API

Isochromat Operators

BlochSimulators.IsochromatType
struct Isochromat{T<:Real} <: FieldVector{3,T}
    x::T
    y::T
    z::T
end

Holds the x,y,z components of a spin isochromat in a FieldVector, which is a StaticVector (from the package StaticArrays) with custom fieldnames.

source
BlochSimulators.decayMethod
decay(m::Isochromat{T}, E₁, E₂) where T

Apply T₂ decay to transverse component and T₁ decay to longitudinal component of Isochromat.

source
BlochSimulators.initialize_statesMethod
initialize_states(::AbstractResource, ::IsochromatSimulator{T}) where T

Initialize a spin isochromat to be used throughout a simulation of the sequence.

This may seem redundant but to is necessary to share the same programming interface with EPGSimulators.

source
BlochSimulators.invertMethod
invert(m::Isochromat{T}, p::AbstractTissueParameters) where T

Invert Isochromat with B₁ insenstive (i.e. adiabatic) inversion pulse

source
BlochSimulators.invertMethod
invert(m::Isochromat{T}, p::AbstractTissueParameters) where T

Invert z-component of Isochromat (assuming spoiled transverse magnetization so xy-component zero).

source
BlochSimulators.rotateMethod
rotate(m::Isochromat, γΔtGRz, z, Δt, p::AbstractTissueParameters)

Rotation of Isochromat without RF (so around z-axis only) due to gradients and B0 (i.e. refocussing slice select gradient).

source
BlochSimulators.rotateMethod
rotate(m::Isochromat{T}, γΔtRF::Complex, γΔtGR::Tuple, (x,y,z), Δt, p::AbstractTissueParameters, Δω = zero(T)) where T

RF, gradient and/or ΔB₀ induced rotation of Isochromat computed using Rodrigues rotation formula (https://en.wikipedia.org/wiki/Rodrigues%27rotationformula).

source
BlochSimulators.sample_transverse!Method
sample!(output, index::Union{Integer,CartesianIndex}, m::Isochromat)

Sample transverse magnetization from Isochromat. The "+=" is needed for 2D sequences where slice profile is taken into account.

source
BlochSimulators.sample_xyz!Method
sample_xyz!(output, index::Union{Integer,CartesianIndex}, m::Isochromat)

Sample m.x, m.y and m.z components from Isochromat. The "+=" is needed for 2D sequences where slice profile is taken into account.

source

EPG Operators

BlochSimulators.EPGStatesType
EPGStates = Union{MMatrix{3}, SizedMatrix{3}}

In the EPG model, the configuration state matrix Ω will be updated inplace. On CPU, we use StaticArrays.MMatrix. The MMatrix will not escape _simulate! and therefore should not result in allocations. On GPU, we use shared memory (CUDA.CuStaticSharedArray). The shared memory is allocated for all threads within a block simultaneously. We then take a @view and wrap it in a SizedArray. Without the SizedArray, the type would be long and unreadable. By wrapping, we can then simply dispatch on a SizedArray instead.

source
BlochSimulators.F̄₋Method
F̄₋(Ω)

View into the second row of the configuration state matrix Ω, corresponding to the F̄₋ states.

source
BlochSimulators.F₊Method
F₊(Ω)

View into the first row of the configuration state matrix Ω, corresponding to the F₊ states.

source
BlochSimulators.ZMethod
Z(Ω)

View into the third row of the configuration state matrix Ω, corresponding to the Z states.

source
BlochSimulators.decay!Method
decay!(Ω::EPGStates, E₁, E₂)

T₂ decay for F-components, T₁ decay for Z-component of each state.

source
BlochSimulators.dephasing!Method
dephasing!(Ω::EPGStates)

Shift states around due to dephasing gradient: The F₊ go up one, the F̄₋ go down one and Z do not change

source
BlochSimulators.excite!Method
excite!(Ω::EPGStates, RF::Complex, p::AbstractTissueParameters)

Mixing of states due to RF pulse. Magnitude of RF is the flip angle in degrees. Phase of RF is the phase of the pulse. If RF is real, the computations simplify a little bit.

source
BlochSimulators.excite!Method
excite!(Ω::EPGStates, RF::T, p::AbstractTissueParameters) where T<:Union{Real, Quantity{<:Real}}

If RF is real, the calculations simplify (and probably Ω is real too, reducing memory (access) requirements).

