Tensor¶
Each Tensor instance is a multi-dimensional array allocated on a specific Device instance. Tensor instances store variables and provide linear algebra operations over different types of hardware devices without user awareness. Note that users need to make sure the tensor operands are allocated on the same device except copy functions.
Tensor implementation¶
SINGA has three different sets of implmentations of Tensor functions, one for each type of Device.
‘tensor_math_cpp.h’ implements operations using Cpp (with CBLAS) for CppGPU devices.
‘tensor_math_cuda.h’ implements operations using Cuda (with cuBLAS) for CudaGPU devices.
‘tensor_math_opencl.h’ implements operations using OpenCL for OpenclGPU devices.
Python API¶
Example usage:
import numpy as np
from singa import tensor
from singa import device
# create a tensor with shape (2,3), default CppCPU device and float32
x = tensor.Tensor((2, 3))
x.set_value(0.4)
# create a tensor from a numpy array
npy = np.zeros((3, 3), dtype=np.float32)
y = tensor.from_numpy(npy)
y.uniform(-1, 1) # sample values from the uniform distribution
z = tensor.mult(x, y) # gemm -> z of shape (2, 3)
x += z # element-wise addition
dev = device.get_default_device()
x.to_device(dev) # move the data to a gpu device
s = tensor.to_numpy(x) # tensor -> numpy array
There are two sets of tensor functions,
- Tensor member functions
which would change the internal state of the Tensor instance.
- Tensor module functions
which accept Tensor instances as arguments and return Tensor instances.
Every Tesor instance must be initialized before reading data from it.
-
class
singa.tensor.Tensor(shape=(), device=None, dtype=0, data=None, requires_grad=True, stores_grad=False, creator=None, name=None)¶ Python Tensor, which wraps a swig converted Tensor from CPP Tensor.
- Parameters
shape (tuple<int>) – a tuple of integers for the tensor shape. If shape is not specified, the created tensor is called a dummy tensor.
device – a swig device. If None, the default host device is used.
dtype – data type. currently, most operations only accept float32.
data – a numpy array or swig tensor.
requires_grad – boolean indicator for computing the gradient.
stores_grad – boolean indicator for storing and returning the gradient. Some intermediate tensors’ gradient can be released during the backward propagation. A tensor may require grad but not store grad; But if a tensor stores grad then it must require grad.
-
T()¶ shallow copy.
- Returns
a new Tensor which shares the underlying data memory (shallow copy).
-
add_column(v)¶ (DEPRECATED, use broadcast)Add a tensor to each column of this tensor.
- Parameters
v (Tensor) – a Tensor to be added as a column to this tensor.
-
add_row(v)¶ (DEPRECATED, use broadcast)Add a tensor to each row of this tensor.
- Parameters
v (Tensor) – a Tensor to be added as a row to this tensor.
-
as_type(dtype)¶ Change the data type.
- Parameters
dtype – accepts ‘int’, ‘float’, ‘singa.kFloat32’, ‘singa.kInt’
- Returns
new tensor with new type
-
bernoulli(p, inplace=True)¶ Sample 0/1 for each element according to the given probability.
- Parameters
p (float) – with probability p, each element is sample to 1.
inplace – inplace flag
- Returns
this tensor
-
clone()¶ - Returns
a new Tensor which does deep copy of this tensor
-
copy()¶ shallow copy calls copy constructor of singa::Tensor
- Returns
new tensor copied
-
copy_from_numpy(np_array, offset=0)¶ Copy the data from the numpy array.
- Parameters
np_array – source numpy array
offset (int) – destination offset
-
deepcopy()¶ Same as clone().
- Returns
a new Tensor
-
div_column(v)¶ (DEPRECATED, use broadcast)Divide each column of this tensor by v.
- Parameters
v (Tensor) – 1d tensor of the same length the column of self.
-
div_row(v)¶ (DEPRECATED, use broadcast)Divide each row of this tensor by v.
- Parameters
v (Tensor) – 1d tensor of the same length the row of self.
-
gaussian(mean, std, inplace=True)¶ Generate a value for each element following a Gaussian distribution.
- Parameters
mean (float) – mean of the distribution
std (float) – standard variance of the distribution
inplace – inplace flag
- Returns
this tensor
-
is_empty()¶ - Returns
True if the tensor is empty according to its shape
-
is_transpose()¶ - Returns
True if the internal data is transposed; otherwise False.
-
l1()¶ - Returns
the L1 norm.
