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数学公式库--非常不错 The GNU Scientific Library (GSL) is a collection of routines for numerical computing. T

** Added an error check to trap multifit calls with fewer observations
than parameters.  Previously calling the multifit routines with n<p
would cause invalid memory access.

** Added the Debye unit to physical constants.

** Added cumulative distribution functions for the discrete
distributions, including binomial, poisson, geometric, negative
binomial, pascal and hypergeometric.

** Added the functions gsl_cdf_beta_{Pinv,Qinv} and
gsl_cdf_fdist_{Pinv,Qinv} for computing the inverse of the cumulative
beta and F distributions.

** Added the multilinear fit estimator function gsl_multifit_linear_est
for computing model values and their errors.

** Avoid division by zero in gsl_multimin_fdfminimizer_vector_bfgs
if the step-size becomes too small.

** Users on DEC Alpha systems will need to specify their desired IEEE
arithmetic options via CFLAGS when building the library, as these are
no longer added automatically.

** Added new random variate generators gsl_ran_gaussian_ziggurat
and gsl_ran_gamma_mt for the Gaussian and Gamma distributions based on
the Marsaglia-Tsang ziggurat and fast gamma methods.

** Improved the speed of the exponential power distribution
gsl_ran_exppow.

** Improved the speed of the Gaussian ratio method by adding quadratic
bounds in gsl_ran_gaussian_ratio_method.

** Added an extra term to the taylor series of the synchrotron
functions gsl_sf_synchrotron_1 and gsl_sf_synchrotron_2 for small x to
ensure smooth matching with the chebyshev expansion.

** The binomial pdf gsl_ran_binomial_pdf now handles the cases p=0
and p=1 and is more accurate for the case of small p with k=0.

** Fixed the spherical bessel function gsl_sf_bessel_jl_e) to limit
the use of gsl_sf_bessel_Jnu_asympx_e to the range x>100*l*l to
satisfy he requirement x>>l*l in the asymptotic expansion.

** The scaled bessel function gsl_sf_bessel_In_scaled now handles
larger arguments x > 1e7 correctly for n < 150 using the uniform
asymptotic expansion instead of the continued fraction expansion.

** The functions gsl_stats_min/max now return NaN if the data contains
NaN. Similarly, the functions gsl_stats_min/max_index return the index
of the first occurring NaN in the data when it contains a NaN.

** Fixed an invalid memory access that caused incorrect results for
the special case in periodic cubic spline interpolation of 3 points.

** Added Debye functions for n=5 and n=6

** Added the missing functions gsl_spline_name() and
gsl_spline_min_size()

** The function gsl_rng_uniform_int(r,n) now returns an error for n=0,
which can occur when passing an unsigned integer value of 2^32.

* What was new in gsl-1.7:

** Switched gsl_randist_binomial to use the faster binomial random
variate TPE algorithm by default.  The previous binomial variate
algorithm is available as gsl_randist_binomial_knuth.  This will
result in a different sequence of binomial variates in programs using
this function.

** Improved the algorithm for gsl_sf_elljac_e to avoid cancellation
errors near quarter periods.

** Fixed the branch selection in gsl_sf_gamma_inc_Q_e to avoid
inaccurate results for large a,x where x~=~a.

** The multilinear fitting functions now have forms which accept a
user-specified tolerance for the SVD cutoff and return the
corresponding effective rank of the design matrix.

** The quadratic solvers in poly/ now handle linear equations
gracefully (i.e. quadratrics with a leading coefficient of zero).

** The output of "make check" now only shows test failures by default,
to reduce the amount of output.  Set the environment variable
GSL_TEST_VERBOSE=1 to display all the output.  To assist debugging,
the test number of each failure is shown in square brackets at the
line-end [NNNN].

** Fixed bugs in gsl_linalg_SV_decomp_jacobi which caused
incorrect results for some input matrices.

** Bessel, coulomb, dilogarithm and legendre_H3d functions now use
hypot internally to avoid overflow when computing terms like
sqrt(1+x*x).

** The 'Usage' chapter of the reference manual now explains how to
handle deprecated functions using the GSL_DISABLE_DEPRECATED macro.

** The conflicting enum definitions for 'forward' and 'backward' in
gsl_ftt.h and gsl_wavelet.h are deprecated.  User code should switch
to the new definitions gsl_fft_forward, gsl_fft_backward,
gsl_wavelet_forward and gsl_wavelet_backward. Selectively define
GSL_DISABLE_DEPRECATED before including the headers to use the new
definitions on either or both modules.