source
BlochSimulators.initialize_statesMethod
initialize_states(::AbstractResource, sequence::EPGSimulator{T,Ns}) where {T,Ns}

Initialize an MMatrix of EPG states on CPU to be used throughout the simulation.

source
BlochSimulators.initialize_statesMethod
initialize_states(::CUDALibs, sequence::EPGSimulator{T,Ns}) where {T,Ns}

Initialize an array of EPG states on a CUDA GPU to be used throughout the simulation.

source
BlochSimulators.invert!Method
invert!(Ω::EPGStates, p::AbstractTissueParameters)

Invert Z-component of states of all orders. Assumes fully spoiled transverse magnetization.

source
BlochSimulators.rotate!Method
rotate!(Ω::EPGStates, eⁱᶿ::T) where T

Rotate F₊ and F̄₋ states under the influence of eⁱᶿ = exp(i * ΔB₀ * Δt)

source
BlochSimulators.sample_transverse!Method
sample_transverse!(output, index::Union{Integer,CartesianIndex}, Ω::EPGStates)

Sample the measurable transverse magnetization, that is, the F₊ component of the 0th state. The += is needed for 2D sequences where slice profile is taken into account.

source
BlochSimulators.sample_Ω!Method
sample_Ω!(output, index::Union{Integer,CartesianIndex}, Ω::EPGStates)

Sample the entire configuration state matrix Ω. The += is needed for 2D sequences where slice profile is taken into account.

source
BlochSimulators.Ω_eltypeMethod
Ω_eltype(sequence::EPGSimulator{T,Ns}) where {T,Ns} = Complex{T}

By default, configuration states are complex. For some sequences, they will only ever be real (no RF phase, no complex slice profile correction) and for these sequences a method needs to be added to this function.

source

Tissue Parameters

BlochSimulators.AbstractTissueParametersType
AbstractTissueParameters{N,T} <: FieldVector{N,T}

Abstract type for structs that hold different combinations of tissue parameters.

Possible fields

  • T₁::T: T₁ relaxation parameters of a voxel
  • T₂::T: T₂ relaxation parameters of a voxel
  • B₁::T: Scaling factor for effective B₁ excitation field within a voxel
  • B₀::T: Off-resonance with respect to main magnetic field within a voxel
  • ρˣ::T: Real part of proton density within a voxel
  • ρʸ::T: Imaginary part of proton density within a voxel

The structs are subtypes of FieldVector, which is a StaticVector with named fields (see the documentation of StaticArrays.jl). There are three reasons for letting the structs be subtypes of FieldVector:

  1. FieldVectors/StaticVectors have sizes that are known at compile time. This is beneficial for performance reasons
  2. The named fields improve readability of the code (e.g. p.B₁ vs p[3])
  3. Linear algebra operations can be performed on instances of the structs. This allows, for example, subtraction (without having to manually define methods) and that is useful for comparing parameter maps.
source

Sequences

Abstract Types

BlochSimulators.BlochSimulatorType
BlochSimulator{T}

The abstract type of which all sequence simulators will be a subtype. The parameter T should be a number type (e.g. Float64, Float32) and the tissueparameters that are used as input to the simulator should have the same number type. By convention, a BlochSimulator will be used to simulate magnetization at echo times only without taking into account spatial encoding gradients (i.e. readout or phase encoding gradients). To simulate the magnetization at other readout times, including phase from spatial encoding gradients, an AbstractTrajectory will be needed as well.

To make a simulator for a particular pulse sequence:

  1. Make a struct that's a subtype of either IsochromatSimulator or EPGSimulator. The struct will hold parameters that are necessary for performing the simulations.

  2. Add a method to simulate_magnetization! that implements the pulse sequence. For both performance and GPU compatibility, make sure that simulate_magnetization! does not do any heap allocations. Examples for pSSFP and FISP sequences are found in src/sequences.

