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ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
See the latest version documentation. |
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ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
See the latest version documentation. |
This is the ParaMonte Fortran documentation website for the Fortran users and developers.
ParaMonte is a library of serial and parallel Monte Carlo and Machine Learning routines scientific inference, e.g., for sampling mathematical density functions of arbitrary-dimensions, with the design goal of unifying
The ParaMonte library is open-source and is permanently located and maintained on GitHub at:
https://github.com/cdslaborg/paramonte
The pre-built releases of the ParaMonte library for select configurations and compilers are available on GitHub Release page at:
https://github.com/cdslaborg/paramonte/releases
For instructions to build the ParaMonte library from source files, visit the ParaMonte library main documentation website linked below.
For information about the ParaMonte library in general and in other supported programming languages, visit:
https://www.cdslab.org/paramonte
The documentation for the latest version of the ParaMonte Fortran library is always available on this page.
The ParaMonte Fortran library contains,
The following is an incomplete list of the functionalities available in the ParaMonte Fortran library.
For a full list of all available functionalities and modules, see the modules listing of this documentation website.
| Module | Functionality |
|---|---|
| pm_array | This module contains abstract and concrete derived types that are required for compile-time resolution of procedures within the generic interfaces of the ParaMonte library for various array operations. |
| pm_arrayCenter | This module contains procedures and generic interfaces for resizing an input array and centering the original contents of the array in a new array. |
| pm_arrayChange | This module contains procedures and generic interfaces for selecting uniformly-distributed random choices from a given character or integer range. |
| pm_arrayChoice | This module contains procedures and generic interfaces for selecting uniformly-distributed or arbitrarily-distributed random choices from a given list of intrinsic type of arbitrary kind. |
| pm_arrayCompact | This module contains procedures and generic interfaces for condensing (removing duplicate sequential the elements of) an array of arbitrary intrinsic type. |
| pm_arrayCompareLex | This module contains procedures and generic interfaces for performing lexicographic comparisons of two arrays of similar type, kind, and rank. |
| pm_arrayComplement | This module contains procedures and generic interfaces for computing the absolute or relative complement of one set in another set. |
| pm_arrayCopy | This module contains procedures and generic interfaces for copying strided or indexed elements of one scalar string or vector of arbitrary intrinsic type and kind to strided or indexed elements of another scalar string or vector of the same type and kind. |
| pm_arrayFill | This module contains procedures and generic interfaces for convenient allocation and filling of arrays of arbitrary intrinsic types (i.e., character, integer, logical, complex, real), kinds, and non-zero ranks (up to 3). |
| pm_arrayFind | This module contains procedures and generic interfaces for finding locations of a pattern in arrays of various types at the specified instances of occurrence of pattern. |
| pm_arrayInit | This module contains procedures and generic interfaces for efficient initialization of arbitrary rectangular cores and surrounding halos of arrays of arbitrary size, shape, and rank of arbitrary intrinsic type and kind. |
| pm_arrayInsert | This module contains procedures and generic interfaces for inserting an insertion into the specified locations of an input arrays of various types. |
| pm_arrayMembership | This module contains procedures and generic interfaces for assessing whether particular value(s) or any values or all values within a collection are members of another collection of values, or within a range of values that specifies a mathematical set. |
| pm_arrayMerge | This module contains procedures and generic interfaces for sorting and merging two previously-sorted arrays. |
| pm_arrayMinMax | This module contains procedures and generic interfaces for finding the minimum and maximum of two input scalar numbers through lexical comparison. |
| pm_arrayPad | This module contains procedures and generic interfaces for resizing an input array and padding them with symbols on the left or right. |
| pm_arrayRange | This module contains procedures and generic interfaces for generating ranges of discrete character, integer, or real -valued sequences with minimum-possible or user-specified fixed linear spacings. |
| pm_arrayRank | This module contains procedures and generic interfaces for obtaining the Ordinal Ranking of the elements of arrays of various types. |
| pm_arrayRebill | This module contains procedures and generic interfaces for resizing allocatable arrays of various types, relocating their contents, and rebinding (re-indexing) their lower and upper bounds, and refilling the newly added elements. |
| pm_arrayRebind | This module contains procedures and generic interfaces for resizing allocatable arrays of various types, relocating their contents and rebinding (re-indexing) their lower and upper bounds. |
| pm_arrayRefill | This module contains procedures and generic interfaces for resizing allocatable arrays of various types, relocating their contents and filling the newly added elements with specific values. |
| pm_arrayRefine | This module contains procedures and generic interfaces for refining (thinning) (weighted) arrays of arbitrary intrinsic types. |
