NDArray API¶
Overview¶
This document lists the routines of the n-dimensional array package:
mxnet.ndarray |
NDArray API of MXNet. |
The NDArray
API, defined in the ndarray
(or simply nd
) package, provides
imperative tensor operations on CPU/GPU.
An NDArray
represents a multi-dimensional, fixed-size homogenous array.
>>> x = mx.nd.array([[1, 2, 3], [4, 5, 6]])
>>> type(x)
>>> x.shape
(2, 3)
>>> y = x + mx.nd.ones(x.shape)*3
>>> print(y.asnumpy())
[[ 4. 5. 6.]
[ 7. 8. 9.]]
>>> z = y.as_in_context(mx.gpu(0))
>>> print(z)
A detailed tutorial is available at
NDArray - Imperative tensor operations on CPU/GPU.
Note
mxnet.ndarray
is similar to numpy.ndarray
in some aspects. But the differences are not negligible. For instance:
mxnet.ndarray.NDArray.T
does real data transpose to return new a copied array, instead of returning a view of the input array.mxnet.ndarray.dot
performs dot product between the last axis of the first input array and the first axis of the second input, while numpy.dot uses the second last axis of the input array.
In addition, mxnet.ndarray.NDArray
supports GPU computation and various neural
network layers.
Note
ndarray
provides almost the same routines as symbol
. Most
routines between these two packages share the source code. But ndarray
differs from symbol
in few aspects:
ndarray
adopts imperative programming, namely sentences are executed step-by-step so that the results can be obtained immediately whereassymbol
adopts declarative programming.- Most binary operators in
ndarray
such as+
and>
have broadcasting enabled by default.
In the rest of this document, we first overview the methods provided by the
ndarray.NDArray
class, and then list other routines provided by the ndarray
package.
The ndarray
package provides several classes:
NDArray |
An array object representing a multidimensional, homogeneous array of fixed-size items. |
sparse.CSRNDArray |
A sparse representation of 2D NDArray in the Compressed Sparse Row format. |
sparse.RowSparseNDArray |
A sparse representation of a set of NDArray row slices at given indices. |
The NDArray
class¶
Array attributes¶
NDArray.shape |
Tuple of array dimensions. |
NDArray.size |
Number of elements in the array. |
NDArray.context |
Device context of the array. |
NDArray.dtype |
Data-type of the array’s elements. |
NDArray.stype |
Storage-type of the array. |
Array conversion¶
NDArray.copy |
Makes a copy of this NDArray , keeping the same context. |
NDArray.copyto |
Copies the value of this array to another array. |
NDArray.as_in_context |
Returns an array on the target device with the same value as this array. |
NDArray.asnumpy |
Returns a numpy.ndarray object with value copied from this array. |
NDArray.asscalar |
Returns a scalar whose value is copied from this array. |
NDArray.astype |
Returns a copy of the array after casting to a specified type. |
NDArray.tostype |
Return a copy of the array with chosen storage type. |
Array creation¶
NDArray.zeros_like |
Convenience fluent method for zeros_like() . |
NDArray.ones_like |
Convenience fluent method for ones_like() . |
Array change shape¶
NDArray.T |
Returns a copy of the array with axes transposed. |
NDArray.shape_array |
Convenience fluent method for shape_array() . |
NDArray.size_array |
Convenience fluent method for size_array() . |
NDArray.reshape |
Returns a view of this array with a new shape without altering any data. |
NDArray.reshape_like |
Convenience fluent method for reshape_like() . |
NDArray.flatten |
Convenience fluent method for flatten() . |
NDArray.expand_dims |
Convenience fluent method for expand_dims() . |
NDArray.split |
Convenience fluent method for split() . |
NDArray.diag |
Convenience fluent method for diag() . |
Array expand elements¶
NDArray.broadcast_to |
Broadcasts the input array to a new shape. |
NDArray.broadcast_axes |
Convenience fluent method for broadcast_axes() . |
NDArray.broadcast_like |
Broadcasts the input array to the shape of other. |
NDArray.tile |
Convenience fluent method for tile() . |
NDArray.pad |
Convenience fluent method for pad() . |
Array rearrange elements¶
NDArray.transpose |
Convenience fluent method for transpose() . |
NDArray.swapaxes |
Convenience fluent method for swapaxes() . |
NDArray.flip |
Convenience fluent method for flip() . |
NDArray.depth_to_space |
Convenience fluent method for depth_to_space() . |
NDArray.space_to_depth |
Convenience fluent method for space_to_depth() . |
Array reduction¶
NDArray.sum |
Convenience fluent method for sum() . |
NDArray.nansum |
Convenience fluent method for nansum() . |
NDArray.prod |
Convenience fluent method for prod() . |
NDArray.nanprod |
Convenience fluent method for nanprod() . |
NDArray.mean |
Convenience fluent method for mean() . |
NDArray.max |
Convenience fluent method for max() . |
NDArray.min |
Convenience fluent method for min() . |
NDArray.norm |
Convenience fluent method for norm() . |
Array rounding¶
NDArray.round |
Convenience fluent method for round() . |
NDArray.rint |
Convenience fluent method for rint() . |
NDArray.fix |
Convenience fluent method for fix() . |
NDArray.floor |
Convenience fluent method for floor() . |
NDArray.ceil |
Convenience fluent method for ceil() . |
NDArray.trunc |
Convenience fluent method for trunc() . |
Array sorting and searching¶
NDArray.sort |
Convenience fluent method for sort() . |
NDArray.argsort |
Convenience fluent method for argsort() . |
NDArray.topk |
Convenience fluent method for topk() . |
NDArray.argmax |
Convenience fluent method for argmax() . |
NDArray.argmin |
Convenience fluent method for argmin() . |
NDArray.argmax_channel |
Convenience fluent method for argmax_channel() . |
Arithmetic operations¶
NDArray.__add__ |
x.__add__(y) <=> x+y <=> mx.nd.add(x, y) |
NDArray.__sub__ |
x.__sub__(y) <=> x-y <=> mx.nd.subtract(x, y) |
NDArray.__rsub__ |
x.__rsub__(y) <=> y-x <=> mx.nd.subtract(y, x) |
NDArray.__neg__ |
x.__neg__(y) <=> -x |
NDArray.__mul__ |
x.__mul__(y) <=> x*y <=> mx.nd.multiply(x, y) |
NDArray.__div__ |
x.__div__(y) <=> x/y <=> mx.nd.divide(x, y) |
NDArray.__rdiv__ |
x.__rdiv__(y) <=> y/x <=> mx.nd.divide(y, x) |
NDArray.__mod__ |
x.__mod__(y) <=> x%y <=> mx.nd.modulo(x, y) |
NDArray.__rmod__ |
x.__rmod__(y) <=> y%x <=> mx.nd.modulo(y, x) |
NDArray.__pow__ |
x.__pow__(y) <=> x**y <=> mx.nd.power(x,y) |
Trigonometric functions¶
NDArray.sin |
Convenience fluent method for sin() . |
NDArray.cos |
Convenience fluent method for cos() . |
NDArray.tan |
Convenience fluent method for tan() . |
NDArray.arcsin |
Convenience fluent method for arcsin() . |
NDArray.arccos |
Convenience fluent method for arccos() . |
NDArray.arctan |
Convenience fluent method for arctan() . |
NDArray.degrees |
Convenience fluent method for degrees() . |
NDArray.radians |
Convenience fluent method for radians() . |
Hyperbolic functions¶
NDArray.sinh |
Convenience fluent method for sinh() . |
NDArray.cosh |
Convenience fluent method for cosh() . |
NDArray.tanh |
Convenience fluent method for tanh() . |
NDArray.arcsinh |
Convenience fluent method for arcsinh() . |
NDArray.arccosh |
Convenience fluent method for arccosh() . |
NDArray.arctanh |
Convenience fluent method for arctanh() . |
Exponents and logarithms¶
NDArray.exp |
Convenience fluent method for exp() . |
NDArray.expm1 |
Convenience fluent method for expm1() . |
NDArray.log |
Convenience fluent method for log() . |
NDArray.log10 |
Convenience fluent method for log10() . |
NDArray.log2 |
Convenience fluent method for log2() . |
NDArray.log1p |
Convenience fluent method for log1p() . |
Powers¶
NDArray.sqrt |
Convenience fluent method for sqrt() . |
NDArray.rsqrt |
Convenience fluent method for rsqrt() . |
NDArray.cbrt |
Convenience fluent method for cbrt() . |
NDArray.rcbrt |
Convenience fluent method for rcbrt() . |
NDArray.square |
Convenience fluent method for square() . |
NDArray.reciprocal |
Convenience fluent method for reciprocal() . |
Basic neural network functions¶
NDArray.relu |
Convenience fluent method for relu() . |
NDArray.sigmoid |
Convenience fluent method for sigmoid() . |
NDArray.softmax |
Convenience fluent method for softmax() . |
NDArray.log_softmax |
Convenience fluent method for log_softmax() . |
In-place arithmetic operations¶
NDArray.__iadd__ |
x.__iadd__(y) <=> x+=y |
NDArray.__isub__ |
x.__isub__(y) <=> x-=y |
NDArray.__imul__ |
x.__imul__(y) <=> x*=y |
NDArray.__idiv__ |
x.__rdiv__(y) <=> x/=y |
NDArray.__imod__ |
x.__rmod__(y) <=> x%=y |
Comparison operators¶
NDArray.__lt__ |
x.__lt__(y) <=> x |
NDArray.__le__ |
x.__le__(y) <=> x<=y <=> mx.nd.less_equal(x, y) |
NDArray.__gt__ |
x.__gt__(y) <=> x>y <=> mx.nd.greater(x, y) |
NDArray.__ge__ |
x.__ge__(y) <=> x>=y <=> mx.nd.greater_equal(x, y) |
NDArray.__eq__ |
x.__eq__(y) <=> x==y <=> mx.nd.equal(x, y) |
NDArray.__ne__ |
x.__ne__(y) <=> x!=y <=> mx.nd.not_equal(x, y) |
Indexing¶
NDArray.__getitem__ |
x.__getitem__(i) <=> x[i] |
NDArray.__setitem__ |
x.__setitem__(i, y) <=> x[i]=y |
NDArray.slice |
Convenience fluent method for slice() . |
NDArray.slice_axis |
Convenience fluent method for slice_axis() . |
NDArray.slice_like |
Convenience fluent method for slice_like() . |
NDArray.take |
Convenience fluent method for take() . |
NDArray.one_hot |
Convenience fluent method for one_hot() . |
NDArray.pick |
Convenience fluent method for pick() . |
Lazy evaluation¶
NDArray.wait_to_read |
Waits until all previous write operations on the current array are finished. |
Miscellaneous¶
NDArray.clip |
Convenience fluent method for clip() . |
NDArray.sign |
Convenience fluent method for sign() . |
Array creation routines¶
array |
Creates an array from any object exposing the array interface. |
empty |
Returns a new array of given shape and type, without initializing entries. |
zeros |
Return a new array of given shape and type, filled with zeros. |
zeros_like |
Return an array of zeros with the same shape, type and storage type as the input array. |
ones |
Returns a new array filled with all ones, with the given shape and type. |
ones_like |
Return an array of ones with the same shape and type as the input array. |
full |
Returns a new array of given shape and type, filled with the given value val. |
arange |
Returns evenly spaced values within a given interval. |
diag |
Extracts a diagonal or constructs a diagonal array. |
load |
Loads an array from file. |
save |
Saves a list of arrays or a dict of str->array to file. |
Array manipulation routines¶
Changing array shape and type¶
cast |
Casts all elements of the input to a new type. |
shape_array |
Returns a 1D int64 array containing the shape of data. |
size_array |
Returns a 1D int64 array containing the size of data. |
reshape |
Reshapes the input array. |
reshape_like |
Reshape some or all dimensions of lhs to have the same shape as some or all dimensions of rhs. |
flatten |
Flattens the input array into a 2-D array by collapsing the higher dimensions. |
expand_dims |
Inserts a new axis of size 1 into the array shape |
Expanding array elements¶
broadcast_to |
Broadcasts the input array to a new shape. |
broadcast_axes |
Broadcasts the input array over particular axes. |
broadcast_like |
Broadcasts lhs to have the same shape as rhs. |
repeat |
Repeats elements of an array. |
tile |
Repeats the whole array multiple times. |
pad |
Pads an input array with a constant or edge values of the array. |
Rearranging elements¶
transpose |
Permutes the dimensions of an array. |
swapaxes |
Interchanges two axes of an array. |
flip |
Reverses the order of elements along given axis while preserving array shape. |
depth_to_space |
Rearranges(permutes) data from depth into blocks of spatial data. |
space_to_depth |
Rearranges(permutes) blocks of spatial data into depth. |
Joining and splitting arrays¶
concat |
Joins input arrays along a given axis. |
split |
Splits an array along a particular axis into multiple sub-arrays. |
stack |
Join a sequence of arrays along a new axis. |
Indexing routines¶
slice |
Slices a region of the array. |
slice_axis |
Slices along a given axis. |
slice_like |
Slices a region of the array like the shape of another array. |
take |
Takes elements from an input array along the given axis. |
batch_take |
Takes elements from a data batch. |
one_hot |
Returns a one-hot array. |
pick |
Picks elements from an input array according to the input indices along the given axis. |
where |
Return the elements, either from x or y, depending on the condition. |
ravel_multi_index |
Converts a batch of index arrays into an array of flat indices. |
unravel_index |
Converts an array of flat indices into a batch of index arrays. |
Mathematical functions¶
Arithmetic operations¶
add |
Returns element-wise sum of the input arrays with broadcasting. |
subtract |
Returns element-wise difference of the input arrays with broadcasting. |
negative |
Numerical negative of the argument, element-wise. |
multiply |
Returns element-wise product of the input arrays with broadcasting. |
divide |
Returns element-wise division of the input arrays with broadcasting. |
modulo |
Returns element-wise modulo of the input arrays with broadcasting. |
dot |
Dot product of two arrays. |
batch_dot |
Batchwise dot product. |
add_n |
Adds all input arguments element-wise. |
Trigonometric functions¶
sin |
Computes the element-wise sine of the input array. |
cos |
Computes the element-wise cosine of the input array. |
tan |
Computes the element-wise tangent of the input array. |
arcsin |
Returns element-wise inverse sine of the input array. |
arccos |
Returns element-wise inverse cosine of the input array. |
arctan |
Returns element-wise inverse tangent of the input array. |
broadcast_hypot |
Returns the hypotenuse of a right angled triangle, given its “legs” with broadcasting. |
degrees |
Converts each element of the input array from radians to degrees. |
radians |
Converts each element of the input array from degrees to radians. |
Hyperbolic functions¶
sinh |
Returns the hyperbolic sine of the input array, computed element-wise. |
cosh |
Returns the hyperbolic cosine of the input array, computed element-wise. |
tanh |
Returns the hyperbolic tangent of the input array, computed element-wise. |
arcsinh |
Returns the element-wise inverse hyperbolic sine of the input array, computed element-wise. |
arccosh |
Returns the element-wise inverse hyperbolic cosine of the input array, computed element-wise. |
arctanh |
Returns the element-wise inverse hyperbolic tangent of the input array, computed element-wise. |
Reduce functions¶
sum |
Computes the sum of array elements over given axes. |
nansum |
Computes the sum of array elements over given axes treating Not a Numbers (NaN ) as zero. |
prod |
Computes the product of array elements over given axes. |
nanprod |
Computes the product of array elements over given axes treating Not a Numbers (NaN ) as one. |
mean |
Computes the mean of array elements over given axes. |
max |
Computes the max of array elements over given axes. |
min |
Computes the min of array elements over given axes. |
norm |
Computes the norm on an NDArray. |
Rounding¶
round |
Returns element-wise rounded value to the nearest integer of the input. |
rint |
Returns element-wise rounded value to the nearest integer of the input. |
fix |
Returns element-wise rounded value to the nearest integer towards zero of the input. |
floor |
Returns element-wise floor of the input. |
ceil |
Returns element-wise ceiling of the input. |
trunc |
Return the element-wise truncated value of the input. |
Exponents and logarithms¶
exp |
Returns element-wise exponential value of the input. |
expm1 |
Returns exp(x) - 1 computed element-wise on the input. |
log |
Returns element-wise Natural logarithmic value of the input. |
log10 |
Returns element-wise Base-10 logarithmic value of the input. |
log2 |
Returns element-wise Base-2 logarithmic value of the input. |
log1p |
Returns element-wise log(1 + x) value of the input. |
Powers¶
power |
Returns result of first array elements raised to powers from second array, element-wise with broadcasting. |
sqrt |
Returns element-wise square-root value of the input. |
rsqrt |
Returns element-wise inverse square-root value of the input. |
cbrt |
Returns element-wise cube-root value of the input. |
rcbrt |
Returns element-wise inverse cube-root value of the input. |
square |
Returns element-wise squared value of the input. |
reciprocal |
Returns the reciprocal of the argument, element-wise. |
Comparison¶
equal |
Returns the result of element-wise equal to (==) comparison operation with broadcasting. |
not_equal |
Returns the result of element-wise not equal to (!=) comparison operation with broadcasting. |
greater |
Returns the result of element-wise greater than (>) comparison operation with broadcasting. |
greater_equal |
Returns the result of element-wise greater than or equal to (>=) comparison operation with broadcasting. |
lesser |
Returns the result of element-wise lesser than (<) comparison operation with broadcasting. |
lesser_equal |
Returns the result of element-wise lesser than or equal to (<=) comparison operation with broadcasting. |
Logical operators¶
logical_and |
Returns the result of element-wise logical and comparison operation with broadcasting. |
logical_or |
Returns the result of element-wise logical or comparison operation with broadcasting. |
logical_xor |
Returns the result of element-wise logical xor comparison operation with broadcasting. |
logical_not |
Returns the result of logical NOT (!) function |
Random sampling¶
mxnet.ndarray.random.uniform |
Draw random samples from a uniform distribution. |
mxnet.ndarray.random.normal |
Draw random samples from a normal (Gaussian) distribution. |
mxnet.ndarray.random.gamma |
Draw random samples from a gamma distribution. |
mxnet.ndarray.random.exponential |
Draw samples from an exponential distribution. |
mxnet.ndarray.random.poisson |
Draw random samples from a Poisson distribution. |
mxnet.ndarray.random.negative_binomial |
Draw random samples from a negative binomial distribution. |
mxnet.ndarray.random.generalized_negative_binomial |
Draw random samples from a generalized negative binomial distribution. |
mxnet.ndarray.random.multinomial |
Concurrent sampling from multiple multinomial distributions. |
mxnet.ndarray.random.shuffle |
Shuffle the elements randomly. |
mxnet.random.seed |
Seeds the random number generators in MXNet. |
Sorting and searching¶
sort |
Returns a sorted copy of an input array along the given axis. |
topk |
Returns the top k elements in an input array along the given axis. |
argsort |
Returns the indices that would sort an input array along the given axis. |
argmax |
Returns indices of the maximum values along an axis. |
argmin |
Returns indices of the minimum values along an axis. |
Sequence operation¶
SequenceLast |
Takes the last element of a sequence. |
SequenceMask |
Sets all elements outside the sequence to a constant value. |
SequenceReverse |
Reverses the elements of each sequence. |
Miscellaneous¶
maximum |
Returns element-wise maximum of the input arrays with broadcasting. |
minimum |
Returns element-wise minimum of the input arrays with broadcasting. |
clip |
Clips (limits) the values in an array. |
abs |
Returns element-wise absolute value of the input. |
sign |
Returns element-wise sign of the input. |
gamma |
Returns the gamma function (extension of the factorial function to the reals), computed element-wise on the input array. |
gammaln |
Returns element-wise log of the absolute value of the gamma function of the input. |
Neural network¶
Basic¶
FullyConnected |
Applies a linear transformation: \(Y = XW^T + b\). |
Convolution |
Compute N-D convolution on (N+2)-D input. |
Activation |
Applies an activation function element-wise to the input. |
BatchNorm |
Batch normalization. |
Pooling |
Performs pooling on the input. |
SoftmaxOutput |
Computes the gradient of cross entropy loss with respect to softmax output. |
softmax |
Applies the softmax function. |
log_softmax |
Computes the log softmax of the input. |
relu |
Computes rectified linear. |
sigmoid |
Computes sigmoid of x element-wise. |
More¶
Correlation |
Applies correlation to inputs. |
Deconvolution |
Computes 1D or 2D transposed convolution (aka fractionally strided convolution) of the input tensor. |
RNN |
Applies recurrent layers to input data. |
Embedding |
Maps integer indices to vector representations (embeddings). |
LeakyReLU |
Applies Leaky rectified linear unit activation element-wise to the input. |
InstanceNorm |
Applies instance normalization to the n-dimensional input array. |
LayerNorm |
Layer normalization. |
L2Normalization |
Normalize the input array using the L2 norm. |
LRN |
Applies local response normalization to the input. |
ROIPooling |
Performs region of interest(ROI) pooling on the input array. |
SoftmaxActivation |
Applies softmax activation to input. |
Dropout |
Applies dropout operation to input array. |
BilinearSampler |
Applies bilinear sampling to input feature map. |
GridGenerator |
Generates 2D sampling grid for bilinear sampling. |
UpSampling |
Performs nearest neighbor/bilinear up sampling to inputs. |
SpatialTransformer |
Applies a spatial transformer to input feature map. |
LinearRegressionOutput |
Computes and optimizes for squared loss during backward propagation. |
LogisticRegressionOutput |
Applies a logistic function to the input. |
MAERegressionOutput |
Computes mean absolute error of the input. |
SVMOutput |
Computes support vector machine based transformation of the input. |
softmax_cross_entropy |
Calculate cross entropy of softmax output and one-hot label. |
smooth_l1 |
Calculate Smooth L1 Loss(lhs, scalar) by summing |
IdentityAttachKLSparseReg |
Apply a sparse regularization to the output a sigmoid activation function. |
MakeLoss |
Make your own loss function in network construction. |
BlockGrad |
Stops gradient computation. |
Custom |
Apply a custom operator implemented in a frontend language (like Python). |
API Reference¶
-
class
mxnet.ndarray.
NDArray
(handle, writable=True)[source]¶ An array object representing a multidimensional, homogeneous array of fixed-size items.
-
__setitem__
(key, value)[source]¶ x.__setitem__(i, y) <=> x[i]=y
Sets value to self[key]. This functions supports advanced indexing defined in the following reference with some restrictions.
- If key is a list type, only a list of integers is supported, e.g. key=[1, 2] is supported, while not for key=[[1, 2]].
- Ellipsis (...) and np.newaxis are not supported.
- Boolean array indexing is not supported.
Parameters: Examples
>>> x = mx.nd.zeros((2,3)) >>> x[:] = 1 >>> x.asnumpy() array([[ 1., 1., 1.], [ 1., 1., 1.]], dtype=float32) >>> x.asnumpy() array([[ 1., 1., 1.], [ 1., 1., 1.]], dtype=float32) >>> x[:,1:2] = 2 >>> x.asnumpy() array([[ 1., 2., 1.], [ 1., 2., 1.]], dtype=float32) >>> x[1:2,1:] = 3 >>> x.asnumpy() array([[ 1., 2., 1.], [ 1., 3., 3.]], dtype=float32) >>> x[1:,0:2] = mx.nd.zeros((1,2)) >>> x.asnumpy() array([[ 1., 2., 1.], [ 0., 0., 3.]], dtype=float32) >>> x[1,2] = 4 >>> x.asnumpy() array([[ 1., 2., 1.], [ 0., 0., 4.]], dtype=float32) >>> x[[0], [1, 2]] = 5 >>> x.asnumpy() array([[ 1., 5., 5.], [ 0., 0., 4.]], dtype=float32) >>> x[::-1, 0:2:2] = [6] >>> x.asnumpy() array([[ 6., 5., 5.], [ 6., 0., 4.]], dtype=float32)
-
__getitem__
(key)[source]¶ x.__getitem__(i) <=> x[i]
Returns a sliced view of this array if the elements fetched are contiguous in memory; otherwise, returns a newly created NDArray. This functions supports advanced indexing defined in the following reference with some restrictions.
- If key is a list type, only a list of integers is supported, e.g. key=[1, 2] is supported, while not for key=[[1, 2]].
- Ellipsis (...) and np.newaxis are not supported.
- Boolean array indexing is not supported.
Parameters: key (int, slice, list, np.ndarray, NDArray, or tuple of all previous types) – Indexing key. Examples
>>> x = mx.nd.arange(0,6).reshape((2,3)) >>> x.asnumpy() array([[ 0., 1., 2.], [ 3., 4., 5.]], dtype=float32) >>> x[1].asnumpy() array([ 3., 4., 5.], dtype=float32) >>> y = x[0:1] >>> y[:] = 2 >>> x.asnumpy() array([[ 2., 2., 2.], [ 3., 4., 5.]], dtype=float32) >>> x = mx.nd.arange(0, 8, dtype='int32').reshape((2, 2, 2)) >>> x[[0, 1]] [[[0 1] [2 3]] [[4 5] [6 7]]] >>> x[1:, [0, 1]] [[[4 5] [6 7]]] >>> y = np.array([0, 1], dtype='int32') >>> x[1:, y] [[[4 5] [6 7]]] >>> y = mx.nd.array([0, 1], dtype='int32') >>> x[1:, y] [[[4 5] [6 7]]]
-
reshape
(*shape, **kwargs)[source]¶ Returns a view of this array with a new shape without altering any data.
Parameters: - shape (tuple of int, or n ints) –
The new shape should not change the array size, namely
np.prod(new_shape)
should be equal tonp.prod(self.shape)
. Some dimensions of the shape can take special values from the set {0, -1, -2, -3, -4}. The significance of each is explained below:0
copy this dimension from the input to the output shape.Example:
- input shape = (2,3,4), shape = (4,0,2), output shape = (4,3,2) - input shape = (2,3,4), shape = (2,0,0), output shape = (2,3,4)
-1
infers the dimension of the output shape by using the remainder of the input dimensions keeping the size of the new array same as that of the input array. At most one dimension of shape can be -1.Example:
- input shape = (2,3,4), shape = (6,1,-1), output shape = (6,1,4) - input shape = (2,3,4), shape = (3,-1,8), output shape = (3,1,8) - input shape = (2,3,4), shape=(-1,), output shape = (24,)
-2
copy all/remainder of the input dimensions to the output shape.Example:
- input shape = (2,3,4), shape = (-2,), output shape = (2,3,4) - input shape = (2,3,4), shape = (2,-2), output shape = (2,3,4) - input shape = (2,3,4), shape = (-2,1,1), output shape = (2,3,4,1,1)
-3
use the product of two consecutive dimensions of the input shape as the output dimension.Example:
- input shape = (2,3,4), shape = (-3,4), output shape = (6,4) - input shape = (2,3,4,5), shape = (-3,-3), output shape = (6,20) - input shape = (2,3,4), shape = (0,-3), output shape = (2,12) - input shape = (2,3,4), shape = (-3,-2), output shape = (6,4)
-4
split one dimension of the input into two dimensions passed subsequent to -4 in shape (can contain -1).Example:
- input shape = (2,3,4), shape = (-4,1,2,-2), output shape =(1,2,3,4) - input shape = (2,3,4), shape = (2,-4,-1,3,-2), output shape = (2,1,3,4)
- If the argument reverse is set to 1, then the special values are inferred from right
to left.
Example:
- without reverse=1, for input shape = (10,5,4), shape = (-1,0), output shape would be
(40,5).- with reverse=1, output shape will be (50,4).
- reverse (bool, default False) – If true then the special values are inferred from right to left. Only supported as keyword argument.
Returns: An array with desired shape that shares data with this array.
Return type: Examples
>>> x = mx.nd.arange(0,6).reshape(2,3) >>> x.asnumpy() array([[ 0., 1., 2.], [ 3., 4., 5.]], dtype=float32) >>> y = x.reshape(3,2) >>> y.asnumpy() array([[ 0., 1.], [ 2., 3.], [ 4., 5.]], dtype=float32) >>> y = x.reshape(3,-1) >>> y.asnumpy() array([[ 0., 1.], [ 2., 3.], [ 4., 5.]], dtype=float32) >>> y = x.reshape(3,2) >>> y.asnumpy() array([[ 0., 1.], [ 2., 3.], [ 4., 5.]], dtype=float32) >>> y = x.reshape(-3) >>> y.asnumpy() array([ 0. 1. 2. 3. 4. 5.], dtype=float32) >>> y[:] = -1 >>> x.asnumpy() array([[-1., -1., -1.], [-1., -1., -1.]], dtype=float32)
- shape (tuple of int, or n ints) –
-
reshape_like
(*args, **kwargs)[source]¶ Convenience fluent method for
reshape_like()
.The arguments are the same as for
reshape_like()
, with this array as data.
-
zeros_like
(*args, **kwargs)[source]¶ Convenience fluent method for
zeros_like()
.The arguments are the same as for
zeros_like()
, with this array as data.
-
ones_like
(*args, **kwargs)[source]¶ Convenience fluent method for
ones_like()
.The arguments are the same as for
ones_like()
, with this array as data.
-
broadcast_axes
(*args, **kwargs)[source]¶ Convenience fluent method for
broadcast_axes()
.The arguments are the same as for
broadcast_axes()
, with this array as data.
-
repeat
(*args, **kwargs)[source]¶ Convenience fluent method for
repeat()
.The arguments are the same as for
repeat()
, with this array as data.
-
pad
(*args, **kwargs)[source]¶ Convenience fluent method for
pad()
.The arguments are the same as for
pad()
, with this array as data.
-
swapaxes
(*args, **kwargs)[source]¶ Convenience fluent method for
swapaxes()
.The arguments are the same as for
swapaxes()
, with this array as data.
-
split
(*args, **kwargs)[source]¶ Convenience fluent method for
split()
.The arguments are the same as for
split()
, with this array as data.
-
slice
(*args, **kwargs)[source]¶ Convenience fluent method for
slice()
.The arguments are the same as for
slice()
, with this array as data.
-
slice_axis
(*args, **kwargs)[source]¶ Convenience fluent method for
slice_axis()
.The arguments are the same as for
slice_axis()
, with this array as data.
-
slice_like
(*args, **kwargs)[source]¶ Convenience fluent method for
slice_like()
.The arguments are the same as for
slice_like()
, with this array as data.
-
take
(*args, **kwargs)[source]¶ Convenience fluent method for
take()
.The arguments are the same as for
take()
, with this array as data.
-
one_hot
(*args, **kwargs)[source]¶ Convenience fluent method for
one_hot()
.The arguments are the same as for
one_hot()
, with this array as data.
-
pick
(*args, **kwargs)[source]¶ Convenience fluent method for
pick()
.The arguments are the same as for
pick()
, with this array as data.
-
sort
(*args, **kwargs)[source]¶ Convenience fluent method for
sort()
.The arguments are the same as for
sort()
, with this array as data.
-
topk
(*args, **kwargs)[source]¶ Convenience fluent method for
topk()
.The arguments are the same as for
topk()
, with this array as data.
-
argsort
(*args, **kwargs)[source]¶ Convenience fluent method for
argsort()
.The arguments are the same as for
argsort()
, with this array as data.
-
argmax
(*args, **kwargs)[source]¶ Convenience fluent method for
argmax()
.The arguments are the same as for
argmax()
, with this array as data.
-
argmax_channel
(*args, **kwargs)[source]¶ Convenience fluent method for
argmax_channel()
.The arguments are the same as for
argmax_channel()
, with this array as data.
-
argmin
(*args, **kwargs)[source]¶ Convenience fluent method for
argmin()
.The arguments are the same as for
argmin()
, with this array as data.
-
clip
(*args, **kwargs)[source]¶ Convenience fluent method for
clip()
.The arguments are the same as for
clip()
, with this array as data.
-
abs
(*args, **kwargs)[source]¶ Convenience fluent method for
abs()
.The arguments are the same as for
abs()
, with this array as data.
-
sign
(*args, **kwargs)[source]¶ Convenience fluent method for
sign()
.The arguments are the same as for
sign()
, with this array as data.
-
flatten
(*args, **kwargs)[source]¶ Convenience fluent method for
flatten()
.The arguments are the same as for
flatten()
, with this array as data.
-
shape_array
(*args, **kwargs)[source]¶ Convenience fluent method for
shape_array()
.The arguments are the same as for
shape_array()
, with this array as data.
-
size_array
(*args, **kwargs)[source]¶ Convenience fluent method for
size_array()
.The arguments are the same as for
size_array()
, with this array as data.
-
expand_dims
(*args, **kwargs)[source]¶ Convenience fluent method for
expand_dims()
.The arguments are the same as for
expand_dims()
, with this array as data.
-
tile
(*args, **kwargs)[source]¶ Convenience fluent method for
tile()
.The arguments are the same as for
tile()
, with this array as data.
-
transpose
(*args, **kwargs)[source]¶ Convenience fluent method for
transpose()
.The arguments are the same as for
transpose()
, with this array as data.
-
flip
(*args, **kwargs)[source]¶ Convenience fluent method for
flip()
.The arguments are the same as for
flip()
, with this array as data.
-
depth_to_space
(*args, **kwargs)[source]¶ Convenience fluent method for
depth_to_space()
.The arguments are the same as for
depth_to_space()
, with this array as data.
-
space_to_depth
(*args, **kwargs)[source]¶ Convenience fluent method for
space_to_depth()
.The arguments are the same as for
space_to_depth()
, with this array as data.
-
diag
(k=0, **kwargs)[source]¶ Convenience fluent method for
diag()
.The arguments are the same as for
diag()
, with this array as data.
-
sum
(*args, **kwargs)[source]¶ Convenience fluent method for
sum()
.The arguments are the same as for
sum()
, with this array as data.
-
nansum
(*args, **kwargs)[source]¶ Convenience fluent method for
nansum()
.The arguments are the same as for
nansum()
, with this array as data.
-
prod
(*args, **kwargs)[source]¶ Convenience fluent method for
prod()
.The arguments are the same as for
prod()
, with this array as data.
-
nanprod
(*args, **kwargs)[source]¶ Convenience fluent method for
nanprod()
.The arguments are the same as for
nanprod()
, with this array as data.
-
mean
(*args, **kwargs)[source]¶ Convenience fluent method for
mean()
.The arguments are the same as for
mean()
, with this array as data.
-
max
(*args, **kwargs)[source]¶ Convenience fluent method for
max()
.The arguments are the same as for
max()
, with this array as data.
-
min
(*args, **kwargs)[source]¶ Convenience fluent method for
min()
.The arguments are the same as for
min()
, with this array as data.
-
norm
(*args, **kwargs)[source]¶ Convenience fluent method for
norm()
.The arguments are the same as for
norm()
, with this array as data.
-
round
(*args, **kwargs)[source]¶ Convenience fluent method for
round()
.The arguments are the same as for
round()
, with this array as data.
-
rint
(*args, **kwargs)[source]¶ Convenience fluent method for
rint()
.The arguments are the same as for
rint()
, with this array as data.
-
fix
(*args, **kwargs)[source]¶ Convenience fluent method for
fix()
.The arguments are the same as for
fix()
, with this array as data.
-
floor
(*args, **kwargs)[source]¶ Convenience fluent method for
floor()
.The arguments are the same as for
floor()
, with this array as data.
-
ceil
(*args, **kwargs)[source]¶ Convenience fluent method for
ceil()
.The arguments are the same as for
ceil()
, with this array as data.
-
trunc
(*args, **kwargs)[source]¶ Convenience fluent method for
trunc()
.The arguments are the same as for
trunc()
, with this array as data.
-
sin
(*args, **kwargs)[source]¶ Convenience fluent method for
sin()
.The arguments are the same as for
sin()
, with this array as data.
-
cos
(*args, **kwargs)[source]¶ Convenience fluent method for
cos()
.The arguments are the same as for
cos()
, with this array as data.
-
tan
(*args, **kwargs)[source]¶ Convenience fluent method for
tan()
.The arguments are the same as for
tan()
, with this array as data.
-
arcsin
(*args, **kwargs)[source]¶ Convenience fluent method for
arcsin()
.The arguments are the same as for
arcsin()
, with this array as data.
-
arccos
(*args, **kwargs)[source]¶ Convenience fluent method for
arccos()
.The arguments are the same as for
arccos()
, with this array as data.
-
arctan
(*args, **kwargs)[source]¶ Convenience fluent method for
arctan()
.The arguments are the same as for
arctan()
, with this array as data.
-
degrees
(*args, **kwargs)[source]¶ Convenience fluent method for
degrees()
.The arguments are the same as for
degrees()
, with this array as data.
-
radians
(*args, **kwargs)[source]¶ Convenience fluent method for
radians()
.The arguments are the same as for
radians()
, with this array as data.
-
sinh
(*args, **kwargs)[source]¶ Convenience fluent method for
sinh()
.The arguments are the same as for
sinh()
, with this array as data.
-
cosh
(*args, **kwargs)[source]¶ Convenience fluent method for
cosh()
.The arguments are the same as for
cosh()
, with this array as data.
-
tanh
(*args, **kwargs)[source]¶ Convenience fluent method for
tanh()
.The arguments are the same as for
tanh()
, with this array as data.
-
arcsinh
(*args, **kwargs)[source]¶ Convenience fluent method for
arcsinh()
.The arguments are the same as for
arcsinh()
, with this array as data.
-
arccosh
(*args, **kwargs)[source]¶ Convenience fluent method for
arccosh()
.The arguments are the same as for
arccosh()
, with this array as data.
-
arctanh
(*args, **kwargs)[source]¶ Convenience fluent method for
arctanh()
.The arguments are the same as for
arctanh()
, with this array as data.
-
exp
(*args, **kwargs)[source]¶ Convenience fluent method for
exp()
.The arguments are the same as for
exp()
, with this array as data.
-
expm1
(*args, **kwargs)[source]¶ Convenience fluent method for
expm1()
.The arguments are the same as for
expm1()
, with this array as data.
-
log
(*args, **kwargs)[source]¶ Convenience fluent method for
log()
.The arguments are the same as for
log()
, with this array as data.
-
log10
(*args, **kwargs)[source]¶ Convenience fluent method for
log10()
.The arguments are the same as for
log10()
, with this array as data.
-
log2
(*args, **kwargs)[source]¶ Convenience fluent method for
log2()
.The arguments are the same as for
log2()
, with this array as data.
-
log1p
(*args, **kwargs)[source]¶ Convenience fluent method for
log1p()
.The arguments are the same as for
log1p()
, with this array as data.
-
sqrt
(*args, **kwargs)[source]¶ Convenience fluent method for
sqrt()
.The arguments are the same as for
sqrt()
, with this array as data.
-
rsqrt
(*args, **kwargs)[source]¶ Convenience fluent method for
rsqrt()
.The arguments are the same as for
rsqrt()
, with this array as data.
-
cbrt
(*args, **kwargs)[source]¶ Convenience fluent method for
cbrt()
.The arguments are the same as for
cbrt()
, with this array as data.
-
rcbrt
(*args, **kwargs)[source]¶ Convenience fluent method for
rcbrt()
.The arguments are the same as for
rcbrt()
, with this array as data.
-
square
(*args, **kwargs)[source]¶ Convenience fluent method for
square()
.The arguments are the same as for
square()
, with this array as data.
-
reciprocal
(*args, **kwargs)[source]¶ Convenience fluent method for
reciprocal()
.The arguments are the same as for
reciprocal()
, with this array as data.
-
relu
(*args, **kwargs)[source]¶ Convenience fluent method for
relu()
.The arguments are the same as for
relu()
, with this array as data.
-
sigmoid
(*args, **kwargs)[source]¶ Convenience fluent method for
sigmoid()
.The arguments are the same as for
sigmoid()
, with this array as data.
-
softmax
(*args, **kwargs)[source]¶ Convenience fluent method for
softmax()
.The arguments are the same as for
softmax()
, with this array as data.
