# Reading data from R matrices in C++

Aaron Lun

#### 30 October 2018

#### Package

beachmat 1.4.0

# 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_matrix_type()` method returns the type of matrix representation pointed to by `dptr`. This can be tested against constants like `beachmat::SIMPLE` or `beachmat::SPARSE`.

    beachmat::matrix_type mat_type = dptr->get_matrix_type();

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 Specialized data extraction

## 4.1 From dense matrices

The `get_const_col()` method returns an iterator to a Rcpp vector pointing to `first` row of column `c`. The arguments are the same as `get_col()`11 Users can also specify `first` and `last`, though we will not do so here for simplicity. with `work` being equivalent to `in`. The type of `work` and the output iterator must correspond to the data type of the matrix - in this case, both should be `Rcpp::NumericVector::iterator` objects.

    Rcpp::NumericVector::iterator it = dptr->get_const_col(
        c, /* size_t */
        work, /* Rcpp::NumericVector::iterator */
    );

For simple/dense matrices, this method is more efficient than `get_col()` as it returns the iterator without needing to copy data into `work`. For other matrices, this function simply calls `get_col()` to copy the data into the vector starting at `work`, and then returns an iterator equal to `work`. Thus, for general use, `work` must point to a writeable block of memory, even if it does not get used when `dptr` points to a simple/dense matrix.

Additional notes

- Calling processes should consider the vector starting at `work` to be read-only after a call to `get_const_col()`. In particular, the underlying data will be modified if `get_const_col()` is called again with the same `work`. This has some consequences if a process calls `get_const_col()` multiple times to obtain more than one iterators for further computation. In such cases, developers should ensure that each `get_const_col()` call uses a `work` pointing to a different vector.

## 4.2 From sparse matrices

The `get_const_col_indexed()` method is guaranteed to index at least all the “non-zero” entries in column `c` of the matrix. For numeric types, this represents non-zero values (obviously), while for character matrices, this represents non-empty strings.

    auto indexinfo = dptr->get_const_col_indexed(
        c, /* size_t */
        work, /* Rcpp::NumericVector::iterator */
        first, /* size_t */
        last /* size_t */
    );

It returns a `const_col_indexed_info` object, which is a tuple consisting of:

1. A `size_t`, specifying the number of entries in column `c` from rows `[first, last)`.
2. A `Rcpp::IntegerVector::iterator`, pointing to a vector containing the row index for each entry in column `c` from rows `[first, last)`.
3. A `Rcpp::NumericVector::iterator`, pointing to a vector containing the value of each entry in column `c` from rows `[first, last)`.

The data type of `work` and the output iterator in (3) must correspond to that of the matrix - in this case, both should be `Rcpp::NumericVector::iterator` objects. Again, `first` and `last` do not have to be specified and will default to the entire column.

This method is quite efficient for `dgCMatrix` objects, as it will directly return iterators to the indices and values of the non-zero entries only. No copying is performed, and the zero values do not have to be explicitly generated as they would be in `get_col`. For all other matrices, `get_const_col` is called22 The comments above regarding the read-only nature of `work` also apply here. and iterator (2) is pointed at an internal array of consecutive integers (which should be treated as read-only).

Note that this method is not guaranteed to index only the non-zero entries. The specific representation may choose to return only the non-zero entries or all of them.

# 5 Multiple data extraction

## 5.1 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.

## 5.2 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.

# 6 Generalizing to other matrices

## 6.1 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. `work` should be an `iterator` to a `Rcpp::IntegerVector` for integer matrices or a `Rcpp::LogicalVector` for logical matrices. Similar changes apply to the iterator in the tuple from `get_const_col_indexed()`.

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.

## 6.2 Alternative matrix representations

The following matrix classes are directly supported by the API:

- numeric: `matrix`, `dgeMatrix`, `dgCMatrix`, `HDF5Matrix`
- integer: `matrix`, `RleMatrix`, `HDF5Matrix`
- logical: `matrix`, `lgeMatrix`, `lgCMatrix`, `HDF5Matrix`
- character: `matrix`, `HDF5Matrix`

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

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.

# 7 Cloning for parallelization

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 useful as direct use of the beachmat API is not thread-safe for simultaneous calls to the `get` methods from different threads. 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
    {
        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();
        }

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

        #pragma omp for schedule(static)
        for (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.