| pm_arrayRemap | This module contains procedures and generic interfaces for remapping arrays of various types. |
| pm_arrayRemove | This module contains procedures and generic interfaces for removing a pattern from arrays of various types at the specified instances of occurrence of pattern. |
| pm_arrayReplace | This module contains procedures and generic interfaces for replacing patterns within arrays of various types. |
| pm_arrayResize | This module contains procedures and generic interfaces for resizing allocatable arrays of various types and relocating their contents, without initializing or filling the newly added elements with specific values. |
| pm_arrayReverse | This module contains procedures and generic interfaces for reversing the order of elements in arrays of various types. |
| pm_arraySearch | This module contains procedures and generic interfaces for finding the specific array index whose element has the largest value smaller than the input value in arrays of various types. |
| pm_arraySelect | This module contains procedures and generic interfaces for selecting the kth smallest element in unsorted arrays of various types. |
| pm_arrayShuffle | This module contains procedures and generic interfaces for shuffling arrays of various types. |
| pm_arraySort | This module contains procedures and generic interfaces for various sorting tasks. |
| pm_arraySpace | This module contains procedures and generic interfaces for generating arrays with linear or logarithmic spacing. |
| pm_arraySplit | This module contains procedures and generic interfaces for splitting arrays of various types at the specified instances of occurrence of pattern. |
| pm_arrayStrip | This module contains procedures and generic interfaces for stripping a given pattern from the left and right ends of an array of arbitrary intrinsic type and kind. |
| pm_arrayUnique | This module contains procedures and generic interfaces for finding unique values of an input array of various types. |
| pm_arrayVerbose | This module contains procedures and generic interfaces for flattening (duplicating the elements of) an array according to a user-specified weight. |
| pm_batse | This module contains procedures and generic interfaces for modeling data and detectors of the BATSE Gamma-Ray satellite onboard the NASA Compton Gamma-Ray Observatory. |
| pm_bench | This module contains abstract interfaces and types that facilitate benchmarking of different procedures. |
| pm_bit | This module contains constants and procedures that are relevant to bit manipulation. |
| pm_blas | This module contains a set of generic interfaces to the BLAS routines used within the ParaMonte library. |
| pm_clustering | This module contains procedures and routines for the computing the Kmeans clustering of a given set of data. |
| pm_complexAbs | This module contains procedures and generic interfaces for performing element-wise comparison of the real and imaginary components of scalars and arrays of arbitrary ranks of various types. |
| pm_complexCompareAll | This module contains procedures and generic interfaces for checking if both of the corresponding real and imaginary components of two complex numbers satisfy a relational operator. |
| pm_complexCompareAny | This module contains procedures and generic interfaces for checking if either of the corresponding real and imaginary components of two complex numbers satisfy a relational operator. |
| pm_complexCompareLex | This module contains procedures and generic interfaces for checking if a complex number is lexicographically comparable to another complex number of the same kind. |
| pm_complexDiv | This module contains procedures and generic interfaces for computing the complex division robustly without potential overflow of computations. |
| pm_complexMinMax | This module contains procedures and generic interfaces for computing element-wise minimum/maximum value/location of the real and imaginary components of scalars and arrays of arbitrary ranks of type complex of arbitrary kinds. |
| pm_container | This module contains the derived types for generating allocatable containers of scalar, vector, matrix, or cube of integer, real, complex, logical, and string values of arbitrary kinds. |
| pm_control | This module contains abstract and concrete derived types that are required for compile-time resolution of procedures within the generic interfaces of the ParaMonte library for Linear Algebra operations. |
| pm_cosmicRate | This module contains procedures and generic interfaces for computing the cosmic rates of celestial phenomena. |
| pm_cosmology | This module contains procedures and generic interfaces and constants for cosmological calculations. |
| pm_dateTime | This module contains classes and procedures for computing, manipulating, and styling dates and times. |
| pm_distanceEuclid | This module contains procedures and generic interfaces for computing the Euclidean norm of a single point (with respect to origin or a given reference) or the pairwise Euclidean distances (squared) of a collection of points with respect to another set of reference points, optionally without undue overflow or underflow. |
| pm_distanceKolm | This module contains classes and procedures for computing the Kolmogorov statistical distance. |
| pm_distanceMahal | This module contains classes and procedures for computing the Mahalanobis statistical distance. |
| pm_distBand | This module contains procedures and generic interfaces for computing the Band photon distribution widely used in modeling the spectra of a class of celestial objects knowns Gamma-Ray Bursts. |
| pm_distBern | This module contains classes and procedures for generating Bernoulli-distributed random numbers. |
| pm_distBeta | This module contains classes and procedures for computing various statistical quantities related to the Beta distribution. |
