Source code for qutip.solver

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from __future__ import print_function

__all__ = ['Options', 'Odeoptions', 'Odedata', 'ExpectOps']

import os
import sys
import warnings
import datetime
import numpy as np
from qutip.qobjevo import QobjEvo
from collections import OrderedDict
from qutip import __version__
from qutip.qobj import Qobj
import qutip.settings as qset
from types import FunctionType, BuiltinFunctionType

solver_safe = {}


class SolverSystem():
    pass


[docs]class ExpectOps: """ Contain and compute expectation values """ def __init__(self, e_ops=[], super_=False): # take care of expectation values, if any self.isfunc = False self.e_ops_dict = False self.raw_e_ops = e_ops self.e_ops_qoevo = [] self.e_num = 0 self.e_ops_isherm = [] if isinstance(e_ops, (Qobj, QobjEvo)): e_ops = [e_ops] elif isinstance(e_ops, dict): self.e_ops_dict = e_ops e_ops = [e for e in e_ops.values()] self.e_ops = e_ops if isinstance(e_ops, list): self.e_num = len(e_ops) self.e_ops_isherm = [e.isherm for e in e_ops] if not super_: self.e_ops_qoevo = np.array([QobjEvo(e) for e in e_ops], dtype=object) else: self.e_ops_qoevo = np.array([QobjEvo(spre(e)) for e in e_ops], dtype=object) [op.compile() for op in self.e_ops_qoevo] elif callable(e_ops): self.isfunc = True self.e_num = 1 def init(self, tlist): self.tlist = tlist if self.isfunc: self.raw_out = [] else: self.raw_out = np.zeros((self.e_num, len(tlist)), dtype=complex) def copy(self): out = ExpectOps.__new__(ExpectOps) out.isfunc = self.isfunc out.e_ops_dict = self.e_ops_dict out.raw_e_ops = self.raw_e_ops out.e_ops = self.e_ops out.e_num = self.e_num out.e_ops_isherm = self.e_ops_isherm out.e_ops_qoevo = self.e_ops_qoevo return out def step(self, iter_, state): if self.isfunc: self.raw_out.append(self.e_ops(t, state)) else: t = self.tlist[iter_] for ii in range(self.e_num): self.raw_out[ii, iter_] = \ self.e_ops_qoevo[ii].compiled_qobjevo.expect(t, state) def finish(self): if self.isfunc: result = self.raw_out else: result = [] for ii in range(self.e_num): if self.e_ops_isherm[ii]: result.append(np.real(self.raw_out[ii, :])) else: result.append(self.raw_out[ii, :]) if self.e_ops_dict: result = {e: result[n] for n, e in enumerate(self.e_ops_dict.keys())} return result def __eq__(self, other): if isinstance(other, ExpectOps): other = other.raw_e_ops return self.raw_e_ops == other def __ne__(self, other): return not (self == other) def __bool__(self): return bool(self.e_num)
[docs]class Options(): """ Class of options for evolution solvers such as :func:`qutip.mesolve` and :func:`qutip.mcsolve`. Options can be specified either as arguments to the constructor:: opts = Options(order=10, ...) or by changing the class attributes after creation:: opts = Options() opts.order = 10 Returns options class to be used as options in evolution solvers. Attributes ---------- atol : float {1e-8} Absolute tolerance. rtol : float {1e-6} Relative tolerance. method : str {'adams','bdf'} Integration method. order : int {12} Order of integrator (<=12 'adams', <=5 'bdf') nsteps : int {2500} Max. number of internal steps/call. first_step : float {0} Size of initial step (0 = automatic). min_step : float {0} Minimum step size (0 = automatic). max_step : float {0} Maximum step size (0 = automatic) tidy : bool {True,False} Tidyup Hamiltonian and initial state by removing small terms. num_cpus : int Number of cpus used by mcsolver (default = # of cpus). norm_tol : float Tolerance used when finding wavefunction norm in mcsolve. norm_steps : int Max. number of steps used to find wavefunction norm to within norm_tol in mcsolve. average_states : bool {False} Average states values over trajectories in stochastic solvers. average_expect : bool {True} Average expectation values over trajectories for stochastic solvers. mc_corr_eps : float {1e-10} Arbitrarily small value for eliminating any divide-by-zero errors in correlation calculations when using mcsolve. ntraj : int {500} Number of trajectories in stochastic solvers. openmp_threads : int Number of OPENMP threads to use. Default is number of cpu cores. rhs_reuse : bool {False,True} Reuse Hamiltonian data. rhs_with_state : bool {False,True} Whether or not to include the state in the Hamiltonian function callback signature. rhs_filename : str