In MXNet, NDArray is the core datastructure for all mathematical computations.
An NDArray represents a multidimensional, fixed-size homogenous array.
If you're familiar with the scientific computing python package NumPy,
you might notice that mxnet.ndarray is similar to numpy.ndarray.
Like the corresponding NumPy data structure, MXNet's NDArray enables imperative computation.
So you might wonder, why not just use NumPy?
MXNet offers two compelling advantages.
First, MXNet's NDArray supports fast execution
on a wide range of hardware configurations,
including CPU, GPU, and multi-GPU machines.
MXNet also scales to distribute systems in the cloud.
Second, MXNet's NDArray executes code lazily,
allowing it to automatically parallelize multiple operations
across the available hardware.
An NDArray is a multidimensional array of numbers with the same type.
We could represent the coordinates of a point in 3D space,
e.g. [2, 1, 6] as a 1D array with shape (3).
Similarly, we could represent a 2D array.
Below, we present an array with length 2 along the first axis and length 3 along the second axis.
[[0, 1, 2]
[3, 4, 5]]Note that here the use of "dimension" is overloaded. When we say a 2D array, we mean an array with 2 axes, not an array with two components.
Each NDArray supports some important attributes that you'll often want to query:
n rows and m columns, its shape will be (n, m). numpy type object describing the type of its elements.shapecpu() or gpu(1).There are a few different ways to create an NDArray.
array function:
In [1]:
import mxnet as mx
# create a 1-dimensional array with a python list
a = mx.nd.array([1,2,3])
# create a 2-dimensional array with a nested python list
b = mx.nd.array([[1,2,3], [2,3,4]])
{'a.shape':a.shape, 'b.shape':b.shape}
Out[1]:
numpy.ndarray object:
In [2]:
import numpy as np
import math
c = np.arange(15).reshape(3,5)
# create a 2-dimensional array from a numpy.ndarray object
a = mx.nd.array(c)
{'a.shape':a.shape}
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We can specify the element type with the option dtype, which accepts a numpy type. By default, float32 is used:
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# float32 is used in deafult
a = mx.nd.array([1,2,3])
# create an int32 array
b = mx.nd.array([1,2,3], dtype=np.int32)
# create a 16-bit float array
c = mx.nd.array([1.2, 2.3], dtype=np.float16)
(a.dtype, b.dtype, c.dtype)
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If we know the size of the desired NDArray, but not the element values, MXNet offers several functions to create arrays with placeholder content:
In [4]:
# create a 2-dimensional array full of zeros with shape (2,3)
a = mx.nd.zeros((2,3))
# create a same shape array full of ones
b = mx.nd.ones((2,3))
# create a same shape array with all elements set to 7
c = mx.nd.full((2,3), 7)
# create a same shape whose initial content is random and
# depends on the state of the memory
d = mx.nd.empty((2,3))
When inspecting the contents of an NDArray, it's often convenient
to first extract its contents as a numpy.ndarray using the asnumpy function.
Numpy uses the following layout:
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b = mx.nd.arange(18).reshape((3,2,3))
b.asnumpy()
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In [6]:
a = mx.nd.ones((2,3))
b = mx.nd.ones((2,3))
# elementwise plus
c = a + b
# elementwise minus
d = - c
# elementwise pow and sin, and then transpose
e = mx.nd.sin(c**2).T
# elementwise max
f = mx.nd.maximum(a, c)
f.asnumpy()
Out[6]:
As in NumPy, * represents element-wise multiplication. For matrix-matrix multiplication, use dot.
In [7]:
a = mx.nd.arange(4).reshape((2,2))
b = a * a
c = mx.nd.dot(a,a)
print("b: %s, \n c: %s" % (b.asnumpy(), c.asnumpy()))
The assignment operators such as += and *= modify arrays in place, and thus don't allocate new memory to create a new array.
In [8]:
a = mx.nd.ones((2,2))
b = mx.nd.ones(a.shape)
b += a
b.asnumpy()
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In [9]:
a = mx.nd.array(np.arange(6).reshape(3,2))
a[1:2] = 1
a[:].asnumpy()
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We can also slice a particular axis with the method slice_axis
In [10]:
d = mx.nd.slice_axis(a, axis=1, begin=1, end=2)
d.asnumpy()
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In [11]:
a = mx.nd.array(np.arange(24))
b = a.reshape((2,3,4))
b.asnumpy()
Out[11]:
The concatenate method stacks multiple arrays along the first axis. (Their shapes must be the same along the other axes).
In [12]:
a = mx.nd.ones((2,3))
b = mx.nd.ones((2,3))*2
c = mx.nd.concatenate([a,b])
c.asnumpy()
Out[12]:
In [13]:
a = mx.nd.ones((2,3))
b = mx.nd.sum(a)
b.asnumpy()
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We can also reduce an array along a particular axis:
In [14]:
c = mx.nd.sum_axis(a, axis=1)
c.asnumpy()
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In [15]:
a = mx.nd.array(np.arange(6).reshape(6,1))
b = a.broadcast_to((6,4)) #
b.asnumpy()
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It's possible to simultaneously broadcast along multiple axes. In the following example, we broadcast along axes 1 and 2:
In [16]:
c = a.reshape((2,1,1,3))
d = c.broadcast_to((2,2,2,3))
d.asnumpy()
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Broadcasting can be applied automatically when executing some operations, e.g. * and + on arrays of different shapes.
In [17]:
a = mx.nd.ones((3,2))
b = mx.nd.ones((1,2))
c = a + b
c.asnumpy()
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In [18]:
a = mx.nd.ones((2,2))
b = a
b is a
Out[18]:
The copy method makes a deep copy of the array and its data:
In [19]:
b = a.copy()
b is a
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The above code allocates a new NDArray and then assigns to b. When we do not want to allocate additional memory, we can use the copyto method or the slice operator [] instead.
