Random samples of the indexes of a data set.

Mathematical and physical constants.

Lightweight named-column catalog.

Abstract class for one-dimensional harmonic-oscillator evolution using the complex-structure formalism.

Abstract class for implementing data objects.

Abstract class for a sample drawn from a one-dimensional distribution.

Abstract class for a sample drawn from a two-dimensional distribution.

Likelihood of Neal’s funnel distribution.

Gaussian data given by its inverse covariance.

Gaussian data given by its covariance.

Multivariate normal data with a fixed covariance.

Gaussian data with a diagonal covariance.

Likelihood of a two-component Gaussian mixture in two dimensions.

Abstract class for binned Poisson data.

Likelihood of the Rosenbrock distribution.

A set of statistically independent NcmData.

Numerical differentiation object.

Base class for FFTLog transforms.

Logarithm fast fourier transform for a kernel given by the square of a Gaussian window function.

Logarithm fast fourier transform for a kernel given by the spatial correlation function multipoles.

Logarithm fast fourier transform for a kernel given by the square of the spherical Bessel function of order one.

Abstract class for best-fit searches.

Ensemble sampler of the posterior of the free parameters of a NcmFit.

Abstract proposal move of NcmFitESMCMC.

Approximate Posterior Ensemble Sampler (APES) move for NcmFitESMCMC.

Stretch move of Goodman and Weare for NcmFitESMCMC.

Walk move of Goodman and Weare for NcmFitESMCMC.

Least-squares best-fit finder using the GSL trust-region solver (gsl_multifit_nlinear) with the Levenberg-Marquardt subproblem.

Best-fit finder using the GSL gradient-based minimizers (gsl_multimin_fdfminimizer).

Best-fit finder using the GSL Nelder-Mead simplex minimizers (gsl_multimin_fminimizer).

Least-squares best-fit finder using the levmar Levenberg-Marquardt library.

Monte Carlo study of a best-fit estimator.

Monte Carlo study of the bootstrap mean.

Metropolis sampler of the posterior of the free parameters.

Best-fit finder using the NLopt library.

State of a NcmFit.

Cache of vector-valued function values keyed by a scalar argument.

Ordered sample set for vector-valued functions $\vec{F}: \mathbb{R} \to \mathbb{R}^n$.

Abstract class for one-dimensional integrals of an integrand $F$.

One-dimensional integral of an integrand given by a function pointer.

Abstract class for integrals of vector-valued functions over hyperrectangles.

Set of indexes in $[0, n)$, where $n$ is NcmISet:max-index.

One-dimensional confidence intervals from the profile likelihood ratio.

Two-dimensional confidence regions from the profile likelihood ratio.

Likelihood combining a NcmDataset and priors.

Reference-counted row-major matrix of doubles, a view over a #gsl_matrix.

Abstract class for a model: a vector of parameters with their descriptions.

Builds a NcmModel subclass at run time.

Records the state of a NcmModel, so a calculation that depends on it can tell whether it changed.

Parameters of Neal’s funnel distribution.

Mean of a multivariate normal distribution.

Parameters of the Rosenbrock distribution.

Abstract class for jobs distributed over MPI ranks.

NcmMPIJob that evaluates a fit’s $-2\ln L$ at given points.

NcmMPIJob that runs a fit from given starting points.

NcmMPIJob that evaluates and accepts or rejects MCMC proposals.

NcmMPIJob for testing the MPI job machinery.

A set of different NcmModel objects.

Ordered table of free-parameter values of a NcmMSet, optionally kept in sync with a FITS file.

Abstract class for functions of the models in a NcmMSet.

Abstract class for NcmMSetFunc functions written in a language binding.

A NcmMSetFunc chosen by name from a registry of C functions.

Abstract proposal distribution over the free parameters of a NcmMSet.

Proposals drawn from a NcmMSetCatalog.

Proposals uniform in the box of the free-parameter bounds.

Multivariate Gaussian proposals centered on the current point.

Non-negative linear least squares.

Spline of the solution of a first-order ODE.

Poisson-Lognormal probability of an integer count.

Abstract class for a power spectrum $P(k, z)$.

Closed-form power spectrum, evaluated directly.

Correlation function of a power spectrum on a grid in $(r, z)$.

Variance of a power spectrum smoothed by a window, on a grid in $(r, z)$.

Power spectrum read from a table: an NcmSpline2d of $\ln P$ on $(z, \ln k)$, with $k$ in $\mathrm{Mpc}^{-1}$ and $P$ in $\mathrm{Mpc}^3$.

Base class for prior distributions.

Base class for flat prior distributions.

Flat prior on a derived quantity.

Flat prior on a sampling parameter.

Base class for Gaussian priors.

Gaussian prior on a derived quantity.

Gaussian prior on a parameter.

Abstract class for a reparametrization of a NcmModel.

Linear reparametrization: the new parameters are $$\vec{p}_n = T \vec{p} + \vec{v},$$ with $\vec{p}$ the original parameters of the model, $T$ (NcmReparamLinear:matrix) an invertible square matrix and $\vec{v}$ (NcmReparamLinear:vector) a shift. Construction factors $T$ and aborts when it is singular.

Pseudo-random number generator wrapping a GSL gsl_rng.

Base class for spherical Bessel integrators.

Reference spherical Bessel integrator for non-oscillatory integrands.

Levin-Bessel method for spherical Bessel function integration.

