EPG Operators#
Defined in sycomore/epg/operators.h
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std::array<Complex, 9> pulse_single_pool(Real angle, Real phase)#
Return the row-wise matrix corresponding to the single-pool EPG pulse operator.
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std::array<Complex, 18> pulse_exchange(Real angle_a, Real phase_a, Real angle_b, Real phase_b)#
Return the row-wise matrix corresponding to the two-pools exchange EPG pulse operator.
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std::array<Complex, 10> pulse_magnetization_transfer(Real angle_a, Real phase_a, Real saturation)#
Return the row-wise matrix corresponding to the two-pools magnetization transfer EPG pulse operator.
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std::pair<Real, Real> relaxation_single_pool(Real R1, Real R2, Real duration)#
Return the scalars associated respectively with relaxation of the \(\tilde{F}\) states and \(\tilde{Z}\) states.
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std::tuple<std::array<Complex, 8>, std::array<Real, 4>, std::array<Real, 2>> relaxation_exchange(Real R1_a, Real R2_a, Real R1_b, Real R2_b, Real k_a, Real k_b, Real delta_b, Real M0_a, Real M0_b, Real duration)#
Return the exchange-relaxation matrices: non-zero terms of \(\Xi_T\) (row-major), row-major \(\Xi_L\), and \((\Xi_L - I) \Lambda_L^{-1} C\).
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std::tuple<Real, std::array<Real, 4>, std::array<Real, 2>> relaxation_magnetization_transfer(Real R1_a, Real R2_a, Real R1_b, Real k_a, Real k_b, Real M0_a, Real M0_b, Real duration)#
Return the magnetization transfer relaxation matrices: \(\Xi_T = e^{-R_{2a} \tau}\), row-major \(\Xi_L\) and \((\Xi_L - I) \Lambda_L^{-1} C\).
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std::array<Complex, 8> relaxation_and_exchange_T(Real R2_a, Real R2_b, Real k_a, Real k_b, Real delta_b, Real duration)#
Return the non-zero terms of \(\Xi_T\) (row-major)
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std::array<Real, 4> relaxation_and_exchange_L(Real R1_a, Real R1_b, Real k_a, Real k_b, Real duration)#
Return \(\Xi_L\) (row-major)
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std::array<Real, 2> relaxation_and_exchange_recovery(Real R1_a, Real R1_b, Real k_a, Real k_b, Real M0_a, Real M0_b, std::array<Real, 4> const &Xi_L)#
Return \((\Xi_L - I) \Lambda_L^{-1} C\).
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template<typename T>
std::tuple<T, T, T> diffusion(Real D, Real duration, T const &k, Real delta_k)# Return the scalars associated respectively with diffusion of respectively the \(\tilde{F}(k)\), \(\tilde{F}^*(-k)\), and \(\tilde{Z}(k)\) states.
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std::pair<Complex, Complex> phase_accumulation(Real angle)#
Return the rotation expressed as a complex exponential associated with phase accumulation of respectively the \(\tilde{F}(k)\) and \(\tilde{F}^*(-k)\) states.
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template<typename TReal, typename TComplex>
std::tuple<TComplex, TComplex, TComplex> bulk_motion(Real v, Real duration, TReal const &k, Real delta_k)# Return the phase accumulation expressed as a complex exponential associated with bulk motion of respectively the \(\tilde{F}(k)\), \(\tilde{F}^*(-k)\), and \(\tilde{Z}(k)\) states.
- Parameters:
v – projection of the velocity vector on the axis associated with k.