| pm_distCosRaised | This module contains classes and procedures for computing various statistical quantities related to the Raised Cosine distribution. |
| pm_distCov | This module contains classes and procedures for generating random matrices distributed on the space of positive definite matrices, such that their determinants is uniformly or power-law distributed. |
| pm_distEggBox | This module contains classes and procedures for computing various statistical quantities related to the mathematical EggBox density function. |
| pm_distExp | This module contains classes and procedures for computing various statistical quantities related to the Exponential distribution. |
| pm_distExpGamma | This module contains classes and procedures for computing various statistical quantities related to the ExpGamma distribution. |
| pm_distGamma | This module contains classes and procedures for computing various statistical quantities related to the Gamma distribution. |
| pm_distGenExpGamma | This module contains classes and procedures for computing various statistical quantities related to the GenExpGamma distribution. |
| pm_distGenGamma | This module contains classes and procedures for computing various statistical quantities related to the GenGamma distribution. |
| pm_distGeom | This module contains classes and procedures for computing various statistical quantities related to the Geometric distribution. |
| pm_distGeomCyclic | This module contains classes and procedures for computing various statistical quantities related to the Cyclic Geometric distribution. |
| pm_distKolm | This module contains classes and procedures for computing various statistical quantities related to the Kolmogorov distribution. |
| pm_distLogNorm | This module contains classes and procedures for computing various statistical quantities related to the Lognormal distribution. |
| pm_distLogUnif | This module contains classes and procedures for computing various statistical quantities related to the LogUniform (or Reciprocal) distribution. |
| pm_distMultiNorm | This module contains classes and procedures for computing various statistical quantities related to the MultiVariate Normal (MVN) distribution. |
| pm_distNegExp | This module contains classes and procedures for computing various statistical quantities related to the Negative Exponential distribution. |
| pm_distNorm | This module contains classes and procedures for computing various statistical quantities related to the univariate Normal distribution. |
| pm_distNormShell | This module contains procedures and generic interfaces for computing the Multivariate Normal Shell density function or mixtures of such densities with varying parameters. |
| pm_distPareto | This module contains classes and procedures for computing various statistical quantities related to the (Truncated) Pareto distribution. |
| pm_distPois | This module contains classes and procedures for computing various statistical quantities related to the Poisson distribution. |
| pm_distPower | This module contains classes and procedures for computing various statistical quantities related to the (Truncated) Power distribution. |
| pm_distPoweto | This module contains classes and procedures for computing various statistical quantities related to the (Truncated) Power/Pareto distribution (hence the name Poweto). |
| pm_distUnif | This module contains classes and procedures for computing various statistical quantities related to the univariate Uniform distribution. |
| pm_distUnifEll | This module contains classes and procedures for computing various statistical quantities related to the MultiVariate Uniform Ellipsoid (MVUE) distribution. |
| pm_distUnifPar | This module contains classes and procedures for setting up and computing the properties of the MultiVariate Uniform Parallelepiped (MVUP) Distribution. |
| pm_distUnifSphere | This module contains classes and procedures for computing various statistical quantities related to the Uniform Spherical distribution. |
| pm_ellipsoid | This module contains classes and procedures for setting up and computing the properties of the hyper-ellipsoids in arbitrary dimensions. |
| pm_err | This module contains classes and procedures for reporting and handling errors. |
| pm_except | This module contains procedures and generic interfaces and generic interfaces for testing for exceptional cases at runtime. |
| pm_fftnr | This module contains procedures and generic interfaces for computing the Discrete Fourier Transform of a real or complex sequence using radix-2 Cooley–Tukey Fast-Fourier Transform. |
| pm_fftpack | This module contains procedures and generic interfaces for computing the Discrete Fourier Transform of a real or complex sequence using a mixed-radix decimation-in-frequency Fast-Fourier Transform. |
| pm_io | This module contains classes and procedures for input/output (IO) or generic display operations on standard displays or internal/external files. |
| pm_kind | This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte library for the two standard supported Fortran and C-Fortran Interoperation (CFI) modes. |
| pm_knn | This module contains procedures and generic interfaces for computing the nearest neighbor statistics of random samples. |
| pm_lapack | This module contains a set of generic interfaces to the LAPACK routines. |
| pm_logicalCompare | This module contains procedures and generic interfaces for performing a variety of logical comparison operations using logical values as if .true. evaluates to 1 and .false. evaluates to 0. |
| pm_math1mexp | This module contains procedures and generic interfaces for computing 1 - exp(x) more precisely for tiny x. |
| pm_mathBeta | This module contains classes and procedures for computing the mathematical Beta Function and its inverse. |
| pm_mathCompare | This module contains the procedures and interfaces for evaluating the relative or absolute proximity of two numeric values. |