-
log_softmax
(*args, **kwargs)[source]¶ Convenience fluent method for
log_softmax()
.The arguments are the same as for
log_softmax()
, with this array as data.
-
squeeze
(*args, **kwargs)[source]¶ Convenience fluent method for
squeeze()
.The arguments are the same as for
squeeze()
, with this array as data.
-
broadcast_to
(shape)[source]¶ Broadcasts the input array to a new shape.
Broadcasting is only allowed on axes with size 1. The new shape cannot change the number of dimensions. For example, you could broadcast from shape (2, 1) to (2, 3), but not from shape (2, 3) to (2, 3, 3).
Parameters: shape (tuple of int) – The shape of the desired array. Returns: A NDArray with the desired shape that is not sharing data with this array, even if the new shape is the same as self.shape
.Return type: NDArray Examples
>>> x = mx.nd.arange(0,3).reshape((1,3,1)) >>> x.asnumpy() array([[[ 0.], [ 1.], [ 2.]]], dtype=float32) >>> y = x.broadcast_to((2,3,3)) >>> y.asnumpy() array([[[ 0., 0., 0.], [ 1., 1., 1.], [ 2., 2., 2.]], [[ 0., 0., 0.], [ 1., 1., 1.], [ 2., 2., 2.]]], dtype=float32)
-
broadcast_like
(other)[source]¶ Broadcasts the input array to the shape of other.
Broadcasting is only allowed on axes with size 1. The new shape cannot change the number of dimensions. For example, you could broadcast from shape (2, 1) to (2, 3), but not from shape (2, 3) to (2, 3, 3).
Parameters: other (NDArray) – Array with shape of the desired array. Returns: A NDArray with the desired shape that is not sharing data with this array, even if the new shape is the same as self.shape
.Return type: NDArray Examples
>>> x = mx.nd.arange(0,3).reshape((1,3,1)) >>> x.asnumpy() array([[[ 0.], [ 1.], [ 2.]]], dtype=float32) >>> y = x.broadcast_like(mx.nd.ones((2,3,3))) >>> y.asnumpy() array([[[ 0., 0., 0.], [ 1., 1., 1.], [ 2., 2., 2.]], [[ 0., 0., 0.], [ 1., 1., 1.], [ 2., 2., 2.]]], dtype=float32)
-
wait_to_read
()[source]¶ Waits until all previous write operations on the current array are finished.
This method guarantees that all previous write operations that pushed into the backend engine for execution are actually finished.
Examples
>>> import time >>> tic = time.time() >>> a = mx.nd.ones((1000,1000)) >>> b = mx.nd.dot(a, a) >>> print(time.time() - tic) 0.003854036331176758 >>> b.wait_to_read() >>> print(time.time() - tic) 0.0893700122833252
-
ndim
¶ Returns the number of dimensions of this array
Examples
>>> x = mx.nd.array([1, 2, 3, 4]) >>> x.ndim 1 >>> x = mx.nd.array([[1, 2], [3, 4]]) >>> x.ndim 2
-
shape
¶ Tuple of array dimensions.
Examples
>>> x = mx.nd.array([1, 2, 3, 4]) >>> x.shape (4L,) >>> y = mx.nd.zeros((2, 3, 4)) >>> y.shape (2L, 3L, 4L)
-
size
¶ Number of elements in the array.
Equivalent to the product of the array’s dimensions.
Examples
>>> import numpy as np >>> x = mx.nd.zeros((3, 5, 2)) >>> x.size 30 >>> np.prod(x.shape) 30
-
context
¶ Device context of the array.
Examples
>>> x = mx.nd.array([1, 2, 3, 4]) >>> x.context cpu(0) >>> type(x.context)
>>> y = mx.nd.zeros((2,3), mx.gpu(0)) >>> y.context gpu(0)
-
dtype
¶ Data-type of the array’s elements.
Returns: This NDArray’s data type. Return type: numpy.dtype Examples
>>> x = mx.nd.zeros((2,3)) >>> x.dtype
>>> y = mx.nd.zeros((2,3), dtype='int32') >>> y.dtype
-
stype
¶ Storage-type of the array.
-
T
¶ Returns a copy of the array with axes transposed.
Equivalent to
mx.nd.transpose(self)
except that self is returned ifself.ndim < 2
.Unlike
numpy.ndarray.T
, this function returns a copy rather than a view of the array unlessself.ndim < 2
.Examples
>>> x = mx.nd.arange(0,6).reshape((2,3)) >>> x.asnumpy() array([[ 0., 1., 2.], [ 3., 4., 5.]], dtype=float32) >>> x.T.asnumpy() array([[ 0., 3.], [ 1., 4.], [ 2., 5.]], dtype=float32)
-
asnumpy
()[source]¶ Returns a
numpy.ndarray
object with value copied from this array.Examples
>>> x = mx.nd.ones((2,3)) >>> y = x.asnumpy() >>> type(y)
>>> y array([[ 1., 1., 1.], [ 1., 1., 1.]], dtype=float32) >>> z = mx.nd.ones((2,3), dtype='int32') >>> z.asnumpy() array([[1, 1, 1], [1, 1, 1]], dtype=int32)
-
asscalar
()[source]¶ Returns a scalar whose value is copied from this array.
This function is equivalent to
self.asnumpy()[0]
. This NDArray must have shape (1,).Examples
>>> x = mx.nd.ones((1,), dtype='int32') >>> x.asscalar() 1 >>> type(x.asscalar())
-
astype
(dtype, copy=True)[source]¶ Returns a copy of the array after casting to a specified type.
Parameters: - dtype (numpy.dtype or str) – The type of the returned array.
- copy (bool) – Default True. By default, astype always returns a newly allocated ndarray on the same context. If this is set to False, and the dtype requested is the same as the ndarray’s dtype, the ndarray is returned instead of a copy.
Returns: The copied array after casting to the specified type, or the same array if copy=False and dtype is the same as the input array.
Return type: Examples
>>> x = mx.nd.zeros((2,3), dtype='float32') >>> y = x.astype('int32') >>> y.dtype
-
copyto
(other)[source]¶ Copies the value of this array to another array.
If
other
is aNDArray
object, thenother.shape
andself.shape
should be the same. This function copies the value fromself
toother
.If
other
is a context, a newNDArray
will be first created on the target context, and the value ofself
is copied.Parameters: other (NDArray or Context) – The destination array or context. Returns: The copied array. If other
is anNDArray
, then the return value andother
will point to the sameNDArray
.Return type: NDArray, CSRNDArray or RowSparseNDArray Examples
>>> x = mx.nd.ones((2,3)) >>> y = mx.nd.zeros((2,3), mx.gpu(0)) >>> z = x.copyto(y) >>> z is y True >>> y.asnumpy() array([[ 1., 1., 1.], [ 1., 1., 1.]], dtype=float32) >>> y.copyto(mx.gpu(0))
-
copy
()[source]¶ Makes a copy of this
NDArray
, keeping the same context.Returns: The copied array Return type: NDArray, CSRNDArray or RowSparseNDArray Examples
>>> x = mx.nd.ones((2,3)) >>> y = x.copy() >>> y.asnumpy() array([[ 1., 1., 1.], [ 1., 1., 1.]], dtype=float32)
-
as_in_context
(context)[source]¶ Returns an array on the target device with the same value as this array.
If the target context is the same as
self.context
, thenself
is returned. Otherwise, a copy is made.Parameters: context (Context) – The target context. Returns: The target array. Return type: NDArray, CSRNDArray or RowSparseNDArray Examples
>>> x = mx.nd.ones((2,3)) >>> y = x.as_in_context(mx.cpu()) >>> y is x True >>> z = x.as_in_context(mx.gpu(0)) >>> z is x False
-
attach_grad
(grad_req='write', stype=None)[source]¶ Attach a gradient buffer to this NDArray, so that backward can compute gradient with respect to it.
Parameters: - grad_req ({'write', 'add', 'null'}) – How gradient will be accumulated. - ‘write’: gradient will be overwritten on every backward. - ‘add’: gradient will be added to existing value on every backward. - ‘null’: do not compute gradient for this NDArray.
- stype (str, optional) – The storage type of the gradient array. Defaults to the same stype of this NDArray.
-
grad
¶ Returns gradient buffer attached to this NDArray.
-
backward
(out_grad=None, retain_graph=False, train_mode=True)[source]¶ Compute the gradients of this NDArray w.r.t variables.
Parameters: - out_grad (NDArray, optional) – Gradient with respect to head.
- retain_graph (bool, optional) – Whether to retain the computaion graph for another backward pass on the same graph. By default the computaion history is cleared.
- train_mode (bool, optional) – Whether to compute gradient for training or inference.
-
tostype
(stype)[source]¶ Return a copy of the array with chosen storage type.
See also
Returns: A copy of the array with the chosen storage stype Return type: NDArray, CSRNDArray or RowSparseNDArray
-
NDArray API of MXNet.
-
mxnet.ndarray.
Activation
(data=None, act_type=_Null, out=None, name=None, **kwargs)¶ Applies an activation function element-wise to the input.
The following activation functions are supported:
- relu: Rectified Linear Unit, \(y = max(x, 0)\)
- sigmoid: \(y = \frac{1}{1 + exp(-x)}\)
- tanh: Hyperbolic tangent, \(y = \frac{exp(x) - exp(-x)}{exp(x) + exp(-x)}\)
- softrelu: Soft ReLU, or SoftPlus, \(y = log(1 + exp(x))\)
- softsign: \(y = \frac{x}{1 + abs(x)}\)
Defined in src/operator/nn/activation.cc:L184
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
BatchNorm
(data=None, gamma=None, beta=None, moving_mean=None, moving_var=None, eps=_Null, momentum=_Null, fix_gamma=_Null, use_global_stats=_Null, output_mean_var=_Null, axis=_Null, cudnn_off=_Null, out=None, name=None, **kwargs)¶ Batch normalization.
Normalizes a data batch by mean and variance, and applies a scale
gamma
as well as offsetbeta
.Assume the input has more than one dimension and we normalize along axis 1. We first compute the mean and variance along this axis:
\[\begin{split}data\_mean[i] = mean(data[:,i,:,...]) \\ data\_var[i] = var(data[:,i,:,...])\end{split}\]Then compute the normalized output, which has the same shape as input, as following:
\[out[:,i,:,...] = \frac{data[:,i,:,...] - data\_mean[i]}{\sqrt{data\_var[i]+\epsilon}} * gamma[i] + beta[i]\]Both mean and var returns a scalar by treating the input as a vector.
Assume the input has size k on axis 1, then both
gamma
andbeta
have shape (k,). Ifoutput_mean_var
is set to be true, then outputs bothdata_mean
and the inverse ofdata_var
, which are needed for the backward pass. Note that gradient of these two outputs are blocked.Besides the inputs and the outputs, this operator accepts two auxiliary states,
moving_mean
andmoving_var
, which are k-length vectors. They are global statistics for the whole dataset, which are updated by:moving_mean = moving_mean * momentum + data_mean * (1 - momentum) moving_var = moving_var * momentum + data_var * (1 - momentum)
If
use_global_stats
is set to be true, thenmoving_mean
andmoving_var
are used instead ofdata_mean
anddata_var
to compute the output. It is often used during inference.The parameter
axis
specifies which axis of the input shape denotes the ‘channel’ (separately normalized groups). The default is 1. Specifying -1 sets the channel axis to be the last item in the input shape.Both
gamma
andbeta
are learnable parameters. But iffix_gamma
is true, then setgamma
to 1 and its gradient to 0.Note:
When fix_gamma is set to True, no sparse support is provided. If fix_gamma is set to False, the sparse tensors will fallback.
Defined in src/operator/nn/batch_norm.cc:L574
Parameters: - data (NDArray) – Input data to batch normalization
- gamma (NDArray) – gamma array
- beta (NDArray) – beta array
- moving_mean (NDArray) – running mean of input
- moving_var (NDArray) – running variance of input
- eps (double, optional, default=0.001) – Epsilon to prevent div 0. Must be no less than CUDNN_BN_MIN_EPSILON defined in cudnn.h when using cudnn (usually 1e-5)
- momentum (float, optional, default=0.9) – Momentum for moving average
- fix_gamma (boolean, optional, default=1) – Fix gamma while training
- use_global_stats (boolean, optional, default=0) – Whether use global moving statistics instead of local batch-norm. This will force change batch-norm into a scale shift operator.
- output_mean_var (boolean, optional, default=0) – Output the mean and inverse std
- axis (int, optional, default='1') – Specify which shape axis the channel is specified
- cudnn_off (boolean, optional, default=0) – Do not select CUDNN operator, if available
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
BatchNorm_v1
(data=None, gamma=None, beta=None, eps=_Null, momentum=_Null, fix_gamma=_Null, use_global_stats=_Null, output_mean_var=_Null, out=None, name=None, **kwargs)¶ Batch normalization.
This operator is DEPRECATED. Perform BatchNorm on the input.
Normalizes a data batch by mean and variance, and applies a scale
gamma
as well as offsetbeta
.Assume the input has more than one dimension and we normalize along axis 1. We first compute the mean and variance along this axis:
\[\begin{split}data\_mean[i] = mean(data[:,i,:,...]) \\ data\_var[i] = var(data[:,i,:,...])\end{split}\]Then compute the normalized output, which has the same shape as input, as following:
\[out[:,i,:,...] = \frac{data[:,i,:,...] - data\_mean[i]}{\sqrt{data\_var[i]+\epsilon}} * gamma[i] + beta[i]\]Both mean and var returns a scalar by treating the input as a vector.
Assume the input has size k on axis 1, then both
gamma
andbeta
have shape (k,). Ifoutput_mean_var
is set to be true, then outputs bothdata_mean
anddata_var
as well, which are needed for the backward pass.Besides the inputs and the outputs, this operator accepts two auxiliary states,
moving_mean
andmoving_var
, which are k-length vectors. They are global statistics for the whole dataset, which are updated by:moving_mean = moving_mean * momentum + data_mean * (1 - momentum) moving_var = moving_var * momentum + data_var * (1 - momentum)
If
use_global_stats
is set to be true, thenmoving_mean
andmoving_var
are used instead ofdata_mean
anddata_var
to compute the output. It is often used during inference.Both
gamma
andbeta
are learnable parameters. But iffix_gamma
is true, then setgamma
to 1 and its gradient to 0.There’s no sparse support for this operator, and it will exhibit problematic behavior if used with sparse tensors.
Defined in src/operator/batch_norm_v1.cc:L95
Parameters: - data (NDArray) – Input data to batch normalization
- gamma (NDArray) – gamma array
- beta (NDArray) – beta array
- eps (float, optional, default=0.001) – Epsilon to prevent div 0
- momentum (float, optional, default=0.9) – Momentum for moving average
- fix_gamma (boolean, optional, default=1) – Fix gamma while training
- use_global_stats (boolean, optional, default=0) – Whether use global moving statistics instead of local batch-norm. This will force change batch-norm into a scale shift operator.
- output_mean_var (boolean, optional, default=0) – Output All,normal mean and var
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
BilinearSampler
(data=None, grid=None, out=None, name=None, **kwargs)¶ Applies bilinear sampling to input feature map.
Bilinear Sampling is the key of [NIPS2015] “Spatial Transformer Networks”. The usage of the operator is very similar to remap function in OpenCV, except that the operator has the backward pass.
Given \(data\) and \(grid\), then the output is computed by
\[\begin{split}x_{src} = grid[batch, 0, y_{dst}, x_{dst}] \\ y_{src} = grid[batch, 1, y_{dst}, x_{dst}] \\ output[batch, channel, y_{dst}, x_{dst}] = G(data[batch, channel, y_{src}, x_{src})\end{split}\]\(x_{dst}\), \(y_{dst}\) enumerate all spatial locations in \(output\), and \(G()\) denotes the bilinear interpolation kernel. The out-boundary points will be padded with zeros.The shape of the output will be (data.shape[0], data.shape[1], grid.shape[2], grid.shape[3]).
The operator assumes that \(data\) has ‘NCHW’ layout and \(grid\) has been normalized to [-1, 1].
BilinearSampler often cooperates with GridGenerator which generates sampling grids for BilinearSampler. GridGenerator supports two kinds of transformation:
affine
andwarp
. If users want to design a CustomOp to manipulate \(grid\), please firstly refer to the code of GridGenerator.Example 1:
## Zoom out data two times data = array([[[[1, 4, 3, 6], [1, 8, 8, 9], [0, 4, 1, 5], [1, 0, 1, 3]]]]) affine_matrix = array([[2, 0, 0], [0, 2, 0]]) affine_matrix = reshape(affine_matrix, shape=(1, 6)) grid = GridGenerator(data=affine_matrix, transform_type='affine', target_shape=(4, 4)) out = BilinearSampler(data, grid) out [[[[ 0, 0, 0, 0], [ 0, 3.5, 6.5, 0], [ 0, 1.25, 2.5, 0], [ 0, 0, 0, 0]]]
Example 2:
## shift data horizontally by -1 pixel data = array([[[[1, 4, 3, 6], [1, 8, 8, 9], [0, 4, 1, 5], [1, 0, 1, 3]]]]) warp_maxtrix = array([[[[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]], [[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]]]) grid = GridGenerator(data=warp_matrix, transform_type='warp') out = BilinearSampler(data, grid) out [[[[ 4, 3, 6, 0], [ 8, 8, 9, 0], [ 4, 1, 5, 0], [ 0, 1, 3, 0]]]
Defined in src/operator/bilinear_sampler.cc:L245
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
BlockGrad
(data=None, out=None, name=None, **kwargs)¶ Stops gradient computation.
Stops the accumulated gradient of the inputs from flowing through this operator in the backward direction. In other words, this operator prevents the contribution of its inputs to be taken into account for computing gradients.
Example:
v1 = [1, 2] v2 = [0, 1] a = Variable('a') b = Variable('b') b_stop_grad = stop_gradient(3 * b) loss = MakeLoss(b_stop_grad + a) executor = loss.simple_bind(ctx=cpu(), a=(1,2), b=(1,2)) executor.forward(is_train=True, a=v1, b=v2) executor.outputs [ 1. 5.] executor.backward() executor.grad_arrays [ 0. 0.] [ 1. 1.]
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L265
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
Cast
(data=None, dtype=_Null, out=None, name=None, **kwargs)¶ Casts all elements of the input to a new type.
Note
Cast
is deprecated. Usecast
instead.Example:
cast([0.9, 1.3], dtype='int32') = [0, 1] cast([1e20, 11.1], dtype='float16') = [inf, 11.09375] cast([300, 11.1, 10.9, -1, -3], dtype='uint8') = [44, 11, 10, 255, 253]
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L594
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
Concat
(*data, **kwargs)¶ Joins input arrays along a given axis.
Note
Concat is deprecated. Use concat instead.
The dimensions of the input arrays should be the same except the axis along which they will be concatenated. The dimension of the output array along the concatenated axis will be equal to the sum of the corresponding dimensions of the input arrays.
The storage type of
concat
output depends on storage types of inputs- concat(csr, csr, ..., csr, dim=0) = csr
- otherwise,
concat
generates output with default storage
Example:
x = [[1,1],[2,2]] y = [[3,3],[4,4],[5,5]] z = [[6,6], [7,7],[8,8]] concat(x,y,z,dim=0) = [[ 1., 1.], [ 2., 2.], [ 3., 3.], [ 4., 4.], [ 5., 5.], [ 6., 6.], [ 7., 7.], [ 8., 8.]] Note that you cannot concat x,y,z along dimension 1 since dimension 0 is not the same for all the input arrays. concat(y,z,dim=1) = [[ 3., 3., 6., 6.], [ 4., 4., 7., 7.], [ 5., 5., 8., 8.]]
Defined in src/operator/nn/concat.cc:L368
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
Convolution
(data=None, weight=None, bias=None, kernel=_Null, stride=_Null, dilate=_Null, pad=_Null, num_filter=_Null, num_group=_Null, workspace=_Null, no_bias=_Null, cudnn_tune=_Null, cudnn_off=_Null, layout=_Null, out=None, name=None, **kwargs)¶ Compute N-D convolution on (N+2)-D input.
In the 2-D convolution, given input data with shape (batch_size, channel, height, width), the output is computed by
\[out[n,i,:,:] = bias[i] + \sum_{j=0}^{channel} data[n,j,:,:] \star weight[i,j,:,:]\]where \(\star\) is the 2-D cross-correlation operator.
For general 2-D convolution, the shapes are
- data: (batch_size, channel, height, width)
- weight: (num_filter, channel, kernel[0], kernel[1])
- bias: (num_filter,)
- out: (batch_size, num_filter, out_height, out_width).
Define:
f(x,k,p,s,d) = floor((x+2*p-d*(k-1)-1)/s)+1
then we have:
out_height=f(height, kernel[0], pad[0], stride[0], dilate[0]) out_width=f(width, kernel[1], pad[1], stride[1], dilate[1])
If
no_bias
is set to be true, then thebias
term is ignored.The default data
layout
is NCHW, namely (batch_size, channel, height, width). We can choose other layouts such as NWC.If
num_group
is larger than 1, denoted by g, then split the inputdata
evenly into g parts along the channel axis, and also evenly splitweight
along the first dimension. Next compute the convolution on the i-th part of the data with the i-th weight part. The output is obtained by concatenating all the g results.1-D convolution does not have height dimension but only width in space.
- data: (batch_size, channel, width)
- weight: (num_filter, channel, kernel[0])
- bias: (num_filter,)
- out: (batch_size, num_filter, out_width).
3-D convolution adds an additional depth dimension besides height and width. The shapes are
- data: (batch_size, channel, depth, height, width)
- weight: (num_filter, channel, kernel[0], kernel[1], kernel[2])
- bias: (num_filter,)
- out: (batch_size, num_filter, out_depth, out_height, out_width).
Both
weight
andbias
are learnable parameters.There are other options to tune the performance.
- cudnn_tune: enable this option leads to higher startup time but may give
faster speed. Options are
- off: no tuning
- limited_workspace:run test and pick the fastest algorithm that doesn’t exceed workspace limit.
- fastest: pick the fastest algorithm and ignore workspace limit.
- None (default): the behavior is determined by environment variable
MXNET_CUDNN_AUTOTUNE_DEFAULT
. 0 for off, 1 for limited workspace (default), 2 for fastest.
- workspace: A large number leads to more (GPU) memory usage but may improve the performance.
Defined in src/operator/nn/convolution.cc:L474
Parameters: - data (NDArray) – Input data to the ConvolutionOp.
- weight (NDArray) – Weight matrix.
- bias (NDArray) – Bias parameter.
- kernel (Shape(tuple), required) – Convolution kernel size: (w,), (h, w) or (d, h, w)
- stride (Shape(tuple), optional, default=[]) – Convolution stride: (w,), (h, w) or (d, h, w). Defaults to 1 for each dimension.
- dilate (Shape(tuple), optional, default=[]) – Convolution dilate: (w,), (h, w) or (d, h, w). Defaults to 1 for each dimension.
- pad (Shape(tuple), optional, default=[]) – Zero pad for convolution: (w,), (h, w) or (d, h, w). Defaults to no padding.
- num_filter (int (non-negative), required) – Convolution filter(channel) number
- num_group (int (non-negative), optional, default=1) – Number of group partitions.
- workspace (long (non-negative), optional, default=1024) – Maximum temporary workspace allowed (MB) in convolution.This parameter has two usages. When CUDNN is not used, it determines the effective batch size of the convolution kernel. When CUDNN is used, it controls the maximum temporary storage used for tuning the best CUDNN kernel when limited_workspace strategy is used.
- no_bias (boolean, optional, default=0) – Whether to disable bias parameter.
- cudnn_tune ({None, 'fastest', 'limited_workspace', 'off'},optional, default='None') – Whether to pick convolution algo by running performance test.
- cudnn_off (boolean, optional, default=0) – Turn off cudnn for this layer.
- layout ({None, 'NCDHW', 'NCHW', 'NCW', 'NDHWC', 'NHWC'},optional, default='None') – Set layout for input, output and weight. Empty for default layout: NCW for 1d, NCHW for 2d and NCDHW for 3d.NHWC and NDHWC are only supported on GPU.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
Convolution_v1
(data=None, weight=None, bias=None, kernel=_Null, stride=_Null, dilate=_Null, pad=_Null, num_filter=_Null, num_group=_Null, workspace=_Null, no_bias=_Null, cudnn_tune=_Null, cudnn_off=_Null, layout=_Null, out=None, name=None, **kwargs)¶ This operator is DEPRECATED. Apply convolution to input then add a bias.
Parameters: - data (NDArray) – Input data to the ConvolutionV1Op.
- weight (NDArray) – Weight matrix.
- bias (NDArray) – Bias parameter.
- kernel (Shape(tuple), required) – convolution kernel size: (h, w) or (d, h, w)
- stride (Shape(tuple), optional, default=[]) – convolution stride: (h, w) or (d, h, w)
- dilate (Shape(tuple), optional, default=[]) – convolution dilate: (h, w) or (d, h, w)
- pad (Shape(tuple), optional, default=[]) – pad for convolution: (h, w) or (d, h, w)
- num_filter (int (non-negative), required) – convolution filter(channel) number
- num_group (int (non-negative), optional, default=1) – Number of group partitions. Equivalent to slicing input into num_group partitions, apply convolution on each, then concatenate the results
- workspace (long (non-negative), optional, default=1024) – Maximum temporary workspace allowed for convolution (MB).This parameter determines the effective batch size of the convolution kernel, which may be smaller than the given batch size. Also, the workspace will be automatically enlarged to make sure that we can run the kernel with batch_size=1
- no_bias (boolean, optional, default=0) – Whether to disable bias parameter.
- cudnn_tune ({None, 'fastest', 'limited_workspace', 'off'},optional, default='None') – Whether to pick convolution algo by running performance test. Leads to higher startup time but may give faster speed. Options are: ‘off’: no tuning ‘limited_workspace’: run test and pick the fastest algorithm that doesn’t exceed workspace limit. ‘fastest’: pick the fastest algorithm and ignore workspace limit. If set to None (default), behavior is determined by environment variable MXNET_CUDNN_AUTOTUNE_DEFAULT: 0 for off, 1 for limited workspace (default), 2 for fastest.
- cudnn_off (boolean, optional, default=0) – Turn off cudnn for this layer.
- layout ({None, 'NCDHW', 'NCHW', 'NDHWC', 'NHWC'},optional, default='None') – Set layout for input, output and weight. Empty for default layout: NCHW for 2d and NCDHW for 3d.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
Correlation
(data1=None, data2=None, kernel_size=_Null, max_displacement=_Null, stride1=_Null, stride2=_Null, pad_size=_Null, is_multiply=_Null, out=None, name=None, **kwargs)¶ Applies correlation to inputs.
The correlation layer performs multiplicative patch comparisons between two feature maps.
Given two multi-channel feature maps \(f_{1}, f_{2}\), with \(w\), \(h\), and \(c\) being their width, height, and number of channels, the correlation layer lets the network compare each patch from \(f_{1}\) with each patch from \(f_{2}\).
For now we consider only a single comparison of two patches. The ‘correlation’ of two patches centered at \(x_{1}\) in the first map and \(x_{2}\) in the second map is then defined as:
\[c(x_{1}, x_{2}) = \sum_{o \in [-k,k] \times [-k,k]}\] for a square patch of size \(K:=2k+1\).
Note that the equation above is identical to one step of a convolution in neural networks, but instead of convolving data with a filter, it convolves data with other data. For this reason, it has no training weights.
Computing \(c(x_{1}, x_{2})\) involves \(c * K^{2}\) multiplications. Comparing all patch combinations involves \(w^{2}*h^{2}\) such computations.
Given a maximum displacement \(d\), for each location \(x_{1}\) it computes correlations \(c(x_{1}, x_{2})\) only in a neighborhood of size \(D:=2d+1\), by limiting the range of \(x_{2}\). We use strides \(s_{1}, s_{2}\), to quantize \(x_{1}\) globally and to quantize \(x_{2}\) within the neighborhood centered around \(x_{1}\).
The final output is defined by the following expression:
\[out[n, q, i, j] = c(x_{i, j}, x_{q})\]where \(i\) and \(j\) enumerate spatial locations in \(f_{1}\), and \(q\) denotes the \(q^{th}\) neighborhood of \(x_{i,j}\).
Defined in src/operator/correlation.cc:L198
Parameters: - data1 (NDArray) – Input data1 to the correlation.
- data2 (NDArray) – Input data2 to the correlation.
- kernel_size (int (non-negative), optional, default=1) – kernel size for Correlation must be an odd number
- max_displacement (int (non-negative), optional, default=1) – Max displacement of Correlation
- stride1 (int (non-negative), optional, default=1) – stride1 quantize data1 globally
- stride2 (int (non-negative), optional, default=1) – stride2 quantize data2 within the neighborhood centered around data1
- pad_size (int (non-negative), optional, default=0) – pad for Correlation
- is_multiply (boolean, optional, default=1) – operation type is either multiplication or subduction
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
Crop
(*data, **kwargs)¶ Note
Crop is deprecated. Use slice instead.
Crop the 2nd and 3rd dim of input data, with the corresponding size of h_w or with width and height of the second input symbol, i.e., with one input, we need h_w to specify the crop height and width, otherwise the second input symbol’s size will be used
Defined in src/operator/crop.cc:L50
Parameters: - data (Symbol or Symbol[]) – Tensor or List of Tensors, the second input will be used as crop_like shape reference
- offset (Shape(tuple), optional, default=[0,0]) – crop offset coordinate: (y, x)
- h_w (Shape(tuple), optional, default=[0,0]) – crop height and width: (h, w)
- center_crop (boolean, optional, default=0) – If set to true, then it will use be the center_crop,or it will crop using the shape of crop_like
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
Custom
(*data, **kwargs)¶ Apply a custom operator implemented in a frontend language (like Python).
Custom operators should override required methods like forward and backward. The custom operator must be registered before it can be used. Please check the tutorial here: /versions/1.3.1/faq/new_op.html.
Defined in src/operator/custom/custom.cc:L547
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
Example
Applies a custom operator named my_custom_operator to input.
>>> output = mx.symbol.Custom(op_type='my_custom_operator', data=input)
-
mxnet.ndarray.
Deconvolution
(data=None, weight=None, bias=None, kernel=_Null, stride=_Null, dilate=_Null, pad=_Null, adj=_Null, target_shape=_Null, num_filter=_Null, num_group=_Null, workspace=_Null, no_bias=_Null, cudnn_tune=_Null, cudnn_off=_Null, layout=_Null, out=None, name=None, **kwargs)¶ Computes 1D or 2D transposed convolution (aka fractionally strided convolution) of the input tensor. This operation can be seen as the gradient of Convolution operation with respect to its input. Convolution usually reduces the size of the input. Transposed convolution works the other way, going from a smaller input to a larger output while preserving the connectivity pattern.
Parameters: - data (NDArray) – Input tensor to the deconvolution operation.
- weight (NDArray) – Weights representing the kernel.
- bias (NDArray) – Bias added to the result after the deconvolution operation.
- kernel (Shape(tuple), required) – Deconvolution kernel size: (w,), (h, w) or (d, h, w). This is same as the kernel size used for the corresponding convolution
- stride (Shape(tuple), optional, default=[]) – The stride used for the corresponding convolution: (w,), (h, w) or (d, h, w). Defaults to 1 for each dimension.
- dilate (Shape(tuple), optional, default=[]) – Dilation factor for each dimension of the input: (w,), (h, w) or (d, h, w). Defaults to 1 for each dimension.
- pad (Shape(tuple), optional, default=[]) – The amount of implicit zero padding added during convolution for each dimension of the input: (w,), (h, w) or (d, h, w).
(kernel-1)/2
is usually a good choice. If target_shape is set, pad will be ignored and a padding that will generate the target shape will be used. Defaults to no padding. - adj (Shape(tuple), optional, default=[]) – Adjustment for output shape: (w,), (h, w) or (d, h, w). If target_shape is set, adj will be ignored and computed accordingly.
- target_shape (Shape(tuple), optional, default=[]) – Shape of the output tensor: (w,), (h, w) or (d, h, w).
- num_filter (int (non-negative), required) – Number of output filters.
- num_group (int (non-negative), optional, default=1) – Number of groups partition.
- workspace (long (non-negative), optional, default=512) – Maximum temporary workspace allowed (MB) in deconvolution.This parameter has two usages. When CUDNN is not used, it determines the effective batch size of the deconvolution kernel. When CUDNN is used, it controls the maximum temporary storage used for tuning the best CUDNN kernel when limited_workspace strategy is used.
- no_bias (boolean, optional, default=1) – Whether to disable bias parameter.
- cudnn_tune ({None, 'fastest', 'limited_workspace', 'off'},optional, default='None') – Whether to pick convolution algorithm by running performance test.
- cudnn_off (boolean, optional, default=0) – Turn off cudnn for this layer.
- layout ({None, 'NCDHW', 'NCHW', 'NCW', 'NDHWC', 'NHWC'},optional, default='None') – Set layout for input, output and weight. Empty for default layout, NCW for 1d, NCHW for 2d and NCDHW for 3d.NHWC and NDHWC are only supported on GPU.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
Dropout
(data=None, p=_Null, mode=_Null, axes=_Null, out=None, name=None, **kwargs)¶ Applies dropout operation to input array.
- During training, each element of the input is set to zero with probability p. The whole array is rescaled by \(1/(1-p)\) to keep the expected sum of the input unchanged.
- During testing, this operator does not change the input if mode is ‘training’. If mode is ‘always’, the same computaion as during training will be applied.
Example:
random.seed(998) input_array = array([[3., 0.5, -0.5, 2., 7.], [2., -0.4, 7., 3., 0.2]]) a = symbol.Variable('a') dropout = symbol.Dropout(a, p = 0.2) executor = dropout.simple_bind(a = input_array.shape) ## If training executor.forward(is_train = True, a = input_array) executor.outputs [[ 3.75 0.625 -0. 2.5 8.75 ] [ 2.5 -0.5 8.75 3.75 0. ]] ## If testing executor.forward(is_train = False, a = input_array) executor.outputs [[ 3. 0.5 -0.5 2. 7. ] [ 2. -0.4 7. 3. 0.2 ]]
Defined in src/operator/nn/dropout.cc:L76
Parameters: - data (NDArray) – Input array to which dropout will be applied.
- p (float, optional, default=0.5) – Fraction of the input that gets dropped out during training time.
- mode ({'always', 'training'},optional, default='training') – Whether to only turn on dropout during training or to also turn on for inference.
- axes (Shape(tuple), optional, default=[]) – Axes for variational dropout kernel.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
ElementWiseSum
(*args, **kwargs)¶ Adds all input arguments element-wise.
\[add\_n(a_1, a_2, ..., a_n) = a_1 + a_2 + ... + a_n\]add_n
is potentially more efficient than callingadd
by n times.The storage type of
add_n
output depends on storage types of inputs- add_n(row_sparse, row_sparse, ..) = row_sparse
- add_n(default, csr, default) = default
- add_n(any input combinations longer than 4 (>4) with at least one default type) = default
- otherwise,
add_n
falls all inputs back to default storage and generates default storage
Defined in src/operator/tensor/elemwise_sum.cc:L156
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
Embedding
(data=None, weight=None, input_dim=_Null, output_dim=_Null, dtype=_Null, sparse_grad=_Null, out=None, name=None, **kwargs)¶ Maps integer indices to vector representations (embeddings).
This operator maps words to real-valued vectors in a high-dimensional space, called word embeddings. These embeddings can capture semantic and syntactic properties of the words. For example, it has been noted that in the learned embedding spaces, similar words tend to be close to each other and dissimilar words far apart.
For an input array of shape (d1, ..., dK), the shape of an output array is (d1, ..., dK, output_dim). All the input values should be integers in the range [0, input_dim).
If the input_dim is ip0 and output_dim is op0, then shape of the embedding weight matrix must be (ip0, op0).
By default, if any index mentioned is too large, it is replaced by the index that addresses the last vector in an embedding matrix.
Examples:
input_dim = 4 output_dim = 5 // Each row in weight matrix y represents a word. So, y = (w0,w1,w2,w3) y = [[ 0., 1., 2., 3., 4.], [ 5., 6., 7., 8., 9.], [ 10., 11., 12., 13., 14.], [ 15., 16., 17., 18., 19.]] // Input array x represents n-grams(2-gram). So, x = [(w1,w3), (w0,w2)] x = [[ 1., 3.], [ 0., 2.]] // Mapped input x to its vector representation y. Embedding(x, y, 4, 5) = [[[ 5., 6., 7., 8., 9.], [ 15., 16., 17., 18., 19.]], [[ 0., 1., 2., 3., 4.], [ 10., 11., 12., 13., 14.]]]
The storage type of weight can be either row_sparse or default.
Note
If “sparse_grad” is set to True, the storage type of gradient w.r.t weights will be “row_sparse”. Only a subset of optimizers support sparse gradients, including SGD, AdaGrad and Adam. Note that by default lazy updates is turned on, which may perform differently from standard updates. For more details, please check the Optimization API at: /api/python/optimization/optimization.html
Defined in src/operator/tensor/indexing_op.cc:L267
Parameters: - data (NDArray) – The input array to the embedding operator.
- weight (NDArray) – The embedding weight matrix.
- input_dim (int, required) – Vocabulary size of the input indices.
- output_dim (int, required) – Dimension of the embedding vectors.
- dtype ({'float16', 'float32', 'float64', 'int32', 'int64', 'int8', 'uint8'},optional, default='float32') – Data type of weight.
- sparse_grad (boolean, optional, default=0) – Compute row sparse gradient in the backward calculation. If set to True, the grad’s storage type is row_sparse.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
Flatten
(data=None, out=None, name=None, **kwargs)¶ Flattens the input array into a 2-D array by collapsing the higher dimensions.
Note
Flatten is deprecated. Use flatten instead.
For an input array with shape
(d1, d2, ..., dk)
, flatten operation reshapes the input array into an output array of shape(d1, d2*...*dk)
.Note that the bahavior of this function is different from numpy.ndarray.flatten, which behaves similar to mxnet.ndarray.reshape((-1,)).
Example:
x = [[ [1,2,3], [4,5,6], [7,8,9] ], [ [1,2,3], [4,5,6], [7,8,9] ]], flatten(x) = [[ 1., 2., 3., 4., 5., 6., 7., 8., 9.], [ 1., 2., 3., 4., 5., 6., 7., 8., 9.]]
Defined in src/operator/tensor/matrix_op.cc:L259
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
FullyConnected
(data=None, weight=None, bias=None, num_hidden=_Null, no_bias=_Null, flatten=_Null, out=None, name=None, **kwargs)¶ Applies a linear transformation: \(Y = XW^T + b\).
If
flatten
is set to be true, then the shapes are:- data: (batch_size, x1, x2, ..., xn)
- weight: (num_hidden, x1 * x2 * ... * xn)
- bias: (num_hidden,)
- out: (batch_size, num_hidden)
If
flatten
is set to be false, then the shapes are:- data: (x1, x2, ..., xn, input_dim)
- weight: (num_hidden, input_dim)
- bias: (num_hidden,)
- out: (x1, x2, ..., xn, num_hidden)
The learnable parameters include both
weight
andbias
.If
no_bias
is set to be true, then thebias
term is ignored.Note
The sparse support for FullyConnected is limited to forward evaluation with row_sparse weight and bias, where the length of weight.indices and bias.indices must be equal to num_hidden. This could be useful for model inference with row_sparse weights trained with importance sampling or noise contrastive estimation.
To compute linear transformation with ‘csr’ sparse data, sparse.dot is recommended instead of sparse.FullyConnected.
Defined in src/operator/nn/fully_connected.cc:L272
Parameters: - data (NDArray) – Input data.
- weight (NDArray) – Weight matrix.
- bias (NDArray) – Bias parameter.
- num_hidden (int, required) – Number of hidden nodes of the output.
- no_bias (boolean, optional, default=0) – Whether to disable bias parameter.
