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Tutorial of mshadow

This is a beginner's tutorial for mshadow. If you like mshadow and have ideas to improve this tutorial, you are more than welcome to contribute :) Please send a pull-request if you would like to share your experience.

See also other related materials about mshadow

List of Topics

Tensor Data Structure

The basic data structure of mshadow is Tensor. The following is a simplified equivalent version of the declaration in mashadow/tensor.h

typedef unsigned index_t;
template<int dimension>
struct Shape {
  index_t shape_[dimension];
template<typename Device, int dimension, typename DType = float>
struct Tensor {
  DType *dptr_;
  Shape<dimension> shape_;
  Stream<Device> stream_;
  index_t stride_;
// this is how shape object declaration look like
Shape<2> shape2;
// this is how tensor object declaration look like
// you can
Tensor<cpu, 2> ts2;
Tensor<gpu, 3, float> ts3;

Tensor<cpu,2> is a two dimensional tensor in host memory, while Tensor<gpu,3> is a three dimensional tensor in device memory. Shape<k> gives the shape information of a k-dimensional tensor. The declarations use templates and can be specialized to tensors on a specific device and of a specific dimension. This is what a two dimensional tensor would look like:

struct Shape<2> {
  index_t shape_[2];
struct Tensor<cpu, 2, float> {
  float *dptr_;
  Shape<2> shape_;
  index_t stride_;
  • Tensor<cpu, 2> contains dptr_, which points to the space that backs up the tensor.
  • Shape<2> is a structure that stores shape information, the convention is the same as numpy.
  • stride_ gives the number of cell spaces allocated in the smallest dimension (if we use numpy convention, the dimension corresponds to shape_[-1]). This is introduced when we introduce some padding cells in lowest dimension to make sure memory is aligned. stride_ is automatically set during memory allocation of a tensor in mshadow.

To understand the data structure, consider the following code:

float data[9] = {0, 1, 2, 3, 4, 5, 6, 7, 8};
Tensor<cpu, 2> ts;
ts.dptr_ = data;
ts.shape_ = mshadow::Shape2(3, 2);
ts.stride_ = 3;
// now: ts[0][0] == 0, ts[0][1] == 1 , ts[1][0] == 3, ts[1][1] == 4
for (index_t i = 0; i < ts.size(0); ++i) {
  for (index_t j = 0; j < ts.size(1); ++j) {
    printf("ts[%u][%u]=%f\n", i, j, ts[i][j]);

The result ts should be a 3 * 2 matrix, where data[2], data[5], data[8] are padding cells that are ignored. If you want a continuous memory, set stride_=shape_[1].

NOTICE: We highly recommend use stream in gpu mode, there will be an error thrown out if no stream is set. Check for more detail.

Memory Allocation

An important design choice in mshadow was making the data structure Tensor a whitebox, it works so long as we set the space pointer dptr_ corresponding shape_ and stride_:

  • For Tensor<cpu, k> dptr_ must point to space created by new float[] or to some existing space such as the float array in the last example.
  • For Tensor<gpu, k> dptr_ must point to space on the device created by cudaMallocPitch.

mshadow also provides an explicit memory allocation routine, as shown in following code:

// create a 5 x 3 tensor on the device, and allocate space
Tensor<gpu, 2> ts2(Shape2(5, 3));
// allocate 5 x 3 x 2 tensor on the host, initialized by 0
Tensor<cpu, 3> ts3 = NewTensor<cpu>(Shape3(5,3,2), 0.0f);
// free space
FreeSpace(&ts2); FreeSpace(&ts3);

All memory allocations in mshadow are explicit. There are no implicit memory allocations or de-allocations during any operations. This means Tensor<cpu, k> variable is more like a reference handle(pointer), instead of a object. If we assign a tensor to another variable, the two share the same content space.

This also allows user to use mshadow in their existing project easily, simply give mshadow the pointer of the memory and you can get the benefit of all the mshadow expressions with zero cost:)

We also have STL style container object called TensorContainer, they behave exactly the same as Tensors, but the memory will be automatically freed during destruction.

