tatami is a spiritual successor to the beachmat C++ API that provides read access to different matrix representations. Specifically, applications can use tatami to read rows and/or columns of a matrix without any knowledge of the specific matrix representation. This allows application developers to write a single piece of code that will work seamlessly with different inputs, even if the underlying representation varies at run-time. In particular, tatami is motivated by analyses of processed genomics data, where matrices are often interpreted as a collection of row- or column-wise vectors. Many applications involve looping over rows or columns to compute some statistic or summary - for example, testing for differential expression within each row of the matrix. tatami aims to optimize this access pattern across a variety of different matrix representations, depending on how the data is provided to the application.
tatami is a header-only library, so it can be easily used by just #includeing the relevant source files:
#include "tatami/tatami.hpp"
std::shared_ptr<tatami::NumericMatrix> mat(new tatami::DenseRowMatrix<double>(nrows, ncols, vals));
// Get the dimensions:
int NR = mat->nrow(), NC = mat->ncol();
// Extract the 'i'-th column.
auto extractor = mat->dense_column();
std::vector<double> buffer(NR);
auto ptr = extractor->fetch(i, buffer.data());
ptr[0];
// Extract the [5, 12) rows of the 'i'-th column.
auto sliced_extractor = mat->dense_column(5, 7)
auto sliced_ptr = sliced_extractor->fetch(i, buffer.data());The key idea here is that, once mat is created, the application does not need to worry about the exact format of the matrix referenced by the pointer.
Application developers can write code that works interchangeably with a variety of different matrix representations.
Users can create an instance of a concrete tatami::Matrix subclass by using one of the constructors or the equivalent make_* utility:
| Description | Class or function |
|---|---|
| Dense matrix | DenseMatrix |
| Compressed sparse matrix | CompressedSparseMatrix |
| List of lists sparse matrix | FragmentedSparseMatrix |
| Delayed isometric unary operation | make_DelayedUnaryIsometricOp() |
| Delayed isometric binary operation | make_DelayedBinaryIsometricOp() |
| Delayed combination | make_DelayedBind() |
| Delayed subset | make_DelayedSubset() |
| Delayed transpose | make_DelayedTranspose() |
| Delayed cast | make_DelayedCast() |
For example, to create a compressed sparse matrix from sparse triplet data, we could do:
#include "tatami/tatami.hpp"
int NROW = 10, NCOL = 20;
auto indptrs = tatami::compress_sparse_triplets<false>(NR, NC, x, i, j);
auto raw_ptr = new tatami::CompressedSparseColumnMatrix(
NR,
NC,
std::move(x),
std::move(i),
std::move(indptrs)
);
std::shared_ptr<tatami::Matrix<double, int> > mat(raw_ptr);We typically create a shared_ptr to a tatami::Matrix to leverage run-time polymorphism.
This enables downstream applications to accept many different matrix representations by compiling against the tatami::Matrix interface.
Alternatively, applications may use templating to achieve compile-time polymorphism on the different tatami subclasses,
but this is rather restrictive without providing obvious performance benefits.
We use templating to define the type of values returned by the interface.
This includes the type of the data (most typically double) as well as the type of row/column indices (default int, but one could imagine using, e.g., size_t).
It is worth noting that the storage type does not need to be the same as the interface type.
For example, developers could store a matrix of small counts as uint16_t while returning doubles for compatibility with downstream mathematical code.
The delayed operations are stolen from inspired by those in the DelayedArray package.
Isometric operations are particularly useful as they accommodate matrix-scalar/vector arithmetic and various mathematical operations.
For example, we could apply a sparsity-breaking delayed operation to our sparse matrix mat without actually creating a dense matrix:
tatami::DelayedAddScalarHelper<double> op(1);
auto mat2 = tatami::make_DelayedIsometricOp(mat, std::move(op));Some libraries in the @tatami-inc organization implement further extensions of tatami's interface, e.g., for HDF5-backed matrices and R-based matrices.
Given an abstract tatami::Matrix, we create an Extractor instance to actually extract the matrix data.
Each Extractor object can store intermediate data for re-use during iteration through the matrix, which is helpful for some matrix implementations that do not easily support random access.