- flatten (boolean, optional, default=1) – Whether to collapse all but the first axis of the input data tensor.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
GridGenerator
(data=None, transform_type=_Null, target_shape=_Null, out=None, name=None, **kwargs)¶ Generates 2D sampling grid for bilinear sampling.
Parameters: - data (NDArray) – Input data to the function.
- transform_type ({'affine', 'warp'}, required) – The type of transformation. For affine, input data should be an affine matrix of size (batch, 6). For warp, input data should be an optical flow of size (batch, 2, h, w).
- target_shape (Shape(tuple), optional, default=[0,0]) – Specifies the output shape (H, W). This is required if transformation type is affine. If transformation type is warp, this parameter is ignored.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
IdentityAttachKLSparseReg
(data=None, sparseness_target=_Null, penalty=_Null, momentum=_Null, out=None, name=None, **kwargs)¶ Apply a sparse regularization to the output a sigmoid activation function.
Parameters: - data (NDArray) – Input data.
- sparseness_target (float, optional, default=0.1) – The sparseness target
- penalty (float, optional, default=0.001) – The tradeoff parameter for the sparseness penalty
- momentum (float, optional, default=0.9) – The momentum for running average
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
InstanceNorm
(data=None, gamma=None, beta=None, eps=_Null, out=None, name=None, **kwargs)¶ Applies instance normalization to the n-dimensional input array.
This operator takes an n-dimensional input array where (n>2) and normalizes the input using the following formula:
\[out = \frac{x - mean[data]}{ \sqrt{Var[data]} + \epsilon} * gamma + beta\]This layer is similar to batch normalization layer (BatchNorm) with two differences: first, the normalization is carried out per example (instance), not over a batch. Second, the same normalization is applied both at test and train time. This operation is also known as contrast normalization.
If the input data is of shape [batch, channel, spacial_dim1, spacial_dim2, ...], gamma and beta parameters must be vectors of shape [channel].
This implementation is based on paper:
[1] Instance Normalization: The Missing Ingredient for Fast Stylization, D. Ulyanov, A. Vedaldi, V. Lempitsky, 2016 (arXiv:1607.08022v2). Examples:
// Input of shape (2,1,2) x = [[[ 1.1, 2.2]], [[ 3.3, 4.4]]] // gamma parameter of length 1 gamma = [1.5] // beta parameter of length 1 beta = [0.5] // Instance normalization is calculated with the above formula InstanceNorm(x,gamma,beta) = [[[-0.997527 , 1.99752665]], [[-0.99752653, 1.99752724]]]
Defined in src/operator/instance_norm.cc:L95
Parameters: - data (NDArray) – An n-dimensional input array (n > 2) of the form [batch, channel, spatial_dim1, spatial_dim2, ...].
- gamma (NDArray) – A vector of length ‘channel’, which multiplies the normalized input.
- beta (NDArray) – A vector of length ‘channel’, which is added to the product of the normalized input and the weight.
- eps (float, optional, default=0.001) – An epsilon parameter to prevent division by 0.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
L2Normalization
(data=None, eps=_Null, mode=_Null, out=None, name=None, **kwargs)¶ Normalize the input array using the L2 norm.
For 1-D NDArray, it computes:
out = data / sqrt(sum(data ** 2) + eps)
For N-D NDArray, if the input array has shape (N, N, ..., N),
with
mode
=instance
, it normalizes each instance in the multidimensional array by its L2 norm.:for i in 0...N out[i,:,:,...,:] = data[i,:,:,...,:] / sqrt(sum(data[i,:,:,...,:] ** 2) + eps)
with
mode
=channel
, it normalizes each channel in the array by its L2 norm.:for i in 0...N out[:,i,:,...,:] = data[:,i,:,...,:] / sqrt(sum(data[:,i,:,...,:] ** 2) + eps)
with
mode
=spatial
, it normalizes the cross channel norm for each position in the array by its L2 norm.:for dim in 2...N for i in 0...N out[.....,i,...] = take(out, indices=i, axis=dim) / sqrt(sum(take(out, indices=i, axis=dim) ** 2) + eps) -dim-
Example:
x = [[[1,2], [3,4]], [[2,2], [5,6]]] L2Normalization(x, mode='instance') =[[[ 0.18257418 0.36514837] [ 0.54772252 0.73029673]] [[ 0.24077171 0.24077171] [ 0.60192931 0.72231513]]] L2Normalization(x, mode='channel') =[[[ 0.31622776 0.44721359] [ 0.94868326 0.89442718]] [[ 0.37139067 0.31622776] [ 0.92847669 0.94868326]]] L2Normalization(x, mode='spatial') =[[[ 0.44721359 0.89442718] [ 0.60000002 0.80000001]] [[ 0.70710677 0.70710677] [ 0.6401844 0.76822126]]]
Defined in src/operator/l2_normalization.cc:L98
Parameters: - data (NDArray) – Input array to normalize.
- eps (float, optional, default=1e-10) – A small constant for numerical stability.
- mode ({'channel', 'instance', 'spatial'},optional, default='instance') – Specify the dimension along which to compute L2 norm.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
LRN
(data=None, alpha=_Null, beta=_Null, knorm=_Null, nsize=_Null, out=None, name=None, **kwargs)¶ Applies local response normalization to the input.
The local response normalization layer performs “lateral inhibition” by normalizing over local input regions.
If \(a_{x,y}^{i}\) is the activity of a neuron computed by applying kernel \(i\) at position \((x, y)\) and then applying the ReLU nonlinearity, the response-normalized activity \(b_{x,y}^{i}\) is given by the expression:
\[b_{x,y}^{i} = \frac{a_{x,y}^{i}}{\Bigg({k + \frac{\alpha}{n} \sum_{j=max(0, i-\frac{n}{2})}^{min(N-1, i+\frac{n}{2})} (a_{x,y}^{j})^{2}}\Bigg)^{\beta}}\]where the sum runs over \(n\) “adjacent” kernel maps at the same spatial position, and \(N\) is the total number of kernels in the layer.
Defined in src/operator/nn/lrn.cc:L178
Parameters: - data (NDArray) – Input data to LRN
- alpha (float, optional, default=0.0001) – The variance scaling parameter \(lpha\) in the LRN expression.
- beta (float, optional, default=0.75) – The power parameter \(eta\) in the LRN expression.
- knorm (float, optional, default=2) – The parameter \(k\) in the LRN expression.
- nsize (int (non-negative), required) – normalization window width in elements.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
LayerNorm
(data=None, gamma=None, beta=None, axis=_Null, eps=_Null, output_mean_var=_Null, out=None, name=None, **kwargs)¶ Layer normalization.
Normalizes the channels of the input tensor by mean and variance, and applies a scale
gamma
as well as offsetbeta
.Assume the input has more than one dimension and we normalize along axis 1. We first compute the mean and variance along this axis and then compute the normalized output, which has the same shape as input, as following:
\[out = \frac{data - mean(data, axis)}{\sqrt{var(data, axis) + \epsilon}} * gamma + beta\]Both
gamma
andbeta
are learnable parameters.Unlike BatchNorm and InstanceNorm, the mean and var are computed along the channel dimension.
Assume the input has size k on axis 1, then both
gamma
andbeta
have shape (k,). Ifoutput_mean_var
is set to be true, then outputs bothdata_mean
anddata_std
. Note that no gradient will be passed through these two outputs.The parameter
axis
specifies which axis of the input shape denotes the ‘channel’ (separately normalized groups). The default is -1, which sets the channel axis to be the last item in the input shape.Defined in src/operator/nn/layer_norm.cc:L94
Parameters: - data (NDArray) – Input data to layer normalization
- gamma (NDArray) – gamma array
- beta (NDArray) – beta array
- axis (int, optional, default='-1') – The axis to perform layer normalization. Usually, this should be be axis of the channel dimension. Negative values means indexing from right to left.
- eps (float, optional, default=1e-05) – An epsilon parameter to prevent division by 0.
- output_mean_var (boolean, optional, default=0) – Output the mean and std calculated along the given axis.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
LeakyReLU
(data=None, gamma=None, act_type=_Null, slope=_Null, lower_bound=_Null, upper_bound=_Null, out=None, name=None, **kwargs)¶ Applies Leaky rectified linear unit activation element-wise to the input.
Leaky ReLUs attempt to fix the “dying ReLU” problem by allowing a small slope when the input is negative and has a slope of one when input is positive.
The following modified ReLU Activation functions are supported:
- elu: Exponential Linear Unit. y = x > 0 ? x : slope * (exp(x)-1)
- selu: Scaled Exponential Linear Unit. y = lambda * (x > 0 ? x : alpha * (exp(x) - 1)) where lambda = 1.0507009873554804934193349852946 and alpha = 1.6732632423543772848170429916717.
- leaky: Leaky ReLU. y = x > 0 ? x : slope * x
- prelu: Parametric ReLU. This is same as leaky except that slope is learnt during training.
- rrelu: Randomized ReLU. same as leaky but the slope is uniformly and randomly chosen from [lower_bound, upper_bound) for training, while fixed to be (lower_bound+upper_bound)/2 for inference.
Defined in src/operator/leaky_relu.cc:L65
Parameters: - data (NDArray) – Input data to activation function.
- gamma (NDArray) – Slope parameter for PReLU. Only required when act_type is ‘prelu’. It should be either a vector of size 1, or the same size as the second dimension of data.
- act_type ({'elu', 'leaky', 'prelu', 'rrelu', 'selu'},optional, default='leaky') – Activation function to be applied.
- slope (float, optional, default=0.25) – Init slope for the activation. (For leaky and elu only)
- lower_bound (float, optional, default=0.125) – Lower bound of random slope. (For rrelu only)
- upper_bound (float, optional, default=0.334) – Upper bound of random slope. (For rrelu only)
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
LinearRegressionOutput
(data=None, label=None, grad_scale=_Null, out=None, name=None, **kwargs)¶ Computes and optimizes for squared loss during backward propagation. Just outputs
data
during forward propagation.If \(\hat{y}_i\) is the predicted value of the i-th sample, and \(y_i\) is the corresponding target value, then the squared loss estimated over \(n\) samples is defined as
\(\text{SquaredLoss}(\textbf{Y}, \hat{\textbf{Y}} ) = \frac{1}{n} \sum_{i=0}^{n-1} \lVert \textbf{y}_i - \hat{\textbf{y}}_i \rVert_2\)
Note
Use the LinearRegressionOutput as the final output layer of a net.
The storage type of
label
can bedefault
orcsr
- LinearRegressionOutput(default, default) = default
- LinearRegressionOutput(default, csr) = default
By default, gradients of this loss function are scaled by factor 1/m, where m is the number of regression outputs of a training example. The parameter grad_scale can be used to change this scale to grad_scale/m.
Defined in src/operator/regression_output.cc:L92
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
LogisticRegressionOutput
(data=None, label=None, grad_scale=_Null, out=None, name=None, **kwargs)¶ Applies a logistic function to the input.
The logistic function, also known as the sigmoid function, is computed as \(\frac{1}{1+exp(-\textbf{x})}\).
Commonly, the sigmoid is used to squash the real-valued output of a linear model \(wTx+b\) into the [0,1] range so that it can be interpreted as a probability. It is suitable for binary classification or probability prediction tasks.
Note
Use the LogisticRegressionOutput as the final output layer of a net.
The storage type of
label
can bedefault
orcsr
- LogisticRegressionOutput(default, default) = default
- LogisticRegressionOutput(default, csr) = default
The loss function used is the Binary Cross Entropy Loss:
\(-{(y\log(p) + (1 - y)\log(1 - p))}\)
Where y is the ground truth probability of positive outcome for a given example, and p the probability predicted by the model. By default, gradients of this loss function are scaled by factor 1/m, where m is the number of regression outputs of a training example. The parameter grad_scale can be used to change this scale to grad_scale/m.
Defined in src/operator/regression_output.cc:L152
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
MAERegressionOutput
(data=None, label=None, grad_scale=_Null, out=None, name=None, **kwargs)¶ Computes mean absolute error of the input.
MAE is a risk metric corresponding to the expected value of the absolute error.
If \(\hat{y}_i\) is the predicted value of the i-th sample, and \(y_i\) is the corresponding target value, then the mean absolute error (MAE) estimated over \(n\) samples is defined as
\(\text{MAE}(\textbf{Y}, \hat{\textbf{Y}} ) = \frac{1}{n} \sum_{i=0}^{n-1} \lVert \textbf{y}_i - \hat{\textbf{y}}_i \rVert_1\)
Note
Use the MAERegressionOutput as the final output layer of a net.
The storage type of
label
can bedefault
orcsr
- MAERegressionOutput(default, default) = default
- MAERegressionOutput(default, csr) = default
By default, gradients of this loss function are scaled by factor 1/m, where m is the number of regression outputs of a training example. The parameter grad_scale can be used to change this scale to grad_scale/m.
Defined in src/operator/regression_output.cc:L120
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
MakeLoss
(data=None, grad_scale=_Null, valid_thresh=_Null, normalization=_Null, out=None, name=None, **kwargs)¶ Make your own loss function in network construction.
This operator accepts a customized loss function symbol as a terminal loss and the symbol should be an operator with no backward dependency. The output of this function is the gradient of loss with respect to the input data.
For example, if you are a making a cross entropy loss function. Assume
out
is the predicted output andlabel
is the true label, then the cross entropy can be defined as:cross_entropy = label * log(out) + (1 - label) * log(1 - out) loss = MakeLoss(cross_entropy)
We will need to use
MakeLoss
when we are creating our own loss function or we want to combine multiple loss functions. Also we may want to stop some variables’ gradients from backpropagation. See more detail inBlockGrad
orstop_gradient
.In addition, we can give a scale to the loss by setting
grad_scale
, so that the gradient of the loss will be rescaled in the backpropagation.Note
This operator should be used as a Symbol instead of NDArray.
Defined in src/operator/make_loss.cc:L71
Parameters: - data (NDArray) – Input array.
- grad_scale (float, optional, default=1) – Gradient scale as a supplement to unary and binary operators
- valid_thresh (float, optional, default=0) – clip each element in the array to 0 when it is less than
valid_thresh
. This is used whennormalization
is set to'valid'
. - normalization ({'batch', 'null', 'valid'},optional, default='null') – If this is set to null, the output gradient will not be normalized. If this is set to batch, the output gradient will be divided by the batch size. If this is set to valid, the output gradient will be divided by the number of valid input elements.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
Pad
(data=None, mode=_Null, pad_width=_Null, constant_value=_Null, out=None, name=None, **kwargs)¶ Pads an input array with a constant or edge values of the array.
Note
Pad is deprecated. Use pad instead.
Note
Current implementation only supports 4D and 5D input arrays with padding applied only on axes 1, 2 and 3. Expects axes 4 and 5 in pad_width to be zero.
This operation pads an input array with either a constant_value or edge values along each axis of the input array. The amount of padding is specified by pad_width.
pad_width is a tuple of integer padding widths for each axis of the format
(before_1, after_1, ... , before_N, after_N)
. The pad_width should be of length2*N
whereN
is the number of dimensions of the array.For dimension
N
of the input array,before_N
andafter_N
indicates how many values to add before and after the elements of the array along dimensionN
. The widths of the higher two dimensionsbefore_1
,after_1
,before_2
,after_2
must be 0.Example:
x = [[[[ 1. 2. 3.] [ 4. 5. 6.]] [[ 7. 8. 9.] [ 10. 11. 12.]]] [[[ 11. 12. 13.] [ 14. 15. 16.]] [[ 17. 18. 19.] [ 20. 21. 22.]]]] pad(x,mode="edge", pad_width=(0,0,0,0,1,1,1,1)) = [[[[ 1. 1. 2. 3. 3.] [ 1. 1. 2. 3. 3.] [ 4. 4. 5. 6. 6.] [ 4. 4. 5. 6. 6.]] [[ 7. 7. 8. 9. 9.] [ 7. 7. 8. 9. 9.] [ 10. 10. 11. 12. 12.] [ 10. 10. 11. 12. 12.]]] [[[ 11. 11. 12. 13. 13.] [ 11. 11. 12. 13. 13.] [ 14. 14. 15. 16. 16.] [ 14. 14. 15. 16. 16.]] [[ 17. 17. 18. 19. 19.] [ 17. 17. 18. 19. 19.] [ 20. 20. 21. 22. 22.] [ 20. 20. 21. 22. 22.]]]] pad(x, mode="constant", constant_value=0, pad_width=(0,0,0,0,1,1,1,1)) = [[[[ 0. 0. 0. 0. 0.] [ 0. 1. 2. 3. 0.] [ 0. 4. 5. 6. 0.] [ 0. 0. 0. 0. 0.]] [[ 0. 0. 0. 0. 0.] [ 0. 7. 8. 9. 0.] [ 0. 10. 11. 12. 0.] [ 0. 0. 0. 0. 0.]]] [[[ 0. 0. 0. 0. 0.] [ 0. 11. 12. 13. 0.] [ 0. 14. 15. 16. 0.] [ 0. 0. 0. 0. 0.]] [[ 0. 0. 0. 0. 0.] [ 0. 17. 18. 19. 0.] [ 0. 20. 21. 22. 0.] [ 0. 0. 0. 0. 0.]]]]
Defined in src/operator/pad.cc:L766
Parameters: - data (NDArray) – An n-dimensional input array.
- mode ({'constant', 'edge', 'reflect'}, required) – Padding type to use. “constant” pads with constant_value “edge” pads using the edge values of the input array “reflect” pads by reflecting values with respect to the edges.
- pad_width (Shape(tuple), required) – Widths of the padding regions applied to the edges of each axis. It is a tuple of integer padding widths for each axis of the format
(before_1, after_1, ... , before_N, after_N)
. It should be of length2*N
whereN
is the number of dimensions of the array.This is equivalent to pad_width in numpy.pad, but flattened. - constant_value (double, optional, default=0) – The value used for padding when mode is “constant”.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
Pooling
(data=None, kernel=_Null, pool_type=_Null, global_pool=_Null, cudnn_off=_Null, pooling_convention=_Null, stride=_Null, pad=_Null, p_value=_Null, count_include_pad=_Null, out=None, name=None, **kwargs)¶ Performs pooling on the input.
The shapes for 1-D pooling are
- data: (batch_size, channel, width),
- out: (batch_size, num_filter, out_width).
The shapes for 2-D pooling are
data: (batch_size, channel, height, width)
out: (batch_size, num_filter, out_height, out_width), with:
out_height = f(height, kernel[0], pad[0], stride[0]) out_width = f(width, kernel[1], pad[1], stride[1])
The definition of f depends on
pooling_convention
, which has two options:valid (default):
f(x, k, p, s) = floor((x+2*p-k)/s)+1
full, which is compatible with Caffe:
f(x, k, p, s) = ceil((x+2*p-k)/s)+1
But
global_pool
is set to be true, then do a global pooling, namely resetkernel=(height, width)
.Three pooling options are supported by
pool_type
:- avg: average pooling
- max: max pooling
- sum: sum pooling
- lp: Lp pooling
For 3-D pooling, an additional depth dimension is added before height. Namely the input data will have shape (batch_size, channel, depth, height, width).
Notes on Lp pooling:
Lp pooling was first introduced by this paper: https://arxiv.org/pdf/1204.3968.pdf. L-1 pooling is simply sum pooling, while L-inf pooling is simply max pooling. We can see that Lp pooling stands between those two, in practice the most common value for p is 2.
For each window
X
, the mathematical expression for Lp pooling is:\(f(X) = \sqrt[p]{\sum_{x}^{X} x^p}\)
Defined in src/operator/nn/pooling.cc:L388
Parameters: - data (NDArray) – Input data to the pooling operator.
- kernel (Shape(tuple), optional, default=[]) – Pooling kernel size: (y, x) or (d, y, x)
- pool_type ({'avg', 'lp', 'max', 'sum'},optional, default='max') – Pooling type to be applied.
- global_pool (boolean, optional, default=0) – Ignore kernel size, do global pooling based on current input feature map.
- cudnn_off (boolean, optional, default=0) – Turn off cudnn pooling and use MXNet pooling operator.
- pooling_convention ({'full', 'valid'},optional, default='valid') – Pooling convention to be applied.
- stride (Shape(tuple), optional, default=[]) – Stride: for pooling (y, x) or (d, y, x). Defaults to 1 for each dimension.
- pad (Shape(tuple), optional, default=[]) – Pad for pooling: (y, x) or (d, y, x). Defaults to no padding.
- p_value (int or None, optional, default='None') – Value of p for Lp pooling, can be 1 or 2, required for Lp Pooling.
- count_include_pad (boolean or None, optional, default=None) – Only used for AvgPool, specify whether to count padding elements for averagecalculation. For example, with a 5*5 kernel on a 3*3 corner of a image,the sum of the 9 valid elements will be divided by 25 if this is set to true,or it will be divided by 9 if this is set to false. Defaults to true.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
Pooling_v1
(data=None, kernel=_Null, pool_type=_Null, global_pool=_Null, pooling_convention=_Null, stride=_Null, pad=_Null, out=None, name=None, **kwargs)¶ This operator is DEPRECATED. Perform pooling on the input.
The shapes for 2-D pooling is
data: (batch_size, channel, height, width)
out: (batch_size, num_filter, out_height, out_width), with:
out_height = f(height, kernel[0], pad[0], stride[0]) out_width = f(width, kernel[1], pad[1], stride[1])
The definition of f depends on
pooling_convention
, which has two options:valid (default):
f(x, k, p, s) = floor((x+2*p-k)/s)+1
full, which is compatible with Caffe:
f(x, k, p, s) = ceil((x+2*p-k)/s)+1
But
global_pool
is set to be true, then do a global pooling, namely resetkernel=(height, width)
.Three pooling options are supported by
pool_type
:- avg: average pooling
- max: max pooling
- sum: sum pooling
1-D pooling is special case of 2-D pooling with weight=1 and kernel[1]=1.
For 3-D pooling, an additional depth dimension is added before height. Namely the input data will have shape (batch_size, channel, depth, height, width).
Defined in src/operator/pooling_v1.cc:L104
Parameters: - data (NDArray) – Input data to the pooling operator.
- kernel (Shape(tuple), optional, default=[]) – pooling kernel size: (y, x) or (d, y, x)
- pool_type ({'avg', 'max', 'sum'},optional, default='max') – Pooling type to be applied.
- global_pool (boolean, optional, default=0) – Ignore kernel size, do global pooling based on current input feature map.
- pooling_convention ({'full', 'valid'},optional, default='valid') – Pooling convention to be applied.
- stride (Shape(tuple), optional, default=[]) – stride: for pooling (y, x) or (d, y, x)
- pad (Shape(tuple), optional, default=[]) – pad for pooling: (y, x) or (d, y, x)
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
RNN
(data=None, parameters=None, state=None, state_cell=None, state_size=_Null, num_layers=_Null, bidirectional=_Null, mode=_Null, p=_Null, state_outputs=_Null, projection_size=_Null, lstm_state_clip_min=_Null, lstm_state_clip_max=_Null, lstm_state_clip_nan=_Null, out=None, name=None, **kwargs)¶ Applies recurrent layers to input data. Currently, vanilla RNN, LSTM and GRU are implemented, with both multi-layer and bidirectional support.
Vanilla RNN
Applies a single-gate recurrent layer to input X. Two kinds of activation function are supported: ReLU and Tanh.
With ReLU activation function:
\[h_t = relu(W_{ih} * x_t + b_{ih} + W_{hh} * h_{(t-1)} + b_{hh})\]With Tanh activtion function:
\[h_t = \tanh(W_{ih} * x_t + b_{ih} + W_{hh} * h_{(t-1)} + b_{hh})\]Reference paper: Finding structure in time - Elman, 1988. https://crl.ucsd.edu/~elman/Papers/fsit.pdf
LSTM
Long Short-Term Memory - Hochreiter, 1997. http://www.bioinf.jku.at/publications/older/2604.pdf
\[\begin{split}\begin{array}{ll} i_t = \mathrm{sigmoid}(W_{ii} x_t + b_{ii} + W_{hi} h_{(t-1)} + b_{hi}) \\ f_t = \mathrm{sigmoid}(W_{if} x_t + b_{if} + W_{hf} h_{(t-1)} + b_{hf}) \\ g_t = \tanh(W_{ig} x_t + b_{ig} + W_{hc} h_{(t-1)} + b_{hg}) \\ o_t = \mathrm{sigmoid}(W_{io} x_t + b_{io} + W_{ho} h_{(t-1)} + b_{ho}) \\ c_t = f_t * c_{(t-1)} + i_t * g_t \\ h_t = o_t * \tanh(c_t) \end{array}\end{split}\]GRU
Gated Recurrent Unit - Cho et al. 2014. http://arxiv.org/abs/1406.1078
The definition of GRU here is slightly different from paper but compatible with CUDNN.
\[\begin{split}\begin{array}{ll} r_t = \mathrm{sigmoid}(W_{ir} x_t + b_{ir} + W_{hr} h_{(t-1)} + b_{hr}) \\ z_t = \mathrm{sigmoid}(W_{iz} x_t + b_{iz} + W_{hz} h_{(t-1)} + b_{hz}) \\ n_t = \tanh(W_{in} x_t + b_{in} + r_t * (W_{hn} h_{(t-1)}+ b_{hn})) \\ h_t = (1 - z_t) * n_t + z_t * h_{(t-1)} \\ \end{array}\end{split}\]Parameters: - data (NDArray) – Input data to RNN
- parameters (NDArray) – Vector of all RNN trainable parameters concatenated
- state (NDArray) – initial hidden state of the RNN
- state_cell (NDArray) – initial cell state for LSTM networks (only for LSTM)
- state_size (int (non-negative), required) – size of the state for each layer
- num_layers (int (non-negative), required) – number of stacked layers
- bidirectional (boolean, optional, default=0) – whether to use bidirectional recurrent layers
- mode ({'gru', 'lstm', 'rnn_relu', 'rnn_tanh'}, required) – the type of RNN to compute
- p (float, optional, default=0) – drop rate of the dropout on the outputs of each RNN layer, except the last layer.
- state_outputs (boolean, optional, default=0) – Whether to have the states as symbol outputs.
- projection_size (int or None, optional, default='None') – size of project size
- lstm_state_clip_min (double or None, optional, default=None) – Minimum clip value of LSTM states. This option must be used together with lstm_state_clip_max.
- lstm_state_clip_max (double or None, optional, default=None) – Maximum clip value of LSTM states. This option must be used together with lstm_state_clip_min.
- lstm_state_clip_nan (boolean, optional, default=0) – Whether to stop NaN from propagating in state by clipping it to min/max. If clipping range is not specified, this option is ignored.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
ROIPooling
(data=None, rois=None, pooled_size=_Null, spatial_scale=_Null, out=None, name=None, **kwargs)¶ Performs region of interest(ROI) pooling on the input array.
ROI pooling is a variant of a max pooling layer, in which the output size is fixed and region of interest is a parameter. Its purpose is to perform max pooling on the inputs of non-uniform sizes to obtain fixed-size feature maps. ROI pooling is a neural-net layer mostly used in training a Fast R-CNN network for object detection.
This operator takes a 4D feature map as an input array and region proposals as rois, then it pools over sub-regions of input and produces a fixed-sized output array regardless of the ROI size.
To crop the feature map accordingly, you can resize the bounding box coordinates by changing the parameters rois and spatial_scale.
The cropped feature maps are pooled by standard max pooling operation to a fixed size output indicated by a pooled_size parameter. batch_size will change to the number of region bounding boxes after ROIPooling.
The size of each region of interest doesn’t have to be perfectly divisible by the number of pooling sections(pooled_size).
Example:
x = [[[[ 0., 1., 2., 3., 4., 5.], [ 6., 7., 8., 9., 10., 11.], [ 12., 13., 14., 15., 16., 17.], [ 18., 19., 20., 21., 22., 23.], [ 24., 25., 26., 27., 28., 29.], [ 30., 31., 32., 33., 34., 35.], [ 36., 37., 38., 39., 40., 41.], [ 42., 43., 44., 45., 46., 47.]]]] // region of interest i.e. bounding box coordinates. y = [[0,0,0,4,4]] // returns array of shape (2,2) according to the given roi with max pooling. ROIPooling(x, y, (2,2), 1.0) = [[[[ 14., 16.], [ 26., 28.]]]] // region of interest is changed due to the change in `spacial_scale` parameter. ROIPooling(x, y, (2,2), 0.7) = [[[[ 7., 9.], [ 19., 21.]]]]
Defined in src/operator/roi_pooling.cc:L295
Parameters: - data (NDArray) – The input array to the pooling operator, a 4D Feature maps
- rois (NDArray) – Bounding box coordinates, a 2D array of [[batch_index, x1, y1, x2, y2]], where (x1, y1) and (x2, y2) are top left and bottom right corners of designated region of interest. batch_index indicates the index of corresponding image in the input array
- pooled_size (Shape(tuple), required) – ROI pooling output shape (h,w)
- spatial_scale (float, required) – Ratio of input feature map height (or w) to raw image height (or w). Equals the reciprocal of total stride in convolutional layers
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
Reshape
(data=None, shape=_Null, reverse=_Null, target_shape=_Null, keep_highest=_Null, out=None, name=None, **kwargs)¶ Reshapes the input array.
Note
Reshape
is deprecated, usereshape
Given an array and a shape, this function returns a copy of the array in the new shape. The shape is a tuple of integers such as (2,3,4). The size of the new shape should be same as the size of the input array.
Example:
reshape([1,2,3,4], shape=(2,2)) = [[1,2], [3,4]]
Some dimensions of the shape can take special values from the set {0, -1, -2, -3, -4}. The significance of each is explained below:
0
copy this dimension from the input to the output shape.Example:
- input shape = (2,3,4), shape = (4,0,2), output shape = (4,3,2) - input shape = (2,3,4), shape = (2,0,0), output shape = (2,3,4)
-1
infers the dimension of the output shape by using the remainder of the input dimensions keeping the size of the new array same as that of the input array. At most one dimension of shape can be -1.Example:
- input shape = (2,3,4), shape = (6,1,-1), output shape = (6,1,4) - input shape = (2,3,4), shape = (3,-1,8), output shape = (3,1,8) - input shape = (2,3,4), shape=(-1,), output shape = (24,)
-2
copy all/remainder of the input dimensions to the output shape.Example:
- input shape = (2,3,4), shape = (-2,), output shape = (2,3,4) - input shape = (2,3,4), shape = (2,-2), output shape = (2,3,4) - input shape = (2,3,4), shape = (-2,1,1), output shape = (2,3,4,1,1)
-3
use the product of two consecutive dimensions of the input shape as the output dimension.Example:
- input shape = (2,3,4), shape = (-3,4), output shape = (6,4) - input shape = (2,3,4,5), shape = (-3,-3), output shape = (6,20) - input shape = (2,3,4), shape = (0,-3), output shape = (2,12) - input shape = (2,3,4), shape = (-3,-2), output shape = (6,4)
-4
split one dimension of the input into two dimensions passed subsequent to -4 in shape (can contain -1).Example:
- input shape = (2,3,4), shape = (-4,1,2,-2), output shape =(1,2,3,4) - input shape = (2,3,4), shape = (2,-4,-1,3,-2), output shape = (2,1,3,4)
If the argument reverse is set to 1, then the special values are inferred from right to left.
Example:
- without reverse=1, for input shape = (10,5,4), shape = (-1,0), output shape would be (40,5) - with reverse=1, output shape will be (50,4).
Defined in src/operator/tensor/matrix_op.cc:L169
Parameters: - data (NDArray) – Input data to reshape.
- shape (Shape(tuple), optional, default=[]) – The target shape
- reverse (boolean, optional, default=0) – If true then the special values are inferred from right to left
- target_shape (Shape(tuple), optional, default=[]) – (Deprecated! Use
shape
instead.) Target new shape. One and only one dim can be 0, in which case it will be inferred from the rest of dims - keep_highest (boolean, optional, default=0) – (Deprecated! Use
shape
instead.) Whether keep the highest dim unchanged.If set to true, then the first dim in target_shape is ignored,and always fixed as input - out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
Examples
Reshapes the input array into a new shape.
>>> x = mx.nd.array([1, 2, 3, 4]) >>> y = mx.nd.reshape(x, shape=(2, 2)) >>> x.shape (4L,) >>> y.shape (2L, 2L) >>> y.asnumpy() array([[ 1., 2.], [ 3., 4.]], dtype=float32)
You can use
0
to copy a particular dimension from the input to the output shape and ‘-1’ to infer the dimensions of the output.>>> x = mx.nd.ones((2, 3, 4)) >>> x.shape (2L, 3L, 4L) >>> y = mx.nd.reshape(x, shape=(4, 0, -1)) >>> y.shape (4L, 3L, 2L)
-
mxnet.ndarray.
SVMOutput
(data=None, label=None, margin=_Null, regularization_coefficient=_Null, use_linear=_Null, out=None, name=None, **kwargs)¶ Computes support vector machine based transformation of the input.
This tutorial demonstrates using SVM as output layer for classification instead of softmax: https://github.com/dmlc/mxnet/tree/master/example/svm_mnist.
Parameters: - data (NDArray) – Input data for SVM transformation.
- label (NDArray) – Class label for the input data.
- margin (float, optional, default=1) – The loss function penalizes outputs that lie outside this margin. Default margin is 1.
- regularization_coefficient (float, optional, default=1) – Regularization parameter for the SVM. This balances the tradeoff between coefficient size and error.
- use_linear (boolean, optional, default=0) – Whether to use L1-SVM objective. L2-SVM objective is used by default.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
SequenceLast
(data=None, sequence_length=None, use_sequence_length=_Null, axis=_Null, out=None, name=None, **kwargs)¶ Takes the last element of a sequence.
This function takes an n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims] and returns a (n-1)-dimensional array of the form [batch_size, other_feature_dims].
Parameter sequence_length is used to handle variable-length sequences. sequence_length should be an input array of positive ints of dimension [batch_size]. To use this parameter, set use_sequence_length to True, otherwise each example in the batch is assumed to have the max sequence length.
Note
Alternatively, you can also use take operator.
Example:
x = [[[ 1., 2., 3.], [ 4., 5., 6.], [ 7., 8., 9.]], [[ 10., 11., 12.], [ 13., 14., 15.], [ 16., 17., 18.]], [[ 19., 20., 21.], [ 22., 23., 24.], [ 25., 26., 27.]]] // returns last sequence when sequence_length parameter is not used SequenceLast(x) = [[ 19., 20., 21.], [ 22., 23., 24.], [ 25., 26., 27.]] // sequence_length is used SequenceLast(x, sequence_length=[1,1,1], use_sequence_length=True) = [[ 1., 2., 3.], [ 4., 5., 6.], [ 7., 8., 9.]] // sequence_length is used SequenceLast(x, sequence_length=[1,2,3], use_sequence_length=True) = [[ 1., 2., 3.], [ 13., 14., 15.], [ 25., 26., 27.]]
Defined in src/operator/sequence_last.cc:L92
Parameters: - data (NDArray) – n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims] where n>2
- sequence_length (NDArray) – vector of sequence lengths of the form [batch_size]
- use_sequence_length (boolean, optional, default=0) – If set to true, this layer takes in an extra input parameter sequence_length to specify variable length sequence
- axis (int, optional, default='0') – The sequence axis. Only values of 0 and 1 are currently supported.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
SequenceMask
(data=None, sequence_length=None, use_sequence_length=_Null, value=_Null, axis=_Null, out=None, name=None, **kwargs)¶ Sets all elements outside the sequence to a constant value.
This function takes an n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims] and returns an array of the same shape.
Parameter sequence_length is used to handle variable-length sequences. sequence_length should be an input array of positive ints of dimension [batch_size]. To use this parameter, set use_sequence_length to True, otherwise each example in the batch is assumed to have the max sequence length and this operator works as the identity operator.
Example:
x = [[[ 1., 2., 3.], [ 4., 5., 6.]], [[ 7., 8., 9.], [ 10., 11., 12.]], [[ 13., 14., 15.], [ 16., 17., 18.]]] // Batch 1 B1 = [[ 1., 2., 3.], [ 7., 8., 9.], [ 13., 14., 15.]] // Batch 2 B2 = [[ 4., 5., 6.], [ 10., 11., 12.], [ 16., 17., 18.]] // works as identity operator when sequence_length parameter is not used SequenceMask(x) = [[[ 1., 2., 3.], [ 4., 5., 6.]], [[ 7., 8., 9.], [ 10., 11., 12.]], [[ 13., 14., 15.], [ 16., 17., 18.]]] // sequence_length [1,1] means 1 of each batch will be kept // and other rows are masked with default mask value = 0 SequenceMask(x, sequence_length=[1,1], use_sequence_length=True) = [[[ 1., 2., 3.], [ 4., 5., 6.]], [[ 0., 0., 0.], [ 0., 0., 0.]], [[ 0., 0., 0.], [ 0., 0., 0.]]] // sequence_length [2,3] means 2 of batch B1 and 3 of batch B2 will be kept // and other rows are masked with value = 1 SequenceMask(x, sequence_length=[2,3], use_sequence_length=True, value=1) = [[[ 1., 2., 3.], [ 4., 5., 6.]], [[ 7., 8., 9.], [ 10., 11., 12.]], [[ 1., 1., 1.], [ 16., 17., 18.]]]
Defined in src/operator/sequence_mask.cc:L114
Parameters: - data (NDArray) – n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims] where n>2
- sequence_length (NDArray) – vector of sequence lengths of the form [batch_size]
- use_sequence_length (boolean, optional, default=0) – If set to true, this layer takes in an extra input parameter sequence_length to specify variable length sequence
- value (float, optional, default=0) – The value to be used as a mask.
- axis (int, optional, default='0') – The sequence axis. Only values of 0 and 1 are currently supported.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
SequenceReverse
(data=None, sequence_length=None, use_sequence_length=_Null, axis=_Null, out=None, name=None, **kwargs)¶ Reverses the elements of each sequence.
This function takes an n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims] and returns an array of the same shape.
Parameter sequence_length is used to handle variable-length sequences. sequence_length should be an input array of positive ints of dimension [batch_size]. To use this parameter, set use_sequence_length to True, otherwise each example in the batch is assumed to have the max sequence length.
Example:
x = [[[ 1., 2., 3.], [ 4., 5., 6.]], [[ 7., 8., 9.], [ 10., 11., 12.]], [[ 13., 14., 15.], [ 16., 17., 18.]]] // Batch 1 B1 = [[ 1., 2., 3.], [ 7., 8., 9.], [ 13., 14., 15.]] // Batch 2 B2 = [[ 4., 5., 6.], [ 10., 11., 12.], [ 16., 17., 18.]] // returns reverse sequence when sequence_length parameter is not used SequenceReverse(x) = [[[ 13., 14., 15.], [ 16., 17., 18.]], [[ 7., 8., 9.], [ 10., 11., 12.]], [[ 1., 2., 3.], [ 4., 5., 6.]]] // sequence_length [2,2] means 2 rows of // both batch B1 and B2 will be reversed. SequenceReverse(x, sequence_length=[2,2], use_sequence_length=True) = [[[ 7., 8., 9.], [ 10., 11., 12.]], [[ 1., 2., 3.], [ 4., 5., 6.]], [[ 13., 14., 15.], [ 16., 17., 18.]]] // sequence_length [2,3] means 2 of batch B2 and 3 of batch B3 // will be reversed. SequenceReverse(x, sequence_length=[2,3], use_sequence_length=True) = [[[ 7., 8., 9.], [ 16., 17., 18.]], [[ 1., 2., 3.], [ 10., 11., 12.]], [[ 13., 14, 15.], [ 4., 5., 6.]]]
