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| subroutine, public | exponential_init (te, namespace, full_batch) |
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| subroutine, public | exponential_copy (teo, tei) |
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| subroutine | exponential_apply_single (te, namespace, mesh, hm, zpsi, ist, ik, deltat, imag_time) |
| | Wrapper to batchified routine for applying exponential to an array. More...
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| subroutine | exponential_apply_batch (te, namespace, mesh, hm, psib, deltat, psib2, deltat2, imag_time, inh_psib, op) |
| | This routine performs the operation: More...
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| subroutine | exponential_taylor_series_batch (te, namespace, mesh, hm, psib, deltat, op, psib2, deltat2, inh_psib, phik_shift) |
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| subroutine | exponential_lanczos_batch (te, namespace, mesh, hm, psib, deltat, op, inh_psib) |
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| subroutine, public | exponential_lanczos_function_batch (te, namespace, mesh, hm, psib, deltat, fun, op) |
| | Compute fun(H) psib, i.e. the application of a function of the Hamiltonian to a batch. More...
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| subroutine | exponential_cheby_batch (te, namespace, mesh, hm, psib, chebyshev_function, op) |
| | Calculates the exponential of the Hamiltonian through an expansion in Chebyshev polynomials. More...
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| subroutine, public | exponential_apply_all (te, namespace, gr, hm, st, deltat, order) |
| | Note that this routine not only computes the exponential, but also an extra term if there is a inhomogeneous term in the Hamiltonian hm. More...
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| subroutine | exponential_apply_phi_batch (te, namespace, mesh, hm, psib, deltat, k, op) |
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| type(hamiltonian_operator_t) function, pointer | hamiltonian_operator_constructor (namespace, mesh, hm) |
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| subroutine | hamiltonian_operator_init (this, namespace, mesh, hm) |
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| subroutine | hamiltonian_operator_apply (this, psib, hpsib) |
| |
| subroutine exponential_oct_m::exponential_apply_batch |
( |
class(exponential_t), intent(inout) |
te, |
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type(namespace_t), intent(in) |
namespace, |
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class(mesh_t), intent(in) |
mesh, |
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class(hamiltonian_abst_t), intent(inout) |
hm, |
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class(batch_t), intent(inout) |
psib, |
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real(real64), intent(in) |
deltat, |
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class(batch_t), intent(inout), optional |
psib2, |
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real(real64), intent(in), optional |
deltat2, |
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logical, intent(in), optional |
imag_time, |
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class(batch_t), intent(inout), optional |
inh_psib, |
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class(operator_t), intent(in), optional, target |
op |
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) |
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private |
This routine performs the operation:
\[
\exp{-i*\Delta t*hm(t)}|\psi> <-- |\psi>
\]
If imag_time is present and is set to true, it performs instead:
\[
\exp{ \Delta t*hm(t)}|\psi> <-- |\psi>
\]
If an inhomogeneous term is present, the operation is:
\[
\exp{-i*\Delta t*hm(t)}|\psi> + \Delta t*\phi_1{-i*\Delta t*hm(t)}|inh\psi> <-- |\psi>
\]
where:
\[
\phi_1(x) = (e^x - 1)/x
\]
- Parameters
-
| [in,out] | inh_psib | inhomogeneous term |
| [in] | op | operator to be applied in the exponential |
Definition at line 433 of file exponential.F90.
| subroutine, public exponential_oct_m::exponential_lanczos_function_batch |
( |
type(exponential_t), intent(inout) |
te, |
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type(namespace_t), intent(in) |
namespace, |
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class(mesh_t), intent(in) |
mesh, |
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class(hamiltonian_abst_t), intent(inout) |
hm, |
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class(batch_t), intent(inout) |
psib, |
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complex(real64), intent(in) |
deltat, |
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fun, |
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class(operator_t), intent(in) |
op |
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) |
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Compute fun(H) psib, i.e. the application of a function of the Hamiltonian to a batch.
Usually, the function is an exponential, or a related function.
Some details of the implementation can be understood from Saad, Y. (1992). Analysis of some Krylov subspace approximations to the matrix exponential operator. SIAM Journal on Numerical Analysis, 29(1), 209-228.
A pdf can be accessed [here](https: or [via the DOI](https: Equation numbers below refer to this paper.
- Parameters
-
| [in] | op | operator to be applied in the exponential |
Definition at line 678 of file exponential.F90.
| subroutine exponential_oct_m::exponential_cheby_batch |
( |
type(exponential_t), intent(inout) |
te, |
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type(namespace_t), intent(in) |
namespace, |
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class(mesh_t), intent(in) |
mesh, |
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class(hamiltonian_abst_t), intent(inout) |
hm, |
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class(batch_t), intent(inout) |
psib, |
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class(chebyshev_function_t), intent(in) |
chebyshev_function, |
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class(operator_t), intent(in) |
op |
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) |
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private |
Calculates the exponential of the Hamiltonian through an expansion in Chebyshev polynomials.
It uses the algorithm as outlined in [Hochbruck, M. & Ostermann, A.: Exponential Runge–Kutta methods for parabolic problems. Applied Numerical Mathematics 53, 323–339 (2005)](https: Section 4.1. See also [Kosloff, J. Phys. Chem. (1988), 92, 2087-2100](http: Section III.1 and [Kosloff, Annu. Rev. Phys. Chem. (1994), 45, 145–178](https: equations 7.1ff and especially figure 2 for the convergence properties of the coefficients.
- Parameters
-
| [in] | op | operator to be applied in the exponential |
Definition at line 839 of file exponential.F90.
1.9.4