This is gsl-ref.info, produced by makeinfo version 4.6 from gsl-ref.texi. INFO-DIR-SECTION Scientific software START-INFO-DIR-ENTRY * gsl-ref: (gsl-ref). GNU Scientific Library - Reference END-INFO-DIR-ENTRY Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006 The GSL Team. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with the Invariant Sections being "GNU General Public License" and "Free Software Needs Free Documentation", the Front-Cover text being "A GNU Manual", and with the Back-Cover Text being (a) (see below). A copy of the license is included in the section entitled "GNU Free Documentation License". (a) The Back-Cover Text is: "You have freedom to copy and modify this GNU Manual, like GNU software."  File: gsl-ref.info, Node: Minimization Algorithms using Derivatives, Next: Minimization Algorithms without Derivatives, Prev: Search Stopping Parameters for Minimization Algorithms, Up: Nonlinear Least-Squares Fitting Minimization Algorithms using Derivatives ========================================= The minimization algorithms described in this section make use of both the function and its derivative. They require an initial guess for the location of the minimum. There is no absolute guarantee of convergence--the function must be suitable for this technique and the initial guess must be sufficiently close to the minimum for it to work. - Derivative Solver: gsl_multifit_fdfsolver_lmsder This is a robust and efficient version of the Levenberg-Marquardt algorithm as implemented in the scaled LMDER routine in MINPACK. Minpack was written by Jorge J. More', Burton S. Garbow and Kenneth E. Hillstrom. The algorithm uses a generalized trust region to keep each step under control. In order to be accepted a proposed new position x' must satisfy the condition |D (x' - x)| < \delta, where D is a diagonal scaling matrix and \delta is the size of the trust region. The components of D are computed internally, using the column norms of the Jacobian to estimate the sensitivity of the residual to each component of x. This improves the behavior of the algorithm for badly scaled functions. On each iteration the algorithm attempts to minimize the linear system |F + J p| subject to the constraint |D p| < \Delta. The solution to this constrained linear system is found using the Levenberg-Marquardt method. The proposed step is now tested by evaluating the function at the resulting point, x'. If the step reduces the norm of the function sufficiently, and follows the predicted behavior of the function within the trust region, then it is accepted and the size of the trust region is increased. If the proposed step fails to improve the solution, or differs significantly from the expected behavior within the trust region, then the size of the trust region is decreased and another trial step is computed. The algorithm also monitors the progress of the solution and returns an error if the changes in the solution are smaller than the machine precision. The possible error codes are, `GSL_ETOLF' the decrease in the function falls below machine precision `GSL_ETOLX' the change in the position vector falls below machine precision `GSL_ETOLG' the norm of the gradient, relative to the norm of the function, falls below machine precision These error codes indicate that further iterations will be unlikely to change the solution from its current value. - Derivative Solver: gsl_multifit_fdfsolver_lmder This is an unscaled version of the LMDER algorithm. The elements of the diagonal scaling matrix D are set to 1. This algorithm may be useful in circumstances where the scaled version of LMDER converges too slowly, or the function is already scaled appropriately.  File: gsl-ref.info, Node: Minimization Algorithms without Derivatives, Next: Computing the covariance matrix of best fit parameters, Prev: Minimization Algorithms using Derivatives, Up: Nonlinear Least-Squares Fitting Minimization Algorithms without Derivatives =========================================== There are no algorithms implemented in this section at the moment.  File: gsl-ref.info, Node: Computing the covariance matrix of best fit parameters, Next: Example programs for Nonlinear Least-Squares Fitting, Prev: Minimization Algorithms without Derivatives, Up: Nonlinear Least-Squares Fitting Computing the covariance matrix of best fit parameters ====================================================== - Function: int gsl_multifit_covar (const gsl_matrix * J, double EPSREL, gsl_matrix * COVAR) This function uses the Jacobian matrix J to compute the covariance matrix of the best-fit parameters, COVAR. The parameter EPSREL is used to remove linear-dependent columns when J is rank deficient. The covariance matrix is given by, covar = (J^T J)^{-1} and is computed by QR decomposition of J with column-pivoting. Any columns of R which satisfy |R_{kk}| <= epsrel |R_{11}| are considered linearly-dependent and are excluded from the covariance matrix (the corresponding rows and columns of the covariance matrix are set to zero). If the minimisation uses the weighted least-squares function f_i = (Y(x, t_i) - y_i) / \sigma_i then the covariance matrix above gives the statistical error on the best-fit parameters resulting from the gaussian errors \sigma_i on the underlying data y_i. This can be verified from the relation \delta f = J \delta c and the fact that the fluctuations in f from the data y_i are normalised by \sigma_i and so satisfy <\delta f \delta f^T> = I. For an unweighted least-squares function f_i = (Y(x, t_i) - y_i) the covariance matrix above should be multiplied by the variance of the residuals about the best-fit \sigma^2 = \sum (y_i - Y(x,t_i))^2 / (n-p) to give the variance-covariance matrix \sigma^2 C. This estimates the statistical error on the best-fit parameters from the scatter of the underlying data. For more information about covariance matrices see *Note Fitting Overview::.  File: gsl-ref.info, Node: Example programs for Nonlinear Least-Squares Fitting, Next: References and Further Reading for Nonlinear Least-Squares Fitting, Prev: Computing the covariance matrix of best fit parameters, Up: Nonlinear Least-Squares Fitting Examples ======== The following example program fits a weighted exponential model with background to experimental data, Y = A \exp(-\lambda t) + b. The first part of the program sets up the functions `expb_f' and `expb_df' to calculate the model and its Jacobian. The appropriate fitting function is given by, f_i = ((A \exp(-\lambda t_i) + b) - y_i)/\sigma_i where we have chosen t_i = i. The Jacobian matrix J is the derivative of these functions with respect to the three parameters (A, \lambda, b). It is given by, J_{ij} = d f_i / d x_j where x_0 = A, x_1 = \lambda and x_2 = b. /* expfit.c -- model functions for exponential + background */ struct data { size_t n; double * y; double * sigma; }; int expb_f (const gsl_vector * x, void *data, gsl_vector * f) { size_t n = ((struct data *)data)->n; double *y = ((struct data *)data)->y; double *sigma = ((struct data *) data)->sigma; double A = gsl_vector_get (x, 0); double lambda = gsl_vector_get (x, 1); double b = gsl_vector_get (x, 2); size_t i; for (i = 0; i < n; i++) { /* Model Yi = A * exp(-lambda * i) + b */ double t = i; double Yi = A * exp (-lambda * t) + b; gsl_vector_set (f, i, (Yi - y[i])/sigma[i]); } return GSL_SUCCESS; } int expb_df (const gsl_vector * x, void *data, gsl_matrix * J) { size_t n = ((struct data *)data)->n; double *sigma = ((struct data *) data)->sigma; double A = gsl_vector_get (x, 0); double lambda = gsl_vector_get (x, 1); size_t i; for (i = 0; i < n; i++) { /* Jacobian matrix J(i,j) = dfi / dxj, */ /* where fi = (Yi - yi)/sigma[i], */ /* Yi = A * exp(-lambda * i) + b */ /* and the xj are the parameters (A,lambda,b) */ double t = i; double s = sigma[i]; double e = exp(-lambda * t); gsl_matrix_set (J, i, 0, e/s); gsl_matrix_set (J, i, 1, -t * A * e/s); gsl_matrix_set (J, i, 2, 1/s); } return GSL_SUCCESS; } int expb_fdf (const gsl_vector * x, void *data, gsl_vector * f, gsl_matrix * J) { expb_f (x, data, f); expb_df (x, data, J); return GSL_SUCCESS; } The main part of the program sets up a Levenberg-Marquardt solver and some simulated random data. The data uses the known parameters (1.0,5.0,0.1) combined with gaussian noise (standard deviation = 0.1) over a range of 40 timesteps. The initial guess for the parameters is chosen as (0.0, 1.0, 0.0). #include #include #include #include #include #include #include #include "expfit.c" #define N 40 void print_state (size_t iter, gsl_multifit_fdfsolver * s); int main (void) { const gsl_multifit_fdfsolver_type *T; gsl_multifit_fdfsolver *s; int status; size_t i, iter = 0; const size_t n = N; const size_t p = 3; gsl_matrix *covar = gsl_matrix_alloc (p, p); double y[N], sigma[N]; struct data d = { n, y, sigma}; gsl_multifit_function_fdf f; double x_init[3] = { 1.0, 0.0, 0.0 }; gsl_vector_view x = gsl_vector_view_array (x_init, p); const gsl_rng_type * type; gsl_rng * r; gsl_rng_env_setup(); type = gsl_rng_default; r = gsl_rng_alloc (type); f.f = &expb_f; f.df = &expb_df; f.fdf = &expb_fdf; f.n = n; f.p = p; f.params = &d; /* This is the data to be fitted */ for (i = 0; i < n; i++) { double t = i; y[i] = 1.0 + 5 * exp (-0.1 * t) + gsl_ran_gaussian (r, 0.1); sigma[i] = 0.1; printf ("data: %d %g %g\n", i, y[i], sigma[i]); }; T = gsl_multifit_fdfsolver_lmsder; s = gsl_multifit_fdfsolver_alloc (T, n, p); gsl_multifit_fdfsolver_set (s, &f, &x.vector); print_state (iter, s); do { iter++; status = gsl_multifit_fdfsolver_iterate (s); printf ("status = %s\n", gsl_strerror (status)); print_state (iter, s); if (status) break; status = gsl_multifit_test_delta (s->dx, s->x, 1e-4, 1e-4); } while (status == GSL_CONTINUE && iter < 500); gsl_multifit_covar (s->J, 0.0, covar); #define FIT(i) gsl_vector_get(s->x, i) #define ERR(i) sqrt(gsl_matrix_get(covar,i,i)) { double chi = gsl_blas_dnrm2(s->f); double dof = n - p; double c = GSL_MAX_DBL(1, chi / sqrt(dof)); printf("chisq/dof = %g\n", pow(chi, 2.0) / dof); printf ("A = %.5f +/- %.5f\n", FIT(0), c*ERR(0)); printf ("lambda = %.5f +/- %.5f\n", FIT(1), c*ERR(1)); printf ("b = %.5f +/- %.5f\n", FIT(2), c*ERR(2)); } printf ("status = %s\n", gsl_strerror (status)); gsl_multifit_fdfsolver_free (s); return 0; } void print_state (size_t iter, gsl_multifit_fdfsolver * s) { printf ("iter: %3u x = % 15.8f % 15.8f % 15.8f " "|f(x)| = %g\n", iter, gsl_vector_get (s->x, 0), gsl_vector_get (s->x, 1), gsl_vector_get (s->x, 2), gsl_blas_dnrm2 (s->f)); } The iteration terminates when the change in x is smaller than 0.0001, as both an absolute and relative change. Here are the results of running the program: iter: 0 x=1.00000000 0.00000000 0.00000000 |f(x)|=117.349 status=success iter: 1 x=1.64659312 0.01814772 0.64659312 |f(x)|=76.4578 status=success iter: 2 x=2.85876037 0.08092095 1.44796363 |f(x)|=37.6838 status=success iter: 3 x=4.94899512 0.11942928 1.09457665 |f(x)|=9.58079 status=success iter: 4 x=5.02175572 0.10287787 1.03388354 |f(x)|=5.63049 status=success iter: 5 x=5.04520433 0.10405523 1.01941607 |f(x)|=5.44398 status=success iter: 6 x=5.04535782 0.10404906 1.01924871 |f(x)|=5.44397 chisq/dof = 0.800996 A = 5.04536 +/- 0.06028 lambda = 0.10405 +/- 0.00316 b = 1.01925 +/- 0.03782 status = success The approximate values of the parameters are found correctly, and the chi-squared value indicates a good fit (the chi-squared per degree of freedom is approximately 1). In this case the errors on the parameters can be estimated from the square roots of the diagonal elements of the covariance matrix. If the chi-squared value shows a poor fit (i.e. chi^2/dof >> 1) then the error estimates obtained from the covariance matrix will be too small. In the example program the error estimates are multiplied by \sqrt{\chi^2/dof} in this case, a common way of increasing the errors for a poor fit. Note that a poor fit will result from the use an inappropriate model, and the scaled error estimates may then be outside the range of validity for gaussian errors.  File: gsl-ref.info, Node: References and Further Reading for Nonlinear Least-Squares Fitting, Prev: Example programs for Nonlinear Least-Squares Fitting, Up: Nonlinear Least-Squares Fitting References and Further Reading ============================== The MINPACK algorithm is described in the following article, J.J. More', `The Levenberg-Marquardt Algorithm: Implementation and Theory', Lecture Notes in Mathematics, v630 (1978), ed G. Watson. The following paper is also relevant to the algorithms described in this section, J.J. More', B.S. Garbow, K.E. Hillstrom, "Testing Unconstrained Optimization Software", ACM Transactions on Mathematical Software, Vol 7, No 1 (1981), p 17-41.  File: gsl-ref.info, Node: Physical Constants, Next: IEEE floating-point arithmetic, Prev: Nonlinear Least-Squares Fitting, Up: Top Physical Constants ****************** This chapter describes macros for the values of physical constants, such as the speed of light, c, and gravitational constant, G. The values are available in different unit systems, including the standard MKSA system (meters, kilograms, seconds, amperes) and the CGSM system (centimeters, grams, seconds, gauss), which is commonly used in Astronomy. The definitions of constants in the MKSA system are available in the file `gsl_const_mksa.h'. The constants in the CGSM system are defined in `gsl_const_cgsm.h'. Dimensionless constants, such as the fine structure constant, which are pure numbers are defined in `gsl_const_num.h'. * Menu: * Fundamental Constants:: * Astronomy and Astrophysics:: * Atomic and Nuclear Physics:: * Measurement of Time:: * Imperial Units :: * Speed and Nautical Units:: * Printers Units:: * Volume Area and Length:: * Mass and Weight :: * Thermal Energy and Power:: * Pressure:: * Viscosity:: * Light and Illumination:: * Radioactivity:: * Force and Energy:: * Prefixes:: * Physical Constant Examples:: * Physical Constant References and Further Reading:: The full list of constants is described briefly below. Consult the header files themselves for the values of the constants used in the library.  File: gsl-ref.info, Node: Fundamental Constants, Next: Astronomy and Astrophysics, Up: Physical Constants Fundamental Constants ===================== `GSL_CONST_MKSA_SPEED_OF_LIGHT' The speed of light in vacuum, c. `GSL_CONST_MKSA_VACUUM_PERMEABILITY' The permeability of free space, \mu_0. This constant is defined in the MKSA system only. `GSL_CONST_MKSA_VACUUM_PERMITTIVITY' The permittivity of free space, \epsilon_0. This constant is defined in the MKSA system only. `GSL_CONST_MKSA_PLANCKS_CONSTANT_H' Planck's constant, h. `GSL_CONST_MKSA_PLANCKS_CONSTANT_HBAR' Planck's constant divided by 2\pi, \hbar. `GSL_CONST_NUM_AVOGADRO' Avogadro's number, N_a. `GSL_CONST_MKSA_FARADAY' The molar charge of 1 Faraday. `GSL_CONST_MKSA_BOLTZMANN' The Boltzmann constant, k. `GSL_CONST_MKSA_MOLAR_GAS' The molar gas constant, R_0. `GSL_CONST_MKSA_STANDARD_GAS_VOLUME' The standard gas volume, V_0. `GSL_CONST_MKSA_STEFAN_BOLTZMANN_CONSTANT' The Stefan-Boltzmann radiation constant, \sigma. `GSL_CONST_MKSA_GAUSS' The magnetic field of 1 Gauss.  File: gsl-ref.info, Node: Astronomy and Astrophysics, Next: Atomic and Nuclear Physics, Prev: Fundamental Constants, Up: Physical Constants Astronomy and Astrophysics ========================== `GSL_CONST_MKSA_ASTRONOMICAL_UNIT' The length of 1 astronomical unit (mean earth-sun distance), au. `GSL_CONST_MKSA_GRAVITATIONAL_CONSTANT' The gravitational constant, G. `GSL_CONST_MKSA_LIGHT_YEAR' The distance of 1 light-year, ly. `GSL_CONST_MKSA_PARSEC' The distance of 1 parsec, pc. `GSL_CONST_MKSA_GRAV_ACCEL' The standard gravitational acceleration on Earth, g. `GSL_CONST_MKSA_SOLAR_MASS' The mass of the Sun.  File: gsl-ref.info, Node: Atomic and Nuclear Physics, Next: Measurement of Time, Prev: Astronomy and Astrophysics, Up: Physical Constants Atomic and Nuclear Physics ========================== `GSL_CONST_MKSA_ELECTRON_CHARGE' The charge of the electron, e. `GSL_CONST_MKSA_ELECTRON_VOLT' The energy of 1 electron volt, eV. `GSL_CONST_MKSA_UNIFIED_ATOMIC_MASS' The unified atomic mass, amu. `GSL_CONST_MKSA_MASS_ELECTRON' The mass of the electron, m_e. `GSL_CONST_MKSA_MASS_MUON' The mass of the muon, m_\mu. `GSL_CONST_MKSA_MASS_PROTON' The mass of the proton, m_p. `GSL_CONST_MKSA_MASS_NEUTRON' The mass of the neutron, m_n. `GSL_CONST_NUM_FINE_STRUCTURE' The electromagnetic fine structure constant \alpha. `GSL_CONST_MKSA_RYDBERG' The Rydberg constant, Ry, in units of energy. This is related to the Rydberg inverse wavelength R by Ry = h c R. `GSL_CONST_MKSA_BOHR_RADIUS' The Bohr radius, a_0. `GSL_CONST_MKSA_ANGSTROM' The length of 1 angstrom. `GSL_CONST_MKSA_BARN' The area of 1 barn. `GSL_CONST_MKSA_BOHR_MAGNETON' The Bohr Magneton, \mu_B. `GSL_CONST_MKSA_NUCLEAR_MAGNETON' The Nuclear Magneton, \mu_N. `GSL_CONST_MKSA_ELECTRON_MAGNETIC_MOMENT' The absolute value of the magnetic moment of the electron, \mu_e. The physical magnetic moment of the electron is negative. `GSL_CONST_MKSA_PROTON_MAGNETIC_MOMENT' The magnetic moment of the proton, \mu_p. `GSL_CONST_MKSA_THOMSON_CROSS_SECTION' The Thomson cross section, \sigma_T. `GSL_CONST_MKSA_DEBYE' The electric dipole moment of 1 Debye, D.  File: gsl-ref.info, Node: Measurement of Time, Next: Imperial Units, Prev: Atomic and Nuclear Physics, Up: Physical Constants Measurement of Time =================== `GSL_CONST_MKSA_MINUTE' The number of seconds in 1 minute. `GSL_CONST_MKSA_HOUR' The number of seconds in 1 hour. `GSL_CONST_MKSA_DAY' The number of seconds in 1 day. `GSL_CONST_MKSA_WEEK' The number of seconds in 1 week.  File: gsl-ref.info, Node: Imperial Units, Next: Speed and Nautical Units, Prev: Measurement of Time, Up: Physical Constants Imperial Units ============== `GSL_CONST_MKSA_INCH' The length of 1 inch. `GSL_CONST_MKSA_FOOT' The length of 1 foot. `GSL_CONST_MKSA_YARD' The length of 1 yard. `GSL_CONST_MKSA_MILE' The length of 1 mile. `GSL_CONST_MKSA_MIL' The length of 1 mil (1/1000th of an inch).  File: gsl-ref.info, Node: Speed and Nautical Units, Next: Printers Units, Prev: Imperial Units, Up: Physical Constants Speed and Nautical Units ======================== `GSL_CONST_MKSA_KILOMETERS_PER_HOUR' The speed of 1 kilometer per hour. `GSL_CONST_MKSA_MILES_PER_HOUR' The speed of 1 mile per hour. `GSL_CONST_MKSA_NAUTICAL_MILE' The length of 1 nautical mile. `GSL_CONST_MKSA_FATHOM' The length of 1 fathom. `GSL_CONST_MKSA_KNOT' The speed of 1 knot.  File: gsl-ref.info, Node: Printers Units, Next: Volume Area and Length, Prev: Speed and Nautical Units, Up: Physical Constants Printers Units ============== `GSL_CONST_MKSA_POINT' The length of 1 printer's point (1/72 inch). `GSL_CONST_MKSA_TEXPOINT' The length of 1 TeX point (1/72.27 inch).  File: gsl-ref.info, Node: Volume Area and Length, Next: Mass and Weight, Prev: Printers Units, Up: Physical Constants Volume, Area and Length ======================= `GSL_CONST_MKSA_MICRON' The length of 1 micron. `GSL_CONST_MKSA_HECTARE' The area of 1 hectare. `GSL_CONST_MKSA_ACRE' The area of 1 acre. `GSL_CONST_MKSA_LITER' The volume of 1 liter. `GSL_CONST_MKSA_US_GALLON' The volume of 1 US gallon. `GSL_CONST_MKSA_CANADIAN_GALLON' The volume of 1 Canadian gallon. `GSL_CONST_MKSA_UK_GALLON' The volume of 1 UK gallon. `GSL_CONST_MKSA_QUART' The volume of 1 quart. `GSL_CONST_MKSA_PINT' The volume of 1 pint.  File: gsl-ref.info, Node: Mass and Weight, Next: Thermal Energy and Power, Prev: Volume Area and Length, Up: Physical Constants Mass and Weight =============== `GSL_CONST_MKSA_POUND_MASS' The mass of 1 pound. `GSL_CONST_MKSA_OUNCE_MASS' The mass of 1 ounce. `GSL_CONST_MKSA_TON' The mass of 1 ton. `GSL_CONST_MKSA_METRIC_TON' The mass of 1 metric ton (1000 kg). `GSL_CONST_MKSA_UK_TON' The mass of 1 UK ton. `GSL_CONST_MKSA_TROY_OUNCE' The mass of 1 troy ounce. `GSL_CONST_MKSA_CARAT' The mass of 1 carat. `GSL_CONST_MKSA_GRAM_FORCE' The force of 1 gram weight. `GSL_CONST_MKSA_POUND_FORCE' The force of 1 pound weight. `GSL_CONST_MKSA_KILOPOUND_FORCE' The force of 1 kilopound weight. `GSL_CONST_MKSA_POUNDAL' The force of 1 poundal.  File: gsl-ref.info, Node: Thermal Energy and Power, Next: Pressure, Prev: Mass and Weight, Up: Physical Constants Thermal Energy and Power ======================== `GSL_CONST_MKSA_CALORIE' The energy of 1 calorie. `GSL_CONST_MKSA_BTU' The energy of 1 British Thermal Unit, btu. `GSL_CONST_MKSA_THERM' The energy of 1 Therm. `GSL_CONST_MKSA_HORSEPOWER' The power of 1 horsepower.  File: gsl-ref.info, Node: Pressure, Next: Viscosity, Prev: Thermal Energy and Power, Up: Physical Constants Pressure ======== `GSL_CONST_MKSA_BAR' The pressure of 1 bar. `GSL_CONST_MKSA_STD_ATMOSPHERE' The pressure of 1 standard atmosphere. `GSL_CONST_MKSA_TORR' The pressure of 1 torr. `GSL_CONST_MKSA_METER_OF_MERCURY' The pressure of 1 meter of mercury. `GSL_CONST_MKSA_INCH_OF_MERCURY' The pressure of 1 inch of mercury. `GSL_CONST_MKSA_INCH_OF_WATER' The pressure of 1 inch of water. `GSL_CONST_MKSA_PSI' The pressure of 1 pound per square inch.  File: gsl-ref.info, Node: Viscosity, Next: Light and Illumination, Prev: Pressure, Up: Physical Constants Viscosity ========= `GSL_CONST_MKSA_POISE' The dynamic viscosity of 1 poise. `GSL_CONST_MKSA_STOKES' The kinematic viscosity of 1 stokes.  File: gsl-ref.info, Node: Light and Illumination, Next: Radioactivity, Prev: Viscosity, Up: Physical Constants Light and Illumination ====================== `GSL_CONST_MKSA_STILB' The luminance of 1 stilb. `GSL_CONST_MKSA_LUMEN' The luminous flux of 1 lumen. `GSL_CONST_MKSA_LUX' The illuminance of 1 lux. `GSL_CONST_MKSA_PHOT' The illuminance of 1 phot. `GSL_CONST_MKSA_FOOTCANDLE' The illuminance of 1 footcandle. `GSL_CONST_MKSA_LAMBERT' The luminance of 1 lambert. `GSL_CONST_MKSA_FOOTLAMBERT' The luminance of 1 footlambert.  File: gsl-ref.info, Node: Radioactivity, Next: Force and Energy, Prev: Light and Illumination, Up: Physical Constants Radioactivity ============= `GSL_CONST_MKSA_CURIE' The activity of 1 curie. `GSL_CONST_MKSA_ROENTGEN' The exposure of 1 roentgen. `GSL_CONST_MKSA_RAD' The absorbed dose of 1 rad.  File: gsl-ref.info, Node: Force and Energy, Next: Prefixes, Prev: Radioactivity, Up: Physical Constants Force and Energy ================ `GSL_CONST_MKSA_NEWTON' The SI unit of force, 1 Newton. `GSL_CONST_MKSA_DYNE' The force of 1 Dyne = 10^-5 Newton. `GSL_CONST_MKSA_JOULE' The SI unit of energy, 1 Joule. `GSL_CONST_MKSA_ERG' The energy 1 erg = 10^-7 Joule.  