-
l2()¶ - Returns
the L2 norm.
-
memsize()¶ - Returns
the number of Bytes allocated for this tensor.
-
mult_column(v)¶ (DEPRECATED, use broadcast)Multiply each column of this tensor by v element-wisely.
- Parameters
v (Tensor) – 1d tensor of the same length the column of self.
-
mult_row(v)¶ (DEPRECATED, use broadcast)Multiply each row of this tensor by v element-wisely.
- Parameters
v (Tensor) – 1d tensor of the same length the row of self.
-
ndim()¶ - Returns
the number of dimensions of the tensor.
-
repeat(repeats, axis)¶ Repeat data of a tensor
- Parameters
repeats (int or a sequence) – the number that the tensor need to repeat for
axis (int) – the axis to do repeat If it is None, then the repeated tensor will be flattened.If it isn’t None, the repeats could be sequence, but it’s size should match the axis’s shape
- Returns
the tensor which has been repeated
-
reset_like(t)¶ Reset the shape, dtype and device as the given tensor.
- Parameters
t (Tensor) – a tensor
-
reshape(shape)¶ - Return a new tensor with the given shape, and the original
tensor is not changed.
- Parameters
shape (list<int>) – new shape, which should have the same volumn as the original shape.
- Returns
new tensor reshaped
-
set_value(x, inplace=True)¶ Set all elements of the tensor to be the give value.
- Parameters
x (float) – a float value to be set to all elements.
inplace – inplace flag
- Returns
this tensor
-
size()¶ - Returns
the number of elements of the tensor.
-
to_device(device)¶ Move the tensor data onto a given device.
- Parameters
device – a swig Device converted from CudaGPU or CppCPU or OpenclGPU
-
to_host()¶ Move the tensor data onto the default host CppCPU device.
-
transpose(axes=None)¶ To transpose the tensor
- Parameters
axes – axes to transpose
- Returns
new transposed tensor
-
uniform(low, high, inplace=True)¶ Generate a value for each element following a uniform distribution.
- Parameters
low (float) – the lower bound
high (float) – the hight bound
inplace – inplace flag
- Returns
this tensor
-
singa.tensor.abs(t)¶ - Parameters
t (Tensor) – input Tensor
- Returns
a new Tensor whose element y = abs(x), x is an element of t
-
singa.tensor.add(lhs, rhs, ret=None)¶ Elementi-wise addition.
-
singa.tensor.add_column(alpha, v, beta, M)¶ Add v to each column of M.
Denote each column of M as m, m = alpha * v + beta * m
-
singa.tensor.add_row(alpha, v, beta, M)¶ Add v to each row of M.
Denote each row of M as m, m = alpha * v + beta * m
-
singa.tensor.average(t, axis=None)¶ - Parameters
t (Tensor) – input Tensor
axis (int, optional) – if None, average all elements; otherwise average along the given dimension. 0 for averaging each column; 1 for averaging each row.
- Returns
a float value if axis is None; otherwise, a new Tensor for the result.
-
singa.tensor.axpy(alpha, x, y)¶ Element-wise operation for y += alpha * x.
-
singa.tensor.bernoulli(p, t)¶ Generate a binary value for each element of t.
- Parameters
p (float) – each element is 1 with probability p; and 0 with 1 - p
t (Tensor) – the results are put into t
- Returns
t
-
singa.tensor.ceil(t)¶ - Parameters
t (Tensor) – input Tensor
- Returns
a new Tensor whose element y = ceil(x), x is an element of t
-
singa.tensor.concatenate(tensors, axis)¶ concatenate list of tensors together based on given axis
- Parameters
tensors – list of tensors.
axis – number of axis to cancatenate on, all the dim should be the same except the axis to be concatenated.
- Returns
new tensor concatenated
-
singa.tensor.copy_data_to_from(dst, src, size, dst_offset=0, src_offset=0)¶ Copy the data between two Tensor instances which could be on different devices.
-
singa.tensor.copy_from_numpy(data, np_array)¶ - Copy the data from the numpy array.
used as static method
- Parameters
data – singa ctensor
np_array – source numpy array
-
singa.tensor.div(lhs, rhs, ret=None)¶ Elementi-wise division.
