
• bessel_k1_values.py returns some values of the K1 Bessel function.
• bessel_kn_values.py returns some values of the Kn Bessel function.
• bessel_kx_values.py returns some values of the Kn Bessel function for NONINTEGER order.
• bessel_y0_values.py returns some values of the Y0 Bessel function.
• bessel_y0_int_values.py returns some values of the integral of the Y0 Bessel function.
• bessel_y0_spherical_values.py returns some values of the Spherical Bessel function y0.
• bessel_y1_values.py returns some values of the Y1 Bessel function.
• bessel_y1_spherical_values.py returns some values of the Spherical Bessel function y1.
• bessel_yn_values.py returns some values of the Yn Bessel function.
• bessel_yx_values.py returns some values of the Yn Bessel function for NONINTEGER order.
• beta_values.py returns some values of the Beta function.
• beta_cdf_values.py returns some values of the Beta CDF.
• beta_inc_values.py returns some values of the incomplete Beta function.
• beta_log_values.py returns some values of the logarithm of the Beta function.
• beta_noncentral_cdf_values.py returns some values of the noncentral incomplete Beta function.
• beta_pdf_values.py returns some values of the Beta PDF.
• binomial_values.py returns some values of the binomial coefficients.
• binomial_cdf_values.py returns some values of the binomial CDF.
• binomial_pdf_values.py returns some values of the binomial PDF.
• bivariate_normal_cdf_values.py returns some values of the bivariate normal CDF.
• catalan_values.py returns some values of the Catalan numbers.
• cauchy_cdf_values.py returns some values of the Cauchy CDF.
• cbrt_values.py returns some values of the cube root function.
• cheby_t_poly_values.py returns values of the Chebyshev polynomial T(n,x).
• cheby_t01_poly_values.py returns values of the shifted Chebyshev polynomial T01(n,x).
• cheby_u_poly_values.py returns values of the Chebyshev polynomial U(n,x).
• cheby_u01_poly_values.py returns values of the shifted Chebyshev polynomial U01(n,x).
• cheby_v_poly_values.py returns values of the Chebyshev polynomial V(n,x).
• cheby_v01_poly_values.py returns values of the shifted Chebyshev polynomial V01(n,x).
• cheby_w_poly_values.py returns values of the Chebyshev polynomial W(n,x).
• cheby_w01_poly_values.py returns values of the shifted Chebyshev polynomial W01(n,x).
• chi_values.py returns some values of the hyperbolic cosine integral function.
• chi_square_cdf_values.py returns some values of the Chi-Square CDF.
• chi_square_pdf_values.py returns some values of the Chi-Square PDF.
• chi_square_noncentral_cdf_values.py returns some values of the noncentral Chi-Square CDF.
• ci_values.py returns some values of the cosine integral function.
• cin_values.py returns some values of the alternate cosine integral function.
• cinh_values.py returns some values of the alternate hyperbolic cosine integral function.
• clausen_values.py returns some values of Clausen's integral function.
• clebsch_gordan_values.py returns some values of the Clebsch-Gordan coefficients.
• collatz_count_values.py returns some values of the length of the Collatz sequence.
• cos_values.py returns some values of the cosine function.
• cos_degree_values.py returns some values of the cosine function for arguments in degrees.
• cos_power_int_values.py returns some values of the integral of the N-th power of the cosine function;
• cosh_values.py returns some values of the hyperbolic cosine function.
• cot_values.py returns some values of the cotangent function.
• cp_values.py returns some values of the specific heat at constant pressure.
• dawson_values.py returns some values of Dawson's integral.
• debye1_values.py returns some values of the Debye1 function of order 1.
• debye2_values.py returns some values of the Debye1 function of order 2.
• debye3_values.py returns some values of the Debye1 function of order 3.
• debye4_values.py returns some values of the Debye1 function of order 4.
• dedekind_sum_values.py returns some values of the Dedekind sum.
• dielectric_values.py returns some values of the static dielectric constant.
• dilogarithm_values.py returns some values of the dilogarithm function.
• e1_values.py returns some values of the exponential integral function E1(X).
• ei_values.py returns some values of the exponential integral function EI(X).
• elliptic_ea_values.py returns values of the complete elliptic integral E(A).
• elliptic_ek_values.py returns values of the complete elliptic integral E(K).
• elliptic_em_values.py returns values of the complete elliptic integral E(M).
• elliptic_fa_values.py returns values of the complete elliptic integral F(A).