File: gsl-ref.info, Node: Prefixes, Next: Physical Constant Examples, Prev: Force and Energy, Up: Physical Constants Prefixes ======== These constants are dimensionless scaling factors. `GSL_CONST_NUM_YOTTA' 10^24 `GSL_CONST_NUM_ZETTA' 10^21 `GSL_CONST_NUM_EXA' 10^18 `GSL_CONST_NUM_PETA' 10^15 `GSL_CONST_NUM_TERA' 10^12 `GSL_CONST_NUM_GIGA' 10^9 `GSL_CONST_NUM_MEGA' 10^6 `GSL_CONST_NUM_KILO' 10^3 `GSL_CONST_NUM_MILLI' 10^-3 `GSL_CONST_NUM_MICRO' 10^-6 `GSL_CONST_NUM_NANO' 10^-9 `GSL_CONST_NUM_PICO' 10^-12 `GSL_CONST_NUM_FEMTO' 10^-15 `GSL_CONST_NUM_ATTO' 10^-18 `GSL_CONST_NUM_ZEPTO' 10^-21 `GSL_CONST_NUM_YOCTO' 10^-24  File: gsl-ref.info, Node: Physical Constant Examples, Next: Physical Constant References and Further Reading, Prev: Prefixes, Up: Physical Constants Examples ======== The following program demonstrates the use of the physical constants in a calculation. In this case, the goal is to calculate the range of light-travel times from Earth to Mars. The required data is the average distance of each planet from the Sun in astronomical units (the eccentricities and inclinations of the orbits will be neglected for the purposes of this calculation). The average radius of the orbit of Mars is 1.52 astronomical units, and for the orbit of Earth it is 1 astronomical unit (by definition). These values are combined with the MKSA values of the constants for the speed of light and the length of an astronomical unit to produce a result for the shortest and longest light-travel times in seconds. The figures are converted into minutes before being displayed. #include #include int main (void) { double c = GSL_CONST_MKSA_SPEED_OF_LIGHT; double au = GSL_CONST_MKSA_ASTRONOMICAL_UNIT; double minutes = GSL_CONST_MKSA_MINUTE; /* distance stored in meters */ double r_earth = 1.00 * au; double r_mars = 1.52 * au; double t_min, t_max; t_min = (r_mars - r_earth) / c; t_max = (r_mars + r_earth) / c; printf ("light travel time from Earth to Mars:\n"); printf ("minimum = %.1f minutes\n", t_min / minutes); printf ("maximum = %.1f minutes\n", t_max / minutes); return 0; } Here is the output from the program, light travel time from Earth to Mars: minimum = 4.3 minutes maximum = 21.0 minutes  File: gsl-ref.info, Node: Physical Constant References and Further Reading, Prev: Physical Constant Examples, Up: Physical Constants References and Further Reading ============================== The authoritative sources for physical constanst are the 2002 CODATA recommended values, published in the articles below. Further information on the values of physical constants is also available from the cited articles and the NIST website. Journal of Physical and Chemical Reference Data, 28(6), 1713-1852, 1999 Reviews of Modern Physics, 72(2), 351-495, 2000 `http://www.physics.nist.gov/cuu/Constants/index.html' `http://physics.nist.gov/Pubs/SP811/appenB9.html'  File: gsl-ref.info, Node: IEEE floating-point arithmetic, Next: Debugging Numerical Programs, Prev: Physical Constants, Up: Top IEEE floating-point arithmetic ****************************** This chapter describes functions for examining the representation of floating point numbers and controlling the floating point environment of your program. The functions described in this chapter are declared in the header file `gsl_ieee_utils.h'. * Menu: * Representation of floating point numbers:: * Setting up your IEEE environment:: * IEEE References and Further Reading::  File: gsl-ref.info, Node: Representation of floating point numbers, Next: Setting up your IEEE environment, Up: IEEE floating-point arithmetic Representation of floating point numbers ======================================== The IEEE Standard for Binary Floating-Point Arithmetic defines binary formats for single and double precision numbers. Each number is composed of three parts: a "sign bit" (s), an "exponent" (E) and a "fraction" (f). The numerical value of the combination (s,E,f) is given by the following formula, (-1)^s (1.fffff...) 2^E The sign bit is either zero or one. The exponent ranges from a minimum value E_min to a maximum value E_max depending on the precision. The exponent is converted to an unsigned number e, known as the "biased exponent", for storage by adding a "bias" parameter, e = E + bias. The sequence fffff... represents the digits of the binary fraction f. The binary digits are stored in "normalized form", by adjusting the exponent to give a leading digit of 1. Since the leading digit is always 1 for normalized numbers it is assumed implicitly and does not have to be stored. Numbers smaller than 2^(E_min) are be stored in "denormalized form" with a leading zero, (-1)^s (0.fffff...) 2^(E_min) This allows gradual underflow down to 2^(E_min - p) for p bits of precision. A zero is encoded with the special exponent of 2^(E_min - 1) and infinities with the exponent of 2^(E_max + 1). The format for single precision numbers uses 32 bits divided in the following way, seeeeeeeefffffffffffffffffffffff s = sign bit, 1 bit e = exponent, 8 bits (E_min=-126, E_max=127, bias=127) f = fraction, 23 bits The format for double precision numbers uses 64 bits divided in the following way, seeeeeeeeeeeffffffffffffffffffffffffffffffffffffffffffffffffffff s = sign bit, 1 bit e = exponent, 11 bits (E_min=-1022, E_max=1023, bias=1023) f = fraction, 52 bits It is often useful to be able to investigate the behavior of a calculation at the bit-level and the library provides functions for printing the IEEE representations in a human-readable form. - Function: void gsl_ieee_fprintf_float (FILE * STREAM, const float * X) - Function: void gsl_ieee_fprintf_double (FILE * STREAM, const double * X) These functions output a formatted version of the IEEE floating-point number pointed to by X to the stream STREAM. A pointer is used to pass the number indirectly, to avoid any undesired promotion from `float' to `double'. The output takes one of the following forms, `NaN' the Not-a-Number symbol `Inf, -Inf' positive or negative infinity `1.fffff...*2^E, -1.fffff...*2^E' a normalized floating point number `0.fffff...*2^E, -0.fffff...*2^E' a denormalized floating point number `0, -0' positive or negative zero The output can be used directly in GNU Emacs Calc mode by preceding it with `2#' to indicate binary. - Function: void gsl_ieee_printf_float (const float * X) - Function: void gsl_ieee_printf_double (const double * X) These functions output a formatted version of the IEEE floating-point number pointed to by X to the stream `stdout'. The following program demonstrates the use of the functions by printing the single and double precision representations of the fraction 1/3. For comparison the representation of the value promoted from single to double precision is also printed. #include #include int main (void) { float f = 1.0/3.0; double d = 1.0/3.0; double fd = f; /* promote from float to double */ printf (" f="); gsl_ieee_printf_float(&f); printf ("\n"); printf ("fd="); gsl_ieee_printf_double(&fd); printf ("\n"); printf (" d="); gsl_ieee_printf_double(&d); printf ("\n"); return 0; } The binary representation of 1/3 is 0.01010101... . The output below shows that the IEEE format normalizes this fraction to give a leading digit of 1, f= 1.01010101010101010101011*2^-2 fd= 1.0101010101010101010101100000000000000000000000000000*2^-2 d= 1.0101010101010101010101010101010101010101010101010101*2^-2 The output also shows that a single-precision number is promoted to double-precision by adding zeros in the binary representation.  File: gsl-ref.info, Node: Setting up your IEEE environment, Next: IEEE References and Further Reading, Prev: Representation of floating point numbers, Up: IEEE floating-point arithmetic Setting up your IEEE environment ================================ The IEEE standard defines several "modes" for controlling the behavior of floating point operations. These modes specify the important properties of computer arithmetic: the direction used for rounding (e.g. whether numbers should be rounded up, down or to the nearest number), the rounding precision and how the program should handle arithmetic exceptions, such as division by zero. Many of these features can now be controlled via standard functions such as `fpsetround', which should be used whenever they are available. Unfortunately in the past there has been no universal API for controlling their behavior--each system has had its own low-level way of accessing them. To help you write portable programs GSL allows you to specify modes in a platform-independent way using the environment variable `GSL_IEEE_MODE'. The library then takes care of all the necessary machine-specific initializations for you when you call the function `gsl_ieee_env_setup'. - Function: void gsl_ieee_env_setup () This function reads the environment variable `GSL_IEEE_MODE' and attempts to set up the corresponding specified IEEE modes. The environment variable should be a list of keywords, separated by commas, like this, `GSL_IEEE_MODE' = "KEYWORD,KEYWORD,..." where KEYWORD is one of the following mode-names, `single-precision' `double-precision' `extended-precision' `round-to-nearest' `round-down' `round-up' `round-to-zero' `mask-all' `mask-invalid' `mask-denormalized' `mask-division-by-zero' `mask-overflow' `mask-underflow' `trap-inexact' `trap-common' If `GSL_IEEE_MODE' is empty or undefined then the function returns immediately and no attempt is made to change the system's IEEE mode. When the modes from `GSL_IEEE_MODE' are turned on the function prints a short message showing the new settings to remind you that the results of the program will be affected. If the requested modes are not supported by the platform being used then the function calls the error handler and returns an error code of `GSL_EUNSUP'. When options are specified using this method, the resulting mode is based on a default setting of the highest available precision (double precision or extended precision, depending on the platform) in round-to-nearest mode, with all exceptions enabled apart from the INEXACT exception. The INEXACT exception is generated whenever rounding occurs, so it must generally be disabled in typical scientific calculations. All other floating-point exceptions are enabled by default, including underflows and the use of denormalized numbers, for safety. They can be disabled with the individual `mask-' settings or together using `mask-all'. The following adjusted combination of modes is convenient for many purposes, GSL_IEEE_MODE="double-precision,"\ "mask-underflow,"\ "mask-denormalized" This choice ignores any errors relating to small numbers (either denormalized, or underflowing to zero) but traps overflows, division by zero and invalid operations. To demonstrate the effects of different rounding modes consider the following program which computes e, the base of natural logarithms, by summing a rapidly-decreasing series, e = 1 + 1/2! + 1/3! + 1/4! + ... = 2.71828182846... #include #include #include int main (void) { double x = 1, oldsum = 0, sum = 0; int i = 0; gsl_ieee_env_setup (); /* read GSL_IEEE_MODE */ do { i++; oldsum = sum; sum += x; x = x / i; printf ("i=%2d sum=%.18f error=%g\n", i, sum, sum - M_E); if (i > 30) break; } while (sum != oldsum); return 0; } Here are the results of running the program in `round-to-nearest' mode. This is the IEEE default so it isn't really necessary to specify it here, $ GSL_IEEE_MODE="round-to-nearest" ./a.out i= 1 sum=1.000000000000000000 error=-1.71828 i= 2 sum=2.000000000000000000 error=-0.718282 .... i=18 sum=2.718281828459045535 error=4.44089e-16 i=19 sum=2.718281828459045535 error=4.44089e-16 After nineteen terms the sum converges to within 4 \times 10^-16 of the correct value. If we now change the rounding mode to `round-down' the final result is less accurate, $ GSL_IEEE_MODE="round-down" ./a.out i= 1 sum=1.000000000000000000 error=-1.71828 .... i=19 sum=2.718281828459041094 error=-3.9968e-15 The result is about 4 \times 10^-15 below the correct value, an order of magnitude worse than the result obtained in the `round-to-nearest' mode. If we change to rounding mode to `round-up' then the series no longer converges (the reason is that when we add each term to the sum the final result is always rounded up. This is guaranteed to increase the sum by at least one tick on each iteration). To avoid this problem we would need to use a safer converge criterion, such as `while (fabs(sum - oldsum) > epsilon)', with a suitably chosen value of epsilon. Finally we can see the effect of computing the sum using single-precision rounding, in the default `round-to-nearest' mode. In this case the program thinks it is still using double precision numbers but the CPU rounds the result of each floating point operation to single-precision accuracy. This simulates the effect of writing the program using single-precision `float' variables instead of `double' variables. The iteration stops after about half the number of iterations and the final result is much less accurate, $ GSL_IEEE_MODE="single-precision" ./a.out .... i=12 sum=2.718281984329223633 error=1.5587e-07 with an error of O(10^-7), which corresponds to single precision accuracy (about 1 part in 10^7). Continuing the iterations further does not decrease the error because all the subsequent results are rounded to the same value.  File: gsl-ref.info, Node: IEEE References and Further Reading, Prev: Setting up your IEEE environment, Up: IEEE floating-point arithmetic References and Further Reading ============================== The reference for the IEEE standard is, ANSI/IEEE Std 754-1985, IEEE Standard for Binary Floating-Point Arithmetic. A more pedagogical introduction to the standard can be found in the following paper, David Goldberg: What Every Computer Scientist Should Know About Floating-Point Arithmetic. `ACM Computing Surveys', Vol. 23, No. 1 (March 1991), pages 5-48. Corrigendum: `ACM Computing Surveys', Vol. 23, No. 3 (September 1991), page 413. and see also the sections by B. A. Wichmann and Charles B. Dunham in Surveyor's Forum: "What Every Computer Scientist Should Know About Floating-Point Arithmetic". `ACM Computing Surveys', Vol. 24, No. 3 (September 1992), page 319. A detailed textbook on IEEE arithmetic and its practical use is available from SIAM Press, Michael L. Overton, `Numerical Computing with IEEE Floating Point Arithmetic', SIAM Press, ISBN 0898715717.  File: gsl-ref.info, Node: Debugging Numerical Programs, Next: Contributors to GSL, Prev: IEEE floating-point arithmetic, Up: Top Debugging Numerical Programs **************************** This chapter describes some tips and tricks for debugging numerical programs which use GSL. * Menu: * Using gdb:: * Examining floating point registers:: * Handling floating point exceptions:: * GCC warning options for numerical programs:: * Debugging References::  File: gsl-ref.info, Node: Using gdb, Next: Examining floating point registers, Up: Debugging Numerical Programs Using gdb ========= Any errors reported by the library are passed to the function `gsl_error'. By running your programs under gdb and setting a breakpoint in this function you can automatically catch any library errors. You can add a breakpoint for every session by putting break gsl_error into your `.gdbinit' file in the directory where your program is started. If the breakpoint catches an error then you can use a backtrace (`bt') to see the call-tree, and the arguments which possibly caused the error. By moving up into the calling function you can investigate the values of variables at that point. Here is an example from the program `fft/test_trap', which contains the following line, status = gsl_fft_complex_wavetable_alloc (0, &complex_wavetable); The function `gsl_fft_complex_wavetable_alloc' takes the length of an FFT as its first argument. When this line is executed an error will be generated because the length of an FFT is not allowed to be zero. To debug this problem we start `gdb', using the file `.gdbinit' to define a breakpoint in `gsl_error', $ gdb test_trap GDB is free software and you are welcome to distribute copies of it under certain conditions; type "show copying" to see the conditions. There is absolutely no warranty for GDB; type "show warranty" for details. GDB 4.16 (i586-debian-linux), Copyright 1996 Free Software Foundation, Inc. Breakpoint 1 at 0x8050b1e: file error.c, line 14. When we run the program this breakpoint catches the error and shows the reason for it. (gdb) run Starting program: test_trap Breakpoint 1, gsl_error (reason=0x8052b0d "length n must be positive integer", file=0x8052b04 "c_init.c", line=108, gsl_errno=1) at error.c:14 14 if (gsl_error_handler) The first argument of `gsl_error' is always a string describing the error. Now we can look at the backtrace to see what caused the problem, (gdb) bt #0 gsl_error (reason=0x8052b0d "length n must be positive integer", file=0x8052b04 "c_init.c", line=108, gsl_errno=1) at error.c:14 #1 0x8049376 in gsl_fft_complex_wavetable_alloc (n=0, wavetable=0xbffff778) at c_init.c:108 #2 0x8048a00 in main (argc=1, argv=0xbffff9bc) at test_trap.c:94 #3 0x80488be in ___crt_dummy__ () We can see that the error was generated in the function `gsl_fft_complex_wavetable_alloc' when it was called with an argument of N=0. The original call came from line 94 in the file `test_trap.c'. By moving up to the level of the original call we can find the line that caused the error, (gdb) up #1 0x8049376 in gsl_fft_complex_wavetable_alloc (n=0, wavetable=0xbffff778) at c_init.c:108 108 GSL_ERROR ("length n must be positive integer", GSL_EDOM); (gdb) up #2 0x8048a00 in main (argc=1, argv=0xbffff9bc) at test_trap.c:94 94 status = gsl_fft_complex_wavetable_alloc (0, &complex_wavetable); Thus we have found the line that caused the problem. From this point we could also print out the values of other variables such as `complex_wavetable'.  File: gsl-ref.info, Node: Examining floating point registers, Next: Handling floating point exceptions, Prev: Using gdb, Up: Debugging Numerical Programs Examining floating point registers ================================== The contents of floating point registers can be examined using the command `info float' (on supported platforms). (gdb) info float st0: 0xc4018b895aa17a945000 Valid Normal -7.838871e+308 st1: 0x3ff9ea3f50e4d7275000 Valid Normal 0.0285946 st2: 0x3fe790c64ce27dad4800 Valid Normal 6.7415931e-08 st3: 0x3ffaa3ef0df6607d7800 Spec Normal 0.0400229 st4: 0x3c028000000000000000 Valid Normal 4.4501477e-308 st5: 0x3ffef5412c22219d9000 Zero Normal 0.9580257 st6: 0x3fff8000000000000000 Valid Normal 1 st7: 0xc4028b65a1f6d243c800 Valid Normal -1.566206e+309 fctrl: 0x0272 53 bit; NEAR; mask DENOR UNDER LOS; fstat: 0xb9ba flags 0001; top 7; excep DENOR OVERF UNDER LOS ftag: 0x3fff fip: 0x08048b5c fcs: 0x051a0023 fopoff: 0x08086820 fopsel: 0x002b Individual registers can be examined using the variables $REG, where REG is the register name. (gdb) p $st1 $1 = 0.02859464454261210347719  File: gsl-ref.info, Node: Handling floating point exceptions, Next: GCC warning options for numerical programs, Prev: Examining floating point registers, Up: Debugging Numerical Programs Handling floating point exceptions ================================== It is possible to stop the program whenever a `SIGFPE' floating point exception occurs. This can be useful for finding the cause of an unexpected infinity or `NaN'. The current handler settings can be shown with the command `info signal SIGFPE'. (gdb) info signal SIGFPE Signal Stop Print Pass to program Description SIGFPE Yes Yes Yes Arithmetic exception Unless the program uses a signal handler the default setting should be changed so that SIGFPE is not passed to the program, as this would cause it to exit. The command `handle SIGFPE stop nopass' prevents this. (gdb) handle SIGFPE stop nopass Signal Stop Print Pass to program Description SIGFPE Yes Yes No Arithmetic exception Depending on the platform it may be necessary to instruct the kernel to generate signals for floating point exceptions. For programs using GSL this can be achieved using the `GSL_IEEE_MODE' environment variable in conjunction with the function `gsl_ieee_env_setup()' as described in *note IEEE floating-point arithmetic::. (gdb) set env GSL_IEEE_MODE=double-precision  File: gsl-ref.info, Node: GCC warning options for numerical programs, Next: Debugging References, Prev: Handling floating point exceptions, Up: Debugging Numerical Programs GCC warning options for numerical programs ========================================== Writing reliable numerical programs in C requires great care. The following GCC warning options are recommended when compiling numerical programs: gcc -ansi -pedantic -Werror -Wall -W -Wmissing-prototypes -Wstrict-prototypes -Wtraditional -Wconversion -Wshadow -Wpointer-arith -Wcast-qual -Wcast-align -Wwrite-strings -Wnested-externs -fshort-enums -fno-common -Dinline= -g -O4 For details of each option consult the manual `Using and Porting GCC'. The following table gives a brief explanation of what types of errors these options catch. `-ansi -pedantic' Use ANSI C, and reject any non-ANSI extensions. These flags help in writing portable programs that will compile on other systems. `-Werror' Consider warnings to be errors, so that compilation stops. This prevents warnings from scrolling off the top of the screen and being lost. You won't be able to compile the program until it is completely warning-free. `-Wall' This turns on a set of warnings for common programming problems. You need `-Wall', but it is not enough on its own. `-O2' Turn on optimization. The warnings for uninitialized variables in `-Wall' rely on the optimizer to analyze the code. If there is no optimization then these warnings aren't generated. `-W' This turns on some extra warnings not included in `-Wall', such as missing return values and comparisons between signed and unsigned integers. `-Wmissing-prototypes -Wstrict-prototypes' Warn if there are any missing or inconsistent prototypes. Without prototypes it is harder to detect problems with incorrect arguments. `-Wtraditional' This warns about certain constructs that behave differently in traditional and ANSI C. Whether the traditional or ANSI interpretation is used might be unpredictable on other compilers. `-Wconversion' The main use of this option is to warn about conversions from signed to unsigned integers. For example, `unsigned int x = -1'. If you need to perform such a conversion you can use an explicit cast. `-Wshadow' This warns whenever a local variable shadows another local variable. If two variables have the same name then it is a potential source of confusion. `-Wpointer-arith -Wcast-qual -Wcast-align' These options warn if you try to do pointer arithmetic for types which don't have a size, such as `void', if you remove a `const' cast from a pointer, or if you cast a pointer to a type which has a different size, causing an invalid alignment. `-Wwrite-strings' This option gives string constants a `const' qualifier so that it will be a compile-time error to attempt to overwrite them. `-fshort-enums' This option makes the type of `enum' as short as possible. Normally this makes an `enum' different from an `int'. Consequently any attempts to assign a pointer-to-int to a pointer-to-enum will generate a cast-alignment warning. `-fno-common' This option prevents global variables being simultaneously defined in different object files (you get an error at link time). Such a variable should be defined in one file and referred to in other files with an `extern' declaration. `-Wnested-externs' This warns if an `extern' declaration is encountered within a function. `-Dinline=' The `inline' keyword is not part of ANSI C. Thus if you want to use `-ansi' with a program which uses inline functions you can use this preprocessor definition to remove the `inline' keywords. `-g' It always makes sense to put debugging symbols in the executable so that you can debug it using `gdb'. The only effect of debugging symbols is to increase the size of the file, and you can use the `strip' command to remove them later if necessary.  