** Fixed an error in the the brent minimisation algorithm.  Iterations
should now follow Brent's original description correctly.

** The bound coulomb function gsl_sf_hydrogenicR_e no longer reports
an underflow for exact zeroes of the wavefunction.

** gsl_linalg_SV_decomp_jacobi now reports an error for the
unimplemented case M<N correctly.

** Fixed conformance test for the SYRK and HERK blas functions
gsl_blas_{s,d,c,z}syrk and gsl_blas_{c,z}herk for non-square matrices.

** Configure now checks for presence of ieeefp.h if needed.

** Differential equation solvers now propagate error codes returned
from user-defined functions to the top-level in all cases.

** Sort functions now avoid an infinite loop if Nans are present in
the input vector.  The order of nans in the output is undefined,
although other elements will be sorted correctly.

* What was new in gsl-1.6:

** Added a new wavelet directory, with 1-dimensional and 2-dimensional
discrete wavelet transforms.

** Added support for LQ and P^T LQ decompositions.  To find the QR
decomposition of large systems (M>>N) use the LQ decomposition,
solving the transpose of the original system.  This allows more
efficient memory access, and is useful for solving large least-squares
problems.

** Fixed a bug in the SYRK and HERK blas functions gsl_blas_{s,d,c,z}syrk 
and gsl_blas_{c,z}herk which caused invalid memory access for non-square 
matrices.

** Fixed a bug in gsl_swap_vectors which caused it to return incorrect
results when swapping vectors with different strides.

** Corrected the error estimate for gsl_cheb_eval_n_err to use
evaluation order instead of the approximation order.

** Improved the reliability of the gsl_sf_gamma_inc family of
functions.

** Equal abscissae are now handled gracefully in the cspline and
periodic cspline interpolations.

** Removed potential cancellation error in calculation of uniform
histogram ranges.

** Improved numerical stability of integration for akima and cspline
interpolation.

** Differential equation solvers now handle error codes returned from
user-defined functions.

** Improved error estimates in ode-initval solvers, and provide exact
derivatives on output.  Added new semi-implicit ode-initval solver,
gsl_odeiv_step_rk2simp.

** Added missing function definition for gsl_sf_psi_1.

** Fixed the function gsl_sf_expint_Ei_scaled to call
gsl_sf_expint_Ei_scaled_e instead of gsl_sf_expint_Ei_e.

** Added cumulative distribution function for exponential power
distribution.

** The functions gsl_cdf_beta_P and gsl_cdf_beta_Q now return
consistent results of 0 or 1 for out of range values, x<0 and x>1,
rather than 0 for left and right tails simultaneously.

** The Jacobi eigensolvers gsl_eigen_jacobi and gsl_eigen_jacobi_invert 
have new implementations from Golub and Van Loan.

** The standard output and standard error streams are now flushed by
the default error handler before the program aborts, in order to
ensure that error messages are properly displayed on some platforms.

* What was new in gsl-1.5:

** Multifit routines now handle iterations where |f| is already
minimised to zero, without division by zero.

** Fixed the singular value tolerance test in the multifit covariance
calculation from < to <= to match the original MINPACK code.

** The macro HAVE_INLINE is now tested with #ifdef instead of #if as
in versions prior to 1.4, to match the documentation, and the macro
GSL_RANGE_CHECK_OFF now works correctly.  An alternative macro
GSL_RANGE_CHECK={0,1} can be used to control range-checking.

** Fixed a potential array overflow in gsl_ran_landau.

** Fixed a small discrepancy in the tolerance calculation of the
one-dimensional brent minimiser.

** Numerical derivatives should now be calculated using the
gsl_deriv_forward, gsl_deriv_central and gsl_deriv_backward functions,
which accept a step-size argument in addition to the position x.  The
original gsl_diff functions (without the step-size) are deprecated.

** Corrected documentation for gsl_ran_hypergeometric_pdf()

** The tridiagonal matrix solvers gsl_linalg_solve_symm_tridiag,
gsl_linalg_solve_tridiag, gsl_linalg_solve_symm_cyc_tridiag,
gsl_linalg_solve_cyc_tridiag now use the GSL_ERROR macro to report
errors, instead of simply returning an error code.  The arguments to
these functions must now use exact lengths with no additional
elements.  For cyclic systems all vectors must be of length N, for
tridiagonal systems the offdiagonal elements must be of length N-1.

** The singular value decomposition routines gsl_linalg_SV_decomp and
gsl_linalg_SV_decomp_mod now handle the SVD of a column vector (N=1,
arbitrary M), which can occur in linear fitting.

