Tensor

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Overview

Tensor is a basic data structure in the MindSpore network computing. For details about data types in tensors, see dtype.

Tensors of different dimensions represent different data. For example, a 0-dimensional tensor represents a scalar, a 1-dimensional tensor represents a vector, a 2-dimensional tensor represents a matrix, and a 3-dimensional tensor may represent the three channels of RGB images.

Tensor Structure

During tensor creation, the Tensor, float, int, bool, tuple, list, complex, and NumPy.array types can be transferred, while tuple and list can only store float, int, bool and complex data, where complex represets the complex data types.

dtype can be specified when Tensor is initialized. When the dtype is not specified, if the initial value is int, float, bool or complex, then a 0-dimensional Tensor with data types mindspore.int32, mindspore.float64 , mindspore.bool_ or mindspore.complex128 will be generated respectively. If the initial values are tuple and list, the generated 1-dimensional Tensor data type corresponds to the type stored in tuple and list. If it contains multiple different types of data, follow the below priority: bool < int < float < complex, to select the mindspore data type corresponding to the highest relative priority type. If the initial value is Tensor, the consistent data type Tensor is generated. If the initial value is NumPy.array, the corresponding data type Tensor is generated.

A code example is as follows:

import numpy as np
from mindspore import Tensor
from mindspore import dtype as mstype

x = Tensor(np.array([[1, 2], [3, 4]]), mstype.int32)
y = Tensor(1.0, mstype.int32)
z = Tensor(2, mstype.int32)
m = Tensor(True, mstype.bool_)
n = Tensor((1, 2, 3), mstype.int16)
p = Tensor([4.0, 5.0, 6.0], mstype.float64)
q = Tensor(p, mstype.float64)

print(x, "\n\n", y, "\n\n", z, "\n\n", m, "\n\n", n, "\n\n", p, "\n\n", q)

The following information is displayed:

[[1 2]
 [3 4]]

1

2

True

[1 2 3]

[4. 5. 6.]

[4. 5. 6.]

Tensor Operations, Attributes and Methods

Operations

Tensor supports a variety of operations, including arithmetic operations and logical operations. When two arrays of different shapes are subjected to numerical operations, the broadcast mechanism similar to Numpy will be triggered. Some commonly used operators are as follows:

  • arithmetic operations: add (+), subtract (-), multiply (*), divide (/), modulus (%), power (**), divide (//)

  • logical operations：equal to (==), not equal to (!=), greater than (>), greater than or equal to (>=), less than (<), less than or equal to (<=)

A code example is as follows:

import numpy as np
from mindspore import Tensor
from mindspore import dtype as mstype

x = Tensor(np.array([1, 2, 3]), mstype.float32)
y = Tensor(np.array([4, 5, 6]), mstype.float32)
output_add = x + y
output_sub = x - y
output_mul = x * y
output_div = y / x
output_mod = x % y
output_pow = x ** 2
output_floordiv = y // x
print("add:", output_add)
print("sub:", output_sub)
print("mul:", output_mul)
print("div:", output_div)
print("mod:", output_mod)
print("pow:", output_pow)
print("floordiv:", output_floordiv)

a = Tensor(np.array([2, 2, 2]), mstype.int32)
b = Tensor(np.array([1, 2, 3]), mstype.int32)
output_eq = a == b
output_ne = a != b
output_gt = a > b
output_gq = a >= b
output_lt = a < b
output_lq = a <= b
print("equal:", output_eq)
print("not equal:", output_ne)
print("greater than:", output_gt)
print("greater or equal:", output_gq)
print("less than:", output_lt)
print("less or equal:", output_lq)

The following information is displayed:

add: [5. 7. 9.]
sub: [-3. -3. -3.]
mul: [ 4. 10. 18.]
div: [4. 2.5 2. ]
mod: [1. 2. 3.]
pow: [1. 4. 9.]
floordiv: [4. 2. 2.]
equal: [False True False]
not equal: [ True False True]
greater than: [ True False False]
greater or equal: [ True True False]
less than: [False False True]
less or equal: [False True True]

Attributes

Tensor attributes include shape，dtype, T, itemsize, nbytes, ndim, size, strides.

  • shape: a tuple

  • dtype: a data type of MindSpore

  • T: transposed view of original tensor

  • itemsize: an integer, representing the number of bytes consumed by a single element in the Tensor

  • nbytes: an integer, representing the total number of bytes consumed by Tensor

  • ndim: an integer, representing the rank of the Tensor

  • size: an integer, representing the total number of elements in Tensor

  • strides: the tuple of bytes to traverse in each dimension in Tensor

A code example is as follows:

import numpy as np
from mindspore import Tensor
from mindspore import dtype as mstype

x = Tensor(np.array([[1, 2], [3, 4]]), mstype.int32)
x_shape = x.shape
x_dtype = x.dtype
x_transposed = x.T
x_itemsize = x.itemsize
x_nbytes = x.nbytes
x_ndim = x.ndim
x_size = x.size
x_strides = x.strides
print("x_shape:", x_shape)
print("x_dtype:", x_dtype)
print("x_transposed:", x_transposed)
print("x_itemsize:", x_itemsize)
print("x_nbytes:", x_nbytes)
print("x_ndim:", x_ndim)
print("x_size:", x_size)
print("x_strides:", x_strides)

The following information is displayed:

x_shape: (2, 2)
x_dtype: Int32
x_transposed: [[1 3]
 [2 4]]
x_itemsize: 4
x_nbytes: 16
x_ndim: 2
x_size: 4
x_strides: (8, 4)

Methods

Tensor methods include len, str, repr, hash, all, any, asnumpy and many other functions. Numpy-like ndarray methods are also provided. For a full description of all tensor methods, please see API: mindspore.Tensor. The following is a brief introduction to some of the tensor methods.