• elliptic_fk_values.py returns values of the complete elliptic integral F(K).
• elliptic_fm_values.py returns values of the complete elliptic integral F(M).
• elliptic_pia_values.py returns values of the complete elliptic integral Pi(A).
• elliptic_pik_values.py returns values of the complete elliptic integral Pi(K).
• elliptic_pim_values.py returns values of the complete elliptic integral Pi(M).
• elliptic_inc_ea_values.py returns values of the incomplete elliptic integral E(PHI,A).
• elliptic_inc_ek_values.py returns values of the incomplete elliptic integral E(PHI,K).
• elliptic_inc_em_values.py returns values of the incomplete elliptic integral E(PHI,M).
• elliptic_inc_fa_values.py returns values of the incomplete elliptic integral F(PHI,A).
• elliptic_inc_fk_values.py returns values of the incomplete elliptic integral F(PHI,K).
• elliptic_inc_fm_values.py returns values of the incomplete elliptic integral F(PHI,M).
• elliptic_inc_pia_values.py returns values of the incomplete elliptic integral Pi(PHI,A).
• elliptic_inc_pik_values.py returns values of the incomplete elliptic integral Pi(PHI,K).
• elliptic_inc_pim_values.py returns values of the incomplete elliptic integral Pi(PHI,M).
• erf_values.py returns some values of the ERF or "error" function.
• erfc_values.py returns some values of the ERFC or "complementary error" function.
• euler_number_values.py returns some values of the Euler numbers.
• euler_poly_values.py returns some values of the Euler polynomials.
• exp_values.py returns some values of the exponential function.
• exp3_int_values.py returns some values of the EXP3 integral function.
• exponential_01_pdf_values.py returns some values of the standard exponential PDF.
• exponential_cdf_values.py returns some values of the exponential CDF.
• exponential_pdf_values.py returns some values of the exponential PDF.
• extreme_values_cdf_values.py returns some values of the extreme_values CDF.
• f_cdf_values.py returns some values of the F CDF.
• f_noncentral_cdf_values.py returns some values of the noncentral F CDF.
• fresnel_cos_values.py returns some values of the Fresnel cosine integral function.
• fresnel_sin_values.py returns some values of the Fresnel sine integral function.
• frobenius_number_data_values.py returns some data values for the general Frobenius number problem.
• frobenius_number_order_values.py returns some order values for the general Frobenius number problem.
• frobenius_number_order2_values.py returns some values of the Frobenius number of order2.
• gamma_values.py, returns selected values of the Gamma function.
• gamma_01_pdf_values.py, returns selected values of the standard Gamma PDF.
• gamma_cdf_values.py, returns selected values of the Gamma CDF.
• gamma_inc_values.py, returns selected values of the incomplete Gamma function.
• gamma_inc_p_values.py, returns selected values of the incomplete Gamma P function.
• gamma_inc_q_values.py, returns selected values of the incomplete Gamma Q function.
• gamma_inc_tricomi_values.py, returns selected values of Tricomi's incomplete Gamma function.
• gamma_log_values.py returns some values of the logarithm of the Gamma function.
• gegenbauer_poly_values.py returns some values of the Gegenbauer polynomials.
• geometric_cdf_values.py returns some values of the geometric CDF.
• goodwin_values.py returns some values of the Goodwin function.
• gud_values.py, returns selected values of the Gudermannian function.
• hermite_function_values.py returns some values of the Hermite function Hf(n,x).
• hermite_poly_phys_values.py returns some values of the physicist's Hermite polynomial H(n,x).
• hermite_poly_prob_values.py returns some values of the probabilist's Hermite polynomial He(n,x).
• hyper_1f1_values.py returns some values of the hypergeometric 1F1 function.
• hyper_2f1_values.py returns some values of the hypergeometric 2F1 function.
• hypergeometric_cdf_values.py returns some values of the hypergeometric CDF.
• hypergeometric_pdf_values.py returns some values of the hypergeometric PDF.
• hypergeometric_u_values.py returns some values of the hypergeometric function U(a,b,x).
• i0ml0_values.py returns some values of the I0ML0 function.
• i1ml1_values.py returns some values of the I1ML1 function.
• i4_factorial_values.py, returns selected values of the integer factorial function.
• i4_factorial2_values.py returns values of the double factorial function.
• i4_fall_values.py, returns selected values of the falling factorial function.
• i4_rise_values.py, returns selected values of the rising factorial function.
• int_values.py returns some values of the "int" function.
