# Eigen Tensors {#eigen_tensors}
Tensors are multidimensional arrays of elements. Elements are typically scalars,
but more complex types such as strings are also supported.
[TOC]
## Tensor Classes
You can manipulate a tensor with one of the following classes. They all are in
the namespace `::Eigen.`
### Class Tensor<data_type, rank>
This is the class to use to create a tensor and allocate memory for it. The
class is templatized with the tensor datatype, such as float or int, and the
tensor rank. The rank is the number of dimensions, for example rank 2 is a
matrix.
Tensors of this class are resizable. For example, if you assign a tensor of a
different size to a Tensor, that tensor is resized to match its new value.
#### Constructor `Tensor<data_type, rank>(size0, size1, ...)`
Constructor for a Tensor. The constructor must be passed `rank` integers
indicating the sizes of the instance along each of the the `rank`
dimensions.
// Create a tensor of rank 3 of sizes 2, 3, 4. This tensor owns
// memory to hold 24 floating point values (24 = 2 x 3 x 4).
Tensor<float, 3> t_3d(2, 3, 4);
// Resize t_3d by assigning a tensor of different sizes, but same rank.
t_3d = Tensor<float, 3>(3, 4, 3);
#### Constructor `Tensor<data_type, rank>(size_array)`
Constructor where the sizes for the constructor are specified as an array of
values instead of an explicitly list of parameters. The array type to use is
`Eigen::array<Eigen::Index>`. The array can be constructed automatically
from an initializer list.
// Create a tensor of strings of rank 2 with sizes 5, 7.
Tensor<string, 2> t_2d({5, 7});
### Class `TensorFixedSize<data_type, Sizes<size0, size1, ...>>`
Class to use for tensors of fixed size, where the size is known at compile
time. Fixed sized tensors can provide very fast computations because all their
dimensions are known by the compiler. FixedSize tensors are not resizable.
If the total number of elements in a fixed size tensor is small enough the
tensor data is held onto the stack and does not cause heap allocation and free.
// Create a 4 x 3 tensor of floats.
TensorFixedSize<float, Sizes<4, 3>> t_4x3;
### Class `TensorMap<Tensor<data_type, rank>>`
This is the class to use to create a tensor on top of memory allocated and
owned by another part of your code. It allows to view any piece of allocated
memory as a Tensor. Instances of this class do not own the memory where the
data are stored.
A TensorMap is not resizable because it does not own the memory where its data
are stored.
#### Constructor `TensorMap<Tensor<data_type, rank>>(data, size0, size1, ...)`
Constructor for a Tensor. The constructor must be passed a pointer to the
storage for the data, and "rank" size attributes. The storage has to be
large enough to hold all the data.
// Map a tensor of ints on top of stack-allocated storage.
int storage[128]; // 2 x 4 x 2 x 8 = 128
TensorMap<Tensor<int, 4>> t_4d(storage, 2, 4, 2, 8);
// The same storage can be viewed as a different tensor.
// You can also pass the sizes as an array.
TensorMap<Tensor<int, 2>> t_2d(storage, 16, 8);
// You can also map fixed-size tensors. Here we get a 1d view of
// the 2d fixed-size tensor.
TensorFixedSize<float, Sizes<4, 5>> t_4x3;
TensorMap<Tensor<float, 1>> t_12(t_4x3.data(), 12);
#### Class `TensorRef`
See Assigning to a TensorRef below.
## Accessing Tensor Elements
#### `<data_type> tensor(index0, index1...)`
Return the element at position `(index0, index1...)` in tensor
`tensor`. You must pass as many parameters as the rank of `tensor`.
The expression can be used as an l-value to set the value of the element at the
specified position. The value returned is of the datatype of the tensor.
