TwoSiteVUMPSEngine
full name: tenpy.algorithms.vumps.TwoSiteVUMPSEngine
parent module:
tenpy.algorithms.vumps
type: class
Inheritance Diagram
Methods
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In VUMPS we don't want to do this as we regenerate the environment each time we do an update. |
Gives an approximate prediction for the required memory usage. |
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Remove no longer needed environments after an update. |
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Return necessary data to resume a |
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Sweep from site 0 to L-1 |
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(Re-)initialize the environment. |
Determines if the algorithm is converged. |
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Create new instance of self.EffectiveH at self.i0. |
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Get (truncated) B from the new theta (as returned by diag). |
Set self.mixer to the class specified by options['mixer']. |
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For uniform MPS there is no need to clean up after the mixer. |
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Deactivate the mixer. |
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Polar decompositions on two sites: Given AC1 and C1, find AR1 such that AC1 = C1 AR1 and from AC2 and C3, find AL2 such that AC2 = AC2 C3 |
Perform any final steps or clean up after the main loop has terminated. |
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Perform post-update actions. |
Perform preparations before |
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For each update, we need to rebuild the environments from scratch using the most recent tensors |
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Reset the statistics, useful if you want to start a new sweep run. |
Resume a run that was interrupted. |
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Run the VUMPS simulation to find the ground state. |
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Perform a single iteration, consisting of |
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Emits a status message to the logging system after an iteration. |
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Determines if the main loop should be terminated. |
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One 'sweep' of a sweeper algorithm. |
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Initialize algorithm from another algorithm instance of a different class. |
The ground state projector P_GS |
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Update the left and right environments after an update of the state. |
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Perform two-site update on the site |
Class Attributes and Properties
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Deprecated alias of |
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The number of sites to be optimized at once. |
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- class tenpy.algorithms.vumps.TwoSiteVUMPSEngine(psi, model, options, **kwargs)[source]
Bases:
VUMPSEngine
Engine for the two-site VUMPS algorithm.
- Parameters:
Options
- config TwoSiteDMRGEngine
option summary By default (``None``) this feature is disabled. [...]
chi_list_reactivates_mixer (from Sweep) in IterativeSweeps.sweep
If True, the mixer is reset/reactivated each time the bond dimension growth [...]
Whether to combine legs into pipes. This combines the virtual and [...]
diag_method (from DMRGEngine) in DMRGEngine.diag
One of the following strings: [...]
E_tol_max (from DMRGEngine) in DMRGEngine.run_iteration
See `E_tol_to_trunc`
E_tol_min (from DMRGEngine) in DMRGEngine.run_iteration
See `E_tol_to_trunc`
E_tol_to_trunc (from DMRGEngine) in DMRGEngine.run_iteration
It's reasonable to choose the Lanczos convergence criteria [...]
lanczos_params (from Sweep) in Sweep
Lanczos parameters as described in :cfg:config:`KrylovBased`.
max_E_err (from DMRGEngine) in DMRGEngine.is_converged
Convergence if the change of the energy in each step [...]
max_hours (from IterativeSweeps) in DMRGEngine.stopping_criterion
If the DMRG took longer (measured in wall-clock time), [...]
max_N_for_ED (from DMRGEngine) in DMRGEngine.diag
Maximum matrix dimension of the effective hamiltonian [...]
max_N_sites_per_ring (from Algorithm) in Algorithm
Threshold for raising errors on too many sites per ring. Default ``18``. [...]
max_S_err (from DMRGEngine) in DMRGEngine.is_converged
Convergence if the relative change of the entropy in each step [...]
max_sweeps (from IterativeSweeps) in DMRGEngine.stopping_criterion
Maximum number of sweeps to perform.
max_trunc_err (from IterativeSweeps) in IterativeSweeps
Threshold for raising errors on too large truncation errors. Default ``0.00 [...]
min_sweeps (from IterativeSweeps) in DMRGEngine.stopping_criterion
Minimum number of sweeps to perform.
Specifies which :class:`Mixer` to use, if any. [...]
mixer_params (from Sweep) in DMRGEngine.mixer_activate
Mixer parameters as described in :cfg:config:`Mixer`.