Ultraspherical coefficient solver for the spherical-Bessel operator.

Serialization, deserialization and duplication of GObject instances.

Spherical Bessel function array evaluator with automatic cutoff.

Recursions for the spherical harmonics.

Abstract sky region with sampling and density.

Rectangular sky footprint in right ascension and declination.

Description of a scalar model parameter: name, symbol, bounds, scale, absolute tolerance, default value and NcmParamType. NcmModel keeps one for each scalar parameter.

Chebyshev series of functions on an interval.

Maps on the sphere in the HEALPix pixelization.

Nearest-neighbour search for points given in spherical coordinates.

Abstract base class of the one-dimensional interpolating splines.

Abstract class for splines of two variables on a rectangular grid.

Bicubic spline on a rectangular grid.

Bicubic spline on a rectangular grid from NcmSplineGsl splines.

Spline of splines on a rectangular grid.

Interpolating B-spline of order 2 to NCM_SPLINE_BSPLINE_MAX_ORDER.

Abstract base class of the cubic splines, $$s(x) = y_i + b_i \Delta x + c_i \Delta x^2 + d_i \Delta x^3, \qquad \Delta x = x - x_i,$$ on each interval $[x_i, x_{i+1}]$. It evaluates the interpolant, its derivatives and integrals from the coefficients $b_i, c_i, d_i$; the subclasses compute them, and differ in how the second derivatives, $2c_i$, are fixed. Outside the knots the boundary cubic is extrapolated.

Cubic spline with given second derivatives at the knots, so that no linear system is solved. The second derivatives are copied, by ncm_spline_cubic_d2_new() and ncm_spline_cubic_d2_set_d2(); changing the knots or values alone keeps them.

Cubic spline with not-a-knot end conditions: the third derivative is continuous at the second and the next-to-last knots, so the first two and the last two intervals are each one cubic. It needs at least six knots, strictly increasing; preparing aborts otherwise.

Spline that delegates to a GSL interpolation method.

Vector-valued function $\vec{F}(x)$ whose components are splines on the same knots.

Integrated autocorrelation time $\tau$ of one or more scalar series, updated one sample at a time.

Base class for N-dimensional probability distributions reconstructed from samples.

Base class for one-dimensional probability distributions on $[x_i, x_f]$.

Kernel density estimate of a one-dimensional distribution from weighted observations.

One-dimensional distribution tabulated by a spline, of $-2\ln p(x)$ or of $p(x)$.

Base class for two-dimensional probability distributions.

Two-dimensional distribution with $-2\ln p(x, y)$ given by a spline.

Kernel mixture with one scale matrix shared by all kernels.

Abstract kernel of the kernel mixture densities of NcmStatsDist.

Multivariate Gaussian kernel for NcmStatsDist.

Multivariate Student’s t kernel for NcmStatsDist.

Kernel mixture with one scale matrix per kernel.

Online weighted statistics for vectors.

Wall-clock timer with progress tracking for a task of a known number of items.

Reference-counted vector of doubles, a view over a #gsl_vector.

Description of a vector model parameter: one NcmSParam per component, each a copy of NcmVParam:default-sparam named name_i with symbol {symbol}_i until changed. NcmModel keeps one for each vector parameter.

Binary splitting of rational series in arbitrary precision.

Boxed complex double.

A point $(\alpha, \gamma)$ of the hyperbolic plane at a time $t$ in a given NcmCSQ1DFrame. The point is a complex structure $J_{ab}$, which fixes a mode of the oscillator up to a time-dependent phase, see ncm_csq1d_state_get_J().

A pair of doubles.

A triple of doubles.

Container for gradient functions.

Iterator for traversing samples in a NcmFunctionSampleSet. Provides O(1) access to sample data once positioned, making it efficient for sequential traversal and interval operations.

Gauss-Legendre rules on equal panels with a stored weight, see ncm_integral_fixed_new().

An integrand $f(x, y)$ with its user data, for ncm_integrate_2dim() and ncm_integrate_2dim_divonne().

An integrand $f(x, y, z)$ with its user data, for ncm_integrate_3dim_divonne().

Workspace of the LAPACK wrappers, grown as needed; see ncm_lapack_ws_new().

Laurent polynomial with complex coefficients, $$a(w) = \sum_{h = h_\mathrm{min}}^{h_\mathrm{max}} c_h w^h.$$.

Truncated power series of order $N$ in $g$ with Laurent polynomial coefficients, $$\sum_{n=0}^{N} L_n(w)\,g^n \mod g^{N+1}.$$.

Border of a two-dimensional confidence region, as a closed polygon.

Thread-safe pool of reusable objects.

Structure defining a function in the model set function list. This holds metadata for functions that can be evaluated on model parameter sets.

Reference-counted array of GObject, serializable by NcmSerialize.

Reference-counted dictionary from integers to GObject, serializable by NcmSerialize.

Reference-counted dictionary from strings to GObject, serializable by NcmSerialize.

Quaternions and three-vectors, for rotations in three dimensions.

Opaque boxed type for a configured spectral operator.

Coefficients of the step $\bar{Y}{l+2}^m = K^{l+1}{lm}\,x\,\bar{Y}{l+1}^m - K^l{lm}\,\bar{Y}_l^m$.

State of the recursion at one angle; see NcmSFSphericalHarmonics.