• inverse_chi_square_pdf_values.py returns some values of the inverse chi square PDF.
• inverse_gamma_pdf_values.py returns some values of the inverse gamma PDF.
• jacobi_cn_values.py returns some values of the Jacobi elliptic function CN(U,M).
• jacobi_dn_values.py returns some values of the Jacobi elliptic function DN(U,M).
• jacobi_poly_values.py returns some values of the Jacobi polynomial.
• jacobi_sn_values.py returns some values of the Jacobi elliptic function SN(U,M).
• jed_ce_values.py returns some values of the Julian Ephemeris Date and the corresponding Common Era year/month/day/fraction date.
• jed_mjd_values.py returns some values of the Julian Ephemeris Date and the corresponding Modified Julian Day count.
• jed_rd_values.py returns some values of the Julian Ephemeris Date and the corresponding Reingold Dershowitz date.
• jed_weekday_values.py returns some values of the Julian Ephemeris Date and the day of the week.
• kei0_values.py, returns selected values of the Kelvin KEI function for NU = 0.
• kei1_values.py, returns selected values of the Kelvin KEI function for NU = 1.
• ker0_values.py, returns selected values of the Kelvin KER function for NU = 0.
• ker1_values.py, returns selected values of the Kelvin KER function for NU = 1.
• laguerre_associated_values.py returns values of associated Laguerre functions.
• laguerre_general_values.py returns values of generalized Laguerre functions.
• laguerre_polynomial_values.py returns some values of the Laguerre polynomial.
• lambert_w_values.py returns values of the Lambert W function.
• laplace_cdf_values.py returns values of the Laplace CDF.
• legendre_associated_values.py returns values of associated Legendre functions.
• legendre_associated_normalized_values.py returns values of the normalized associated Legendre functions.
• legendre_associated_normalized_sphere_values.py returns values of the associated Legendre functions, normalized for the surface of the unit sphere.
• legendre_function_q_values.py returns values of the Legendre Q function.
• legendre_polynomial_values.py returns values of the Legendre polynomials.
• legendre_normalized_polynomial_values.py returns values of the normalized Legendre polynomials.
• legendre_shifted_polynomial_values.py returns values of the shifted Legendre polynomials.
• lerch_values.py returns values of the Lerch transcendent function.
• lobachevsky_values.py returns values of the Lobachevsky function.
• lobatto_polynomial_values.py returns values of the Lobatto polynomials.
• lobatto_polynomial_derivatives.py returns derivatives of the Lobatto polynomials.
• log_values.py returns some values of the natural logarithm function.
• log_normal_cdf_values.py returns values of the LogNormal CDF.
• log_series_cdf_values.py returns values of the LogSeries CDF.
• log10_values.py returns some values of the logarithm base 10 function.
• logarithmic_integral_values.py returns values of the logarithmic integral.
• logistic_cdf_values.py returns values of the logistic CDF.
• mertens_values.py returns some values of the Mertens function.
• mittag_leffler_ea_values.py returns some values of the one-parameter Mittag-Leffler function.
• mittag_leffler_eab_values.py returns some values of the two-parameter Mittag-Leffler function.
• moebius_values.py returns some values of the Moebius function.
• multinomial_pdf_values.py returns some values of the multinomial PDF.
• negative_binomial_cdf_values.py returns some values of the Negative Binomial CDF.
• nine_j_values.py returns some values of the Wigner 9J coefficients;
• normal_01_cdf_values.py returns values of the standard Normal CDF.
• normal_01_pdf_values.py returns values of the standard Normal PDF.
• normal_cdf_values.py returns some values of the Normal CDF.
• normal_pdf_values.py returns some values of the Normal PDF.
• omega_values.py returns some values of the OMEGA function.
• owen_values.py returns some values of Owen's T function.
• partition_count_values.py returns some values of the integer partition count.
• partition_distinct_count_values.py returns some values of Q(N).
• phi_values.py returns some values of the PHI function.
• pi_values.py returns some values of the PI function.
• poisson_cdf_values.py returns some values of the Poisson CDF.
• polylogarithm_values.py returns some values of the polylogarithm function.
• polyomino_chiral_count_values.py returns some values of the number of chiral polyominoes of given order.
• polyomino_fixed_count_values.py returns some values of the number of fixed polyominoes of given order.
• polyomino_free_count_values.py returns some values of the number of free polyominoes of given order.
• prandtl_values.py returns some values of the Prandtl number.
• prime_values.py returns some values of the prime function.
• psat_values.py returns some values of the saturation pressure.