N_sweeps_check (from DMRGEngine) in DMRGEngine.run_iteration
Number of sweeps to perform between checking convergence [...]
norm_tol (from DMRGEngine) in DMRGEngine.post_run_cleanup
After the DMRG run, update the environment with at most [...]
norm_tol_final (from DMRGEngine) in DMRGEngine.post_run_cleanup
After performing `norm_tol_iter`*`update_env` sweeps, if [...]
norm_tol_iter (from DMRGEngine) in DMRGEngine.post_run_cleanup
Perform at most `norm_tol_iter`*`update_env` sweeps to [...]
P_tol_max (from DMRGEngine) in DMRGEngine.run_iteration
See `P_tol_to_trunc`
P_tol_min (from DMRGEngine) in DMRGEngine.run_iteration
See `P_tol_to_trunc`
P_tol_to_trunc (from DMRGEngine) in DMRGEngine.run_iteration
It's reasonable to choose the Lanczos convergence criteria [...]
Number of sweeps to be performed without optimization to update the environment.
trunc_params (from Algorithm) in Algorithm
Truncation parameters as described in :cfg:config:`truncation`.
update_env (from DMRGEngine) in DMRGEngine.run_iteration
Number of sweeps without bond optimization to update the [...]
- DefaultMixer[source]
alias of
SubspaceExpansion
- update_env(**update_data)[source]
Update the left and right environments after an update of the state.
- Parameters:
**update_data – Whatever is returned by
update_local()
.
- polar_max(AC1, AC2, C1, C3)[source]
Polar decompositions on two sites: Given AC1 and C1, find AR1 such that AC1 = C1 AR1 and from AC2 and C3, find AL2 such that AC2 = AC2 C3
- Parameters:
- Returns:
AL2 (
Array
) – Left-orthonormal tensor such that AL2 C3 = AC2AR1 (
Array
) – Right-orthonormal tensor such that C1 AR1 = AC1eps_L (float) – Norm error, || AC1 - AL2 C3 ||
eps_R (float) – Norm error, || AC2 - C1 AR1 ||
entropy_left (float) – entanglement entropy left of site
i0
entropy_right (float) – entanglement entropy right of site
i0+1
- mixed_svd(theta)[source]
Get (truncated) B from the new theta (as returned by diag).
The goal is to split theta and truncate it:
| -- theta -- ==> -- U -- S -- VH - | | | | |
Without a mixer, this is done by a simple svd and truncation of Schmidt values.
With a mixer, the state is perturbed before the SVD. The details of the perturbation are defined by the
Mixer
class.Note that the returned S is a general (not diagonal) matrix, with labels
'vL', 'vR'
.- Parameters:
theta (
Array
) – The optimized wave function, prepared for svd.- Returns:
U (
Array
) – Left-canonical part of theta. Labels'(vL.p)', 'vR'
.S (2D
Array
) – Without mixer just the singular values of the array; with mixer it might be a general matrix with labels'vL', 'vR'
; see comment above.VH (
Array
) – Right-canonical part of theta. Labels'vL', '(p.vR)'
.err (
TruncationError
) – The truncation error introduced.S_approx (ndarray) – Just the S if a 1D ndarray, or an approximation of the correct S (which was used for truncation) in case S is 2D Array.
- environment_sweeps(N_sweeps)[source]
In VUMPS we don’t want to do this as we regenerate the environment each time we do an update.
- estimate_RAM(mem_saving_factor=None)[source]
Gives an approximate prediction for the required memory usage.
This calculation is based on the requested bond dimension, the local Hilbert space dimension, the number of sites, and the boundary conditions.
- Parameters:
mem_saving_factor (float) – Represents the amount of RAM saved due to conservation laws. By default, it is ‘None’ and is extracted from the model automatically. However, this is only possible in a few cases and needs to be estimated in most cases. This is due to the fact that it is dependent on the model parameters. If one has a better estimate, one can pass the value directly. This value can be extracted by building the initial state psi (usually by performing DMRG) and then calling
print(psi.get_B(0).sparse_stats())
TeNPy will automatically print the fraction of nonzero entries in the first line, for example,6 of 16 entries (=0.375) nonzero
. This fraction corresponds to the mem_saving_factor; in our example, it is 0.375.- Returns:
usage – Required RAM in MB.
- Return type:
See also
tenpy.simulations.simulation.estimate_simulation_RAM
global function calling this.
- free_no_longer_needed_envs()[source]
Remove no longer needed environments after an update.