File: gsl-ref.info, Node: Debugging References, Prev: GCC warning options for numerical programs, Up: Debugging Numerical Programs References and Further Reading ============================== The following books are essential reading for anyone writing and debugging numerical programs with GCC and GDB. R.M. Stallman, `Using and Porting GNU CC', Free Software Foundation, ISBN 1882114388 R.M. Stallman, R.H. Pesch, `Debugging with GDB: The GNU Source-Level Debugger', Free Software Foundation, ISBN 1882114779 For a tutorial introduction to the GNU C Compiler and related programs, see B.J. Gough, `An Introduction to GCC', Network Theory Ltd, ISBN 0954161793  File: gsl-ref.info, Node: Contributors to GSL, Next: Autoconf Macros, Prev: Debugging Numerical Programs, Up: Top Contributors to GSL ******************* (See the AUTHORS file in the distribution for up-to-date information.) *Mark Galassi* Conceived GSL (with James Theiler) and wrote the design document. Wrote the simulated annealing package and the relevant chapter in the manual. *James Theiler* Conceived GSL (with Mark Galassi). Wrote the random number generators and the relevant chapter in this manual. *Jim Davies* Wrote the statistical routines and the relevant chapter in this manual. *Brian Gough* FFTs, numerical integration, random number generators and distributions, root finding, minimization and fitting, polynomial solvers, complex numbers, physical constants, permutations, vector and matrix functions, histograms, statistics, ieee-utils, revised CBLAS Level 2 & 3, matrix decompositions, eigensystems, cumulative distribution functions, testing, documentation and releases. *Reid Priedhorsky* Wrote and documented the initial version of the root finding routines while at Los Alamos National Laboratory, Mathematical Modeling and Analysis Group. *Gerard Jungman* Special Functions, Series acceleration, ODEs, BLAS, Linear Algebra, Eigensystems, Hankel Transforms. *Mike Booth* Wrote the Monte Carlo library. *Jorma Olavi Ta"htinen* Wrote the initial complex arithmetic functions. *Thomas Walter* Wrote the initial heapsort routines and cholesky decomposition. *Fabrice Rossi* Multidimensional minimization. *Carlo Perassi* Implementation of the random number generators in Knuth's `Seminumerical Algorithms', 3rd Ed. *Szymon Jaroszewicz* Wrote the routines for generating combinations. *Nicolas Darnis* Wrote the initial routines for canonical permutations. *Jason H. Stover* Wrote the major cumulative distribution functions. *Ivo Alxneit* Wrote the routines for wavelet transforms. *Tuomo Keskitalo* Improved the implementation of the ODE solvers. Thanks to Nigel Lowry for help in proofreading the manual.  File: gsl-ref.info, Node: Autoconf Macros, Next: GSL CBLAS Library, Prev: Contributors to GSL, Up: Top Autoconf Macros *************** For applications using `autoconf' the standard macro `AC_CHECK_LIB' can be used to link with GSL automatically from a `configure' script. The library itself depends on the presence of a CBLAS and math library as well, so these must also be located before linking with the main `libgsl' file. The following commands should be placed in the `configure.ac' file to perform these tests, AC_CHECK_LIB(m,main) AC_CHECK_LIB(gslcblas,main) AC_CHECK_LIB(gsl,main) It is important to check for `libm' and `libgslcblas' before `libgsl', otherwise the tests will fail. Assuming the libraries are found the output during the configure stage looks like this, checking for main in -lm... yes checking for main in -lgslcblas... yes checking for main in -lgsl... yes If the library is found then the tests will define the macros `HAVE_LIBGSL', `HAVE_LIBGSLCBLAS', `HAVE_LIBM' and add the options `-lgsl -lgslcblas -lm' to the variable `LIBS'. The tests above will find any version of the library. They are suitable for general use, where the versions of the functions are not important. An alternative macro is available in the file `gsl.m4' to test for a specific version of the library. To use this macro simply add the following line to your `configure.in' file instead of the tests above: AM_PATH_GSL(GSL_VERSION, [action-if-found], [action-if-not-found]) The argument `GSL_VERSION' should be the two or three digit MAJOR.MINOR or MAJOR.MINOR.MICRO version number of the release you require. A suitable choice for `action-if-not-found' is, AC_MSG_ERROR(could not find required version of GSL) Then you can add the variables `GSL_LIBS' and `GSL_CFLAGS' to your Makefile.am files to obtain the correct compiler flags. `GSL_LIBS' is equal to the output of the `gsl-config --libs' command and `GSL_CFLAGS' is equal to `gsl-config --cflags' command. For example, libfoo_la_LDFLAGS = -lfoo $(GSL_LIBS) -lgslcblas Note that the macro `AM_PATH_GSL' needs to use the C compiler so it should appear in the `configure.in' file before the macro `AC_LANG_CPLUSPLUS' for programs that use C++. To test for `inline' the following test should be placed in your `configure.in' file, AC_C_INLINE if test "$ac_cv_c_inline" != no ; then AC_DEFINE(HAVE_INLINE,1) AC_SUBST(HAVE_INLINE) fi and the macro will then be defined in the compilation flags or by including the file `config.h' before any library headers. The following autoconf test will check for `extern inline', dnl Check for "extern inline", using a modified version dnl of the test for AC_C_INLINE from acspecific.mt dnl AC_CACHE_CHECK([for extern inline], ac_cv_c_extern_inline, [ac_cv_c_extern_inline=no AC_TRY_COMPILE([extern $ac_cv_c_inline double foo(double x); extern $ac_cv_c_inline double foo(double x) { return x+1.0; }; double foo (double x) { return x + 1.0; };], [ foo(1.0) ], [ac_cv_c_extern_inline="yes"]) ]) if test "$ac_cv_c_extern_inline" != no ; then AC_DEFINE(HAVE_INLINE,1) AC_SUBST(HAVE_INLINE) fi The substitution of portability functions can be made automatically if you use `autoconf'. For example, to test whether the BSD function `hypot' is available you can include the following line in the configure file `configure.in' for your application, AC_CHECK_FUNCS(hypot) and place the following macro definitions in the file `config.h.in', /* Substitute gsl_hypot for missing system hypot */ #ifndef HAVE_HYPOT #define hypot gsl_hypot #endif The application source files can then use the include command `#include ' to substitute `gsl_hypot' for each occurrence of `hypot' when `hypot' is not available.  File: gsl-ref.info, Node: GSL CBLAS Library, Next: Free Software Needs Free Documentation, Prev: Autoconf Macros, Up: Top GSL CBLAS Library ***************** The prototypes for the low-level CBLAS functions are declared in the file `gsl_cblas.h'. For the definition of the functions consult the documentation available from Netlib (*note BLAS References and Further Reading::). * Menu: * Level 1 CBLAS Functions:: * Level 2 CBLAS Functions:: * Level 3 CBLAS Functions:: * GSL CBLAS Examples::  File: gsl-ref.info, Node: Level 1 CBLAS Functions, Next: Level 2 CBLAS Functions, Up: GSL CBLAS Library Level 1 ======= - Function: float cblas_sdsdot (const int N, const float ALPHA, const float * X, const int INCX, const float * Y, const int INCY) - Function: double cblas_dsdot (const int N, const float * X, const int INCX, const float * Y, const int INCY) - Function: float cblas_sdot (const int N, const float * X, const int INCX, const float * Y, const int INCY) - Function: double cblas_ddot (const int N, const double * X, const int INCX, const double * Y, const int INCY) - Function: void cblas_cdotu_sub (const int N, const void * X, const int INCX, const void * Y, const int INCY, void * DOTU) - Function: void cblas_cdotc_sub (const int N, const void * X, const int INCX, const void * Y, const int INCY, void * DOTC) - Function: void cblas_zdotu_sub (const int N, const void * X, const int INCX, const void * Y, const int INCY, void * DOTU) - Function: void cblas_zdotc_sub (const int N, const void * X, const int INCX, const void * Y, const int INCY, void * DOTC) - Function: float cblas_snrm2 (const int N, const float * X, const int INCX) - Function: float cblas_sasum (const int N, const float * X, const int INCX) - Function: double cblas_dnrm2 (const int N, const double * X, const int INCX) - Function: double cblas_dasum (const int N, const double * X, const int INCX) - Function: float cblas_scnrm2 (const int N, const void * X, const int INCX) - Function: float cblas_scasum (const int N, const void * X, const int INCX) - Function: double cblas_dznrm2 (const int N, const void * X, const int INCX) - Function: double cblas_dzasum (const int N, const void * X, const int INCX) - Function: CBLAS_INDEX cblas_isamax (const int N, const float * X, const int INCX) - Function: CBLAS_INDEX cblas_idamax (const int N, const double * X, const int INCX) - Function: CBLAS_INDEX cblas_icamax (const int N, const void * X, const int INCX) - Function: CBLAS_INDEX cblas_izamax (const int N, const void * X, const int INCX) - Function: void cblas_sswap (const int N, float * X, const int INCX, float * Y, const int INCY) - Function: void cblas_scopy (const int N, const float * X, const int INCX, float * Y, const int INCY) - Function: void cblas_saxpy (const int N, const float ALPHA, const float * X, const int INCX, float * Y, const int INCY) - Function: void cblas_dswap (const int N, double * X, const int INCX, double * Y, const int INCY) - Function: void cblas_dcopy (const int N, const double * X, const int INCX, double * Y, const int INCY) - Function: void cblas_daxpy (const int N, const double ALPHA, const double * X, const int INCX, double * Y, const int INCY) - Function: void cblas_cswap (const int N, void * X, const int INCX, void * Y, const int INCY) - Function: void cblas_ccopy (const int N, const void * X, const int INCX, void * Y, const int INCY) - Function: void cblas_caxpy (const int N, const void * ALPHA, const void * X, const int INCX, void * Y, const int INCY) - Function: void cblas_zswap (const int N, void * X, const int INCX, void * Y, const int INCY) - Function: void cblas_zcopy (const int N, const void * X, const int INCX, void * Y, const int INCY) - Function: void cblas_zaxpy (const int N, const void * ALPHA, const void * X, const int INCX, void * Y, const int INCY) - Function: void cblas_srotg (float * A, float * B, float * C, float * S) - Function: void cblas_srotmg (float * D1, float * D2, float * B1, const float B2, float * P) - Function: void cblas_srot (const int N, float * X, const int INCX, float * Y, const int INCY, const float C, const float S) - Function: void cblas_srotm (const int N, float * X, const int INCX, float * Y, const int INCY, const float * P) - Function: void cblas_drotg (double * A, double * B, double * C, double * S) - Function: void cblas_drotmg (double * D1, double * D2, double * B1, const double B2, double * P) - Function: void cblas_drot (const int N, double * X, const int INCX, double * Y, const int INCY, const double C, const double S) - Function: void cblas_drotm (const int N, double * X, const int INCX, double * Y, const int INCY, const double * P) - Function: void cblas_sscal (const int N, const float ALPHA, float * X, const int INCX) - Function: void cblas_dscal (const int N, const double ALPHA, double * X, const int INCX) - Function: void cblas_cscal (const int N, const void * ALPHA, void * X, const int INCX) - Function: void cblas_zscal (const int N, const void * ALPHA, void * X, const int INCX) - Function: void cblas_csscal (const int N, const float ALPHA, void * X, const int INCX) - Function: void cblas_zdscal (const int N, const double ALPHA, void * X, const int INCX)  File: gsl-ref.info, Node: Level 2 CBLAS Functions, Next: Level 3 CBLAS Functions, Prev: Level 1 CBLAS Functions, Up: GSL CBLAS Library Level 2 ======= - Function: void cblas_sgemv (const enum CBLAS_ORDER ORDER, const enum CBLAS_TRANSPOSE TRANSA, const int M, const int N, const float ALPHA, const float * A, const int LDA, const float * X, const int INCX, const float BETA, float * Y, const int INCY) - Function: void cblas_sgbmv (const enum CBLAS_ORDER ORDER, const enum CBLAS_TRANSPOSE TRANSA, const int M, const int N, const int KL, const int KU, const float ALPHA, const float * A, const int LDA, const float * X, const int INCX, const float BETA, float * Y, const int INCY) - Function: void cblas_strmv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int N, const float * A, const int LDA, float * X, const int INCX) - Function: void cblas_stbmv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int N, const int K, const float * A, const int LDA, float * X, const int INCX) - Function: void cblas_stpmv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int N, const float * AP, float * X, const int INCX) - Function: void cblas_strsv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int N, const float * A, const int LDA, float * X, const int INCX) - Function: void cblas_stbsv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int N, const int K, const float * A, const int LDA, float * X, const int INCX) - Function: void cblas_stpsv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int N, const float * AP, float * X, const int INCX) - Function: void cblas_dgemv (const enum CBLAS_ORDER ORDER, const enum CBLAS_TRANSPOSE TRANSA, const int M, const int N, const double ALPHA, const double * A, const int LDA, const double * X, const int INCX, const double BETA, double * Y, const int INCY) - Function: void cblas_dgbmv (const enum CBLAS_ORDER ORDER, const enum CBLAS_TRANSPOSE TRANSA, const int M, const int N, const int KL, const int KU, const double ALPHA, const double * A, const int LDA, const double * X, const int INCX, const double BETA, double * Y, const int INCY) - Function: void cblas_dtrmv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int N, const double * A, const int LDA, double * X, const int INCX) - Function: void cblas_dtbmv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int N, const int K, const double * A, const int LDA, double * X, const int INCX) - Function: void cblas_dtpmv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int N, const double * AP, double * X, const int INCX) - Function: void cblas_dtrsv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int N, const double * A, const int LDA, double * X, const int INCX) - Function: void cblas_dtbsv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int N, const int K, const double * A, const int LDA, double * X, const int INCX) - Function: void cblas_dtpsv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int N, const double * AP, double * X, const int INCX) - Function: void cblas_cgemv (const enum CBLAS_ORDER ORDER, const enum CBLAS_TRANSPOSE TRANSA, const int M, const int N, const void * ALPHA, const void * A, const int LDA, const void * X, const int INCX, const void * BETA, void * Y, const int INCY) - Function: void cblas_cgbmv (const enum CBLAS_ORDER ORDER, const enum CBLAS_TRANSPOSE TRANSA, const int M, const int N, const int KL, const int KU, const void * ALPHA, const void * A, const int LDA, const void * X, const int INCX, const void * BETA, void * Y, const int INCY) - Function: void cblas_ctrmv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int N, const void * A, const int LDA, void * X, const int INCX) - Function: void cblas_ctbmv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int N, const int K, const void * A, const int LDA, void * X, const int INCX) - Function: void cblas_ctpmv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int N, const void * AP, void * X, const int INCX) - Function: void cblas_ctrsv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int N, const void * A, const int LDA, void * X, const int INCX) - Function: void cblas_ctbsv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int N, const int K, const void * A, const int LDA, void * X, const int INCX) - Function: void cblas_ctpsv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int N, const void * AP, void * X, const int INCX) - Function: void cblas_zgemv (const enum CBLAS_ORDER ORDER, const enum CBLAS_TRANSPOSE TRANSA, const int M, const int N, const void * ALPHA, const void * A, const int LDA, const void * X, const int INCX, const void * BETA, void * Y, const int INCY) - Function: void cblas_zgbmv (const enum CBLAS_ORDER ORDER, const enum CBLAS_TRANSPOSE TRANSA, const int M, const int N, const int KL, const int KU, const void * ALPHA, const void * A, const int LDA, const void * X, const int INCX, const void * BETA, void * Y, const int INCY) - Function: void cblas_ztrmv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int N, const void * A, const int LDA, void * X, const int INCX) - Function: void cblas_ztbmv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int N, const int K, const void * A, const int LDA, void * X, const int INCX) - Function: void cblas_ztpmv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int N, const void * AP, void * X, const int INCX) - Function: void cblas_ztrsv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int N, const void * A, const int LDA, void * X, const int INCX) - Function: void cblas_ztbsv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int N, const int K, const void * A, const int LDA, void * X, const int INCX) - Function: void cblas_ztpsv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int N, const void * AP, void * X, const int INCX) - Function: void cblas_ssymv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const int N, const float ALPHA, const float * A, const int LDA, const float * X, const int INCX, const float BETA, float * Y, const int INCY) - Function: void cblas_ssbmv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const int N, const int K, const float ALPHA, const float * A, const int LDA, const float * X, const int INCX, const float BETA, float * Y, const int INCY) - Function: void cblas_sspmv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const int N, const float ALPHA, const float * AP, const float * X, const int INCX, const float BETA, float * Y, const int INCY) - Function: void cblas_sger (const enum CBLAS_ORDER ORDER, const int M, const int N, const float ALPHA, const float * X, const int INCX, const float * Y, const int INCY, float * A, const int LDA) - Function: void cblas_ssyr (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const int N, const float ALPHA, const float * X, const int INCX, float * A, const int LDA) - Function: void cblas_sspr (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const int N, const float ALPHA, const float * X, const int INCX, float * AP) - Function: void cblas_ssyr2 (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const int N, const float ALPHA, const float * X, const int INCX, const float * Y, const int INCY, float * A, const int LDA) - Function: void cblas_sspr2 (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const int N, const float ALPHA, const float * X, const int INCX, const float * Y, const int INCY, float * A) - Function: void cblas_dsymv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const int N, const double ALPHA, const double * A, const int LDA, const double * X, const int INCX, const double BETA, double * Y, const int INCY) - Function: void cblas_dsbmv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const int N, const int K, const double ALPHA, const double * A, const int LDA, const double * X, const int INCX, const double BETA, double * Y, const int INCY) - Function: void cblas_dspmv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const int N, const double ALPHA, const double * AP, const double * X, const int INCX, const double BETA, double * Y, const int INCY) - Function: void cblas_dger (const enum CBLAS_ORDER ORDER, const int M, const int N, const double ALPHA, const double * X, const int INCX, const double * Y, const int INCY, double * A, const int LDA) - Function: void cblas_dsyr (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const int N, const double ALPHA, const double * X, const int INCX, double * A, const int LDA) - Function: void cblas_dspr (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const int N, const double ALPHA, const double * X, const int INCX, double * AP) - Function: void cblas_dsyr2 (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const int N, const double ALPHA, const double * X, const int INCX, const double * Y, const int INCY, double * A, const int LDA) - Function: void cblas_dspr2 (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const int N, const double ALPHA, const double * X, const int INCX, const double * Y, const int INCY, double * A) - Function: void cblas_chemv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const int N, const void * ALPHA, const void * A, const int LDA, const void * X, const int INCX, const void * BETA, void * Y, const int INCY) - Function: void cblas_chbmv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const int N, const int K, const void * ALPHA, const void * A, const int LDA, const void * X, const int INCX, const void * BETA, void * Y, const int INCY) - Function: void cblas_chpmv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const int N, const void * ALPHA, const void * AP, const void * X, const int INCX, const void * BETA, void * Y, const int INCY) - Function: void cblas_cgeru (const enum CBLAS_ORDER ORDER, const int M, const int N, const void * ALPHA, const void * X, const int INCX, const void * Y, const int INCY, void * A, const int LDA) - Function: void cblas_cgerc (const enum CBLAS_ORDER ORDER, const int M, const int N, const void * ALPHA, const void * X, const int INCX, const void * Y, const int INCY, void * A, const int LDA) - Function: void cblas_cher (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const int N, const float ALPHA, const void * X, const int INCX, void * A, const int LDA) - Function: void cblas_chpr (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const int N, const float ALPHA, const void * X, const int INCX, void * A) - Function: void cblas_cher2 (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const int N, const void * ALPHA, const void * X, const int INCX, const void * Y, const int INCY, void * A, const int LDA) - Function: void cblas_chpr2 (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const int N, const void * ALPHA, const void * X, const int INCX, const void * Y, const int INCY, void * AP) - Function: void cblas_zhemv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const int N, const void * ALPHA, const void * A, const int LDA, const void * X, const int INCX, const void * BETA, void * Y, const int INCY) - Function: void cblas_zhbmv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const int N, const int K, const void * ALPHA, const void * A, const int LDA, const void * X, const int INCX, const void * BETA, void * Y, const int INCY) - Function: void cblas_zhpmv (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const int N, const void * ALPHA, const void * AP, const void * X, const int INCX, const void * BETA, void * Y, const int INCY) - Function: void cblas_zgeru (const enum CBLAS_ORDER ORDER, const int M, const int N, const void * ALPHA, const void * X, const int INCX, const void * Y, const int INCY, void * A, const int LDA) - Function: void cblas_zgerc (const enum CBLAS_ORDER ORDER, const int M, const int N, const void * ALPHA, const void * X, const int