** Restored missing header files gsl_const_mks.h and gsl_const_cgs.h.
The incorrect values of the electrical units for gsl_const_cgs
(VACUUM_PERMEABILITY and VACUUM_PERMITTIVITY) have been removed.

** Fixed gsl_linalg_SV_decomp() to avoid an infinite loop when
computing the SVD of matrices containing Inf and Nan.

** Fixed gsl_linalg_balance_columns() to avoid an infinite loop when
rescaling matrices containing Inf and NaN.

** Fixed header file <gsl/gsl_sf_log.h> to include declarations for 
error codes in inline versions of gsl_sf_log functions

** Fixed header file <gsl/gsl_const.h> to include new MKSA and CGSM
header files.

** Added Stefan-Boltzmann constant and Thomson cross section to
physical constants

* What was new in gsl-1.4:

** Added cumulative distribution functions and their inverses for the
continuous random distributions including: gaussian, lognormal, gamma,
beta, cauchy, laplace, chisq, exponential, gumbel, weibull,
F-distribution, t-distribution, logistic, pareto and rayleigh.

** Added faster binomial random variates using the TPE rejection
algorithm, in the function gsl_randist_binomial_tpe.

** Added new functions gsl_rng_fwrite and gsl_rnd_fread for storing
the state of random number generators in a file.

** Added a new function gsl_combination_memcpy()

** Corrected values of electrical constants in CGS units.  To take
account of different electrical systems of units the values are now
prefixed by GSL_CONST_MKSA (for the SI Metre, Kilogram, Second, Ampere
system) or GSL_CONST_CGSM (for the Centimetre, Gram, Second, Magnetic
system with the Gauss as the fundamental unit of magnetic field
strength).  The previous GSL_CONST_MKS and GSL_CONST_CGS prefixes have
been removed, as have the permeability and permittivity constants in
the CGS system since this uses different defining equations.

** Fixed bugs in the random number generators gsl_rng_fishman18,
gsl_rng_fishman2x, and gsl_rng_knuthran2 which caused them to return
incorrect results.  Minor corrections were made to the parameters in
the other Knuth generators borosh13, coveyou, fishman20, lecuyer21,
and waterman14.

** Fixed a missing transpose bug in the gsl_linalg_QR_QRsolve
and gsl_linalg_QRPT_QRsolve routines which were computing the
solution to Q^T R x = b instead of Q R x = b.

** Fixed gsl_sf_gammainv to return zero instead of a domain
error for arguments corresponding to singularities in gamma.

** Fixed a bug in the simplex minimization algorithm which
caused it to fail to find the second highest point correctly
when searching the set of simplex points.

** Fixed a bug in the conjugate gradient minimizers conjugate_pr,
conjugate_fr and vector_bgfs which caused the search
directions to be updated incorrectly.

** Fixed a bug in gsl_sf_psi_1_int(1) which caused it to
return the incorrect sign for psi(1,1).

** Fixed the simulated annealing routine gsl_siman_solve to use the
parameter iters_fixed_T for the number of iterations at fixed
temperature instead of n_tries.

** Fixed a bug in gsl_combination_valid which caused it to return the
incorrect status.

** Fixed a bug in gsl_permutation_canonical_to_linear which caused the
output to always be zero, and the input permutation to be incorrectly
replaced by the output.

** Fixed a bug is gsl_ran_discrete which could cause uninitialised
data to be returned for some distributions.

** Fixed the dependencies for gsl_chebyshev.h to include gsl_math.h.

** Fixed a bug in gsl_complex_arccsc_real which caused it to return 
the incorrect sign for the imaginary part when -1<x<0.

** Fixed a bug in the QAWC Cauchy integration routine which could
allow the singularity to fall on an interval boundary, leading to
division by zero.

** Improved gsl_sf_gamma_inc_P(a,x) to avoid a domain error for x<<a
when a>10.

** Improved the accuracy of gsl_sf_coupling_3j for large arguments.

** Improved the performance of gsl_sf_choose(m,n) by separating the
calculations for small and large arguments.

** On platforms without IEEE comparisons gsl_{isnan,isinf,finite} will
fall back to the system versions of isnan, isinf and finite if
available.

** gsl_linalg_householder_hv now uses BLAS routines internally

** The script configure.in is now compatible with autoconf-2.50 and
later.

** Reduced the memory usage of the multifit algorithms from MxM to MxN
for large M by performing the QR decomposition of the Jacobian