  3. Add methods to output_eltype and output_size that are used to allocate an output array within the simulate function.

  4. [Optional] Add a method to show for nicer printing of the sequence in the REPL

  5. [Optional] Add a method to getindex to easily reduce the length of the sequence

  6. [Optional] Add a constructor for the struct that takes in data from Matlab or something else and assembles the struct

IMPORTANT

The simulate_magnetization! functions (which dispatch on the provided sequence) are assumed to be type-stable and non-allocating Should be possible to achieve when using functions from operators/epg.jlandoperators/isochromat.jl` and a properly parametrized sequence struct.

source
BlochSimulators.IsochromatSimulatorType
IsochromatSimulator{T} <: BlochSimulator{T}

Abstract type of which all sequence simulators that are based on the isochromat model will be a subtype. The parameter T should be a number type (e.g. Float64, Float32) and the tissueparameters that are used as input to the simulator should have the same number type.

source
BlochSimulators.EPGSimulatorType
EPGSimulator{T,Ns} <: BlochSimulator{T}

Abstract type of which all sequence simulators that are based on the EPG model will be a subtype. The parameter T should be a number type (e.g. Float64, Float32) and the tissueparameters that are used as input to the simulator should have the same number type. The parameter Ns corresponds to the maximum order of configuration states that are tracked in the simulations.

source

Interface

Examples

BlochSimulators.Generic2DType
Generic2D{T,V,M,S} where {T<:AbstractFloat, V<:AbstractVector, M<:AbstractMatrix, S} <: IsochromatSimulator{T}

Simulate a generic 2D sequence defined by arrays containing RF and gradient waveforms. Contains a loop over z locations to take into account slice profile effects. The Δt vector stores the time intervals for the waveforms.

Fields

  • RF::V{Complex{T}}: Vector with (complex) RF values during each time interval
  • GR::M{T}: Matrix with GRx, GRy and GRz values during each time interval
  • sample::S: Vector with Bool's to indicate the sample points
  • Δt::V{T}: Vector with time intervals
  • z::V{T}: Vector with different positions along the slice direction
source
BlochSimulators.Generic3DType
Generic3D{T,V<:AbstractVector{Complex{T}},W<:AbstractVector{T},M<:AbstractMatrix{T},S} <: IsochromatSimulator{T}

Simulate a generic sequence defined by arrays containing RF and gradient waveforms. Unlike the Generic2D sequence, it is assumed that the excitation is homogenous over the voxel and therefore no summation over a slice direction is applied. The Δt vector stores the time intervals for the waveforms.

Fields

  • RF::V{Complex{T}}: Vector with (complex) RF values during each time interval
  • GR::M{T}: Matrix with GRx, GRy and GRz values during each time interval
  • sample::S: Vector with Bool's to indicate the sample points
  • Δt::V{T}: Vector with time intervals
source

Trajectories

Abstract types

BlochSimulators.AbstractTrajectoryType
AbstractTrajectory{T}

The abstract type of which all gradient trajectories will be a subtype. The subtypes should contain fields that can describe the full trajectory during a sequence. The type T refers to the precision of the floating point values within the trajectory struct.

source
BlochSimulators.SpokesTrajectoryType
SpokesTrajectory{T} <: AbstractTrajectory{T}

Typical Cartesian and radial trajectories have a lot in common: a readout can be described by a starting point in k-space and a Δk per sample point. To avoid code repetition, both type of trajectories are made a subtype of SpokesTrajectory such that some methods that would be the same for both trajectories otherwise are written for SpokesTrajectory instead.

source

Interface

Examples

BlochSimulators.CartesianTrajectoryType
CartesianTrajectory{T,I,U,V} <: SpokesTrajectory{T}

Struct that is used to implement a typical Cartesian gradient trajectory. The trajectory is described in a compact fashion by only storing the starting position in k-space (k_start_readout) for each readout as well as the step in k-space per readout point Δk_adc.

Note that CartesianTrajectory and RadialTrajectory are essentially the same in when using when using this compact description. A SpokesTrajectory struct is therefore defined as a supertype of both and methods are defined for SpokesTrajectory instead to avoid code repetition.

The type parameters are intentionally left vague. The J, for example, may be an integer for sequences where each readout has the same number of samples, but for sequences with different numbers of samples per readout it may be a vector of integers.