State of the recursion at several angles; see NcmSFSphericalHarmonics. Yl0m and Ylm are indexed with NCM_SF_SPHERICAL_HARMONICS_ARRAY_INDEX().

The coefficients of the bicubic polynomial of a grid cell with lower corner $(x_j, y_i)$: element ij[k][l] multiplies $(x - x_j)^k (y - y_i)^l$.

Reference-counted dictionary from strings to GVariant, serializable by NcmSerialize.

Logical type of a catalog column. All values are physically stored in the double backing matrix; the type is schema metadata used to restore the intended dtype when converting to/from external table formats.

The variables the evolution is integrated in. The evolution switches between them with the adiabatic threshold, see ncm_csq1d_set_adiab_threshold().

Frames the state can be expressed in: canonical transformations of the original variables, which act on the hyperbolic plane as isometries. The adiabatic vacuum of order $n$ is near the origin of the adiabatic frame $n$, within $\vert F_1\vert$ in the first and $\vert F_2\vert$ in the second. The non-adiabatic frames use $q_0 = \int\mathrm{d}t/m$, $q_1 = \int q_0^2 m\nu^2\,\mathrm{d}t$, $p_1 = \int q_0 m\nu^2\,\mathrm{d}t$ and $r_1 = \frac{1}{2}\int m\nu^2\,\mathrm{d}t$, see ncm_csq1d_eval_int_1_m() and the related methods; they suit times where these are small, and see ncm_csq1d_change_frame() for the precision of the boosts.

How ncm_csq1d_prepare() sets the initial conditions. The type also selects the order of ncm_csq1d_compute_adiab(): second order for NCM_CSQ1D_INITIAL_CONDITION_TYPE_ADIABATIC2, fourth order otherwise.

Types of Poisson-distributed data. These specify the data format for Poisson likelihood calculations.

Bootstrap types.

Kernel used to build the approximate posterior.

Estimator of the approximate posterior.

Defines the type of gradient calculation.

GSL Multidimensional minimization algorithms.

GSL Multidimensional minimization algorithms without derivatives.

Levmar algorithms.

Resampling of NcmFitMC.

Defines the type of messages to be printed during the fit.

Defines the subclasse of NcmFit to be used.

Side of $x$ on which ncm_function_cache_get_near() searches.

How NcmIntegralND measures the error of a vector-valued integral.

The cubature algorithms of NcmIntegralND.

Origin of the data of a NcmMatrix, used internally.

Scalar parameters of NcmModelFunnel.

Vector parameters of NcmModelFunnel.

Vector parameters of NcmModelMVND.

Parameters of NcmModelRosenbrock.

Control messages from master to slave. All messages have the same size, specifying tag #NCM_MPI_CTRL_TAG_CMD.

MPI tags for master-slave communication. If NCM_MPI_CTRL_TAG_CMD is used, the message is a control message.

NCM_MPI_CTRL_SLAVE_INIT must be followed by #NCM_MPI_CTRL_TAG_JOB containing the serialized job.

NCM_MPI_CTRL_SLAVE_WORK must be followed by #NCM_MPI_CTRL_TAG_WORK_INPUT containing the serialized input.

NCM_MPI_CTRL_SLAVE_WORK is followed by #NCM_MPI_CTRL_TAG_WORK_RETURN containing the serialized return.

NCM_MPI_CTRL_SLAVE_FREE does not need to be followed by any message. The slave can be reinitialized with #NCM_MPI_CTRL_SLAVE_INIT.

NCM_MPI_CTRL_SLAVE_KILL should not be followed by any message. The slave will exit.

The estimators of ncm_mset_catalog_get_post_lnnorm().

Catalog sync modes.

Sampling methods of NcmMSetTransKernCat.

Method for the unconstrained least-squares problems of ncm_nnls_solve().

NcmParamType indicates if the parameter must be fitted, NCM_PARAM_TYPE_FREE, or if it remains fixed, NCM_PARAM_TYPE_FIXED, when a statistical analysis is carried out.

Shape of the growth factor $D(z)$, normalized so that $D(0) = 1$.

Shape of the transfer function $T(k)$ in $P(k,z) = A k^{n_s} T(k)^2 B(k) D(z)^2$.

Filter type to apply to the power spectrum. See also NcmFftlogTophatwin2 and NcmFftlogGausswin2, for the top-hat and Gaussian filters, respectively.

Which two linear conditions close the two-point problem. Truncating the expansion at $N$ Chebyshev coefficients and keeping the first $N-2$ rows of the discretized equation leaves $N$ unknowns against $N-2$ equations, so two conditions have to be added; under the tau constraint the truncation itself supplies them. The solution family they choose from is the same in all three cases, since the homogeneous solutions $x j_\ell$ and $x y_\ell$ span a two-parameter space. The Levin boundary functional is invariant under that choice, so the constraint decides which member of the family has to be represented, not what the panel integral is.

Sphere map coordinate system.

Sphere map pixel ordering.

Curvature density $c(x)$ of the curvature functionals, such as ncm_spline_curvature_lp_norm().

The knot placement methods of NcmSplineFunc.

GSL interpolation methods of NcmSplineGsl.

Rule that picks the order of the auto-regressive fit.

Estimator used to turn the accumulated autocovariances into an integrated autocorrelation time.

How NcmStatsDist1dEPDF chooses its kernel bandwidth.

Cross-validation method to be applied.