INCX, const void * Y, const int INCY, void * A, const int LDA) - Function: void cblas_zher (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const int N, const double ALPHA, const void * X, const int INCX, void * A, const int LDA) - Function: void cblas_zhpr (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const int N, const double ALPHA, const void * X, const int INCX, void * A) - Function: void cblas_zher2 (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const int N, const void * ALPHA, const void * X, const int INCX, const void * Y, const int INCY, void * A, const int LDA) - Function: void cblas_zhpr2 (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const int N, const void * ALPHA, const void * X, const int INCX, const void * Y, const int INCY, void * AP)  File: gsl-ref.info, Node: Level 3 CBLAS Functions, Next: GSL CBLAS Examples, Prev: Level 2 CBLAS Functions, Up: GSL CBLAS Library Level 3 ======= - Function: void cblas_sgemm (const enum CBLAS_ORDER ORDER, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_TRANSPOSE TRANSB, const int M, const int N, const int K, const float ALPHA, const float * A, const int LDA, const float * B, const int LDB, const float BETA, float * C, const int LDC) - Function: void cblas_ssymm (const enum CBLAS_ORDER ORDER, const enum CBLAS_SIDE SIDE, const enum CBLAS_UPLO UPLO, const int M, const int N, const float ALPHA, const float * A, const int LDA, const float * B, const int LDB, const float BETA, float * C, const int LDC) - Function: void cblas_ssyrk (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANS, const int N, const int K, const float ALPHA, const float * A, const int LDA, const float BETA, float * C, const int LDC) - Function: void cblas_ssyr2k (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANS, const int N, const int K, const float ALPHA, const float * A, const int LDA, const float * B, const int LDB, const float BETA, float * C, const int LDC) - Function: void cblas_strmm (const enum CBLAS_ORDER ORDER, const enum CBLAS_SIDE SIDE, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int M, const int N, const float ALPHA, const float * A, const int LDA, float * B, const int LDB) - Function: void cblas_strsm (const enum CBLAS_ORDER ORDER, const enum CBLAS_SIDE SIDE, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int M, const int N, const float ALPHA, const float * A, const int LDA, float * B, const int LDB) - Function: void cblas_dgemm (const enum CBLAS_ORDER ORDER, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_TRANSPOSE TRANSB, const int M, const int N, const int K, const double ALPHA, const double * A, const int LDA, const double * B, const int LDB, const double BETA, double * C, const int LDC) - Function: void cblas_dsymm (const enum CBLAS_ORDER ORDER, const enum CBLAS_SIDE SIDE, const enum CBLAS_UPLO UPLO, const int M, const int N, const double ALPHA, const double * A, const int LDA, const double * B, const int LDB, const double BETA, double * C, const int LDC) - Function: void cblas_dsyrk (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANS, const int N, const int K, const double ALPHA, const double * A, const int LDA, const double BETA, double * C, const int LDC) - Function: void cblas_dsyr2k (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANS, const int N, const int K, const double ALPHA, const double * A, const int LDA, const double * B, const int LDB, const double BETA, double * C, const int LDC) - Function: void cblas_dtrmm (const enum CBLAS_ORDER ORDER, const enum CBLAS_SIDE SIDE, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int M, const int N, const double ALPHA, const double * A, const int LDA, double * B, const int LDB) - Function: void cblas_dtrsm (const enum CBLAS_ORDER ORDER, const enum CBLAS_SIDE SIDE, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int M, const int N, const double ALPHA, const double * A, const int LDA, double * B, const int LDB) - Function: void cblas_cgemm (const enum CBLAS_ORDER ORDER, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_TRANSPOSE TRANSB, const int M, const int N, const int K, const void * ALPHA, const void * A, const int LDA, const void * B, const int LDB, const void * BETA, void * C, const int LDC) - Function: void cblas_csymm (const enum CBLAS_ORDER ORDER, const enum CBLAS_SIDE SIDE, const enum CBLAS_UPLO UPLO, const int M, const int N, const void * ALPHA, const void * A, const int LDA, const void * B, const int LDB, const void * BETA, void * C, const int LDC) - Function: void cblas_csyrk (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANS, const int N, const int K, const void * ALPHA, const void * A, const int LDA, const void * BETA, void * C, const int LDC) - Function: void cblas_csyr2k (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANS, const int N, const int K, const void * ALPHA, const void * A, const int LDA, const void * B, const int LDB, const void * BETA, void * C, const int LDC) - Function: void cblas_ctrmm (const enum CBLAS_ORDER ORDER, const enum CBLAS_SIDE SIDE, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int M, const int N, const void * ALPHA, const void * A, const int LDA, void * B, const int LDB) - Function: void cblas_ctrsm (const enum CBLAS_ORDER ORDER, const enum CBLAS_SIDE SIDE, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int M, const int N, const void * ALPHA, const void * A, const int LDA, void * B, const int LDB) - Function: void cblas_zgemm (const enum CBLAS_ORDER ORDER, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_TRANSPOSE TRANSB, const int M, const int N, const int K, const void * ALPHA, const void * A, const int LDA, const void * B, const int LDB, const void * BETA, void * C, const int LDC) - Function: void cblas_zsymm (const enum CBLAS_ORDER ORDER, const enum CBLAS_SIDE SIDE, const enum CBLAS_UPLO UPLO, const int M, const int N, const void * ALPHA, const void * A, const int LDA, const void * B, const int LDB, const void * BETA, void * C, const int LDC) - Function: void cblas_zsyrk (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANS, const int N, const int K, const void * ALPHA, const void * A, const int LDA, const void * BETA, void * C, const int LDC) - Function: void cblas_zsyr2k (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANS, const int N, const int K, const void * ALPHA, const void * A, const int LDA, const void * B, const int LDB, const void * BETA, void * C, const int LDC) - Function: void cblas_ztrmm (const enum CBLAS_ORDER ORDER, const enum CBLAS_SIDE SIDE, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int M, const int N, const void * ALPHA, const void * A, const int LDA, void * B, const int LDB) - Function: void cblas_ztrsm (const enum CBLAS_ORDER ORDER, const enum CBLAS_SIDE SIDE, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int M, const int N, const void * ALPHA, const void * A, const int LDA, void * B, const int LDB) - Function: void cblas_chemm (const enum CBLAS_ORDER ORDER, const enum CBLAS_SIDE SIDE, const enum CBLAS_UPLO UPLO, const int M, const int N, const void * ALPHA, const void * A, const int LDA, const void * B, const int LDB, const void * BETA, void * C, const int LDC) - Function: void cblas_cherk (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANS, const int N, const int K, const float ALPHA, const void * A, const int LDA, const float BETA, void * C, const int LDC) - Function: void cblas_cher2k (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANS, const int N, const int K, const void * ALPHA, const void * A, const int LDA, const void * B, const int LDB, const float BETA, void * C, const int LDC) - Function: void cblas_zhemm (const enum CBLAS_ORDER ORDER, const enum CBLAS_SIDE SIDE, const enum CBLAS_UPLO UPLO, const int M, const int N, const void * ALPHA, const void * A, const int LDA, const void * B, const int LDB, const void * BETA, void * C, const int LDC) - Function: void cblas_zherk (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANS, const int N, const int K, const double ALPHA, const void * A, const int LDA, const double BETA, void * C, const int LDC) - Function: void cblas_zher2k (const enum CBLAS_ORDER ORDER, const enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANS, const int N, const int K, const void * ALPHA, const void * A, const int LDA, const void * B, const int LDB, const double BETA, void * C, const int LDC) - Function: void cblas_xerbla (int P, const char * ROUT, const char * FORM, ...)  File: gsl-ref.info, Node: GSL CBLAS Examples, Prev: Level 3 CBLAS Functions, Up: GSL CBLAS Library Examples ======== The following program computes the product of two matrices using the Level-3 BLAS function SGEMM, [ 0.11 0.12 0.13 ] [ 1011 1012 ] [ 367.76 368.12 ] [ 0.21 0.22 0.23 ] [ 1021 1022 ] = [ 674.06 674.72 ] [ 1031 1032 ] The matrices are stored in row major order but could be stored in column major order if the first argument of the call to `cblas_sgemm' was changed to `CblasColMajor'. #include #include int main (void) { int lda = 3; float A[] = { 0.11, 0.12, 0.13, 0.21, 0.22, 0.23 }; int ldb = 2; float B[] = { 1011, 1012, 1021, 1022, 1031, 1032 }; int ldc = 2; float C[] = { 0.00, 0.00, 0.00, 0.00 }; /* Compute C = A B */ cblas_sgemm (CblasRowMajor, CblasNoTrans, CblasNoTrans, 2, 2, 3, 1.0, A, lda, B, ldb, 0.0, C, ldc); printf ("[ %g, %g\n", C[0], C[1]); printf (" %g, %g ]\n", C[2], C[3]); return 0; } To compile the program use the following command line, $ gcc -Wall demo.c -lgslcblas There is no need to link with the main library `-lgsl' in this case as the CBLAS library is an independent unit. Here is the output from the program, $ ./a.out [ 367.76, 368.12 674.06, 674.72 ]  File: gsl-ref.info, Node: Free Software Needs Free Documentation, Next: GNU General Public License, Prev: GSL CBLAS Library, Up: Top Free Software Needs Free Documentation ************************************** The following article was written by Richard Stallman, founder of the GNU Project. The biggest deficiency in the free software community today is not in the software--it is the lack of good free documentation that we can include with the free software. Many of our most important programs do not come with free reference manuals and free introductory texts. Documentation is an essential part of any software package; when an important free software package does not come with a free manual and a free tutorial, that is a major gap. We have many such gaps today. Consider Perl, for instance. The tutorial manuals that people normally use are non-free. How did this come about? Because the authors of those manuals published them with restrictive terms--no copying, no modification, source files not available--which exclude them from the free software world. That wasn't the first time this sort of thing happened, and it was far from the last. Many times we have heard a GNU user eagerly describe a manual that he is writing, his intended contribution to the community, only to learn that he had ruined everything by signing a publication contract to make it non-free. Free documentation, like free software, is a matter of freedom, not price. The problem with the non-free manual is not that publishers charge a price for printed copies--that in itself is fine. (The Free Software Foundation sells printed copies of manuals, too.) The problem is the restrictions on the use of the manual. Free manuals are available in source code form, and give you permission to copy and modify. Non-free manuals do not allow this. The criteria of freedom for a free manual are roughly the same as for free software. Redistribution (including the normal kinds of commercial redistribution) must be permitted, so that the manual can accompany every copy of the program, both on-line and on paper. Permission for modification of the technical content is crucial too. When people modify the software, adding or changing features, if they are conscientious they will change the manual too--so they can provide accurate and clear documentation for the modified program. A manual that leaves you no choice but to write a new manual to document a changed version of the program is not really available to our community. Some kinds of limits on the way modification is handled are acceptable. For example, requirements to preserve the original author's copyright notice, the distribution terms, or the list of authors, are ok. It is also no problem to require modified versions to include notice that they were modified. Even entire sections that may not be deleted or changed are acceptable, as long as they deal with nontechnical topics (like this one). These kinds of restrictions are acceptable because they don't obstruct the community's normal use of the manual. However, it must be possible to modify all the _technical_ content of the manual, and then distribute the result in all the usual media, through all the usual channels. Otherwise, the restrictions obstruct the use of the manual, it is not free, and we need another manual to replace it. Please spread the word about this issue. Our community continues to lose manuals to proprietary publishing. If we spread the word that free software needs free reference manuals and free tutorials, perhaps the next person who wants to contribute by writing documentation will realize, before it is too late, that only free manuals contribute to the free software community. If you are writing documentation, please insist on publishing it under the GNU Free Documentation License or another free documentation license. Remember that this decision requires your approval--you don't have to let the publisher decide. Some commercial publishers will use a free license if you insist, but they will not propose the option; it is up to you to raise the issue and say firmly that this is what you want. If the publisher you are dealing with refuses, please try other publishers. If you're not sure whether a proposed license is free, write to . You can encourage commercial publishers to sell more free, copylefted manuals and tutorials by buying them, and particularly by buying copies from the publishers that paid for their writing or for major improvements. Meanwhile, try to avoid buying non-free documentation at all. Check the distribution terms of a manual before you buy it, and insist that whoever seeks your business must respect your freedom. Check the history of the book, and try reward the publishers that have paid or pay the authors to work on it. The Free Software Foundation maintains a list of free documentation published by other publishers: `http://www.fsf.org/doc/other-free-books.html'  File: gsl-ref.info, Node: GNU General Public License, Next: GNU Free Documentation License, Prev: Free Software Needs Free Documentation, Up: Top GNU General Public License ************************** Version 2, June 1991 Copyright (C) 1989, 1991 Free Software Foundation, Inc. 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. Preamble ======== The licenses for most software are designed to take away your freedom to share and change it. By contrast, the GNU General Public License is intended to guarantee your freedom to share and change free software--to make sure the software is free for all its users. This General Public License applies to most of the Free Software Foundation's software and to any other program whose authors commit to using it. (Some other Free Software Foundation software is covered by the GNU Library General Public License instead.) You can apply it to your programs, too. When we speak of free software, we are referring to freedom, not price. Our General Public Licenses are designed to make sure that you have the freedom to distribute copies of free software (and charge for this service if you wish), that you receive source code or can get it if you want it, that you can change the software or use pieces of it in new free programs; and that you know you can do these things. To protect your rights, we need to make restrictions that forbid anyone to deny you these rights or to ask you to surrender the rights. These restrictions translate to certain responsibilities for you if you distribute copies of the software, or if you modify it. For example, if you distribute copies of such a program, whether gratis or for a fee, you must give the recipients all the rights that you have. You must make sure that they, too, receive or can get the source code. And you must show them these terms so they know their rights. We protect your rights with two steps: (1) copyright the software, and (2) offer you this license which gives you legal permission to copy, distribute and/or modify the software. Also, for each author's protection and ours, we want to make certain that everyone understands that there is no warranty for this free software. If the software is modified by someone else and passed on, we want its recipients to know that what they have is not the original, so that any problems introduced by others will not reflect on the original authors' reputations. Finally, any free program is threatened constantly by software patents. We wish to avoid the danger that redistributors of a free program will individually obtain patent licenses, in effect making the program proprietary. To prevent this, we have made it clear that any patent must be licensed for everyone's free use or not licensed at all. The precise terms and conditions for copying, distribution and modification follow. TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION 0. This License applies to any program or other work which contains a notice placed by the copyright holder saying it may be distributed under the terms of this General Public License. The "Program", below, refers to any such program or work, and a "work based on the Program" means either the Program or any derivative work under copyright law: that is to say, a work containing the Program or a portion of it, either verbatim or with modifications and/or translated into another language. (Hereinafter, translation is included without limitation in the term "modification".) Each licensee is addressed as "you". Activities other than copying, distribution and modification are not covered by this License; they are outside its scope. The act of running the Program is not restricted, and the output from the Program is covered only if its contents constitute a work based on the Program (independent of having been made by running the Program). Whether that is true depends on what the Program does. 1. You may copy and distribute verbatim copies of the Program's source code as you receive it, in any medium, provided that you conspicuously and appropriately publish on each copy an appropriate copyright notice and disclaimer of warranty; keep intact all the notices that refer to this License and to the absence of any warranty; and give any other recipients of the Program a copy of this License along with the Program. You may charge a fee for the physical act of transferring a copy, and you may at your option offer warranty protection in exchange for a fee. 2. 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IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. END OF TERMS AND CONDITIONS Appendix: How to Apply These Terms to Your New Programs ======================================================= If you develop a new program, and you want it to be of the greatest possible use to the public, the best way to achieve this is to make it free software which everyone can redistribute and change under these terms. To do so, attach the following notices to the program. It is safest to attach them to the start of each source file to most effectively convey the exclusion of warranty; and each file should have at least the "copyright" line and a pointer to where the full notice is found. one line to give the program's name and a brief idea of whAT IT DOES. Copyright (C) YYYY NAME OF AUTHOR This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. Also add information on how to contact you by electronic and paper mail. If the program is interactive, make it output a short notice like this when it starts in an interactive mode: Gnomovision version 69, Copyright (C) 19YY NAME OF AUTHOR Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'. This is free software, and you are welcome to redistribute it under certain conditions; type `show c' for details. The hypothetical commands `show w' and `show c' should show the appropriate parts of the General Public License. Of course, the commands you use may be called something other than `show w' and `show c'; they could even be mouse-clicks or menu items--whatever suits your program. You should also get your employer (if you work as a programmer) or your school, if any, to sign a "copyright disclaimer" for the program, if necessary. Here is a sample; alter the names: Yoyodyne, Inc., hereby disclaims all copyright interest in the program `Gnomovision' (which makes passes at compilers) written by James Hacker. SIGNATURE OF TY COON, 1 April 1989 Ty Coon, President of Vice This General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Library General Public License instead of this License.  File: gsl-ref.info, Node: GNU Free Documentation License, Next: Function Index, Prev: GNU General Public License, Up: Top GNU Free Documentation License ****************************** Version 1.2, November 2002 Copyright (C) 2000,2001,2002 Free Software Foundation, Inc. 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. 0. PREAMBLE The purpose of this License is to make a manual, textbook, or other functional and useful document "free" in the sense of freedom: to assure everyone the effective freedom to copy and redistribute it, with or without modifying it, either commercially or noncommercially. Secondarily, this License preserves for the author and publisher a way to get credit for their work, while not being considered responsible for modifications made by others. This License is a kind of "copyleft", which means that derivative works of the document must themselves be free in the same sense. It complements the GNU General Public License, which is a copyleft license designed for free software. We have designed this License in order to use it for manuals for free software, because free software needs free documentation: a free program should come with manuals providing the same freedoms that the software does. But this License is not limited to software manuals; it can be used for any textual work, regardless of subject matter or whether it is published as a printed book. We recommend this License principally for works whose purpose is instruction or reference. 1. APPLICABILITY AND DEFINITIONS This License applies to any manual or other work, in any medium, that contains a notice placed by the copyright holder saying it can be distributed under the terms of this License. Such a notice grants a world-wide, royalty-free license, unlimited in duration, to use that work under the conditions stated herein. The "Document", below, refers to any such manual or work. Any member of the public is a licensee, and is addressed as "you". You accept the license if you copy, modify or distribute the work in a way requiring permission under copyright law. A "Modified Version" of the Document means any work containing the Document or a portion of it, either copied verbatim, or with modifications and/or translated into another language. A "Secondary Section" is a named appendix or a front-matter section of the Document that deals exclusively with the relationship of the publishers or authors of the Document to the Document's overall subject (or to related matters) and contains nothing that could fall directly within that overall subject. (Thus, if the Document is in part a textbook of mathematics, a Secondary Section may not explain any mathematics.) 