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# The TREXIO library

## Table of Contents

- 1. Format specification
  - 1.1. Organization of the data
  - 1.2. Data types
- 2. The TREXIO library
  - 2.1. The front-end
  - 2.2. The back-end
  - 2.3. Supported languages
  - 2.4. Source code generation and documentation
  - 2.5. Availability

## 1 Format specification

The TREXIO format is designed to store all the necessary information to represent a wave function. One notable feature of TREXIO is that it is self-contained, meaning that all the parameters needed to recreate the wave function are explicitly stored within the file, eliminating the need for external databases. For example, instead of storing the name of a basis set (such as cc-pVDZ), the actual basis set parameters used in the calculation are stored.

### 1.1 Organization of the data

The data in TREXIO are organized into groups, each containing multiple attributes defined by their type and dimensions. Each attribute within a group corresponds to a single scalar or array variable in a code. In what follows, the notation `<group>.<attribute>` will be used to identify an attribute within a group. For example, `nucleus.charge` refers to the `charge` attribute in the `nucleus` group. It is an array of type `float` with dimensions `nucleus.num`, the attribute describing the number of nuclei.

### 1.2 Data types

So that TREXIO can be used in any language, we use a limited number of data types. The main data types are `int` for integers, `float` for floating-point values, and `str` for character strings. For complex numbers, their real and imaginary parts are stored as `float`. To minimize the risk of integer overflow and accuracy loss, numerical data types are stored using 64-bit representations by default. However, in specific cases where integers are bounded (such as orbital indices in four-index integrals), the smallest possible representation is used to reduce the file size. The API handles any necessary type conversions.

There are also two types derived from `int`: `dim` and `index`. `dim` is used for dimensioning variables, which are positive integers used to specify the dimensions of an array. In the previous example, `nucleus.num` is a dimensioning variable that specifies the dimensions of the `nucleus.charge` array. `index` is used for integers that correspond to array indices, because some languages (such as C or Python) use zero-based indexing, while others (such as Fortran) use one-based indexing. For convenience, values of the `index` type are shifted by one when TREXIO is used in one-based languages to be consistent with the semantics of the language. You may also encounter some `dim readonly` variables. It means that the value is automatically computed and written by the TREXIO library, thus it is read-only and cannot be (over)written by the user.

Arrays can be stored in either dense or sparse formats. If the sparse format is selected, the data is stored in coordinate format. For example, the element `A(i,j,k,l)` is stored as a quadruplet of integers \((i,j,k,l)\) along with the corresponding value. Typically, two-dimensional arrays are stored as dense arrays, while arrays with higher dimensions are stored in sparse format. For sparse data structures the data can be too large to fit in memory and the data needs to be fetched using multiple function calls to perform I/O on buffers. For more information on how to read/write sparse data structures, see the examples.

For the Configuration Interaction (CI) and Configuration State Function (CSF) groups, the `buffered` data type is introduced, which allows similar incremental I/O as for `sparse` data but without the need to write indices of the sparse values.

For determinant lists (integer bit fields), the `special` attribute is present in the type. This means that the source code is not produced by the generator, but hand-written.

Some data may be complex. In that case, the real part should be stored in the variable, and the imaginary part will be stored in the variable with the same name suffixed by `_im`.

## 2 The TREXIO library

The TREXIO library is written is the C language, and is licensed under the open-source 3-clause BSD license to allow for use in all types of quantum chemistry software, whether commercial or not.

The design of the library is divided into two main sections: the front-end and the back-end. The front-end serves as the interface between users and the library, while the back-end acts as the interface between the library and the physical storage.

### 2.1 The front-end

By using the TREXIO library, users can store and extract data in a consistent and organized manner. The library provides a user-friendly API, including functions for reading, writing, and checking for the existence of data. The functions follow the pattern `trexio_[has|read|write]_<group>_<attribute>`, where the group and attribute specify the particular data being accessed. It also includes an error handling mechanism, in which each function call returns an exit code of type `trexio_exit_code`, explaining the type of error. This can be used to catch exceptions and improve debugging in the upstream user application.