For example, to perform extract dense rows from our mat:
int NR = mat->nrow();
int NC = mat->ncol();
auto ext = mat->dense_row();
std::vector<double> buffer(NC);
for (int r = 0; r < NR; ++r) {
auto current = ext->fetch(r, buffer.data());
// Do something with the 'current' pointer.
}The tatami::MyopicDenseExtractor::fetch() method returns a pointer to an array of length equal to the number of columns that contains each row's contents.
In some matrix representations (e.g., DenseMatrix), the returned pointer directly refers to the matrix's internal data store.
However, this is not the case in general so we need to allocate a buffer of appropriate length (buffer) in which the dense contents can be stored;
if this buffer is used, the returned pointer refers to the buffer start.
Users can also use tatami::MyopicDenseExtractor::fetch_copy() if they want to force a copy of the row contents into the buffer, regardless of the representation.
Alternatively, we could extract sparse columns via tatami::MyopicSparseExtractor::fetch(),
which returns a tatami::SparseRange containing pointers to arrays of (structurally non-zero) values and their row indices.
This provides some opportunities for optimization in algorithms that only need to operate on non-zero values.
The fetch() call requires buffers for both arrays - again, this may not be used for matrix subclasses with contiguous internal storage of the values/indices.
auto sext = mat->sparse_column();
std::vector<double> vbuffer(NR);
std::vector<int> ibuffer(NR);
for (int c = 0; c < NC; ++c) {
auto current = sext->fetch(c, vbuffer.data(), ibuffer.data());
current.number; // Number of structural non-zeros
current.value; // Pointer to the value array
current.index; // Pointer to the index array
}In both the dense and sparse cases, we can restrict the values that are extracted by fetch().
This provides some opportunities for optimization by avoiding the unnecessary extraction of uninteresting data.
To do so, we define a range of elements or supply a vector containing the indices of the elements of interest during Extractor construction:
// Get rows [5, 17) from each column.
auto bext = mat->dense_column(5, 12);
// Get these columns from each row.
auto iext = mat->sparse_row(std::vector<int>{ 1, 3, 5, 7 });In performance-critical sections, it may be desirable to customize the extraction based on properties of the matrix. This is supported with the following methods:
tatami::Matrix::sparse()indicates whether a matrix is sparse.tatami::Matrix::prefer_rows()indicates whether a matrix is more efficiently accessed along its rows (e.g., row-major dense matrices).
Users can then write dedicated code paths to take advantage of these properties.
For example, we might use different algorithms for dense data, where we don't have to look up indices; and for sparse data, if we can avoid the uninteresting zero values.
Similarly, if we want to compute a row-wise statistic, but the matrix is more efficiently accessed by column according to prefer_rows(),
we could iterate on the columns and attempt to compute the statistic in a "running" manner (see colsums.cpp for an example).
In the most complex cases, this leads to code like:
if (mat->sparse()) {
if (mat->prefer_rows()) {
auto sext = mat->sparse_row();
// Do compute along sparse rows.
} else {
auto sext = mat->sparse_column();
// Do compute along sparse columns.
}
} else {
if (mat->prefer_rows()) {
auto sext = mat->dense_row();
// Do compute along dense rows.
} else {
auto sext = mat->dense_column();
// Do compute along dense columns.
}
}Of course, this assumes that it is possible to provide sparse-specific optimizations as well as running calculations for the statistic of interest. In most cases, only a subset of the extraction patterns are actually feasible so special code paths would not be beneficial.
The mutable nature of an Extractor instance means that the fetch() calls themselves are not const.
This means that the same extractor cannot be safely re-used across different threads as each call to fetch() will modify the extractor's contents.
Fortunately, the solution is simple - just create a separate Extractor (and the associated buffers) for each thread.
With OpenMP, this looks like:
#pragma omp parallel num_threads(nthreads);
{
auto wrk = mat->dense_row();
std::vector<double> buffer(NC);
#pragma omp for
for (int r = 0; r < NR; ++r) {
auto ptr = wrk->fetch(r, buffer.data());
// Do something in each thread.
}
}Users may also consider using the tatami::parallelize() function, which accepts a function with the range of jobs (in this case, rows) to be processed in each thread.