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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled ``GNU Free Documentation License''. If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts, replace the "with...Texts." line with this: with the Invariant Sections being LIST THEIR TITLES, with the Front-Cover Texts being LIST, and with the Back-Cover Texts being LIST. If you have Invariant Sections without Cover Texts, or some other combination of the three, merge those two alternatives to suit the situation. If your document contains nontrivial examples of program code, we recommend releasing these examples in parallel under your choice of free software license, such as the GNU General Public License, to permit their use in free software.  File: gsl-ref.info, Node: Function Index, Next: Variable Index, Prev: GNU Free Documentation License, Up: Top Function Index ************** * Menu: * cblas_caxpy: Level 1 CBLAS Functions. * cblas_ccopy: Level 1 CBLAS Functions. * cblas_cdotc_sub: Level 1 CBLAS Functions. * cblas_cdotu_sub: Level 1 CBLAS Functions. * cblas_cgbmv: Level 2 CBLAS Functions. * cblas_cgemm: Level 3 CBLAS Functions. * cblas_cgemv: Level 2 CBLAS Functions. * cblas_cgerc: Level 2 CBLAS Functions. * cblas_cgeru: Level 2 CBLAS Functions. * cblas_chbmv: Level 2 CBLAS Functions. * cblas_chemm: Level 3 CBLAS Functions. * cblas_chemv: Level 2 CBLAS Functions. * cblas_cher: Level 2 CBLAS Functions. * cblas_cher2: Level 2 CBLAS Functions. * cblas_cher2k: Level 3 CBLAS Functions. * cblas_cherk: Level 3 CBLAS Functions. * cblas_chpmv: Level 2 CBLAS Functions. * cblas_chpr: Level 2 CBLAS Functions. * cblas_chpr2: Level 2 CBLAS Functions. * cblas_cscal: Level 1 CBLAS Functions. * cblas_csscal: Level 1 CBLAS Functions. * cblas_cswap: Level 1 CBLAS Functions. * cblas_csymm: Level 3 CBLAS Functions. * cblas_csyr2k: Level 3 CBLAS Functions. * cblas_csyrk: Level 3 CBLAS Functions. * cblas_ctbmv: Level 2 CBLAS Functions. * cblas_ctbsv: Level 2 CBLAS Functions. * cblas_ctpmv: Level 2 CBLAS Functions. * cblas_ctpsv: Level 2 CBLAS Functions. * cblas_ctrmm: Level 3 CBLAS Functions. * cblas_ctrmv: Level 2 CBLAS Functions. * cblas_ctrsm: Level 3 CBLAS Functions. * cblas_ctrsv: Level 2 CBLAS Functions. * cblas_dasum: Level 1 CBLAS Functions. * cblas_daxpy: Level 1 CBLAS Functions. * cblas_dcopy: Level 1 CBLAS Functions. * cblas_ddot: Level 1 CBLAS Functions. * cblas_dgbmv: Level 2 CBLAS Functions. * cblas_dgemm: Level 3 CBLAS Functions. * cblas_dgemv: Level 2 CBLAS Functions. * cblas_dger: Level 2 CBLAS Functions. * cblas_dnrm2: Level 1 CBLAS Functions. * cblas_drot: Level 1 CBLAS Functions. * cblas_drotg: Level 1 CBLAS Functions. * cblas_drotm: Level 1 CBLAS Functions. * cblas_drotmg: Level 1 CBLAS Functions. * cblas_dsbmv: Level 2 CBLAS Functions. * cblas_dscal: Level 1 CBLAS Functions. * cblas_dsdot: Level 1 CBLAS Functions. * cblas_dspmv: Level 2 CBLAS Functions. * cblas_dspr: Level 2 CBLAS Functions. * cblas_dspr2: Level 2 CBLAS Functions. * cblas_dswap: Level 1 CBLAS Functions. * cblas_dsymm: Level 3 CBLAS Functions. * cblas_dsymv: Level 2 CBLAS Functions. * cblas_dsyr: Level 2 CBLAS Functions. * cblas_dsyr2: Level 2 CBLAS Functions. * cblas_dsyr2k: Level 3 CBLAS Functions. * cblas_dsyrk: Level 3 CBLAS Functions. * cblas_dtbmv: Level 2 CBLAS Functions. * cblas_dtbsv: Level 2 CBLAS Functions. * cblas_dtpmv: Level 2 CBLAS Functions. * cblas_dtpsv: Level 2 CBLAS Functions. * cblas_dtrmm: Level 3 CBLAS Functions. * cblas_dtrmv: Level 2 CBLAS Functions. * cblas_dtrsm: Level 3 CBLAS Functions. * cblas_dtrsv: Level 2 CBLAS Functions. * cblas_dzasum: Level 1 CBLAS Functions. * cblas_dznrm2: Level 1 CBLAS Functions. * cblas_icamax: Level 1 CBLAS Functions. * cblas_idamax: Level 1 CBLAS Functions. * cblas_isamax: Level 1 CBLAS Functions. * cblas_izamax: Level 1 CBLAS Functions. * cblas_sasum: Level 1 CBLAS Functions. * cblas_saxpy: Level 1 CBLAS Functions. * cblas_scasum: Level 1 CBLAS Functions. * cblas_scnrm2: Level 1 CBLAS Functions. * cblas_scopy: Level 1 CBLAS Functions. * cblas_sdot: Level 1 CBLAS Functions. * cblas_sdsdot: Level 1 CBLAS Functions. * cblas_sgbmv: Level 2 CBLAS Functions. * cblas_sgemm: Level 3 CBLAS Functions. * cblas_sgemv: Level 2 CBLAS Functions. * cblas_sger: Level 2 CBLAS Functions. * cblas_snrm2: Level 1 CBLAS Functions. * cblas_srot: Level 1 CBLAS Functions. * cblas_srotg: Level 1 CBLAS Functions. * cblas_srotm: Level 1 CBLAS Functions. * cblas_srotmg: Level 1 CBLAS Functions. * cblas_ssbmv: Level 2 CBLAS Functions. * cblas_sscal: Level 1 CBLAS Functions. * cblas_sspmv: Level 2 CBLAS Functions. * cblas_sspr: Level 2 CBLAS Functions. * cblas_sspr2: Level 2 CBLAS Functions. * cblas_sswap: Level 1 CBLAS Functions. * cblas_ssymm: Level 3 CBLAS Functions. * cblas_ssymv: Level 2 CBLAS Functions. * cblas_ssyr: Level 2 CBLAS Functions. * cblas_ssyr2: Level 2 CBLAS Functions. * cblas_ssyr2k: Level 3 CBLAS Functions. * cblas_ssyrk: Level 3 CBLAS Functions. * cblas_stbmv: Level 2 CBLAS Functions. * cblas_stbsv: Level 2 CBLAS Functions. * cblas_stpmv: Level 2 CBLAS Functions. * cblas_stpsv: Level 2 CBLAS Functions. * cblas_strmm: Level 3 CBLAS Functions. * cblas_strmv: Level 2 CBLAS Functions. * cblas_strsm: Level 3 CBLAS Functions. * cblas_strsv: Level 2 CBLAS Functions. * cblas_xerbla: Level 3 CBLAS Functions. * cblas_zaxpy: Level 1 CBLAS Functions. * cblas_zcopy: Level 1 CBLAS Functions. * cblas_zdotc_sub: Level 1 CBLAS Functions. * cblas_zdotu_sub: Level 1 CBLAS Functions. * cblas_zdscal: Level 1 CBLAS Functions. * cblas_zgbmv: Level 2 CBLAS Functions. * cblas_zgemm: Level 3 CBLAS Functions. * cblas_zgemv: Level 2 CBLAS Functions. * cblas_zgerc: Level 2 CBLAS Functions. * cblas_zgeru: Level 2 CBLAS Functions. * cblas_zhbmv: Level 2 CBLAS Functions. * cblas_zhemm: Level 3 CBLAS Functions. * cblas_zhemv: Level 2 CBLAS Functions. * cblas_zher: Level 2 CBLAS Functions. * cblas_zher2: Level 2 CBLAS Functions. * cblas_zher2k: Level 3 CBLAS Functions. * cblas_zherk: Level 3 CBLAS Functions. * cblas_zhpmv: Level 2 CBLAS Functions. * cblas_zhpr: Level 2 CBLAS Functions. * cblas_zhpr2: Level 2 CBLAS Functions. * cblas_zscal: Level 1 CBLAS Functions. * cblas_zswap: Level 1 CBLAS Functions. * cblas_zsymm: Level 3 CBLAS Functions. * cblas_zsyr2k: Level 3 CBLAS Functions. * cblas_zsyrk: Level 3 CBLAS Functions. * cblas_ztbmv: Level 2 CBLAS Functions. * cblas_ztbsv: Level 2 CBLAS Functions. * cblas_ztpmv: Level 2 CBLAS Functions. * cblas_ztpsv: Level 2 CBLAS Functions. * cblas_ztrmm: Level 3 CBLAS Functions. * cblas_ztrmv: Level 2 CBLAS Functions. * cblas_ztrsm: Level 3 CBLAS Functions. * cblas_ztrsv: Level 2 CBLAS Functions. * gsl_acosh: Elementary Functions. * gsl_asinh: Elementary Functions. * gsl_atanh: Elementary Functions. * gsl_blas_caxpy: Level 1 GSL BLAS Interface. * gsl_blas_ccopy: Level 1 GSL BLAS Interface. * gsl_blas_cdotc: Level 1 GSL BLAS Interface. * gsl_blas_cdotu: Level 1 GSL BLAS Interface. * gsl_blas_cgemm: Level 3 GSL BLAS Interface. * gsl_blas_cgemv: Level 2 GSL BLAS Interface. * gsl_blas_cgerc: Level 2 GSL BLAS Interface. * gsl_blas_cgeru: Level 2 GSL BLAS Interface. * gsl_blas_chemm: Level 3 GSL BLAS Interface. * gsl_blas_chemv: Level 2 GSL BLAS Interface. * gsl_blas_cher: Level 2 GSL BLAS Interface. * gsl_blas_cher2: Level 2 GSL BLAS Interface. * gsl_blas_cher2k: Level 3 GSL BLAS Interface. * gsl_blas_cherk: Level 3 GSL BLAS Interface. * gsl_blas_cscal: Level 1 GSL BLAS Interface. * gsl_blas_csscal: Level 1 GSL BLAS Interface. * gsl_blas_cswap: Level 1 GSL BLAS Interface. * gsl_blas_csymm: Level 3 GSL BLAS Interface. * gsl_blas_csyr2k: Level 3 GSL BLAS Interface. * gsl_blas_csyrk: Level 3 GSL BLAS Interface. * gsl_blas_ctrmm: Level 3 GSL BLAS Interface. * gsl_blas_ctrmv: Level 2 GSL BLAS Interface. * gsl_blas_ctrsm: Level 3 GSL BLAS Interface. * gsl_blas_ctrsv: Level 2 GSL BLAS Interface. * gsl_blas_dasum: Level 1 GSL BLAS Interface. * gsl_blas_daxpy: Level 1 GSL BLAS Interface. * gsl_blas_dcopy: Level 1 GSL BLAS Interface. * gsl_blas_ddot: Level 1 GSL BLAS Interface. * gsl_blas_dgemm: Level 3 GSL BLAS Interface. * gsl_blas_dgemv: Level 2 GSL BLAS Interface. * gsl_blas_dger: Level 2 GSL BLAS Interface. * gsl_blas_dnrm2: Level 1 GSL BLAS Interface. * gsl_blas_drot: Level 1 GSL BLAS Interface. * gsl_blas_drotg: Level 1 GSL BLAS Interface. * gsl_blas_drotm: Level 1 GSL BLAS Interface. * gsl_blas_drotmg: Level 1 GSL BLAS Interface. * gsl_blas_dscal: Level 1 GSL BLAS Interface. * gsl_blas_dsdot: Level 1 GSL BLAS Interface. * gsl_blas_dswap: Level 1 GSL BLAS Interface. * gsl_blas_dsymm: Level 3 GSL BLAS Interface. * gsl_blas_dsymv: Level 2 GSL BLAS Interface. * gsl_blas_dsyr: Level 2 GSL BLAS Interface. * gsl_blas_dsyr2: Level 2 GSL BLAS Interface. * gsl_blas_dsyr2k: Level 3 GSL BLAS Interface. * gsl_blas_dsyrk: Level 3 GSL BLAS Interface. * gsl_blas_dtrmm: Level 3 GSL BLAS Interface. * gsl_blas_dtrmv: Level 2 GSL BLAS Interface. * gsl_blas_dtrsm: Level 3 GSL BLAS Interface. * gsl_blas_dtrsv: Level 2 GSL BLAS Interface. * gsl_blas_dzasum: Level 1 GSL BLAS Interface. * gsl_blas_dznrm2: Level 1 GSL BLAS Interface. * gsl_blas_icamax: Level 1 GSL BLAS Interface. * gsl_blas_idamax: Level 1 GSL BLAS Interface. * gsl_blas_isamax: Level 1 GSL BLAS Interface. * gsl_blas_izamax: Level 1 GSL BLAS Interface. * gsl_blas_sasum: Level 1 GSL BLAS Interface. * gsl_blas_saxpy: Level 1 GSL BLAS Interface. * gsl_blas_scasum: Level 1 GSL BLAS Interface. * gsl_blas_scnrm2: Level 1 GSL BLAS Interface. * gsl_blas_scopy: Level 1 GSL BLAS Interface. * gsl_blas_sdot: Level 1 GSL BLAS Interface. * gsl_blas_sdsdot: Level 1 GSL BLAS Interface. * gsl_blas_sgemm: Level 3 GSL BLAS Interface. * gsl_blas_sgemv: Level 2 GSL BLAS Interface. * gsl_blas_sger: Level 2 GSL BLAS Interface. * gsl_blas_snrm2: Level 1 GSL BLAS Interface. * gsl_blas_srot: Level 1 GSL BLAS Interface. * gsl_blas_srotg: Level 1 GSL BLAS Interface. * gsl_blas_srotm: Level 1 GSL BLAS Interface. * gsl_blas_srotmg: Level 1 GSL BLAS Interface. * gsl_blas_sscal: Level 1 GSL BLAS Interface. * gsl_blas_sswap: Level 1 GSL BLAS Interface. * gsl_blas_ssymm: Level 3 GSL BLAS Interface. * gsl_blas_ssymv: Level 2 GSL BLAS Interface. * gsl_blas_ssyr: Level 2 GSL BLAS Interface. * gsl_blas_ssyr2: Level 2 GSL BLAS Interface. * gsl_blas_ssyr2k: Level 3 GSL BLAS Interface. * gsl_blas_ssyrk: Level 3 GSL BLAS Interface. * gsl_blas_strmm: Level 3 GSL BLAS Interface. * gsl_blas_strmv: Level 2 GSL BLAS Interface. * gsl_blas_strsm: Level 3 GSL BLAS Interface. * gsl_blas_strsv: Level 2 GSL BLAS Interface. * gsl_blas_zaxpy: Level 1 GSL BLAS Interface. * gsl_blas_zcopy: Level 1 GSL BLAS Interface. * gsl_blas_zdotc: Level 1 GSL BLAS Interface. * gsl_blas_zdotu: Level 1 GSL BLAS Interface. * gsl_blas_zdscal: Level 1 GSL BLAS Interface. * gsl_blas_zgemm: Level 3 GSL BLAS Interface. * gsl_blas_zgemv: Level 2 GSL BLAS Interface. * gsl_blas_zgerc: Level 2 GSL BLAS Interface. * gsl_blas_zgeru: Level 2 GSL BLAS Interface. * gsl_blas_zhemm: Level 3 GSL BLAS Interface. * gsl_blas_zhemv: Level 2 GSL BLAS Interface. * gsl_blas_zher: Level 2 GSL BLAS Interface. * gsl_blas_zher2: Level 2 GSL BLAS Interface. * gsl_blas_zher2k: Level 3 GSL BLAS Interface. * gsl_blas_zherk: Level 3 GSL BLAS Interface. * gsl_blas_zscal: Level 1 GSL BLAS Interface. * gsl_blas_zswap: Level 1 GSL BLAS Interface. * gsl_blas_zsymm: Level 3 GSL BLAS Interface. * gsl_blas_zsyr2k: Level 3 GSL BLAS Interface. * gsl_blas_zsyrk: Level 3 GSL BLAS Interface. * gsl_blas_ztrmm: Level 3 GSL BLAS Interface. * gsl_blas_ztrmv: Level 2 GSL BLAS Interface. * gsl_blas_ztrsm: Level 3 GSL BLAS Interface. * gsl_blas_ztrsv: Level 2 GSL BLAS Interface. * gsl_block_alloc: Block allocation. * gsl_block_calloc: Block allocation. * gsl_block_fprintf: Reading and writing blocks. * gsl_block_fread: Reading and writing blocks. * gsl_block_free: Block allocation. * gsl_block_fscanf: Reading and writing blocks. * gsl_block_fwrite: Reading and writing blocks. * gsl_cdf_beta_P: The Beta Distribution. * gsl_cdf_beta_Pinv: The Beta Distribution. * gsl_cdf_beta_Q: The Beta Distribution. * gsl_cdf_beta_Qinv: The Beta Distribution. * gsl_cdf_binomial_P: The Binomial Distribution. * gsl_cdf_binomial_Q: The Binomial Distribution. * gsl_cdf_cauchy_P: The Cauchy Distribution. * gsl_cdf_cauchy_Pinv: The Cauchy Distribution. * gsl_cdf_cauchy_Q: The Cauchy Distribution. * gsl_cdf_cauchy_Qinv: The Cauchy Distribution. * gsl_cdf_chisq_P: The Chi-squared Distribution. * gsl_cdf_chisq_Pinv: The Chi-squared Distribution. * gsl_cdf_chisq_Q: The Chi-squared Distribution. * gsl_cdf_chisq_Qinv: The Chi-squared Distribution. * gsl_cdf_exponential_P: The Exponential Distribution. * gsl_cdf_exponential_Pinv: The Exponential Distribution. * gsl_cdf_exponential_Q: The Exponential Distribution. * gsl_cdf_exponential_Qinv: The Exponential Distribution. * gsl_cdf_exppow_P: The Exponential Power Distribution. * gsl_cdf_exppow_Q: The Exponential Power Distribution. * gsl_cdf_fdist_P: The F-distribution. * gsl_cdf_fdist_Pinv: The F-distribution. * gsl_cdf_fdist_Q: The F-distribution. * gsl_cdf_fdist_Qinv: The F-distribution. * gsl_cdf_flat_P: The Flat (Uniform) Distribution. * gsl_cdf_flat_Pinv: The Flat (Uniform) Distribution. * gsl_cdf_flat_Q: The Flat (Uniform) Distribution. * gsl_cdf_flat_Qinv: The Flat (Uniform) Distribution. * gsl_cdf_gamma_P: The Gamma Distribution. * gsl_cdf_gamma_Pinv: The Gamma Distribution. * gsl_cdf_gamma_Q: The Gamma Distribution. * gsl_cdf_gamma_Qinv: The Gamma Distribution. * gsl_cdf_gaussian_P: The Gaussian Distribution. * gsl_cdf_gaussian_Pinv: The Gaussian Distribution. * gsl_cdf_gaussian_Q: The Gaussian Distribution. * gsl_cdf_gaussian_Qinv: The Gaussian Distribution. * gsl_cdf_geometric_P: The Geometric Distribution. * gsl_cdf_geometric_Q: The Geometric Distribution. * gsl_cdf_gumbel1_P: The Type-1 Gumbel Distribution. * gsl_cdf_gumbel1_Pinv: The Type-1 Gumbel Distribution. * gsl_cdf_gumbel1_Q: The Type-1 Gumbel Distribution. * gsl_cdf_gumbel1_Qinv: The Type-1 Gumbel Distribution. * gsl_cdf_gumbel2_P: The Type-2 Gumbel Distribution. * gsl_cdf_gumbel2_Pinv: The Type-2 Gumbel Distribution. * gsl_cdf_gumbel2_Q: The Type-2 Gumbel Distribution. * gsl_cdf_gumbel2_Qinv: The Type-2 Gumbel Distribution. * gsl_cdf_hypergeometric_P: The Hypergeometric Distribution. * gsl_cdf_hypergeometric_Q: The Hypergeometric Distribution. * gsl_cdf_laplace_P: The Laplace Distribution. * gsl_cdf_laplace_Pinv: The Laplace Distribution. * gsl_cdf_laplace_Q: The Laplace Distribution. * gsl_cdf_laplace_Qinv: The Laplace Distribution. * gsl_cdf_logistic_P: The Logistic Distribution. * gsl_cdf_logistic_Pinv: The Logistic Distribution. * gsl_cdf_logistic_Q: The Logistic Distribution. * gsl_cdf_logistic_Qinv: The Logistic Distribution. * gsl_cdf_lognormal_P: The Lognormal Distribution. * gsl_cdf_lognormal_Pinv: The Lognormal Distribution. * gsl_cdf_lognormal_Q: The Lognormal Distribution. * gsl_cdf_lognormal_Qinv: The Lognormal Distribution. * gsl_cdf_negative_binomial_P: The Negative Binomial Distribution. * gsl_cdf_negative_binomial_Q: The Negative Binomial Distribution. * gsl_cdf_pareto_P: The Pareto Distribution. * gsl_cdf_pareto_Pinv: The Pareto Distribution. * gsl_cdf_pareto_Q: The Pareto Distribution. * gsl_cdf_pareto_Qinv: The Pareto Distribution. * gsl_cdf_pascal_P: The Pascal Distribution. * gsl_cdf_pascal_Q: The Pascal Distribution. * gsl_cdf_poisson_P: The Poisson Distribution. * gsl_cdf_poisson_Q: The Poisson Distribution. * gsl_cdf_rayleigh_P: The Rayleigh Distribution. * gsl_cdf_rayleigh_Pinv: The Rayleigh Distribution. * gsl_cdf_rayleigh_Q: The Rayleigh Distribution. * gsl_cdf_rayleigh_Qinv: The Rayleigh Distribution. * gsl_cdf_tdist_P: The t-distribution. * gsl_cdf_tdist_Pinv: The t-distribution. * gsl_cdf_tdist_Q: The t-distribution. * gsl_cdf_tdist_Qinv: The t-distribution. * gsl_cdf_ugaussian_P: The Gaussian Distribution. * gsl_cdf_ugaussian_Pinv: The Gaussian Distribution. * gsl_cdf_ugaussian_Q: The Gaussian Distribution. * gsl_cdf_ugaussian_Qinv: The Gaussian Distribution. * gsl_cdf_weibull_P: The Weibull Distribution. * gsl_cdf_weibull_Pinv: The Weibull Distribution. * gsl_cdf_weibull_Q: The Weibull Distribution. * gsl_cdf_weibull_Qinv: The Weibull Distribution. * gsl_cheb_alloc: Creation and Calculation of Chebyshev Series. * gsl_cheb_calc_deriv: Derivatives and Integrals. * gsl_cheb_calc_integ: Derivatives and Integrals. * gsl_cheb_eval: Chebyshev Series Evaluation. * gsl_cheb_eval_err: Chebyshev Series Evaluation. * gsl_cheb_eval_n: Chebyshev Series Evaluation. * gsl_cheb_eval_n_err: Chebyshev Series Evaluation. * gsl_cheb_free: Creation and Calculation of Chebyshev Series. * gsl_cheb_init: Creation and Calculation of Chebyshev Series. * gsl_combination_alloc: Combination allocation. * gsl_combination_calloc: Combination allocation. * gsl_combination_data: Combination properties. * gsl_combination_fprintf: Reading and writing combinations. * gsl_combination_fread: Reading and writing combinations. * gsl_combination_free: Combination allocation. * gsl_combination_fscanf: Reading and writing combinations. * gsl_combination_fwrite: Reading and writing combinations. * gsl_combination_get: Accessing combination elements. * gsl_combination_init_first: Combination allocation. * gsl_combination_init_last: Combination allocation. * gsl_combination_k: Combination properties. * gsl_combination_memcpy: Combination allocation. * gsl_combination_n: Combination properties. * gsl_combination_next: Combination functions. * gsl_combination_prev: Combination functions. * gsl_combination_valid: Combination properties. * gsl_complex_abs: Properties of complex numbers. * gsl_complex_abs2: Properties of complex numbers. * gsl_complex_add: Complex arithmetic operators. * gsl_complex_add_imag: Complex arithmetic operators. * gsl_complex_add_real: Complex arithmetic operators. * gsl_complex_arccos: Inverse Complex Trigonometric Functions. * gsl_complex_arccos_real: Inverse Complex Trigonometric Functions. * gsl_complex_arccosh: Inverse Complex Hyperbolic Functions. * gsl_complex_arccosh_real: Inverse Complex Hyperbolic Functions. * gsl_complex_arccot: Inverse Complex Trigonometric Functions. * gsl_complex_arccoth: Inverse Complex Hyperbolic Functions. * gsl_complex_arccsc: Inverse Complex Trigonometric Functions. * gsl_complex_arccsc_real: Inverse Complex Trigonometric Functions. * gsl_complex_arccsch: Inverse Complex Hyperbolic Functions. * gsl_complex_arcsec: Inverse Complex Trigonometric Functions. * gsl_complex_arcsec_real: Inverse Complex Trigonometric Functions. * gsl_complex_arcsech: Inverse Complex Hyperbolic Functions. * gsl_complex_arcsin: Inverse Complex Trigonometric Functions. * gsl_complex_arcsin_real: Inverse Complex Trigonometric Functions. * gsl_complex_arcsinh: Inverse Complex Hyperbolic Functions. * gsl_complex_arctan: Inverse Complex Trigonometric Functions. * gsl_complex_arctanh: Inverse Complex Hyperbolic Functions. * gsl_complex_arctanh_real: Inverse Complex Hyperbolic Functions. * gsl_complex_arg: Properties of complex numbers. * gsl_complex_conjugate: Complex arithmetic operators. * gsl_complex_cos: Complex Trigonometric Functions. * gsl_complex_cosh: Complex Hyperbolic Functions. * gsl_complex_cot: Complex Trigonometric Functions. * gsl_complex_coth: Complex Hyperbolic Functions. * gsl_complex_csc: Complex Trigonometric Functions. * gsl_complex_csch: Complex Hyperbolic Functions. * gsl_complex_div: Complex arithmetic operators. * gsl_complex_div_imag: Complex arithmetic operators. * gsl_complex_div_real: Complex arithmetic operators. * gsl_complex_exp: Elementary Complex Functions. * gsl_complex_inverse: Complex arithmetic operators. * gsl_complex_log: Elementary Complex Functions. * gsl_complex_log10: Elementary Complex Functions. * gsl_complex_log_b: Elementary Complex Functions. * gsl_complex_logabs: Properties of complex numbers. * gsl_complex_mul: Complex arithmetic operators. * gsl_complex_mul_imag: Complex arithmetic operators. * gsl_complex_mul_real: Complex arithmetic operators. * gsl_complex_negative: Complex arithmetic operators. * gsl_complex_polar: Complex numbers. * gsl_complex_pow: Elementary Complex Functions. * gsl_complex_pow_real: Elementary Complex Functions. * gsl_complex_rect: Complex numbers. * gsl_complex_sec: Complex Trigonometric Functions. * gsl_complex_sech: Complex Hyperbolic Functions. * gsl_complex_sin: Complex Trigonometric Functions. * gsl_complex_sinh: Complex Hyperbolic Functions. * gsl_complex_sqrt: Elementary Complex Functions. * gsl_complex_sqrt_real: Elementary Complex Functions. * gsl_complex_sub: Complex arithmetic operators. * gsl_complex_sub_imag: Complex arithmetic operators. * gsl_complex_sub_real: Complex arithmetic operators. * gsl_complex_tan: Complex Trigonometric Functions. * gsl_complex_tanh: Complex Hyperbolic Functions. * gsl_deriv_backward: Numerical Differentiation functions. * gsl_deriv_central: Numerical Differentiation functions. * gsl_deriv_forward: Numerical Differentiation functions. * gsl_dht_alloc: Discrete Hankel Transform Functions. * gsl_dht_apply: Discrete Hankel Transform Functions. * gsl_dht_free: Discrete Hankel Transform Functions. * gsl_dht_init: Discrete Hankel Transform Functions. * gsl_dht_k_sample: Discrete Hankel Transform Functions. * gsl_dht_new: Discrete Hankel Transform Functions. * gsl_dht_x_sample: Discrete Hankel Transform Functions. * GSL_EDOM: Error Codes. * gsl_eigen_herm: Complex Hermitian Matrices. * gsl_eigen_herm_alloc: Complex Hermitian Matrices. * gsl_eigen_herm_free: Complex Hermitian Matrices. * gsl_eigen_hermv: Complex Hermitian Matrices. * gsl_eigen_hermv_alloc: Complex Hermitian Matrices. * gsl_eigen_hermv_free: Complex Hermitian Matrices. * gsl_eigen_hermv_sort: Sorting Eigenvalues and Eigenvectors. * gsl_eigen_symm: Real Symmetric Matrices. * gsl_eigen_symm_alloc: Real Symmetric Matrices. * gsl_eigen_symm_free: Real Symmetric Matrices. * gsl_eigen_symmv: Real Symmetric Matrices. * gsl_eigen_symmv_alloc: Real Symmetric Matrices. * gsl_eigen_symmv_free: Real Symmetric Matrices. * gsl_eigen_symmv_sort: Sorting Eigenvalues and Eigenvectors. * GSL_EINVAL: Error Codes. * GSL_ENOMEM: Error Codes. * GSL_ERANGE: Error Codes. * GSL_ERROR: Using GSL error reporting in your own functions. * GSL_ERROR_VAL: Using GSL error reporting in your own functions. * gsl_expm1: Elementary Functions. * gsl_fcmp: Approximate Comparison of Floating Point Numbers. * gsl_fft_complex_backward: Mixed-radix FFT routines for complex data. * gsl_fft_complex_forward: Mixed-radix FFT routines for complex data. * gsl_fft_complex_inverse: Mixed-radix FFT routines for complex data. * gsl_fft_complex_radix2_backward: Radix-2 FFT routines for complex data. * gsl_fft_complex_radix2_dif_backward: Radix-2 FFT routines for complex data. * gsl_fft_complex_radix2_dif_forward: Radix-2 FFT routines