| pm_mathConst | This module contains relevant mathematical constants. |
| pm_mathCumPropExp | This module contains the procedures and interfaces for computing the cumulative sum of the exponential of an array without undue numerical overflow. |
| pm_mathCumSum | This module contains the procedures and interfaces for computing the cumulative sum of an array |
| pm_mathDivMul | This module contains procedures and generic interfaces for evaluating the mathematical division and multiplication operators acting on integer, complex, or real values. |
| pm_mathErf | This module contains classes and procedures for computing the mathematical Inverse Error Function. |
| pm_mathExp | This module contains procedures and generic interfaces for computing the previous/next integer exponent for the given base that yields a number smaller/larger than the absolute input value. |
| pm_mathFactorial | This module contains procedures and generic interfaces for the Factorial function. |
| pm_mathFactoring | This module contains procedures and generic interfaces and generic interfaces for computing the prime factors of integers. |
| pm_mathGamma | This module contains procedures and generic interfaces for the Lower and Upper Incomplete Gamma functions. |
| pm_mathLog1p | This module contains procedures and generic interfaces for computing log(1 + x) more precisely for tiny x. |
| pm_mathLogAddExp | This module contains procedures and generic interfaces for adding two real or complex values without causing overflow or underflow. |
| pm_mathLogSubExp | This module contains procedures and generic interfaces for subtracting two real or complex values without causing overflow or underflow. |
| pm_mathLogSumExp | This module contains the procedures and interfaces for computing the natural logarithm of the sum of exponentials the elements of an array. |
| pm_mathMinMax | This module contains procedures and generic interfaces for finding the minimum and maximum of two input scalar values through lexical comparison. |
| pm_mathNumSys | This module contains procedures and generic interfaces for converting numbers to different bases in different numeral systems. |
| pm_mathRoot | This module contains classes and procedures for computing the roots of one-dimensional continuous mathematical functions using various root-finding methods. |
| pm_mathRootTest | This module contains a collection of example functions for testing or examining the root-finding routines of the ParaMonte library. |
| pm_mathSqrt | This module contains procedures and generic interfaces and generic interfaces for computing the square root of integers. |
| pm_mathSubAdd | This module contains procedures and generic interfaces for evaluating the mathematical operator ∓ acting on integer, complex, or real values. |
| pm_mathUnsigned | This module contains procedures and generic interfaces and generic interfaces for various operations with positive integers with results that have the same binary representation as an unsigned integer. |
| pm_matrixChol | This module contains procedures and generic interfaces for computing the Cholesky factorization of positive definite matrices. |
| pm_matrixClass | This module contains abstract and concrete derived types that are required for compile-time resolution of procedures within the generic interfaces of the ParaMonte library for Linear Algebra operations. |
| pm_matrixCopy | This module contains procedures and generic interfaces relevant to copying (diagonal or upper/lower triangular) subsets of matrices of arbitrary intrinsic types and kinds from one matrix of arbitrary shape and packing format to another matrix of arbitrary shape and packing format. |
| pm_matrixDet | This module contains procedures and generic interfaces relevant to the computation of the determinants of square matrices. |
| pm_matrixIndex | This module contains procedures and generic interfaces for converting the indices of matrix elements between different packing and storage formats. |
| pm_matrixInit | This module contains procedures and generic interfaces relevant to generating and initializing matrices of arbitrary shapes (:, :). |
| pm_matrixInv | This module contains abstract and concrete derived types and procedures related to the inversion of square matrices. |
| pm_matrixLUP | This module contains procedures and generic interfaces relevant to the partially LU Pivoted decomposition of matrix operations and linear algebra. |
| pm_matrixMulAdd | This module contains procedures and generic interfaces relevant to combined matrix-matrix or matrix-vector multiplication and addition. |
| pm_matrixMulTri | This module contains the procedures for multiplication of a square triangular matrix in various transpositions with a general matrix. |
| pm_matrixPack | This module contains abstract and concrete derived types that are required for compile-time resolution of procedures within the generic interfaces of the ParaMonte library for Linear Algebra operations. |
| pm_matrixSubset | This module contains abstract and concrete derived types that are required for compile-time resolution of procedures within the generic interfaces of the ParaMonte library for Linear Algebra operations. |
| pm_matrixTrace | This module contains procedures and generic interfaces for computing the additive or multiplicative trace of a given square matrix in arbitrary packing formats. |
| pm_matrixTrans | This module contains abstract and concrete derived types and procedures related to various common matrix transposition operations for which there is a corresponding matrix class defined in pm_matrixClass. |
| pm_matrixUpdate | This module contains procedures and generic interfaces relevant to arbitrary-rank updates to vectors, general matrices, or Symmetric/Hermitian triangular matrices of type integer, complex, and real of arbitrary type-kind parameters. |
