# 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<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<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.
Tensor<float, Sizes<4, 5>> t_4x3;
TensorMap<float, 1> t_12(t_4x3, 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
eigen3.3.3版本安装包 （2000个子文件） 
CMakeCCompilerId.c 20KB ztbmv.c 19KB ctbmv.c 19KB zhbmv.c 15KB chbmv.c 15KB zhpmv.c 13KB chpmv.c 13KB dtbmv.c 11KB stbmv.c 11KB ssbmv.c 10KB dsbmv.c 10KB dspmv.c 8KB sspmv.c 8KB drotmg.c 6KB srotmg.c 6KB drotm.c 5KB srotm.c 5KB lsame.c 3KB complexdots.c 2KB example.c 2KB feature_tests.c 688B d_cnjg.c 117B r_cnjg.c 105B NonLinearOptimization.cpp 64KB cxx11_tensor_symmetry.cpp 58KB levenberg_marquardt.cpp 54KB cxx11_tensor_image_patch.cpp 33KB analyze-blocking-sizes.cpp 28KB sparse_basic.cpp 25KB packetmath.cpp 24KB geo_transformations.cpp 23KB benchmark-blocking-sizes.cpp 22KB cxx11_tensor_contraction.cpp 21KB vectorization_logic.cpp 19KB evaluators.cpp 19KB CMakeCXXCompilerId.cpp 19KB array.cpp 19KB quaternion_demo.cpp 19KB sparse_product.cpp 18KB cxx11_tensor_index_list.cpp 18KB cxx11_meta.cpp 18KB cholesky.cpp 17KB mixingtypes.cpp 16KB special_functions.cpp 16KB cxx11_tensor_morphing.cpp 15KB product_extra.cpp 14KB cxx11_tensor_reduction.cpp 14KB sparse_setter.cpp 13KB cxx11_tensor_chipping.cpp 13KB cxx11_tensor_fft.cpp 12KB cxx11_tensor_thread_pool.cpp 12KB qr_colpivoting.cpp 12KB sparse_block.cpp 12KB product_small.cpp 12KB array_for_matrix.cpp 12KB nullary.cpp 11KB bench_norm.cpp 11KB block.cpp 11KB eigensolver_selfadjoint.cpp 11KB ref.cpp 11KB bench_gemm.cpp 11KB openglsupport.cpp 10KB basicstuff.cpp 10KB autodiff.cpp 10KB geo_quaternion.cpp 10KB sparse_permutations.cpp 10KB lu.cpp 9KB cxx11_tensor_assign.cpp 9KB cxx11_tensor_simple.cpp 9KB triangular.cpp 9KB FFTW.cpp 9KB cxx11_tensor_argmax.cpp 9KB half_float.cpp 9KB kronecker_product.cpp 9KB sparse_product.cpp 9KB product_notemporary.cpp 9KB nomalloc.cpp 9KB vectorwiseop.cpp 9KB splines.cpp 8KB cxx11_tensor_expr.cpp 8KB adjoint.cpp 8KB mapped_matrix.cpp 8KB stable_norm.cpp 8KB redux.cpp 8KB geo_hyperplane.cpp 7KB mandelbrot.cpp 7KB mapstaticmethods.cpp 7KB product_syrk.cpp 7KB mapstride.cpp 7KB eig33.cpp 7KB cxx11_tensor_fixed_size.cpp 7KB BVH.cpp 7KB matrix_power.cpp 7KB cxx11_runqueue.cpp 7KB polynomialsolver.cpp 7KB matrix_function.cpp 7KB cxx11_tensor_ref.cpp 7KB cxx11_tensor_map.cpp 7KB corners.cpp 6KB EulerAngles.cpp 6KB共 2000 条
- 1
- 2
- 3
- 4
- 5
- 6
- 20
评论0