// Set the value of the element at position (0, 1, 0);
Tensor<float, 3> t_3d(2, 3, 4);
t_3d(0, 1, 0) = 12.0f;
// Initialize all elements to random values.
for (int i = 0; i < 2; ++i) {
for (int j = 0; j < 3; ++j) {
for (int k = 0; k < 4; ++k) {
t_3d(i, j, k) = ...some random value...;
}
}
}
// Print elements of a tensor.
for (int i = 0; i < 2; ++i) {
LOG(INFO) << t_3d(i, 0, 0);
}
## TensorLayout
The tensor library supports 2 layouts: `ColMajor` (the default) and
`RowMajor`. Only the default column major layout is currently fully
supported, and it is therefore not recommended to attempt to use the row major
layout at the moment.
The layout of a tensor is optionally specified as part of its type. If not
specified explicitly column major is assumed.
Tensor<float, 3, ColMajor> col_major; // equivalent to Tensor<float, 3>
TensorMap<Tensor<float, 3, RowMajor> > row_major(data, ...);
All the arguments to an expression must use the same layout. Attempting to mix
different layouts will result in a compilation error.
It is possible to change the layout of a tensor or an expression using the
`swap_layout()` method. Note that this will also reverse the order of the
dimensions.
Tensor<float, 2, ColMajor> col_major(2, 4);
Tensor<float, 2, RowMajor> row_major(2, 4);
Tensor<float, 2> col_major_result = col_major; // ok, layouts match
Tensor<float, 2> col_major_result = row_major; // will not compile
// Simple layout swap
col_major_result = row_major.swap_layout();
eigen_assert(col_major_result.dimension(0) == 4);
eigen_assert(col_major_result.dimension(1) == 2);
// Swap the layout and preserve the order of the dimensions
array<int, 2> shuffle(1, 0);
col_major_result = row_major.swap_layout().shuffle(shuffle);
eigen_assert(col_major_result.dimension(0) == 2);
eigen_assert(col_major_result.dimension(1) == 4);
## Tensor Operations
The Eigen Tensor library provides a vast library of operations on Tensors:
numerical operations such as addition and multiplication, geometry operations
such as slicing and shuffling, etc. These operations are available as methods
of the Tensor classes, and in some cases as operator overloads. For example
the following code computes the elementwise addition of two tensors:
Tensor<float, 3> t1(2, 3, 4);
...set some values in t1...
Tensor<float, 3> t2(2, 3, 4);
...set some values in t2...
// Set t3 to the element wise sum of t1 and t2
Tensor<float, 3> t3 = t1 + t2;
While the code above looks easy enough, it is important to understand that the
expression `t1 + t2` is not actually adding the values of the tensors. The
expression instead constructs a "tensor operator" object of the class
TensorCwiseBinaryOp<scalar_sum>, which has references to the tensors
`t1` and `t2`. This is a small C++ object that knows how to add
`t1` and `t2`. It is only when the value of the expression is assigned
to the tensor `t3` that the addition is actually performed. Technically,
this happens through the overloading of `operator=()` in the Tensor class.
This mechanism for computing tensor expressions allows for lazy evaluation and
optimizations which are what make the tensor library very fast.
