Tensor at a glance

This page provides an overview of most commonly used tensor functions by category.

For a complete, alphabetical reference of all tensor functions see Tensor<'T> and the device-specific functions in HostTensor and CudaTensor.

Creation functions

Use these functions to create a new tensor.

Function	Description
arange	Creates a new vector filled with equaly spaced values using a specifed increment.
counting	Creates a new vector filled with the integers from zero to the specified maximum.
empty	Creates a new, empty tensor with the given number of dimensions.
falses	Creates a new boolean tensor filled with falses.
filled	Creates a new tensor filled with the specified value.
identity	Creates a new identity matrix.
ones	Creates a new tensor filled with ones (1).
onesLike	Creates a new tensor filled with ones using the specified tensor as template.
linspace	Creates a new vector of given size filled with equaly spaced values.
scalar	Creates a new zero-dimensional (scalar) tensor with the specified value.
scalarLike	Creates a new zero-dimensional (scalar) tensor using the specified tensor as template and with the specified value.
trues	Creates a new boolean tensor filled with trues.
zeros	Creates a new tensor filled with zeros (0).
zerosLike	Creates a new tensor filled with zeros using the specified tensor as template.

Slicing and element access functions

Use these functions to slice tensors or access individual elements of them.

Function	Description
Item	Accesses a slice (part) of the tensor.
M	Picks elements from a tensor using one or more boolean mask tensors.
Value	Gets the value of a zero-dimensional (scalar) tensor.

Element-wise operations

These mathematical operations are applied element-wise to each element of the tensor(s).

Function	Description
( ~- )	Element-wise negation.
( + )	Element-wise addition.
( - )	Element-wise substraction.
( * )	Element-wise multiplication.
( / )	Element-wise division.
( % )	Element-wise remainder of division.
Abs	Element-wise absolute value.
Acos	Element-wise arccosine (inverse cosine).
Asin	Element-wise arcsine (inverse sine).
Atan	Element-wise arctanget (inverse tangent).
Ceiling	Element-wise ceiling (round towards positive infinity).
Cos	Element-wise cosine.
Cosh	Element-wise hyperbolic cosine.
Exp	Element-wise exponential function.
Floor	Element-wise floor (round towards negative infinity).
Log	Element-wise natural logarithm.
Log10	Element-wise common logarithm.
Pow	Element-wise exponentiation.
Round	Element-wise rounding.
Sgn	Element-wise sign.
Sin	Element-wise sine.
Sinh	Element-wise hyperbolic sine.
Sqrt	Element-wise square root.
Tan	Element-wise tangent.
Tanh	Element-wise hyperbolic tangent.
Truncate	Element-wise truncation (rounding towards zero).

Tensor operations

These functions perform various operations on one or more tensors.

Function	Description
concat	Concatenates tensors along an axis.
copy	Returns a copy of the tensor.
diag	Returns a view of the diagonal of the matrix.
diagAxis	Returns a view of the diagonal along the given axes.
diagMat	Creates a matrix with the specified diagonal.
diagMatAxis	Creates a tensor with the specified diagonal along the given axes.
diff	Calculates the difference between adjoining elements of the vector.
diffAxis	Calculates the difference between adjoining elements along the specified axes.
ofBlocks	Builds a tensor out of tensor blocks.
replicate	Repeats the tensor along an axis.
T	Transpose of a matrix.

Linear algebra functions

Use these functions to perform basic linear algebra operations on tensors.

Function	Description
( .* )	Computes the (batched) matrix product, (batched) matrix-vector product or scalar product.
norm	Calculates the norm of the (flattened) tensor.
normAxis	Calculates the norm along the specified axis.
invert	(Batch) inverts a matrix.
pseudoInvert	Computes the (batched) Moore-Penrose pseudo-inverse of the specified matrix.
SVD	Computes the (batched) singular value decomposition (SVD) of the specified matrix.
symmetricEigenDecomposition	Computes the (real) eigendecomposition of a symmetric matrix.
tensorProduct	Computes the tensor product between two tensors.

Shape functions

Use these functions to work with the shape and memory layout of a tensor.

Function	Description
atLeastND	Pads the tensor from the left with size-one dimensions until it has at least the specified number of dimensions.
broadcastDim	Broadcast a dimension to a specified size.
broadcastTo	Broadcasts the specified tensor to the specified shape.
broadcastToSame	Broadcasts all specified tensors to have the same shape.
broadcastToSameInDims	Broadcasts all specified tensors to have the same size in the specified dimensions.
cutLeft	Removes the first dimension.
cutRight	Removes the last dimension.
flatten	Flattens the tensor into a (one-dimensional) vector.
insertAxis	Insert a dimension of size one before the specifed dimension.
isBroadcasted	Checks if the specified tensor is broadcasted in at least one dimension.
Layout	Memory layout of the tensor.
NDims	Dimensionality of the tensor.
NElems	Total number of elements within the tensor.
padLeft	Insert a dimension of size one as the first dimension.
padRight	Append a dimension of size one after the last dimension.
padToSame	Pads all specified tensors from the left with dimensions of size one until they have the same dimensionality.
permuteAxes	Permutes the axes as specified.
reshape	Changes the shape of a tensor.
reverseAxis	Reverses the elements in the specified dimension.
relayout	Creates a tensor with the specified layout sharing its storage with the original tensor.
Shape	Shape of the tensor.
swapDim	Swaps the specified dimensions of the tensor.

Data type functions

Use these functions to query or change the data type of the elements of a tensor.