Name for compiled Cython file. seeds : ndarray Array containing random number seeds for mcsolver. store_final_state : bool {False, True} Whether or not to store the final state of the evolution in the result class. store_states : bool {False, True} Whether or not to store the state vectors or density matrices in the result class, even if expectation values operators are given. If no expectation are provided, then states are stored by default and this option has no effect. use_openmp : bool {True, False} Use OPENMP for sparse matrix vector multiplication. Default None means auto check. """ def __init__(self, atol=1e-8, rtol=1e-6, method='adams', order=12, nsteps=1000, first_step=0, max_step=0, min_step=0, average_expect=True, average_states=False, tidy=True, num_cpus=0, norm_tol=1e-3, norm_t_tol=1e-6, norm_steps=5, rhs_reuse=False, rhs_filename=None, ntraj=500, gui=False, rhs_with_state=False, store_final_state=False, store_states=False, steady_state_average=False, seeds=None, normalize_output=True, use_openmp=None, openmp_threads=None): # Absolute tolerance (default = 1e-8) self.atol = atol # Relative tolerance (default = 1e-6) self.rtol = rtol # Integration method (default = 'adams', for stiff 'bdf') self.method = method # Max. number of internal steps/call self.nsteps = nsteps # Size of initial step (0 = determined by solver) self.first_step = first_step # Minimal step size (0 = determined by solver) self.min_step = min_step # Max step size (0 = determined by solver) self.max_step = max_step # Maximum order used by integrator (<=12 for 'adams', <=5 for 'bdf') self.order = order # Average expectation values over trajectories (default = True) self.average_states = average_states # average expectation values self.average_expect = average_expect # Number of trajectories (default = 500) self.ntraj = ntraj # Holds seeds for rand num gen self.seeds = seeds # tidyup Hamiltonian before calculation (default = True) self.tidy = tidy # include the state in the function callback signature self.rhs_with_state = rhs_with_state # Use preexisting RHS function for time-dependent solvers self.rhs_reuse = rhs_reuse # Use filename for preexisting RHS function (will default to last # compiled function if None & rhs_exists=True) self.rhs_filename = rhs_filename # small value in mc solver for computing correlations self.mc_corr_eps = 1e-10 # Number of processors to use (mcsolve only) if num_cpus: self.num_cpus = num_cpus else: self.num_cpus = qset.num_cpus # Tolerance for wavefunction norm (mcsolve only) self.norm_tol = norm_tol # Tolerance for collapse time precision (mcsolve only) self.norm_t_tol = norm_t_tol # Max. number of steps taken to find wavefunction norm to within # norm_tol (mcsolve only) self.norm_steps = norm_steps # Number of threads for openmp if openmp_threads is None: self.openmp_threads = qset.num_cpus else: self.openmp_threads = openmp_threads # store final state? self.store_final_state = store_final_state # store states even if expectation operators are given? self.store_states = store_states # average mcsolver density matricies assuming steady state evolution self.steady_state_average = steady_state_average # Normalize output of solvers # (turned off for batch unitary propagator mode) self.normalize_output = normalize_output # Use OPENMP for sparse matrix vector multiplication self.use_openmp = use_openmp def __str__(self): if self.seeds is None: seed_length = 0 else: seed_length = len(self.seeds) s = "" s += "Options:\n" s += "-----------\n" s += "atol: " + str(self.atol) + "\n" s += "rtol: " + str(self.rtol) + "\n" s += "method: " + str(self.method) + "\n" s += "order: " + str(self.order) + "\n" s += "nsteps: " + str(self.nsteps) + "\n" s += "first_step: " + str(self.first_step) + "\n" s += "min_step: " + str(self.min_step) + "\n" s += "max_step: " + str(self.max_step) + "\n" s += "tidy: " + str(self.tidy) + "\n" s += "num_cpus: " + str(self.num_cpus) + "\n" s += "norm_tol: " + str(self.norm_tol) + "\n" s += "norm_steps: " + str(self.norm_steps) + "\n" s += "rhs_filename: " + str(self.rhs_filename) + "\n" s += "rhs_reuse: " + str(self.rhs_reuse) + "\n" s += "seeds: " + str(seed_length) + "\n" s += "rhs_with_state: " + str(self.rhs_with_state) + "\n" s += "average_expect: " + str(self.average_expect) + "\n" s += "average_states: " + str(self.average_states) + "\n" s += "ntraj: " + str(self.ntraj) + "\n" s += "store_states: " + str(self.store_states) + "\n" s += "store_final_state: " + str(self.store_final_state) + "\n" return s