for complex data. * gsl_fft_complex_radix2_dif_inverse: Radix-2 FFT routines for complex data. * gsl_fft_complex_radix2_dif_transform: Radix-2 FFT routines for complex data. * gsl_fft_complex_radix2_forward: Radix-2 FFT routines for complex data. * gsl_fft_complex_radix2_inverse: Radix-2 FFT routines for complex data. * gsl_fft_complex_radix2_transform: Radix-2 FFT routines for complex data. * gsl_fft_complex_transform: Mixed-radix FFT routines for complex data. * gsl_fft_complex_wavetable_alloc: Mixed-radix FFT routines for complex data. * gsl_fft_complex_wavetable_free: Mixed-radix FFT routines for complex data. * gsl_fft_complex_workspace_alloc: Mixed-radix FFT routines for complex data. * gsl_fft_complex_workspace_free: Mixed-radix FFT routines for complex data. * gsl_fft_halfcomplex_radix2_backward: Radix-2 FFT routines for real data. * gsl_fft_halfcomplex_radix2_inverse: Radix-2 FFT routines for real data. * gsl_fft_halfcomplex_transform: Mixed-radix FFT routines for real data. * gsl_fft_halfcomplex_unpack: Mixed-radix FFT routines for real data. * gsl_fft_halfcomplex_wavetable_alloc: Mixed-radix FFT routines for real data. * gsl_fft_halfcomplex_wavetable_free: Mixed-radix FFT routines for real data. * gsl_fft_real_radix2_transform: Radix-2 FFT routines for real data. * gsl_fft_real_transform: Mixed-radix FFT routines for real data. * gsl_fft_real_unpack: Mixed-radix FFT routines for real data. * gsl_fft_real_wavetable_alloc: Mixed-radix FFT routines for real data. * gsl_fft_real_wavetable_free: Mixed-radix FFT routines for real data. * gsl_fft_real_workspace_alloc: Mixed-radix FFT routines for real data. * gsl_fft_real_workspace_free: Mixed-radix FFT routines for real data. * gsl_finite: Infinities and Not-a-number. * gsl_fit_linear: Linear regression. * gsl_fit_linear_est: Linear regression. * gsl_fit_mul: Linear fitting without a constant term. * gsl_fit_mul_est: Linear fitting without a constant term. * gsl_fit_wlinear: Linear regression. * gsl_fit_wmul: Linear fitting without a constant term. * gsl_frexp: Elementary Functions. * gsl_heapsort: Sorting objects. * gsl_heapsort_index: Sorting objects. * gsl_histogram2d_accumulate: Updating and accessing 2D histogram elements. * gsl_histogram2d_add: 2D Histogram Operations. * gsl_histogram2d_alloc: 2D Histogram allocation. * gsl_histogram2d_clone: Copying 2D Histograms. * gsl_histogram2d_cov: 2D Histogram Statistics. * gsl_histogram2d_div: 2D Histogram Operations. * gsl_histogram2d_equal_bins_p: 2D Histogram Operations. * gsl_histogram2d_find: Searching 2D histogram ranges. * gsl_histogram2d_fprintf: Reading and writing 2D histograms. * gsl_histogram2d_fread: Reading and writing 2D histograms. * gsl_histogram2d_free: 2D Histogram allocation. * gsl_histogram2d_fscanf: Reading and writing 2D histograms. * gsl_histogram2d_fwrite: Reading and writing 2D histograms. * gsl_histogram2d_get: Updating and accessing 2D histogram elements. * gsl_histogram2d_get_xrange: Updating and accessing 2D histogram elements. * gsl_histogram2d_get_yrange: Updating and accessing 2D histogram elements. * gsl_histogram2d_increment: Updating and accessing 2D histogram elements. * gsl_histogram2d_max_bin: 2D Histogram Statistics. * gsl_histogram2d_max_val: 2D Histogram Statistics. * gsl_histogram2d_memcpy: Copying 2D Histograms. * gsl_histogram2d_min_bin: 2D Histogram Statistics. * gsl_histogram2d_min_val: 2D Histogram Statistics. * gsl_histogram2d_mul: 2D Histogram Operations. * gsl_histogram2d_nx: Updating and accessing 2D histogram elements. * gsl_histogram2d_ny: Updating and accessing 2D histogram elements. * gsl_histogram2d_pdf_alloc: Resampling from 2D histograms. * gsl_histogram2d_pdf_free: Resampling from 2D histograms. * gsl_histogram2d_pdf_init: Resampling from 2D histograms. * gsl_histogram2d_pdf_sample: Resampling from 2D histograms. * gsl_histogram2d_reset: Updating and accessing 2D histogram elements. * gsl_histogram2d_scale: 2D Histogram Operations. * gsl_histogram2d_set_ranges: 2D Histogram allocation. * gsl_histogram2d_set_ranges_uniform: 2D Histogram allocation. * gsl_histogram2d_shift: 2D Histogram Operations. * gsl_histogram2d_sub: 2D Histogram Operations. * gsl_histogram2d_sum: 2D Histogram Statistics. * gsl_histogram2d_xmax: Updating and accessing 2D histogram elements. * gsl_histogram2d_xmean: 2D Histogram Statistics. * gsl_histogram2d_xmin: Updating and accessing 2D histogram elements. * gsl_histogram2d_xsigma: 2D Histogram Statistics. * gsl_histogram2d_ymax: Updating and accessing 2D histogram elements. * gsl_histogram2d_ymean: 2D Histogram Statistics. * gsl_histogram2d_ymin: Updating and accessing 2D histogram elements. * gsl_histogram2d_ysigma: 2D Histogram Statistics. * gsl_histogram_accumulate: Updating and accessing histogram elements. * gsl_histogram_add: Histogram Operations. * gsl_histogram_alloc: Histogram allocation. * gsl_histogram_bins: Updating and accessing histogram elements. * gsl_histogram_clone: Copying Histograms. * gsl_histogram_div: Histogram Operations. * gsl_histogram_equal_bins_p: Histogram Operations. * gsl_histogram_find: Searching histogram ranges. * gsl_histogram_fprintf: Reading and writing histograms. * gsl_histogram_fread: Reading and writing histograms. * gsl_histogram_free: Histogram allocation. * gsl_histogram_fscanf: Reading and writing histograms. * gsl_histogram_fwrite: Reading and writing histograms. * gsl_histogram_get: Updating and accessing histogram elements. * gsl_histogram_get_range: Updating and accessing histogram elements. * gsl_histogram_increment: Updating and accessing histogram elements. * gsl_histogram_max: Updating and accessing histogram elements. * gsl_histogram_max_bin: Histogram Statistics. * gsl_histogram_max_val: Histogram Statistics. * gsl_histogram_mean: Histogram Statistics. * gsl_histogram_memcpy: Copying Histograms. * gsl_histogram_min: Updating and accessing histogram elements. * gsl_histogram_min_bin: Histogram Statistics. * gsl_histogram_min_val: Histogram Statistics. * gsl_histogram_mul: Histogram Operations. * gsl_histogram_pdf_alloc: The histogram probability distribution struct. * gsl_histogram_pdf_free: The histogram probability distribution struct. * gsl_histogram_pdf_init: The histogram probability distribution struct. * gsl_histogram_pdf_sample: The histogram probability distribution struct. * gsl_histogram_reset: Updating and accessing histogram elements. * gsl_histogram_scale: Histogram Operations. * gsl_histogram_set_ranges: Histogram allocation. * gsl_histogram_set_ranges_uniform: Histogram allocation. * gsl_histogram_shift: Histogram Operations. * gsl_histogram_sigma: Histogram Statistics. * gsl_histogram_sub: Histogram Operations. * gsl_histogram_sum: Histogram Statistics. * gsl_hypot: Elementary Functions. * gsl_ieee_env_setup: Setting up your IEEE environment. * gsl_ieee_fprintf_double: Representation of floating point numbers. * gsl_ieee_fprintf_float: Representation of floating point numbers. * gsl_ieee_printf_double: Representation of floating point numbers. * gsl_ieee_printf_float: Representation of floating point numbers. * GSL_IMAG: Complex numbers. * gsl_integration_qag: QAG adaptive integration. * gsl_integration_qagi: QAGI adaptive integration on infinite intervals. * gsl_integration_qagil: QAGI adaptive integration on infinite intervals. * gsl_integration_qagiu: QAGI adaptive integration on infinite intervals. * gsl_integration_qagp: QAGP adaptive integration with known singular points. * gsl_integration_qags: QAGS adaptive integration with singularities. * gsl_integration_qawc: QAWC adaptive integration for Cauchy principal values. * gsl_integration_qawf: QAWF adaptive integration for Fourier integrals. * gsl_integration_qawo: QAWO adaptive integration for oscillatory functions. * gsl_integration_qawo_table_alloc: QAWO adaptive integration for oscillatory functions. * gsl_integration_qawo_table_free: QAWO adaptive integration for oscillatory functions. * gsl_integration_qawo_table_set: QAWO adaptive integration for oscillatory functions. * gsl_integration_qawo_table_set_length: QAWO adaptive integration for oscillatory functions. * gsl_integration_qaws: QAWS adaptive integration for singular functions. * gsl_integration_qaws_table_alloc: QAWS adaptive integration for singular functions. * gsl_integration_qaws_table_free: QAWS adaptive integration for singular functions. * gsl_integration_qaws_table_set: QAWS adaptive integration for singular functions. * gsl_integration_qng: QNG non-adaptive Gauss-Kronrod integration. * gsl_integration_workspace_alloc: QAG adaptive integration. * gsl_integration_workspace_free: QAG adaptive integration. * gsl_interp_accel_alloc: Index Look-up and Acceleration. * gsl_interp_accel_find: Index Look-up and Acceleration. * gsl_interp_accel_free: Index Look-up and Acceleration. * gsl_interp_akima: Interpolation Types. * gsl_interp_akima_periodic: Interpolation Types. * gsl_interp_alloc: Interpolation Functions. * gsl_interp_bsearch: Index Look-up and Acceleration. * gsl_interp_cspline: Interpolation Types. * gsl_interp_cspline_periodic: Interpolation Types. * gsl_interp_eval: Evaluation of Interpolating Functions. * gsl_interp_eval_deriv: Evaluation of Interpolating Functions. * gsl_interp_eval_deriv2: Evaluation of Interpolating Functions. * gsl_interp_eval_deriv2_e: Evaluation of Interpolating Functions. * gsl_interp_eval_deriv_e: Evaluation of Interpolating Functions. * gsl_interp_eval_e: Evaluation of Interpolating Functions. * gsl_interp_eval_integ: Evaluation of Interpolating Functions. * gsl_interp_eval_integ_e: Evaluation of Interpolating Functions. * gsl_interp_free: Interpolation Functions. * gsl_interp_init: Interpolation Functions. * gsl_interp_linear: Interpolation Types. * gsl_interp_min_size: Interpolation Types. * gsl_interp_name: Interpolation Types. * gsl_interp_polynomial: Interpolation Types. * GSL_IS_EVEN: Testing for Odd and Even Numbers. * GSL_IS_ODD: Testing for Odd and Even Numbers. * gsl_isinf: Infinities and Not-a-number. * gsl_isnan: Infinities and Not-a-number. * gsl_ldexp: Elementary Functions. * gsl_linalg_bidiag_decomp: Bidiagonalization. * gsl_linalg_bidiag_unpack: Bidiagonalization. * gsl_linalg_bidiag_unpack2: Bidiagonalization. * gsl_linalg_bidiag_unpack_B: Bidiagonalization. * gsl_linalg_cholesky_decomp: Cholesky Decomposition. * gsl_linalg_cholesky_solve: Cholesky Decomposition. * gsl_linalg_cholesky_svx: Cholesky Decomposition. * gsl_linalg_complex_LU_decomp: LU Decomposition. * gsl_linalg_complex_LU_det: LU Decomposition. * gsl_linalg_complex_LU_invert: LU Decomposition. * gsl_linalg_complex_LU_lndet: LU Decomposition. * gsl_linalg_complex_LU_refine: LU Decomposition. * gsl_linalg_complex_LU_sgndet: LU Decomposition. * gsl_linalg_complex_LU_solve: LU Decomposition. * gsl_linalg_complex_LU_svx: LU Decomposition. * gsl_linalg_hermtd_decomp: Tridiagonal Decomposition of Hermitian Matrices. * gsl_linalg_hermtd_unpack: Tridiagonal Decomposition of Hermitian Matrices. * gsl_linalg_hermtd_unpack_T: Tridiagonal Decomposition of Hermitian Matrices. * gsl_linalg_HH_solve: Householder solver for linear systems. * gsl_linalg_HH_svx: Householder solver for linear systems. * gsl_linalg_householder_hm: Householder Transformations. * gsl_linalg_householder_hv: Householder Transformations. * gsl_linalg_householder_mh: Householder Transformations. * gsl_linalg_householder_transform: Householder Transformations. * gsl_linalg_LU_decomp: LU Decomposition. * gsl_linalg_LU_det: LU Decomposition. * gsl_linalg_LU_invert: LU Decomposition. * gsl_linalg_LU_lndet: LU Decomposition. * gsl_linalg_LU_refine: LU Decomposition. * gsl_linalg_LU_sgndet: LU Decomposition. * gsl_linalg_LU_solve: LU Decomposition. * gsl_linalg_LU_svx: LU Decomposition. * gsl_linalg_QR_decomp: QR Decomposition. * gsl_linalg_QR_lssolve: QR Decomposition. * gsl_linalg_QR_QRsolve: QR Decomposition. * gsl_linalg_QR_QTvec: QR Decomposition. * gsl_linalg_QR_Qvec: QR Decomposition. * gsl_linalg_QR_Rsolve: QR Decomposition. * gsl_linalg_QR_Rsvx: QR Decomposition. * gsl_linalg_QR_solve: QR Decomposition. * gsl_linalg_QR_svx: QR Decomposition. * gsl_linalg_QR_unpack: QR Decomposition. * gsl_linalg_QR_update: QR Decomposition. * gsl_linalg_QRPT_decomp: QR Decomposition with Column Pivoting. * gsl_linalg_QRPT_decomp2: QR Decomposition with Column Pivoting. * gsl_linalg_QRPT_QRsolve: QR Decomposition with Column Pivoting. * gsl_linalg_QRPT_Rsolve: QR Decomposition with Column Pivoting. * gsl_linalg_QRPT_Rsvx: QR Decomposition with Column Pivoting. * gsl_linalg_QRPT_solve: QR Decomposition with Column Pivoting. * gsl_linalg_QRPT_svx: QR Decomposition with Column Pivoting. * gsl_linalg_QRPT_update: QR Decomposition with Column Pivoting. * gsl_linalg_R_solve: QR Decomposition. * gsl_linalg_R_svx: QR Decomposition. * gsl_linalg_solve_cyc_tridiag: Tridiagonal Systems. * gsl_linalg_solve_symm_cyc_tridiag: Tridiagonal Systems. * gsl_linalg_solve_symm_tridiag: Tridiagonal Systems. * gsl_linalg_solve_tridiag: Tridiagonal Systems. * gsl_linalg_SV_decomp: Singular Value Decomposition. * gsl_linalg_SV_decomp_jacobi: Singular Value Decomposition. * gsl_linalg_SV_decomp_mod: Singular Value Decomposition. * gsl_linalg_SV_solve: Singular Value Decomposition. * gsl_linalg_symmtd_decomp: Tridiagonal Decomposition of Real Symmetric Matrices. * gsl_linalg_symmtd_unpack: Tridiagonal Decomposition of Real Symmetric Matrices. * gsl_linalg_symmtd_unpack_T: Tridiagonal Decomposition of Real Symmetric Matrices. * gsl_log1p: Elementary Functions. * gsl_matrix_add: Matrix operations. * gsl_matrix_add_constant: Matrix operations. * gsl_matrix_alloc: Matrix allocation. * gsl_matrix_calloc: Matrix allocation. * gsl_matrix_column: Creating row and column views. * gsl_matrix_const_column: Creating row and column views. * gsl_matrix_const_diagonal: Creating row and column views. * gsl_matrix_const_ptr: Accessing matrix elements. * gsl_matrix_const_row: Creating row and column views. * gsl_matrix_const_subdiagonal: Creating row and column views. * gsl_matrix_const_submatrix: Matrix views. * gsl_matrix_const_superdiagonal: Creating row and column views. * gsl_matrix_const_view_array: Matrix views. * gsl_matrix_const_view_array_with_tda: Matrix views. * gsl_matrix_const_view_vector: Matrix views. * gsl_matrix_const_view_vector_with_tda: Matrix views. * gsl_matrix_diagonal: Creating row and column views. * gsl_matrix_div_elements: Matrix operations. * gsl_matrix_fprintf: Reading and writing matrices. * gsl_matrix_fread: Reading and writing matrices. * gsl_matrix_free: Matrix allocation. * gsl_matrix_fscanf: Reading and writing matrices. * gsl_matrix_fwrite: Reading and writing matrices. * gsl_matrix_get: Accessing matrix elements. * gsl_matrix_get_col: Copying rows and columns. * gsl_matrix_get_row: Copying rows and columns. * gsl_matrix_isnull: Matrix properties. * gsl_matrix_max: Finding maximum and minimum elements of matrices. * gsl_matrix_max_index: Finding maximum and minimum elements of matrices. * gsl_matrix_memcpy: Copying matrices. * gsl_matrix_min: Finding maximum and minimum elements of matrices. * gsl_matrix_min_index: Finding maximum and minimum elements of matrices. * gsl_matrix_minmax: Finding maximum and minimum elements of matrices. * gsl_matrix_minmax_index: Finding maximum and minimum elements of matrices. * gsl_matrix_mul_elements: Matrix operations. * gsl_matrix_ptr: Accessing matrix elements. * gsl_matrix_row: Creating row and column views. * gsl_matrix_scale: Matrix operations. * gsl_matrix_set: Accessing matrix elements. * gsl_matrix_set_all: Initializing matrix elements. * gsl_matrix_set_col: Copying rows and columns. * gsl_matrix_set_identity: Initializing matrix elements. * gsl_matrix_set_row: Copying rows and columns. * gsl_matrix_set_zero: Initializing matrix elements. * gsl_matrix_sub: Matrix operations. * gsl_matrix_subdiagonal: Creating row and column views. * gsl_matrix_submatrix: Matrix views. * gsl_matrix_superdiagonal: Creating row and column views. * gsl_matrix_swap: Copying matrices. * gsl_matrix_swap_columns: Exchanging rows and columns. * gsl_matrix_swap_rowcol: Exchanging rows and columns. * gsl_matrix_swap_rows: Exchanging rows and columns. * gsl_matrix_transpose: Exchanging rows and columns. * gsl_matrix_transpose_memcpy: Exchanging rows and columns. * gsl_matrix_view_array: Matrix views. * gsl_matrix_view_array_with_tda: Matrix views. * gsl_matrix_view_vector: Matrix views. * gsl_matrix_view_vector_with_tda: Matrix views. * GSL_MAX: Maximum and Minimum functions. * GSL_MAX_DBL: Maximum and Minimum functions. * GSL_MAX_INT: Maximum and Minimum functions. * GSL_MAX_LDBL: Maximum and Minimum functions. * GSL_MIN: Maximum and Minimum functions. * GSL_MIN_DBL: Maximum and Minimum functions. * gsl_min_fminimizer_alloc: Initializing the Minimizer. * gsl_min_fminimizer_brent: Minimization Algorithms. * gsl_min_fminimizer_f_lower: Minimization Iteration. * gsl_min_fminimizer_f_minimum: Minimization Iteration. * gsl_min_fminimizer_f_upper: Minimization Iteration. * gsl_min_fminimizer_free: Initializing the Minimizer. * gsl_min_fminimizer_goldensection: Minimization Algorithms. * gsl_min_fminimizer_iterate: Minimization Iteration. * gsl_min_fminimizer_name: Initializing the Minimizer. * gsl_min_fminimizer_set: Initializing the Minimizer. * gsl_min_fminimizer_set_with_values: Initializing the Minimizer. * gsl_min_fminimizer_x_lower: Minimization Iteration. * gsl_min_fminimizer_x_minimum: Minimization Iteration. * gsl_min_fminimizer_x_upper: Minimization Iteration. * GSL_MIN_INT: Maximum and Minimum functions. * GSL_MIN_LDBL: Maximum and Minimum functions. * gsl_min_test_interval: Minimization Stopping Parameters. * gsl_monte_miser_alloc: MISER. * gsl_monte_miser_free: MISER. * gsl_monte_miser_init: MISER. * gsl_monte_miser_integrate: MISER. * gsl_monte_plain_alloc: PLAIN Monte Carlo. * gsl_monte_plain_free: PLAIN Monte Carlo. * gsl_monte_plain_init: PLAIN Monte Carlo. * gsl_monte_plain_integrate: PLAIN Monte Carlo. * gsl_monte_vegas_alloc: VEGAS. * gsl_monte_vegas_free: VEGAS. * gsl_monte_vegas_init: VEGAS. * gsl_monte_vegas_integrate: VEGAS. * gsl_multifit_covar: Computing the covariance matrix of best fit parameters. * gsl_multifit_fdfsolver_alloc: Initializing the Nonlinear Least-Squares Solver. * gsl_multifit_fdfsolver_free: Initializing the Nonlinear Least-Squares Solver. * gsl_multifit_fdfsolver_iterate: Iteration of the Minimization Algorithm. * gsl_multifit_fdfsolver_lmder: Minimization Algorithms using Derivatives. * gsl_multifit_fdfsolver_lmsder: Minimization Algorithms using Derivatives. * gsl_multifit_fdfsolver_name: Initializing the Nonlinear Least-Squares Solver. * gsl_multifit_fdfsolver_position: Iteration of the Minimization Algorithm. * gsl_multifit_fdfsolver_set: Initializing the Nonlinear Least-Squares Solver. * gsl_multifit_fsolver_alloc: Initializing the Nonlinear Least-Squares Solver. * gsl_multifit_fsolver_free: Initializing the Nonlinear Least-Squares Solver. * gsl_multifit_fsolver_iterate: Iteration of the Minimization Algorithm. * gsl_multifit_fsolver_name: Initializing the Nonlinear Least-Squares Solver. * gsl_multifit_fsolver_position: Iteration of the Minimization Algorithm. * gsl_multifit_fsolver_set: Initializing the Nonlinear Least-Squares Solver. * gsl_multifit_gradient: Search Stopping Parameters for Minimization Algorithms. * gsl_multifit_linear: Multi-parameter fitting. * gsl_multifit_linear_alloc: Multi-parameter fitting. * gsl_multifit_linear_est: Multi-parameter fitting. * gsl_multifit_linear_free: Multi-parameter fitting. * gsl_multifit_linear_svd: Multi-parameter fitting. * gsl_multifit_test_delta: Search Stopping Parameters for Minimization Algorithms. * gsl_multifit_test_gradient: Search Stopping Parameters for Minimization Algorithms. * gsl_multifit_wlinear: Multi-parameter fitting. * gsl_multifit_wlinear_svd: Multi-parameter fitting. * gsl_multimin_fdfminimizer_alloc: Initializing the Multidimensional Minimizer. * gsl_multimin_fdfminimizer_conjugate_fr: Multimin Algorithms. * gsl_multimin_fdfminimizer_conjugate_pr: Multimin Algorithms. * gsl_multimin_fdfminimizer_free: Initializing the Multidimensional Minimizer. * gsl_multimin_fdfminimizer_gradient: Multimin Iteration. * gsl_multimin_fdfminimizer_iterate: Multimin Iteration. * gsl_multimin_fdfminimizer_minimum: Multimin Iteration. * gsl_multimin_fdfminimizer_name: Initializing the Multidimensional Minimizer. * gsl_multimin_fdfminimizer_restart: Multimin Iteration. * gsl_multimin_fdfminimizer_set: Initializing the Multidimensional Minimizer. * gsl_multimin_fdfminimizer_steepest_descent: Multimin Algorithms. * gsl_multimin_fdfminimizer_vector_bfgs: Multimin Algorithms. * gsl_multimin_fdfminimizer_x: Multimin Iteration. * gsl_multimin_fminimizer_alloc: Initializing the Multidimensional Minimizer. * gsl_multimin_fminimizer_free: Initializing the Multidimensional Minimizer. * gsl_multimin_fminimizer_iterate: Multimin Iteration. * gsl_multimin_fminimizer_minimum: Multimin Iteration. * gsl_multimin_fminimizer_name: Initializing the Multidimensional Minimizer. * gsl_multimin_fminimizer_nmsimplex: Multimin Algorithms. * gsl_multimin_fminimizer_set: Initializing the Multidimensional Minimizer. * gsl_multimin_fminimizer_size: Multimin Iteration. * gsl_multimin_fminimizer_x: Multimin Iteration. * gsl_multimin_test_gradient: Multimin Stopping Criteria. * gsl_multimin_test_size: Multimin Stopping Criteria. * gsl_multiroot_fdfsolver_alloc: Initializing the Multidimensional Solver. * gsl_multiroot_fdfsolver_dx: Iteration of the multidimensional solver. * gsl_multiroot_fdfsolver_f: Iteration of the multidimensional solver. * gsl_multiroot_fdfsolver_free: Initializing the Multidimensional Solver. * gsl_multiroot_fdfsolver_gnewton: Algorithms using Derivatives. * gsl_multiroot_fdfsolver_hybridj: Algorithms using Derivatives. * gsl_multiroot_fdfsolver_hybridsj: Algorithms using Derivatives. * gsl_multiroot_fdfsolver_iterate: Iteration of the multidimensional solver. * gsl_multiroot_fdfsolver_name: Initializing the Multidimensional Solver. * gsl_multiroot_fdfsolver_newton: Algorithms using Derivatives. * gsl_multiroot_fdfsolver_root: Iteration of the multidimensional solver. * gsl_multiroot_fdfsolver_set: Initializing the Multidimensional Solver. * gsl_multiroot_fsolver_alloc: Initializing the Multidimensional Solver. * gsl_multiroot_fsolver_broyden: Algorithms without Derivatives. * gsl_multiroot_fsolver_dnewton: Algorithms without Derivatives. * gsl_multiroot_fsolver_dx: Iteration of the multidimensional solver. * gsl_multiroot_fsolver_f: Iteration of the multidimensional solver. * gsl_multiroot_fsolver_free: Initializing the Multidimensional Solver. * gsl_multiroot_fsolver_hybrid: Algorithms without Derivatives. * gsl_multiroot_fsolver_hybrids: Algorithms without Derivatives. * gsl_multiroot_fsolver_iterate: Iteration of the multidimensional solver. * gsl_multiroot_fsolver_name: Initializing the Multidimensional Solver. * gsl_multiroot_fsolver_root: Iteration of the multidimensional solver. * gsl_multiroot_fsolver_set: Initializing the Multidimensional Solver. * gsl_multiroot_test_delta: Search Stopping Parameters for the multidimensional solver. * gsl_multiroot_test_residual: Search Stopping Parameters for the multidimensional solver. * GSL_NAN: Infinities and Not-a-number. * GSL_NEGINF: Infinities and Not-a-number. * gsl_ntuple_bookdata: Writing ntuples. * gsl_ntuple_close: Closing an ntuple file. * gsl_ntuple_create: Creating ntuples. * gsl_ntuple_open: Opening an existing ntuple file. * gsl_ntuple_project: Histogramming ntuple values. * gsl_ntuple_read: Reading ntuples. * gsl_ntuple_write: Writing ntuples. * gsl_odeiv_control_alloc: Adaptive Step-size Control. * gsl_odeiv_control_free: Adaptive Step-size Control. * gsl_odeiv_control_hadjust: Adaptive Step-size Control. * gsl_odeiv_control_init: Adaptive Step-size Control. * gsl_odeiv_control_name: Adaptive Step-size Control. * gsl_odeiv_control_scaled_new: Adaptive Step-size Control. * gsl_odeiv_control_standard_new: Adaptive Step-size Control. * gsl_odeiv_control_y_new: Adaptive Step-size Control. * gsl_odeiv_control_yp_new: Adaptive Step-size Control. * gsl_odeiv_evolve_alloc: Evolution. * gsl_odeiv_evolve_apply: Evolution. * gsl_odeiv_evolve_free: Evolution. * gsl_odeiv_evolve_reset: Evolution. * gsl_odeiv_step_alloc: Stepping Functions. * gsl_odeiv_step_apply: Stepping Functions. * gsl_odeiv_step_bsimp: Stepping Functions. * gsl_odeiv_step_free: Stepping Functions. * gsl_odeiv_step_gear1: Stepping Functions. * gsl_odeiv_step_gear2: Stepping Functions. * gsl_odeiv_step_name: Stepping Functions. * gsl_odeiv_step_order: Stepping Functions. * gsl_odeiv_step_reset: Stepping Functions. * gsl_odeiv_step_rk2: Stepping Functions. * gsl_odeiv_step_rk2imp: Stepping Functions. * gsl_odeiv_step_rk4: Stepping Functions. * gsl_odeiv_step_rk4imp: Stepping Functions. * gsl_odeiv_step_rk8pd: Stepping Functions. * gsl_odeiv_step_rkck: Stepping Functions. * gsl_odeiv_step_rkf45: Stepping Functions. * gsl_permutation_alloc: Permutation allocation. * gsl_permutation_calloc: Permutation allocation. * gsl_permutation_canonical_cycles: Permutations in cyclic form. * gsl_permutation_canonical_to_linear: Permutations in cyclic form. * gsl_permutation_data: Permutation properties. * gsl_permutation_fprintf: Reading and writing permutations. * gsl_permutation_fread: Reading and writing permutations. * gsl_permutation_free: Permutation allocation. * gsl_permutation_fscanf: Reading and writing permutations. * gsl_permutation_fwrite: Reading and writing permutations. * gsl_permutation_get: Accessing permutation elements. * gsl_permutation_init: Permutation allocation. * gsl_permutation_inverse: Permutation functions. * gsl_permutation_inversions: Permutations in cyclic form. * gsl_permutation_linear_cycles: Permutations in cyclic form. * gsl_permutation_linear_to_canonical: Permutations in cyclic form. * gsl_permutation_memcpy: Permutation allocation. * gsl_permutation_mul: Applying Permutations. * gsl_permutation_next: Permutation functions. * gsl_permutation_prev: Permutation functions. * gsl_permutation_reverse: Permutation functions. * gsl_permutation_size: Permutation properties. * gsl_permutation_swap: Accessing permutation elements. * gsl_permutation_valid: Permutation properties. * gsl_permute: Applying Permutations. * gsl_permute_inverse: Applying Permutations. * gsl_permute_vector: Applying Permutations. * gsl_permute_vector_inverse: Applying Permutations. * gsl_poly_complex_solve: General Polynomial Equations. * gsl_poly_complex_solve_cubic: Cubic Equations. * gsl_poly_complex_solve_quadratic: Quadratic Equations. * gsl_poly_complex_workspace_alloc: General Polynomial Equations. * gsl_poly_complex_workspace_free: General Polynomial Equations. * gsl_poly_dd_eval: Divided Difference Representation of Polynomials. * gsl_poly_dd_init: Divided Difference Representation of Polynomials. * gsl_poly_dd_taylor: Divided Difference Representation of Polynomials. * gsl_poly_eval: Polynomial Evaluation. * gsl_poly_solve_cubic: Cubic Equations. * gsl_poly_solve_quadratic: Quadratic Equations. * GSL_POSINF: Infinities and Not-a-number. * gsl_pow_2: Small integer powers. * gsl_pow_3: Small integer powers. * gsl_pow_4: Small integer powers. * gsl_pow_5: Small integer powers. * gsl_pow_6: Small integer powers. * gsl_pow_7: Small integer powers. * gsl_pow_8: Small integer powers. * gsl_pow_9: Small integer powers. * gsl_pow_int: Small integer powers. * gsl_qrng_alloc: Quasi-random number generator initialization. * gsl_qrng_clone: Saving and resorting quasi-random number generator state. * gsl_qrng_free: Quasi-random number generator initialization. * gsl_qrng_get: Sampling from a quasi-random number generator. * gsl_qrng_init: Quasi-random number generator initialization. * gsl_qrng_memcpy: Saving and resorting quasi-random number generator state. * gsl_qrng_name: Auxiliary quasi-random number generator functions. * gsl_qrng_niederreiter_2: Quasi-random number generator algorithms. * gsl_qrng_size: Auxiliary quasi-random number generator functions. * gsl_qrng_sobol: Quasi-random number generator algorithms. * gsl_qrng_state: Auxiliary quasi-random number generator functions. * gsl_ran_bernoulli: The Bernoulli Distribution. * gsl_ran_bernoulli_pdf: The Bernoulli Distribution. * gsl_ran_beta: The Beta Distribution. * gsl_ran_beta_pdf: The Beta Distribution. * gsl_ran_binomial: The Binomial Distribution. * gsl_ran_binomial_pdf: The Binomial Distribution. * gsl_ran_bivariate_gaussian: The Bivariate Gaussian Distribution. * gsl_ran_bivariate_gaussian_pdf: The Bivariate Gaussian Distribution. * gsl_ran_cauchy: The Cauchy Distribution. * gsl_ran_cauchy_pdf: The Cauchy Distribution. * gsl_ran_chisq: The Chi-squared Distribution. * gsl_ran_chisq_pdf: The Chi-squared Distribution. * gsl_ran_choose: Shuffling and Sampling. * gsl_ran_dir_2d: Spherical Vector Distributions. * gsl_ran_dir_2d_trig_method: Spherical Vector Distributions. * gsl_ran_dir_3d: Spherical Vector Distributions. * gsl_ran_dir_nd: Spherical Vector Distributions. * gsl_ran_dirichlet: The Dirichlet Distribution. * gsl_ran_dirichlet_lnpdf: The Dirichlet Distribution. * gsl_ran_dirichlet_pdf: The Dirichlet Distribution. * gsl_ran_discrete: General Discrete Distributions. * gsl_ran_discrete_free: General Discrete Distributions. * gsl_ran_discrete_pdf: General Discrete Distributions. * gsl_ran_discrete_preproc: General Discrete Distributions. * gsl_ran_exponential: The Exponential Distribution. * gsl_ran_exponential_pdf: The Exponential Distribution. * gsl_ran_exppow: The Exponential Power Distribution. * gsl_ran_exppow_pdf: The Exponential Power Distribution. * gsl_ran_fdist: The F-distribution. * gsl_ran_fdist_pdf: The F-distribution. * gsl_ran_flat: The Flat (Uniform) Distribution. * gsl_ran_flat_pdf: The Flat (Uniform) Distribution. * gsl_ran_gamma: The Gamma Distribution. * gsl_ran_gamma_mt: The Gamma Distribution. * gsl_ran_gamma_pdf: The Gamma Distribution. * gsl_ran_gaussian: The Gaussian Distribution. * gsl_ran_gaussian_pdf: The Gaussian Distribution. * gsl_ran_gaussian_ratio_method: The Gaussian Distribution. * gsl_ran_gaussian_tail: The Gaussian Tail Distribution. * gsl_ran_gaussian_tail_pdf: The Gaussian Tail Distribution. * gsl_ran_gaussian_ziggurat: The Gaussian Distribution. * gsl_ran_geometric: The Geometric Distribution. * gsl_ran_geometric_pdf: The Geometric Distribution. * gsl_ran_gumbel1: The Type-1 Gumbel Distribution. * gsl_ran_gumbel1_pdf: The Type-1 Gumbel Distribution. * gsl_ran_gumbel2: The Type-2 Gumbel Distribution. * gsl_ran_gumbel2_pdf: The Type-2 Gumbel Distribution. * gsl_ran_hypergeometric: The Hypergeometric Distribution. * gsl_ran_hypergeometric_pdf: The Hypergeometric Distribution. * gsl_ran_landau: The Landau Distribution. * gsl_ran_landau_pdf: The Landau Distribution. * gsl_ran_laplace: The Laplace Distribution. * gsl_ran_laplace_pdf: The Laplace Distribution. * gsl_ran_levy: The Levy alpha-Stable Distributions. * gsl_ran_levy_skew: The Levy skew alpha-Stable Distribution. * gsl_ran_logarithmic: The Logarithmic Distribution. * gsl_ran_logarithmic_pdf: The Logarithmic Distribution. * gsl_ran_logistic: The Logistic Distribution. * gsl_ran_logistic_pdf: The Logistic Distribution. * gsl_ran_lognormal: The Lognormal Distribution. * gsl_ran_lognormal_pdf: The Lognormal Distribution. * gsl_ran_multinomial: The Multinomial Distribution. * gsl_ran_multinomial_lnpdf: The Multinomial Distribution. * gsl_ran_multinomial_pdf: The Multinomial Distribution. * gsl_ran_negative_binomial: The Negative Binomial Distribution. * gsl_ran_negative_binomial_pdf: The Negative Binomial Distribution. * gsl_ran_pareto: The Pareto Distribution. * gsl_ran_pareto_pdf: The Pareto Distribution. * gsl_ran_pascal: The Pascal Distribution. * gsl_ran_pascal_pdf: The Pascal Distribution. * gsl_ran_poisson: The Poisson Distribution. * gsl_ran_poisson_pdf: The Poisson Distribution. * gsl_ran_rayleigh: The Rayleigh Distribution. * gsl_ran_rayleigh_pdf: The Rayleigh Distribution. * gsl_ran_rayleigh_tail: The Rayleigh Tail Distribution. * gsl_ran_rayleigh_tail_pdf: The Rayleigh Tail Distribution. * gsl_ran_sample: Shuffling and Sampling. * gsl_ran_shuffle: Shuffling and Sampling. * gsl_ran_tdist: The t-distribution. * gsl_ran_tdist_pdf: The t-distribution. * gsl_ran_ugaussian: The Gaussian Distribution. * gsl_ran_ugaussian_pdf: The Gaussian Distribution. * gsl_ran_ugaussian_ratio_method: The Gaussian Distribution. * gsl_ran_ugaussian_tail: The Gaussian Tail Distribution. * gsl_ran_ugaussian_tail_pdf: The Gaussian Tail Distribution. * gsl_ran_weibull: The Weibull Distribution. * gsl_ran_weibull_pdf: The Weibull Distribution. * GSL_REAL: Complex numbers. * gsl_rng_alloc: Random number generator initialization. * gsl_rng_borosh13: Other random number generators. * gsl_rng_clone: Copying random number generator state. * gsl_rng_cmrg: Random number generator algorithms. * gsl_rng_coveyou: Other random number generators. * gsl_rng_env_setup: Random number environment variables. * gsl_rng_fishman18: Other random number generators. * gsl_rng_fishman20: Other random number generators. * gsl_rng_fishman2x: Other random number generators. * gsl_rng_fread: Reading and writing random number generator state. * gsl_rng_free: Random number generator initialization. * gsl_rng_fwrite: Reading and writing random number generator state. * gsl_rng_get: Sampling from a random number generator. * gsl_rng_gfsr4: Random number generator algorithms. * gsl_rng_knuthran: Other random number generators. * gsl_rng_knuthran2: Other random number generators. * gsl_rng_lecuyer21: Other random number generators. * gsl_rng_max: Auxiliary random number generator functions. * gsl_rng_memcpy: Copying random number generator state. * gsl_rng_min: Auxiliary random number generator functions. * gsl_rng_minstd: Other random number generators. * gsl_rng_mrg: Random number generator algorithms. * gsl_rng_mt19937: Random number generator algorithms. * gsl_rng_name: Auxiliary random number generator functions. * gsl_rng_r250: Other random number generators. * gsl_rng_rand: Unix random number generators. * gsl_rng_rand48: Unix random number generators. * gsl_rng_random_bsd: Unix random number generators. * gsl_rng_random_glibc2: Unix random number generators. * gsl_rng_random_libc5: Unix random number generators. * gsl_rng_randu: Other random number generators. * gsl_rng_ranf: Other random number generators. * gsl_rng_ranlux: Random number generator algorithms. * gsl_rng_ranlux389: Random number generator algorithms. * gsl_rng_ranlxd1: Random number generator algorithms. * gsl_rng_ranlxd2: Random number generator algorithms. * gsl_rng_ranlxs0: Random number generator algorithms. * gsl_rng_ranlxs1: Random number generator algorithms. * gsl_rng_ranlxs2: Random number generator algorithms. * gsl_rng_ranmar: Other random number generators. * gsl_rng_set: Random number generator initialization. * gsl_rng_size: Auxiliary random number generator functions. * gsl_rng_slatec: Other random number generators. * gsl_rng_state: Auxiliary random number generator functions. * gsl_rng_taus: Random number generator algorithms. * gsl_rng_taus2: Random number generator algorithms. * gsl_rng_transputer: Other random number generators. * gsl_rng_tt800: Other random number generators. * gsl_rng_types_setup: Auxiliary random number generator functions. * gsl_rng_uni: Other random number generators. * gsl_rng_uni32: Other random number generators. * gsl_rng_uniform: Sampling from a random number generator. * gsl_rng_uniform_int: Sampling from a random number generator. * gsl_rng_uniform_pos: Sampling from a random number generator. * gsl_rng_vax: Other random number generators. * gsl_rng_waterman14: Other random number generators. * gsl_rng_zuf: Other random number generators. * gsl_root_fdfsolver_alloc: Initializing the Solver. * gsl_root_fdfsolver_free: Initializing the Solver. * gsl_root_fdfsolver_iterate: Root Finding Iteration. * gsl_root_fdfsolver_name: Initializing the Solver. * gsl_root_fdfsolver_newton: Root Finding Algorithms using Derivatives. * gsl_root_fdfsolver_root: Root Finding Iteration. * gsl_root_fdfsolver_secant: Root Finding Algorithms using Derivatives. * gsl_root_fdfsolver_set: Initializing the Solver. * gsl_root_fdfsolver_steffenson: Root Finding Algorithms using Derivatives. * gsl_root_fsolver_alloc: Initializing the Solver. * gsl_root_fsolver_bisection: Root Bracketing Algorithms. * gsl_root_fsolver_brent: Root Bracketing Algorithms. * gsl_root_fsolver_falsepos: Root Bracketing Algorithms. * gsl_root_fsolver_free: Initializing the Solver. * gsl_root_fsolver_iterate: Root Finding Iteration. * gsl_root_fsolver_name: Initializing the Solver. * gsl_root_fsolver_root: Root Finding Iteration. * gsl_root_fsolver_set: Initializing the Solver. * gsl_root_fsolver_x_lower: Root Finding Iteration. * gsl_root_fsolver_x_upper: Root Finding Iteration. * gsl_root_test_delta: Search Stopping Parameters. * gsl_root_test_interval: Search Stopping Parameters. * gsl_root_test_residual: Search Stopping Parameters. * GSL_SET_COMPLEX: Complex numbers. * gsl_set_error_handler: Error Handlers. * gsl_set_error_handler_off: Error Handlers. * GSL_SET_IMAG: Complex numbers. * GSL_SET_REAL: Complex numbers. * gsl_sf_airy_Ai: Airy Functions. * gsl_sf_airy_Ai_deriv: Derivatives of Airy Functions. * gsl_sf_airy_Ai_deriv_e: Derivatives of Airy Functions. * gsl_sf_airy_Ai_deriv_scaled: Derivatives of Airy Functions. * gsl_sf_airy_Ai_deriv_scaled_e: Derivatives of Airy Functions. * gsl_sf_airy_Ai_e: Airy Functions. * gsl_sf_airy_Ai_scaled: Airy Functions. * gsl_sf_airy_Ai_scaled_e: Airy Functions. * gsl_sf_airy_Bi: Airy Functions. * gsl_sf_airy_Bi_deriv: Derivatives of Airy Functions. * gsl_sf_airy_Bi_deriv_e: Derivatives of Airy Functions. * gsl_sf_airy_Bi_deriv_scaled: Derivatives of Airy Functions. * gsl_sf_airy_Bi_deriv_scaled_e: Derivatives of Airy Functions. * gsl_sf_airy_Bi_e: Airy Functions. * gsl_sf_airy_Bi_scaled: Airy Functions. * gsl_sf_airy_Bi_scaled_e: Airy Functions. * gsl_sf_airy_zero_Ai: Zeros of Airy Functions. * gsl_sf_airy_zero_Ai_deriv: Zeros of Derivatives of Airy Functions. * gsl_sf_airy_zero_Ai_deriv_e: Zeros of Derivatives of Airy Functions. * gsl_sf_airy_zero_Ai_e: Zeros of Airy Functions. * gsl_sf_airy_zero_Bi: Zeros of Airy Functions. * gsl_sf_airy_zero_Bi_deriv: Zeros of Derivatives of Airy Functions. * gsl_sf_airy_zero_Bi_deriv_e: Zeros of Derivatives of Airy Functions. * gsl_sf_airy_zero_Bi_e: Zeros of Airy Functions. * gsl_sf_angle_restrict_pos: Restriction Functions. * gsl_sf_angle_restrict_pos_e: Restriction Functions. * gsl_sf_angle_restrict_symm: Restriction Functions. * gsl_sf_angle_restrict_symm_e: Restriction Functions. * gsl_sf_atanint: Arctangent Integral. * gsl_sf_atanint_e: Arctangent Integral. * gsl_sf_bessel_I0: Regular Modified Cylindrical Bessel Functions. * gsl_sf_bessel_I0_e: Regular Modified Cylindrical Bessel Functions. * gsl_sf_bessel_i0_scaled: Regular Modified Spherical Bessel Functions. * gsl_sf_bessel_I0_scaled: Regular Modified Cylindrical Bessel Functions. * gsl_sf_bessel_i0_scaled_e: Regular Modified Spherical Bessel Functions. * gsl_sf_bessel_I0_scaled_e: Regular Modified Cylindrical Bessel Functions. * gsl_sf_bessel_I1: Regular Modified Cylindrical Bessel Functions. * gsl_sf_bessel_I1_e: Regular Modified Cylindrical Bessel Functions. * gsl_sf_bessel_i1_scaled: Regular Modified Spherical Bessel Functions. * gsl_sf_bessel_I1_scaled: Regular Modified Cylindrical Bessel Functions. * gsl_sf_bessel_i1_scaled_e: Regular Modified Spherical Bessel Functions. * gsl_sf_bessel_I1_scaled_e: Regular Modified Cylindrical Bessel Functions. * gsl_sf_bessel_i2_scaled: Regular Modified Spherical Bessel Functions. * gsl_sf_bessel_i2_scaled_e: Regular Modified Spherical Bessel Functions. * gsl_sf_bessel_il_scaled: Regular Modified Spherical Bessel Functions. * gsl_sf_bessel_il_scaled_array: Regular Modified Spherical Bessel Functions. * gsl_sf_bessel_il_scaled_e: Regular Modified Spherical Bessel Functions. * gsl_sf_bessel_In: Regular Modified Cylindrical Bessel Functions. * gsl_sf_bessel_In_array: Regular Modified Cylindrical Bessel Functions. * gsl_sf_bessel_In_e: Regular Modified Cylindrical Bessel Functions. * gsl_sf_bessel_In_scaled: Regular Modified Cylindrical Bessel Functions. * gsl_sf_bessel_In_scaled_array: Regular Modified Cylindrical Bessel Functions. * gsl_sf_bessel_In_scaled_e: Regular Modified Cylindrical Bessel Functions. * gsl_sf_bessel_Inu: Regular Modified Bessel Functions - Fractional Order. * gsl_sf_bessel_Inu_e: Regular Modified Bessel Functions - Fractional Order. * gsl_sf_bessel_Inu_scaled: Regular Modified Bessel Functions - Fractional Order. * gsl_sf_bessel_Inu_scaled_e: Regular Modified Bessel Functions - Fractional Order. * gsl_sf_bessel_j0: Regular Spherical Bessel Functions. * gsl_sf_bessel_J0: Regular Cylindrical Bessel Functions. * gsl_sf_bessel_j0_e: Regular Spherical Bessel Functions. * gsl_sf_bessel_J0_e: Regular Cylindrical Bessel Functions. * gsl_sf_bessel_j1: Regular Spherical Bessel Functions. * gsl_sf_bessel_J1: Regular Cylindrical Bessel Functions. * gsl_sf_bessel_j1_e: Regular Spherical Bessel Functions. * gsl_sf_bessel_J1_e: Regular Cylindrical Bessel Functions. * gsl_sf_bessel_j2: Regular Spherical Bessel Functions. * gsl_sf_bessel_j2_e: Regular Spherical Bessel Functions. * gsl_sf_bessel_jl: Regular Spherical Bessel Functions. * gsl_sf_bessel_jl_array: Regular Spherical Bessel Functions. * gsl_sf_bessel_jl_e: Regular Spherical Bessel Functions. * gsl_sf_bessel_jl_steed_array: Regular Spherical Bessel Functions. * gsl_sf_bessel_Jn: Regular Cylindrical Bessel Functions. * gsl_sf_bessel_Jn_array: Regular Cylindrical Bessel Functions. * gsl_sf_bessel_Jn_e: Regular Cylindrical Bessel Functions. * gsl_sf_bessel_Jnu: Regular Bessel Function - Fractional Order. * gsl_sf_bessel_Jnu_e: Regular Bessel Function - Fractional Order. * gsl_sf_bessel_K0: Irregular Modified Cylindrical Bessel Functions. * gsl_sf_bessel_K0_e: Irregular Modified Cylindrical Bessel Functions. * gsl_sf_bessel_k0_scaled: Irregular Modified Spherical Bessel Functions. * gsl_sf_bessel_K0_scaled: Irregular Modified Cylindrical Bessel Functions. * gsl_sf_bessel_k0_scaled_e: Irregular Modified Spherical Bessel Functions. * gsl_sf_bessel_K0_scaled_e: Irregular Modified Cylindrical Bessel Functions. * gsl_sf_bessel_K1: Irregular Modified Cylindrical Bessel Functions. * gsl_sf_bessel_K1_e: Irregular Modified Cylindrical Bessel Functions. * gsl_sf_bessel_k1_scaled: Irregular Modified Spherical Bessel Functions. * gsl_sf_bessel_K1_scaled: Irregular Modified Cylindrical Bessel Functions. * gsl_sf_bessel_k1_scaled_e: Irregular Modified Spherical Bessel Functions. * gsl_sf_bessel_K1_scaled_e: Irregular Modified Cylindrical Bessel Functions. * gsl_sf_bessel_k2_scaled: Irregular Modified Spherical Bessel Functions. * gsl_sf_bessel_k2_scaled_e: Irregular Modified Spherical Bessel Functions. * gsl_sf_bessel_kl_scaled: Irregular Modified Spherical Bessel Functions. * gsl_sf_bessel_kl_scaled_array: Irregular Modified Spherical Bessel Functions. * gsl_sf_bessel_kl_scaled_e: Irregular Modified Spherical Bessel Functions. * gsl_sf_bessel_Kn: Irregular Modified Cylindrical Bessel Functions. * gsl_sf_bessel_Kn_array: Irregular Modified Cylindrical Bessel Functions. * gsl_sf_bessel_Kn_e: Irregular Modified Cylindrical Bessel Functions. * gsl_sf_bessel_Kn_scaled: Irregular Modified Cylindrical Bessel Functions. * gsl_sf_bessel_Kn_scaled_array: Irregular Modified Cylindrical Bessel Functions. * gsl_sf_bessel_Kn_scaled_e: Irregular Modified Cylindrical Bessel Functions. * gsl_sf_bessel_Knu: Irregular Modified Bessel Functions - Fractional Order. * gsl_sf_bessel_Knu_e: Irregular Modified Bessel Functions - Fractional Order. * gsl_sf_bessel_Knu_scaled: Irregular Modified Bessel Functions - Fractional Order. * gsl_sf_bessel_Knu_scaled_e: Irregular Modified Bessel Functions - Fractional Order. * gsl_sf_bessel_lnKnu: Irregular Modified Bessel Functions - Fractional Order. * gsl_sf_bessel_lnKnu_e: Irregular Modified Bessel Functions - Fractional Order. * gsl_sf_bessel_sequence_Jnu_e: Regular Bessel Function - Fractional Order. * gsl_sf_bessel_y0: Irregular Spherical Bessel Functions. * gsl_sf_bessel_Y0: Irregular Cylindrical Bessel Functions. * gsl_sf_bessel_y0_e: Irregular Spherical Bessel Functions. * gsl_sf_bessel_Y0_e: Irregular Cylindrical Bessel Functions. * gsl_sf_bessel_y1: Irregular Spherical Bessel Functions. * gsl_sf_bessel_Y1: Irregular Cylindrical Bessel Functions. * gsl_sf_bessel_y1_e: Irregular Spherical Bessel Functions. * gsl_sf_bessel_Y1_e: Irregular Cylindrical Bessel Functions. * gsl_sf_bessel_y2: Irregular Spherical Bessel Functions. * gsl_sf_bessel_y2_e: Irregular Spherical Bessel Functions. * gsl_sf_bessel_yl: Irregular Spherical Bessel Functions. * gsl_sf_bessel_yl_array: Irregular Spherical Bessel Functions. * gsl_sf_bessel_yl_e: Irregular Spherical Bessel Functions. * gsl_sf_bessel_Yn: Irregular Cylindrical Bessel Functions. * gsl_sf_bessel_Yn_array: Irregular Cylindrical Bessel Functions. * gsl_sf_bessel_Yn_e: Irregular Cylindrical Bessel Functions. * gsl_sf_bessel_Ynu: Irregular Bessel Functions - Fractional Order. * gsl_sf_bessel_Ynu_e: Irregular Bessel Functions - Fractional Order. * gsl_sf_bessel_zero_J0: Zeros of Regular Bessel Functions. * gsl_sf_bessel_zero_J0_e: Zeros of Regular Bessel Functions. * gsl_sf_bessel_zero_J1: Zeros of Regular Bessel Functions. * gsl_sf_bessel_zero_J1_e: Zeros of Regular Bessel Functions. * gsl_sf_bessel_zero_Jnu: Zeros of Regular Bessel Functions. * gsl_sf_bessel_zero_Jnu_e: Zeros of Regular Bessel Functions. * gsl_sf_beta: Beta Functions. * gsl_sf_beta_e: Beta Functions. * gsl_sf_beta_inc: Incomplete Beta Function. * gsl_sf_beta_inc_e: Incomplete Beta Function. * gsl_sf_Chi: Hyperbolic Integrals. * gsl_sf_Chi_e: Hyperbolic Integrals. * gsl_sf_choose: Factorials. * gsl_sf_choose_e: Factorials. * gsl_sf_Ci: Trigonometric Integrals. * gsl_sf_Ci_e: Trigonometric Integrals. * gsl_sf_clausen: Clausen Functions. * gsl_sf_clausen_e: Clausen Functions. * gsl_sf_complex_cos_e: Trigonometric Functions for Complex Arguments. * gsl_sf_complex_dilog_e: Complex Argument. * gsl_sf_complex_log_e: Logarithm and Related Functions. * gsl_sf_complex_logsin_e: Trigonometric Functions for Complex Arguments. * gsl_sf_complex_sin_e: Trigonometric Functions for Complex Arguments. * gsl_sf_conicalP_0: Conical Functions. * gsl_sf_conicalP_0_e: Conical Functions. * gsl_sf_conicalP_1: Conical Functions. * gsl_sf_conicalP_1_e: Conical Functions. * gsl_sf_conicalP_cyl_reg: Conical Functions. * gsl_sf_conicalP_cyl_reg_e: Conical Functions. * gsl_sf_conicalP_half: Conical Functions. * gsl_sf_conicalP_half_e: Conical Functions. * gsl_sf_conicalP_mhalf: Conical Functions. * gsl_sf_conicalP_mhalf_e: Conical Functions. * gsl_sf_conicalP_sph_reg: Conical Functions. * gsl_sf_conicalP_sph_reg_e: Conical Functions. * gsl_sf_cos: Circular Trigonometric Functions. * gsl_sf_cos_e: Circular Trigonometric Functions. * gsl_sf_cos_err_e: Trigonometric Functions With Error Estimates. * gsl_sf_coulomb_CL_array: Coulomb Wave Function Normalization Constant. * gsl_sf_coulomb_CL_e: Coulomb Wave Function Normalization Constant. * gsl_sf_coulomb_wave_F_array: Coulomb Wave Functions. * gsl_sf_coulomb_wave_FG_array: Coulomb Wave Functions. * gsl_sf_coulomb_wave_FG_e: Coulomb Wave Functions. * gsl_sf_coulomb_wave_FGp_array: Coulomb Wave Functions. * gsl_sf_coulomb_wave_sphF_array: Coulomb Wave Functions. * gsl_sf_coupling_3j: 3-j Symbols. * gsl_sf_coupling_3j_e: 3-j Symbols. * gsl_sf_coupling_6j: 6-j Symbols. * gsl_sf_coupling_6j_e: 6-j Symbols. * gsl_sf_coupling_9j: 9-j Symbols. * gsl_sf_coupling_9j_e: 9-j Symbols. * gsl_sf_dawson: Dawson Function. * gsl_sf_dawson_e: Dawson Function. * gsl_sf_debye_1: Debye Functions. * gsl_sf_debye_1_e: Debye Functions. * gsl_sf_debye_2: Debye Functions. * gsl_sf_debye_2_e: Debye Functions. * gsl_sf_debye_3: Debye Functions. * gsl_sf_debye_3_e: Debye Functions. * gsl_sf_debye_4: Debye Functions. * gsl_sf_debye_4_e: Debye Functions. * gsl_sf_debye_5: Debye Functions. * gsl_sf_debye_5_e: Debye Functions. * gsl_sf_debye_6: Debye Functions. * gsl_sf_debye_6_e: Debye Functions. * gsl_sf_dilog: Real Argument. * gsl_sf_dilog_e: Real Argument. * gsl_sf_doublefact: Factorials. * gsl_sf_doublefact_e: Factorials. * gsl_sf_ellint_D: Legendre Form of Incomplete Elliptic Integrals. * gsl_sf_ellint_D_e: Legendre Form of Incomplete Elliptic Integrals. * gsl_sf_ellint_E: Legendre Form of Incomplete Elliptic Integrals. * gsl_sf_ellint_E_e: Legendre Form of Incomplete Elliptic Integrals. * gsl_sf_ellint_Ecomp: Legendre Form of Complete Elliptic Integrals. * gsl_sf_ellint_Ecomp_e: Legendre Form of Complete Elliptic Integrals. * gsl_sf_ellint_F: Legendre Form of Incomplete Elliptic Integrals. * gsl_sf_ellint_F_e: Legendre Form of Incomplete Elliptic Integrals. * gsl_sf_ellint_Kcomp: Legendre Form of Complete Elliptic Integrals. * gsl_sf_ellint_Kcomp_e: Legendre Form of Complete Elliptic Integrals. * gsl_sf_ellint_P: Legendre Form of Incomplete Elliptic Integrals. * gsl_sf_ellint_P_e: Legendre Form of Incomplete Elliptic Integrals. * gsl_sf_ellint_RC: Carlson Forms. * gsl_sf_ellint_RC_e: Carlson Forms. * gsl_sf_ellint_RD: Carlson Forms. * gsl_sf_ellint_RD_e: Carlson Forms. * gsl_sf_ellint_RF: Carlson Forms. * gsl_sf_ellint_RF_e: Carlson Forms. * gsl_sf_ellint_RJ: Carlson Forms. * gsl_sf_ellint_RJ_e: Carlson Forms. * gsl_sf_elljac_e: Elliptic Functions (Jacobi). * gsl_sf_erf: Error Function. * gsl_sf_erf_e: Error Function. * gsl_sf_erf_Q: Probability functions. * gsl_sf_erf_Q_e: Probability functions. * gsl_sf_erf_Z: Probability functions. * gsl_sf_erf_Z_e: Probability functions. * gsl_sf_erfc: Complementary Error Function. * gsl_sf_erfc_e: Complementary Error Function. * gsl_sf_eta: Eta Function. * gsl_sf_eta_e: Eta Function. * gsl_sf_eta_int: Eta Function. * gsl_sf_eta_int_e: Eta Function. * gsl_sf_exp: Exponential Function. * gsl_sf_exp_e: Exponential Function. * gsl_sf_exp_e10_e: Exponential Function. * gsl_sf_exp_err_e: Exponentiation With Error Estimate. * gsl_sf_exp_err_e10_e: Exponentiation With Error Estimate. * gsl_sf_exp_mult: Exponential Function. * gsl_sf_exp_mult_e: Exponential Function. * gsl_sf_exp_mult_e10_e: Exponential Function. * gsl_sf_exp_mult_err_e: Exponentiation With Error Estimate. * gsl_sf_exp_mult_err_e10_e: Exponentiation With Error Estimate. * gsl_sf_expint_3: Ei_3(x). * gsl_sf_expint_3_e: Ei_3(x). * gsl_sf_expint_E1: Exponential Integral. * gsl_sf_expint_E1_e: Exponential Integral. * gsl_sf_expint_E2: Exponential Integral. * gsl_sf_expint_E2_e: Exponential Integral. * gsl_sf_expint_Ei: Ei(x). * gsl_sf_expint_Ei_e: Ei(x). * gsl_sf_expm1: Relative Exponential Functions. * gsl_sf_expm1_e: Relative Exponential Functions. * gsl_sf_exprel: Relative Exponential Functions. * gsl_sf_exprel_2: Relative Exponential Functions. * gsl_sf_exprel_2_e: Relative Exponential Functions. * gsl_sf_exprel_e: Relative Exponential Functions. * gsl_sf_exprel_n: Relative Exponential Functions. * gsl_sf_exprel_n_e: Relative Exponential Functions. * gsl_sf_fact: Factorials. * gsl_sf_fact_e: Factorials. * gsl_sf_fermi_dirac_0: Complete Fermi-Dirac Integrals. * gsl_sf_fermi_dirac_0_e: Complete Fermi-Dirac Integrals. * gsl_sf_fermi_dirac_1: Complete Fermi-Dirac Integrals. * gsl_sf_fermi_dirac_1_e: Complete Fermi-Dirac Integrals. * gsl_sf_fermi_dirac_2: Complete Fermi-Dirac Integrals. * gsl_sf_fermi_dirac_2_e: Complete Fermi-Dirac Integrals. * gsl_sf_fermi_dirac_3half: Complete Fermi-Dirac Integrals. * gsl_sf_fermi_dirac_3half_e: Complete Fermi-Dirac Integrals. * gsl_sf_fermi_dirac_half: Complete Fermi-Dirac Integrals. * gsl_sf_fermi_dirac_half_e: Complete Fermi-Dirac Integrals. * gsl_sf_fermi_dirac_inc_0: Incomplete Fermi-Dirac Integrals. * gsl_sf_fermi_dirac_inc_0_e: Incomplete Fermi-Dirac Integrals. * gsl_sf_fermi_dirac_int: Complete Fermi-Dirac Integrals. * gsl_sf_fermi_dirac_int_e: Complete Fermi-Dirac Integrals. * gsl_sf_fermi_dirac_m1: Complete Fermi-Dirac Integrals. * gsl_sf_fermi_dirac_m1_e: Complete Fermi-Dirac Integrals. * gsl_sf_fermi_dirac_mhalf: Complete Fermi-Dirac Integrals. * gsl_sf_fermi_dirac_mhalf_e: Complete Fermi-Dirac Integrals. * gsl_sf_gamma: Gamma Functions. * gsl_sf_gamma_e: Gamma Functions. * gsl_sf_gamma_inc: Incomplete Gamma Functions. * gsl_sf_gamma_inc_e: Incomplete Gamma Functions. * gsl_sf_gamma_inc_P: Incomplete Gamma Functions. * gsl_sf_gamma_inc_P_e: Incomplete Gamma Functions. * gsl_sf_gamma_inc_Q: Incomplete Gamma Functions. * gsl_sf_gamma_inc_Q_e: Incomplete Gamma Functions. * gsl_sf_gammainv: Gamma Functions. * gsl_sf_gammainv_e: Gamma Functions. * gsl_sf_gammastar: Gamma Functions. * gsl_sf_gammastar_e: Gamma Functions. * gsl_sf_gegenpoly_1: Gegenbauer Functions. * gsl_sf_gegenpoly_1_e: Gegenbauer Functions. * gsl_sf_gegenpoly_2: Gegenbauer Functions. * gsl_sf_gegenpoly_2_e: Gegenbauer Functions. * gsl_sf_gegenpoly_3: Gegenbauer Functions. * gsl_sf_gegenpoly_3_e: Gegenbauer Functions. * gsl_sf_gegenpoly_array: Gegenbauer Functions. * gsl_sf_gegenpoly_n: Gegenbauer Functions. * gsl_sf_gegenpoly_n_e: Gegenbauer Functions. * gsl_sf_hazard: Probability functions. * gsl_sf_hazard_e: Probability functions. * gsl_sf_hydrogenicR: Normalized Hydrogenic Bound States. * gsl_sf_hydrogenicR_1: Normalized Hydrogenic Bound States. * gsl_sf_hydrogenicR_1_e: Normalized Hydrogenic Bound States. * gsl_sf_hydrogenicR_e: Normalized Hydrogenic Bound States. * gsl_sf_hyperg_0F1: Hypergeometric Functions. * gsl_sf_hyperg_0F1_e: Hypergeometric Functions. * gsl_sf_hyperg_1F1: Hypergeometric Functions. * gsl_sf_hyperg_1F1_e: Hypergeometric Functions. * gsl_sf_hyperg_1F1_int: Hypergeometric Functions. * gsl_sf_hyperg_1F1_int_e: Hypergeometric Functions. * gsl_sf_hyperg_2F0: Hypergeometric Functions. * gsl_sf_hyperg_2F0_e: Hypergeometric Functions. * gsl_sf_hyperg_2F1: Hypergeometric Functions. * gsl_sf_hyperg_2F1_conj: Hypergeometric Functions. * gsl_sf_hyperg_2F1_conj_e: Hypergeometric Functions. * gsl_sf_hyperg_2F1_conj_renorm: Hypergeometric Functions. * gsl_sf_hyperg_2F1_conj_renorm_e: Hypergeometric Functions. * gsl_sf_hyperg_2F1_e: Hypergeometric Functions. * gsl_sf_hyperg_2F1_renorm: Hypergeometric Functions. * gsl_sf_hyperg_2F1_renorm_e: Hypergeometric Functions. * gsl_sf_hyperg_U: Hypergeometric Functions. * gsl_sf_hyperg_U_e: Hypergeometric Functions. * gsl_sf_hyperg_U_e10_e: Hypergeometric Functions. * gsl_sf_hyperg_U_int: Hypergeometric Functions. * gsl_sf_hyperg_U_int_e: Hypergeometric Functions. * gsl_sf_hyperg_U_int_e10_e: Hypergeometric Functions. * gsl_sf_hypot: Circular Trigonometric Functions. * gsl_sf_hypot_e: Circular Trigonometric Functions. * gsl_sf_hzeta: Hurwitz Zeta Function. * gsl_sf_hzeta_e: Hurwitz Zeta Function. * gsl_sf_laguerre_1: Laguerre Functions. * gsl_sf_laguerre_1_e: Laguerre Functions. * gsl_sf_laguerre_2: Laguerre Functions. * gsl_sf_laguerre_2_e: Laguerre Functions. * gsl_sf_laguerre_3: Laguerre Functions. * gsl_sf_laguerre_3_e: Laguerre Functions. * gsl_sf_laguerre_n: Laguerre Functions. * gsl_sf_laguerre_n_e: Laguerre Functions. * gsl_sf_lambert_W0: Lambert W Functions. * gsl_sf_lambert_W0_e: Lambert W Functions. * gsl_sf_lambert_Wm1: Lambert W Functions. * gsl_sf_lambert_Wm1_e: Lambert W Functions. * gsl_sf_legendre_array_size: Associated Legendre Polynomials and Spherical Harmonics. * gsl_sf_legendre_H3d: Radial Functions for Hyperbolic Space. * gsl_sf_legendre_H3d_0: Radial Functions for Hyperbolic Space. * gsl_sf_legendre_H3d_0_e: Radial Functions for Hyperbolic Space. * gsl_sf_legendre_H3d_1: Radial Functions for Hyperbolic Space. * gsl_sf_legendre_H3d_1_e: Radial Functions for Hyperbolic Space. * gsl_sf_legendre_H3d_array: Radial Functions for Hyperbolic Space. * gsl_sf_legendre_H3d_e: Radial Functions for Hyperbolic Space. * gsl_sf_legendre_P1: Legendre Polynomials. * gsl_sf_legendre_P1_e: Legendre Polynomials. * gsl_sf_legendre_P2: Legendre Polynomials. * gsl_sf_legendre_P2_e: Legendre Polynomials. * gsl_sf_legendre_P3: Legendre Polynomials. * gsl_sf_legendre_P3_e: Legendre Polynomials. * gsl_sf_legendre_Pl: Legendre Polynomials. * gsl_sf_legendre_Pl_array: Legendre Polynomials. * gsl_sf_legendre_Pl_deriv_array: Legendre Polynomials. * gsl_sf_legendre_Pl_e: Legendre Polynomials. * gsl_sf_legendre_Plm: Associated Legendre Polynomials and Spherical Harmonics. * gsl_sf_legendre_Plm_array: Associated Legendre Polynomials and Spherical Harmonics. * gsl_sf_legendre_Plm_deriv_array: Associated Legendre Polynomials and Spherical Harmonics. * gsl_sf_legendre_Plm_e: Associated Legendre Polynomials and Spherical Harmonics. * gsl_sf_legendre_Q0: Legendre Polynomials. * gsl_sf_legendre_Q0_e: Legendre Polynomials. * gsl_sf_legendre_Q1: Legendre Polynomials. * gsl_sf_legendre_Q1_e: Legendre Polynomials. * gsl_sf_legendre_Ql: Legendre Polynomials. * gsl_sf_legendre_Ql_e: Legendre Polynomials. * gsl_sf_legendre_sphPlm: Associated Legendre Polynomials and Spherical Harmonics. * gsl_sf_legendre_sphPlm_array: Associated Legendre Polynomials and Spherical Harmonics. * gsl_sf_legendre_sphPlm_deriv_array: Associated Legendre Polynomials and Spherical Harmonics. * gsl_sf_legendre_sphPlm_e: Associated Legendre Polynomials and Spherical Harmonics. * gsl_sf_lnbeta: Beta Functions. * gsl_sf_lnbeta_e: Beta Functions. * gsl_sf_lnchoose: Factorials. * gsl_sf_lnchoose_e: Factorials. * gsl_sf_lncosh: Hyperbolic Trigonometric Functions. * gsl_sf_lncosh_e: Hyperbolic Trigonometric Functions. * gsl_sf_lndoublefact: Factorials. * gsl_sf_lndoublefact_e: Factorials. * gsl_sf_lnfact: Factorials. * gsl_sf_lnfact_e: Factorials. * gsl_sf_lngamma: Gamma Functions. * gsl_sf_lngamma_complex_e: Gamma Functions. * gsl_sf_lngamma_e: Gamma Functions. * gsl_sf_lngamma_sgn_e: Gamma Functions. * gsl_sf_lnpoch: Pochhammer Symbol. * gsl_sf_lnpoch_e: Pochhammer Symbol. * gsl_sf_lnpoch_sgn_e: Pochhammer Symbol. * gsl_sf_lnsinh: Hyperbolic Trigonometric Functions. * gsl_sf_lnsinh_e: Hyperbolic Trigonometric Functions. * gsl_sf_log: Logarithm and Related Functions. * gsl_sf_log_1plusx: Logarithm and Related Functions. * gsl_sf_log_1plusx_e: Logarithm and Related Functions. * gsl_sf_log_1plusx_mx: Logarithm and Related Functions. * gsl_sf_log_1plusx_mx_e: Logarithm and Related Functions. * gsl_sf_log_abs: Logarithm and Related Functions. * gsl_sf_log_abs_e: Logarithm and Related Functions. * gsl_sf_log_e: Logarithm and Related Functions. * gsl_sf_log_erfc: Log Complementary Error Function. * gsl_sf_log_erfc_e: Log Complementary Error Function. * gsl_sf_multiply_e: Elementary Operations. * gsl_sf_multiply_err_e: Elementary Operations. * gsl_sf_poch: Pochhammer Symbol. * gsl_sf_poch_e: Pochhammer Symbol. * gsl_sf_pochrel: Pochhammer Symbol. * gsl_sf_pochrel_e: Pochhammer Symbol. * gsl_sf_polar_to_rect: Conversion Functions. * gsl_sf_pow_int: Power Function. * gsl_sf_pow_int_e: Power Function. * gsl_sf_psi: Digamma Function. * gsl_sf_psi_1: Trigamma Function. * gsl_sf_psi_1_e: Trigamma Function. * gsl_sf_psi_1_int: Trigamma Function. * gsl_sf_psi_1_int_e: Trigamma Function. * gsl_sf_psi_1piy: Digamma Function. * gsl_sf_psi_1piy_e: Digamma Function. * gsl_sf_psi_e: Digamma Function. * gsl_sf_psi_int: Digamma Function. * gsl_sf_psi_int_e: Digamma Function. * gsl_sf_psi_n: Polygamma Function. * gsl_sf_psi_n_e: Polygamma Function. * gsl_sf_rect_to_polar: Conversion Functions. * gsl_sf_Shi: Hyperbolic Integrals. * gsl_sf_Shi_e: Hyperbolic Integrals. * gsl_sf_Si: Trigonometric Integrals. * gsl_sf_Si_e: Trigonometric Integrals. * gsl_sf_sin: Circular Trigonometric Functions. * gsl_sf_sin_e: Circular Trigonometric Functions. * gsl_sf_sin_err_e: Trigonometric Functions With Error Estimates. * gsl_sf_sinc: Circular Trigonometric Functions. * gsl_sf_sinc_e: Circular Trigonometric Functions. * gsl_sf_synchrotron_1: Synchrotron Functions. * gsl_sf_synchrotron_1_e: Synchrotron Functions. * gsl_sf_synchrotron_2: Synchrotron Functions. * gsl_sf_synchrotron_2_e: Synchrotron Functions. * gsl_sf_taylorcoeff: Factorials. * gsl_sf_taylorcoeff_e: Factorials. * gsl_sf_transport_2: Transport Functions. * gsl_sf_transport_2_e: Transport Functions. * gsl_sf_transport_3: Transport Functions. * gsl_sf_transport_3_e: Transport Functions. * gsl_sf_transport_4: Transport Functions. * gsl_sf_transport_4_e: Transport Functions. * gsl_sf_transport_5: Transport Functions. * gsl_sf_transport_5_e: Transport Functions. * gsl_sf_zeta: Riemann Zeta Function. * gsl_sf_zeta_e: Riemann Zeta Function. * gsl_sf_zeta_int: Riemann Zeta Function. * gsl_sf_zeta_int_e: Riemann Zeta Function. * gsl_sf_zetam1: Riemann Zeta Function Minus One. * gsl_sf_zetam1_e: Riemann Zeta Function Minus One. * gsl_sf_zetam1_int: Riemann Zeta Function Minus One. * gsl_sf_zetam1_int_e: Riemann Zeta Function Minus One. * GSL_SIGN: Testing the Sign of Numbers. * gsl_siman_solve: Simulated Annealing functions. * gsl_sort: Sorting vectors. * gsl_sort_index: Sorting vectors. * gsl_sort_largest: Selecting the k smallest or largest elements. * gsl_sort_largest_index: Selecting the k smallest or largest elements. * gsl_sort_smallest: Selecting the k smallest or largest elements. * gsl_sort_smallest_index: Selecting the k smallest or largest elements. * gsl_sort_vector: Sorting vectors. * gsl_sort_vector_index: Sorting vectors. * gsl_sort_vector_largest: Selecting the k smallest or largest elements. * gsl_sort_vector_largest_index: Selecting the k smallest or largest elements. * gsl_sort_vector_smallest: Selecting the k smallest or largest elements. * gsl_sort_vector_smallest_index: Selecting the k smallest or largest elements. * gsl_spline_alloc: Higher-level Interface. * gsl_spline_eval: Higher-level Interface. * gsl_spline_eval_deriv: Higher-level Interface. * gsl_spline_eval_deriv2: Higher-level Interface. * gsl_spline_eval_deriv2_e: Higher-level Interface. * gsl_spline_eval_deriv_e: Higher-level Interface. * gsl_spline_eval_e: Higher-level Interface. * gsl_spline_eval_integ: Higher-level Interface. * gsl_spline_eval_integ_e: Higher-level Interface. * gsl_spline_free: Higher-level Interface. * gsl_spline_init: Higher-level Interface. * gsl_spline_min_size: Higher-level Interface. * gsl_spline_name: Higher-level Interface. * gsl_stats_absdev: Absolute deviation. * gsl_stats_absdev_m: Absolute deviation. * gsl_stats_covariance: Covariance. * gsl_stats_covariance_m: Covariance. * gsl_stats_kurtosis: Higher moments (skewness and kurtosis). * gsl_stats_kurtosis_m_sd: Higher moments (skewness and kurtosis). * gsl_stats_lag1_autocorrelation: Autocorrelation. * gsl_stats_lag1_autocorrelation_m: Autocorrelation. * gsl_stats_max: Maximum and Minimum values. * gsl_stats_max_index: Maximum and Minimum values. * gsl_stats_mean: Mean and standard deviation and variance. * gsl_stats_median_from_sorted_data: Median and Percentiles. * gsl_stats_min: Maximum and Minimum values. * gsl_stats_min_index: Maximum and Minimum values. * gsl_stats_minmax: Maximum and Minimum values. * gsl_stats_minmax_index: Maximum and Minimum values. * gsl_stats_quantile_from_sorted_data: Median and Percentiles. * gsl_stats_sd: Mean and standard deviation and variance. * gsl_stats_sd_m: Mean and standard deviation and variance. * gsl_stats_sd_with_fixed_mean: Mean and standard deviation and variance. * gsl_stats_skew: Higher moments (skewness and kurtosis). * gsl_stats_skew_m_sd: Higher moments (skewness and kurtosis). * gsl_stats_variance: Mean and standard deviation and variance. * gsl_stats_variance_m: Mean and standard deviation and variance. * gsl_stats_variance_with_fixed_mean: Mean and standard deviation and variance. * gsl_stats_wabsdev: Weighted Samples. * gsl_stats_wabsdev_m: Weighted Samples. * gsl_stats_wkurtosis: Weighted Samples. * gsl_stats_wkurtosis_m_sd: Weighted Samples. * gsl_stats_wmean: Weighted Samples. * gsl_stats_wsd: Weighted Samples. * gsl_stats_wsd_m: Weighted Samples. * gsl_stats_wsd_with_fixed_mean: Weighted Samples. * gsl_stats_wskew: Weighted Samples. * gsl_stats_wskew_m_sd: Weighted Samples. * gsl_stats_wvariance: Weighted Samples. * gsl_stats_wvariance_m: Weighted Samples. * gsl_stats_wvariance_with_fixed_mean: Weighted Samples. * gsl_strerror: Error Codes. * gsl_sum_levin_u_accel: Acceleration functions. * gsl_sum_levin_u_alloc: Acceleration functions. * gsl_sum_levin_u_free: Acceleration functions. * gsl_sum_levin_utrunc_accel: Acceleration functions without error estimation. * gsl_sum_levin_utrunc_alloc: Acceleration functions without error estimation. * gsl_sum_levin_utrunc_free: Acceleration functions without error estimation. * gsl_vector_add: Vector operations. * gsl_vector_add_constant: Vector operations. * gsl_vector_alloc: Vector allocation. * gsl_vector_calloc: Vector allocation. * gsl_vector_complex_const_imag: Vector views. * gsl_vector_complex_const_real: Vector views. * gsl_vector_complex_imag: Vector views. * gsl_vector_complex_real: Vector views. * gsl_vector_const_ptr: Accessing vector elements. * gsl_vector_const_subvector: Vector views. * gsl_vector_const_subvector_with_stride: Vector views. * gsl_vector_const_view_array: Vector views. * gsl_vector_const_view_array_with_stride: Vector views. * gsl_vector_div: Vector operations. * gsl_vector_fprintf: Reading and writing vectors. * gsl_vector_fread: Reading and writing vectors. * gsl_vector_free: Vector allocation. * gsl_vector_fscanf: Reading and writing vectors. * gsl_vector_fwrite: Reading and writing vectors. * gsl_vector_get: Accessing vector elements. * gsl_vector_isnull: Vector properties. * gsl_vector_max: Finding maximum and minimum elements of vectors. * gsl_vector_max_index: Finding maximum and minimum elements of vectors. * gsl_vector_memcpy: Copying vectors. * gsl_vector_min: Finding maximum and minimum elements of vectors. * gsl_vector_min_index: Finding maximum and minimum elements of vectors. * gsl_vector_minmax: Finding maximum and minimum elements of vectors. * gsl_vector_minmax_index: Finding maximum and minimum elements of vectors. * gsl_vector_mul: Vector operations. * gsl_vector_ptr: Accessing vector elements. * gsl_vector_reverse: Exchanging elements. * gsl_vector_scale: Vector operations. * gsl_vector_set: Accessing vector elements. * gsl_vector_set_all: Initializing vector elements. * gsl_vector_set_basis: Initializing vector elements. * gsl_vector_set_zero: Initializing vector elements. * gsl_vector_sub: Vector operations. * gsl_vector_subvector: Vector views. * gsl_vector_subvector_with_stride: Vector views. * gsl_vector_swap: Copying vectors. * gsl_vector_swap_elements: Exchanging elements. * gsl_vector_view_array: Vector views. * gsl_vector_view_array_with_stride: Vector views. * gsl_wavelet2d_nstransform: DWT in two dimension. * gsl_wavelet2d_nstransform_forward: DWT in two dimension. * gsl_wavelet2d_nstransform_inverse: DWT in two dimension. * gsl_wavelet2d_nstransform_matrix: DWT in two dimension. * gsl_wavelet2d_nstransform_matrix_forward: DWT in two dimension. * gsl_wavelet2d_nstransform_matrix_inverse: DWT in two dimension. * gsl_wavelet2d_transform: DWT in two dimension. * gsl_wavelet2d_transform_forward: DWT in two dimension. * gsl_wavelet2d_transform_inverse: DWT in two dimension. * gsl_wavelet2d_transform_matrix: DWT in two dimension. * gsl_wavelet2d_transform_matrix_forward: DWT in two dimension. * gsl_wavelet2d_transform_matrix_inverse: DWT in two dimension. * gsl_wavelet_alloc: DWT Initialization. * gsl_wavelet_bspline: DWT Initialization. * gsl_wavelet_bspline_centered: DWT Initialization. * gsl_wavelet_daubechies: DWT Initialization. * gsl_wavelet_daubechies_centered: DWT Initialization. * gsl_wavelet_free: DWT Initialization. * gsl_wavelet_haar: DWT Initialization. * gsl_wavelet_haar_centered: DWT Initialization. * gsl_wavelet_name: DWT Initialization. * gsl_wavelet_transform: DWT in one dimension. * gsl_wavelet_transform_forward: DWT in one dimension. * gsl_wavelet_transform_inverse: DWT in one dimension. * gsl_wavelet_workspace_alloc: DWT Initialization. * gsl_wavelet_workspace_free: DWT Initialization.  File: gsl-ref.info, Node: Variable Index, Next: Type Index, Prev: Function Index, Up: Top Variable Index ************** * Menu: * alpha <1>: VEGAS. * alpha: MISER. * chisq: VEGAS. * dither: MISER. * estimate_frac: MISER. * iterations: VEGAS. * min_calls: MISER. * min_calls_per_bisection: MISER. * mode: VEGAS. * ostream: VEGAS. * result: VEGAS. * sigma: VEGAS. * stage: VEGAS. * verbose: VEGAS.  File: gsl-ref.info, Node: Type Index, Next: Concept Index, Prev: Variable Index, Up: Top Type Index ********** * Menu: * gsl_error_handler_t: Error Handlers. * gsl_fft_complex_wavetable: Mixed-radix FFT routines for complex data. * gsl_function: Providing the function to solve. * gsl_function_fdf: Providing the function to solve. * gsl_histogram: The histogram struct. * gsl_histogram2d: The 2D histogram struct. * gsl_histogram2d_pdf: Resampling from 2D histograms. * gsl_histogram_pdf: The histogram probability distribution struct. * gsl_monte_function: Monte Carlo Interface. * gsl_multifit_function: Providing the Function to be Minimized. * gsl_multifit_function_fdf: Providing the Function to be Minimized. * gsl_multimin_function: Providing a function to minimize. * gsl_multimin_function_fdf: Providing a function to minimize. * gsl_multiroot_function: Providing the multidimensional system of equations to solve. * gsl_multiroot_function_fdf: Providing the multidimensional system of equations to solve. * gsl_odeiv_system: Defining the ODE System. * gsl_siman_copy_construct_t: Simulated Annealing functions. * gsl_siman_copy_t: Simulated Annealing functions. * gsl_siman_destroy_t: Simulated Annealing functions. * gsl_siman_Efunc_t: Simulated Annealing functions. * gsl_siman_metric_t: Simulated Annealing functions. * gsl_siman_params_t: Simulated Annealing functions. * gsl_siman_print_t: Simulated Annealing functions. * gsl_siman_step_t: Simulated Annealing functions.