Fields

  • nreadouts::I: The total number of readouts for this trajectory
  • nsamplesperreadout::I: The total number of samples per readout
  • Δt::T: Time between sample points
  • k_start_readout::U: Starting position in k-space for each readout
  • Δk_adc::U: k-space step Δkₓ per sample point (same for all readouts)
  • py::V: Phase encoding index for each readout
  • readout_oversampling::I: Readout oversampling factor
source
BlochSimulators.kspace_coordinatesMethod
kspace_coordinates(tr::CartesianTrajectory)

Return matrix (nrsamplesperreadout, nrreadouts) with kspace coordinates for the trajectory. Needed for nuFFT reconstructions.

source
BlochSimulators.magnetization_to_signalMethod
magnetization_to_signal(resource, magnetization, parameters, trajectory, coordinates, coil_sensitivities)

Arguments

  • magnetization: Matrix{Complex} of size (# readouts, # voxels) with phase-encoded magnetization at echo times.
  • parameters: Tissue parameters of all voxels, including spatial coordinates.
  • trajectory: Cartesian trajectory struct.
  • coordinates: Vector{Coordinates} with spatial coordinates for each voxel.
  • coil_sensitivities: Matrix{Complex} of size (# voxels, # coils) with coil sensitivities.

Output:

  • signal: Vector of length (# coils) with each element a Matrix{Complex} of size (# readouts, # samples per readout)

Description:

As noted in the description of the simulate_signal function (see src/simulate/signal.jl), we simulate the MR signal at timepoint t from coil i as: signalᵢ[t] = sum(m[t,v] * cᵢ[v] * ρ[v] for v in 1:(# voxels)), where cᵢis the coil sensitivity profile of coil i, ρ is the proton density map and m the matrix with the magnetization at all timepoints for each voxel obtained through Bloch simulations.

The output (signalᵢ) for each coil is in principle a Vector{Complex}of length (# samples per readout) * (# readouts). If we reshape the output into aMatrix{Complex}of size (# samples per readout, # readouts) instead, and do something similar form`, then the signal value associated with the s-th sample point of the r-th readout can be expressed as signalᵢ[r,s] = sum( m[r,s,v]] * cᵢ[v] * ρ[v] for v in 1:(# voxels)).

The problem here is that we typically cannot store the full m. Instead, we compute the magnetization at echo times only. The reason is that, if mᵣ is the magnetization at the r-th echo time in some voxel, and E = exp(-ΔtR₂[v]) * exp(im(Δkₓ*x[v])) is the change per sample point (WHICH FOR CARTESIAN SEQUENCES IS THE SAME FOR ALL READOUTS AND SAMPLES), then the magnetization at the s-th sample relative the the echo time can can be computed as mₛ = mᵣ * E[v]^s

Therefore we can write

signalⱼ[r,s] = sum( magnetization[r,v] * E[v]^s * ρ[v] * cⱼ[v] for v in 1:(# voxels)) signalⱼ[r,s] = magnetization[r,:] * (E.^s .* ρ .* cⱼ)

Because the (E.^s .* ρ .* cⱼ)-part is the same for all readouts, we can simply perform this computation for all readouts simultaneously as signalⱼ[:,s] = magnetization * (E.^s .* ρ .* cⱼ)

If we define the matrix Eˢ as E .^ (-(ns÷2):(ns÷2)-1), then we can do the computation for all different sample points at the same time as well using a single matrix-matrix multiplication: signalⱼ = magnetization * (Eˢ .* (ρ .* cⱼ))

The signalⱼ array is of size (# readouts, # samples per readout). We prefer to have it transposed, therefore we compute signalⱼ = transpose(Eˢ .* (ρ .* cⱼ)) * transpose(magnetization) instead.

For the final output, we do this calculation for each coil j and get a vector of signal matrices (one matrix for each coil) as a result.

Note that this implementation relies entirely on vectorized code and works on both CPU and GPU. The matrix-matrix multiplications are - I think - already multi-threaded so a separate multi-threaded implementation is not needed.

source
BlochSimulators.sampling_maskMethod
sampling_mask(tr::CartesianTrajectory)

For undersampled Cartesian trajectories, the gradient trajectory can also be described by a sampling mask.

source
BlochSimulators.RadialTrajectoryType
RadialTrajectory{T,I,U,V} <: SpokesTrajectory{T}

Struct that is used to implement a typical radial gradient trajectory. The trajectory can is described in a compact fashion by only storing the starting position in k-space (k_start_readout) for each readout as well as the step in k-space per readout point Δk_adc.

Note that CartesianTrajectory and RadialTrajectory are essentially the same in when using when using this compact description. A SpokesTrajectory struct is therefore defined as a supertype of both and methods are defined for SpokesTrajectory instead to avoid code repetition.