-
singa.tensor.einsum(ops, *args)¶ function TODO list to finish the function in cpp(just like numpy function): 1.sum(A,axis = None) 2.repeat(A,repeats) 3.transpose(A,axes = None) Do the matrix to matrix einsum calculation according to the operands Warning : this function could only support two matrix’ einsum calcultion
- Parameters
ops (string) – the string specifies the subscripts for summation such as ‘ki,kj->kij’ Here all the 26 lowercase letter can be used here.
args (list of array_like) – These are the tensors for the operation, but here only support two tensors.
- Returns
Singa.Tensor the output matirx of the einsum calculation
The best way to understand this function is to try the examples below: A_ = [0,1,2,3,4,5,6,7,8,9,10,11] A = A_.reshape(4,3) B = A_.reshape(3,4)
Here this einsum calculation is the same as normal ‘mult’ Res = einsum(‘ij,jk->ik’,A,B)
>>> [[ 20 23 26 29] [ 56 68 80 92] [ 92 113 134 155] [128 158 188 218]]
A_ = [0,1,2,3,4,5,6,7,8,9,10,11] A = A_.reshape(4,3) B = A_.reshape(4,3)
Here the einsum calculation is the same as normol ‘eltwise_mult’ Res = einsum(‘ki,ki->ki’,A,B)
>>> [[ 0 1 4] [ 9 16 25] [ 36 49 64] [ 81 100 121]]
A = [0,1,2,3,4,5,6,7,8,9,10,11] A = A.reshape(4,3)
Res = einsum(‘ki,kj->kij’,A,A) >>> [[[ 0 0 0]
[ 0 1 2] [ 0 2 4]]
- [[ 9 12 15]
[ 12 16 20] [ 15 20 25]]
- [[ 36 42 48]
[ 42 49 56] [ 48 56 64]]
- [[ 81 90 99]
[ 90 100 110] [ 99 110 121]]]
A_ = [0,1,2,3,4,5,6,7,8,9,10,11] A = A_.reshape(3,2,2)
Res = einsum(‘kia,kja->kij’,A,A) >>> [[[ 1 3]
[ 3 13]]
- [[ 41 59]
[ 59 85]]
- [[145 179]
[179 221]]]
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singa.tensor.eltwise_mult(lhs, rhs, ret=None)¶ Elementi-wise multiplication.
-
singa.tensor.exp(t)¶ - Parameters
t (Tensor) – input Tensor
- Returns
a new Tensor whose element y = exp(x), x is an element of t
-
singa.tensor.from_numpy(np_array)¶ Create a Tensor instance with the shape, dtype and values from the numpy array.
- Parameters
np_array – the numpy array.
- Returns
A Tensor instance allocated on the default CppCPU device.
-
singa.tensor.gaussian(mean, std, t)¶ Generate values following a Gaussian distribution.
- Parameters
mean (float) – the mean of the Gaussian distribution.
std (float) – the standard variance of the Gaussian distribution.
t (Tensor) – the results are put into t
- Returns
t
-
singa.tensor.ge(t, x)¶ Elementi-wise comparison for t >= x.
-
singa.tensor.gt(t, x)¶ Elementi-wise comparison for t > x.
-
singa.tensor.le(t, x)¶ Elementi-wise comparison for t <= x.
-
singa.tensor.log(t)¶ - Parameters
t (Tensor) – input Tensor
- Returns
a new Tensor whose element y = log(x), x is an element of t
-
singa.tensor.lt(t, x)¶ Elementi-wise comparison for t < x
-
singa.tensor.mult(A, B, C=None, alpha=1.0, beta=0.0)¶ Do matrix-matrix or matrix-vector multiplication. This function returns C = alpha * A * B + beta * C Currently below cases are supported
- case 1 - matrix * vector:
A (Tensor): 2d Tensor B (Tensor): 1d Tensor, GEMV would be invoked
- case 2 - matrix * matrix:
A (Tensor): 2d Tensor B (Tensor): 2d Tensor, GEMM would be invoked
- case 3 - batched matrix * batched matrix:
A (Tensor): 3/4d Tensor B (Tensor): 3/4d Tensor, batched GEMM would be invoked Where first/first and second dimension(s) of A, B should be exactly the same e.g. C{2,3,4,6} = A{2,3,4,5} * B{2,3,5,6}
- Parameters
A – n-d tensor
B – n-d tensor
C (Tensor, optional) – for storing the result; If None, a new Tensor would be created.
alpha (float) – scaling factor
beta (float) – scaling factor
- Returns
the result Tensor
-
singa.tensor.pow(t, x, out=None)¶
-
singa.tensor.repeat(t, repeats, axis=None)¶ Return the repeated tensor
- Parameters
t (tensor) – the tensor to be repeated
repeats (int or a sequence) – the number that the tensor need to repeat for
axis (int) – the axis to do repeat If it is None, then the repeated tensor will be flattened.If it isn’t None, the repeats could be sequence, but it’s size should match the axis’s shape
- Returns
the tensor which has been repeated
-
singa.tensor.reshape(tensor, shape)¶ Reshape the input tensor with the given shape and the original tensor is not changed
- Parameters
tensor (Tensor) – the tensor to be changed
shape (list<int>) – the new shape, which should have the same volumn as the old shape.