| pm_memory | This module contains abstract and concrete derived types that are required for compile-time resolution of procedures within the generic interfaces of the ParaMonte library for various search operations. |
| pm_optimization | This module contains procedures, generic interfaces, and types for numerical optimizations of mathematical functions. |
| pm_option | This module contains convenience functions for generating default values for optional arguments. |
| pm_os | This module contains procedures and generic interfaces for inferring the processor operating system. |
| pm_parallelism | This module contains procedures and generic interfaces for facilitating parallel computations or computing the performance of the parallel Coarray/MPI/OpenMP algorithms. |
| pm_paramonte | This module contains procedures and data that provide general information about the ParaMonte library, its interfaces, and its build. |
| pm_physUnit | This module contains relevant physical constants. |
| pm_polation | This module contains procedures and data types for interpolation of finite samples of data. |
| pm_polynomial | This module contains procedures and generic interfaces for performing various mathematical operations involving polynomials. |
| pm_quadPack | This module contains classes and procedures for non-adaptive and adaptive global numerical quadrature and Cauchy Principal Value of 1D functions with various types of singularities and points of difficulties via the Gauss-Kronrod and Clenshaw-Curtis quadrature formulae. |
| pm_quadRomb | This module contains classes and procedures to perform numerical integrations. |
| pm_quadTest | This module contains a collection of interesting or challenging integrands for testing or examining the integration routines of the ParaMonte library. |
| pm_sampleACT | This module contains classes and procedures for computing properties related to the auto correlation time (ACT) of random sequences. |
| pm_sampleAffinity | This module contains classes and procedures for affine transformation of multivariate samples. |
| pm_sampleCCF | This module contains classes and procedures for computing properties related to the cross correlation of random samples. |
| pm_sampleCor | This module contains classes and procedures for computing properties related to the correlation matrices of random samples. |
| pm_sampleCov | This module contains classes and procedures for computing the properties related to the covariance matrices of a random sample. |
| pm_sampleECDF | This module contains classes and procedures for computing the Empirical Cumulative Distribution Function (ECDF) of an observational sample and the associated the various properties. |
| pm_sampleMean | This module contains classes and procedures for computing the first moment (i.e., the statistical mean) of random weighted samples. |
| pm_sampleNorm | This module contains classes and procedures for normalizing univariate or multivariate samples by arbitrary amounts along specific directions. |
| pm_sampleQuan | This module contains procedures and data types for computing sample quantile. |
| pm_sampleScale | This module contains classes and procedures for scaling (i.e., multiplying) univariate or multivariate samples by arbitrary amounts along specific directions. |
| pm_sampleShift | This module contains classes and procedures for shifting univariate or multivariate samples by arbitrary amounts along specific directions. |
| pm_sampleVar | This module contains classes and procedures for computing the properties related to the covariance matrices of a random sample. |
| pm_sampleWeight | This module contains the types, classes, and procedures relevant to weights of random samples. |
| pm_sampling | This module contains procedures and generic interfaces for the ParaMonte library sampler routines. |
| pm_search | This module contains abstract and concrete derived types that are required for compile-time resolution of procedures within the generic interfaces of the ParaMonte library for various search operations. |
| pm_statest | This module contains classes and procedures for performing various statistical tests. |
| pm_str | This module contains classes and procedures for various string manipulations and inquiries. |
| pm_strANSI | This module contains procedures and generic interfaces for styling strings according for display on DEC VT100 or compatible terminals. |
| pm_strASCII | This module contains the uncommon and hardly representable ASCII characters as well as procedures for operating on strings that exclusively contain the 128 ASCII characters. |
| pm_swap | This module contains procedures and generic interfaces for swapping values of intrinsic Fortran types of arbitrary kinds. |
| pm_sysInfo | This module contains procedures and generic interfaces for inferring the operating system kernel type, name, and other information. |
| pm_sysPath | This module contains classes and procedures for manipulating system file/folder paths. |
| pm_sysShell | This module contains procedures and generic interfaces for inferring the runtime system shell type and fetching information from the shell. |
| pm_test | This module contains a simple unit-testing framework for the Fortran libraries, including the ParaMonte library. |
| pm_timer | This module contains the timer procedures and derived types to facilitate timing applications at runtime. |
| pm_val2complex | This module contains procedures and types for facilitating the conversion of values of different types (e.g., intrinsic Fortran string and logical) to complex values of different kinds. |
| pm_val2int | This module contains procedures and types for facilitating the conversion of values of different types (e.g., intrinsic Fortran string and logical) to integer values of different kinds. |
| pm_val2logical | This module contains procedures and types for facilitating the conversion of values of different types (e.g., intrinsic Fortran strings) to logical values of different kinds. |