The type parameters are intentionally left vague. The J, for example, may be an integer for sequences where each readout has the same number of samples, but for sequences with different numbers of samples per readout it may be a vector of integers.

Fields

  • nreadouts::I: The total number of readouts for this trajectory
  • nsamplesperreadout::I: The total number of samples per readout
  • Δt::T: Time between sample points
  • k_start_readout::U: Starting position in k-space for each readout
  • Δk_adc::U: k-space step Δk between each readout
  • φ::V: Radial angle for each readout
  • readout_oversampling::I: Readout oversampling factor
source
BlochSimulators.add_gradient_delay!Method
add_gradient_delay!(tr::RadialTrajectory, S)

Apply gradient delay to radial trajectory in in-place fashion. The delay is described by the 2x2 matrix S and is assumed to influence the start of the readout only, not the readout direction.

source
BlochSimulators.kspace_coordinatesMethod
kspace_coordinates(tr::RadialTrajectory)

Return matrix (nrsamplesperreadout, nrreadouts) with kspace coordinates for the trajectory. Needed for nuFFT reconstructions.

source

Dictionary Simulation

Missing docstring.

Missing docstring for simulate_magnetization(resource, sequence, parameters). Check Documenter's build log for details.

BlochSimulators._allocate_array_on_resourceMethod
_allocate_array_on_resource(::CPUProcesses, _eltype, _size)

Allocate a distributed array for use with multiple CPU processes. The array is distributed in the "voxel" dimension (last dimension) over the workers.

source
BlochSimulators._allocate_magnetization_arrayMethod
_allocate_magnetization_array(resource, sequence, parameters)

Allocate an array to store the output of the Bloch simulations (per voxel, echo times only) to be performed with the sequence. For each BlochSimulator, methods should have been added to output_eltype and output_size for this function to work properly.

Arguments

  • resource::AbstractResource: The computational resource (e.g., CPU, GPU) to be used for the allocation.
  • sequence::BlochSimulator{T}: The simulator, which defines the type of simulation to be performed.
  • parameters::AbstractVector{<:AbstractTissueParameters{N,T}}: A vector with each element containing the tissue parameters for a voxel.

Returns

  • magnetization_array: An array allocated on the specified resource, formatted to store the simulation results for each voxel across the specified echo times.
source
BlochSimulators.simulate_magnetization!Method
simulate_magnetization!(magnetization, resource, sequence, parameters)

Simulate the magnetization at echo times (without any spatial encoding gradients applied) for all combinations of tissue parameters contained in parameters. Stores the magnetization response (typically the transverse magnetization at echo times) in the magnetization array.

  • magnetization::AbstractArray: Pre-allocated output array to store simulation results.
  • resource::AbstractResource: Computational resource (e.g., CPU1(), CPUThreads(), CPUProcesses(), CUDALibs()).
  • sequence::BlochSimulator: Custom sequence struct
  • parameters::AbstractVector{<:AbstractTissueParameters}: Vector with different combinations of tissue parameters
source
BlochSimulators.simulate_magnetizationMethod
simulate_magnetization(resource, sequence, parameters)

Simulate the magnetization response (typically the transverse magnetization at echo times without any spatial encoding gradients applied) for all combinations of tissue parameters contained in parameters.

This function can also be used to generate dictionaries for MR Fingerprinting purposes.

Arguments

  • resource::AbstractResource: Either CPU1(), CPUThreads(), CPUProcesses() or CUDALibs()
  • sequence::BlochSimulator: Custom sequence struct
  • parameters::AbstractVector{<:AbstractTissueParameters}: Vector with different combinations of tissue parameters

Returns

  • magnetization::AbstractArray: Array of size (output_size(sequence), length(parameters)) containing the magnetization response of the sequence for all combinations of input tissue parameters.
source

Signal Simulation

Missing docstring.

Missing docstring for simulate_signal(resource, sequence, parameters, trajectory, coil_sensitivities). Check Documenter's build log for details.