This allows to minimize the number of environments to be kept. For large MPO bond dimensions, these environments are by far the biggest part in memory, so this is a valuable optimization to reduce memory requirements.
- get_resume_data(sequential_simulations=False)[source]
Return necessary data to resume a
run()
interrupted at a checkpoint.At a
checkpoint
, you can savepsi
,model
andoptions
along with the data returned by this function. When the simulation aborts, you can resume it using this saved data with:eng = AlgorithmClass(psi, model, options, resume_data=resume_data) eng.resume_run()
An algorithm which doesn’t support this should override resume_run to raise an Error.
- Parameters:
sequential_simulations (bool) – If True, return only the data for re-initializing a sequential simulation run, where we “adiabatically” follow the evolution of a ground state (for variational algorithms), or do series of quenches (for time evolution algorithms); see
run_seq_simulations()
.- Returns:
resume_data – Dictionary with necessary data (apart from copies of psi, model, options) that allows to continue the algorithm run from where we are now. It might contain an explicit copy of psi.
- Return type:
- init_env(model=None, resume_data=None, orthogonal_to=None)[source]
(Re-)initialize the environment.
This function is useful to (re-)start a Sweep with a slightly different model or different (engine) parameters. Note that we assume that we still have the same psi. Calls
reset_stats()
.- Parameters:
model (
MPOModel
) – The model representing the Hamiltonian for which we want to find the ground state. IfNone
, keep the model used before.resume_data (None | dict) – Given when resuming a simulation, as returned by
get_resume_data()
. Can contain another dict under the key init_env_data; the contents of init_env_data get passed as keyword arguments to the environment initialization.orthogonal_to (None | list of
MPS
| list of dict) – List of other matrix product states to orthogonalize against. Instead of just the state, you can specify a dict with the state as ket and further keyword arguments for initializing theMPSEnvironment
; thepsi
to be optimized is used as bra. Works only for finite or segment MPS; for infinite MPS it must be None. This can be used to find (a few) excited states as follows. First, run DMRG to find the ground state, and then run DMRG again while orthogonalizing against the ground state, which yields the first excited state (in the same symmetry sector), and so on. Note thatresume_data['orthogonal_to']
takes precedence over the argument.
Options
- option Sweep.start_env: int
Number of sweeps to be performed without optimization to update the environment.
- Raises:
ValueError – If the engine is re-initialized with a new model, which legs are incompatible with those of hte old model.
- is_converged()[source]
Determines if the algorithm is converged.
Does not cover any other reasons to abort, such as reaching a time limit. Such checks are covered by
stopping_condition()
.Options
- option VUMPSEngine.max_E_err: float
Convergence if the change of the energy in each step satisfies
|Delta E / max(E, 1)| < max_E_err
. Note that this might be satisfied even ifDelta E > 0
, i.e., if the energy increases (due to truncation).
- option VUMPSEngine.max_S_err: float
Convergence if the relative change of the entropy in each step satisfies
|Delta S|/S < max_S_err
- option VUMPSEngine.max_split_err: float
Convergence if the norm error between AC=AL-C and AC=C_AR is smaller than max_split_err.
- property lanczos_options
Deprecated alias of
lanczos_params
.
- make_eff_H()[source]
Create new instance of self.EffectiveH at self.i0. Also create zero-site Hamiltonians left of self.i0 and right of self.i0+self.n_optimize.
- mixer_activate()[source]
Set self.mixer to the class specified by options[‘mixer’].
- option Sweep.mixer: str | class | bool | None
Specifies which
Mixer
to use, if any. A string stands for one of the mixers defined in this module. A class is assumed to have the same interface asMixer
and is used to instantiate themixer
.None
uses no mixer.True
uses the mixer specified by theDefaultMixer
class attribute. The default depends on the subclass ofSweep
.
See also
- mixer_deactivate()[source]
Deactivate the mixer.
Set
self.mixer=None
and revert any other effects ofmixer_activate()
.
- property n_optimize
The number of sites to be optimized at once.
Indirectly set by the class attribute
EffectiveH
and it’s length. For example,TwoSiteDMRGEngine
uses theTwoSiteH
and hence hasn_optimize=2
, while theSingleSiteDMRGEngine
hasn_optimize=1
.
- post_run_cleanup()[source]
Perform any final steps or clean up after the main loop has terminated. Try to convert uniform MPS back to iMPS.
