# Reading data from R matrices in C++

Aaron Lun

#### 28 April 2020

#### Package

beachmat 2.4.0

# 1 Overview of the input API

This document describes the use of the beachmat API for accessing data in R matrices. We will demonstrate the API on numeric matrices, though same semantics are used for matrices of other types (e.g., logical, integer, character). First, we include the relevant header file:

    #include "beachmat/numeric_matrix.h"

A double-precision matrix object `dmat` is handled in C++ by passing the `SEXP` struct from `.Call` to `create_numeric_matrix`:

    auto dptr = beachmat::create_numeric_matrix(dmat);

This creates a unique pointer that points to an object of the `numeric_matrix` base class. The exact derived class that is actually instantiated depends on the type of matrix in `dmat`, though the behaviour of the user-level functions are not affected by this detail.

Additional notes

- The `auto` keyword just avoids the need to write the full type of the returned pointer, which is `std::unique_ptr<beachmat::numeric_matrix>`. We use unique pointers to control ownership and smoothly handle destruction and memory deallocation at the end of the function.
- The API will happily throw exceptions of the `std::exception` class, containing an informative error message. These should be caught and handled gracefully by the end-user code, otherwise a segmentation fault will probably occur. See the error-handling mechanism in Rcpp for how to deal with these exceptions.

# 2 Querying matrix information

The `get_nrow()` method returns the number of rows in the matrix:

    size_t nrow = dptr->get_nrow();

The `get_ncol()` method returns the number of columns in the matrix:

    size_t ncol = dptr->get_ncol();

The `get_class()` method returns the class of the matrix representation pointed to by `dptr`, while the `get_package()` method returns the package in which that class is defined1 1 1 In case two packages define the same class name..

    std::string mat_type = dptr->get_class();

The `yield()` method returns the original R matrix that was used to create `dptr`.

    Rcpp::RObject original = dptr->yield();

# 3 Basic data extraction

## 3.1 From columns

The `get_col()` method fills an iterator `in` to an Rcpp vector with values from a column `c` of the matrix. There should be at least `nrow` accessible elements, i.e., `*in` and `*(in+nrow-1)` should be valid entries.

    dptr->get_col(
        c, /* size_t */
        in /* Rcpp::Vector::iterator */
    );

Extraction of a range of the column can be specified with the `first` and `last` arguments. This will fill `in` with values at column `c` from row `first` to `last-1`. There should be at least `last-first` accessible elements, i.e., `*in` and `*(in+last-first-1)` should be valid entries.

    dptr->get_col(
        c, /* size_t */
        in, /* Rcpp::Vector::iterator */
        first, /* size_t */
        last /* size_t */
    );

No value is returned by either of these methods. Note that `c` should be a zero-indexed integer in `[0, ncol)`. Similarly, both `first` and `last` should be in `[0, nrow]` and zero-indexed, with the additional requirement that `last >= first`.

## 3.2 From rows

The `get_row()` method takes an iterator `in` to a Rcpp vector and fills it with values at row `r`. There should be at least `ncol` accessible elements, i.e., `*in` and `*(in+ncol-1)` should be valid entries.

    dptr->get_row(
        r, /* size_t */
        in /* Rcpp::Vector::iterator */
    );

Extraction of a range of the row can be specified with the `first` and `last` arguments. This will fill `in` with values at row `r` from column `first` to `last-1`. There should be at least `last-first` accessible elements, i.e., `*in` and `*(in+last-first-1)` should be valid entries.

    dptr->get_row(
        r, /* size_t */
        in, /* Rcpp::Vector::iterator */
        first, /* size_t */
        last /* size_t */
    );

No value is returned by either of these methods. Again, `r` should be a zero-indexed integer in `[0, nrow)`. Both `first` and `last` should be in `[0, ncol]` and zero-indexed, with the additional requirement that `last >= first`.

## 3.3 From individual cells

The `get()` method returns a double-precision value at the matrix entry for row `r` and column `c`. Both `r` and `c` should be zero-indexed integers in `[0, nrow)` and `[0, ncol)` respectively.

    double val = dptr->get(
        r, /* size_t */
        c /* size_t */
    );

## 3.4 Type conversions

If the object `in` is a `Rcpp::NumericVector::iterator` instance, matrix entries will be extracted as double-precision values. If it is a `Rcpp::IntegerVector::iterator` instance, matrix entries will be extracted as integers with implicit conversion from the double-precision type in `dptr`. It is also possible to use a `Rcpp::LogicalVector::iterator`, though see the warnings below.

# 4 Multiple data extraction

## 4.1 From columns

The `get_cols()` method fills an iterator `in` to an Rcpp vector with values from multiple columns of the matrix. The `idx` iterator should point to an array of integers of length `n`, containing the column indices to use for extraction. The indices should be zero-based and strictly increasing, i.e., no duplicates.

    dptr->get_cols(
        idx, /* Rcpp::IntegerVector::iterator */
        n, /* size_t */
        in, /* Rcpp::Vector::iterator */
        first, /* size_t */
        last /* size_t */
    );

For each column, the range of values in `[first, last)` are extracted. If `first` and `last` are not specified, the range will default to `[0, nrow)`. Thus, there should be at least `n*(last-first)` accessible elements pointed to by `in`.