Function	Description
convert	Convert the elements of a tensor to the specifed type.
DataType	Type of data stored within the tensor.

Device and storage functions

Use these functions to query or change the storage device of a tensor.

Function	Description
Dev	Device the data of tensor is stored on.
Storage	The storage object that holds the data of this tensor.
transfer	Transfers a tensor to the specifed device.

Comparison functions

Use these functions to perform comparisons of tensors. The results are mostly boolean tensors.

Function	Description
( ==== )	Element-wise equality test.
( <<<< )	Element-wise less-than test.
( <<== )	Element-wise less-than-or-equal test.
( >>>> )	Element-wise greater-than test.
( >>== )	Element-wise greater-than-or-equal test.
( <<>> )	Element-wise not-equality test.
almostEqual	Checks if two tensors have the same (within machine precision) values in all elements.
isClose	Element-wise check if two tensors have same (within machine precision) values.
isFinite	Element-wise finity check (not -Inf, Inf or NaN).
maxElemwise	Element-wise maximum.
minElemwise	Element-wise minimum.
allFinite	Checks that all elements of the tensor are finite.

Logical functions

Use these functions to work with boolean tensors.

Function	Description
( ~~~~ )	Element-wise logical negation.
( &&&& )	Element-wise loigcal and.
( |||| )	Element-wise loigcal or.
( ^^^^ )	Element-wise loigcal xor.
all	Checks if all elements of the tensor are true.
allAxis	Checks if all elements along the specified axis are true.
allElems	Gets a sequence of all all elements within the tensor.
allTensor	Checks if all elements of the tensor are true returning the result as a tensor.
any	Checks if any elements of the tensor are true.
anyAxis	Checks if any element along the specified axis is true.
anyTensor	Checks if any element of the tensor is true returning the result as a tensor.
countTrue	Counts the elements being true.
countTrueAxis	Counts the elements being true along the specified axis.
ifThenElse	Element-wise choice between two sources depending on a condition.

Index functions

These functions return tensor of indices or work with them.

Function	Description
allIdx	Gets a sequence of all indices to enumerate all elements within the tensor.
argMax	Finds the indicies of the maximum value of the tensor.
argMaxAxis	Finds the index of the maximum value along the specified axis.
argMin	Finds the indicies of the minimum value of the tensor.
argMinAxis	Finds the index of the minimum value along the specified axis.
find	Finds the first occurence of the specfied value and returns its indices.
findAxis	Finds the first occurence of the specfied value along the specified axis and returns its index.
gather	Selects elements from a tensor according to specified indices.
scatter	Disperses elements from a source tensor to a new tensor according to the specified indices.
trueIdx	Finds the indices of all element that are true.

Reduction functions

These functions perform operations on tensors that reduce their dimensionality.

Function	Description
max	Calculates the maximum of all elements.
maxAxis	Calculates the maximum value of the elements along the specified axis.
min	Calculates the minimum of all elements.
minAxis	Calculates the minimum value of the elements along the specified axis.
mean	Calculates the mean of the tensor.
meanAxis	Calculates the mean of the elements along the specified axis.
product	Calculates the product of all elements.
productAxis	Calculates the product of the elements along the specified axis.
std	Calculates the standard deviation of the tensor.
stdAxis	Calculates the standard deviation of the elements along the specified axis.
sum	Sums all elements.
sumAxis	Sums the elements along the specified axis.
var	Calculates the variance of the tensor.
varAxis	Calculates the variance of the elements along the specified axis.
trace	Calculates the trace of the matrix.
traceAxis	Calculates the trace along the specified axes.

Functional operations (host only)

Use these functions to perform operations that are common in functional programming languages. They require the tensor to be stored in host memory.

Function	Description
HostTensor.foldAxis	Applies to specified function to all elements of the tensor, threading an accumulator through the computation.
HostTensor.init	Creates a new tensor with values returned by the specified function.
HostTensor.map	Applies to specified function to all elements of the tensor.
HostTensor.map2	Applies to specified function to all elements of the two tensors.
HostTensor.mapi	Applies to specified indexed function to all elements of the tensor.
HostTensor.mapi2	Applies to specified indexed function to all elements of the two tensors.

Data exchange (host only)

Use these functions to convert tensors to and from other storage modalities. They require the tensor to be stored in host memory.

Function	Description
HostTensor.ofArray	Creates a one-dimensional tensor copying the specified data.
HostTensor.ofList	Creates a one-dimensional tensor from the specified list.
HostTensor.ofSeq	Creates a one-dimensional tensor from the specified sequence.
HostTensor.read	Reads a tensor from the specified HDF5 object path in an HDF5 file.
HostTensor.readUntyped	Reads a tensor with unspecified data type from the specified HDF5 object path in an HDF5 file.
HostTensor.toArray	Creates an array from a one-dimensional tensor.
HostTensor.toList	Creates a list from a one-dimensional tensor.
HostTensor.toSeq	A sequence of all elements contained in the tensor.
HostTensor.usingArray	Creates a one-dimensional tensor referencing the specified data.
HostTensor.write	Writes the tensor into the HDF5 file under the specfied HDF5 object path.

Random number generation (host only)

Use these functions to generate tensors filled with random numbers.

Function	Description
HostTensor.randomInt	Creates a tensor filled with random integer numbers from a uniform distribution.
HostTensor.randomNormal	Creates a tensor filled with random numbers from a normale distribution.
HostTensor.randomUniform	Creates a tensor filled with random floating-point numbers from a uniform distribution.