The scale matrix shared by the kernels of NcmStatsDistKDE.

Statistical types for vector statistics computation. These determine which statistical quantities are computed and stored during data accumulation.

Origin of the data of a NcmVector, used internally.

See ncm_mset_catalog_calc_max_ess_time() and ncm_mset_catalog_calc_heidel_diag().

Options of NcmSerialize.

Conditions attached to an estimate. Every one of them means the estimate is not to be read as a converged autocorrelation time.

Error codes returned by the NcmCatalog class.

Error codes of the #NCM_CFG_ERROR domain.

Error codes returned by the NcmModel class.

Error codes returned by the NcmMSet class.

Sets bs to the sum of the terms in $[n_1, n_2)$ of a series, see ncm_binsplit_eval.c.

Function receiving log messages, see ncm_cfg_set_log_handler().

The fisher_matrix virtual method of NcmData, see ncm_data_fisher_matrix().

Function $f: \mathbb{R} \to \mathbb{R}$.

Function $f: \mathbb{R} \to \mathbb{R}^M$, writing $f(x)$ into y.

Function $f: \mathbb{R}^N \to \mathbb{R}$.

Function $f: \mathbb{R}^N \to \mathbb{R}^M$, writing $f(x)$ into y.

Vector-valued function type $\vec{F}: \mathbb{R} \to \mathbb{R}^n$. The function should evaluate at x and write the result into y.

The integrand of NcmIntegral1d.

The integrand of NcmIntegral1dPtr.

The integrand of NcmIntegralND, computing $F$ at each point of x into fval, point after point. npoints is one except for the vectorized methods.

Gets the dimensions of the integrand of NcmIntegralND.

The eval1 virtual function of NcmMSetFunc1.

The right-hand side of the ODE of NcmOdeSpline.

Function type for reparameterization. See also NcmReparam.

The radial kernel $K(\chi, k)$ of NcmSBesselIntegrator.

Callback function type for the forcing $F(x)$ of the spherical Bessel ODE in Riccati-Bessel form $u = x\,w$, whose right-hand side is $x F(x)$. The function is evaluated at physical coordinates $x \in [a,b]$ and returns $F(x)$ itself, not the right-hand side.

Function expanded on an interval $[a, b]$.

Vector-valued function expanded on an interval $[a, b]$; one call fills every component.

Updates the accumulated statistics with one weighted sample.

Function of a vector component, see ncm_vector_log_vals_func().

Allocates an empty NcmBinSplit, with $B = 1$.

Adds the next nt terms of the series to bs.

Sets bs to the sum of the first step terms, then adds step terms at a time until the next term is prec bits below the sum, see ncm_binsplit_test_next().

Frees bs and the buffers it allocated; the user data is not freed.

Computes the sum $T / (BQ)$ into res, rounding toward $-\infty$.

Sets q to the sum $T / (BQ)$, in lowest terms.

Sets bs to the sum over $[n_1, n_3)$. bs may be bs_l or bs_r; the two ranges must be consecutive.

Evaluates the next nt terms of the series, without adding them to bs.

Resizes a to the length of var and copies its elements, which must have the element size of a.

Creates a GVariant array of etype sharing the data of a, which it holds a reference to.

Joins argv with spaces, quoting with single quotes the arguments that contain a space.

Restores the GSL error handler that ncm_cfg_init() turned off, so that GSL errors abort.

Writes the current values of entries as keys of group_name in kfile, each commented with the entry description. Callback entries are skipped.

Prints to standard output a table of the values, names and nicks of every member of enum_type, in declaration order.

Starts creating FFTW plans: loads the FFTW wisdom of this MPI rank, once per process, from ncm_cfg_wisdom_rank<rank>.fftw3 in the NumCosmo user data directory, see ncm_cfg_init(), and takes the planning lock, see ncm_cfg_lock_plan_fftw(). key identifies the plans: the caller and everything that makes a plan different, such as the transform sizes and kinds and the number of transforms; the current default planner flag is added to it. It only tells whether the process planned the same before, and the wisdom file is the same for every key. Pass the return value to ncm_cfg_fftw_plan_end().

Destroys plan holding the planning lock, see ncm_cfg_lock_plan_fftw(): FFTW’s plan destruction is not thread-safe either. Does nothing for NULL, so it can be the free function of a GPtrArray of plans.

Releases the planning lock and, when first is TRUE, rewrites the wisdom file if the wisdom changed. A key planned before adds no wisdom, so its save, which exports the whole wisdom to compare it, is skipped. Wisdom is neither loaded nor saved under FFTW_ESTIMATE.

Looks for the data directory in the same places as ncm_cfg_get_data_filename(). Aborts if none exists.

Looks for filename in the data directory under, in order, the path in

NCM_CFG_DATA_DIR_ENV, the installed package data directory and the source directory.

Looks up id_name_nick in enum_type: a decimal integer is taken as the value, otherwise as the name, then as the nick.

Initializes the library; it must be called before any other NumCosmo function, and later calls return immediately. It.

Same as ncm_cfg_init_full_ptr(), for bindings: the arguments are copied and the possibly modified copy is returned.

Initializes the library; it must be called before any other NumCosmo function, and later calls return immediately. It.

Appends to argv, starting at position argc, the command-line arguments equivalent to the keys of group_name in kfile that match entries, and updates argc. Boolean keys become a flag when true, empty values are skipped and list keys repeat the option. argv must have room for them. Aborts if a key cannot be parsed.