In [20]:
b = mx.nd.ones(a.shape)
c = b
c[:] = a
d = b
a.copyto(d)
(c is b, d is b)
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MXNet's NDArray offers some advanced features that differentiate it from the offerings you'll find in most other libraries.
By default, NDArray operators are executed on CPU. But with MXNet, it's easy to switch to another computation resource, such as GPU, when available. Each NDArray's device information is stored in ndarray.context. When MXNet is compiled with flag USE_CUDA=1 and the machine has at least one NVIDIA GPU, we can cause all computations to run on GPU 0 by using context mx.gpu(0), or simply mx.gpu(). When we have access to two or more GPUs, the 2nd GPU is represented by mx.gpu(1), etc.
In [21]:
def f():
a = mx.nd.ones((100,100))
b = mx.nd.ones((100,100))
c = a + b
print(c)
# in default mx.cpu() is used
f()
# change the default context to the first GPU
with mx.Context(mx.gpu()):
f()
We can also explicitly specify the context when creating an array:
In [22]:
a = mx.nd.ones((100, 100), mx.gpu(0))
a
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Currently, MXNet requires two arrays to sit on the same device for computation. There are several methods for copying data between devices.
In [23]:
import mxnet as mx
a = mx.nd.ones((100,100), mx.cpu())
b = mx.nd.ones((100,100), mx.gpu())
c = mx.nd.ones((100,100), mx.gpu())
a.copyto(c) # copy from CPU to GPU
d = b + c
e = b.as_in_context(c.context) + c # same to above
{'d':d, 'e':e}
Out[23]:
In [24]:
import pickle as pkl
a = mx.nd.ones((2, 3))
# pack and then dump into disk
data = pkl.dumps(a)
pkl.dump(data, open('tmp.pickle', 'wb'))
# load from disk and then unpack
data = pkl.load(open('tmp.pickle', 'rb'))
b = pkl.loads(data)
b.asnumpy()
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The second way is to directly dump to disk in binary format by using the save and load methods. We can save/load a single NDArray, or a list of NDArrays:
In [25]:
a = mx.nd.ones((2,3))
b = mx.nd.ones((5,6))
mx.nd.save("temp.ndarray", [a,b])
c = mx.nd.load("temp.ndarray")
c
Out[25]:
It's also possible to save or load a dict of NDArrays in this fashion:
In [26]:
d = {'a':a, 'b':b}
mx.nd.save("temp.ndarray", d)
c = mx.nd.load("temp.ndarray")
c
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The load and save methods are preferable to pickle in two respects
a = mx.nd.ones((2, 3))
mx.save("temp.ndarray", [a,])
a <- mx.nd.load("temp.ndarray")
as.array(a[[1]])
## [,1] [,2] [,3]
## [1,] 1 1 1
## [2,] 1 1 1
mx.nd.save('s3://mybucket/mydata.ndarray', [a,]) # if compiled with USE_S3=1
mx.nd.save('hdfs///users/myname/mydata.bin', [a,]) # if compiled with USE_HDFS=1
MXNet uses lazy evaluation to achieve superior performance.
When we run a=b+1 in Python, the Python thread
just pushes this operation into the backend engine and then returns.
There are two benefits for to this approach:
The backend engine can resolve data dependencies and schedule the computations correctly. It is transparent to frontend users. We can explicitly call the method wait_to_read on the result array to wait until the computation finishes. Operations that copy data from an array to other packages, such as asnumpy, will implicitly call wait_to_read.
In [27]:
# @@@ AUTOTEST_OUTPUT_IGNORED_CELL
import time
def do(x, n):
"""push computation into the backend engine"""
return [mx.nd.dot(x,x) for i in range(n)]
def wait(x):
"""wait until all results are available"""
for y in x:
y.wait_to_read()
tic = time.time()
a = mx.nd.ones((1000,1000))
b = do(a, 50)
print('time for all computations are pushed into the backend engine:\n %f sec' % (time.time() - tic))
wait(b)
print('time for all computations are finished:\n %f sec' % (time.time() - tic))
Besides analyzing data read and write dependencies, the backend engine is able to schedule computations with no dependency in parallel. For example, in the following code:
a = mx.nd.ones((2,3))
b = a + 1
c = a + 2
d = b * c
the second and third lines can be executed in parallel. The following example first runs on CPU and then on GPU:
In [29]:
# @@@ AUTOTEST_OUTPUT_IGNORED_CELL
n = 10
a = mx.nd.ones((1000,1000))
b = mx.nd.ones((6000,6000), mx.gpu(1))
tic = time.time()
c = do(a, n)
wait(c)
print('Time to finish the CPU workload: %f sec' % (time.time() - tic))
d = do(b, n)
wait(d)
print('Time to finish both CPU/CPU workloads: %f sec' % (time.time() - tic))
Now we issue all workloads at the same time. The backend engine will try to parallel the CPU and GPU computations.
In [30]:
# @@@ AUTOTEST_OUTPUT_IGNORED_CELL
tic = time.time()
c = do(a, n)
d = do(b, n)
wait(c)
wait(d)
print('Both as finished in: %f sec' % (time.time() - tic))
Whenever possible, we try to keep the NDArray API as similar as possible to the NumPy API. But you should note that NDArray is not fully yet fully NumPy-compatible. Here we summary the major differences, which we hope to be resolve quickly. (If you'd like to contribute, fork us on Github)
x[:, 1] to slice both dimensions.x[1:2:3]x[y==1].max, min...
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