  • len(): returns the length of the tensor.

  • str(): returns the string representation of the tensor.

  • repr(): returns the string representation of the tensor for the interpreter to read.

  • hash(): get the hash value of the tensor.

  • all(axis, keep_dims): performs the and operation on a specified dimension to reduce the dimension. axis indicates the reduced dimension, and keep_dims indicates whether to retain the reduced dimension.

  • any(axis, keep_dims): performs the or operation on a specified dimension to reduce the dimension. The parameter meaning is the same as that of all.

  • asnumpy(): converts Tensor to an array of NumPy.

  • sum(axis, dtype, keepdims, initial): sums the tensor over the given axis, axis indicates the reduced dimension, dtype specifies the output data type, keepdims indicates whether to retain the reduced dimension, and initial indicates the starting value for the sum.

A code example is as follows:

import numpy as np
from mindspore import Tensor
from mindspore import dtype as mstype

t = Tensor(np.array([1, 2, 3]), mstype.int32)
t_len = len(t)
t_str = str(t)
t_repr = repr(t)
t_hash = hash(t)
print("t_len:", t_len)
print("t_str:", t_str)
print("t_repr:", t_repr)
print("t_hash:", t_hash)

x = Tensor(np.array([[True, True], [False, False]]), mstype.bool_)
x_all = x.all()
x_any = x.any()
x_array = x.asnumpy()
print("x_all:", x_all)
print("x_any:", x_any)
print("x_array:", x_array)

import mindspore.numpy as mnp
y = Tensor(np.array([[1., 2.], [3., 4.]]), mstype.float32)
# y.sum() and mindspore.numpy.sum(y) are equivalent methods
y_sum_tensor = y.sum()
y_sum_mnp = mnp.sum(y)
print("y_sum_tensor:", y_sum_tensor)
print("y_sum_mnp:", y_sum_mnp)

The following information is displayed:

t_len: 3
t_str: [1 2 3]
t_repr: Tensor(shape=[3], dtype=Int32, value= [1, 2, 3])
t_hash: 281470264268272
x_all: False
x_any: True
x_array: [[ True  True]
 [False False]]
y_sum_tensor: 10.0
y_sum_mnp: 10.0

Sparse Tensor

Sparse tensor is a special kind of tensor which most of the elements are zero. In some scenario, like in the recommendation system, the data is sparse. If we use common dense tensors to represent the data, we may introduce many unnecessary calculations, storage and communication costs. In this situation, it is better to use sparse tensor to represent the data.

The common structure of sparse tensor is <indices:Tensor,values:Tensor,dense_shape:Tensor>. indices means index of non-zero elements, values means the values of these non-zero elements and dense_shape means the dense shape of the sparse tensor. Using this structure, we define data structure RowTensor and SparseTensor.

Now, PyNative mode does not support sparse tensor.

RowTensor

RowTensor is typically used to represent a subset of a larger tensor dense of shape [L0, D1, ..., DN] where L0 >> D0, and D0 is the number of non-zero elements.

  • indices: A 1-D integer tensor of shape [D0]. Represents the position of non-zero elements.

  • values: A tensor of any data type of shape [D0, D1, ..., DN]. Represents the value of non-zero elements.

  • dense_shape: An integer tuple which contains the shape of the corresponding dense tensor.

RowTensor can only be used in the Cell’s construct method. For details, see mindspore.RowTensor. A code example is as follows:

import mindspore as ms
import mindspore.nn as nn
from mindspore import Tensor
from mindspore import RowTensor

class Net(nn.Cell):
    def __init__(self, dense_shape):
        super(Net, self).__init__()
        self.dense_shape = dense_shape
    def construct(self, indices, values):
        x = RowTensor(indices, values, self.dense_shape)
        return x.values, x.indices, x.dense_shape

indices = Tensor([0])
values = Tensor([[1, 2]], dtype=ms.float32)
out = Net((3, 2))(indices, values)
print(out[0])
print(out[1])
print(out[2])

The following information is displayed:

[[1. 2.]]

[0]

(3, 2)

SparseTensor

SparseTensor represents a set of nonzero elememts from a tensor at given indices. If the number of non-zero elements is N and the dense shape of the sparse tensor is ndims：

  • indices: A 2-D integer Tensor of shape [N, ndims]. Each line represents the index of non-zero elements.

  • values: A 1-D tensor of any type and shape [N]. Represents the value of non-zero elements.

  • dense_shape: A integer tuple of size ndims, which specifies the dense shape of the sparse tensor.

SparseTensor can only be used in the Cell’s construct method. For details, see mindspore.SparseTensor. A code example is as follows:

import mindspore as ms
import mindspore.nn as nn
from mindspore import Tensor
from mindspore import SparseTensor

class Net(nn.Cell):
    def __init__(self, dense_shape):
       super(Net, self).__init__()
       self.dense_shape = dense_shape
    def construct(self, indices, values):
       x = SparseTensor(indices, values, self.dense_shape)
       return x.values, x.indices, x.dense_shape

indices = Tensor([[0, 1], [1, 2]])
values = Tensor([1, 2], dtype=ms.float32)
out = Net((3, 4))(indices, values)
print(out[0])
print(out[1])
print(out[2])

The following information is displayed:

[1. 2.]

[[0 1]
 [1 2]]

(3, 4)