This responds to the TATAMI_CUSTOM_PARALLEL macro, which allows applications to easily change their parallelization scheme.
For example, if a toolchain does not support OpenMP, an application can set the macro to switch to <thread> instead.
tatami::parallelize([&](int thread, int start, int length) -> void {
auto wrk = mat->dense_row();
std::vector<double> buffer(NC);
for (int r = 0; r < length; ++r) {
auto ptr = wrk->fetch(r + start, buffer.data());
// Do something in each thread.
}
}, NR, nthreads);When calling the tatami::Matrix methods, advanced users can supply an Oracle that specifies the sequence of rows/columns to be accessed.
Knowledge of the future access pattern enables optimizations in some Matrix implementations,
e.g., file-backed matrices can reduce the number of disk reads by pre-fetching the right data for future accesses.
The most obvious use case involves accessing consecutive rows/columns:
auto o = std::make_shared<tatami::ConsecutiveOracle<int> >(0, NR));
auto wrk = mat->dense_row(o);
for (int r = 0; r < NR; ++r) {
// No need to specify the index to fetch, as 'wrk' already knows the
// sequence of indices as prediced by the oracle.
auto ptr = wrk->fetch(buffer.data());
}In fact, this use case is so common that we can just use the tatami::consecutive_extractor() wrapper to construct the oracle and pass it to tatami::Matrix.
This will return a tatami::OracularDenseExtractor instance that contains the oracle's predictions.
// Same as 'wrk' above.
auto cwrk = tatami::consecutive_extractor<false>(mat.get(), row, 0, NR);Alternatively, we can use the FixedOracle class with an array of row/column indices that are known ahead of time.
Advanced users can also define their own Oracle subclasses to provide dynamic custom predictions, e.g., based on PRNG output.
As previously mentioned, tatami is designed to pull out rows or columns of a matrix, and little else. Some support is provided for basic statistics in the same vein as the matrixStats R package - see the tatami_stats library for more information.
tatami does not directly support matrix algebra or decompositions.
If these high-level operations are needed, applications should write their own code, e.g., by using tatami's extractors to implement matrix multiplication.
Alternatively, we can transfer data from tatami into other frameworks like Eigen for complex matrix operations,
effectively trading the diversity of representations for a more comprehensive suite of operations.
For example, we often use tatami to represent the input data in a custom format to save memory for large datasets;
process it into a much smaller submatrix, e.g., by selecting features of interest in a genome-scale analysis;
and then copy this cheaply into an Eigen::MatrixXd or Eigen::SparseMatrix for more computationally intensive work.
It is not possible to modify the matrix contents via the tatami API. This is especially relevant for matrices with delayed operations or those referring to remote data stores, where reading the matrix data is trivial but writing is not guaranteed to work. Experience suggests that a matrix writer abstraction is less useful than the equivalent reader abstraction. This is because applications typically control the output format, so there is no need to accommodate a diversity of formats via an abstract interface.
If you're using CMake, you just need to add something like this to your CMakeLists.txt:
include(FetchContent)
FetchContent_Declare(
tatami
GIT_REPOSITORY https://github.com/tatami-inc/tatami
GIT_TAG master # or any version of interest
)
FetchContent_MakeAvailable(tatami)Then you can link to tatami to make the headers available during compilation:
# For executables:
target_link_libraries(myexe tatami)
# For libaries
target_link_libraries(mylib INTERFACE tatami)You can install the library by cloning a suitable version of this repository and running the following commands:
mkdir build && cd build
cmake .. -DTATAMI_TESTS=OFF
cmake --build . --target installThen you can use find_package() as usual:
find_package(tatami_tatami CONFIG REQUIRED)
target_link_libraries(mylib INTERFACE tatami::tatami)If you're not using CMake, the simple approach is to just copy the files the include/ subdirectory -
either directly or with Git submodules - and include their path during compilation with, e.g., GCC's -I.
Check out the reference documentation for more details on each function and class.
The gallery also contains worked examples for common operations based on row/column traversals.
The tatami_hdf5 repository contains tatami bindings for HDF5-backed matrices.
The tatami_r repository contains tatami bindings for matrix-like objects in R.
The beachmat package vendors the tatami headers for easy use by other R packages.