To ensure the consistency of the data, the attributes can only be written if all the other attributes on which they explicitly depend have been written. For example, as the `nucleus.coord` array is dimensioned by the number of nuclei `nucleus.num`, the `nucleus.coord` attribute can only be written after `nucleus.num`. However, the library is not aware of non-explicit dependencies, such as the relation between the electron repulsion integrals (ERIs) and MO coefficients. A complete control of the consistency of the data is therefore impossible, so the attributes were chosen to be by default immutable. By only allowing data to be written only once, the risk of modifying data in a way that creates inconsistencies is reduced. For example, if the ERIs have already been written, it would be inconsistent to later modify the MO coefficients. To allow for flexibility, the library also allows for the use of an unsafe mode, in which data can be overwritten. However, this mode carries the risk of producing inconsistent files, and the `metadata` group's `unsafe` attribute is set to `1` to indicate that the file has potentially been modified in a dangerous way. This attribute can be manually reset to `0` if the user is confident that the modifications made are safe.

### 2.2 The back-end

At present, TREXIO supports two back-ends: one relying only on the C standard library to produce plain text files (the so-called text back-end), and one relying on the HDF5 library.

With the text back-end, the TREXIO "file" is a directory containing multiple text files, one for each group. This back end is intended to be used in development environments, as it gives access to the user to the standard tools such as `diff` and `grep`. In addition, text files are better adapted than binary files for version control systems such as Git, so this format can be also used for storing reference data for unit tests.

HDF5 is a binary file format and library for storing and managing large amounts of data in a hierarchical structure. It allows users to manipulate data in a way similar to how files and directories are manipulated within the file system. The HDF5 library provides optimal performance through its memory mapping mechanism and supports advanced features such as serial and parallel I/O, chunking, and compression filters. However, HDF5 files are in binary format, which requires additional tools such as `h5dump` to view them in a human-readable format. It is widely used in scientific and engineering applications, and is known for its high performance and ability to handle large data sets efficiently.

The TREXIO HDF5 back-end is the recommended choice for production environments, as it provides high I/O performance. Furthermore, all data is stored in a single file, making it especially suitable for parallel file systems like Lustre. These file systems are optimized for large, sequential I/O operations and are not well-suited for small, random I/O operations. When multiple small files are used, the file system may become overwhelmed with metadata operations like creating, deleting, or modifying files, which can adversely affect performance.

In a benchmarking program designed to compare the two back-ends of the library, the HDF5 back-end was found to be significantly faster than the text back-end. The program wrote a wave function made up of 100 million Slater determinants and measured the time taken to write the Slater determinants and CI coefficients. The HDF5 back-end achieved a speed of \(10.4\times10^6\) Slater determinants per second and a data transfer rate of 406 MB/s, while the text back-end had a speed of \(1.1\times10^6\) determinants per second and a transfer rate of 69 MB/s. These results were obtained on a DELL 960 GB mix-use solid-state drive (SSD). The HDF5 back-end was able to achieve a performance level close to the peak performance of the SSD, while the text back-end's performance was limited by the speed of the CPU for performing binary to ASCII conversions.

In addition to the HDF5 and text back-ends, it is also possible to introduce new back-ends to the library. For example, a back-end could be created to support object storage systems, such as those used in cloud-based applications or for archiving in open data repositories.

### 2.3 Supported languages

One of the main benefits of using C as the interface for a library is that it is easy to use from other programming languages. Many programming languages, such as Python or Julia, provide built-in support for calling C functions, which means that it is relatively straightforward to write a wrapper that allows a library written in C to be called from another language. In general, libraries with a C interface are the easiest to use from other programming languages, because C is widely supported and has a simple, stable application binary interface (ABI). Other languages, such as Fortran and C++, may have more complex ABIs and may require more work to interface with them.