Elementwise Operations

All the operators(+, -, *, /, += etc.) in mshadow are element-wise. Consider the following SGD update code:

void UpdateSGD(Tensor<cpu, 2> weight, Tensor<cpu, 2> grad, float eta, float lambda) {
  weight -= eta * (grad + lambda * weight);

During compilation, this code will be translated to the following form:

void UpdateSGD(Tensor<cpu,2> weight, Tensor<cpu,2> grad, float eta, float lambda) {
  for (index_t y = 0; y < weight.size(0); ++y) {
    for (index_t x = 0; x < weight.size(1); ++x) {
      weight[y][x] -= eta * (grad[y][x] + lambda * weight[y][x]);

As we can see, no memory allocation happens in the translated code. For Tensor<gpu, k>, the corresponding function will be translated into a CUDA kernel of the same spirit. Using an Expression Template, the translation happens at compile time. We can write simple lines of code while getting the full performance of the translated code.

One code for both CPU and GPU

Since mshadow has an identical interface for Tensor<cpu, k> and Tensor<gpu, k>, we can easily write code that works on both the CPU and GPU. For example, the following code compiles for both GPU and CPU Tensors.

template<typename xpu>
void UpdateSGD(Tensor<xpu, 2> weight, const Tensor<xpu, 2> &grad,
               float eta, float lambda) {
  weight -= eta * (grad + lambda * weight);

Matrix Multiplications

We also have a shorthand for dot product that will be translated to call standard packages such as MKL and CuBLAS.

template<typename xpu>
void Backprop(Tensor<xpu, 2> gradin,
              const Tensor<xpu, 2> &gradout,
              const Tensor<xpu, 2> &netweight) {
  gradin = dot(gradout, netweight.T());

Again, the code can compile for both GPU and CPU Tensors.

User Defined Operator

There are common cases when we want to define our own function. For example, assume we do not have an element-wise sigmoid transformation in mshadow. We simply use the following code to add sigmoid to mshadow

struct sigmoid {
  MSHADOW_XINLINE static float Map(float a) {
    return 1.0f / (1.0f + expf(-a));
template<typename xpu>
void ExampleSigmoid(Tensor<xpu, 2> out, const Tensor<xpu, 2> &in) {
  out = F<sigmoid>(in * 2.0f) + 1.0f;

The translated code for CPU is given by

template<typename xpu>
void ExampleSigmoid(Tensor<xpu, 2> out, const Tensor<xpu, 2> &in) {
  for (index_t y = 0; y < out.size(0); ++y) {
    for(index_t x = 0; x < out.size(1); ++x) {
      out[y][x] = sigmoid::Map(in[y][x] * 2.0f) + 1.0f;

Also note that the defined operation can be composited into expressions, not only we can write out = F<sigmoid>(in), we can also write out = F<sigmoid>+2.0 or out = F<sigmoid>(F<sigmoid>(in)).

There will also be a translated CUDA kernel version that runs on the GPU. Check out defop.cpp for a complete example.

Complete Example

The following code is from basic.cpp. It illustrates basic usage of mshadow.

// header file to use mshadow
#include "mshadow/tensor.h"
// this namespace contains all data structures, functions
using namespace mshadow;
// this namespace contains all operator overloads
using namespace mshadow::expr;

int main(void) {
  // intialize tensor engine before using tensor operation, needed for CuBLAS
  // assume we have a float space
  float data[20];
  // create a 2 x 5 x 2 tensor, from existing space
  Tensor<cpu, 3> ts(data, Shape3(2,5,2));
    // take first subscript of the tensor
  Tensor<cpu, 2> mat = ts[0];
  // Tensor object is only a handle, assignment means they have same data content
  // we can specify content type of a Tensor, if not specified, it is float bydefault
  Tensor<cpu, 2, float> mat2 = mat;

  // shape of matrix, note size order is the same as numpy
  printf("%u X %u matrix\n", mat.size(0), mat.size(1));

  // initialize all element to zero
  mat = 0.0f;
  // assign some values
  mat[0][1] = 1.0f; mat[1][0] = 2.0f;
  // elementwise operations
  mat += (mat + 10.0f) / 10.0f + 2.0f;

  // print out matrix, note: mat2 and mat1 are handles(pointers)
  for (index_t i = 0; i < mat.size(0); ++i) {
    for (index_t j = 0; j < mat.size(1); ++j) {
      printf("%.2f ", mat2[i][j]);
  // shutdown tensor enigne after usage
  return 0;