Defined in src/operator/sequence_reverse.cc:L113
Parameters: - data (NDArray) – n-dimensional input array of the form [max_sequence_length, batch_size, other dims] where n>2
- sequence_length (NDArray) – vector of sequence lengths of the form [batch_size]
- use_sequence_length (boolean, optional, default=0) – If set to true, this layer takes in an extra input parameter sequence_length to specify variable length sequence
- axis (int, optional, default='0') – The sequence axis. Only 0 is currently supported.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
SliceChannel
(data=None, num_outputs=_Null, axis=_Null, squeeze_axis=_Null, out=None, name=None, **kwargs)¶ Splits an array along a particular axis into multiple sub-arrays.
Note
SliceChannel
is deprecated. Usesplit
instead.Note that num_outputs should evenly divide the length of the axis along which to split the array.
Example:
x = [[[ 1.] [ 2.]] [[ 3.] [ 4.]] [[ 5.] [ 6.]]] x.shape = (3, 2, 1) y = split(x, axis=1, num_outputs=2) // a list of 2 arrays with shape (3, 1, 1) y = [[[ 1.]] [[ 3.]] [[ 5.]]] [[[ 2.]] [[ 4.]] [[ 6.]]] y[0].shape = (3, 1, 1) z = split(x, axis=0, num_outputs=3) // a list of 3 arrays with shape (1, 2, 1) z = [[[ 1.] [ 2.]]] [[[ 3.] [ 4.]]] [[[ 5.] [ 6.]]] z[0].shape = (1, 2, 1)
squeeze_axis=1 removes the axis with length 1 from the shapes of the output arrays. Note that setting squeeze_axis to
1
removes axis with length 1 only along the axis which it is split. Also squeeze_axis can be set to true only ifinput.shape[axis] == num_outputs
.Example:
z = split(x, axis=0, num_outputs=3, squeeze_axis=1) // a list of 3 arrays with shape (2, 1) z = [[ 1.] [ 2.]] [[ 3.] [ 4.]] [[ 5.] [ 6.]] z[0].shape = (2 ,1 )
Defined in src/operator/slice_channel.cc:L107
Parameters: - data (NDArray) – The input
- num_outputs (int, required) – Number of splits. Note that this should evenly divide the length of the axis.
- axis (int, optional, default='1') – Axis along which to split.
- squeeze_axis (boolean, optional, default=0) – If true, Removes the axis with length 1 from the shapes of the output arrays. Note that setting squeeze_axis to
true
removes axis with length 1 only along the axis which it is split. Also squeeze_axis can be set totrue
only ifinput.shape[axis] == num_outputs
. - out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
Softmax
(data=None, grad_scale=_Null, ignore_label=_Null, multi_output=_Null, use_ignore=_Null, preserve_shape=_Null, normalization=_Null, out_grad=_Null, smooth_alpha=_Null, out=None, name=None, **kwargs)¶ Please use SoftmaxOutput.
Note
This operator has been renamed to SoftmaxOutput, which computes the gradient of cross-entropy loss w.r.t softmax output. To just compute softmax output, use the softmax operator.
Defined in src/operator/softmax_output.cc:L138
Parameters: - data (NDArray) – Input array.
- grad_scale (float, optional, default=1) – Scales the gradient by a float factor.
- ignore_label (float, optional, default=-1) – The instances whose labels == ignore_label will be ignored during backward, if use_ignore is set to
true
). - multi_output (boolean, optional, default=0) – If set to
true
, the softmax function will be computed along axis1
. This is applied when the shape of input array differs from the shape of label array. - use_ignore (boolean, optional, default=0) – If set to
true
, the ignore_label value will not contribute to the backward gradient. - preserve_shape (boolean, optional, default=0) – If set to
true
, the softmax function will be computed along the last axis (-1
). - normalization ({'batch', 'null', 'valid'},optional, default='null') – Normalizes the gradient.
- out_grad (boolean, optional, default=0) – Multiplies gradient with output gradient element-wise.
- smooth_alpha (float, optional, default=0) – Constant for computing a label smoothed version of cross-entropyfor the backwards pass. This constant gets subtracted from theone-hot encoding of the gold label and distributed uniformly toall other labels.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
SoftmaxActivation
(data=None, mode=_Null, out=None, name=None, **kwargs)¶ Applies softmax activation to input. This is intended for internal layers.
Note
This operator has been deprecated, please use softmax.
If mode =
instance
, this operator will compute a softmax for each instance in the batch. This is the default mode.If mode =
channel
, this operator will compute a k-class softmax at each position of each instance, where k =num_channel
. This mode can only be used when the input array has at least 3 dimensions. This can be used for fully convolutional network, image segmentation, etc.Example:
>>> input_array = mx.nd.array([[3., 0.5, -0.5, 2., 7.], >>> [2., -.4, 7., 3., 0.2]]) >>> softmax_act = mx.nd.SoftmaxActivation(input_array) >>> print softmax_act.asnumpy() [[ 1.78322066e-02 1.46375655e-03 5.38485940e-04 6.56010211e-03 9.73605454e-01] [ 6.56221947e-03 5.95310994e-04 9.73919690e-01 1.78379621e-02 1.08472735e-03]]
Defined in src/operator/nn/softmax_activation.cc:L59
Parameters: - data (NDArray) – The input array.
- mode ({'channel', 'instance'},optional, default='instance') – Specifies how to compute the softmax. If set to
instance
, it computes softmax for each instance. If set tochannel
, It computes cross channel softmax for each position of each instance. - out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
SoftmaxOutput
(data=None, label=None, grad_scale=_Null, ignore_label=_Null, multi_output=_Null, use_ignore=_Null, preserve_shape=_Null, normalization=_Null, out_grad=_Null, smooth_alpha=_Null, out=None, name=None, **kwargs)¶ Computes the gradient of cross entropy loss with respect to softmax output.
This operator computes the gradient in two steps. The cross entropy loss does not actually need to be computed.
- Applies softmax function on the input array.
- Computes and returns the gradient of cross entropy loss w.r.t. the softmax output.
The softmax function, cross entropy loss and gradient is given by:
Softmax Function:
\[\text{softmax}(x)_i = \frac{exp(x_i)}{\sum_j exp(x_j)}\]Cross Entropy Function:
\[\text{CE(label, output)} = - \sum_i \text{label}_i \log(\text{output}_i)\]The gradient of cross entropy loss w.r.t softmax output:
\[\text{gradient} = \text{output} - \text{label}\]
During forward propagation, the softmax function is computed for each instance in the input array.
For general N-D input arrays with shape \((d_1, d_2, ..., d_n)\). The size is \(s=d_1 \cdot d_2 \cdot \cdot \cdot d_n\). We can use the parameters preserve_shape and multi_output to specify the way to compute softmax:
- By default, preserve_shape is
false
. This operator will reshape the input array into a 2-D array with shape \((d_1, \frac{s}{d_1})\) and then compute the softmax function for each row in the reshaped array, and afterwards reshape it back to the original shape \((d_1, d_2, ..., d_n)\). - If preserve_shape is
true
, the softmax function will be computed along the last axis (axis =-1
). - If multi_output is
true
, the softmax function will be computed along the second axis (axis =1
).
- By default, preserve_shape is
During backward propagation, the gradient of cross-entropy loss w.r.t softmax output array is computed. The provided label can be a one-hot label array or a probability label array.
If the parameter use_ignore is
true
, ignore_label can specify input instances with a particular label to be ignored during backward propagation. This has no effect when softmax `output` has same shape as `label`.Example:
data = [[1,2,3,4],[2,2,2,2],[3,3,3,3],[4,4,4,4]] label = [1,0,2,3] ignore_label = 1 SoftmaxOutput(data=data, label = label,\ multi_output=true, use_ignore=true,\ ignore_label=ignore_label) ## forward softmax output [[ 0.0320586 0.08714432 0.23688284 0.64391428] [ 0.25 0.25 0.25 0.25 ] [ 0.25 0.25 0.25 0.25 ] [ 0.25 0.25 0.25 0.25 ]] ## backward gradient output [[ 0. 0. 0. 0. ] [-0.75 0.25 0.25 0.25] [ 0.25 0.25 -0.75 0.25] [ 0.25 0.25 0.25 -0.75]] ## notice that the first row is all 0 because label[0] is 1, which is equal to ignore_label.
The parameter grad_scale can be used to rescale the gradient, which is often used to give each loss function different weights.
This operator also supports various ways to normalize the gradient by normalization, The normalization is applied if softmax output has different shape than the labels. The normalization mode can be set to the followings:
'null'
: do nothing.'batch'
: divide the gradient by the batch size.'valid'
: divide the gradient by the number of instances which are not ignored.
Defined in src/operator/softmax_output.cc:L123
Parameters: - data (NDArray) – Input array.
- label (NDArray) – Ground truth label.
- grad_scale (float, optional, default=1) – Scales the gradient by a float factor.
- ignore_label (float, optional, default=-1) – The instances whose labels == ignore_label will be ignored during backward, if use_ignore is set to
true
). - multi_output (boolean, optional, default=0) – If set to
true
, the softmax function will be computed along axis1
. This is applied when the shape of input array differs from the shape of label array. - use_ignore (boolean, optional, default=0) – If set to
true
, the ignore_label value will not contribute to the backward gradient. - preserve_shape (boolean, optional, default=0) – If set to
true
, the softmax function will be computed along the last axis (-1
). - normalization ({'batch', 'null', 'valid'},optional, default='null') – Normalizes the gradient.
- out_grad (boolean, optional, default=0) – Multiplies gradient with output gradient element-wise.
- smooth_alpha (float, optional, default=0) – Constant for computing a label smoothed version of cross-entropyfor the backwards pass. This constant gets subtracted from theone-hot encoding of the gold label and distributed uniformly toall other labels.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
SpatialTransformer
(data=None, loc=None, target_shape=_Null, transform_type=_Null, sampler_type=_Null, out=None, name=None, **kwargs)¶ Applies a spatial transformer to input feature map.
Parameters: - data (NDArray) – Input data to the SpatialTransformerOp.
- loc (NDArray) – localisation net, the output dim should be 6 when transform_type is affine. You shold initialize the weight and bias with identity tranform.
- target_shape (Shape(tuple), optional, default=[0,0]) – output shape(h, w) of spatial transformer: (y, x)
- transform_type ({'affine'}, required) – transformation type
- sampler_type ({'bilinear'}, required) – sampling type
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
SwapAxis
(data=None, dim1=_Null, dim2=_Null, out=None, name=None, **kwargs)¶ Interchanges two axes of an array.
Examples:
x = [[1, 2, 3]]) swapaxes(x, 0, 1) = [[ 1], [ 2], [ 3]] x = [[[ 0, 1], [ 2, 3]], [[ 4, 5], [ 6, 7]]] // (2,2,2) array swapaxes(x, 0, 2) = [[[ 0, 4], [ 2, 6]], [[ 1, 5], [ 3, 7]]]
Defined in src/operator/swapaxis.cc:L70
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
UpSampling
(*data, **kwargs)¶ Performs nearest neighbor/bilinear up sampling to inputs.
Parameters: - data (NDArray[]) – Array of tensors to upsample
- scale (int (non-negative), required) – Up sampling scale
- num_filter (int (non-negative), optional, default=0) – Input filter. Only used by bilinear sample_type.
- sample_type ({'bilinear', 'nearest'}, required) – upsampling method
- multi_input_mode ({'concat', 'sum'},optional, default='concat') – How to handle multiple input. concat means concatenate upsampled images along the channel dimension. sum means add all images together, only available for nearest neighbor upsampling.
- workspace (long (non-negative), optional, default=512) – Tmp workspace for deconvolution (MB)
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
abs
(data=None, out=None, name=None, **kwargs)¶ Returns element-wise absolute value of the input.
Example:
abs([-2, 0, 3]) = [2, 0, 3]
The storage type of
abs
output depends upon the input storage type:- abs(default) = default
- abs(row_sparse) = row_sparse
- abs(csr) = csr
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L668
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
adam_update
(weight=None, grad=None, mean=None, var=None, lr=_Null, beta1=_Null, beta2=_Null, epsilon=_Null, wd=_Null, rescale_grad=_Null, clip_gradient=_Null, lazy_update=_Null, out=None, name=None, **kwargs)¶ Update function for Adam optimizer. Adam is seen as a generalization of AdaGrad.
Adam update consists of the following steps, where g represents gradient and m, v are 1st and 2nd order moment estimates (mean and variance).
\[\begin{split}g_t = \nabla J(W_{t-1})\\ m_t = \beta_1 m_{t-1} + (1 - \beta_1) g_t\\ v_t = \beta_2 v_{t-1} + (1 - \beta_2) g_t^2\\ W_t = W_{t-1} - \alpha \frac{ m_t }{ \sqrt{ v_t } + \epsilon }\end{split}\]It updates the weights using:
m = beta1*m + (1-beta1)*grad v = beta2*v + (1-beta2)*(grad**2) w += - learning_rate * m / (sqrt(v) + epsilon)
However, if grad’s storage type is
row_sparse
,lazy_update
is True and the storage type of weight is the same as those of m and v, only the row slices whose indices appear in grad.indices are updated (for w, m and v):for row in grad.indices: m[row] = beta1*m[row] + (1-beta1)*grad[row] v[row] = beta2*v[row] + (1-beta2)*(grad[row]**2) w[row] += - learning_rate * m[row] / (sqrt(v[row]) + epsilon)
Defined in src/operator/optimizer_op.cc:L495
Parameters: - weight (NDArray) – Weight
- grad (NDArray) – Gradient
- mean (NDArray) – Moving mean
- var (NDArray) – Moving variance
- lr (float, required) – Learning rate
- beta1 (float, optional, default=0.9) – The decay rate for the 1st moment estimates.
- beta2 (float, optional, default=0.999) – The decay rate for the 2nd moment estimates.
- epsilon (float, optional, default=1e-08) – A small constant for numerical stability.
- wd (float, optional, default=0) – Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.
- rescale_grad (float, optional, default=1) – Rescale gradient to grad = rescale_grad*grad.
- clip_gradient (float, optional, default=-1) – Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).
- lazy_update (boolean, optional, default=1) – If true, lazy updates are applied if gradient’s stype is row_sparse and all of w, m and v have the same stype
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
add_n
(*args, **kwargs)¶ Adds all input arguments element-wise.
\[add\_n(a_1, a_2, ..., a_n) = a_1 + a_2 + ... + a_n\]add_n
is potentially more efficient than callingadd
by n times.The storage type of
add_n
output depends on storage types of inputs- add_n(row_sparse, row_sparse, ..) = row_sparse
- add_n(default, csr, default) = default
- add_n(any input combinations longer than 4 (>4) with at least one default type) = default
- otherwise,
add_n
falls all inputs back to default storage and generates default storage
Defined in src/operator/tensor/elemwise_sum.cc:L156
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
arccos
(data=None, out=None, name=None, **kwargs)¶ Returns element-wise inverse cosine of the input array.
The input should be in range [-1, 1]. The output is in the closed interval \([0, \pi]\)
\[arccos([-1, -.707, 0, .707, 1]) = [\pi, 3\pi/4, \pi/2, \pi/4, 0]\]The storage type of
arccos
output is always denseDefined in src/operator/tensor/elemwise_unary_op_trig.cc:L123
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
arccosh
(data=None, out=None, name=None, **kwargs)¶ Returns the element-wise inverse hyperbolic cosine of the input array, computed element-wise.
The storage type of
arccosh
output is always denseDefined in src/operator/tensor/elemwise_unary_op_trig.cc:L264
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
arcsin
(data=None, out=None, name=None, **kwargs)¶ Returns element-wise inverse sine of the input array.
The input should be in the range [-1, 1]. The output is in the closed interval of [\(-\pi/2\), \(\pi/2\)].
\[arcsin([-1, -.707, 0, .707, 1]) = [-\pi/2, -\pi/4, 0, \pi/4, \pi/2]\]The storage type of
arcsin
output depends upon the input storage type:- arcsin(default) = default
- arcsin(row_sparse) = row_sparse
- arcsin(csr) = csr
Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L104
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
arcsinh
(data=None, out=None, name=None, **kwargs)¶ Returns the element-wise inverse hyperbolic sine of the input array, computed element-wise.
The storage type of
arcsinh
output depends upon the input storage type:- arcsinh(default) = default
- arcsinh(row_sparse) = row_sparse
- arcsinh(csr) = csr
Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L250
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
arctan
(data=None, out=None, name=None, **kwargs)¶ Returns element-wise inverse tangent of the input array.
The output is in the closed interval \([-\pi/2, \pi/2]\)
\[arctan([-1, 0, 1]) = [-\pi/4, 0, \pi/4]\]The storage type of
arctan
output depends upon the input storage type:- arctan(default) = default
- arctan(row_sparse) = row_sparse
- arctan(csr) = csr
Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L144
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
arctanh
(data=None, out=None, name=None, **kwargs)¶ Returns the element-wise inverse hyperbolic tangent of the input array, computed element-wise.
The storage type of
arctanh
output depends upon the input storage type:- arctanh(default) = default
- arctanh(row_sparse) = row_sparse
- arctanh(csr) = csr
Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L281
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
argmax
(data=None, axis=_Null, keepdims=_Null, out=None, name=None, **kwargs)¶ Returns indices of the maximum values along an axis.
In the case of multiple occurrences of maximum values, the indices corresponding to the first occurrence are returned.
Examples:
x = [[ 0., 1., 2.], [ 3., 4., 5.]] // argmax along axis 0 argmax(x, axis=0) = [ 1., 1., 1.] // argmax along axis 1 argmax(x, axis=1) = [ 2., 2.] // argmax along axis 1 keeping same dims as an input array argmax(x, axis=1, keepdims=True) = [[ 2.], [ 2.]]
Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L52
Parameters: - data (NDArray) – The input
- axis (int or None, optional, default='None') – The axis along which to perform the reduction. Negative values means indexing from right to left.
Requires axis to be set as int, because global reduction is not supported yet.
- keepdims (boolean, optional, default=0) – If this is set to True, the reduced axis is left in the result as dimension with size one.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
argmax_channel
(data=None, out=None, name=None, **kwargs)¶ Returns argmax indices of each channel from the input array.
The result will be an NDArray of shape (num_channel,).
In case of multiple occurrences of the maximum values, the indices corresponding to the first occurrence are returned.
Examples:
x = [[ 0., 1., 2.], [ 3., 4., 5.]] argmax_channel(x) = [ 2., 2.]
Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L97
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
argmin
(data=None, axis=_Null, keepdims=_Null, out=None, name=None, **kwargs)¶ Returns indices of the minimum values along an axis.
In the case of multiple occurrences of minimum values, the indices corresponding to the first occurrence are returned.
Examples:
x = [[ 0., 1., 2.], [ 3., 4., 5.]] // argmin along axis 0 argmin(x, axis=0) = [ 0., 0., 0.] // argmin along axis 1 argmin(x, axis=1) = [ 0., 0.] // argmin along axis 1 keeping same dims as an input array argmin(x, axis=1, keepdims=True) = [[ 0.], [ 0.]]
Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L77
Parameters: - data (NDArray) – The input
- axis (int or None, optional, default='None') – The axis along which to perform the reduction. Negative values means indexing from right to left.
Requires axis to be set as int, because global reduction is not supported yet.
- keepdims (boolean, optional, default=0) – If this is set to True, the reduced axis is left in the result as dimension with size one.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
argsort
(data=None, axis=_Null, is_ascend=_Null, dtype=_Null, out=None, name=None, **kwargs)¶ Returns the indices that would sort an input array along the given axis.
This function performs sorting along the given axis and returns an array of indices having same shape as an input array that index data in sorted order.
Examples:
x = [[ 0.3, 0.2, 0.4], [ 0.1, 0.3, 0.2]] // sort along axis -1 argsort(x) = [[ 1., 0., 2.], [ 0., 2., 1.]] // sort along axis 0 argsort(x, axis=0) = [[ 1., 0., 1.] [ 0., 1., 0.]] // flatten and then sort argsort(x) = [ 3., 1., 5., 0., 4., 2.]
Defined in src/operator/tensor/ordering_op.cc:L177
Parameters: - data (NDArray) – The input array
- axis (int or None, optional, default='-1') – Axis along which to sort the input tensor. If not given, the flattened array is used. Default is -1.
- is_ascend (boolean, optional, default=1) – Whether to sort in ascending or descending order.
- dtype ({'float16', 'float32', 'float64', 'int32', 'uint8'},optional, default='float32') – DType of the output indices. It is only valid when ret_typ is “indices” or “both”. An error will be raised if the selected data type cannot precisely represent the indices.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
batch_dot
(lhs=None, rhs=None, transpose_a=_Null, transpose_b=_Null, forward_stype=_Null, out=None, name=None, **kwargs)¶ Batchwise dot product.
batch_dot
is used to compute dot product ofx
andy
whenx
andy
are data in batch, namely 3D arrays in shape of (batch_size, :, :).For example, given
x
with shape (batch_size, n, m) andy
with shape (batch_size, m, k), the result array will have shape (batch_size, n, k), which is computed by:batch_dot(x,y)[i,:,:] = dot(x[i,:,:], y[i,:,:])
Defined in src/operator/tensor/dot.cc:L125
Parameters: - lhs (NDArray) – The first input
- rhs (NDArray) – The second input
- transpose_a (boolean, optional, default=0) – If true then transpose the first input before dot.
- transpose_b (boolean, optional, default=0) – If true then transpose the second input before dot.
- forward_stype ({None, 'csr', 'default', 'row_sparse'},optional, default='None') – The desired storage type of the forward output given by user, if thecombination of input storage types and this hint does not matchany implemented ones, the dot operator will perform fallback operationand still produce an output of the desired storage type.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
batch_take
(a=None, indices=None, out=None, name=None, **kwargs)¶ Takes elements from a data batch.
Note
batch_take is deprecated. Use pick instead.
Given an input array of shape
(d0, d1)
and indices of shape(i0,)
, the result will be an output array of shape(i0,)
with:output[i] = input[i, indices[i]]
Examples:
x = [[ 1., 2.], [ 3., 4.], [ 5., 6.]] // takes elements with specified indices batch_take(x, [0,1,0]) = [ 1. 4. 5.]
Defined in src/operator/tensor/indexing_op.cc:L490
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
broadcast_add
(lhs=None, rhs=None, out=None, name=None, **kwargs)¶ Returns element-wise sum of the input arrays with broadcasting.
broadcast_plus is an alias to the function broadcast_add.
Example:
x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_add(x, y) = [[ 1., 1., 1.], [ 2., 2., 2.]] broadcast_plus(x, y) = [[ 1., 1., 1.], [ 2., 2., 2.]]
Supported sparse operations:
broadcast_add(csr, dense(1D)) = dense broadcast_add(dense(1D), csr) = denseDefined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L58
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
broadcast_axes
(data=None, axis=_Null, size=_Null, out=None, name=None, **kwargs)¶ Broadcasts the input array over particular axes.
Broadcasting is allowed on axes with size 1, such as from (2,1,3,1) to (2,8,3,9). Elements will be duplicated on the broadcasted axes.
Example:
// given x of shape (1,2,1) x = [[[ 1.], [ 2.]]] // broadcast x on on axis 2 broadcast_axis(x, axis=2, size=3) = [[[ 1., 1., 1.], [ 2., 2., 2.]]] // broadcast x on on axes 0 and 2 broadcast_axis(x, axis=(0,2), size=(2,3)) = [[[ 1., 1., 1.], [ 2., 2., 2.]], [[ 1., 1., 1.], [ 2., 2., 2.]]]
Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L237
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
broadcast_axis
(data=None, axis=_Null, size=_Null, out=None, name=None, **kwargs)¶ Broadcasts the input array over particular axes.
Broadcasting is allowed on axes with size 1, such as from (2,1,3,1) to (2,8,3,9). Elements will be duplicated on the broadcasted axes.
Example:
// given x of shape (1,2,1) x = [[[ 1.], [ 2.]]] // broadcast x on on axis 2 broadcast_axis(x, axis=2, size=3) = [[[ 1., 1., 1.], [ 2., 2., 2.]]] // broadcast x on on axes 0 and 2 broadcast_axis(x, axis=(0,2), size=(2,3)) = [[[ 1., 1., 1.], [ 2., 2., 2.]], [[ 1., 1., 1.], [ 2., 2., 2.]]]
Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L237
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
broadcast_div
(lhs=None, rhs=None, out=None, name=None, **kwargs)¶ Returns element-wise division of the input arrays with broadcasting.
Example:
x = [[ 6., 6., 6.], [ 6., 6., 6.]] y = [[ 2.], [ 3.]] broadcast_div(x, y) = [[ 3., 3., 3.], [ 2., 2., 2.]]
Supported sparse operations:
broadcast_div(csr, dense(1D)) = csrDefined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L187
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
broadcast_equal
(lhs=None, rhs=None, out=None, name=None, **kwargs)¶ Returns the result of element-wise equal to (==) comparison operation with broadcasting.
Example:
x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_equal(x, y) = [[ 0., 0., 0.], [ 1., 1., 1.]]
Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L46
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
broadcast_greater
(lhs=None, rhs=None, out=None, name=None, **kwargs)¶ Returns the result of element-wise greater than (>) comparison operation with broadcasting.
Example:
x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_greater(x, y) = [[ 1., 1., 1.], [ 0., 0., 0.]]
Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L82
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
broadcast_greater_equal
(lhs=None, rhs=None, out=None, name=None, **kwargs)¶ Returns the result of element-wise greater than or equal to (>=) comparison operation with broadcasting.
Example:
x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_greater_equal(x, y) = [[ 1., 1., 1.], [ 1., 1., 1.]]
Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L100
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
broadcast_hypot
(lhs=None, rhs=None, out=None, name=None, **kwargs)¶ Returns the hypotenuse of a right angled triangle, given its “legs” with broadcasting.
It is equivalent to doing \(sqrt(x_1^2 + x_2^2)\).
Example:
x = [[ 3., 3., 3.]] y = [[ 4.], [ 4.]] broadcast_hypot(x, y) = [[ 5., 5., 5.], [ 5., 5., 5.]] z = [[ 0.], [ 4.]] broadcast_hypot(x, z) = [[ 3., 3., 3.], [ 5., 5., 5.]]
Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L156
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
broadcast_lesser
(lhs=None, rhs=None, out=None, name=None, **kwargs)¶ Returns the result of element-wise lesser than (<) comparison operation with broadcasting.
Example:
x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_lesser(x, y) = [[ 0., 0., 0.], [ 0., 0., 0.]]
Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L118
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
broadcast_lesser_equal
(lhs=None, rhs=None, out=None, name=None, **kwargs)¶ Returns the result of element-wise lesser than or equal to (<=) comparison operation with broadcasting.
Example:
x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_lesser_equal(x, y) = [[ 0., 0., 0.], [ 1., 1., 1.]]
Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L136
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
broadcast_like
(lhs=None, rhs=None, out=None, name=None, **kwargs)¶ Broadcasts lhs to have the same shape as rhs.
Broadcasting is a mechanism that allows NDArrays to perform arithmetic operations with arrays of different shapes efficiently without creating multiple copies of arrays. Also see, Broadcasting for more explanation.
Broadcasting is allowed on axes with size 1, such as from (2,1,3,1) to (2,8,3,9). Elements will be duplicated on the broadcasted axes.
For example:
broadcast_like([[1,2,3]], [[5,6,7],[7,8,9]]) = [[ 1., 2., 3.], [ 1., 2., 3.]])
Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L312
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
broadcast_logical_and
(lhs=None, rhs=None, out=None, name=None, **kwargs)¶ Returns the result of element-wise logical and with broadcasting.
Example:
x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_logical_and(x, y) = [[ 0., 0., 0.], [ 1., 1., 1.]]
Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L154
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
broadcast_logical_or
(lhs=None, rhs=None, out=None, name=None, **kwargs)¶ Returns the result of element-wise logical or with broadcasting.
Example:
x = [[ 1., 1., 0.], [ 1., 1., 0.]] y = [[ 1.], [ 0.]] broadcast_logical_or(x, y) = [[ 1., 1., 1.], [ 1., 1., 0.]]
Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L172
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
broadcast_logical_xor
(lhs=None, rhs=None, out=None, name=None, **kwargs)¶ Returns the result of element-wise logical xor with broadcasting.
Example:
x = [[ 1., 1., 0.], [ 1., 1., 0.]] y = [[ 1.], [ 0.]] broadcast_logical_xor(x, y) = [[ 0., 0., 1.], [ 1., 1., 0.]]
Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L190
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
broadcast_maximum
(lhs=None, rhs=None, out=None, name=None, **kwargs)¶ Returns element-wise maximum of the input arrays with broadcasting.
This function compares two input arrays and returns a new array having the element-wise maxima.
Example:
x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_maximum(x, y) = [[ 1., 1., 1.], [ 1., 1., 1.]]
Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L80
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
broadcast_minimum
(lhs=None, rhs=None, out=None, name=None, **kwargs)¶ Returns element-wise minimum of the input arrays with broadcasting.
This function compares two input arrays and returns a new array having the element-wise minima.
Example:
x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_maximum(x, y) = [[ 0., 0., 0.], [ 1., 1., 1.]]
Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L115
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
broadcast_minus
(lhs=None, rhs=None, out=None, name=None, **kwargs)¶ Returns element-wise difference of the input arrays with broadcasting.
broadcast_minus is an alias to the function broadcast_sub.
Example:
x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_sub(x, y) = [[ 1., 1., 1.], [ 0., 0., 0.]] broadcast_minus(x, y) = [[ 1., 1., 1.], [ 0., 0., 0.]]
Supported sparse operations:
broadcast_sub/minus(csr, dense(1D)) = dense broadcast_sub/minus(dense(1D), csr) = denseDefined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L106
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
broadcast_mod
(lhs=None, rhs=None, out=None, name=None, **kwargs)¶ Returns element-wise modulo of the input arrays with broadcasting.
Example:
x = [[ 8., 8., 8.], [ 8., 8., 8.]] y = [[ 2.], [ 3.]] broadcast_mod(x, y) = [[ 0., 0., 0.], [ 2., 2., 2.]]
Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L222
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
broadcast_mul
(lhs=None, rhs=None, out=None, name=None, **kwargs)¶ Returns element-wise product of the input arrays with broadcasting.
Example:
x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_mul(x, y) = [[ 0., 0., 0.], [ 1., 1., 1.]]
Supported sparse operations:
broadcast_mul(csr, dense(1D)) = csrDefined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L146
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
broadcast_not_equal
(lhs=None, rhs=None, out=None, name=None, **kwargs)¶ Returns the result of element-wise not equal to (!=) comparison operation with broadcasting.
Example:
x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_not_equal(x, y) = [[ 1., 1., 1.], [ 0., 0., 0.]]
Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L64
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
broadcast_plus
(lhs=None, rhs=None, out=None, name=None, **kwargs)¶ Returns element-wise sum of the input arrays with broadcasting.
broadcast_plus is an alias to the function broadcast_add.
Example:
x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_add(x, y) = [[ 1., 1., 1.], [ 2., 2., 2.]] broadcast_plus(x, y) = [[ 1., 1., 1.], [ 2., 2., 2.]]
Supported sparse operations:
broadcast_add(csr, dense(1D)) = dense broadcast_add(dense(1D), csr) = denseDefined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L58
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
broadcast_power
(lhs=None, rhs=None, out=None, name=None, **kwargs)¶ Returns result of first array elements raised to powers from second array, element-wise with broadcasting.
Example:
x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_power(x, y) = [[ 2., 2., 2.], [ 4., 4., 4.]]
Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L45
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
broadcast_sub
(lhs=None, rhs=None, out=None, name=None, **kwargs)¶ Returns element-wise difference of the input arrays with broadcasting.
broadcast_minus is an alias to the function broadcast_sub.
Example:
x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_sub(x, y) = [[ 1., 1., 1.], [ 0., 0., 0.]] broadcast_minus(x, y) = [[ 1., 1., 1.], [ 0., 0., 0.]]
Supported sparse operations:
broadcast_sub/minus(csr, dense(1D)) = dense broadcast_sub/minus(dense(1D), csr) = denseDefined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L106
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
broadcast_to
(data=None, shape=_Null, out=None, name=None, **kwargs)¶ Broadcasts the input array to a new shape.
Broadcasting is a mechanism that allows NDArrays to perform arithmetic operations with arrays of different shapes efficiently without creating multiple copies of arrays. Also see, Broadcasting for more explanation.
Broadcasting is allowed on axes with size 1, such as from (2,1,3,1) to (2,8,3,9). Elements will be duplicated on the broadcasted axes.
For example:
broadcast_to([[1,2,3]], shape=(2,3)) = [[ 1., 2., 3.], [ 1., 2., 3.]])
The dimension which you do not want to change can also be kept as 0 which means copy the original value. So with shape=(2,0), we will obtain the same result as in the above example.
Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L261
Parameters: - data (NDArray) – The input
- shape (Shape(tuple), optional, default=[]) – The shape of the desired array. We can set the dim to zero if it’s same as the original. E.g A = broadcast_to(B, shape=(10, 0, 0)) has the same meaning as A = broadcast_axis(B, axis=0, size=10).
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
cast
(data=None, dtype=_Null, out=None, name=None, **kwargs)¶ Casts all elements of the input to a new type.
Note
Cast
is deprecated. Usecast
instead.Example:
cast([0.9, 1.3], dtype='int32') = [0, 1] cast([1e20, 11.1], dtype='float16') = [inf, 11.09375] cast([300, 11.1, 10.9, -1, -3], dtype='uint8') = [44, 11, 10, 255, 253]
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L594
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
cast_storage
(data=None, stype=_Null, out=None, name=None, **kwargs)¶ Casts tensor storage type to the new type.
When an NDArray with default storage type is cast to csr or row_sparse storage, the result is compact, which means:
- for csr, zero values will not be retained
- for row_sparse, row slices of all zeros will not be retained
The storage type of
cast_storage
output depends on stype parameter:- cast_storage(csr, ‘default’) = default
- cast_storage(row_sparse, ‘default’) = default
- cast_storage(default, ‘csr’) = csr
- cast_storage(default, ‘row_sparse’) = row_sparse
- cast_storage(csr, ‘csr’) = csr
- cast_storage(row_sparse, ‘row_sparse’) = row_sparse
Example:
dense = [[ 0., 1., 0.], [ 2., 0., 3.], [ 0., 0., 0.], [ 0., 0., 0.]] # cast to row_sparse storage type rsp = cast_storage(dense, 'row_sparse') rsp.indices = [0, 1] rsp.values = [[ 0., 1., 0.], [ 2., 0., 3.]] # cast to csr storage type csr = cast_storage(dense, 'csr') csr.indices = [1, 0, 2] csr.values = [ 1., 2., 3.] csr.indptr = [0, 1, 3, 3, 3]
Defined in src/operator/tensor/cast_storage.cc:L71
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
cbrt
(data=None, out=None, name=None, **kwargs)¶ Returns element-wise cube-root value of the input.
\[cbrt(x) = \sqrt[3]{x}\]Example:
cbrt([1, 8, -125]) = [1, 2, -5]
The storage type of
cbrt
output depends upon the input storage type:- cbrt(default) = default
- cbrt(row_sparse) = row_sparse
- cbrt(csr) = csr
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L889
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
ceil
(data=None, out=None, name=None, **kwargs)¶ Returns element-wise ceiling of the input.
The ceil of the scalar x is the smallest integer i, such that i >= x.
Example:
ceil([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-2., -1., 2., 2., 3.]
The storage type of
ceil
output depends upon the input storage type:- ceil(default) = default
- ceil(row_sparse) = row_sparse
- ceil(csr) = csr
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L746
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
choose_element_0index
(lhs=None, rhs=None, out=None, name=None, **kwargs)¶ Choose one element from each line(row for python, column for R/Julia) in lhs according to index indicated by rhs. This function assume rhs uses 0-based index.
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
clip
(data=None, a_min=_Null, a_max=_Null, out=None, name=None, **kwargs)¶ Clips (limits) the values in an array.
Given an interval, values outside the interval are clipped to the interval edges. Clipping
x
between a_min and a_x would be:clip(x, a_min, a_max) = max(min(x, a_max), a_min))
Example:
x = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] clip(x,1,8) = [ 1., 1., 2., 3., 4., 5., 6., 7., 8., 8.]
The storage type of
clip
output depends on storage types of inputs and the a_min, a_max parameter values:- clip(default) = default
- clip(row_sparse, a_min <= 0, a_max >= 0) = row_sparse
- clip(csr, a_min <= 0, a_max >= 0) = csr
- clip(row_sparse, a_min < 0, a_max < 0) = default
- clip(row_sparse, a_min > 0, a_max > 0) = default
- clip(csr, a_min < 0, a_max < 0) = csr
- clip(csr, a_min > 0, a_max > 0) = csr
Defined in src/operator/tensor/matrix_op.cc:L618
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
concat
(*data, **kwargs)¶ Joins input arrays along a given axis.
Note
Concat is deprecated. Use concat instead.
The dimensions of the input arrays should be the same except the axis along which they will be concatenated. The dimension of the output array along the concatenated axis will be equal to the sum of the corresponding dimensions of the input arrays.
The storage type of
concat
output depends on storage types of inputs- concat(csr, csr, ..., csr, dim=0) = csr
- otherwise,
concat
generates output with default storage
Example:
x = [[1,1],[2,2]] y = [[3,3],[4,4],[5,5]] z = [[6,6], [7,7],[8,8]] concat(x,y,z,dim=0) = [[ 1., 1.], [ 2., 2.], [ 3., 3.], [ 4., 4.], [ 5., 5.], [ 6., 6.], [ 7., 7.], [ 8., 8.]] Note that you cannot concat x,y,z along dimension 1 since dimension 0 is not the same for all the input arrays. concat(y,z,dim=1) = [[ 3., 3., 6., 6.], [ 4., 4., 7., 7.], [ 5., 5., 8., 8.]]
Defined in src/operator/nn/concat.cc:L368
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
cos
(data=None, out=None, name=None, **kwargs)¶ Computes the element-wise cosine of the input array.
The input should be in radians (\(2\pi\) rad equals 360 degrees).
\[cos([0, \pi/4, \pi/2]) = [1, 0.707, 0]\]The storage type of
cos
output is always denseDefined in src/operator/tensor/elemwise_unary_op_trig.cc:L63
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
cosh
(data=None, out=None, name=None, **kwargs)¶ Returns the hyperbolic cosine of the input array, computed element-wise.
\[cosh(x) = 0.5\times(exp(x) + exp(-x))\]The storage type of
cosh
output is always denseDefined in src/operator/tensor/elemwise_unary_op_trig.cc:L216
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
crop
(data=None, begin=_Null, end=_Null, step=_Null, out=None, name=None, **kwargs)¶ Slices a region of the array.
Note
crop
is deprecated. Useslice
instead.This function returns a sliced array between the indices given by begin and end with the corresponding step.
For an input array of
shape=(d_0, d_1, ..., d_n-1)
, slice operation withbegin=(b_0, b_1...b_m-1)
,end=(e_0, e_1, ..., e_m-1)
, andstep=(s_0, s_1, ..., s_m-1)
, where m <= n, results in an array with the shape(|e_0-b_0|/|s_0|, ..., |e_m-1-b_m-1|/|s_m-1|, d_m, ..., d_n-1)
.The resulting array’s k-th dimension contains elements from the k-th dimension of the input array starting from index
b_k
(inclusive) with steps_k
until reachinge_k
(exclusive).If the k-th elements are None in the sequence of begin, end, and step, the following rule will be used to set default values. If s_k is None, set s_k=1. If s_k > 0, set b_k=0, e_k=d_k; else, set b_k=d_k-1, e_k=-1.
The storage type of
slice
output depends on storage types of inputs- slice(csr) = csr
- otherwise,
slice
generates output with default storage
Note
When input data storage type is csr, it only supports
step=(), or step=(None,), or step=(1,) to generate a csr output. For other step parameter values, it falls back to slicing a dense tensor.