Locks the global lock that serializes FFTW planning, which is not thread-safe.

Turns the log messages on or off.

Turns on or off flushing the log stream after each message.

Flushes the log stream.

Logs a separator line.

Registers, once per process, the NcmMSetFuncList functions of the library models. Called by ncm_cfg_init().

Registers obj and initializes its class, so that it can be found by name, for example when deserializing.

Registers the library types with ncm_cfg_register_obj(). Called by ncm_cfg_init().

Sets the number of BLIS threads, if NumCosmo was built with BLIS.

Sends the error and critical log messages to logger, also while ncm_cfg_logfile() is off.

Sets the planner flag used for new FFTW plans and FFTW’s planner time limit; a negative timeout means no limit. Sets error, or aborts if error is NULL, for any other flag.

Same as ncm_cfg_set_fftw_default_flag() with the flag named by flag_str. Sets error, or aborts if error is NULL, for any other string.

Same as ncm_cfg_set_fftw_default_flag() with the flag named in NCM_FFTW_PLANNER and the time limit in NCM_FFTW_PLANNER_TIMELIMIT. Sets error, or aborts if error is NULL, if either is invalid.

Same as ncm_cfg_set_fftw_default_from_env() with the fallback flag given by name.

Sends the message, info and debug log messages to logger instead of the log stream.

Sends the log messages to filename, which is truncated. Aborts if it cannot be opened.

Sends the log messages to stream.

Sets the number of MKL threads, if NumCosmo was built with MKL.

Sets the number of OpenBLAS threads, if NumCosmo was built with OpenBLAS.

Sets the number of OpenMP threads, if NumCosmo was built with OpenMP.

Unlocks the lock taken by ncm_cfg_lock_plan_fftw().

Compares x and y, which are equal when $|x - y| \leq \epsilon_\mathrm{rel} \max(|x|, |y|) + \epsilon_\mathrm{abs}$. If one of them is zero, $\max(|x|, |y|)$ is replaced by one, so reltol also acts as an absolute tolerance.

Sets the maximum number of threads of the global pool, used by every caller of the ncm_func_eval functions. A value of -1 means unlimited.

Calls ncm_func_eval_threaded_loop_nw() with one worker per pool thread, one per processor for an unlimited pool, and serially for a pool of zero threads.

Calls lfunc with data on each index of [i, f) as a separate pool task and returns after all finish. Runs a single serial call if the pool has zero threads.

Splits [i, f) into nworkers contiguous ranges, the first one also taking the remainder, and calls lfunc with data on each range in the pool. Returns after all calls finish. Uses at most f - i workers, and runs a single serial call if the pool has zero threads. Requires f > i and nworkers > 0.

Computes $\int_0^x F$ as the cached integral up to the nearest cached limit $x_n$ plus $\int_{x_n}^x F$, with the tolerances of cache, and caches the result at x.

Computes $\int_x^\infty F$ as the cached integral from the nearest cached limit $x_n$ plus $\int_x^{x_n} F$, with the tolerances of cache, and caches the result at x.

Takes a GSL integration workspace of NCM_INTEGRAL_PARTITION subintervals from a thread-safe pool, allocating one when the pool is empty. It must be given back with ncm_memory_pool_return().

Integrates F over [a, b] with gsl_integration_qag(), the 61-point rule and a pooled workspace; a GSL failure other than GSL_EROUND aborts.

Integrates F over $[a, \infty)$ with gsl_integration_qagiu() and a pooled workspace; a GSL failure other than GSL_EROUND aborts.

Integrates over [xi, xf] by [yi, yf] with the Cuhre algorithm of Cuba, at most $10^7$ evaluations, warning when they are exhausted.

Integrates over [xi, xf] by [yi, yf] with the Divonne algorithm of Cuba, at most $10^7$ evaluations; aborts when Cuba is older than 4.0.

Integrates over the box [xi, xf] by [yi, yf] by [zi, zf] with the Divonne algorithm of Cuba, with no evaluation limit; aborts when Cuba is older than 4.0.

Computes the eigenvalues and, optionally, the eigenvectors of the general a, with LAPACK DGEEV. LAPACK reads the transpose, whose left and right eigenvectors are the right and left ones of a, so the two are exchanged in the call. a is overwritten. Aborts without LAPACK.

Same as ncm_lapack_dgeev() with balancing and condition numbers, with LAPACK DGEEVX. Aborts without LAPACK.

Computes the LQ factorization $A = L Q$ of the row-major a by calling LAPACK DGEQRF on the transpose that LAPACK reads; a is overwritten by the factors, as described by LAPACK DGEQRF. Aborts without LAPACK.

Solves the least-squares or minimum-norm problem for the full-rank a, with LAPACK DGELS; trans is converted and m and n are exchanged for the column-major call. a is overwritten by its QR or LQ factorization and b by the solutions. Aborts without LAPACK.

Solves the least-squares problem by the singular value decomposition, with LAPACK DGELSD, passing the arguments unchanged, so a is read in column-major order. Aborts without LAPACK.

Computes the QL factorization $A = Q L$ of the row-major a by calling LAPACK DGERQF on the transpose that LAPACK reads; a is overwritten by the factors, as described by LAPACK DGERQF. Aborts without LAPACK.