[docs]class Result(): """Class for storing simulation results from any of the dynamics solvers. Attributes ---------- solver : str Which solver was used [e.g., 'mesolve', 'mcsolve', 'brmesolve', ...] times : list/array Times at which simulation data was collected. expect : list/array Expectation values (if requested) for simulation. states : array State of the simulation (density matrix or ket) evaluated at ``times``. num_expect : int Number of expectation value operators in simulation. num_collapse : int Number of collapse operators in simualation. ntraj : int/list Number of trajectories (for stochastic solvers). A list indicates that averaging of expectation values was done over a subset of total number of trajectories. col_times : list Times at which state collpase occurred. Only for Monte Carlo solver. col_which : list Which collapse operator was responsible for each collapse in ``col_times``. Only for Monte Carlo solver. """ def __init__(self): self.solver = None self.times = None self.states = [] self.expect = [] self.num_expect = 0 self.num_collapse = 0 self.ntraj = None self.seeds = None self.col_times = None self.col_which = None def __str__(self): s = "Result object " if self.solver: s += "with " + self.solver + " data.\n" else: s += "missing solver information.\n" s += "-" * (len(s) - 1) + "\n" if self.states is not None and len(self.states) > 0: s += "states = True\n" elif self.expect is not None and len(self.expect) > 0: s += "expect = True\nnum_expect = " + str(self.num_expect) + ", " else: s += "states = True, expect = True\n" + \ "num_expect = " + str(self.num_expect) + ", " s += "num_collapse = " + str(self.num_collapse) if self.solver == 'mcsolve': s += ", ntraj = " + str(self.ntraj) return s def __repr__(self): return self.__str__() def __getstate__(self): # defines what happens when Qobj object gets pickled self.__dict__.update({'qutip_version': __version__[:5]}) return self.__dict__ def __setstate__(self, state): # defines what happens when loading a pickled Qobj if 'qutip_version' in state.keys(): del state['qutip_version'] (self.__dict__).update(state)
# %%%%%%%%%%% remove ?
[docs]class SolverConfiguration(): def __init__(self): self.cgen_num = 0 self.reset() def reset(self): # General stuff self.tlist = None # evaluations times self.ntraj = None # number / list of trajectories self.options = None # options for solvers self.norm_tol = None # tolerance for wavefunction norm self.norm_steps = None # max. number of steps to take in finding # Initial state stuff self.psi0 = None # initial state self.psi0_dims = None # initial state dims self.psi0_shape = None # initial state shape # flags for setting time-dependence, collapse ops, and number of times # codegen has been run self.cflag = 0 # Flag signaling collapse operators self.tflag = 0 # Flag signaling time-dependent problem self.soft_reset() def soft_reset(self): # Hamiltonian stuff self.h_td_inds = [] # indicies of time-dependent Hamiltonian operators self.h_tdterms = [] # List of td strs and funcs self.h_data = None # List of sparse matrix data self.h_ind = None # List of sparse matrix indices self.h_ptr = None # List of sparse matrix ptrs # Expectation operator stuff self.e_num = 0 # number of expect ops self.e_ops_data = [] # expect op data self.e_ops_ind = [] # expect op indices self.e_ops_ptr = [] # expect op indptrs self.e_ops_isherm = [] # expect op isherm # Collapse operator stuff self.c_num = 0 # number of collapse ops self.c_const_inds = [] # indicies of constant collapse operators self.c_td_inds = [] # indicies of time-dependent collapse operators self.c_ops_data = [] # collapse op data self.c_ops_ind = [] # collapse op indices self.c_ops_ptr = [] # collapse op indptrs self.c_args = [] # store args for time-dependent collapse func. # Norm collapse operator stuff self.n_ops_data = [] # norm collapse op data self.n_ops_ind = [] # norm collapse op indices self.n_ops_ptr = [] # norm collapse op indptrs # holds executable strings for time-dependent collapse evaluation self.col_expect_code = None self.col_spmv_code = None # hold stuff for function list based time dependence self.h_td_inds = [] self.h_td_data = [] self.h_td_ind = [] self.h_td_ptr = [] self.h_funcs = None self.h_func_args = None self.c_funcs = None self.c_func_args = None # time-dependent (TD) function stuff self.tdfunc = None # Placeholder for TD RHS function. self.tdname = None # Name of td .pyx file self.colspmv = None # Placeholder for TD col-spmv function. self.colexpect = None # Placeholder for TD col_expect function. self.string = None # Holds string of variables passed to td solver