Example:
x = [[ 1., 2., 3., 4.], [ 5., 6., 7., 8.], [ 9., 10., 11., 12.]] slice(x, begin=(0,1), end=(2,4)) = [[ 2., 3., 4.], [ 6., 7., 8.]] slice(x, begin=(None, 0), end=(None, 3), step=(-1, 2)) = [[9., 11.], [5., 7.], [1., 3.]]
Defined in src/operator/tensor/matrix_op.cc:L413
Parameters: - data (NDArray) – Source input
- begin (Shape(tuple), required) – starting indices for the slice operation, supports negative indices.
- end (Shape(tuple), required) – ending indices for the slice operation, supports negative indices.
- step (Shape(tuple), optional, default=[]) – step for the slice operation, supports negative values.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
degrees
(data=None, out=None, name=None, **kwargs)¶ Converts each element of the input array from radians to degrees.
\[degrees([0, \pi/2, \pi, 3\pi/2, 2\pi]) = [0, 90, 180, 270, 360]\]The storage type of
degrees
output depends upon the input storage type:- degrees(default) = default
- degrees(row_sparse) = row_sparse
- degrees(csr) = csr
Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L163
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
depth_to_space
(data=None, block_size=_Null, out=None, name=None, **kwargs)¶ Rearranges(permutes) data from depth into blocks of spatial data. Similar to ONNX DepthToSpace operator: https://github.com/onnx/onnx/blob/master/docs/Operators.md#DepthToSpace. The output is a new tensor where the values from depth dimension are moved in spatial blocks to height and width dimension. The reverse of this operation is
space_to_depth
.\[\begin{split}\begin{gather*} x \prime = reshape(x, [N, block\_size, block\_size, C / (block\_size ^ 2), H * block\_size, W * block\_size]) \\ x \prime \prime = transpose(x \prime, [0, 3, 4, 1, 5, 2]) \\ y = reshape(x \prime \prime, [N, C / (block\_size ^ 2), H * block\_size, W * block\_size]) \end{gather*}\end{split}\]where \(x\) is an input tensor with default layout as \([N, C, H, W]\): [batch, channels, height, width] and \(y\) is the output tensor of layout \([N, C / (block\_size ^ 2), H * block\_size, W * block\_size]\)
Example:
x = [[[[0, 1, 2], [3, 4, 5]], [[6, 7, 8], [9, 10, 11]], [[12, 13, 14], [15, 16, 17]], [[18, 19, 20], [21, 22, 23]]]] depth_to_space(x, 2) = [[[[0, 6, 1, 7, 2, 8], [12, 18, 13, 19, 14, 20], [3, 9, 4, 10, 5, 11], [15, 21, 16, 22, 17, 23]]]]
Defined in src/operator/tensor/matrix_op.cc:L945
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
diag
(data=None, k=_Null, out=None, name=None, **kwargs)¶ Extracts a diagonal or constructs a diagonal array.
diag
‘s behavior depends on the input array dimensions:- 1-D arrays: constructs a 2-D array with the input as its diagonal, all other elements are zero
- 2-D arrays: returns elements in the diagonal as a new 1-D array
- N-D arrays: not supported yet
Examples:
x = [[1, 2, 3], [4, 5, 6]] diag(x) = [1, 5] diag(x, k=1) = [2, 6] diag(x, k=-1) = [4] x = [1, 2, 3] diag(x) = [[1, 0, 0], [0, 2, 0], [0, 0, 3]] diag(x, k=1) = [[0, 1, 0], [0, 0, 2], [0, 0, 0]] diag(x, k=-1) = [[0, 0, 0], [1, 0, 0], [0, 2, 0]]
Defined in src/operator/tensor/diag_op.cc:L68
Parameters: - data (NDArray) – Input ndarray
- k (int or None, optional, default='0') – Diagonal in question. The default is 0. Use k>0 for diagonals above the main diagonal, and k<0 for diagonals below the main diagonal. If input has shape (S0 S1) k must be between -S0 and S1
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
dot
(lhs=None, rhs=None, transpose_a=_Null, transpose_b=_Null, forward_stype=_Null, out=None, name=None, **kwargs)¶ Dot product of two arrays.
dot
‘s behavior depends on the input array dimensions:1-D arrays: inner product of vectors
2-D arrays: matrix multiplication
N-D arrays: a sum product over the last axis of the first input and the first axis of the second input
For example, given 3-D
x
with shape (n,m,k) andy
with shape (k,r,s), the result array will have shape (n,m,r,s). It is computed by:dot(x,y)[i,j,a,b] = sum(x[i,j,:]*y[:,a,b])
Example:
x = reshape([0,1,2,3,4,5,6,7], shape=(2,2,2)) y = reshape([7,6,5,4,3,2,1,0], shape=(2,2,2)) dot(x,y)[0,0,1,1] = 0 sum(x[0,0,:]*y[:,1,1]) = 0
The storage type of
dot
output depends on storage types of inputs, transpose option and forward_stype option for output storage type. Implemented sparse operations include:- dot(default, default, transpose_a=True/False, transpose_b=True/False) = default
- dot(csr, default, transpose_a=True) = default
- dot(csr, default, transpose_a=True) = row_sparse
- dot(csr, default) = default
- dot(csr, row_sparse) = default
- dot(default, csr) = csr (CPU only)
- dot(default, csr, forward_stype=’default’) = default
- dot(default, csr, transpose_b=True, forward_stype=’default’) = default
If the combination of input storage types and forward_stype does not match any of the above patterns,
dot
will fallback and generate output with default storage.Note
If the storage type of the lhs is “csr”, the storage type of gradient w.r.t rhs will be “row_sparse”. Only a subset of optimizers support sparse gradients, including SGD, AdaGrad and Adam. Note that by default lazy updates is turned on, which may perform differently from standard updates. For more details, please check the Optimization API at: /api/python/optimization/optimization.html
Defined in src/operator/tensor/dot.cc:L77
Parameters: - lhs (NDArray) – The first input
- rhs (NDArray) – The second input
- transpose_a (boolean, optional, default=0) – If true then transpose the first input before dot.
- transpose_b (boolean, optional, default=0) – If true then transpose the second input before dot.
- forward_stype ({None, 'csr', 'default', 'row_sparse'},optional, default='None') – The desired storage type of the forward output given by user, if thecombination of input storage types and this hint does not matchany implemented ones, the dot operator will perform fallback operationand still produce an output of the desired storage type.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
elemwise_add
(lhs=None, rhs=None, out=None, name=None, **kwargs)¶ Adds arguments element-wise.
The storage type of
elemwise_add
output depends on storage types of inputs- elemwise_add(row_sparse, row_sparse) = row_sparse
- elemwise_add(csr, csr) = csr
- elemwise_add(default, csr) = default
- elemwise_add(csr, default) = default
- elemwise_add(default, rsp) = default
- elemwise_add(rsp, default) = default
- otherwise,
elemwise_add
generates output with default storage
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
Example
>>> x = mx.nd.array([1, 2, 3, 4]) >>> y = mx.nd.array([1.1, 2.1, 3.1, 4.1]) >>> mx.nd.elemwise_add(x, y).asnumpy() array([ 2.0999999 , 4.0999999 , 6.0999999 , 8.10000038], dtype=float32)
-
mxnet.ndarray.
elemwise_div
(lhs=None, rhs=None, out=None, name=None, **kwargs)¶ Divides arguments element-wise.
The storage type of
elemwise_div
output is always denseParameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
elemwise_mul
(lhs=None, rhs=None, out=None, name=None, **kwargs)¶ Multiplies arguments element-wise.
The storage type of
elemwise_mul
output depends on storage types of inputs- elemwise_mul(default, default) = default
- elemwise_mul(row_sparse, row_sparse) = row_sparse
- elemwise_mul(default, row_sparse) = row_sparse
- elemwise_mul(row_sparse, default) = row_sparse
- elemwise_mul(csr, csr) = csr
- otherwise,
elemwise_mul
generates output with default storage
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
elemwise_sub
(lhs=None, rhs=None, out=None, name=None, **kwargs)¶ Subtracts arguments element-wise.
The storage type of
elemwise_sub
output depends on storage types of inputs- elemwise_sub(row_sparse, row_sparse) = row_sparse
- elemwise_sub(csr, csr) = csr
- elemwise_sub(default, csr) = default
- elemwise_sub(csr, default) = default
- elemwise_sub(default, rsp) = default
- elemwise_sub(rsp, default) = default
- otherwise,
elemwise_sub
generates output with default storage
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
exp
(data=None, out=None, name=None, **kwargs)¶ Returns element-wise exponential value of the input.
\[exp(x) = e^x \approx 2.718^x\]Example:
exp([0, 1, 2]) = [1., 2.71828175, 7.38905621]
The storage type of
exp
output is always denseDefined in src/operator/tensor/elemwise_unary_op_basic.cc:L929
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
expand_dims
(data=None, axis=_Null, out=None, name=None, **kwargs)¶ Inserts a new axis of size 1 into the array shape
For example, given
x
with shape(2,3,4)
, thenexpand_dims(x, axis=1)
will return a new array with shape(2,1,3,4)
.Defined in src/operator/tensor/matrix_op.cc:L347
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
expm1
(data=None, out=None, name=None, **kwargs)¶ Returns
exp(x) - 1
computed element-wise on the input.This function provides greater precision than
exp(x) - 1
for small values ofx
.The storage type of
expm1
output depends upon the input storage type:- expm1(default) = default
- expm1(row_sparse) = row_sparse
- expm1(csr) = csr
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L1008
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
fill_element_0index
(lhs=None, mhs=None, rhs=None, out=None, name=None, **kwargs)¶ Fill one element of each line(row for python, column for R/Julia) in lhs according to index indicated by rhs and values indicated by mhs. This function assume rhs uses 0-based index.
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
fix
(data=None, out=None, name=None, **kwargs)¶ Returns element-wise rounded value to the nearest integer towards zero of the input.
Example:
fix([-2.1, -1.9, 1.9, 2.1]) = [-2., -1., 1., 2.]
The storage type of
fix
output depends upon the input storage type:- fix(default) = default
- fix(row_sparse) = row_sparse
- fix(csr) = csr
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L803
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
flatten
(data=None, out=None, name=None, **kwargs)¶ Flattens the input array into a 2-D array by collapsing the higher dimensions.
Note
Flatten is deprecated. Use flatten instead.
For an input array with shape
(d1, d2, ..., dk)
, flatten operation reshapes the input array into an output array of shape(d1, d2*...*dk)
.Note that the bahavior of this function is different from numpy.ndarray.flatten, which behaves similar to mxnet.ndarray.reshape((-1,)).
Example:
x = [[ [1,2,3], [4,5,6], [7,8,9] ], [ [1,2,3], [4,5,6], [7,8,9] ]], flatten(x) = [[ 1., 2., 3., 4., 5., 6., 7., 8., 9.], [ 1., 2., 3., 4., 5., 6., 7., 8., 9.]]
Defined in src/operator/tensor/matrix_op.cc:L259
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
flip
(data=None, axis=_Null, out=None, name=None, **kwargs)¶ Reverses the order of elements along given axis while preserving array shape.
Note: reverse and flip are equivalent. We use reverse in the following examples.
Examples:
x = [[ 0., 1., 2., 3., 4.], [ 5., 6., 7., 8., 9.]] reverse(x, axis=0) = [[ 5., 6., 7., 8., 9.], [ 0., 1., 2., 3., 4.]] reverse(x, axis=1) = [[ 4., 3., 2., 1., 0.], [ 9., 8., 7., 6., 5.]]
Defined in src/operator/tensor/matrix_op.cc:L793
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
floor
(data=None, out=None, name=None, **kwargs)¶ Returns element-wise floor of the input.
The floor of the scalar x is the largest integer i, such that i <= x.
Example:
floor([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-3., -2., 1., 1., 2.]
The storage type of
floor
output depends upon the input storage type:- floor(default) = default
- floor(row_sparse) = row_sparse
- floor(csr) = csr
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L765
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
ftml_update
(weight=None, grad=None, d=None, v=None, z=None, lr=_Null, beta1=_Null, beta2=_Null, epsilon=_Null, t=_Null, wd=_Null, rescale_grad=_Null, clip_grad=_Null, out=None, name=None, **kwargs)¶ The FTML optimizer described in FTML - Follow the Moving Leader in Deep Learning, available at http://proceedings.mlr.press/v70/zheng17a/zheng17a.pdf.
\[\begin{split}g_t = \nabla J(W_{t-1})\\ v_t = \beta_2 v_{t-1} + (1 - \beta_2) g_t^2\\ d_t = \frac{ 1 - \beta_1^t }{ \eta_t } (\sqrt{ \frac{ v_t }{ 1 - \beta_2^t } } + \epsilon) \sigma_t = d_t - \beta_1 d_{t-1} z_t = \beta_1 z_{ t-1 } + (1 - \beta_1^t) g_t - \sigma_t W_{t-1} W_t = - \frac{ z_t }{ d_t }\end{split}\]Defined in src/operator/optimizer_op.cc:L447
Parameters: - weight (NDArray) – Weight
- grad (NDArray) – Gradient
- d (NDArray) – Internal state
d_t
- v (NDArray) – Internal state
v_t
- z (NDArray) – Internal state
z_t
- lr (float, required) – Learning rate.
- beta1 (float, optional, default=0.6) – Generally close to 0.5.
- beta2 (float, optional, default=0.999) – Generally close to 1.
- epsilon (double, optional, default=1e-08) – Epsilon to prevent div 0.
- t (int, required) – Number of update.
- wd (float, optional, default=0) – Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.
- rescale_grad (float, optional, default=1) – Rescale gradient to grad = rescale_grad*grad.
- clip_grad (float, optional, default=-1) – Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
ftrl_update
(weight=None, grad=None, z=None, n=None, lr=_Null, lamda1=_Null, beta=_Null, wd=_Null, rescale_grad=_Null, clip_gradient=_Null, out=None, name=None, **kwargs)¶ Update function for Ftrl optimizer. Referenced from Ad Click Prediction: a View from the Trenches, available at http://dl.acm.org/citation.cfm?id=2488200.
It updates the weights using:
rescaled_grad = clip(grad * rescale_grad, clip_gradient) z += rescaled_grad - (sqrt(n + rescaled_grad**2) - sqrt(n)) * weight / learning_rate n += rescaled_grad**2 w = (sign(z) * lamda1 - z) / ((beta + sqrt(n)) / learning_rate + wd) * (abs(z) > lamda1)
If w, z and n are all of
row_sparse
storage type, only the row slices whose indices appear in grad.indices are updated (for w, z and n):for row in grad.indices: rescaled_grad[row] = clip(grad[row] * rescale_grad, clip_gradient) z[row] += rescaled_grad[row] - (sqrt(n[row] + rescaled_grad[row]**2) - sqrt(n[row])) * weight[row] / learning_rate n[row] += rescaled_grad[row]**2 w[row] = (sign(z[row]) * lamda1 - z[row]) / ((beta + sqrt(n[row])) / learning_rate + wd) * (abs(z[row]) > lamda1)
Defined in src/operator/optimizer_op.cc:L632
Parameters: - weight (NDArray) – Weight
- grad (NDArray) – Gradient
- z (NDArray) – z
- n (NDArray) – Square of grad
- lr (float, required) – Learning rate
- lamda1 (float, optional, default=0.01) – The L1 regularization coefficient.
- beta (float, optional, default=1) – Per-Coordinate Learning Rate beta.
- wd (float, optional, default=0) – Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.
- rescale_grad (float, optional, default=1) – Rescale gradient to grad = rescale_grad*grad.
- clip_gradient (float, optional, default=-1) – Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
gamma
(data=None, out=None, name=None, **kwargs)¶ Returns the gamma function (extension of the factorial function to the reals), computed element-wise on the input array.
The storage type of
gamma
output is always denseParameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
gammaln
(data=None, out=None, name=None, **kwargs)¶ Returns element-wise log of the absolute value of the gamma function of the input.
The storage type of
gammaln
output is always denseParameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
gather_nd
(data=None, indices=None, out=None, name=None, **kwargs)¶ Gather elements or slices from data and store to a tensor whose shape is defined by indices.
Given data with shape (X_0, X_1, ..., X_{N-1}) and indices with shape (M, Y_0, ..., Y_{K-1}), the output will have shape (Y_0, ..., Y_{K-1}, X_M, ..., X_{N-1}), where M <= N. If M == N, output shape will simply be (Y_0, ..., Y_{K-1}).
The elements in output is defined as follows:
output[y_0, ..., y_{K-1}, x_M, ..., x_{N-1}] = data[indices[0, y_0, ..., y_{K-1}], ..., indices[M-1, y_0, ..., y_{K-1}], x_M, ..., x_{N-1}]
Examples:
data = [[0, 1], [2, 3]] indices = [[1, 1, 0], [0, 1, 0]] gather_nd(data, indices) = [2, 3, 0] data = [[[1, 2], [3, 4]], [[5, 6], [7, 8]]] indices = [[0, 1], [1, 0]] gather_nd(data, indices) = [[3, 4], [5, 6]]
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
hard_sigmoid
(data=None, alpha=_Null, beta=_Null, out=None, name=None, **kwargs)¶ Computes hard sigmoid of x element-wise.
\[y = max(0, min(1, alpha * x + beta))\]Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L115
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
identity
(data=None, out=None, name=None, **kwargs)¶ Returns a copy of the input.
From:src/operator/tensor/elemwise_unary_op_basic.cc:200
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
khatri_rao
(*args, **kwargs)¶ Computes the Khatri-Rao product of the input matrices.
Given a collection of \(n\) input matrices,
\[A_1 \in \mathbb{R}^{M_1 \times M}, \ldots, A_n \in \mathbb{R}^{M_n \times N},\]the (column-wise) Khatri-Rao product is defined as the matrix,
\[X = A_1 \otimes \cdots \otimes A_n \in \mathbb{R}^{(M_1 \cdots M_n) \times N},\]where the \(k\) th column is equal to the column-wise outer product \({A_1}_k \otimes \cdots \otimes {A_n}_k\) where \({A_i}_k\) is the kth column of the ith matrix.
Example:
>>> A = mx.nd.array([[1, -1], >>> [2, -3]]) >>> B = mx.nd.array([[1, 4], >>> [2, 5], >>> [3, 6]]) >>> C = mx.nd.khatri_rao(A, B) >>> print(C.asnumpy()) [[ 1. -4.] [ 2. -5.] [ 3. -6.] [ 2. -12.] [ 4. -15.] [ 6. -18.]]
Defined in src/operator/contrib/krprod.cc:L108
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
linalg_gelqf
(A=None, out=None, name=None, **kwargs)¶ LQ factorization for general matrix. Input is a tensor A of dimension n >= 2.
If n=2, we compute the LQ factorization (LAPACK gelqf, followed by orglq). A must have shape (x, y) with x <= y, and must have full rank =x. The LQ factorization consists of L with shape (x, x) and Q with shape (x, y), so that:
A = L * QHere, L is lower triangular (upper triangle equal to zero) with nonzero diagonal, and Q is row-orthonormal, meaning that
Q * QTis equal to the identity matrix of shape (x, x).
If n>2, gelqf is performed separately on the trailing two dimensions for all inputs (batch mode).
Note
The operator supports float32 and float64 data types only.
Examples:
// Single LQ factorization A = [[1., 2., 3.], [4., 5., 6.]] Q, L = gelqf(A) Q = [[-0.26726124, -0.53452248, -0.80178373], [0.87287156, 0.21821789, -0.43643578]] L = [[-3.74165739, 0.], [-8.55235974, 1.96396101]] // Batch LQ factorization A = [[[1., 2., 3.], [4., 5., 6.]], [[7., 8., 9.], [10., 11., 12.]]] Q, L = gelqf(A) Q = [[[-0.26726124, -0.53452248, -0.80178373], [0.87287156, 0.21821789, -0.43643578]], [[-0.50257071, -0.57436653, -0.64616234], [0.7620735, 0.05862104, -0.64483142]]] L = [[[-3.74165739, 0.], [-8.55235974, 1.96396101]], [[-13.92838828, 0.], [-19.09768702, 0.52758934]]]
Defined in src/operator/tensor/la_op.cc:L552
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
linalg_gemm
(A=None, B=None, C=None, transpose_a=_Null, transpose_b=_Null, alpha=_Null, beta=_Null, axis=_Null, out=None, name=None, **kwargs)¶ Performs general matrix multiplication and accumulation. Input are tensors A, B, C, each of dimension n >= 2 and having the same shape on the leading n-2 dimensions.
If n=2, the BLAS3 function gemm is performed:
out = alpha * op(A) * op(B) + beta * CHere, alpha and beta are scalar parameters, and op() is either the identity or matrix transposition (depending on transpose_a, transpose_b).
If n>2, gemm is performed separately for a batch of matrices. The column indices of the matrices are given by the last dimensions of the tensors, the row indices by the axis specified with the axis parameter. By default, the trailing two dimensions will be used for matrix encoding.
For a non-default axis parameter, the operation performed is equivalent to a series of swapaxes/gemm/swapaxes calls. For example let A, B, C be 5 dimensional tensors. Then gemm(A, B, C, axis=1) is equivalent to
A1 = swapaxes(A, dim1=1, dim2=3) B1 = swapaxes(B, dim1=1, dim2=3) C = swapaxes(C, dim1=1, dim2=3) C = gemm(A1, B1, C) C = swapaxis(C, dim1=1, dim2=3)without the overhead of the additional swapaxis operations.
Note
The operator supports float32 and float64 data types only.
Examples:
// Single matrix multiply-add A = [[1.0, 1.0], [1.0, 1.0]] B = [[1.0, 1.0], [1.0, 1.0], [1.0, 1.0]] C = [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]] gemm(A, B, C, transpose_b=True, alpha=2.0, beta=10.0) = [[14.0, 14.0, 14.0], [14.0, 14.0, 14.0]] // Batch matrix multiply-add A = [[[1.0, 1.0]], [[0.1, 0.1]]] B = [[[1.0, 1.0]], [[0.1, 0.1]]] C = [[[10.0]], [[0.01]]] gemm(A, B, C, transpose_b=True, alpha=2.0 , beta=10.0) = [[[104.0]], [[0.14]]]
Defined in src/operator/tensor/la_op.cc:L81
Parameters: - A (NDArray) – Tensor of input matrices
- B (NDArray) – Tensor of input matrices
- C (NDArray) – Tensor of input matrices
- transpose_a (boolean, optional, default=0) – Multiply with transposed of first input (A).
- transpose_b (boolean, optional, default=0) – Multiply with transposed of second input (B).
- alpha (double, optional, default=1) – Scalar factor multiplied with A*B.
- beta (double, optional, default=1) – Scalar factor multiplied with C.
- axis (int, optional, default='-2') – Axis corresponding to the matrix rows.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
linalg_gemm2
(A=None, B=None, transpose_a=_Null, transpose_b=_Null, alpha=_Null, axis=_Null, out=None, name=None, **kwargs)¶ Performs general matrix multiplication. Input are tensors A, B, each of dimension n >= 2 and having the same shape on the leading n-2 dimensions.
If n=2, the BLAS3 function gemm is performed:
out = alpha * op(A) * op(B)Here alpha is a scalar parameter and op() is either the identity or the matrix transposition (depending on transpose_a, transpose_b).
If n>2, gemm is performed separately for a batch of matrices. The column indices of the matrices are given by the last dimensions of the tensors, the row indices by the axis specified with the axis parameter. By default, the trailing two dimensions will be used for matrix encoding.
For a non-default axis parameter, the operation performed is equivalent to a series of swapaxes/gemm/swapaxes calls. For example let A, B be 5 dimensional tensors. Then gemm(A, B, axis=1) is equivalent to
A1 = swapaxes(A, dim1=1, dim2=3) B1 = swapaxes(B, dim1=1, dim2=3) C = gemm2(A1, B1) C = swapaxis(C, dim1=1, dim2=3)without the overhead of the additional swapaxis operations.
Note
The operator supports float32 and float64 data types only.
Examples:
// Single matrix multiply A = [[1.0, 1.0], [1.0, 1.0]] B = [[1.0, 1.0], [1.0, 1.0], [1.0, 1.0]] gemm2(A, B, transpose_b=True, alpha=2.0) = [[4.0, 4.0, 4.0], [4.0, 4.0, 4.0]] // Batch matrix multiply A = [[[1.0, 1.0]], [[0.1, 0.1]]] B = [[[1.0, 1.0]], [[0.1, 0.1]]] gemm2(A, B, transpose_b=True, alpha=2.0) = [[[4.0]], [[0.04 ]]]
Defined in src/operator/tensor/la_op.cc:L151
Parameters: - A (NDArray) – Tensor of input matrices
- B (NDArray) – Tensor of input matrices
- transpose_a (boolean, optional, default=0) – Multiply with transposed of first input (A).
- transpose_b (boolean, optional, default=0) – Multiply with transposed of second input (B).
- alpha (double, optional, default=1) – Scalar factor multiplied with A*B.
- axis (int, optional, default='-2') – Axis corresponding to the matrix row indices.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
linalg_potrf
(A=None, out=None, name=None, **kwargs)¶ Performs Cholesky factorization of a symmetric positive-definite matrix. Input is a tensor A of dimension n >= 2.
If n=2, the Cholesky factor L of the symmetric, positive definite matrix A is computed. L is lower triangular (entries of upper triangle are all zero), has positive diagonal entries, and:
A = L * LTIf n>2, potrf is performed separately on the trailing two dimensions for all inputs (batch mode).
Note
The operator supports float32 and float64 data types only.
Examples:
// Single matrix factorization A = [[4.0, 1.0], [1.0, 4.25]] potrf(A) = [[2.0, 0], [0.5, 2.0]] // Batch matrix factorization A = [[[4.0, 1.0], [1.0, 4.25]], [[16.0, 4.0], [4.0, 17.0]]] potrf(A) = [[[2.0, 0], [0.5, 2.0]], [[4.0, 0], [1.0, 4.0]]]
Defined in src/operator/tensor/la_op.cc:L201
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
linalg_potri
(A=None, out=None, name=None, **kwargs)¶ Performs matrix inversion from a Cholesky factorization. Input is a tensor A of dimension n >= 2.
If n=2, A is a lower triangular matrix (entries of upper triangle are all zero) with positive diagonal. We compute:
out = A-T * A-1In other words, if A is the Cholesky factor of a symmetric positive definite matrix B (obtained by potrf), then
out = B-1If n>2, potri is performed separately on the trailing two dimensions for all inputs (batch mode).
Note
The operator supports float32 and float64 data types only.
Note
Use this operator only if you are certain you need the inverse of B, and cannot use the Cholesky factor A (potrf), together with backsubstitution (trsm). The latter is numerically much safer, and also cheaper.
Examples:
// Single matrix inverse A = [[2.0, 0], [0.5, 2.0]] potri(A) = [[0.26563, -0.0625], [-0.0625, 0.25]] // Batch matrix inverse A = [[[2.0, 0], [0.5, 2.0]], [[4.0, 0], [1.0, 4.0]]] potri(A) = [[[0.26563, -0.0625], [-0.0625, 0.25]], [[0.06641, -0.01562], [-0.01562, 0,0625]]]
Defined in src/operator/tensor/la_op.cc:L259
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
linalg_sumlogdiag
(A=None, out=None, name=None, **kwargs)¶ Computes the sum of the logarithms of the diagonal elements of a square matrix. Input is a tensor A of dimension n >= 2.
If n=2, A must be square with positive diagonal entries. We sum the natural logarithms of the diagonal elements, the result has shape (1,).
If n>2, sumlogdiag is performed separately on the trailing two dimensions for all inputs (batch mode).
Note
The operator supports float32 and float64 data types only.
Examples:
// Single matrix reduction A = [[1.0, 1.0], [1.0, 7.0]] sumlogdiag(A) = [1.9459] // Batch matrix reduction A = [[[1.0, 1.0], [1.0, 7.0]], [[3.0, 0], [0, 17.0]]] sumlogdiag(A) = [1.9459, 3.9318]
Defined in src/operator/tensor/la_op.cc:L428
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
linalg_syrk
(A=None, transpose=_Null, alpha=_Null, out=None, name=None, **kwargs)¶ Multiplication of matrix with its transpose. Input is a tensor A of dimension n >= 2.
If n=2, the operator performs the BLAS3 function syrk:
out = alpha * A * ATif transpose=False, or
out = alpha * AT * Aif transpose=True.
If n>2, syrk is performed separately on the trailing two dimensions for all inputs (batch mode).
Note
The operator supports float32 and float64 data types only.
Examples:
// Single matrix multiply A = [[1., 2., 3.], [4., 5., 6.]] syrk(A, alpha=1., transpose=False) = [[14., 32.], [32., 77.]] syrk(A, alpha=1., transpose=True) = [[17., 22., 27.], [22., 29., 36.], [27., 36., 45.]] // Batch matrix multiply A = [[[1., 1.]], [[0.1, 0.1]]] syrk(A, alpha=2., transpose=False) = [[[4.]], [[0.04]]]
Defined in src/operator/tensor/la_op.cc:L484
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
linalg_trmm
(A=None, B=None, transpose=_Null, rightside=_Null, alpha=_Null, out=None, name=None, **kwargs)¶ Performs multiplication with a lower triangular matrix. Input are tensors A, B, each of dimension n >= 2 and having the same shape on the leading n-2 dimensions.
If n=2, A must be lower triangular. The operator performs the BLAS3 function trmm:
out = alpha * op(A) * Bif rightside=False, or
out = alpha * B * op(A)if rightside=True. Here, alpha is a scalar parameter, and op() is either the identity or the matrix transposition (depending on transpose).
If n>2, trmm is performed separately on the trailing two dimensions for all inputs (batch mode).
Note
The operator supports float32 and float64 data types only.
Examples:
// Single triangular matrix multiply A = [[1.0, 0], [1.0, 1.0]] B = [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]] trmm(A, B, alpha=2.0) = [[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]] // Batch triangular matrix multiply A = [[[1.0, 0], [1.0, 1.0]], [[1.0, 0], [1.0, 1.0]]] B = [[[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]], [[0.5, 0.5, 0.5], [0.5, 0.5, 0.5]]] trmm(A, B, alpha=2.0) = [[[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]], [[1.0, 1.0, 1.0], [2.0, 2.0, 2.0]]]
Defined in src/operator/tensor/la_op.cc:L316
Parameters: - A (NDArray) – Tensor of lower triangular matrices
- B (NDArray) – Tensor of matrices
- transpose (boolean, optional, default=0) – Use transposed of the triangular matrix
- rightside (boolean, optional, default=0) – Multiply triangular matrix from the right to non-triangular one.
- alpha (double, optional, default=1) – Scalar factor to be applied to the result.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
linalg_trsm
(A=None, B=None, transpose=_Null, rightside=_Null, alpha=_Null, out=None, name=None, **kwargs)¶ Solves matrix equation involving a lower triangular matrix. Input are tensors A, B, each of dimension n >= 2 and having the same shape on the leading n-2 dimensions.
If n=2, A must be lower triangular. The operator performs the BLAS3 function trsm, solving for out in:
op(A) * out = alpha * Bif rightside=False, or
out * op(A) = alpha * Bif rightside=True. Here, alpha is a scalar parameter, and op() is either the identity or the matrix transposition (depending on transpose).
If n>2, trsm is performed separately on the trailing two dimensions for all inputs (batch mode).
Note
The operator supports float32 and float64 data types only.
Examples:
// Single matrix solve A = [[1.0, 0], [1.0, 1.0]] B = [[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]] trsm(A, B, alpha=0.5) = [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]] // Batch matrix solve A = [[[1.0, 0], [1.0, 1.0]], [[1.0, 0], [1.0, 1.0]]] B = [[[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]], [[4.0, 4.0, 4.0], [8.0, 8.0, 8.0]]] trsm(A, B, alpha=0.5) = [[[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]], [[2.0, 2.0, 2.0], [2.0, 2.0, 2.0]]]
Defined in src/operator/tensor/la_op.cc:L379
Parameters: - A (NDArray) – Tensor of lower triangular matrices
- B (NDArray) – Tensor of matrices
- transpose (boolean, optional, default=0) – Use transposed of the triangular matrix
- rightside (boolean, optional, default=0) – Multiply triangular matrix from the right to non-triangular one.
- alpha (double, optional, default=1) – Scalar factor to be applied to the result.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
log
(data=None, out=None, name=None, **kwargs)¶ Returns element-wise Natural logarithmic value of the input.
The natural logarithm is logarithm in base e, so that
log(exp(x)) = x
The storage type of
log
output is always denseDefined in src/operator/tensor/elemwise_unary_op_basic.cc:L941
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
log10
(data=None, out=None, name=None, **kwargs)¶ Returns element-wise Base-10 logarithmic value of the input.
10**log10(x) = x
The storage type of
log10
output is always denseDefined in src/operator/tensor/elemwise_unary_op_basic.cc:L953
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
log1p
(data=None, out=None, name=None, **kwargs)¶ Returns element-wise
log(1 + x)
value of the input.This function is more accurate than
log(1 + x)
for smallx
so that \(1+x\approx 1\)The storage type of
log1p
output depends upon the input storage type:- log1p(default) = default
- log1p(row_sparse) = row_sparse
- log1p(csr) = csr
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L990
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
log2
(data=None, out=None, name=None, **kwargs)¶ Returns element-wise Base-2 logarithmic value of the input.
2**log2(x) = x
The storage type of
log2
output is always denseDefined in src/operator/tensor/elemwise_unary_op_basic.cc:L965
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
log_softmax
(data=None, axis=_Null, temperature=_Null, out=None, name=None, **kwargs)¶ Computes the log softmax of the input. This is equivalent to computing softmax followed by log.
Examples:
>>> x = mx.nd.array([1, 2, .1]) >>> mx.nd.log_softmax(x).asnumpy() array([-1.41702998, -0.41702995, -2.31702995], dtype=float32) >>> x = mx.nd.array( [[1, 2, .1],[.1, 2, 1]] ) >>> mx.nd.log_softmax(x, axis=0).asnumpy() array([[-0.34115392, -0.69314718, -1.24115396], [-1.24115396, -0.69314718, -0.34115392]], dtype=float32)
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
logical_not
(data=None, out=None, name=None, **kwargs)¶ Returns the result of logical NOT (!) function
Example
logical_not([-2., 0., 1.]) = [0., 1., 0.]
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
make_loss
(data=None, out=None, name=None, **kwargs)¶ Make your own loss function in network construction.
This operator accepts a customized loss function symbol as a terminal loss and the symbol should be an operator with no backward dependency. The output of this function is the gradient of loss with respect to the input data.
For example, if you are a making a cross entropy loss function. Assume
out
is the predicted output andlabel
is the true label, then the cross entropy can be defined as:cross_entropy = label * log(out) + (1 - label) * log(1 - out) loss = make_loss(cross_entropy)
We will need to use
make_loss
when we are creating our own loss function or we want to combine multiple loss functions. Also we may want to stop some variables’ gradients from backpropagation. See more detail inBlockGrad
orstop_gradient
.The storage type of
make_loss
output depends upon the input storage type:- make_loss(default) = default
- make_loss(row_sparse) = row_sparse
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L298
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
max
(data=None, axis=_Null, keepdims=_Null, exclude=_Null, out=None, name=None, **kwargs)¶ Computes the max of array elements over given axes.
Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L190
Parameters: - data (NDArray) – The input
- axis (Shape or None, optional, default=None) –
The axis or axes along which to perform the reduction.
The default, axis=(), will compute over all elements into a scalar array with shape (1,).If axis is int, a reduction is performed on a particular axis.
If axis is a tuple of ints, a reduction is performed on all the axes specified in the tuple.
If exclude is true, reduction will be performed on the axes that are NOT in axis instead.
Negative values means indexing from right to left.
- keepdims (boolean, optional, default=0) – If this is set to True, the reduced axes are left in the result as dimension with size one.
- exclude (boolean, optional, default=0) – Whether to perform reduction on axis that are NOT in axis instead.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
max_axis
(data=None, axis=_Null, keepdims=_Null, exclude=_Null, out=None, name=None, **kwargs)¶ Computes the max of array elements over given axes.
Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L190
Parameters: - data (NDArray) – The input
- axis (Shape or None, optional, default=None) –
The axis or axes along which to perform the reduction.
The default, axis=(), will compute over all elements into a scalar array with shape (1,).If axis is int, a reduction is performed on a particular axis.
If axis is a tuple of ints, a reduction is performed on all the axes specified in the tuple.
If exclude is true, reduction will be performed on the axes that are NOT in axis instead.
Negative values means indexing from right to left.
- keepdims (boolean, optional, default=0) – If this is set to True, the reduced axes are left in the result as dimension with size one.
- exclude (boolean, optional, default=0) – Whether to perform reduction on axis that are NOT in axis instead.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
mean
(data=None, axis=_Null, keepdims=_Null, exclude=_Null, out=None, name=None, **kwargs)¶ Computes the mean of array elements over given axes.
Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L131
Parameters: - data (NDArray) – The input
- axis (Shape or None, optional, default=None) –
The axis or axes along which to perform the reduction.
The default, axis=(), will compute over all elements into a scalar array with shape (1,).If axis is int, a reduction is performed on a particular axis.
If axis is a tuple of ints, a reduction is performed on all the axes specified in the tuple.
If exclude is true, reduction will be performed on the axes that are NOT in axis instead.
Negative values means indexing from right to left.
- keepdims (boolean, optional, default=0) – If this is set to True, the reduced axes are left in the result as dimension with size one.
- exclude (boolean, optional, default=0) – Whether to perform reduction on axis that are NOT in axis instead.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
min
(data=None, axis=_Null, keepdims=_Null, exclude=_Null, out=None, name=None, **kwargs)¶ Computes the min of array elements over given axes.
Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L204
Parameters: - data (NDArray) – The input
- axis (Shape or None, optional, default=None) –
The axis or axes along which to perform the reduction.
The default, axis=(), will compute over all elements into a scalar array with shape (1,).If axis is int, a reduction is performed on a particular axis.
If axis is a tuple of ints, a reduction is performed on all the axes specified in the tuple.
If exclude is true, reduction will be performed on the axes that are NOT in axis instead.
Negative values means indexing from right to left.
- keepdims (boolean, optional, default=0) – If this is set to True, the reduced axes are left in the result as dimension with size one.
- exclude (boolean, optional, default=0) – Whether to perform reduction on axis that are NOT in axis instead.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
min_axis
(data=None, axis=_Null, keepdims=_Null, exclude=_Null, out=None, name=None, **kwargs)¶ Computes the min of array elements over given axes.
Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L204
Parameters: - data (NDArray) – The input
- axis (Shape or None, optional, default=None) –
The axis or axes along which to perform the reduction.
The default, axis=(), will compute over all elements into a scalar array with shape (1,).If axis is int, a reduction is performed on a particular axis.
If axis is a tuple of ints, a reduction is performed on all the axes specified in the tuple.
If exclude is true, reduction will be performed on the axes that are NOT in axis instead.
Negative values means indexing from right to left.
- keepdims (boolean, optional, default=0) – If this is set to True, the reduced axes are left in the result as dimension with size one.
- exclude (boolean, optional, default=0) – Whether to perform reduction on axis that are NOT in axis instead.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
mp_sgd_mom_update
(weight=None, grad=None, mom=None, weight32=None, lr=_Null, momentum=_Null, wd=_Null, rescale_grad=_Null, clip_gradient=_Null, lazy_update=_Null, out=None, name=None, **kwargs)¶ Updater function for multi-precision sgd optimizer
Parameters: - weight (NDArray) – Weight
- grad (NDArray) – Gradient
- mom (NDArray) – Momentum
- weight32 (NDArray) – Weight32
- lr (float, required) – Learning rate
- momentum (float, optional, default=0) – The decay rate of momentum estimates at each epoch.
- wd (float, optional, default=0) – Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.
- rescale_grad (float, optional, default=1) – Rescale gradient to grad = rescale_grad*grad.
- clip_gradient (float, optional, default=-1) – Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).
