# 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(
没有合适的资源?快使用搜索试试~ 我知道了~
资源推荐
资源详情
资源评论
收起资源包目录
本项目为桂林电子科技大学Evolution战队2021赛季常规机器人视觉项目_Baldr.zip (2000个子文件)
AdolcForward 4KB
AlignedVector3 6KB
ArpackSupport 905B
AutoDiff 1KB
bench_unrolling 651B
benchmark_suite 1KB
BVH 5KB
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
d_cnjg.c 117B
r_cnjg.c 105B
benchmark_main.cc 7KB
tensor_benchmarks_cpu.cc 6KB
contraction_benchmarks_cpu.cc 1KB
tensor_benchmarks_sycl.cc 1KB
Cholesky 1KB
CholmodSupport 2KB
FindBLAS.cmake 43KB
EigenTesting.cmake 26KB
FindPastix.cmake 23KB
FindPTSCOTCH.cmake 14KB
FindBLASEXT.cmake 13KB
FindScotch.cmake 12KB
FindHWLOC.cmake 12KB
FindLAPACK.cmake 10KB
FindComputeCpp.cmake 9KB
FindMetis.cmake 9KB
FindGSL.cmake 5KB
FindEigen3.cmake 3KB
FindGLEW.cmake 3KB
FindMPFR.cmake 3KB
FindEigen2.cmake 3KB
EigenConfigureTesting.cmake 3KB
FindFFTW.cmake 3KB
FindCholmod.cmake 3KB
language_support.cmake 2KB
FindSuperLU.cmake 2KB
FindStandardMathLibrary.cmake 2KB
EigenDetermineVSServicePack.cmake 2KB
FindUmfpack.cmake 2KB
EigenDetermineOSVersion.cmake 2KB
EigenUninstall.cmake 1KB
FindSPQR.cmake 1KB
RegexUtils.cmake 936B
FindGoogleHash.cmake 909B
FindGMP.cmake 554B
CTestConfig.cmake 543B
FindAdolc.cmake 501B
UseEigen3.cmake 177B
Core 18KB
NonLinearOptimization.cpp 64KB
cxx11_tensor_symmetry.cpp 58KB
levenberg_marquardt.cpp 54KB
armorDistinguish.cpp 52KB
cxx11_tensor_image_patch.cpp 33KB
KalmanPredict.cpp 29KB
analyze-blocking-sizes.cpp 28KB
sparse_basic.cpp 25KB
sparse_product.cpp 25KB
packetmath.cpp 24KB
geo_transformations.cpp 23KB
benchmark-blocking-sizes.cpp 22KB
cxx11_tensor_contraction.cpp 21KB
buffTest.cpp 20KB
vectorization_logic.cpp 20KB
evaluators.cpp 19KB
quaternion_demo.cpp 19KB
array.cpp 19KB
angleFactory.cpp 18KB
cxx11_tensor_index_list.cpp 18KB
cxx11_meta.cpp 18KB
cholesky.cpp 17KB
mixingtypes.cpp 17KB
buffDistinguish.cpp 17KB
cameraCalibration.cpp 16KB
special_functions.cpp 16KB
cxx11_tensor_morphing.cpp 15KB
product_extra.cpp 14KB
cxx11_tensor_reduction.cpp 14KB
main.cpp 13KB
sparse_setter.cpp 13KB
serial.cpp 13KB
cxx11_tensor_chipping.cpp 13KB
共 2000 条
- 1
- 2
- 3
- 4
- 5
- 6
- 20
资源评论
好家伙VCC
- 粉丝: 1790
- 资源: 9088
上传资源 快速赚钱
- 我的内容管理 展开
- 我的资源 快来上传第一个资源
- 我的收益 登录查看自己的收益
- 我的积分 登录查看自己的积分
- 我的C币 登录后查看C币余额
- 我的收藏
- 我的下载
- 下载帮助
最新资源
资源上传下载、课程学习等过程中有任何疑问或建议,欢迎提出宝贵意见哦~我们会及时处理!
点击此处反馈
安全验证
文档复制为VIP权益,开通VIP直接复制
信息提交成功