Of course, the tensor operators do nest, and the expression `t1 + t2 * 0.3f`
is actually represented with the (approximate) tree of operators:
TensorCwiseBinaryOp<scalar_sum>(t1, TensorCwiseUnaryOp<scalar_mul>(t2, 0.3f))
### Tensor Operations and C++ "auto"
Because Tensor operations create tensor operators, the C++ `auto` keyword
does not have its intuitive meaning. Consider these 2 lines of code:
Tensor<float, 3> t3 = t1 + t2;
auto t4 = t1 + t2;
In the first line we allocate the tensor `t3` and it will contain the
result of the addition of `t1` and `t2`. In the second line, `t4`
is actually the tree of tensor operators that will compute the addition of
`t1` and `t2`. In fact, `t4` is *not* a tensor and you cannot get
the values of its elements:
Tensor<float, 3> t3 = t1 + t2;
cout << t3(0, 0, 0); // OK prints the value of t1(
gtsam-4.2a7.tar.gz （2000个子文件） 
ccolamd.c 136KB geodesic.c 70KB geodtest.c 32KB SuiteSparse_config.c 16KB ccolamdtestmex.c 14KB csymamdtestmex.c 12KB ccolamdmex.c 7KB csymamdmex.c 6KB ccolamd_l_example.c 6KB ccolamd_example.c 6KB planimeter.c 1KB inverse.c 927B direct.c 923B geoidtest.c 284B xerbla.c 135B GeodesicExactC4.cpp 455KB Geodesic.cpp 73KB NonLinearOptimization.cpp 64KB testSmartProjectionRigFactor.cpp 59KB cxx11_tensor_symmetry.cpp 58KB levenberg_marquardt.cpp 54KB testSmartProjectionPoseFactor.cpp 48KB testPose3.cpp 46KB ShonanAveraging.cpp 39KB GeodesicExact.cpp 37KB testGncOptimizer.cpp 36KB testImuFactor.cpp 34KB dataset.cpp 34KB cxx11_tensor_image_patch.cpp 33KB testTriangulation.cpp 32KB JacobianFactor.cpp 32KB testPose2.cpp 31KB testSerializationSlam.cpp 31KB testRot3.cpp 31KB testSmartProjectionFactor.cpp 29KB testGaussianISAM2.cpp 29KB testNoiseModel.cpp 27KB testJacobianFactor.cpp 25KB testExpressionFactor.cpp 24KB testEssentialMatrixFactor.cpp 23KB NoiseModel.cpp 23KB testNonlinearOptimizer.cpp 23KB TransverseMercator.cpp 22KB GeodesicExact.cpp 21KB cxx11_tensor_contraction.cpp 21KB SolverComparer.cpp 20KB Geodesic.cpp 20KB testHessianFactor.cpp 20KB HessianFactor.cpp 20KB testSimilarity3.cpp 20KB SphericalEngine.cpp 19KB GaussianFactorGraph.cpp 19KB testNonlinearEquality.cpp 19KB testNonlinearFactor.cpp 19KB MGRS.cpp 18KB EllipticFunction.cpp 18KB LambertConformalConic.cpp 18KB cxx11_tensor_index_list.cpp 18KB cxx11_meta.cpp 18KB testAHRSFactor.cpp 18KB testGeneralSFMFactor.cpp 18KB AlbersEqualArea.cpp 17KB elaboratePoint2KalmanFilter.cpp 17KB testGaussianFactorGraph.cpp 17KB Geoid.cpp 17KB testDataset.cpp 17KB testUnit3.cpp 17KB TransverseMercatorExact.cpp 17KB testShonanAveraging.cpp 16KB testGaussianFactorGraphB.cpp 16KB Pose3.cpp 16KB special_functions.cpp 16KB cxx11_tensor_morphing.cpp 15KB SubgraphBuilder.cpp 15KB GeodesicLineExact.cpp 15KB Rhumb.cpp 15KB GeodSolve.cpp 14KB testScenarioRunner.cpp 14KB GeodesicLine.cpp 14KB testGaussianBayesTree.cpp 14KB IMUKittiExampleGPS.cpp 14KB cxx11_tensor_reduction.cpp 14KB testSO3.cpp 14KB lago.cpp 14KB VectorValues.cpp 14KB SfmData.cpp 14KB GravityModel.cpp 14KB testLago.cpp 13KB testGaussianConditional.cpp 13KB testExtendedKalmanFilter.cpp 13KB DMS.cpp 13KB testPinholeCamera.cpp 13KB testNonlinearFactorGraph.cpp 13KB testGeneralSFMFactor_Cal3Bundler.cpp 13KB testGaussianBayesTreeB.cpp 13KB cxx11_tensor_chipping.cpp 13KB MagneticField.cpp 13KB cxx11_tensor_fft.cpp 12KB testGaussianBayesNet.cpp 12KB LossFunctions.cpp 12KB共 2000 条
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