Computes the QR factorization $A = Q R$ of the row-major a by calling LAPACK DGELQF on the transpose that LAPACK reads; a is overwritten by the factors, as described by LAPACK DGELQF. Aborts without LAPACK.

Computes the RQ factorization $A = R Q$ of the row-major a by calling LAPACK DGEQLF on the transpose that LAPACK reads; a is overwritten by the factors, as described by LAPACK DGEQLF. Aborts without LAPACK.

Solves $A x = b$ for a general a by LU factorization with partial pivoting, with LAPACK DGESV. a is read in column-major order, so a row-major NcmMatrix gives the solution for its transpose. a is overwritten by the factorization and b by the solutions. Aborts without LAPACK.

Allocates the workspace of ncm_lapack_dggglm_run() for these arguments, with a LAPACK DGGGLM workspace query. Aborts without LAPACK.

Solves the general Gauss-Markov linear model problem of LAPACK DGGGLM for the given matrices and vectors. Aborts without LAPACK.

Solves $A x = b$ for the symmetric positive definite a, with LAPACK DPOSV: a is overwritten by its Cholesky factor and b by the solutions. Aborts without LAPACK.

Replaces the uplo triangle of the symmetric positive definite a by its Cholesky factor, with LAPACK DPOTRF. Without LAPACK, uses gsl_linalg_cholesky_decomp(), which aborts instead of returning an error.

Replaces the Cholesky factor from ncm_lapack_dpotrf() by the uplo triangle of the inverse, with LAPACK DPOTRI. Without LAPACK, uses gsl_linalg_cholesky_invert(), which aborts instead of returning an error.

Solves $A x = b$ for each right-hand side with the Cholesky factor from ncm_lapack_dpotrf(), with LAPACK DPOTRS; b is overwritten by the solutions. Aborts without LAPACK.

Solves $A x = b$ for the symmetric positive definite tridiagonal $A$ with diagonal d and off-diagonal e, with LAPACK DPTSV, which factors $A = L D L^\intercal$ and overwrites d, e and b. Without LAPACK, uses gsl_linalg_solve_symm_tridiag().

Computes all eigenvalues and, optionally, eigenvectors of the symmetric a by divide and conquer, with LAPACK DSYEVD; with jobz ‘V’ the eigenvectors overwrite a, one per row. Aborts without LAPACK.

Computes selected eigenvalues and, optionally, eigenvectors of the symmetric a by the relatively robust representations algorithm, with LAPACK DSYEVR; a is overwritten. Aborts without LAPACK.

Solves $A x = b$ for the symmetric a, with LAPACK DSYSV. Aborts without LAPACK.

Solves $A x = b$ for the symmetric a, with error bounds and a condition estimate, with LAPACK DSYSVX. Aborts without LAPACK.

Solves $A x = b$ for the symmetric a with iterative refinement and error bounds, with LAPACK DSYSVXX. Aborts without LAPACK.

Replaces the uplo triangle of the symmetric a by its Bunch-Kaufman factorization, with LAPACK DSYTRF. Aborts without LAPACK.

Replaces the factorization from ncm_lapack_dsytrf() by the uplo triangle of the inverse, with LAPACK DSYTRI. Aborts without LAPACK.

Solves $A x = b$ with the factorization from ncm_lapack_dsytrf(), with LAPACK DSYTRS; b is overwritten by the solutions. Aborts without LAPACK.

Logs the formatted message as a message of the NumCosmo log domain.

Logs msg as a message of the NumCosmo log domain.

Logs msg wrapped by ncm_string_ww().

Same as ncm_mpsf_0F1_q() with b and x converted exactly to rationals.

Frees the pool of splitting buffers of the ${}_0F_1$ functions.

Computes ${}_0F_1(b; x)$ into res.

Computes $j_\ell(x)$ into res, see NcmMpsfSBessel.

Same as ncm_mpsf_sbessel() with x converted exactly to a rational.

Frees the pool of splitting buffers of the spherical Bessel functions.

Frees the pools of splitting buffers of the sine integral.

Computes $\mathrm{Si}(x)$ into res, see NcmMpsfTrigInt.

Clears z and every #mpz_t in the list.

Initializes z and every #mpz_t in the list.

Computes the real roots of the cubic, with $a_3 \ne 0$, see NcmPolyRoots.

Computes the real roots of the quadratic, with $a_2 \ne 0$, from $q = -(a_1 + \operatorname{sgn}(a_1)\sqrt{a_1^2 - 4 a_2 a_0})/2$ as $q/a_2$ and $a_0/q$, which avoids cancellation. A double root is returned twice, except the double root zero of $a_2 x^2$, returned once.

Computes the real roots of the quartic, with $a_4 \ne 0$, see NcmPolyRoots.

As ncm_poly_roots_real_quartic(), after dropping the leading coefficients with $|a_i| \le 10^{-14} \sum_j |a_j|$, so the degree may be lower. When every coefficient is dropped, no root is returned.

Sets q to the continued-fraction approximation of x truncated when the next correction is below the double precision. Aborts if the relative difference between q and x exceeds $10^{-15}$.

Same as ncm_mpsf_0F1_d() at 53 bits, rounded to nearest.

Computes the spherical Bessel function $j_\ell(x)$.