- lazy_update (boolean, optional, default=1) – If true, lazy updates are applied if gradient’s stype is row_sparse and both weight and momentum have the same stype
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
mp_sgd_update
(weight=None, grad=None, weight32=None, lr=_Null, wd=_Null, rescale_grad=_Null, clip_gradient=_Null, lazy_update=_Null, out=None, name=None, **kwargs)¶ Updater function for multi-precision sgd optimizer
Parameters: - weight (NDArray) – Weight
- grad (NDArray) – gradient
- weight32 (NDArray) – Weight32
- lr (float, required) – Learning rate
- wd (float, optional, default=0) – Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.
- rescale_grad (float, optional, default=1) – Rescale gradient to grad = rescale_grad*grad.
- clip_gradient (float, optional, default=-1) – Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).
- lazy_update (boolean, optional, default=1) – If true, lazy updates are applied if gradient’s stype is row_sparse.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
nanprod
(data=None, axis=_Null, keepdims=_Null, exclude=_Null, out=None, name=None, **kwargs)¶ Computes the product of array elements over given axes treating Not a Numbers (
NaN
) as one.Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L176
Parameters: - data (NDArray) – The input
- axis (Shape or None, optional, default=None) –
The axis or axes along which to perform the reduction.
The default, axis=(), will compute over all elements into a scalar array with shape (1,).If axis is int, a reduction is performed on a particular axis.
If axis is a tuple of ints, a reduction is performed on all the axes specified in the tuple.
If exclude is true, reduction will be performed on the axes that are NOT in axis instead.
Negative values means indexing from right to left.
- keepdims (boolean, optional, default=0) – If this is set to True, the reduced axes are left in the result as dimension with size one.
- exclude (boolean, optional, default=0) – Whether to perform reduction on axis that are NOT in axis instead.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
nansum
(data=None, axis=_Null, keepdims=_Null, exclude=_Null, out=None, name=None, **kwargs)¶ Computes the sum of array elements over given axes treating Not a Numbers (
NaN
) as zero.Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L161
Parameters: - data (NDArray) – The input
- axis (Shape or None, optional, default=None) –
The axis or axes along which to perform the reduction.
The default, axis=(), will compute over all elements into a scalar array with shape (1,).If axis is int, a reduction is performed on a particular axis.
If axis is a tuple of ints, a reduction is performed on all the axes specified in the tuple.
If exclude is true, reduction will be performed on the axes that are NOT in axis instead.
Negative values means indexing from right to left.
- keepdims (boolean, optional, default=0) – If this is set to True, the reduced axes are left in the result as dimension with size one.
- exclude (boolean, optional, default=0) – Whether to perform reduction on axis that are NOT in axis instead.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
negative
(data=None, out=None, name=None, **kwargs)¶ Numerical negative of the argument, element-wise.
The storage type of
negative
output depends upon the input storage type:- negative(default) = default
- negative(row_sparse) = row_sparse
- negative(csr) = csr
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
norm
(data=None, ord=_Null, axis=_Null, keepdims=_Null, out=None, name=None, **kwargs)¶ Computes the norm on an NDArray.
This operator computes the norm on an NDArray with the specified axis, depending on the value of the ord parameter. By default, it computes the L2 norm on the entire array. Currently only ord=2 supports sparse ndarrays.
Examples:
x = [[[1, 2], [3, 4]], [[2, 2], [5, 6]]] norm(x, ord=2, axis=1) = [[3.1622777 4.472136 ] [5.3851647 6.3245554]] norm(x, ord=1, axis=1) = [[4., 6.], [7., 8.]] rsp = x.cast_storage('row_sparse') norm(rsp) = [5.47722578] csr = x.cast_storage('csr') norm(csr) = [5.47722578]
Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L345
Parameters: - data (NDArray) – The input
- ord (int, optional, default='2') – Order of the norm. Currently ord=1 and ord=2 is supported.
- axis (Shape or None, optional, default=None) –
- The axis or axes along which to perform the reduction.
- The default, axis=(), will compute over all elements into a scalar array with shape (1,). If axis is int, a reduction is performed on a particular axis. If axis is a 2-tuple, it specifies the axes that hold 2-D matrices, and the matrix norms of these matrices are computed.
- keepdims (boolean, optional, default=0) – If this is set to True, the reduced axis is left in the result as dimension with size one.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
normal
(loc=_Null, scale=_Null, shape=_Null, ctx=_Null, dtype=_Null, out=None, name=None, **kwargs)¶ Draw random samples from a normal (Gaussian) distribution.
Note
The existing alias
normal
is deprecated.Samples are distributed according to a normal distribution parametrized by loc (mean) and scale (standard deviation).
Example:
normal(loc=0, scale=1, shape=(2,2)) = [[ 1.89171135, -1.16881478], [-1.23474145, 1.55807114]]
Defined in src/operator/random/sample_op.cc:L112
Parameters: - loc (float, optional, default=0) – Mean of the distribution.
- scale (float, optional, default=1) – Standard deviation of the distribution.
- shape (Shape(tuple), optional, default=[]) – Shape of the output.
- ctx (string, optional, default='') – Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls.
- dtype ({'None', 'float16', 'float32', 'float64'},optional, default='None') – DType of the output in case this can’t be inferred. Defaults to float32 if not defined (dtype=None).
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
one_hot
(indices=None, depth=_Null, on_value=_Null, off_value=_Null, dtype=_Null, out=None, name=None, **kwargs)¶ Returns a one-hot array.
The locations represented by indices take value on_value, while all other locations take value off_value.
one_hot operation with indices of shape
(i0, i1)
and depth ofd
would result in an output array of shape(i0, i1, d)
with:output[i,j,:] = off_value output[i,j,indices[i,j]] = on_value
Examples:
one_hot([1,0,2,0], 3) = [[ 0. 1. 0.] [ 1. 0. 0.] [ 0. 0. 1.] [ 1. 0. 0.]] one_hot([1,0,2,0], 3, on_value=8, off_value=1, dtype='int32') = [[1 8 1] [8 1 1] [1 1 8] [8 1 1]] one_hot([[1,0],[1,0],[2,0]], 3) = [[[ 0. 1. 0.] [ 1. 0. 0.]] [[ 0. 1. 0.] [ 1. 0. 0.]] [[ 0. 0. 1.] [ 1. 0. 0.]]]
Defined in src/operator/tensor/indexing_op.cc:L536
Parameters: - indices (NDArray) – array of locations where to set on_value
- depth (int, required) – Depth of the one hot dimension.
- on_value (double, optional, default=1) – The value assigned to the locations represented by indices.
- off_value (double, optional, default=0) – The value assigned to the locations not represented by indices.
- dtype ({'float16', 'float32', 'float64', 'int32', 'int64', 'int8', 'uint8'},optional, default='float32') – DType of the output
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
ones_like
(data=None, out=None, name=None, **kwargs)¶ Return an array of ones with the same shape and type as the input array.
Examples:
x = [[ 0., 0., 0.], [ 0., 0., 0.]] ones_like(x) = [[ 1., 1., 1.], [ 1., 1., 1.]]
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
pad
(data=None, mode=_Null, pad_width=_Null, constant_value=_Null, out=None, name=None, **kwargs)¶ Pads an input array with a constant or edge values of the array.
Note
Pad is deprecated. Use pad instead.
Note
Current implementation only supports 4D and 5D input arrays with padding applied only on axes 1, 2 and 3. Expects axes 4 and 5 in pad_width to be zero.
This operation pads an input array with either a constant_value or edge values along each axis of the input array. The amount of padding is specified by pad_width.
pad_width is a tuple of integer padding widths for each axis of the format
(before_1, after_1, ... , before_N, after_N)
. The pad_width should be of length2*N
whereN
is the number of dimensions of the array.For dimension
N
of the input array,before_N
andafter_N
indicates how many values to add before and after the elements of the array along dimensionN
. The widths of the higher two dimensionsbefore_1
,after_1
,before_2
,after_2
must be 0.Example:
x = [[[[ 1. 2. 3.] [ 4. 5. 6.]] [[ 7. 8. 9.] [ 10. 11. 12.]]] [[[ 11. 12. 13.] [ 14. 15. 16.]] [[ 17. 18. 19.] [ 20. 21. 22.]]]] pad(x,mode="edge", pad_width=(0,0,0,0,1,1,1,1)) = [[[[ 1. 1. 2. 3. 3.] [ 1. 1. 2. 3. 3.] [ 4. 4. 5. 6. 6.] [ 4. 4. 5. 6. 6.]] [[ 7. 7. 8. 9. 9.] [ 7. 7. 8. 9. 9.] [ 10. 10. 11. 12. 12.] [ 10. 10. 11. 12. 12.]]] [[[ 11. 11. 12. 13. 13.] [ 11. 11. 12. 13. 13.] [ 14. 14. 15. 16. 16.] [ 14. 14. 15. 16. 16.]] [[ 17. 17. 18. 19. 19.] [ 17. 17. 18. 19. 19.] [ 20. 20. 21. 22. 22.] [ 20. 20. 21. 22. 22.]]]] pad(x, mode="constant", constant_value=0, pad_width=(0,0,0,0,1,1,1,1)) = [[[[ 0. 0. 0. 0. 0.] [ 0. 1. 2. 3. 0.] [ 0. 4. 5. 6. 0.] [ 0. 0. 0. 0. 0.]] [[ 0. 0. 0. 0. 0.] [ 0. 7. 8. 9. 0.] [ 0. 10. 11. 12. 0.] [ 0. 0. 0. 0. 0.]]] [[[ 0. 0. 0. 0. 0.] [ 0. 11. 12. 13. 0.] [ 0. 14. 15. 16. 0.] [ 0. 0. 0. 0. 0.]] [[ 0. 0. 0. 0. 0.] [ 0. 17. 18. 19. 0.] [ 0. 20. 21. 22. 0.] [ 0. 0. 0. 0. 0.]]]]
Defined in src/operator/pad.cc:L766
Parameters: - data (NDArray) – An n-dimensional input array.
- mode ({'constant', 'edge', 'reflect'}, required) – Padding type to use. “constant” pads with constant_value “edge” pads using the edge values of the input array “reflect” pads by reflecting values with respect to the edges.
- pad_width (Shape(tuple), required) – Widths of the padding regions applied to the edges of each axis. It is a tuple of integer padding widths for each axis of the format
(before_1, after_1, ... , before_N, after_N)
. It should be of length2*N
whereN
is the number of dimensions of the array.This is equivalent to pad_width in numpy.pad, but flattened. - constant_value (double, optional, default=0) – The value used for padding when mode is “constant”.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
pick
(data=None, index=None, axis=_Null, keepdims=_Null, mode=_Null, out=None, name=None, **kwargs)¶ Picks elements from an input array according to the input indices along the given axis.
Given an input array of shape
(d0, d1)
and indices of shape(i0,)
, the result will be an output array of shape(i0,)
with:output[i] = input[i, indices[i]]
By default, if any index mentioned is too large, it is replaced by the index that addresses the last element along an axis (the clip mode).
This function supports n-dimensional input and (n-1)-dimensional indices arrays.
Examples:
x = [[ 1., 2.], [ 3., 4.], [ 5., 6.]] // picks elements with specified indices along axis 0 pick(x, y=[0,1], 0) = [ 1., 4.] // picks elements with specified indices along axis 1 pick(x, y=[0,1,0], 1) = [ 1., 4., 5.] y = [[ 1.], [ 0.], [ 2.]] // picks elements with specified indices along axis 1 using 'wrap' mode // to place indicies that would normally be out of bounds pick(x, y=[2,-1,-2], 1, mode='wrap') = [ 1., 4., 5.] y = [[ 1.], [ 0.], [ 2.]] // picks elements with specified indices along axis 1 and dims are maintained pick(x,y, 1, keepdims=True) = [[ 2.], [ 3.], [ 6.]]
Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L153
Parameters: - data (NDArray) – The input array
- index (NDArray) – The index array
- axis (int or None, optional, default='-1') – int or None. The axis to picking the elements. Negative values means indexing from right to left. If is None, the elements in the index w.r.t the flattened input will be picked.
- keepdims (boolean, optional, default=0) – If true, the axis where we pick the elements is left in the result as dimension with size one.
- mode ({'clip', 'wrap'},optional, default='clip') – Specify how out-of-bound indices behave. Default is “clip”. “clip” means clip to the range. So, if all indices mentioned are too large, they are replaced by the index that addresses the last element along an axis. “wrap” means to wrap around.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
prod
(data=None, axis=_Null, keepdims=_Null, exclude=_Null, out=None, name=None, **kwargs)¶ Computes the product of array elements over given axes.
Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L146
Parameters: - data (NDArray) – The input
- axis (Shape or None, optional, default=None) –
The axis or axes along which to perform the reduction.
The default, axis=(), will compute over all elements into a scalar array with shape (1,).If axis is int, a reduction is performed on a particular axis.
If axis is a tuple of ints, a reduction is performed on all the axes specified in the tuple.
If exclude is true, reduction will be performed on the axes that are NOT in axis instead.
Negative values means indexing from right to left.
- keepdims (boolean, optional, default=0) – If this is set to True, the reduced axes are left in the result as dimension with size one.
- exclude (boolean, optional, default=0) – Whether to perform reduction on axis that are NOT in axis instead.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
radians
(data=None, out=None, name=None, **kwargs)¶ Converts each element of the input array from degrees to radians.
\[radians([0, 90, 180, 270, 360]) = [0, \pi/2, \pi, 3\pi/2, 2\pi]\]The storage type of
radians
output depends upon the input storage type:- radians(default) = default
- radians(row_sparse) = row_sparse
- radians(csr) = csr
Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L182
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
random_exponential
(lam=_Null, shape=_Null, ctx=_Null, dtype=_Null, out=None, name=None, **kwargs)¶ Draw random samples from an exponential distribution.
Samples are distributed according to an exponential distribution parametrized by lambda (rate).
Example:
exponential(lam=4, shape=(2,2)) = [[ 0.0097189 , 0.08999364], [ 0.04146638, 0.31715935]]
Defined in src/operator/random/sample_op.cc:L136
Parameters: - lam (float, optional, default=1) – Lambda parameter (rate) of the exponential distribution.
- shape (Shape(tuple), optional, default=[]) – Shape of the output.
- ctx (string, optional, default='') – Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls.
- dtype ({'None', 'float16', 'float32', 'float64'},optional, default='None') – DType of the output in case this can’t be inferred. Defaults to float32 if not defined (dtype=None).
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
random_gamma
(alpha=_Null, beta=_Null, shape=_Null, ctx=_Null, dtype=_Null, out=None, name=None, **kwargs)¶ Draw random samples from a gamma distribution.
Samples are distributed according to a gamma distribution parametrized by alpha (shape) and beta (scale).
Example:
gamma(alpha=9, beta=0.5, shape=(2,2)) = [[ 7.10486984, 3.37695289], [ 3.91697288, 3.65933681]]
Defined in src/operator/random/sample_op.cc:L124
Parameters: - alpha (float, optional, default=1) – Alpha parameter (shape) of the gamma distribution.
- beta (float, optional, default=1) – Beta parameter (scale) of the gamma distribution.
- shape (Shape(tuple), optional, default=[]) – Shape of the output.
- ctx (string, optional, default='') – Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls.
- dtype ({'None', 'float16', 'float32', 'float64'},optional, default='None') – DType of the output in case this can’t be inferred. Defaults to float32 if not defined (dtype=None).
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
random_generalized_negative_binomial
(mu=_Null, alpha=_Null, shape=_Null, ctx=_Null, dtype=_Null, out=None, name=None, **kwargs)¶ Draw random samples from a generalized negative binomial distribution.
Samples are distributed according to a generalized negative binomial distribution parametrized by mu (mean) and alpha (dispersion). alpha is defined as 1/k where k is the failure limit of the number of unsuccessful experiments (generalized to real numbers). Samples will always be returned as a floating point data type.
Example:
generalized_negative_binomial(mu=2.0, alpha=0.3, shape=(2,2)) = [[ 2., 1.], [ 6., 4.]]
Defined in src/operator/random/sample_op.cc:L178
Parameters: - mu (float, optional, default=1) – Mean of the negative binomial distribution.
- alpha (float, optional, default=1) – Alpha (dispersion) parameter of the negative binomial distribution.
- shape (Shape(tuple), optional, default=[]) – Shape of the output.
- ctx (string, optional, default='') – Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls.
- dtype ({'None', 'float16', 'float32', 'float64'},optional, default='None') – DType of the output in case this can’t be inferred. Defaults to float32 if not defined (dtype=None).
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
random_negative_binomial
(k=_Null, p=_Null, shape=_Null, ctx=_Null, dtype=_Null, out=None, name=None, **kwargs)¶ Draw random samples from a negative binomial distribution.
Samples are distributed according to a negative binomial distribution parametrized by k (limit of unsuccessful experiments) and p (failure probability in each experiment). Samples will always be returned as a floating point data type.
Example:
negative_binomial(k=3, p=0.4, shape=(2,2)) = [[ 4., 7.], [ 2., 5.]]
Defined in src/operator/random/sample_op.cc:L163
Parameters: - k (int, optional, default='1') – Limit of unsuccessful experiments.
- p (float, optional, default=1) – Failure probability in each experiment.
- shape (Shape(tuple), optional, default=[]) – Shape of the output.
- ctx (string, optional, default='') – Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls.
- dtype ({'None', 'float16', 'float32', 'float64'},optional, default='None') – DType of the output in case this can’t be inferred. Defaults to float32 if not defined (dtype=None).
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
random_normal
(loc=_Null, scale=_Null, shape=_Null, ctx=_Null, dtype=_Null, out=None, name=None, **kwargs)¶ Draw random samples from a normal (Gaussian) distribution.
Note
The existing alias
normal
is deprecated.Samples are distributed according to a normal distribution parametrized by loc (mean) and scale (standard deviation).
Example:
normal(loc=0, scale=1, shape=(2,2)) = [[ 1.89171135, -1.16881478], [-1.23474145, 1.55807114]]
Defined in src/operator/random/sample_op.cc:L112
Parameters: - loc (float, optional, default=0) – Mean of the distribution.
- scale (float, optional, default=1) – Standard deviation of the distribution.
- shape (Shape(tuple), optional, default=[]) – Shape of the output.
- ctx (string, optional, default='') – Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls.
- dtype ({'None', 'float16', 'float32', 'float64'},optional, default='None') – DType of the output in case this can’t be inferred. Defaults to float32 if not defined (dtype=None).
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
random_poisson
(lam=_Null, shape=_Null, ctx=_Null, dtype=_Null, out=None, name=None, **kwargs)¶ Draw random samples from a Poisson distribution.
Samples are distributed according to a Poisson distribution parametrized by lambda (rate). Samples will always be returned as a floating point data type.
Example:
poisson(lam=4, shape=(2,2)) = [[ 5., 2.], [ 4., 6.]]
Defined in src/operator/random/sample_op.cc:L149
Parameters: - lam (float, optional, default=1) – Lambda parameter (rate) of the Poisson distribution.
- shape (Shape(tuple), optional, default=[]) – Shape of the output.
- ctx (string, optional, default='') – Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls.
- dtype ({'None', 'float16', 'float32', 'float64'},optional, default='None') – DType of the output in case this can’t be inferred. Defaults to float32 if not defined (dtype=None).
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
random_uniform
(low=_Null, high=_Null, shape=_Null, ctx=_Null, dtype=_Null, out=None, name=None, **kwargs)¶ Draw random samples from a uniform distribution.
Note
The existing alias
uniform
is deprecated.Samples are uniformly distributed over the half-open interval [low, high) (includes low, but excludes high).
Example:
uniform(low=0, high=1, shape=(2,2)) = [[ 0.60276335, 0.85794562], [ 0.54488319, 0.84725171]]
Defined in src/operator/random/sample_op.cc:L95
Parameters: - low (float, optional, default=0) – Lower bound of the distribution.
- high (float, optional, default=1) – Upper bound of the distribution.
- shape (Shape(tuple), optional, default=[]) – Shape of the output.
- ctx (string, optional, default='') – Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls.
- dtype ({'None', 'float16', 'float32', 'float64'},optional, default='None') – DType of the output in case this can’t be inferred. Defaults to float32 if not defined (dtype=None).
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
ravel_multi_index
(data=None, shape=_Null, out=None, name=None, **kwargs)¶ Converts a batch of index arrays into an array of flat indices. The operator follows numpy conventions so a single multi index is given by a column of the input matrix.
Examples:
A = [[3,6,6],[4,5,1]] ravel(A, shape=(7,6)) = [22,41,37]
Defined in src/operator/tensor/ravel.cc:L41
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
rcbrt
(data=None, out=None, name=None, **kwargs)¶ Returns element-wise inverse cube-root value of the input.
\[rcbrt(x) = 1/\sqrt[3]{x}\]Example:
rcbrt([1,8,-125]) = [1.0, 0.5, -0.2]
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L906
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
reciprocal
(data=None, out=None, name=None, **kwargs)¶ Returns the reciprocal of the argument, element-wise.
Calculates 1/x.
Example:
reciprocal([-2, 1, 3, 1.6.0, 0.2]) = [-0.5, 1.0, 0.33333334, 0.625, 5.0]
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L646
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
relu
(data=None, out=None, name=None, **kwargs)¶ Computes rectified linear.
\[max(features, 0)\]The storage type of
relu
output depends upon the input storage type:- relu(default) = default
- relu(row_sparse) = row_sparse
- relu(csr) = csr
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L85
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
repeat
(data=None, repeats=_Null, axis=_Null, out=None, name=None, **kwargs)¶ Repeats elements of an array.
By default,
repeat
flattens the input array into 1-D and then repeats the elements:x = [[ 1, 2], [ 3, 4]] repeat(x, repeats=2) = [ 1., 1., 2., 2., 3., 3., 4., 4.]
The parameter
axis
specifies the axis along which to perform repeat:repeat(x, repeats=2, axis=1) = [[ 1., 1., 2., 2.], [ 3., 3., 4., 4.]] repeat(x, repeats=2, axis=0) = [[ 1., 2.], [ 1., 2.], [ 3., 4.], [ 3., 4.]] repeat(x, repeats=2, axis=-1) = [[ 1., 1., 2., 2.], [ 3., 3., 4., 4.]]
Defined in src/operator/tensor/matrix_op.cc:L691
Parameters: - data (NDArray) – Input data array
- repeats (int, required) – The number of repetitions for each element.
- axis (int or None, optional, default='None') – The axis along which to repeat values. The negative numbers are interpreted counting from the backward. By default, use the flattened input array, and return a flat output array.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
reshape
(data=None, shape=_Null, reverse=_Null, target_shape=_Null, keep_highest=_Null, out=None, name=None, **kwargs)¶ Reshapes the input array.
Note
Reshape
is deprecated, usereshape
Given an array and a shape, this function returns a copy of the array in the new shape. The shape is a tuple of integers such as (2,3,4). The size of the new shape should be same as the size of the input array.
Example:
reshape([1,2,3,4], shape=(2,2)) = [[1,2], [3,4]]
Some dimensions of the shape can take special values from the set {0, -1, -2, -3, -4}. The significance of each is explained below:
0
copy this dimension from the input to the output shape.Example:
- input shape = (2,3,4), shape = (4,0,2), output shape = (4,3,2) - input shape = (2,3,4), shape = (2,0,0), output shape = (2,3,4)
-1
infers the dimension of the output shape by using the remainder of the input dimensions keeping the size of the new array same as that of the input array. At most one dimension of shape can be -1.Example:
- input shape = (2,3,4), shape = (6,1,-1), output shape = (6,1,4) - input shape = (2,3,4), shape = (3,-1,8), output shape = (3,1,8) - input shape = (2,3,4), shape=(-1,), output shape = (24,)
-2
copy all/remainder of the input dimensions to the output shape.Example:
- input shape = (2,3,4), shape = (-2,), output shape = (2,3,4) - input shape = (2,3,4), shape = (2,-2), output shape = (2,3,4) - input shape = (2,3,4), shape = (-2,1,1), output shape = (2,3,4,1,1)
-3
use the product of two consecutive dimensions of the input shape as the output dimension.Example:
- input shape = (2,3,4), shape = (-3,4), output shape = (6,4) - input shape = (2,3,4,5), shape = (-3,-3), output shape = (6,20) - input shape = (2,3,4), shape = (0,-3), output shape = (2,12) - input shape = (2,3,4), shape = (-3,-2), output shape = (6,4)
-4
split one dimension of the input into two dimensions passed subsequent to -4 in shape (can contain -1).Example:
- input shape = (2,3,4), shape = (-4,1,2,-2), output shape =(1,2,3,4) - input shape = (2,3,4), shape = (2,-4,-1,3,-2), output shape = (2,1,3,4)
If the argument reverse is set to 1, then the special values are inferred from right to left.
Example:
- without reverse=1, for input shape = (10,5,4), shape = (-1,0), output shape would be (40,5) - with reverse=1, output shape will be (50,4).
Defined in src/operator/tensor/matrix_op.cc:L169
Parameters: - data (NDArray) – Input data to reshape.
- shape (Shape(tuple), optional, default=[]) – The target shape
- reverse (boolean, optional, default=0) – If true then the special values are inferred from right to left
- target_shape (Shape(tuple), optional, default=[]) – (Deprecated! Use
shape
instead.) Target new shape. One and only one dim can be 0, in which case it will be inferred from the rest of dims - keep_highest (boolean, optional, default=0) – (Deprecated! Use
shape
instead.) Whether keep the highest dim unchanged.If set to true, then the first dim in target_shape is ignored,and always fixed as input - out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
reshape_like
(lhs=None, rhs=None, out=None, name=None, **kwargs)¶ Reshape some or all dimensions of lhs to have the same shape as some or all dimensions of rhs.
Returns a view of the lhs array with a new shape without altering any data.
Example:
x = [1, 2, 3, 4, 5, 6] y = [[0, -4], [3, 2], [2, 2]] reshape_like(x, y) = [[1, 2], [3, 4], [5, 6]]
More precise control over how dimensions are inherited is achieved by specifying slices over the lhs and rhs array dimensions. Only the sliced lhs dimensions are reshaped to the rhs sliced dimensions, with the non-sliced lhs dimensions staying the same.
Examples:
- lhs shape = (30,7), rhs shape = (15,2,4), lhs_begin=0, lhs_end=1, rhs_begin=0, rhs_end=2, output shape = (15,2,7) - lhs shape = (3, 5), rhs shape = (1,15,4), lhs_begin=0, lhs_end=2, rhs_begin=1, rhs_end=2, output shape = (15)
Negative indices are supported, and None can be used for either lhs_end or rhs_end to indicate the end of the range.
Example:
- lhs shape = (30, 12), rhs shape = (4, 2, 2, 3), lhs_begin=-1, lhs_end=None, rhs_begin=1, rhs_end=None, output shape = (30, 2, 2, 3)
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L453
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
reverse
(data=None, axis=_Null, out=None, name=None, **kwargs)¶ Reverses the order of elements along given axis while preserving array shape.
Note: reverse and flip are equivalent. We use reverse in the following examples.
Examples:
x = [[ 0., 1., 2., 3., 4.], [ 5., 6., 7., 8., 9.]] reverse(x, axis=0) = [[ 5., 6., 7., 8., 9.], [ 0., 1., 2., 3., 4.]] reverse(x, axis=1) = [[ 4., 3., 2., 1., 0.], [ 9., 8., 7., 6., 5.]]
Defined in src/operator/tensor/matrix_op.cc:L793
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
rint
(data=None, out=None, name=None, **kwargs)¶ Returns element-wise rounded value to the nearest integer of the input.
Note
- For input
n.5
rint
returnsn
whileround
returnsn+1
. - For input
-n.5
bothrint
andround
returns-n-1
.
Example:
rint([-1.5, 1.5, -1.9, 1.9, 2.1]) = [-2., 1., -2., 2., 2.]
The storage type of
rint
output depends upon the input storage type:- rint(default) = default
- rint(row_sparse) = row_sparse
- rint(csr) = csr
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L727
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
- For input
-
mxnet.ndarray.
rmsprop_update
(weight=None, grad=None, n=None, lr=_Null, gamma1=_Null, epsilon=_Null, wd=_Null, rescale_grad=_Null, clip_gradient=_Null, clip_weights=_Null, out=None, name=None, **kwargs)¶ Update function for RMSProp optimizer.
RMSprop is a variant of stochastic gradient descent where the gradients are divided by a cache which grows with the sum of squares of recent gradients?
RMSProp is similar to AdaGrad, a popular variant of SGD which adaptively tunes the learning rate of each parameter. AdaGrad lowers the learning rate for each parameter monotonically over the course of training. While this is analytically motivated for convex optimizations, it may not be ideal for non-convex problems. RMSProp deals with this heuristically by allowing the learning rates to rebound as the denominator decays over time.
Define the Root Mean Square (RMS) error criterion of the gradient as \(RMS[g]_t = \sqrt{E[g^2]_t + \epsilon}\), where \(g\) represents gradient and \(E[g^2]_t\) is the decaying average over past squared gradient.
The \(E[g^2]_t\) is given by:
\[E[g^2]_t = \gamma * E[g^2]_{t-1} + (1-\gamma) * g_t^2\]The update step is
\[\theta_{t+1} = \theta_t - \frac{\eta}{RMS[g]_t} g_t\]The RMSProp code follows the version in http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf Tieleman & Hinton, 2012.
Hinton suggests the momentum term \(\gamma\) to be 0.9 and the learning rate \(\eta\) to be 0.001.
Defined in src/operator/optimizer_op.cc:L553
Parameters: - weight (NDArray) – Weight
- grad (NDArray) – Gradient
- n (NDArray) – n
- lr (float, required) – Learning rate
- gamma1 (float, optional, default=0.95) – The decay rate of momentum estimates.
- epsilon (float, optional, default=1e-08) – A small constant for numerical stability.
- wd (float, optional, default=0) – Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.
- rescale_grad (float, optional, default=1) – Rescale gradient to grad = rescale_grad*grad.
- clip_gradient (float, optional, default=-1) – Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).
- clip_weights (float, optional, default=-1) – Clip weights to the range of [-clip_weights, clip_weights] If clip_weights <= 0, weight clipping is turned off. weights = max(min(weights, clip_weights), -clip_weights).
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
rmspropalex_update
(weight=None, grad=None, n=None, g=None, delta=None, lr=_Null, gamma1=_Null, gamma2=_Null, epsilon=_Null, wd=_Null, rescale_grad=_Null, clip_gradient=_Null, clip_weights=_Null, out=None, name=None, **kwargs)¶ Update function for RMSPropAlex optimizer.
RMSPropAlex is non-centered version of RMSProp.
Define \(E[g^2]_t\) is the decaying average over past squared gradient and \(E[g]_t\) is the decaying average over past gradient.
\[\begin{split}E[g^2]_t = \gamma_1 * E[g^2]_{t-1} + (1 - \gamma_1) * g_t^2\\ E[g]_t = \gamma_1 * E[g]_{t-1} + (1 - \gamma_1) * g_t\\ \Delta_t = \gamma_2 * \Delta_{t-1} - \frac{\eta}{\sqrt{E[g^2]_t - E[g]_t^2 + \epsilon}} g_t\\\end{split}\]The update step is
\[\theta_{t+1} = \theta_t + \Delta_t\]The RMSPropAlex code follows the version in http://arxiv.org/pdf/1308.0850v5.pdf Eq(38) - Eq(45) by Alex Graves, 2013.
Graves suggests the momentum term \(\gamma_1\) to be 0.95, \(\gamma_2\) to be 0.9 and the learning rate \(\eta\) to be 0.0001.
Defined in src/operator/optimizer_op.cc:L592
Parameters: - weight (NDArray) – Weight
- grad (NDArray) – Gradient
- n (NDArray) – n
- g (NDArray) – g
- delta (NDArray) – delta
- lr (float, required) – Learning rate
- gamma1 (float, optional, default=0.95) – Decay rate.
- gamma2 (float, optional, default=0.9) – Decay rate.
- epsilon (float, optional, default=1e-08) – A small constant for numerical stability.
- wd (float, optional, default=0) – Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.
- rescale_grad (float, optional, default=1) – Rescale gradient to grad = rescale_grad*grad.
- clip_gradient (float, optional, default=-1) – Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).
- clip_weights (float, optional, default=-1) – Clip weights to the range of [-clip_weights, clip_weights] If clip_weights <= 0, weight clipping is turned off. weights = max(min(weights, clip_weights), -clip_weights).
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
round
(data=None, out=None, name=None, **kwargs)¶ Returns element-wise rounded value to the nearest integer of the input.
Example:
round([-1.5, 1.5, -1.9, 1.9, 2.1]) = [-2., 2., -2., 2., 2.]
The storage type of
round
output depends upon the input storage type:- round(default) = default
- round(row_sparse) = row_sparse
- round(csr) = csr
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L706
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
rsqrt
(data=None, out=None, name=None, **kwargs)¶ Returns element-wise inverse square-root value of the input.
\[rsqrt(x) = 1/\sqrt{x}\]Example:
rsqrt([4,9,16]) = [0.5, 0.33333334, 0.25]
The storage type of
rsqrt
output is always denseDefined in src/operator/tensor/elemwise_unary_op_basic.cc:L866
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
sample_exponential
(lam=None, shape=_Null, dtype=_Null, out=None, name=None, **kwargs)¶ Concurrent sampling from multiple exponential distributions with parameters lambda (rate).
The parameters of the distributions are provided as an input array. Let [s] be the shape of the input array, n be the dimension of [s], [t] be the shape specified as the parameter of the operator, and m be the dimension of [t]. Then the output will be a (n+m)-dimensional array with shape [s]x[t].
For any valid n-dimensional index i with respect to the input array, output[i] will be an m-dimensional array that holds randomly drawn samples from the distribution which is parameterized by the input value at index i. If the shape parameter of the operator is not set, then one sample will be drawn per distribution and the output array has the same shape as the input array.
Examples:
lam = [ 1.0, 8.5 ] // Draw a single sample for each distribution sample_exponential(lam) = [ 0.51837951, 0.09994757] // Draw a vector containing two samples for each distribution sample_exponential(lam, shape=(2)) = [[ 0.51837951, 0.19866663], [ 0.09994757, 0.50447971]]
Defined in src/operator/random/multisample_op.cc:L284
Parameters: - lam (NDArray) – Lambda (rate) parameters of the distributions.
- shape (Shape(tuple), optional, default=[]) – Shape to be sampled from each random distribution.
- dtype ({'None', 'float16', 'float32', 'float64'},optional, default='None') – DType of the output in case this can’t be inferred. Defaults to float32 if not defined (dtype=None).
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
sample_gamma
(alpha=None, beta=None, shape=_Null, dtype=_Null, out=None, name=None, **kwargs)¶ Concurrent sampling from multiple gamma distributions with parameters alpha (shape) and beta (scale).
The parameters of the distributions are provided as input arrays. Let [s] be the shape of the input arrays, n be the dimension of [s], [t] be the shape specified as the parameter of the operator, and m be the dimension of [t]. Then the output will be a (n+m)-dimensional array with shape [s]x[t].
For any valid n-dimensional index i with respect to the input arrays, output[i] will be an m-dimensional array that holds randomly drawn samples from the distribution which is parameterized by the input values at index i. If the shape parameter of the operator is not set, then one sample will be drawn per distribution and the output array has the same shape as the input arrays.
Examples:
alpha = [ 0.0, 2.5 ] beta = [ 1.0, 0.7 ] // Draw a single sample for each distribution sample_gamma(alpha, beta) = [ 0. , 2.25797319] // Draw a vector containing two samples for each distribution sample_gamma(alpha, beta, shape=(2)) = [[ 0. , 0. ], [ 2.25797319, 1.70734084]]
Defined in src/operator/random/multisample_op.cc:L282
Parameters: - alpha (NDArray) – Alpha (shape) parameters of the distributions.
- shape (Shape(tuple), optional, default=[]) – Shape to be sampled from each random distribution.
- dtype ({'None', 'float16', 'float32', 'float64'},optional, default='None') – DType of the output in case this can’t be inferred. Defaults to float32 if not defined (dtype=None).
- beta (NDArray) – Beta (scale) parameters of the distributions.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
sample_generalized_negative_binomial
(mu=None, alpha=None, shape=_Null, dtype=_Null, out=None, name=None, **kwargs)¶ Concurrent sampling from multiple generalized negative binomial distributions with parameters mu (mean) and alpha (dispersion).
The parameters of the distributions are provided as input arrays. Let [s] be the shape of the input arrays, n be the dimension of [s], [t] be the shape specified as the parameter of the operator, and m be the dimension of [t]. Then the output will be a (n+m)-dimensional array with shape [s]x[t].
For any valid n-dimensional index i with respect to the input arrays, output[i] will be an m-dimensional array that holds randomly drawn samples from the distribution which is parameterized by the input values at index i. If the shape parameter of the operator is not set, then one sample will be drawn per distribution and the output array has the same shape as the input arrays.
Samples will always be returned as a floating point data type.
Examples:
mu = [ 2.0, 2.5 ] alpha = [ 1.0, 0.1 ] // Draw a single sample for each distribution sample_generalized_negative_binomial(mu, alpha) = [ 0., 3.] // Draw a vector containing two samples for each distribution sample_generalized_negative_binomial(mu, alpha, shape=(2)) = [[ 0., 3.], [ 3., 1.]]
Defined in src/operator/random/multisample_op.cc:L293
Parameters: - mu (NDArray) – Means of the distributions.
- shape (Shape(tuple), optional, default=[]) – Shape to be sampled from each random distribution.
- dtype ({'None', 'float16', 'float32', 'float64'},optional, default='None') – DType of the output in case this can’t be inferred. Defaults to float32 if not defined (dtype=None).
- alpha (NDArray) – Alpha (dispersion) parameters of the distributions.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
sample_multinomial
(data=None, shape=_Null, get_prob=_Null, dtype=_Null, out=None, name=None, **kwargs)¶ Concurrent sampling from multiple multinomial distributions.
data is an n dimensional array whose last dimension has length k, where k is the number of possible outcomes of each multinomial distribution. This operator will draw shape samples from each distribution. If shape is empty one sample will be drawn from each distribution.
If get_prob is true, a second array containing log likelihood of the drawn samples will also be returned. This is usually used for reinforcement learning where you can provide reward as head gradient for this array to estimate gradient.
Note that the input distribution must be normalized, i.e. data must sum to 1 along its last axis.
Examples:
probs = [[0, 0.1, 0.2, 0.3, 0.4], [0.4, 0.3, 0.2, 0.1, 0]] // Draw a single sample for each distribution sample_multinomial(probs) = [3, 0] // Draw a vector containing two samples for each distribution sample_multinomial(probs, shape=(2)) = [[4, 2], [0, 0]] // requests log likelihood sample_multinomial(probs, get_prob=True) = [2, 1], [0.2, 0.3]
Parameters: - data (NDArray) – Distribution probabilities. Must sum to one on the last axis.
- shape (Shape(tuple), optional, default=[]) – Shape to be sampled from each random distribution.
- get_prob (boolean, optional, default=0) – Whether to also return the log probability of sampled result. This is usually used for differentiating through stochastic variables, e.g. in reinforcement learning.
- dtype ({'float16', 'float32', 'float64', 'int32', 'uint8'},optional, default='int32') – DType of the output in case this can’t be inferred.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
sample_negative_binomial
(k=None, p=None, shape=_Null, dtype=_Null, out=None, name=None, **kwargs)¶ Concurrent sampling from multiple negative binomial distributions with parameters k (failure limit) and p (failure probability).
The parameters of the distributions are provided as input arrays. Let [s] be the shape of the input arrays, n be the dimension of [s], [t] be the shape specified as the parameter of the operator, and m be the dimension of [t]. Then the output will be a (n+m)-dimensional array with shape [s]x[t].
For any valid n-dimensional index i with respect to the input arrays, output[i] will be an m-dimensional array that holds randomly drawn samples from the distribution which is parameterized by the input values at index i. If the shape parameter of the operator is not set, then one sample will be drawn per distribution and the output array has the same shape as the input arrays.