| pm_val2real | This module contains procedures and types for facilitating the conversion of values of different types (e.g., intrinsic Fortran string and logical) to real values of different kinds. |
| pm_val2str | This module contains the generic procedures for converting values of different types and kinds to Fortran strings. |
| pm_ziggurat | This module contains procedures and generic interfaces for computing the Ziggurat set for for pseudo-random number sampling. |
The Fortran language is case-insensitive. However, by convention in this library,
Vec or Vector (for example, proposalStd, ...).mat or Matrix (for example: proposalCor, ...).logical (Boolean) variables with a passive verb.logical variable name should be an English-language statement that evaluates to either .true. or .false..parallelismMpiFinalizeEnabled is one such proposition.is can also be used to label logical objects.getCov means generate (a) covariance matrix.setMatCopy means copy the matrix into the specified buffer.get, or set.get.getMatSym(mat) result(matsym) generates a symmetric version of the input matrix and returns it as the function result.logical result.logical should be preferably prefixed with is or be named such that the name begins with a verb and reads as a proposition, evaluating to either .true. or .false..get should be avoided as a prefix for subroutine names since unlike functions, subroutines do not generate and get a new object as their results, rather they (re)set the state of existing objects passed to them.set, as in, for example, setReplaced.The following list of abbreviations is in alphabetical order to enable faster search:
avg stands for average (rarely used).cdf stands for Cumulative Distribution Function in the context of statistics. Example: getNormCDF().cho stands for Cholesky factorization. Example: setChoLow().chol stands for Cholesky factorization. Example: setMatChol().cor stands for correlation. Example: getCor().cov stands for covariance. Example: getCov().cum stands for cumulative. Example: getCumSum().coef stands for coefficient. Example: corcoef_type().def stands for default in variable names (mostly as a prefix def_ or suffix _def).def stands for definite (mostly in procedure names dealing with positive-definite matrices) den stands for density, mostly in the context of statistical procedures and objects. Example: getLogProbDen().det stands for determinant, mostly in the context of Matrix and linear algebra. Example: getMatDet().dia stands for diagonal, mostly in the context of matrix algebra, matrix packing, or Cholesky factorization. Example: dia_type().diag stands for diagonal, mostly as dummy argument in matrix algebra procedures.desc stands for description, mostly as a dummy argument of setAsserted in tests.diff stands for difference. Example: setDisSortedExpDiff().dist stands for distance or distribution depending on the context. Example: DistMulti_type.eff stands for effective. Example: effSamSize.exp stands for exponential or exponentiated. Example: setDisSortedExpDiff().herm stands for hermitian in matrix algebra.ICE stands for Internal Compiler Error. It typically appears in the bug descriptions tagged via Doxygen command \bug.inv stands for inverse. Example: getMatInv().ks stands for Kolmogorov-Smirnov test. Example: getProbKS().lin stands for linear. Example: getLinSpace().low stands for lower triangle of a matrix or lower limits. Example: setChoLow().mahal stands for Mahalanobis distance. Example: getMahalSq().mat stands for matrix. Example: getMatInv().multi stands for multivariate mostly used in the context of statistical distributions. Example: getMultiNormRand().msn stands for Multivariate Skew-Normal mostly used in the context of the statistical MultiVariate Skew-Normal distribution.mvn stands for MultiVariate Normal mostly used in the context of the statistical MultiVariate Normal distribution.mvu stands for MultiVariate Uniform mostly used in the context of the statistical MultiVariate (ellipsoidal) Uniform distribution.norm stands for normal in the context of statistical distributions or normalization factor. Example: DistMultiNorm_type.normed stands for normalized mostly in the context of statistical samples. Example: NormedSample.pdf stands for Probability Density Function in the context of statistics. Example: getNormLogPDF().pos stands for positive. Example: getInvPosDefMat().piwi stands for piecewise, mostly in the context of statistical applications. Example: pm_PiwiPoweto().prob stands for probability, mostly in the context of statistical applications. Example: getLogProb().proc stands for procedure, particularly, when it appears as the suffix _proc in abstract interface definitions. quan stands for quantile, mostly in the context of statistics. Example: getParetoLogQuan().rand stands for random, mostly in the context of statistics. Example: getUnifRand().ref stands for reference, mostly in the context of testings to represent the reference values for comparison. Example: mean_ref.sam stands for sample, mostly in the context of statistics. Example: effSamSize.sq stands for squared. Example: getMahalSq().stat stands for statistics. Example: StatDRAM_type.std stands for standard deviation. Example: StdVec.sym stands for symmetric.symm stands for symmetric.udf stands for Unnormalized Density Function in the context of statistics. Example: getEggBoxLogUDF().uni stands for univariate, mostly used in the context of statistical distributions. Example: DistUni_type.unif stands for uniform, mostly in the context of the uniform statistical distribution. Example: getUnifRand().upp stands for upper triangle of a matrix or upper limits. Example: setChoUpp().vec stands for vector. Example: stdVec.The ParaMonte Fortran library development and guidelines are summarized in CONTRIBUTING.md.