Computes $j_\ell’(x)$ from precomputed $j_l(x)$ values (such as those filled by ncm_sf_sbessel_array_eval()) using $j_\ell’(x) = j_{\ell-1}(x) - \frac{\ell+1}{x} j_\ell(x)$. The downward form keeps the required indices within $[0, \ell]$; its two terms agree to a factor of about two at small $x$, so no accuracy is lost to cancellation there. For $\ell = 0$ it returns $-j_1(x)$ evaluated directly.

Builds a cubic not-a-knot spline of $j_\ell$ on $[x_i, x_f]$, placing the knots with

NCM_SPLINE_FUNCTION_SPLINE until the interpolation meets reltol.

Computes the Taylor coefficients of $j_\ell$ at x up to third order, $$ \left(j_\ell(x),\; j’\ell(x),\; \frac{j”\ell(x)}{2!},\; \frac{j”’\ell(x)}{3!}\right), $$ from $j\ell(x)$ and $j_{\ell+1}(x)$ given by ncm_sf_sbessel().

Computes $\left(x\, j_\ell(x)\right)’$ from precomputed $j_l(x)$ values using $\left(x\, j_\ell(x)\right)’ = x\, j_{\ell-1}(x) - \ell\, j_\ell(x)$. For $\ell = 0$ it returns $\cos(x)$ exactly.

Same as ncm_mpsf_sin_int_mpfr() at 53 bits, rounded to nearest, with x converted exactly to a rational.

Wraps msg at spaces into lines of at most ncols columns, each ending with a newline.

Computes $1 - \cos x$, as $\sin^2 x / (1 + \cos x)$ when $\cos x \geq 0.9$.

Computes $1 - \sin x$, as $\cos^2 x / (1 + \sin x)$ when $\sin x \geq 0.9$.

Computes $1 + \cos x$, as $\sin^2 x / (1 - \cos x)$ when $\cos x \leq -0.9$.

Computes $1 + \sin x$, as $\cos^2 x / (1 - \sin x)$ when $\sin x \leq -0.9$.

Removes a final “.fits” or “.fit” extension, in any case, from fits_filename.

Computes $\cos(2x)$ as $(\cos x - \sin x)(\cos x + \sin x)$.

Checks the value returned by the SUNDIALS function funcname and logs a message on failure. For opt 0, flagvalue is a pointer that must not be NULL; for 1, a pointer to an int flag that must not be negative; for 2, a pointer returned by a memory allocation that must not be NULL. Aborts for other values of opt.

Logs the integrator statistics of cvode.

Computes the smallest integer $n_f \geq \max(n, 1)$ whose only prime factors are 2, 3, 5 and 7, a size for which FFTW is efficient.

Does nothing if local_error is NULL. Otherwise moves local_error to *error with the formatted message as a prefix, or aborts with both messages if error is NULL.

Parses the function name and its numerical parameters from func. Aborts if a parameter is not a number.

Same as ncm_util_normal_gaussian_integral() for the Gaussian of mean mu and standard deviation sigma.

Computes the angular separation from the Vincenty formula, see great-circle distance.

Computes the principal branch $W_0(y)$ of the Lambert $W$ function from $\ln y$, so that $y$ may exceed the double range. Uses gsl_sf_lambert_W0() for $\ln y < \ln(\mathrm{DBL_MAX}) - 1$, otherwise Newton’s method on $W + \ln W = \ln y$. Aborts if Newton’s method does not converge.

Computes $\ln(1 + e^x)$ without overflow; it returns $x$ when $e^{-x}$ is below the double precision.

Same as ncm_util_log_normal_gaussian_integral() for the Gaussian of mean mu and standard deviation sigma.

Computes the logarithm of the absolute value of ncm_util_normal_gaussian_integral(), keeping the relative precision in both tails and when the integral is close to one.

Computes $$z_1 = z - \ln\left(\frac{1 - i A e^{z}}{1 + i A e^{-z}}\right), \qquad z = \rho + i\theta,$$ from the series of the logarithm in $A$ when $e^{|\rho|}|A| < 0.1$, summed until the bound on its remaining terms is below machine precision, and sets $z_1 = \rho_1 + i\theta_1$.

Computes $\int_{x_l}^{x_u} e^{-x^2/2}\,\mathrm{d}x / \sqrt{2\pi}$, using erfc() when both limits are in the same tail, beyond $3\sqrt{2}$, to keep the relative precision. The result is negative for $x_u < x_l$.

Sets error to a new error with the formatted message, or aborts with that message if error is NULL. Aborts if error is already set.

Computes $\sinh(x)/x$, from its Taylor series for $|x| < 0.9$.

Computes $[\sinh(x) - x] / (x^3/3!)$, from its Taylor series for $|x| < 0.9$.

Computes $[\sinh(x) - x\cosh(x)]/x^3$, without cancellation for $|x| < 0.9$.

Suspends the calling thread for milliseconds.

Computes $f = f_0 \theta_0 + f_1 \theta_1$ with the logistic weights $\theta_0 = 1/(1 + e^{g})$ and $\theta_1 = 1/(1 + e^{-g})$, where $g = 72 (z - z_0 - \Delta z/2)/\Delta z$. At $z_0$ and $z_0 + \Delta z$ the weight of the other value is $e^{-36} \approx 2 \times 10^{-16}$.

Computes the weights of ncm_util_smooth_trans().

Computes $\sqrt{1+x} - 1$ as $x / (\sqrt{1+x} + 1)$, without cancellation at $x \approx 0$.