This method will extract values in column-major format. That is, if one were to compute a submatrix containing the selected columns and the chosen row range, that submatrix would be available in column-major form in `in`.

No value is returned by this method.

## 4.2 From rows

The `get_rows()` method fills an iterator `in` to an Rcpp vector with values from multiple rows of the matrix. The `idx` iterator should point to an array of integers of length `n`, containing the column indices to use for extraction. The indices should be zero-based and strictly increasing, i.e., no duplicates.

    dptr->get_rows(
        idx, /* Rcpp::IntegerVector::iterator */
        n, /* size_t */
        in, /* Rcpp::Vector::iterator */
        first, /* size_t */
        last /* size_t */
    );

For each row, the range of values in `[first, last)` are extracted. If `first` and `last` are not specified, the range will default to `[0, ncol)`. Thus, there should be at least `n*(last-first)` accessible elements pointed to by `in`.

Like `get_cols()`, this method will extract values in column-major format. That is, if one were to compute a submatrix containing the selected columns and the chosen row range, that submatrix would be available in column-major form in `in`. Note that this means that contiguous elements in `in` are not from the same row! Rather, they will be from the same column, but only from the rows specified by `idx`.

No value is returned by this method.

# 5 Generalizing to other matrices

## 5.1 Other data types

To create logical, integer and character matrices, include the following header files:

    #include "beachmat/logical_matrix.h"
    #include "beachmat/integer_matrix.h"
    #include "beachmat/character_matrix.h"

The dispatch function changes correspondingly for logical matrix `lmat`, integer matrix `imat` or character matrix `cmat`. Each function creates a unique pointer to a `*_matrix` of the appropriate type.

    // creates a std::unique_ptr<beachmat::logical_matrix>
    auto lptr=beachmat::create_logical_matrix(lmat);

    // creates a std::unique_ptr<beachmat::integer_matrix>
    auto iptr=beachmat::create_integer_matrix(imat);

    // creates a std::unique_ptr<beachmat::character_matrix>
    auto cptr=beachmat::create_character_matrix(cmat);

Equivalent methods are available for each matrix type with appropriate changes in type.

For integer and logical matrices, `get()` will return an integer. `in` can be any type previously described for `numeric_matrix` objects.

For character matrices, all iterators should be of type `Rcpp::StringVector::iterator`, and `get()` will return a `Rcpp::String`.

Additional notes

- If `in` is a `Rcpp::LogicalVector::iterator` for non-logical matrices, the result may not behave as expected. For `numeric_matrix` instances, double-precision values in `(-1, 1)` are coerced to zero due to double-to-integer casting in C++. This is not consistent with the behaviour in R for non-zero values, which are coerced to `TRUE`. For `integer_matrix` instances, integer values are not coerced to `{0, 1}` when they are assigned to `*in`. Thus, even though the interpretation is correct, the vector produced will not be equivalent to the result of an `as.logical` call. As a general rule, it is unwise to use `Rcpp::LogicalVector::iterator`s for anything other than `logical_matrix` access.
- When accessing `character_matrix` data, we do not return raw `const char*` pointers to the C-style string. Rather, the `Rcpp::String` class is used as it provides a convenient wrapper around the underlying `CHARSXP`. This ensures that the string is stored in R’s global cache and is suitably protected against garbage collection.

## 5.2 Alternative matrix representations

The following matrix classes are natively supported by the API:

- numeric: `matrix`, `dgeMatrix`, `dgCMatrix`
- integer: `matrix`
- logical: `matrix`, `lgeMatrix`, `lgCMatrix`
- character: `matrix`

The API will also natively support `DelayedMatrix` objects using the above matrices as backends and containing only subsetting or transposition operations. It is possible to natively support arbitrary user-supplied matrices, see here for more details and HDF5Array for an example.

For all other matrices, the API indirectly supports data access via a block processing mechanism. This involves a call to R to realize a block of the matrix (containing the requested row or column) as a dense contiguous array. A block is realized so that further requests to rows/columns within the same block do not involve a new call to R. The size of the blocks can be controlled using methods in the DelayedArray package, see `?blockGrid` for details.

Additional notes

- For numeric matrices, beachmat does not support higher-level matrix operations such as addition, multiplication or various factorizations. Rather, the `yield` method can be used to obtain the original `Rcpp::RObject` for input to RcppArmadillo or RcppEigen. This functionality is generally limited to base matrices, though there is also limited support for sparse matrices in these libraries.

# 6 Specialized data extraction

## 6.1 Overview

For specific matrix representations, special methods are available that can improve the efficiency of column-level data access.

- Ordinary matrices or `dgeMatrix` instances are stored as dense arrays, so it is possible to access the columns without copying by returning an iterator to the start of each column.
- If the underlying matrix is a `dgCMatrix`, the column-sparse format allows us to access the non-zero values (and their row indices) directly for each column without copying.