\brief must always be the first line of the documentation of modules, types, and procedures.\details, if it exists, must always immediately follow the Doxygen tag \brief.\param, if any number of it exists, must always immediately follow the Doxygen tag \brief (or \details if it exists).\return, must be exclusively used to indicate the return value of functions.\param tags. Example: getMean().\interface must appear immediately after the Doxygen \return, \param, \details, or \brief tags in the specified order, if any exists.\warning, if any number of it exists, must immediately follow the Doxygen tag \return if it exists, otherwise \param if it exists, otherwise \details if it exists, otherwise \brief.\warning tag must be used to highlight situations that require special attention of the user, otherwise, there is a danger for the code section being documented to not behave normally as one may expect.\attention has the same functionality and usage as \warning.\warning should be preferred wherever \attention is needed.\warning also apply to the tag \attention.\remark, if any number of it exists, must immediately follow the Doxygen tag \warning if it exists, otherwise the Doxygen tag \return if it exists, otherwise \param if it exists, otherwise \details if it exists, otherwise \brief.\remark should be reserved for explaining behavior that is directly related to the code segment being documented, but its knowledge is not so critical as warrant the use of a \warning tag.\note, if it exists, must appear after all \warning and \attention and \remark tags and immediately before the ParaMonte custom command tag \see if it exists, otherwise immediately before \example for examples (if it exists).\see, if it exists, must appear after all \warning and \remark and \note tags.\see command exists, each must be written on a separate line and each line must end with the HTML line-break tag <br>. Example: See below.\see tag, otherwise after \note, \remark, \warning, \param, \details, or \brief if any exists.\example devised in the config.txt file of ParaMonte Doxygen documentation.\include command, followed immediately by the ParaMonte custom Doxygen command \compile which inserts the generic example compile commands for the example, followed optionally but immediately by the output file of the example inserted in the documentation via the \include command, followed immediately by the inclusion of any other visualization or postprocessing scripts and output.\example, otherwise, each empty line will start a new paragraph in the documentation.\test tag, if any exists, must appear immediately after the example section designated by the \example tag.\todo tag, if any exists, must appear immediately after the \test tag or any other tag immediately preceding it.\bug tag, if any exists, must appear immediately after the \todo tag or any other tag immediately preceding it.\finmain separated from the tags before and after by an empty line.\xrefitem authors "Author" "Authors" tag is the last command to appear in any documentation section, and it must preferably have the format exemplified in the example below.ParaMonte Doxygen custom commands.
To simplify documentation and avoid retyping certain frequently used keywords and sentences, a number of Doxygen aliases are predfined in the ParaMonte Doxygen config.txt file. These include (but are not limited to):
\warnpure Inserts a \warning about procedures that are impure when the library is built the preprocessor macro CHECK_ENABLED=1.\elemental Inserts a \remark tag indicating that the procedure of interest is elemental.\pure Inserts a \remark tag indicating that the procedure of interest is pure.\interface Starts a Possible calling interfaces paragraph where different calling interfaces of a procedure can be listed.\benchmark Starts a new Benchmark paragraph which is hyper-linked to the generic anchor #benchmark at the same location on the same page.\benchmark{xxx} Starts a new Benchmark paragraph which is hyper-linked to the specific anchor #benchmark-xxx at the same location on the same page.\benchmark{xxx, This is the benchmark title} Starts a new Benchmark paragraph which is hyper-linked to the specific anchor #benchmark-xxx at the same location on the same page with the title This is the benchmark title.\example Starts a new Example usage paragraph which is hyper-linked to the generic anchor #example at the same location on the same page.\example{xxx} Starts a new Example usage paragraph which is hyper-linked to the specific anchor #example-xxx at the same location on the same page.\compile Inserts the set of example compile commands.\output Inserts a title line for the output section of an example paragraph.\postproc Inserts a title line for the postprocessing section of an example paragraph.\abbr Inserts a \remark tag about the naming abbreviations used in the library.\naming Inserts a \remark tag about the naming conventions used in the library.\license Inserts a \remark tag about the generic licensing of the library.\finmain Inserts the set of final generic remarks that should appear at the end of each documentation section.\RK Inserts a hyper-link reference RK to the default real kind used in the library.\RK32 Inserts a hyper-link reference RK32 to the real32 real kind used in the library.\RK64 Inserts a hyper-link reference RK64 to the real64 real kind used in the library.\RK128 Inserts a hyper-link reference RK128 to the real128 real kind used in the library.\CK Inserts a hyper-link reference CK to the default complex kind used in the library.\CK32 Inserts a hyper-link reference CK32 to the real32 complex kind used in the library.\CK64 Inserts a hyper-link reference CK64 to the real64 complex kind used in the library.\CK128 Inserts a hyper-link reference CK128 to the real128 complex kind used in the library.\IK8 Inserts a hyper-link reference IK8 to the int8 integer kind used in the library.\IK16 Inserts a hyper-link reference IK16 to the int16 integer kind used in the library.\IK32 Inserts a hyper-link reference IK32 to the int32 integer kind used in the library.\IK64 Inserts a hyper-link reference IK64 to the int64 integer kind used in the library.\SKALL Inserts a hyper-link reference to all major character kinds like: any supported by the processor (e.g., SK, SKA, SKD , or SKU).\IKALL Inserts a hyper-link reference to all major integer kinds like: any supported by the processor (e.g., IK, IK8, IK16, IK32, or IK64).\LKALL Inserts a hyper-link reference to all major logical kinds like: any supported by the processor (e.g., LK).\CKALL Inserts a hyper-link reference to all major complex kinds like: any supported by the processor (e.g., CK, CK32, CK64, or CK128).\RKALL Inserts a hyper-link reference to all major real kinds like: any supported by the processor (e.g., RK, RK32, RK64, or RK128). For an up-to-date list of all available aliases, check the value of the Doxygen ALIASES option in config.txt in the ParaMonte Fortran documentation repository.