Test assertion on ncm_cmp() (n1, n2) cmp 0, with relative tolerance GSL_DBL_EPSILON and no absolute tolerance.

Test assertion on ncm_cmp() (n1, n2, epsilon, abstol) cmp 0.

Declares a term function of ncm_binsplit_eval.c, setting v to u times the factor of term n.

A term function that does nothing, for a factor identically one.

Aborts if obj is not prepared. Expands to nothing unless NumCosmo is built with NUMCOSMO_CHECK_PREPARE.

Returns ret if ncm_util_cvode_check_flag() reports a failure.

Static initializer for a NcmDTuple2:

NcmDTuple2 tuple = NCM_DTUPLE2_STATIC_INIT (1.0, 2.0);

Static initializer for a NcmDTuple3:

NcmDTuple3 tuple = NCM_DTUPLE3_STATIC_INIT (1.0, 2.0, 3.0);

Aborts with the CFITSIO error message if status is nonzero.

If s is not NULL, frees it and sets s to NULL.

Sets dest to a new GArray with a copy of the elements of src.

Copies the elements of src to dest, which must have the same length and element size.

Same as NCM_INTEGRAL_ND_DEFINE_TYPE_WITH_FREE with nothing to free.

Defines a final subclass of NcmIntegralND whose instance holds a field data of type user_data.

Aborts with info if it is nonzero.

Declares a function to get the model id from the model namespace. This macro should be used in the header file of the model.

Defines a function to get the model id from the model namespace.

Defines the function to get the model id from the model namespace. This macro should be used in the source file of the model.

Index of the li-th multipole of the ai-th angle in the flat buffers used by the NcmSFSphericalHarmonicsYArray methods.

Test assertion that running cmd in a subprocess aborts.

Test assertion that calling cmd on obj finalizes it.

Aborts with the GSL error message if ret is not GSL_SUCCESS.

Test assertion that running cmd in a subprocess succeeds.

Marks x as unused.

Writes the extra arguments of NCM_UTIL_DECLARE_CALLBACK() and NCM_UTIL_DEFINE_CALLBACK() with a leading comma, or nothing if empty.

Declares the boxed callback type CallBack, holding a function, its data and the functions that free, copy and prepare the data, and the functions named callback followed by _new, _copy, _free, _eval and _prepare. args_decl is written with NCM_UTIL_CALLBACK_ARGS() and may be empty.

Defines the type and functions declared by NCM_UTIL_DECLARE_CALLBACK(). args_decl and args are written with NCM_UTIL_CALLBACK_ARGS() and may be empty.

Evaluates to $10^x$.

If *error is set, adds the formatted prefix to its message, runs body and returns value.

If *error is set, runs body and returns value.

Name of the environment variable with the directory searched first for data files, see ncm_cfg_get_data_filename().

Name of the environment variable that sets the NumCosmo user data directory, see ncm_cfg_init().

Default relative tolerance of the numerical methods.

GVariant type string for NcmDTuple2.

GVariant type string for NcmDTuple3.

Default NcmIntegral1d:abstol.

Default NcmIntegral1d:rule, the 61-point Gauss-Kronrod rule.

Default NcmIntegral1d:partition.

Default NcmIntegral1d:reltol.

The default absolute tolerance.

The default GSL Gauss-Kronrod rule, 61 points.

The default relative tolerance.

Default NcmIntegralND:abstol.

Default NcmIntegralND:reltol.

The number of subintervals of the pooled GSL workspaces.

Id of a main model. Used to identify the main model in hierarchy of models.

Default NcmOdeSpline:abstol.

Smallest relative spacing between knots kept by NcmOdeSpline.

Prefix of the names given with #NCM_SERIALIZE_OPT_AUTONAME_SER.

Printf format of the number that follows #NCM_SERIALIZE_AUTOSAVE_NAME.

GVariant type string of a serialized NcmMatrix.

Key holding the type name of an element in ncm_serialize_array_to_key_file().

Prefix of the key-file groups of the elements written by ncm_serialize_array_to_key_file().

GVariant type string of a serialized NcmObjArray.

GVariant type string of a serialized NcmObjDictInt.

GVariant type string of a serialized NcmObjDictStr.

G_variant_new() format string building a #NCM_SERIALIZE_OBJECT_TYPE from a type name and a GVariant of properties.

GVariant type string of a serialized object, its type name and properties: (sa{sv}).

GVariant type string of the properties of a serialized object: a{sv}.

GVariant type string of one serialized property, a name and a value: {sv}.

GVariant type string of a serialized string array.

GVariant type string of a serialized NcmVarDict.

GVariant type string of a serialized NcmVector.

Default absolute tolerance for NcmSFSphericalHarmonicsYArray.

Default absolute tolerance for NcmSFSphericalHarmonicsY.

Maximum number of angles held by a NcmSFSphericalHarmonicsYArray.

Default B-spline order, degree 7; see NcmSplineBSpline for the measured errors.

Largest B-spline order supported.

Upper bound on the number of knots of ncm_spline_set_func_grid().

Smallest relative knot spacing of the adaptive NcmSplineFunc methods.

Maximum number of threads of the global pool of NcmFuncEval.

Printf format of the seconds in the NcmTimer strings.

Magnitude below which NcDistance and NcWLSurfaceMassDensity treat the curvature $\Omega_{k0}$ as zero, that is, the universe as flat.