• psi_values.py returns some values of the Psi or Digamma function.
• r8_factorial_values.py returns values of the real factorial function.
• r8_factorial_log_values.py returns values of log(n!).
• r8_fall_values.py, returns selected values of the falling factorial function.
• r8_rise_values.py, returns selected values of the rising factorial function.
• rayleigh_values.py returns some values of the Rayleigh CDF.
• scaled_inverse_chi_square_pdf_values.py returns some values of the scaled inverse chi square PDF.
• secvir_values.py returns some values of the second virial coefficient.
• shi_values.py returns some values of the hyperbolic sine integral function.
• si_values.py returns some values of the sine integral function.
• sigma_values.py returns some values of the Sigma function.
• sin_values.py returns some values of the sine function.
• sin_degree_values.py returns some values of the sine function for arguments in degrees.
• sin_power_int_values.py returns some values of the integral of the N-th power of the sine function;
• sinh_values.py returns some values of the hyperbolic sine function.
• six_j_values.py returns some values of the Wigner 6J coefficients;
• sound_values_values.py returns some values of the speed of sound.
• sphere_unit_area_values.py returns some values of the area of the unit sphere in various dimensions.
• sphere_unit_volume_values.py returns some values of the volume of the unit sphere in various dimensions.
• spherical_harmonic_values.py returns some values of the spherical harmonic function.
• sqrt_values.py returns some values of the square root function.
• stirling1_values.py returns some values of the Stirling numbers of the first kind.
• stirling2_values.py returns some values of the Stirling numbers of the second kind.
• stromgen_values.py returns some values of the Stromgen integral function.
• struve_h0_values.py returns some values of the Struve H0 function.
• struve_h1_values.py returns some values of the Struve H1 function.
• struve_l0_values.py returns some values of the Struve L0 function.
• struve_l1_values.py returns some values of the Struve L1 function.
• student_cdf_values.py returns some values of the Student CDF.
• student_noncentral_cdf_values.py returns some values of the noncentral Student CDF.
• subfactorial_values.py returns values of the subfactorial function.
• surten_values.py returns some values of the surface tension.
• synch1_values.py returns some values of the synchrotron function 1.
• synch2_values.py returns some values of the synchrotron function 2.
• tan_values.py returns some values of the tangent function.
• tanh_values.py returns some values of the hyperbolic tangent function.
• tau_values.py returns some values of the Tau function.
• thercon_values.py returns some values of the thermal conductivity.
• three_j_values.py returns some values of the Wigner 3J coefficients;
• timestamp.py, prints the YMDHMS date as a timestamp.
• tran02_values.py returns some values of the transportation function of order 2.
• tran03_values.py returns some values of the transportation function of order 3.
• tran04_values.py returns some values of the transportation function of order 4.
• tran05_values.py returns some values of the transportation function of order 5.
• tran06_values.py returns some values of the transportation function of order 6.
• tran07_values.py returns some values of the transportation function of order 7.
• tran08_values.py returns some values of the transportation function of order 8.
• tran09_values.py returns some values of the transportation function of order 9.
• trigamma_values.py returns some values of the TriGamma function.
• truncated_normal_ab_cdf_values.py returns some values of the CDF of the truncated normal distribution.
• truncated_normal_ab_pdf_values.py returns some values of the PDF of the truncated normal distribution.
• truncated_normal_a_cdf_values.py returns some values of the CDF of the lower truncated normal distribution.
• truncated_normal_a_pdf_values.py returns some values of the PDF of the lower truncated normal distribution.
• truncated_normal_b_cdf_values.py returns some values of the CDF of the upper truncated normal distribution.
• truncated_normal_b_pdf_values.py returns some values of the PDF of the upper truncated normal distribution.
• tsat_values.py returns some values of the saturation temperature.
• van_der_corput_values.py returns some values of the van der Corput sequence.
• viscosity_values.py returns some values of the viscosity function.
• von_mises_cdf_values.py returns some values of the von Mises CDF.
• weekday_values.py 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.py returns some values of the Weibull CDF.
• wright_omega_values.py returns some values of the Wright Omega function.
• zeta_values.py returns some values of the Riemann Zeta function.
• zeta_m1_values.py returns some values of the Riemann Zeta_Minus_One function.

Examples and Tests:

• test_values_test.py, calls all the tests.
• test_values_test.sh, runs all the tests.
• test_values_test.txt, the output from a run of the sample program.

You can go up one level to the Python source codes.