BlochSimulators._allocate_signal_arrayMethod
_allocate_signal_array(resource, trajectory::AbstractTrajectory, coil_sensitivities)

Allocate an array to store the output of the signal simulation (all readout points, integrated over all voxels).

source
BlochSimulators._signal_per_coil!Method
_signal_per_coil!(signal, resource, magnetization, parameters, trajectory, coordinates, coil_sensitivities)

Compute the signal for a given coil by calculating a volume integral of the transverse magnetization in each voxel for each time point separately (using the signalattime_point!` function).

source
BlochSimulators._signal_per_coil!Method
_signal_per_coil!(signal, ::CPU1, magnetization, parameters, trajectory, coordinates, coil_sensitivities)

Loop over the time points to calculate the signal at that time point in a serial fashion on a single CPU.

source
BlochSimulators._signal_per_coil!Method
_signal_per_coil!(signal, ::CPUThreads, magnetization, parameters, trajectory, coordinates, coil_sensitivities)

Loop over the time points to calculate the signal at that time point in a multi-threaded fashion.

source
BlochSimulators._signal_per_coil!Method
_signal_per_coil!(signal, ::CUDALibs, magnetization, parameters, trajectory, coordinates, coil_sensitivities)

Let different threads of an NVIDIA CUDA device calculate the signal at different time points.

source
BlochSimulators.magnetization_to_signalMethod
magnetization_to_signal(resource, magnetization, parameters, trajectory, coordinates, coil_sensitivities)

Allocates memory for the signal and computes the signal for each coil separately using the _signal_per_coil! function. That function is implemented for different computational resources and will be called based on the resource argument. The default implementations loop over all time points and compute the volume integral of the transverse magnetization in each voxel for each time point separately.

This loop order is not necessarily optimal (and performance may be) across all trajectories and computational resources. If a better implementation is available, add new methods to this function for those specific combinations of resources and trajectories.

source
BlochSimulators.magnetization_to_signalMethod
magnetization_to_signal(::CPUProcesses, dmagnetization, dparameters, trajectory, dcoordinates, dcoil_sensitivities)

The "voxels" are assumed to be distributed over the workers. Each worker computes performs a volume integral over the voxels that it owns only (for all time points) using the CPU1() code. The results are then summed up across all workers.

source
BlochSimulators.simulate_signalMethod
simulate_signal(resource, sequence, parameters, trajectory, coil_sensitivities)

Simulate the MR signal at timepoint t from coil i as: sᵢ(t) = ∑ⱼ cᵢⱼρⱼmⱼ(t), where cᵢⱼis the coil sensitivity of coil i at position of voxel j, ρⱼ is the proton density of voxel j and mⱼ(t) the (normalized) transverse magnetization in voxel j obtained through Bloch simulations.

Arguments

  • resource::AbstractResource: Either CPU1(), CPUThreads(), CPUProcesses() or CUDALibs()
  • sequence::BlochSimulator: Custom sequence struct
  • parameters::AbstractVector{<:AbstractTissueParameters}: Vector with tissue parameters for each voxel
  • trajectory::AbstractTrajectory: Custom trajectory struct
  • coordinates::AbstractVector{<:Coordinates}: Vector with spatial coordinates for each voxel
  • coil_sensitivities::AbstractMatrix: Sensitivity of coil j in voxel v is given by coil_sensitivities[v,j]

Returns

  • signal::AbstractMatrix{<:Complex}: Simulated MR signal for the sequence and trajectory.

The matrix is of size (# samples, # coils).

source

Utility Functions

BlochSimulators.f32Method
f32(x)

Change precision of x to Float32. It uses Functors.fmap to recursively traverse the fields of the struct x. For custom structs (e.g. <:BlochSimulator or <:AbstractTrajectory), it is required that typeof(x) be made a Functors.@functor (e.g. @functor FISP).

It may be necessary to add new adapt rules (by adding new methods to adapt_storage) if new structs with complicated nested fields are introduced.

source
BlochSimulators.f64Method
f64(x)

Change precision of x to Float64. It uses Functors.fmap to recursively traverse the fields of the struct x. For custom structs (e.g. <:BlochSimulator or <:AbstractTrajectory), it is required that typeof(x) be made a Functors.@functor (e.g. @functor FISP).

It may be necessary to add new adapt rules (by adding new methods to adapt_storage) if new structs with complicated nested fields are introduced.

source
BlochSimulators.gpuMethod
gpu(x)

Move x to CUDA device. It uses Functors.fmap to recursively traverse the fields of the struct x, converting <:AbstractArrays to CuArrays, and ignoring isbitsarrays. For custom structs (e.g. <:BlochSimulator or <:AbstractTrajectory), it is required that typeof(x) be made a Functors.@functor (e.g. @functor FISP).

source

Index