Samples will always be returned as a floating point data type.
Examples:
k = [ 20, 49 ] p = [ 0.4 , 0.77 ] // Draw a single sample for each distribution sample_negative_binomial(k, p) = [ 15., 16.] // Draw a vector containing two samples for each distribution sample_negative_binomial(k, p, shape=(2)) = [[ 15., 50.], [ 16., 12.]]
Defined in src/operator/random/multisample_op.cc:L289
Parameters: - k (NDArray) – Limits of unsuccessful experiments.
- shape (Shape(tuple), optional, default=[]) – Shape to be sampled from each random distribution.
- dtype ({'None', 'float16', 'float32', 'float64'},optional, default='None') – DType of the output in case this can’t be inferred. Defaults to float32 if not defined (dtype=None).
- p (NDArray) – Failure probabilities in each experiment.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
sample_normal
(mu=None, sigma=None, shape=_Null, dtype=_Null, out=None, name=None, **kwargs)¶ Concurrent sampling from multiple normal distributions with parameters mu (mean) and sigma (standard deviation).
The parameters of the distributions are provided as input arrays. Let [s] be the shape of the input arrays, n be the dimension of [s], [t] be the shape specified as the parameter of the operator, and m be the dimension of [t]. Then the output will be a (n+m)-dimensional array with shape [s]x[t].
For any valid n-dimensional index i with respect to the input arrays, output[i] will be an m-dimensional array that holds randomly drawn samples from the distribution which is parameterized by the input values at index i. If the shape parameter of the operator is not set, then one sample will be drawn per distribution and the output array has the same shape as the input arrays.
Examples:
mu = [ 0.0, 2.5 ] sigma = [ 1.0, 3.7 ] // Draw a single sample for each distribution sample_normal(mu, sigma) = [-0.56410581, 0.95934606] // Draw a vector containing two samples for each distribution sample_normal(mu, sigma, shape=(2)) = [[-0.56410581, 0.2928229 ], [ 0.95934606, 4.48287058]]
Defined in src/operator/random/multisample_op.cc:L279
Parameters: - mu (NDArray) – Means of the distributions.
- shape (Shape(tuple), optional, default=[]) – Shape to be sampled from each random distribution.
- dtype ({'None', 'float16', 'float32', 'float64'},optional, default='None') – DType of the output in case this can’t be inferred. Defaults to float32 if not defined (dtype=None).
- sigma (NDArray) – Standard deviations of the distributions.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
sample_poisson
(lam=None, shape=_Null, dtype=_Null, out=None, name=None, **kwargs)¶ Concurrent sampling from multiple Poisson distributions with parameters lambda (rate).
The parameters of the distributions are provided as an input array. Let [s] be the shape of the input array, n be the dimension of [s], [t] be the shape specified as the parameter of the operator, and m be the dimension of [t]. Then the output will be a (n+m)-dimensional array with shape [s]x[t].
For any valid n-dimensional index i with respect to the input array, output[i] will be an m-dimensional array that holds randomly drawn samples from the distribution which is parameterized by the input value at index i. If the shape parameter of the operator is not set, then one sample will be drawn per distribution and the output array has the same shape as the input array.
Samples will always be returned as a floating point data type.
Examples:
lam = [ 1.0, 8.5 ] // Draw a single sample for each distribution sample_poisson(lam) = [ 0., 13.] // Draw a vector containing two samples for each distribution sample_poisson(lam, shape=(2)) = [[ 0., 4.], [ 13., 8.]]
Defined in src/operator/random/multisample_op.cc:L286
Parameters: - lam (NDArray) – Lambda (rate) parameters of the distributions.
- shape (Shape(tuple), optional, default=[]) – Shape to be sampled from each random distribution.
- dtype ({'None', 'float16', 'float32', 'float64'},optional, default='None') – DType of the output in case this can’t be inferred. Defaults to float32 if not defined (dtype=None).
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
sample_uniform
(low=None, high=None, shape=_Null, dtype=_Null, out=None, name=None, **kwargs)¶ Concurrent sampling from multiple uniform distributions on the intervals given by [low,high).
The parameters of the distributions are provided as input arrays. Let [s] be the shape of the input arrays, n be the dimension of [s], [t] be the shape specified as the parameter of the operator, and m be the dimension of [t]. Then the output will be a (n+m)-dimensional array with shape [s]x[t].
For any valid n-dimensional index i with respect to the input arrays, output[i] will be an m-dimensional array that holds randomly drawn samples from the distribution which is parameterized by the input values at index i. If the shape parameter of the operator is not set, then one sample will be drawn per distribution and the output array has the same shape as the input arrays.
Examples:
low = [ 0.0, 2.5 ] high = [ 1.0, 3.7 ] // Draw a single sample for each distribution sample_uniform(low, high) = [ 0.40451524, 3.18687344] // Draw a vector containing two samples for each distribution sample_uniform(low, high, shape=(2)) = [[ 0.40451524, 0.18017688], [ 3.18687344, 3.68352246]]
Defined in src/operator/random/multisample_op.cc:L277
Parameters: - low (NDArray) – Lower bounds of the distributions.
- shape (Shape(tuple), optional, default=[]) – Shape to be sampled from each random distribution.
- dtype ({'None', 'float16', 'float32', 'float64'},optional, default='None') – DType of the output in case this can’t be inferred. Defaults to float32 if not defined (dtype=None).
- high (NDArray) – Upper bounds of the distributions.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
scatter_nd
(data=None, indices=None, shape=_Null, out=None, name=None, **kwargs)¶ Scatters data into a new tensor according to indices.
Given data with shape (Y_0, ..., Y_{K-1}, X_M, ..., X_{N-1}) and indices with shape (M, Y_0, ..., Y_{K-1}), the output will have shape (X_0, X_1, ..., X_{N-1}), where M <= N. If M == N, data shape should simply be (Y_0, ..., Y_{K-1}).
The elements in output is defined as follows:
output[indices[0, y_0, ..., y_{K-1}], ..., indices[M-1, y_0, ..., y_{K-1}], x_M, ..., x_{N-1}] = data[y_0, ..., y_{K-1}, x_M, ..., x_{N-1}]
all other entries in output are 0.
Warning
If the indices have duplicates, the result will be non-deterministic and the gradient of scatter_nd will not be correct!!
Examples:
data = [2, 3, 0] indices = [[1, 1, 0], [0, 1, 0]] shape = (2, 2) scatter_nd(data, indices, shape) = [[0, 0], [2, 3]] data = [[[1, 2], [3, 4]], [[5, 6], [7, 8]]] indices = [[0, 1], [1, 1]] shape = (2, 2, 2, 2) scatter_nd(data, indices, shape) = [[[[0, 0], [0, 0]], [[1, 2], [3, 4]]], [[[0, 0], [0, 0]], [[5, 6], [7, 8]]]]
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
sgd_mom_update
(weight=None, grad=None, mom=None, lr=_Null, momentum=_Null, wd=_Null, rescale_grad=_Null, clip_gradient=_Null, lazy_update=_Null, out=None, name=None, **kwargs)¶ Momentum update function for Stochastic Gradient Descent (SGD) optimizer.
Momentum update has better convergence rates on neural networks. Mathematically it looks like below:
\[\begin{split}v_1 = \alpha * \nabla J(W_0)\\ v_t = \gamma v_{t-1} - \alpha * \nabla J(W_{t-1})\\ W_t = W_{t-1} + v_t\end{split}\]It updates the weights using:
v = momentum * v - learning_rate * gradient weight += v
Where the parameter
momentum
is the decay rate of momentum estimates at each epoch.However, if grad’s storage type is
row_sparse
,lazy_update
is True and weight’s storage type is the same as momentum’s storage type, only the row slices whose indices appear in grad.indices are updated (for both weight and momentum):for row in gradient.indices: v[row] = momentum[row] * v[row] - learning_rate * gradient[row] weight[row] += v[row]
Defined in src/operator/optimizer_op.cc:L372
Parameters: - weight (NDArray) – Weight
- grad (NDArray) – Gradient
- mom (NDArray) – Momentum
- lr (float, required) – Learning rate
- momentum (float, optional, default=0) – The decay rate of momentum estimates at each epoch.
- wd (float, optional, default=0) – Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.
- rescale_grad (float, optional, default=1) – Rescale gradient to grad = rescale_grad*grad.
- clip_gradient (float, optional, default=-1) – Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).
- lazy_update (boolean, optional, default=1) – If true, lazy updates are applied if gradient’s stype is row_sparse and both weight and momentum have the same stype
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
sgd_update
(weight=None, grad=None, lr=_Null, wd=_Null, rescale_grad=_Null, clip_gradient=_Null, lazy_update=_Null, out=None, name=None, **kwargs)¶ Update function for Stochastic Gradient Descent (SDG) optimizer.
It updates the weights using:
weight = weight - learning_rate * (gradient + wd * weight)
However, if gradient is of
row_sparse
storage type andlazy_update
is True, only the row slices whose indices appear in grad.indices are updated:for row in gradient.indices: weight[row] = weight[row] - learning_rate * (gradient[row] + wd * weight[row])
Defined in src/operator/optimizer_op.cc:L331
Parameters: - weight (NDArray) – Weight
- grad (NDArray) – Gradient
- lr (float, required) – Learning rate
- wd (float, optional, default=0) – Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.
- rescale_grad (float, optional, default=1) – Rescale gradient to grad = rescale_grad*grad.
- clip_gradient (float, optional, default=-1) – Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).
- lazy_update (boolean, optional, default=1) – If true, lazy updates are applied if gradient’s stype is row_sparse.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
shape_array
(data=None, lhs_begin=_Null, lhs_end=_Null, rhs_begin=_Null, rhs_end=_Null, out=None, name=None, **kwargs)¶ Returns a 1D int64 array containing the shape of data.
Example:
shape_array([[1,2,3,4], [5,6,7,8]]) = [2,4]
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L504
Parameters: - data (NDArray) – Input Array.
- lhs_begin (int or None, optional, default='None') – Defaults to 0. The beginning index along which the lhs dimensions are to be reshaped. Supports negative indices.
- lhs_end (int or None, optional, default='None') – Defaults to None. The ending index along which the lhs dimensions are to be used for reshaping. Supports negative indices.
- rhs_begin (int or None, optional, default='None') – Defaults to 0. The beginning index along which the rhs dimensions are to be used for reshaping. Supports negative indices.
- rhs_end (int or None, optional, default='None') – Defaults to None. The ending index along which the rhs dimensions are to be used for reshaping. Supports negative indices.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
shuffle
(data=None, out=None, name=None, **kwargs)¶ Randomly shuffle the elements.
This shuffles the array along the first axis. The order of the elements in each subarray does not change. For example, if a 2D array is given, the order of the rows randomly changes, but the order of the elements in each row does not change.
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
sigmoid
(data=None, out=None, name=None, **kwargs)¶ Computes sigmoid of x element-wise.
\[y = 1 / (1 + exp(-x))\]The storage type of
sigmoid
output is always denseDefined in src/operator/tensor/elemwise_unary_op_basic.cc:L101
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
sign
(data=None, out=None, name=None, **kwargs)¶ Returns element-wise sign of the input.
Example:
sign([-2, 0, 3]) = [-1, 0, 1]
The storage type of
sign
output depends upon the input storage type:- sign(default) = default
- sign(row_sparse) = row_sparse
- sign(csr) = csr
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L687
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
signsgd_update
(weight=None, grad=None, lr=_Null, wd=_Null, rescale_grad=_Null, clip_gradient=_Null, out=None, name=None, **kwargs)¶ Update function for SignSGD optimizer.
\[\begin{split}g_t = \nabla J(W_{t-1})\\ W_t = W_{t-1} - \eta_t \text{sign}(g_t)\end{split}\]It updates the weights using:
weight = weight - learning_rate * sign(gradient)
Note
- sparse ndarray not supported for this optimizer yet.
Defined in src/operator/optimizer_op.cc:L57
Parameters: - weight (NDArray) – Weight
- grad (NDArray) – Gradient
- lr (float, required) – Learning rate
- wd (float, optional, default=0) – Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.
- rescale_grad (float, optional, default=1) – Rescale gradient to grad = rescale_grad*grad.
- clip_gradient (float, optional, default=-1) – Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
signum_update
(weight=None, grad=None, mom=None, lr=_Null, momentum=_Null, wd=_Null, rescale_grad=_Null, clip_gradient=_Null, wd_lh=_Null, out=None, name=None, **kwargs)¶ SIGN momentUM (Signum) optimizer.
\[\begin{split}g_t = \nabla J(W_{t-1})\\ m_t = \beta m_{t-1} + (1 - \beta) g_t\\ W_t = W_{t-1} - \eta_t \text{sign}(m_t)\end{split}\]- It updates the weights using::
- state = momentum * state + (1-momentum) * gradient weight = weight - learning_rate * sign(state)
Where the parameter
momentum
is the decay rate of momentum estimates at each epoch.Note
- sparse ndarray not supported for this optimizer yet.
Defined in src/operator/optimizer_op.cc:L86
Parameters: - weight (NDArray) – Weight
- grad (NDArray) – Gradient
- mom (NDArray) – Momentum
- lr (float, required) – Learning rate
- momentum (float, optional, default=0) – The decay rate of momentum estimates at each epoch.
- wd (float, optional, default=0) – Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.
- rescale_grad (float, optional, default=1) – Rescale gradient to grad = rescale_grad*grad.
- clip_gradient (float, optional, default=-1) – Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).
- wd_lh (float, optional, default=0) – The amount of weight decay that does not go into gradient/momentum calculationsotherwise do weight decay algorithmically only.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
sin
(data=None, out=None, name=None, **kwargs)¶ Computes the element-wise sine of the input array.
The input should be in radians (\(2\pi\) rad equals 360 degrees).
\[sin([0, \pi/4, \pi/2]) = [0, 0.707, 1]\]The storage type of
sin
output depends upon the input storage type:- sin(default) = default
- sin(row_sparse) = row_sparse
- sin(csr) = csr
Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L46
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
sinh
(data=None, out=None, name=None, **kwargs)¶ Returns the hyperbolic sine of the input array, computed element-wise.
\[sinh(x) = 0.5\times(exp(x) - exp(-x))\]The storage type of
sinh
output depends upon the input storage type:- sinh(default) = default
- sinh(row_sparse) = row_sparse
- sinh(csr) = csr
Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L201
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
size_array
(data=None, out=None, name=None, **kwargs)¶ Returns a 1D int64 array containing the size of data.
Example:
size_array([[1,2,3,4], [5,6,7,8]]) = [8]
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L556
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
slice
(data=None, begin=_Null, end=_Null, step=_Null, out=None, name=None, **kwargs)¶ Slices a region of the array.
Note
crop
is deprecated. Useslice
instead.This function returns a sliced array between the indices given by begin and end with the corresponding step.
For an input array of
shape=(d_0, d_1, ..., d_n-1)
, slice operation withbegin=(b_0, b_1...b_m-1)
,end=(e_0, e_1, ..., e_m-1)
, andstep=(s_0, s_1, ..., s_m-1)
, where m <= n, results in an array with the shape(|e_0-b_0|/|s_0|, ..., |e_m-1-b_m-1|/|s_m-1|, d_m, ..., d_n-1)
.The resulting array’s k-th dimension contains elements from the k-th dimension of the input array starting from index
b_k
(inclusive) with steps_k
until reachinge_k
(exclusive).If the k-th elements are None in the sequence of begin, end, and step, the following rule will be used to set default values. If s_k is None, set s_k=1. If s_k > 0, set b_k=0, e_k=d_k; else, set b_k=d_k-1, e_k=-1.
The storage type of
slice
output depends on storage types of inputs- slice(csr) = csr
- otherwise,
slice
generates output with default storage
Note
When input data storage type is csr, it only supports
step=(), or step=(None,), or step=(1,) to generate a csr output. For other step parameter values, it falls back to slicing a dense tensor.
Example:
x = [[ 1., 2., 3., 4.], [ 5., 6., 7., 8.], [ 9., 10., 11., 12.]] slice(x, begin=(0,1), end=(2,4)) = [[ 2., 3., 4.], [ 6., 7., 8.]] slice(x, begin=(None, 0), end=(None, 3), step=(-1, 2)) = [[9., 11.], [5., 7.], [1., 3.]]
Defined in src/operator/tensor/matrix_op.cc:L413
Parameters: - data (NDArray) – Source input
- begin (Shape(tuple), required) – starting indices for the slice operation, supports negative indices.
- end (Shape(tuple), required) – ending indices for the slice operation, supports negative indices.
- step (Shape(tuple), optional, default=[]) – step for the slice operation, supports negative values.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
slice_axis
(data=None, axis=_Null, begin=_Null, end=_Null, out=None, name=None, **kwargs)¶ Slices along a given axis.
Returns an array slice along a given axis starting from the begin index to the end index.
Examples:
x = [[ 1., 2., 3., 4.], [ 5., 6., 7., 8.], [ 9., 10., 11., 12.]] slice_axis(x, axis=0, begin=1, end=3) = [[ 5., 6., 7., 8.], [ 9., 10., 11., 12.]] slice_axis(x, axis=1, begin=0, end=2) = [[ 1., 2.], [ 5., 6.], [ 9., 10.]] slice_axis(x, axis=1, begin=-3, end=-1) = [[ 2., 3.], [ 6., 7.], [ 10., 11.]]
Defined in src/operator/tensor/matrix_op.cc:L500
Parameters: - data (NDArray) – Source input
- axis (int, required) – Axis along which to be sliced, supports negative indexes.
- begin (int, required) – The beginning index along the axis to be sliced, supports negative indexes.
- end (int or None, required) – The ending index along the axis to be sliced, supports negative indexes.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
slice_like
(data=None, shape_like=None, axes=_Null, out=None, name=None, **kwargs)¶ Slices a region of the array like the shape of another array.
This function is similar to
slice
, however, the begin are always 0`s and `end of specific axes are inferred from the second input shape_like.Given the second shape_like input of
shape=(d_0, d_1, ..., d_n-1)
, aslice_like
operator with default empty axes, it performs the following operation:`` out = slice(input, begin=(0, 0, ..., 0), end=(d_0, d_1, ..., d_n-1))``.
When axes is not empty, it is used to speficy which axes are being sliced.
Given a 4-d input data,
slice_like
operator withaxes=(0, 2, -1)
will perform the following operation:`` out = slice(input, begin=(0, 0, 0, 0), end=(d_0, None, d_2, d_3))``.
Note that it is allowed to have first and second input with different dimensions, however, you have to make sure the axes are specified and not exceeding the dimension limits.
For example, given input_1 with
shape=(2,3,4,5)
and input_2 withshape=(1,2,3)
, it is not allowed to use:`` out = slice_like(a, b)`` because ndim of input_1 is 4, and ndim of input_2 is 3.
The following is allowed in this situation:
`` out = slice_like(a, b, axes=(0, 2))``
Example:
x = [[ 1., 2., 3., 4.], [ 5., 6., 7., 8.], [ 9., 10., 11., 12.]] y = [[ 0., 0., 0.], [ 0., 0., 0.]] slice_like(x, y) = [[ 1., 2., 3.] [ 5., 6., 7.]] slice_like(x, y, axes=(0, 1)) = [[ 1., 2., 3.] [ 5., 6., 7.]] slice_like(x, y, axes=(0)) = [[ 1., 2., 3., 4.] [ 5., 6., 7., 8.]] slice_like(x, y, axes=(-1)) = [[ 1., 2., 3.] [ 5., 6., 7.] [ 9., 10., 11.]]
Defined in src/operator/tensor/matrix_op.cc:L569
Parameters: - data (NDArray) – Source input
- shape_like (NDArray) – Shape like input
- axes (Shape(tuple), optional, default=[]) – List of axes on which input data will be sliced according to the corresponding size of the second input. By default will slice on all axes. Negative axes are supported.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
smooth_l1
(data=None, scalar=_Null, out=None, name=None, **kwargs)¶ Calculate Smooth L1 Loss(lhs, scalar) by summing
\[\begin{split}f(x) = \begin{cases} (\sigma x)^2/2,& \text{if }x < 1/\sigma^2\\ |x|-0.5/\sigma^2,& \text{otherwise} \end{cases}\end{split}\]where \(x\) is an element of the tensor lhs and \(\sigma\) is the scalar.
Example:
smooth_l1([1, 2, 3, 4], scalar=1) = [0.5, 1.5, 2.5, 3.5]
Defined in src/operator/tensor/elemwise_binary_scalar_op_extended.cc:L103
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
softmax
(data=None, axis=_Null, temperature=_Null, out=None, name=None, **kwargs)¶ Applies the softmax function.
The resulting array contains elements in the range (0,1) and the elements along the given axis sum up to 1.
\[softmax(\mathbf{z/t})_j = \frac{e^{z_j/t}}{\sum_{k=1}^K e^{z_k/t}}\]for \(j = 1, ..., K\)
t is the temperature parameter in softmax function. By default, t equals 1.0
Example:
x = [[ 1. 1. 1.] [ 1. 1. 1.]] softmax(x,axis=0) = [[ 0.5 0.5 0.5] [ 0.5 0.5 0.5]] softmax(x,axis=1) = [[ 0.33333334, 0.33333334, 0.33333334], [ 0.33333334, 0.33333334, 0.33333334]]
Defined in src/operator/nn/softmax.cc:L100
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
softmax_cross_entropy
(data=None, label=None, out=None, name=None, **kwargs)¶ Calculate cross entropy of softmax output and one-hot label.
This operator computes the cross entropy in two steps: - Applies softmax function on the input array. - Computes and returns the cross entropy loss between the softmax output and the labels.
The softmax function and cross entropy loss is given by:
- Softmax Function:
\[\text{softmax}(x)_i = \frac{exp(x_i)}{\sum_j exp(x_j)}\]- Cross Entropy Function:
\[\text{CE(label, output)} = - \sum_i \text{label}_i \log(\text{output}_i)\]
Example:
x = [[1, 2, 3], [11, 7, 5]] label = [2, 0] softmax(x) = [[0.09003057, 0.24472848, 0.66524094], [0.97962922, 0.01794253, 0.00242826]] softmax_cross_entropy(data, label) = - log(0.66524084) - log(0.97962922) = 0.4281871
Defined in src/operator/loss_binary_op.cc:L59
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
softsign
(data=None, out=None, name=None, **kwargs)¶ Computes softsign of x element-wise.
\[y = x / (1 + abs(x))\]The storage type of
softsign
output is always denseDefined in src/operator/tensor/elemwise_unary_op_basic.cc:L145
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
sort
(data=None, axis=_Null, is_ascend=_Null, out=None, name=None, **kwargs)¶ Returns a sorted copy of an input array along the given axis.
Examples:
x = [[ 1, 4], [ 3, 1]] // sorts along the last axis sort(x) = [[ 1., 4.], [ 1., 3.]] // flattens and then sorts sort(x) = [ 1., 1., 3., 4.] // sorts along the first axis sort(x, axis=0) = [[ 1., 1.], [ 3., 4.]] // in a descend order sort(x, is_ascend=0) = [[ 4., 1.], [ 3., 1.]]
Defined in src/operator/tensor/ordering_op.cc:L127
Parameters: - data (NDArray) – The input array
- axis (int or None, optional, default='-1') – Axis along which to choose sort the input tensor. If not given, the flattened array is used. Default is -1.
- is_ascend (boolean, optional, default=1) – Whether to sort in ascending or descending order.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
space_to_depth
(data=None, block_size=_Null, out=None, name=None, **kwargs)¶ Rearranges(permutes) blocks of spatial data into depth. Similar to ONNX SpaceToDepth operator: https://github.com/onnx/onnx/blob/master/docs/Operators.md#SpaceToDepth
The output is a new tensor where the values from height and width dimension are moved to the depth dimension. The reverse of this operation is
depth_to_space
.\[\begin{split}\begin{gather*} x \prime = reshape(x, [N, C, H / block\_size, block\_size, W / block\_size, block\_size]) \\ x \prime \prime = transpose(x \prime, [0, 3, 5, 1, 2, 4]) \\ y = reshape(x \prime \prime, [N, C * (block\_size ^ 2), H / block\_size, W / block\_size]) \end{gather*}\end{split}\]where \(x\) is an input tensor with default layout as \([N, C, H, W]\): [batch, channels, height, width] and \(y\) is the output tensor of layout \([N, C * (block\_size ^ 2), H / block\_size, W / block\_size]\)
Example:
x = [[[[0, 6, 1, 7, 2, 8], [12, 18, 13, 19, 14, 20], [3, 9, 4, 10, 5, 11], [15, 21, 16, 22, 17, 23]]]] space_to_depth(x, 2) = [[[[0, 1, 2], [3, 4, 5]], [[6, 7, 8], [9, 10, 11]], [[12, 13, 14], [15, 16, 17]], [[18, 19, 20], [21, 22, 23]]]]
Defined in src/operator/tensor/matrix_op.cc:L999
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
split
(data=None, num_outputs=_Null, axis=_Null, squeeze_axis=_Null, out=None, name=None, **kwargs)¶ Splits an array along a particular axis into multiple sub-arrays.
Note
SliceChannel
is deprecated. Usesplit
instead.Note that num_outputs should evenly divide the length of the axis along which to split the array.
Example:
x = [[[ 1.] [ 2.]] [[ 3.] [ 4.]] [[ 5.] [ 6.]]] x.shape = (3, 2, 1) y = split(x, axis=1, num_outputs=2) // a list of 2 arrays with shape (3, 1, 1) y = [[[ 1.]] [[ 3.]] [[ 5.]]] [[[ 2.]] [[ 4.]] [[ 6.]]] y[0].shape = (3, 1, 1) z = split(x, axis=0, num_outputs=3) // a list of 3 arrays with shape (1, 2, 1) z = [[[ 1.] [ 2.]]] [[[ 3.] [ 4.]]] [[[ 5.] [ 6.]]] z[0].shape = (1, 2, 1)
squeeze_axis=1 removes the axis with length 1 from the shapes of the output arrays. Note that setting squeeze_axis to
1
removes axis with length 1 only along the axis which it is split. Also squeeze_axis can be set to true only ifinput.shape[axis] == num_outputs
.Example:
z = split(x, axis=0, num_outputs=3, squeeze_axis=1) // a list of 3 arrays with shape (2, 1) z = [[ 1.] [ 2.]] [[ 3.] [ 4.]] [[ 5.] [ 6.]] z[0].shape = (2 ,1 )
Defined in src/operator/slice_channel.cc:L107
Parameters: - data (NDArray) – The input
- num_outputs (int, required) – Number of splits. Note that this should evenly divide the length of the axis.
- axis (int, optional, default='1') – Axis along which to split.
- squeeze_axis (boolean, optional, default=0) – If true, Removes the axis with length 1 from the shapes of the output arrays. Note that setting squeeze_axis to
true
removes axis with length 1 only along the axis which it is split. Also squeeze_axis can be set totrue
only ifinput.shape[axis] == num_outputs
. - out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
sqrt
(data=None, out=None, name=None, **kwargs)¶ Returns element-wise square-root value of the input.
\[\textrm{sqrt}(x) = \sqrt{x}\]Example:
sqrt([4, 9, 16]) = [2, 3, 4]
The storage type of
sqrt
output depends upon the input storage type:- sqrt(default) = default
- sqrt(row_sparse) = row_sparse
- sqrt(csr) = csr
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L846
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
square
(data=None, out=None, name=None, **kwargs)¶ Returns element-wise squared value of the input.
\[square(x) = x^2\]Example:
square([2, 3, 4]) = [4, 9, 16]
The storage type of
square
output depends upon the input storage type:- square(default) = default
- square(row_sparse) = row_sparse
- square(csr) = csr
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L823
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
squeeze
(*data, **kwargs)¶ Remove single-dimensional entries from the shape of an array. Same behavior of defining the output tensor shape as numpy.squeeze for the most of cases. See the following note for exception.
Examples:
data = [[[0], [1], [2]]] squeeze(data) = [0, 1, 2] squeeze(data, axis=0) = [[0], [1], [2]] squeeze(data, axis=2) = [[0, 1, 2]] squeeze(data, axis=(0, 2)) = [0, 1, 2]
Note
The output of this operator will keep at least one dimension not removed. For example, squeeze([[[4]]]) = [4], while in numpy.squeeze, the output will become a scalar.
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
stack
(*data, **kwargs)¶ Join a sequence of arrays along a new axis.
The axis parameter specifies the index of the new axis in the dimensions of the result. For example, if axis=0 it will be the first dimension and if axis=-1 it will be the last dimension.
Examples:
x = [1, 2] y = [3, 4] stack(x, y) = [[1, 2], [3, 4]] stack(x, y, axis=1) = [[1, 3], [2, 4]]
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
stop_gradient
(data=None, out=None, name=None, **kwargs)¶ Stops gradient computation.
Stops the accumulated gradient of the inputs from flowing through this operator in the backward direction. In other words, this operator prevents the contribution of its inputs to be taken into account for computing gradients.
Example:
v1 = [1, 2] v2 = [0, 1] a = Variable('a') b = Variable('b') b_stop_grad = stop_gradient(3 * b) loss = MakeLoss(b_stop_grad + a) executor = loss.simple_bind(ctx=cpu(), a=(1,2), b=(1,2)) executor.forward(is_train=True, a=v1, b=v2) executor.outputs [ 1. 5.] executor.backward() executor.grad_arrays [ 0. 0.] [ 1. 1.]
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L265
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
sum
(data=None, axis=_Null, keepdims=_Null, exclude=_Null, out=None, name=None, **kwargs)¶ Computes the sum of array elements over given axes.
Note
sum and sum_axis are equivalent. For ndarray of csr storage type summation along axis 0 and axis 1 is supported. Setting keepdims or exclude to True will cause a fallback to dense operator.
Example:
data = [[[1, 2], [2, 3], [1, 3]], [[1, 4], [4, 3], [5, 2]], [[7, 1], [7, 2], [7, 3]]] sum(data, axis=1) [[ 4. 8.] [ 10. 9.] [ 21. 6.]] sum(data, axis=[1,2]) [ 12. 19. 27.] data = [[1, 2, 0], [3, 0, 1], [4, 1, 0]] csr = cast_storage(data, 'csr') sum(csr, axis=0) [ 8. 3. 1.] sum(csr, axis=1) [ 3. 4. 5.]
Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L115
Parameters: - data (NDArray) – The input
- axis (Shape or None, optional, default=None) –
The axis or axes along which to perform the reduction.
The default, axis=(), will compute over all elements into a scalar array with shape (1,).If axis is int, a reduction is performed on a particular axis.
If axis is a tuple of ints, a reduction is performed on all the axes specified in the tuple.
If exclude is true, reduction will be performed on the axes that are NOT in axis instead.
Negative values means indexing from right to left.
- keepdims (boolean, optional, default=0) – If this is set to True, the reduced axes are left in the result as dimension with size one.
- exclude (boolean, optional, default=0) – Whether to perform reduction on axis that are NOT in axis instead.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
sum_axis
(data=None, axis=_Null, keepdims=_Null, exclude=_Null, out=None, name=None, **kwargs)¶ Computes the sum of array elements over given axes.
Note
sum and sum_axis are equivalent. For ndarray of csr storage type summation along axis 0 and axis 1 is supported. Setting keepdims or exclude to True will cause a fallback to dense operator.
Example:
data = [[[1, 2], [2, 3], [1, 3]], [[1, 4], [4, 3], [5, 2]], [[7, 1], [7, 2], [7, 3]]] sum(data, axis=1) [[ 4. 8.] [ 10. 9.] [ 21. 6.]] sum(data, axis=[1,2]) [ 12. 19. 27.] data = [[1, 2, 0], [3, 0, 1], [4, 1, 0]] csr = cast_storage(data, 'csr') sum(csr, axis=0) [ 8. 3. 1.] sum(csr, axis=1) [ 3. 4. 5.]
Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L115
Parameters: - data (NDArray) – The input
- axis (Shape or None, optional, default=None) –
The axis or axes along which to perform the reduction.
The default, axis=(), will compute over all elements into a scalar array with shape (1,).If axis is int, a reduction is performed on a particular axis.
If axis is a tuple of ints, a reduction is performed on all the axes specified in the tuple.
If exclude is true, reduction will be performed on the axes that are NOT in axis instead.
Negative values means indexing from right to left.
- keepdims (boolean, optional, default=0) – If this is set to True, the reduced axes are left in the result as dimension with size one.
- exclude (boolean, optional, default=0) – Whether to perform reduction on axis that are NOT in axis instead.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
swapaxes
(data=None, dim1=_Null, dim2=_Null, out=None, name=None, **kwargs)¶ Interchanges two axes of an array.
Examples:
x = [[1, 2, 3]]) swapaxes(x, 0, 1) = [[ 1], [ 2], [ 3]] x = [[[ 0, 1], [ 2, 3]], [[ 4, 5], [ 6, 7]]] // (2,2,2) array swapaxes(x, 0, 2) = [[[ 0, 4], [ 2, 6]], [[ 1, 5], [ 3, 7]]]
Defined in src/operator/swapaxis.cc:L70
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
take
(a=None, indices=None, axis=_Null, mode=_Null, out=None, name=None, **kwargs)¶ Takes elements from an input array along the given axis.
This function slices the input array along a particular axis with the provided indices.
Given data tensor of rank r >= 1, and indices tensor of rank q, gather entries of the axis dimension of data (by default outer-most one as axis=0) indexed by indices, and concatenates them in an output tensor of rank q + (r - 1).
- Examples::
x = [4. 5. 6.]
// Trivial case, take the second element along the first axis.
take(x, [1]) = [ 5. ]
// The other trivial case, axis=-1, take the third element along the first axis
take(x, [3], axis=-1, mode=’clip’) = [ 6. ]
- x = [[ 1., 2.],
- [ 3., 4.], [ 5., 6.]]
// In this case we will get rows 0 and 1, then 1 and 2. Along axis 0
- take(x, [[0,1],[1,2]]) = [[[ 1., 2.],
- [ 3., 4.]],
- [[ 3., 4.],
- [ 5., 6.]]]
// In this case we will get rows 0 and 1, then 1 and 2 (calculated by wrapping around). // Along axis 1
- take(x, [[0, 3], [-1, -2]], axis=1, mode=’wrap’) = [[[ 1., 2.],
- [ 3., 4.]],
- [[ 3., 4.],
- [ 5., 6.]]]
Defined in src/operator/tensor/indexing_op.cc:L434
Parameters: - a (NDArray) – The input array.
- indices (NDArray) – The indices of the values to be extracted.
- axis (int, optional, default='0') – The axis of input array to be taken.For input tensor of rank r, it could be in the range of [-r, r-1]
- mode ({'clip', 'raise', 'wrap'},optional, default='clip') – Specify how out-of-bound indices bahave. Default is “clip”. “clip” means clip to the range. So, if all indices mentioned are too large, they are replaced by the index that addresses the last element along an axis. “wrap” means to wrap around. “raise” means to raise an error, not supported yet.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
tan
(data=None, out=None, name=None, **kwargs)¶ Computes the element-wise tangent of the input array.
The input should be in radians (\(2\pi\) rad equals 360 degrees).
\[tan([0, \pi/4, \pi/2]) = [0, 1, -inf]\]The storage type of
tan
output depends upon the input storage type:- tan(default) = default
- tan(row_sparse) = row_sparse
- tan(csr) = csr
Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L83
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
tanh
(data=None, out=None, name=None, **kwargs)¶ Returns the hyperbolic tangent of the input array, computed element-wise.
\[tanh(x) = sinh(x) / cosh(x)\]The storage type of
tanh
output depends upon the input storage type:- tanh(default) = default
- tanh(row_sparse) = row_sparse
- tanh(csr) = csr
Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L234
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
tile
(data=None, reps=_Null, out=None, name=None, **kwargs)¶ Repeats the whole array multiple times.
If
reps
has length d, and input array has dimension of n. There are three cases:n=d. Repeat i-th dimension of the input by
reps[i]
times:x = [[1, 2], [3, 4]] tile(x, reps=(2,3)) = [[ 1., 2., 1., 2., 1., 2.], [ 3., 4., 3., 4., 3., 4.], [ 1., 2., 1., 2., 1., 2.], [ 3., 4., 3., 4., 3., 4.]]
n>d.
reps
is promoted to length n by pre-pending 1’s to it. Thus for an input shape(2,3)
,repos=(2,)
is treated as(1,2)
:tile(x, reps=(2,)) = [[ 1., 2., 1., 2.], [ 3., 4., 3., 4.]]
n
. The input is promoted to be d-dimensional by prepending new axes. So a shape (2,2)
array is promoted to(1,2,2)
for 3-D replication:tile(x, reps=(2,2,3)) = [[[ 1., 2., 1., 2., 1., 2.], [ 3., 4., 3., 4., 3., 4.], [ 1., 2., 1., 2., 1., 2.], [ 3., 4., 3., 4., 3., 4.]], [[ 1., 2., 1., 2., 1., 2.], [ 3., 4., 3., 4., 3., 4.], [ 1., 2., 1., 2., 1., 2.], [ 3., 4., 3., 4., 3., 4.]]]
Defined in src/operator/tensor/matrix_op.cc:L752
Parameters: - data (NDArray) – Input data array
- reps (Shape(tuple), required) – The number of times for repeating the tensor a. Each dim size of reps must be a positive integer. If reps has length d, the result will have dimension of max(d, a.ndim); If a.ndim < d, a is promoted to be d-dimensional by prepending new axes. If a.ndim > d, reps is promoted to a.ndim by pre-pending 1’s to it.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
topk
(data=None, axis=_Null, k=_Null, ret_typ=_Null, is_ascend=_Null, dtype=_Null, out=None, name=None, **kwargs)¶ - Returns the top k elements in an input array along the given axis.
- The returned elements will be sorted.
Examples:
x = [[ 0.3, 0.2, 0.4], [ 0.1, 0.3, 0.2]] // returns an index of the largest element on last axis topk(x) = [[ 2.], [ 1.]] // returns the value of top-2 largest elements on last axis topk(x, ret_typ='value', k=2) = [[ 0.4, 0.3], [ 0.3, 0.2]] // returns the value of top-2 smallest elements on last axis topk(x, ret_typ='value', k=2, is_ascend=1) = [[ 0.2 , 0.3], [ 0.1 , 0.2]] // returns the value of top-2 largest elements on axis 0 topk(x, axis=0, ret_typ='value', k=2) = [[ 0.3, 0.3, 0.4], [ 0.1, 0.2, 0.2]] // flattens and then returns list of both values and indices topk(x, ret_typ='both', k=2) = [[[ 0.4, 0.3], [ 0.3, 0.2]] , [[ 2., 0.], [ 1., 2.]]]
Defined in src/operator/tensor/ordering_op.cc:L64
Parameters: - data (NDArray) – The input array
- axis (int or None, optional, default='-1') – Axis along which to choose the top k indices. If not given, the flattened array is used. Default is -1.
- k (int, optional, default='1') – Number of top elements to select, should be always smaller than or equal to the element number in the given axis. A global sort is performed if set k < 1.
- ret_typ ({'both', 'indices', 'mask', 'value'},optional, default='indices') – The return type. “value” means to return the top k values, “indices” means to return the indices of the top k values, “mask” means to return a mask array containing 0 and 1. 1 means the top k values. “both” means to return a list of both values and indices of top k elements.
- is_ascend (boolean, optional, default=0) – Whether to choose k largest or k smallest elements. Top K largest elements will be chosen if set to false.
- dtype ({'float16', 'float32', 'float64', 'int32', 'uint8'},optional, default='float32') – DType of the output indices when ret_typ is “indices” or “both”. An error will be raised if the selected data type cannot precisely represent the indices.
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
transpose
(data=None, axes=_Null, out=None, name=None, **kwargs)¶ Permutes the dimensions of an array.