TREXIO has been employed in codes developed in various programming languages, including C, C++, Fortran, Python, OCaml, and Julia. While Julia is designed to enable the use of C functions without the need for additional manual interfacing, the TREXIO C header file was automatically integrated into Julia programs using the `CBindings.jl` package. In contrast, specific bindings have been provided for Fortran, Python, and OCaml to simplify the user experience.

In particular, the binding for Fortran is not distributed as multiple compiled Fortran module files (`.mod`), but instead as a single Fortran source file (`.F90`). The distribution of the source file instead of the compiled module has multiple benefits. It ensures that the TREXIO module is always compiled with the same compiler as the client code, avoiding the compatibility problem of `.mod` files between different compiler versions and vendors. The single-file model requires very little changes in the build system of the user's codes, and it facilitates the search for the interface of a particular function. In addition, advanced text editors can parse the TREXIO interface to propose interactive auto-completion of the TREXIO function names to the developers.

Finally, the Python module, partly generated with SWIG and fully compatible with NumPy, allows Python users to interact with the library in a more intuitive and user-friendly way. Using the Python interface is likely the easiest way to begin using TREXIO and understanding its features. In order to help users get started with TREXIO and understand its functionality, tutorials in Jupyter notebooks are available on GitHub (https://github.com/TREX-CoE/trexio-tutorials), and can be executed via the Binder platform.

### 2.4 Source code generation and documentation

Source code generation is a valuable technique that can significantly improve the efficiency and consistency of software development. By using templates to generate code automatically, developers can avoid manual coding and reduce the risk of errors or inconsistencies. This approach is particularly useful when a large number of functions follow similar patterns, as in the case of the TREXIO library, where functions are named according to the pattern `trexio_[has|read|write]_<group>_<attribute>`. By generating these functions from the format specification using templates, the developers can ensure that the resulting code follows a consistent structure and is free from errors or inconsistencies.

The description of the format is written in a text file in the Org format. Org is a structured plain text format, containing information expressed in a lightweight markup language similar to the popular Markdown language. While Org was introduced as a mode of the GNU Emacs text editor, its basic functionalities have been implemented in most text editors such as Vim, Atom or VS Code.

There are multiple benefits in using the Org format. The first benefit is that the Org syntax is easy to learn and allows for the insertion of equations in \LaTeX{} syntax. Additionally, Org files can be easily converted to HyperText Markup Language (HTML) or Portable Document Format (PDF) for generating documentation. The second benefit is that GNU Emacs is a programmable text editor and code blocks in Org files can be executed interactively, similar to Jupyter notebooks. These code blocks can also manipulate data defined in tables and this feature is used to automatically transform tables describing groups and attributes in the documentation into a JavaScript Object Notation (JSON) file. This JSON file is then used by a Python script to generate the needed functions in C language, as well as header files and some files required for the Fortran, Python, and OCaml interfaces.

With this approach, contributions to the development of the TREXIO library can be made simply by adding new tables to the Org file, which can be submitted as pull requests on the project's GitHub repository (https://github.com/trex-coe/trexio). Overall, this process allows for a more efficient and consistent development process and enables contributions from a wider range of individuals, regardless of their programming skills.

### 2.5 Availability

The TREXIO library is designed to be portable and easy to install on a wide range of systems. It follows the C99 standard to ensure compatibility with older systems, and can be configured with either the GNU Autotools or the CMake build systems. The only external dependency is the HDF5 library, which is widely available on HPC platforms and as packages on major Linux distributions. Note that it is possible to disable the HDF5 back-end at configuration time, allowing TREXIO to operate only with the text back-end and have zero external dependencies. This can be useful for users who may not be able to install HDF5 on certain systems.

TREXIO is distributed as a tarball containing the source code, generated code, documentation, and Fortran interface. It is also available as a binary `.deb` package for Debian-based Linux distributions and as packages for Guix, Spack and Conda. The Python module can be found in the PyPI repository, the OCaml binding is available in the official OPAM repository, and the `.deb` packages are available in Ubuntu 23.04.

Author: TREX-CoE

Created: 2023-04-26 Wed 08:13

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