The `const_column` class provides a convenient wrapper to exploit these optimizations where possible.

    #include "beachmat/utils/const_column.h"

    // Need a get() as unique_ptr's are not copyable.
    beachmat::const_column<beachmat::numeric_matrix> col_holder(dptr.get());

The `fill` method will instruct the `const_column` object to obtain the relevant column, taking advantage of no-copy methods if supported by the representation. For other matrices, it simply calls `get_col()` to perform a copy to its internal storage.

    col_holder.fill(
        c /* size_t */,
        first /* size_t */,
        last /* size_t */
    );

The `first` and `last` arguments are optional and behave as previously described.

Additional notes

- The lifetime of the `const_column` instance should not exceed that of the `numeric_matrix` with which it was constructed. This is because the former holds a pointer to the latter, which would no longer be valid upon destruction. The `const_column` also keeps iterators to the underlying R-managed data, which could be invalidated upon `numeric_matrix` destruction in some contrived scenarios.

## 6.2 Interpreting the iterators

An iterator to the values of the column is obtained with `get_values`:

    Rcpp::NumericVector::iterator val=col_holder.get_values();

An iterator to the row index of each value is obtained with `get_indices`:

    Rcpp::IntegerVector::iterator idx=col_holder.get_indices();

The number of values pointed to by the iterator is obtained with `get_n`:

    size_t n=col_holder.get_n();

Obviously, sparse matrices will not store any zeroes in the array of values pointed to by `get_values()`, nor will the row indices for zeroes be present in the array pointed to by `get_indices()`. This may or may not require some custom code to take maximum advantage of sparsity:

    if (col_holder.is_sparse()) {
        // Do something fast with non-zero elements.
    } else {
        // Do something with all elements.
    }

## 6.3 Further options

Some applications require representation of all elements including zeroes, e.g., when the subsequent array needs to be accessed by row index. We can ensure that we obtain an iterator to a dense array by constructing the `const_column` with the `allow_sparsity` argument turned off:

    beachmat::const_column<beachmat::numeric_matrix> col_holder(
        dptr.get(), false);

Doing so will force `const_column` to use `get_col()` for accessing sparse matrices, instead of obtaining iterators to the raw structure. However, no-copy optimizations for dense matrices will still be active.

For non-sparse matrices, calling `get_indices()` will cause an internal array to be populated with consecutive iterators. One can share this array across many `const_column` instances by calling `get_indices()` prior to construction of copies:

    beachmat::const_column<beachmat::numeric_matrix> col_holder(dptr.get());
    col_holder.get_indices(); // Effectively 'static' indices.

    // Make any number of copies without re-generating the indices.
    auto holder_copy=col_holder;

This can save some memory if many `const_column` objects are to be created.

# 7 Cloning matrix instances

The `clone()` method returns a unique pointer to a `numeric_matrix` instance of the same type as that pointed to by `dptr`.

    auto dptr_copy = dptr->clone();

This is occasionally useful, e.g., when row and column access is simultaneously required from the same matrix. In such cases, row-specific settings in a single `numeric_matrix` instance (e.g., for HDF5 caching) would preclude efficient column extraction, and vice versa. These problems are avoided by having two separate instances for row and column access.

Cloning also enables multi-threaded access to the same matrix data. Ordinarily, the `get*` methods in beachmat are not thread safe. Some methods use cached class members for greater efficiency, and simultaneous calls will cause race conditions. It is the responsibility of the calling function to coordinate data access across threads. To this end, the `clone` method can be called to generate a unique pointer to a new `*_matrix` instance, which can be used concurrently in another thread. This is fairly cheap as the underlying matrix data are not copied.

An example of parallelized beachmat code using OpenMP might look like this:

    #pragma omp parallel num_threads(nthreads)
    {
        beachmat::numeric_matrix* rptr=NULL;
        std::unique_ptr<beachmat::numeric_matrix> uptr=nullptr;
        if (omp_get_thread_num()==0) {
            rptr=dptr.get();
        } else {
            uptr=dptr->clone();
            rptr=uptr.get();
        }

        const size_t NC=rptr->get_ncol();
        Rcpp::NumericVector output(rptr->get_nrow());

        #pragma omp for schedule(static)
        for (size_t col=0; col<NC; ++col) {
            // Do parallel operation here.
            rptr->get_col(col, output.begin());
        }
    }

The start of the parallel region uses the existing `dptr` in the master thread and clones a new matrix in the other threads. The parallelized `for` loop then uses `rptr` to avoid race conditions in cached variables. Note that a static schedule may be faster than other schedule types, as several of the matrix implementations in beachmat are optimized for consecutive row/column access.

Additional notes

- For community-defined matrices, beachmat may use external linkage to natively access data. Developers of the corresponding shared libraries should ensure that their routines depend on thread-safe libraries. For example, the HDF5 library is not thread safe, so HDF5Array inputs will likely break OpenMP code. This is admittedly rather frustrating as HDF5-backed matrices are often used for large data sets that most require parallel processing. As a workaround, we suggest parallelizing at the R level with BiocParallel.