- Returns
the new Tensor
-
singa.tensor.sigmoid(t)¶ - Parameters
t (Tensor) – input Tensor
- Returns
a new Tensor whose element y = sigmoid(x); x is an element of t
-
singa.tensor.sign(t)¶ - Parameters
t (Tensor) – input Tensor
- Returns
a new Tensor whose element y = sign(x)
-
singa.tensor.sizeof(dtype)¶ Get size of datatype
- Parameters
dtype – singa datatype
- Returns
the number of bytes of the given SINGA data type defined in core.proto
-
singa.tensor.softmax(t, out=None)¶ Apply SoftMax for each row of the Tensor.
-
singa.tensor.sqrt(t)¶ - Parameters
t (Tensor) – input Tensor
- Returns
a new Tensor whose element y = sqrt(x), x is an element of t
-
singa.tensor.square(t)¶ - Parameters
t (Tensor) – input Tensor
- Returns
a new Tensor whose element y = x * x, x is an element of t
-
singa.tensor.sub(lhs, rhs, ret=None)¶ Elementi-wise subtraction.
-
singa.tensor.sum(t, axis=None, out=None)¶ Sum of tensor elements over given axis
- Parameters
t – Singa.tensor The array_like tensor to be sumed
axis – None or int or tuple of ints, optional Axis or axes along which a sum is performed. The default, axis=None, will sum all of the elements of the input array. If axis is negative it counts from the last to the first axis. If axis is a tuple of ints, a sum is performed on all of the axes specified in the tuple instead of a single axis or all the axes as before.
out – Singa.tensor optional Alternative output array in which to place the result. It must have the same shape as the expected output, but the type of the output values will be cast if necessary.
- Returns
A tensor with the same shape as t, with the specified axis removed. If a is a 0-d array, or if axis is None, a scalar is returned. If an output array is specified, a reference to out is returned
-
singa.tensor.sum_columns(M)¶ Sum all columns into a single column.
- Parameters
M (Tensor) – the input 2d tensor.
- Returns
a new Tensor as the resulted column.
-
singa.tensor.sum_rows(M)¶ Sum all rows into a single row.
- Parameters
M (Tensor) – the input 2d tensor.
- Returns
a new Tensor as the resulted row.
-
singa.tensor.tanh(t)¶ - Parameters
t (Tensor) – input Tensor
- Returns
a new Tensor whose element y = tanh(x), x is an element of t
-
singa.tensor.tensordot(A, B, axes=2)¶ Returns the tensor multiplication of two tensors along specified axes.
This is equivalent to compute dot product along the specified axes which are treated as one axis by reshaping.
- Parameters
A – Singa.Tensor
B – Singa.Tensor
axes –
If it is an integer, then ‘’axes’’ represent axes at the last of ‘’a`’’ and the first of ‘’b’’ are used.
If it is a pair of sequences of integers, then these two sequences specify the list of axes for ‘’a’’ and ‘’b’’. The corresponding axes are paired for sum-product.
- Returns
The tensor product of ‘’A’’ and ‘’B’’ along the axes specified by ‘’axes’’.
- Return type
singa.tensor
Thanks to numpy.tensordot. the link is https://github.com/numpy/numpy/blob/v1.14.0/numpy/core/numeric.py#L1123-L1306
-
singa.tensor.to_host(t)¶ Copy the data to a host tensor.
- Parameters
t (Tensor) – a Tensor
- Returns
new Tensor at host
-
singa.tensor.to_numpy(t)¶ Copy the tensor into a numpy array.
- Parameters
t (Tensor) – a Tensor
- Returns
a numpy array
-
singa.tensor.transpose(t, axes=None)¶ To transpose the tensor
- Parameters
t – input tensor
axes – axes to transpose
- Returns
the transposed tensor