Escaping the Doxygen reserved characters.
Doxygen has a set of reserved characters whose usage in the documentation must be handled properly.
\ begins a Doxygen command.\\.% requires special care in some instances.For more information, see the relevant page on Doxygen documentation website.
\warning, \remark, \note and other similar tags. !> \brief
!> Generate and return the variance of the input array of shape `(np)` or `(nd,np)` or `(np,nd)` where `nd` is the number of
!> data dimensions (the number of data attributes) and `np` is the number of data points.
!>
!> \param[in] Sample : The input `contiguous` array of type `real` of kind \RKALL of shape `(np)`, `(nd,np)`, or `(np,nd)`
!> containing the sample. If `Sample` is a 2D array, then the direction along which the variance is computed
!> is dictated by the optional input argument `dim`.
!> \param[in] Weight : The `contiguous` vector of shape `(np)` either type `real` of the same kind as the input `Sample` or type `integer`
!> of kind \IKALL, containing the corresponding weight of each data points in `Sample`
!> (**optional**, default = a vector of ones).
!> \param[in] mean : The input scalar or `contiguous` vector of shape `(nd)` of the same type and kind as the input `Sample` containing
!> the `Sample` mean along the (optionally) specified dimension `dim`. If the input `Sample` is a 1D array, then `mean`
!> must be a scalar. Otherwise, if `mean` is a 2D array, then `mean` must be a vector whose size is the same as
!> the size of at least one of the dimensions of `Sample`.
!> (**optional**. If missing, then the input argument `shifted` must be present indicating whether the input `Sample`
!> is already centered at the origin or it has to be shifted to the origin by the procedure).
!> \param[in] shifted : The input `logical` of default kind \LK indicating whether the input `Sample` is already centered at the origin or
!> the it has to be shifted to the origin by the procedure (**optional**. If missing, then the input
!> argument `mean` must be present).
!> \param[in] biased : The input `logical` of default kind \LK indicating whether the output variance should be corrected for small sample-size
!> bias. Set this argument to `.false.` to avoid biased variance computation, in particular, when the sample size `np`
!> is small.
!> \param[in] dim : An integer of default kind \IK indicating which dimension of the input `Sample` iterates over the individual data points.
!> If `dim = 1` or `dim /= 2`, the input `Sample` is assumed to have the shape `(np,nd)`.
!> If `dim = 2`, the input `Sample` is assumed to have the shape `(nd,np)`
!> (**optional**, default = `2`. **This input argument is available only if the input `Sample` is a 2D array**.).
!>
!> \return
!> `variance` : The output variance of the input sample of the same type and kind as the input `Sample`.
!> It is a scalar only if the input `Sample` is a 1D array. Otherwise, it is an `allocatable` array of shape `(nd)`.
!>
!> \warnpure
!>
!> \note
!> One can also use the concise Fortran syntax to achieve the same goal as this function:
!> \code{.F90}
!>
!> mean = sum(Weight*Sample) / sum(Weight)
!> variance = sum( (Weight*(Sample-mean))**2 ) / (sum(Weight)-1)
!>
!> \endcode
!> But the above concise version will be slightly slower as it involves three loops instead of two.
!>
!> \see
!> [getMean()](@ref pm_sampleMean::getMean)<br>
!>
!> \example
!> \include{lineno} example/test_pm_sampleVar/getVar/main.F90
!> \compilef
!> \output
!> \include{lineno} example/test_pm_sampleVar/getVar/main.out.F90
!>
!> \test
!> [test_pm_sampleVar](@ref test_pm_sampleVar)
!>
!> \todo
!> The performance of this code can improved.
!>
!> \bug
!> This code used to have a well-known bug in version 1.1, but is now resolved.
!>
!> \finmain
!>
!> \author
!> \FatemehBagheri, Monday 02:15 AM, September 27, 2021, Dallas, TX<br> \example.The ParaMonte Fortran library ships with tens of thousands of example usage that are available in the example/fortran folder in the root directory of the project repository.
These examples are also available and discussed in the documentations of individual modules and procedures of this this documentation website.
The ParaMonte Fortran library ships with a large number of performance benchmarks that are available in the benchmark/fortran folder in the root directory of the project repository.
These benchmarks are also available and discussed in the benchmark listing page of this this documentation website.
If you would like to see a relevant benchmark currently not included, discuss it here or raise an issue here for consideration or volunteer to implement it!
For the full listing of all tasks to do see the dedicated ToDo listing page.
The following are the library tasks that need to be accomplished.
pm_distanceHellinger for computing the Hellinger metric distance must be added to the library.pm_distanceManhattan for computing the Manhattan metric distance must be added to the library.pm_distanceMinkowski for computing the Minkowski metric distance must be added to the library.pm_sampleConv for timer series convolution must be added to the library.
1.9.3