Options
- option VUMPSEngine.check_overlap: bool
Since AL C = C AR is not identically true, the MPS defined by AL and AR are not exactly the same. We can compute the overlap of the two to check.
- option VUMPSEngine.norm_tol: float
Check if final state is in canonical form.
- post_update_local(e_L, e_R, eps_L, eps_R, e_C1, e_C2, e_theta, N0_L, N0_R, N1, **update_data)[source]
Perform post-update actions.
Collect statistics.
- Parameters:
**update_data (dict) – What was returned by
update_local()
.
- pre_run_initialize()[source]
Perform preparations before
run_iteration()
is iterated.- Returns:
The object to be returned by
run()
in case of immediate convergence, i.e. if no iterations are performed.- Return type:
result
- prepare_update_local()[source]
For each update, we need to rebuild the environments from scratch using the most recent tensors
- reset_stats(resume_data=None)[source]
Reset the statistics, useful if you want to start a new sweep run.
- resume_run()[source]
Resume a run that was interrupted.
In case we saved an intermediate result at a
checkpoint
, this function allows to resume therun()
of the algorithm (after re-initialization with the resume_data). Since most algorithms just have a while loop with break conditions, the default behavior implemented here is to just callrun()
.
- run()[source]
Run the VUMPS simulation to find the ground state.
- Returns:
E (float) – The energy of the resulting ground state MPS.
psi (
MPS
) – The MPS representing the ground state after the simulation, i.e. just a reference topsi
.
- run_iteration()[source]
Perform a single iteration, consisting of
N_sweeps_check
sweeps.Options
- option VUMPSEngine.diagonal_gauge_frequency: int
Number of sweeps how often we restore the UniformMPS to the diagonal gauge
- option VUMPSEngine.cutoff: float
During DMRG with a mixer, S may be a matrix for which we need the inverse. This is calculated as the Penrose pseudo-inverse, which uses a cutoff for the singular values.
- Returns:
E (float) – The energy of the current ground state approximation.
psi (
UniformMPS
) – The current ground state approximation, i.e. just a reference topsi
.
- status_update(iteration_start_time: float)[source]
Emits a status message to the logging system after an iteration.
- Parameters:
iteration_start_time (float) – The
time.time()
at the start of the last iteration
- stopping_criterion(iteration_start_time: float) bool [source]
Determines if the main loop should be terminated.
- Parameters:
iteration_start_time (float) – The
time.time()
at the start of the last iteration
Options
- option IterativeSweeps.min_sweeps: int
Minimum number of sweeps to perform.
- option IterativeSweeps.max_sweeps: int
Maximum number of sweeps to perform.
- option IterativeSweeps.max_hours: float
If the DMRG took longer (measured in wall-clock time), ‘shelve’ the simulation, i.e. stop and return with the flag
shelve=True
.
- sweep(optimize=True)[source]
One ‘sweep’ of a sweeper algorithm.
Iterate over the bond which is optimized, to the right and then back to the left to the starting point.
- Parameters:
optimize (bool, optional) – Whether we actually optimize the state, e.g. to find the ground state of the effective Hamiltonian in case of a DMRG. (If False, just update the environments).
Options
- option Sweep.chi_list_reactivates_mixer: bool
If True, the mixer is reset/reactivated each time the bond dimension growths due to
Sweep.chi_list
.
- Returns:
max_trunc_err – Maximal truncation error introduced.
- Return type:
- classmethod switch_engine(other_engine, *, options=None, **kwargs)[source]
Initialize algorithm from another algorithm instance of a different class.
You can initialize one engine from another, not too different subclasses. Internally, this function calls
get_resume_data()
to extract data from the other_engine and then initializes the new class.Note that it transfers the data without making copies in most case; even the options! Thus, when you call run() on one of the two algorithm instances, it will modify the state, environment, etc. in the other. We recommend to make the switch as
engine = OtherSubClass.switch_engine(engine)
directly replacing the reference.- Parameters:
cls (class) – Subclass of
Algorithm
to be initialized.other_engine (
Algorithm
) – The engine from which data should be transferred. Another, but not too different algorithm subclass-class; e.g. you can switch from theTwoSiteDMRGEngine
to theOneSiteDMRGEngine
.options (None | dict-like) – If not None, these options are used for the new initialization. If None, take the options from the other_engine.
**kwargs – Further keyword arguments for class initialization. If not defined, resume_data is collected with
get_resume_data()
.