Examples:
x = [[ 1, 2], [ 3, 4]] transpose(x) = [[ 1., 3.], [ 2., 4.]] x = [[[ 1., 2.], [ 3., 4.]], [[ 5., 6.], [ 7., 8.]]] transpose(x) = [[[ 1., 5.], [ 3., 7.]], [[ 2., 6.], [ 4., 8.]]] transpose(x, axes=(1,0,2)) = [[[ 1., 2.], [ 5., 6.]], [[ 3., 4.], [ 7., 8.]]]
Defined in src/operator/tensor/matrix_op.cc:L311
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
trunc
(data=None, out=None, name=None, **kwargs)¶ Return the element-wise truncated value of the input.
The truncated value of the scalar x is the nearest integer i which is closer to zero than x is. In short, the fractional part of the signed number x is discarded.
Example:
trunc([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-2., -1., 1., 1., 2.]
The storage type of
trunc
output depends upon the input storage type:- trunc(default) = default
- trunc(row_sparse) = row_sparse
- trunc(csr) = csr
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L785
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
uniform
(low=_Null, high=_Null, shape=_Null, ctx=_Null, dtype=_Null, out=None, name=None, **kwargs)¶ Draw random samples from a uniform distribution.
Note
The existing alias
uniform
is deprecated.Samples are uniformly distributed over the half-open interval [low, high) (includes low, but excludes high).
Example:
uniform(low=0, high=1, shape=(2,2)) = [[ 0.60276335, 0.85794562], [ 0.54488319, 0.84725171]]
Defined in src/operator/random/sample_op.cc:L95
Parameters: - low (float, optional, default=0) – Lower bound of the distribution.
- high (float, optional, default=1) – Upper bound of the distribution.
- shape (Shape(tuple), optional, default=[]) – Shape of the output.
- ctx (string, optional, default='') – Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls.
- dtype ({'None', 'float16', 'float32', 'float64'},optional, default='None') – DType of the output in case this can’t be inferred. Defaults to float32 if not defined (dtype=None).
- out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
unravel_index
(data=None, shape=_Null, out=None, name=None, **kwargs)¶ Converts an array of flat indices into a batch of index arrays. The operator follows numpy conventions so a single multi index is given by a column of the output matrix.
Examples:
A = [22,41,37] unravel(A, shape=(7,6)) = [[3,6,6],[4,5,1]]
Defined in src/operator/tensor/ravel.cc:L65
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
where
(condition=None, x=None, y=None, out=None, name=None, **kwargs)¶ Return the elements, either from x or y, depending on the condition.
Given three ndarrays, condition, x, and y, return an ndarray with the elements from x or y, depending on the elements from condition are true or false. x and y must have the same shape. If condition has the same shape as x, each element in the output array is from x if the corresponding element in the condition is true, and from y if false.
If condition does not have the same shape as x, it must be a 1D array whose size is the same as x’s first dimension size. Each row of the output array is from x’s row if the corresponding element from condition is true, and from y’s row if false.
Note that all non-zero values are interpreted as
True
in condition.Examples:
x = [[1, 2], [3, 4]] y = [[5, 6], [7, 8]] cond = [[0, 1], [-1, 0]] where(cond, x, y) = [[5, 2], [3, 8]] csr_cond = cast_storage(cond, 'csr') where(csr_cond, x, y) = [[5, 2], [3, 8]]
Defined in src/operator/tensor/control_flow_op.cc:L57
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
zeros_like
(data=None, out=None, name=None, **kwargs)¶ Return an array of zeros with the same shape, type and storage type as the input array.
The storage type of
zeros_like
output depends on the storage type of the input- zeros_like(row_sparse) = row_sparse
- zeros_like(csr) = csr
- zeros_like(default) = default
Examples:
x = [[ 1., 1., 1.], [ 1., 1., 1.]] zeros_like(x) = [[ 0., 0., 0.], [ 0., 0., 0.]]
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays
-
mxnet.ndarray.
concatenate
(arrays, axis=0, always_copy=True)[source]¶ DEPRECATED, use
concat
insteadParameters: - arrays (list of NDArray) – Arrays to be concatenate. They must have identical shape except the first dimension. They also must have the same data type.
- axis (int) – The axis along which to concatenate.
- always_copy (bool) – Default True. When not True, if the arrays only contain one NDArray, that element will be returned directly, avoid copying.
Returns: An NDArray that lives on the same context as arrays[0].context.
Return type:
-
mxnet.ndarray.
ones
(shape, ctx=None, dtype=None, **kwargs)[source]¶ Returns a new array filled with all ones, with the given shape and type.
Parameters: - shape (int or tuple of int or list of int) – The shape of the empty array.
- ctx (Context, optional) – An optional device context.
Defaults to the current default context (
mxnet.context.current_context()
). - dtype (str or numpy.dtype, optional) – An optional value type (default is float32).
- out (NDArray, optional) – The output NDArray (default is None).
Returns: A new array of the specified shape filled with all ones.
Return type: Examples
>>> mx.nd.ones(1).asnumpy() array([ 1.], dtype=float32) >>> mx.nd.ones((1,2), mx.gpu(0))
>>> mx.nd.ones((1,2), dtype='float16').asnumpy() array([[ 1., 1.]], dtype=float16)
-
mxnet.ndarray.
add
(lhs, rhs)[source]¶ Returns element-wise sum of the input arrays with broadcasting.
Equivalent to
lhs + rhs
,mx.nd.broadcast_add(lhs, rhs)
andmx.nd.broadcast_plus(lhs, rhs)
.Note
If the corresponding dimensions of two arrays have the same size or one of them has size 1, then the arrays are broadcastable to a common shape
Parameters: Returns: The element-wise sum of the input arrays.
Return type: Examples
>>> x = mx.nd.ones((2,3)) >>> y = mx.nd.arange(2).reshape((2,1)) >>> z = mx.nd.arange(2).reshape((1,2)) >>> x.asnumpy() array([[ 1., 1., 1.], [ 1., 1., 1.]], dtype=float32) >>> y.asnumpy() array([[ 0.], [ 1.]], dtype=float32) >>> z.asnumpy() array([[ 0., 1.]], dtype=float32) >>> (x+2).asnumpy() array([[ 3., 3., 3.], [ 3., 3., 3.]], dtype=float32) >>> (x+y).asnumpy() array([[ 1., 1., 1.], [ 2., 2., 2.]], dtype=float32) >>> mx.nd.add(x,y).asnumpy() array([[ 1., 1., 1.], [ 2., 2., 2.]], dtype=float32) >>> (z + y).asnumpy() array([[ 0., 1.], [ 1., 2.]], dtype=float32)
-
mxnet.ndarray.
arange
(start, stop=None, step=1.0, repeat=1, ctx=None, dtype=)[source]¶ Returns evenly spaced values within a given interval.
Values are generated within the half-open interval [start, stop). In other words, the interval includes start but excludes stop. The function is similar to the built-in Python function range and to numpy.arange, but returns an NDArray.
Parameters: - start (number, optional) – Start of interval. The default start value is 0.
- stop (number) – End of interval.
- step (number, optional) – Spacing between values. The default step size is 1.
- repeat (int, optional) – Number of times to repeat each element. The default repeat count is 1.
- infer_range (boolean, optional) – When set to True, infer the stop position from the start, step, repeat, and output tensor size.
- ctx (Context, optional) – Device context. Default context is the current default context.
- dtype (str or numpy.dtype, optional) – The data type of the NDArray. The default datatype is np.float32.
Returns: NDArray of evenly spaced values in the specified range.
Return type: Examples
>>> mx.nd.arange(3).asnumpy() array([ 0., 1., 2.], dtype=float32) >>> mx.nd.arange(2, 6).asnumpy() array([ 2., 3., 4., 5.], dtype=float32) >>> mx.nd.arange(2, 6, step=2).asnumpy() array([ 2., 4.], dtype=float32) >>> mx.nd.arange(2, 6, step=1.5, repeat=2).asnumpy() array([ 2. , 2. , 3.5, 3.5, 5. , 5. ], dtype=float32) >>> mx.nd.arange(2, 6, step=2, repeat=3, dtype='int32').asnumpy() array([2, 2, 2, 4, 4, 4], dtype=int32)
-
mxnet.ndarray.
eye
(N, M=0, k=0, ctx=None, dtype=None, **kwargs)[source]¶ Return a 2-D array with ones on the diagonal and zeros elsewhere.
Parameters: - N (int) – Number of rows in the output.
- M (int, optional) – Number of columns in the output. If 0, defaults to N.
- k (int, optional) – Index of the diagonal: 0 (the default) refers to the main diagonal, a positive value refers to an upper diagonal, and a negative value to a lower diagonal.
- ctx (Context, optional) – An optional device context (default is the current default context)
- dtype (str or numpy.dtype, optional) – An optional value type (default is float32)
Returns: A created array
Return type: Examples
>>> mx.nd.eye(2) [[ 1. 0.] [ 0. 1.]]
>>> mx.nd.eye(2, 3, 1) [[ 0. 1. 0.] [ 0. 0. 1.]]
-
mxnet.ndarray.
divide
(lhs, rhs)[source]¶ Returns element-wise division of the input arrays with broadcasting.
Equivalent to
lhs / rhs
andmx.nd.broadcast_div(lhs, rhs)
.Note
If the corresponding dimensions of two arrays have the same size or one of them has size 1, then the arrays are broadcastable to a common shape.
Parameters: Returns: The element-wise division of the input arrays.
Return type: Examples
>>> x = mx.nd.ones((2,3))*6 >>> y = mx.nd.ones((2,1))*2 >>> x.asnumpy() array([[ 6., 6., 6.], [ 6., 6., 6.]], dtype=float32) >>> y.asnumpy() array([[ 2.], [ 2.]], dtype=float32) >>> x/2
>>> (x/3).asnumpy() array([[ 2., 2., 2.], [ 2., 2., 2.]], dtype=float32) >>> (x/y).asnumpy() array([[ 3., 3., 3.], [ 3., 3., 3.]], dtype=float32) >>> mx.nd.divide(x,y).asnumpy() array([[ 3., 3., 3.], [ 3., 3., 3.]], dtype=float32)
-
mxnet.ndarray.
equal
(lhs, rhs)[source]¶ Returns the result of element-wise equal to (==) comparison operation with broadcasting.
For each element in input arrays, return 1(true) if corresponding elements are same, otherwise return 0(false).
Equivalent to
lhs == rhs
andmx.nd.broadcast_equal(lhs, rhs)
.Note
If the corresponding dimensions of two arrays have the same size or one of them has size 1, then the arrays are broadcastable to a common shape.
Parameters: Returns: Output array of boolean values.
Return type: Examples
>>> x = mx.nd.ones((2,3)) >>> y = mx.nd.arange(2).reshape((2,1)) >>> z = mx.nd.arange(2).reshape((1,2)) >>> x.asnumpy() array([[ 1., 1., 1.], [ 1., 1., 1.]], dtype=float32) >>> y.asnumpy() array([[ 0.], [ 1.]], dtype=float32) >>> z.asnumpy() array([[ 0., 1.]], dtype=float32) >>> (x == 1).asnumpy() array([[ 1., 1., 1.], [ 1., 1., 1.]], dtype=float32) >>> (x == y).asnumpy() array([[ 0., 0., 0.], [ 1., 1., 1.]], dtype=float32) >>> mx.nd.equal(x,y).asnumpy() array([[ 0., 0., 0.], [ 1., 1., 1.]], dtype=float32) >>> (z == y).asnumpy() array([[ 1., 0.], [ 0., 1.]], dtype=float32)
-
mxnet.ndarray.
full
(shape, val, ctx=None, dtype=, out=None)[source]¶ Returns a new array of given shape and type, filled with the given value val.
Parameters: - shape (int or tuple of int) – The shape of the new array.
- val (scalar) – Fill value.
- ctx (Context, optional) – Device context (default is the current default context).
- dtype (str or numpy.dtype, optional) – The data type of the returned NDArray. The default datatype is float32.
- out (NDArray, optional) – The output NDArray (default is None).
Returns: NDArray filled with val, with the given shape, ctx, and dtype.
Return type: Examples
>>> mx.nd.full(1, 2.0).asnumpy() array([ 2.], dtype=float32) >>> mx.nd.full((1, 2), 2.0, mx.gpu(0))
>>> mx.nd.full((1, 2), 2.0, dtype='float16').asnumpy() array([[ 2., 2.]], dtype=float16)
-
mxnet.ndarray.
greater
(lhs, rhs)[source]¶ Returns the result of element-wise greater than (>) comparison operation with broadcasting.
For each element in input arrays, return 1(true) if lhs elements are greater than rhs, otherwise return 0(false).
Equivalent to
lhs > rhs
andmx.nd.broadcast_greater(lhs, rhs)
.Note
If the corresponding dimensions of two arrays have the same size or one of them has size 1, then the arrays are broadcastable to a common shape.
Parameters: Returns: Output array of boolean values.
Return type: Examples
>>> x = mx.nd.ones((2,3)) >>> y = mx.nd.arange(2).reshape((2,1)) >>> z = mx.nd.arange(2).reshape((1,2)) >>> x.asnumpy() array([[ 1., 1., 1.], [ 1., 1., 1.]], dtype=float32) >>> y.asnumpy() array([[ 0.], [ 1.]], dtype=float32) >>> z.asnumpy() array([[ 0., 1.]], dtype=float32) >>> (x > 1).asnumpy() array([[ 0., 0., 0.], [ 0., 0., 0.]], dtype=float32) >>> (x > y).asnumpy() array([[ 1., 1., 1.], [ 0., 0., 0.]], dtype=float32) >>> mx.nd.greater(x, y).asnumpy() array([[ 1., 1., 1.], [ 0., 0., 0.]], dtype=float32) >>> (z > y).asnumpy() array([[ 0., 1.], [ 0., 0.]], dtype=float32)
-
mxnet.ndarray.
greater_equal
(lhs, rhs)[source]¶ Returns the result of element-wise greater than or equal to (>=) comparison operation with broadcasting.
For each element in input arrays, return 1(true) if lhs elements are greater than equal to rhs, otherwise return 0(false).
Equivalent to
lhs >= rhs
andmx.nd.broadcast_greater_equal(lhs, rhs)
.Note
If the corresponding dimensions of two arrays have the same size or one of them has size 1, then the arrays are broadcastable to a common shape.
Parameters: Returns: Output array of boolean values.
Return type: Examples
>>> x = mx.nd.ones((2,3)) >>> y = mx.nd.arange(2).reshape((2,1)) >>> z = mx.nd.arange(2).reshape((1,2)) >>> x.asnumpy() array([[ 1., 1., 1.], [ 1., 1., 1.]], dtype=float32) >>> y.asnumpy() array([[ 0.], [ 1.]], dtype=float32) >>> z.asnumpy() array([[ 0., 1.]], dtype=float32) >>> (x >= 1).asnumpy() array([[ 1., 1., 1.], [ 1., 1., 1.]], dtype=float32) >>> (x >= y).asnumpy() array([[ 1., 1., 1.], [ 1., 1., 1.]], dtype=float32) >>> mx.nd.greater_equal(x, y).asnumpy() array([[ 1., 1., 1.], [ 1., 1., 1.]], dtype=float32) >>> (z >= y).asnumpy() array([[ 1., 1.], [ 0., 1.]], dtype=float32)
-
mxnet.ndarray.
imdecode
(str_img, clip_rect=(0, 0, 0, 0), out=None, index=0, channels=3, mean=None)[source]¶ DEPRECATED, use mx.img instead
Parameters: - str_img (str) – Binary image data
- clip_rect (iterable of 4 int) – Clip decoded image to rectangle (x0, y0, x1, y1).
- out (NDArray) – Output buffer. Can be 3 dimensional (c, h, w) or 4 dimensional (n, c, h, w).
- index (int) – Output decoded image to i-th slice of 4 dimensional buffer.
- channels (int) – Number of channels to output. Decode to grey scale when channels = 1.
- mean (NDArray) – Subtract mean from decode image before outputing.
-
mxnet.ndarray.
lesser
(lhs, rhs)[source]¶ Returns the result of element-wise lesser than (<) comparison operation with broadcasting.
For each element in input arrays, return 1(true) if lhs elements are less than rhs, otherwise return 0(false).
Equivalent to
lhs < rhs
andmx.nd.broadcast_lesser(lhs, rhs)
.Note
If the corresponding dimensions of two arrays have the same size or one of them has size 1, then the arrays are broadcastable to a common shape.
Parameters: Returns: Output array of boolean values.
Return type: Examples
>>> x = mx.nd.ones((2,3)) >>> y = mx.nd.arange(2).reshape((2,1)) >>> z = mx.nd.arange(2).reshape((1,2)) >>> x.asnumpy() array([[ 1., 1., 1.], [ 1., 1., 1.]], dtype=float32) >>> y.asnumpy() array([[ 0.], [ 1.]], dtype=float32) >>> z.asnumpy() array([[ 0., 1.]], dtype=float32) >>> (x < 1).asnumpy() array([[ 0., 0., 0.], [ 0., 0., 0.]], dtype=float32) >>> (x < y).asnumpy() array([[ 0., 0., 0.], [ 0., 0., 0.]], dtype=float32) >>> mx.nd.lesser(x, y).asnumpy() array([[ 0., 0., 0.], [ 0., 0., 0.]], dtype=float32) >>> (z < y).asnumpy() array([[ 0., 0.], [ 1., 0.]], dtype=float32)
-
mxnet.ndarray.
lesser_equal
(lhs, rhs)[source]¶ Returns the result of element-wise lesser than or equal to (<=) comparison operation with broadcasting.
For each element in input arrays, return 1(true) if lhs elements are lesser than equal to rhs, otherwise return 0(false).
Equivalent to
lhs <= rhs
andmx.nd.broadcast_lesser_equal(lhs, rhs)
.Note
If the corresponding dimensions of two arrays have the same size or one of them has size 1, then the arrays are broadcastable to a common shape.
Parameters: Returns: Output array of boolean values.
Return type: Examples
>>> x = mx.nd.ones((2,3)) >>> y = mx.nd.arange(2).reshape((2,1)) >>> z = mx.nd.arange(2).reshape((1,2)) >>> x.asnumpy() array([[ 1., 1., 1.], [ 1., 1., 1.]], dtype=float32) >>> y.asnumpy() array([[ 0.], [ 1.]], dtype=float32) >>> z.asnumpy() array([[ 0., 1.]], dtype=float32) >>> (x <= 1).asnumpy() array([[ 1., 1., 1.], [ 1., 1., 1.]], dtype=float32) >>> (x <= y).asnumpy() array([[ 0., 0., 0.], [ 1., 1., 1.]], dtype=float32) >>> mx.nd.lesser_equal(x, y).asnumpy() array([[ 0., 0., 0.], [ 1., 1., 1.]], dtype=float32) >>> (z <= y).asnumpy() array([[ 1., 0.], [ 1., 1.]], dtype=float32)
-
mxnet.ndarray.
logical_and
(lhs, rhs)[source]¶ Returns the result of element-wise logical and comparison operation with broadcasting.
For each element in input arrays, return 1(true) if lhs elements and rhs elements are true, otherwise return 0(false).
Equivalent to
lhs and rhs
andmx.nd.broadcast_logical_and(lhs, rhs)
.Note
If the corresponding dimensions of two arrays have the same size or one of them has size 1, then the arrays are broadcastable to a common shape.
Parameters: Returns: Output array of boolean values.
Return type: Examples
>>> x = mx.nd.ones((2,3)) >>> y = mx.nd.arange(2).reshape((2,1)) >>> z = mx.nd.arange(2).reshape((1,2)) >>> x.asnumpy() array([[ 1., 1., 1.], [ 1., 1., 1.]], dtype=float32) >>> y.asnumpy() array([[ 0.], [ 1.]], dtype=float32) >>> z.asnumpy() array([[ 0., 1.]], dtype=float32) >>> mx.nd.logical_and(x, 1).asnumpy() array([[ 1., 1., 1.], [ 1., 1., 1.]], dtype=float32) >>> mx.nd.logical_and(x, y).asnumpy() array([[ 0., 0., 0.], [ 1., 1., 1.]], dtype=float32) >>> mx.nd.logical_and(z, y).asnumpy() array([[ 0., 0.], [ 0., 1.]], dtype=float32)
-
mxnet.ndarray.
logical_or
(lhs, rhs)[source]¶ Returns the result of element-wise logical or comparison operation with broadcasting.
For each element in input arrays, return 1(true) if lhs elements or rhs elements are true, otherwise return 0(false).
Equivalent to
lhs or rhs
andmx.nd.broadcast_logical_or(lhs, rhs)
.Note
If the corresponding dimensions of two arrays have the same size or one of them has size 1, then the arrays are broadcastable to a common shape.
Parameters: Returns: Output array of boolean values.
Return type: Examples
>>> x = mx.nd.ones((2,3)) >>> y = mx.nd.arange(2).reshape((2,1)) >>> z = mx.nd.arange(2).reshape((1,2)) >>> x.asnumpy() array([[ 1., 1., 1.], [ 1., 1., 1.]], dtype=float32) >>> y.asnumpy() array([[ 0.], [ 1.]], dtype=float32) >>> z.asnumpy() array([[ 0., 1.]], dtype=float32) >>> mx.nd.logical_or(x, 1).asnumpy() array([[ 1., 1., 1.], [ 1., 1., 1.]], dtype=float32) >>> mx.nd.logical_or(x, y).asnumpy() array([[ 1., 1., 1.], [ 1., 1., 1.]], dtype=float32) >>> mx.nd.logical_or(z, y).asnumpy() array([[ 0., 1.], [ 1., 1.]], dtype=float32)
-
mxnet.ndarray.
logical_xor
(lhs, rhs)[source]¶ Returns the result of element-wise logical xor comparison operation with broadcasting.
For each element in input arrays, return 1(true) if lhs elements or rhs elements are true, otherwise return 0(false).
Equivalent to
bool(lhs) ^ bool(rhs)
andmx.nd.broadcast_logical_xor(lhs, rhs)
.Note
If the corresponding dimensions of two arrays have the same size or one of them has size 1, then the arrays are broadcastable to a common shape.
Parameters: Returns: Output array of boolean values.
Return type: Examples
>>> x = mx.nd.ones((2,3)) >>> y = mx.nd.arange(2).reshape((2,1)) >>> z = mx.nd.arange(2).reshape((1,2)) >>> x.asnumpy() array([[ 1., 1., 1.], [ 1., 1., 1.]], dtype=float32) >>> y.asnumpy() array([[ 0.], [ 1.]], dtype=float32) >>> z.asnumpy() array([[ 0., 1.]], dtype=float32) >>> mx.nd.logical_xor(x, y).asnumpy() array([[ 1., 1., 1.], [ 0., 0., 0.]], dtype=float32)
-
mxnet.ndarray.
maximum
(lhs, rhs)[source]¶ Returns element-wise maximum of the input arrays with broadcasting.
Equivalent to
mx.nd.broadcast_maximum(lhs, rhs)
.Note
If the corresponding dimensions of two arrays have the same size or one of them has size 1, then the arrays are broadcastable to a common shape.
Parameters: Returns: The element-wise maximum of the input arrays.
Return type: Examples
>>> x = mx.nd.ones((2,3)) >>> y = mx.nd.arange(2).reshape((2,1)) >>> z = mx.nd.arange(2).reshape((1,2)) >>> x.asnumpy() array([[ 1., 1., 1.], [ 1., 1., 1.]], dtype=float32) >>> y.asnumpy() array([[ 0.], [ 1.]], dtype=float32) >>> z.asnumpy() array([[ 0., 1.]], dtype=float32) >>> mx.nd.maximum(x, 2).asnumpy() array([[ 2., 2., 2.], [ 2., 2., 2.]], dtype=float32) >>> mx.nd.maximum(x, y).asnumpy() array([[ 1., 1., 1.], [ 1., 1., 1.]], dtype=float32) >>> mx.nd.maximum(y, z).asnumpy() array([[ 0., 1.], [ 1., 1.]], dtype=float32)
-
mxnet.ndarray.
minimum
(lhs, rhs)[source]¶ Returns element-wise minimum of the input arrays with broadcasting.
Equivalent to
mx.nd.broadcast_minimum(lhs, rhs)
.Note
If the corresponding dimensions of two arrays have the same size or one of them has size 1, then the arrays are broadcastable to a common shape.
Parameters: Returns: The element-wise minimum of the input arrays.
Return type: Examples
>>> x = mx.nd.ones((2,3)) >>> y = mx.nd.arange(2).reshape((2,1)) >>> z = mx.nd.arange(2).reshape((1,2)) >>> x.asnumpy() array([[ 1., 1., 1.], [ 1., 1., 1.]], dtype=float32) >>> y.asnumpy() array([[ 0.], [ 1.]], dtype=float32) >>> z.asnumpy() array([[ 0., 1.]], dtype=float32) >>> mx.nd.minimum(x, 2).asnumpy() array([[ 1., 1., 1.], [ 1., 1., 1.]], dtype=float32) >>> mx.nd.minimum(x, y).asnumpy() array([[ 0., 0., 0.], [ 1., 1., 1.]], dtype=float32) >>> mx.nd.minimum(z, y).asnumpy() array([[ 0., 0.], [ 0., 1.]], dtype=float32)
-
mxnet.ndarray.
moveaxis
(tensor, source, destination)[source]¶ Moves the source axis into the destination position while leaving the other axes in their original order
Parameters: - tensor (mx.nd.array) – The array which axes should be reordered
- source (int) – Original position of the axes to move.
- destination (int) – Destination position for each of the original axes.
Returns: result – Array with moved axes.
Return type: mx.nd.array
Examples
>>> X = mx.nd.array([[1, 2, 3], [4, 5, 6]]) >>> mx.nd.moveaxis(X, 0, 1).shape (3L, 2L)
-
mxnet.ndarray.
modulo
(lhs, rhs)[source]¶ Returns element-wise modulo of the input arrays with broadcasting.
Equivalent to
lhs % rhs
andmx.nd.broadcast_mod(lhs, rhs)
.Note
If the corresponding dimensions of two arrays have the same size or one of them has size 1, then the arrays are broadcastable to a common shape.
Parameters: Returns: The element-wise modulo of the input arrays.
Return type: Examples
>>> x = mx.nd.ones((2,3))*6 >>> y = mx.nd.ones((2,1))*4 >>> x.asnumpy() array([[ 6., 6., 6.], [ 6., 6., 6.]], dtype=float32) >>> y.asnumpy() array([[ 4.], [ 4.]], dtype=float32) >>> x%5
>>> (x%5).asnumpy() array([[ 1., 1., 1.], [ 1., 1., 1.]], dtype=float32) >>> (x%y).asnumpy() array([[ 2., 2., 2.], [ 2., 2., 2.]], dtype=float32) >>> mx.nd.modulo(x,y).asnumpy() array([[ 2., 2., 2.], [ 2., 2., 2.]], dtype=float32)
-
mxnet.ndarray.
multiply
(lhs, rhs)[source]¶ Returns element-wise product of the input arrays with broadcasting.
Equivalent to
lhs * rhs
andmx.nd.broadcast_mul(lhs, rhs)
.Note
If the corresponding dimensions of two arrays have the same size or one of them has size 1, then the arrays are broadcastable to a common shape.
Parameters: Returns: The element-wise multiplication of the input arrays.
Return type: Examples
>>> x = mx.nd.ones((2,3)) >>> y = mx.nd.arange(2).reshape((2,1)) >>> z = mx.nd.arange(2).reshape((1,2)) >>> x.asnumpy() array([[ 1., 1., 1.], [ 1., 1., 1.]], dtype=float32) >>> y.asnumpy() array([[ 0.], [ 1.]], dtype=float32) >>> z.asnumpy() array([[ 0., 1.]], dtype=float32) >>> (x*2).asnumpy() array([[ 2., 2., 2.], [ 2., 2., 2.]], dtype=float32) >>> (x*y).asnumpy() array([[ 0., 0., 0.], [ 1., 1., 1.]], dtype=float32) >>> mx.nd.multiply(x, y).asnumpy() array([[ 0., 0., 0.], [ 1., 1., 1.]], dtype=float32) >>> (z*y).asnumpy() array([[ 0., 0.], [ 0., 1.]], dtype=float32)
-
mxnet.ndarray.
not_equal
(lhs, rhs)[source]¶ Returns the result of element-wise not equal to (!=) comparison operation with broadcasting.
For each element in input arrays, return 1(true) if corresponding elements are different, otherwise return 0(false).
Equivalent to
lhs != rhs
andmx.nd.broadcast_not_equal(lhs, rhs)
.Note
If the corresponding dimensions of two arrays have the same size or one of them has size 1, then the arrays are broadcastable to a common shape.
Parameters: Returns: Output array of boolean values.
Return type: Examples
>>> x = mx.nd.ones((2,3)) >>> y = mx.nd.arange(2).reshape((2,1)) >>> z = mx.nd.arange(2).reshape((1,2)) >>> x.asnumpy() array([[ 1., 1., 1.], [ 1., 1., 1.]], dtype=float32) >>> y.asnumpy() array([[ 0.], [ 1.]], dtype=float32) >>> z.asnumpy() array([[ 0., 1.]], dtype=float32) >>> (z == y).asnumpy() array([[ 1., 0.], [ 0., 1.]], dtype=float32) >>> (x != 1).asnumpy() array([[ 0., 0., 0.], [ 0., 0., 0.]], dtype=float32) >>> (x != y).asnumpy() array([[ 1., 1., 1.], [ 0., 0., 0.]], dtype=float32) >>> mx.nd.not_equal(x, y).asnumpy() array([[ 1., 1., 1.], [ 0., 0., 0.]], dtype=float32) >>> (z != y).asnumpy() array([[ 0., 1.], [ 1., 0.]], dtype=float32)
-
mxnet.ndarray.
onehot_encode
(indices, out)[source]¶ One-hot encoding indices into matrix out.
Note
onehot_encode is deprecated. Use one_hot instead.
-
mxnet.ndarray.
power
(base, exp)[source]¶ Returns result of first array elements raised to powers from second array, element-wise with broadcasting.
Equivalent to
base ** exp
andmx.nd.broadcast_power(lhs, rhs)
.Note
If the corresponding dimensions of two arrays have the same size or one of them has size 1, then the arrays are broadcastable to a common shape.
Parameters: Returns: The bases in x raised to the exponents in y.
Return type: Examples
>>> x = mx.nd.ones((2,3))*2 >>> y = mx.nd.arange(1,3).reshape((2,1)) >>> z = mx.nd.arange(1,3).reshape((2,1)) >>> x.asnumpy() array([[ 2., 2., 2.], [ 2., 2., 2.]], dtype=float32) >>> y.asnumpy() array([[ 1.], [ 2.]], dtype=float32) >>> z.asnumpy() array([[ 1.], [ 2.]], dtype=float32) >>> (x**2).asnumpy() array([[ 4., 4., 4.], [ 4., 4., 4.]], dtype=float32) >>> (x**y).asnumpy() array([[ 2., 2., 2.], [ 4., 4., 4.]], dtype=float32) >>> mx.nd.power(x,y).asnumpy() array([[ 2., 2., 2.], [ 4., 4., 4.]], dtype=float32) >>> (z**y).asnumpy() array([[ 1.], [ 4.]], dtype=float32)
-
mxnet.ndarray.
subtract
(lhs, rhs)[source]¶ Returns element-wise difference of the input arrays with broadcasting.
Equivalent to
lhs - rhs
,mx.nd.broadcast_sub(lhs, rhs)
andmx.nd.broadcast_minus(lhs, rhs)
.Note
If the corresponding dimensions of two arrays have the same size or one of them has size 1, then the arrays are broadcastable to a common shape.
Parameters: Returns: The element-wise difference of the input arrays.
Return type: Examples
>>> x = mx.nd.ones((2,3)) >>> y = mx.nd.arange(2).reshape((2,1)) >>> z = mx.nd.arange(2).reshape((1,2)) >>> x.asnumpy() array([[ 1., 1., 1.], [ 1., 1., 1.]], dtype=float32) >>> y.asnumpy() array([[ 0.], [ 1.]], dtype=float32) >>> z.asnumpy() array([[ 0., 1.]], dtype=float32) >>> (x-2).asnumpy() array([[-1., -1., -1.], [-1., -1., -1.]], dtype=float32) >>> (x-y).asnumpy() array([[ 1., 1., 1.], [ 0., 0., 0.]], dtype=float32) >>> mx.nd.subtract(x,y).asnumpy() array([[ 1., 1., 1.], [ 0., 0., 0.]], dtype=float32) >>> (z-y).asnumpy() array([[ 0., 1.], [-1., 0.]], dtype=float32)
-
mxnet.ndarray.
waitall
()[source]¶ Wait for all async operations to finish in MXNet.
This function is used for benchmarking only.
-
mxnet.ndarray.
histogram
(a, bins=10, range=None)[source]¶ Compute the histogram of the input data.
Parameters: - a (NDArray) – Input data. The histogram is computed over the flattened array.
- bins (int or sequence of scalars) – If bins is an int, it defines the number of equal-width bins in the given range (10, by default). If bins is a sequence, it defines the bin edges, including the rightmost edge, allowing for non-uniform bin widths.
- range ((float, float), optional) – The lower and upper range of the bins. If not provided, range is simply (a.min(), a.max()). Values outside the range are ignored. The first element of the range must be less than or equal to the second. range affects the automatic bin computation as well, the range will be equally divided by the number of bins.
-
mxnet.ndarray.
zeros
(shape, ctx=None, dtype=None, stype=None, **kwargs)[source]¶ Return a new array of given shape and type, filled with zeros.
Parameters: - shape (int or tuple of int) – The shape of the empty array
- ctx (Context, optional) – An optional device context (default is the current default context)
- dtype (str or numpy.dtype, optional) – An optional value type (default is float32)
- stype (string, optional) – The storage type of the empty array, such as ‘row_sparse’, ‘csr’, etc.
Returns: A created array
Return type: Examples
>>> mx.nd.zeros((1,2), mx.cpu(), stype='csr')
>>> mx.nd.zeros((1,2), mx.cpu(), 'float16', stype='row_sparse').asnumpy() array([[ 0., 0.]], dtype=float16)
-
mxnet.ndarray.
empty
(shape, ctx=None, dtype=None, stype=None)[source]¶ Returns a new array of given shape and type, without initializing entries.
Parameters: - shape (int or tuple of int) – The shape of the empty array.
- ctx (Context, optional) – An optional device context (default is the current default context).
- dtype (str or numpy.dtype, optional) – An optional value type (default is float32).
- stype (str, optional) – An optional storage type (default is default).
Returns: A created array.
Return type: Examples
>>> mx.nd.empty(1)
>>> mx.nd.empty((1,2), mx.gpu(0)) >>> mx.nd.empty((1,2), mx.gpu(0), 'float16') >>> mx.nd.empty((1,2), stype='csr')
-
mxnet.ndarray.
array
(source_array, ctx=None, dtype=None)[source]¶ Creates an array from any object exposing the array interface.
Parameters: - source_array (array_like) – An object exposing the array interface, an object whose __array__ method returns an array, or any (nested) sequence.
- ctx (Context, optional) – Device context (default is the current default context).
- dtype (str or numpy.dtype, optional) – The data type of the output array. The default dtype is
source_array.dtype
if source_array is an NDArray, float32 otherwise.
Returns: An array with the same contents as the source_array.
Return type: Examples
>>> import numpy as np >>> mx.nd.array([1, 2, 3])
>>> mx.nd.array([[1, 2], [3, 4]]) >>> mx.nd.array(np.zeros((3, 2))) >>> mx.nd.array(np.zeros((3, 2)), mx.gpu(0)) >>> mx.nd.array(mx.nd.zeros((3, 2), stype='row_sparse'))
-
mxnet.ndarray.
load
(fname)[source]¶ Loads an array from file.
See more details in
save
.Parameters: fname (str) – The filename. Returns: Loaded data. Return type: list of NDArray, RowSparseNDArray or CSRNDArray, or dict of str to NDArray, RowSparseNDArray or CSRNDArray
-
mxnet.ndarray.
load_frombuffer
(buf)[source]¶ Loads an array dictionary or list from a buffer
See more details in
save
.Parameters: buf (str) – Buffer containing contents of a file as a string or bytes. Returns: Loaded data. Return type: list of NDArray, RowSparseNDArray or CSRNDArray, or dict of str to NDArray, RowSparseNDArray or CSRNDArray
-
mxnet.ndarray.
save
(fname, data)[source]¶ Saves a list of arrays or a dict of str->array to file.
Examples of filenames:
/path/to/file
s3://my-bucket/path/to/file
(if compiled with AWS S3 supports)hdfs://path/to/file
(if compiled with HDFS supports)
Parameters: - fname (str) – The filename.
- data (NDArray, RowSparseNDArray or CSRNDArray, or list of NDArray, RowSparseNDArray or CSRNDArray, or dict of str to NDArray, RowSparseNDArray or CSRNDArray) – The data to save.
Examples
>>> x = mx.nd.zeros((2,3)) >>> y = mx.nd.ones((1,4)) >>> mx.nd.save('my_list', [x,y]) >>> mx.nd.save('my_dict', {'x':x, 'y':y}) >>> mx.nd.load('my_list') [
, >>> mx.nd.load('my_dict') {'y':] , 'x': }
Random number interface of MXNet.
-
mxnet.random.
seed
(seed_state, ctx='all')[source]¶ Seeds the random number generators in MXNet.
This affects the behavior of modules in MXNet that uses random number generators, like the dropout operator and NDArray‘s random sampling operators.
Parameters: - seed_state (int) – The random number seed.
- ctx (Context) – The device context of the generator. The default is “all” which means seeding random number generators of all devices.
Notes
Random number generators in MXNet are device specific. mx.random.seed(seed_state) sets the state of each generator using seed_state and the device id. Therefore, random numbers generated from different devices can be different even if they are seeded using the same seed.
To produce identical random number sequences independent of the device id, set optional ctx argument. This produces the same sequence of random numbers independent of the device id, but the sequence can be different on different kind of devices as MXNet’s random number generators for CPU and GPU use different algorithms.
Example
>>> print(mx.nd.random.normal(shape=(2,2)).asnumpy()) [[ 1.36481571 -0.62203991] [-1.4962182 -0.08511394]] >>> print(mx.nd.random.normal(shape=(2,2)).asnumpy()) [[ 1.09544981 -0.20014545] [-0.20808885 0.2527658 ]] # Same results on the same device with the same seed >>> mx.random.seed(128) >>> print(mx.nd.random.normal(shape=(2,2)).asnumpy()) [[ 0.47400656 -0.75213492] [ 0.20251541 0.95352972]] >>> mx.random.seed(128) >>> print(mx.nd.random.normal(shape=(2,2)).asnumpy()) [[ 0.47400656 -0.75213492] [ 0.20251541 0.95352972]] # Different results on gpu(0) and gpu(1) with the same seed >>> mx.random.seed(128) >>> print(mx.nd.random.normal(shape=(2,2), ctx=mx.gpu(0)).asnumpy()) [[ 2.5020072 -1.6884501] [-0.7931333 -1.4218881]] >>> mx.random.seed(128) >>> print(mx.nd.random.normal(shape=(2,2), ctx=mx.gpu(1)).asnumpy()) [[ 0.24336822 -1.664805 ] [-1.0223296 1.253198 ]] # Seeding with `ctx` argument produces identical results on gpu(0) and gpu(1) >>> mx.random.seed(128, ctx=mx.gpu(0)) >>> print(mx.nd.random.normal(shape=(2,2), ctx=mx.gpu(0)).asnumpy()) [[ 2.5020072 -1.6884501] [-0.7931333 -1.4218881]] >>> mx.random.seed(128, ctx=mx.gpu(1)) >>> print(mx.nd.random.normal(shape=(2,2), ctx=mx.gpu(1)).asnumpy()) [[ 2.5020072 -1.6884501] [-0.7931333 -1.4218881]]