def _format_time(t, tt=None, ttt=None): time_str = str(datetime.timedelta(seconds=t)) if tt is not None and ttt is not None: sect_percent = 100*t/tt solve_percent = 100*t/ttt time_str += " ({:03.2f}% section, {:03.2f}% total)".format( sect_percent, solve_percent) elif tt is not None: sect_percent = 100*t/tt time_str += " ({:03.2f}% section)".format(sect_percent) elif ttt is not None: solve_percent = 100*t/ttt time_str += " ({:03.2f}% total)".format(solve_percent) return time_str
[docs]class Stats(object): """ Statistical information on the solver performance Statistics can be grouped into sections. If no section names are given in the the contructor, then all statistics will be added to one section 'main' Parameters ---------- section_names : list list of keys that will be used as keys for the sections These keys will also be used as names for the sections The text in the output can be overidden by setting the header property of the section If no names are given then one section called 'main' is created Attributes ---------- sections : OrderedDict of _StatsSection These are the sections that are created automatically on instantiation or added using add_section header : string Some text that will be used as the heading in the report By default there is None total_time : float Time in seconds for the solver to complete processing Can be None, meaning that total timing percentages will be reported Methods ------- add_section Add another section add_count Add some stat that is an integer count add_timing Add some timing statistics add_message Add some text type for output in the report report: Output the statistics report to console or file. """ def __init__(self, section_names=None): self._def_section_name = 'main' self.sections = OrderedDict() self.total_time = None self.header = None if isinstance(section_names, list): c = 0 for name in section_names: self.sections[name] = _StatsSection(name, self) if c == 0: self._def_section_name = name c += 1 else: self.sections[self._def_section_name] = \ _StatsSection(self._def_section_name) def _get_section(self, section): if section is None: return self.sections[self._def_section_name] elif isinstance(section, _StatsSection): return section else: sect = self.sections.get(section, None) if sect is None: raise ValueError("Unknown section {}".format(section)) else: return sect
[docs] def add_section(self, name): """ Add another section with the given name Parameters ---------- name : string will be used as key for sections dict will also be the header for the section Returns ------- section : `class` : _StatsSection The new section """ sect = _StatsSection(name, self) self.sections[name] = sect return sect
[docs] def add_count(self, key, value, section=None): """ Add value to count. If key does not already exist in section then it is created with this value. If key already exists it is increased by the give value value is expected to be an integer Parameters ---------- key : string key for the section.counts dictionary reusing a key will result in numerical addition of value value : int Initial value of the count, or added to an existing count section: string or `class` : _StatsSection Section which to add the count to. If None given, the default (first) section will be used """ self._get_section(section).add_count(key, value)
[docs] def add_timing(self, key, value, section=None): """ Add value to timing. If key does not already exist in section then it is created with this value. If key already exists it is increased by the give value value is expected to be a float, and given in seconds. Parameters ---------- key : string key for the section.timings dictionary reusing a key will result in numerical addition of value value : int Initial value of the timing, or added to an existing timing section: string or `class` : _StatsSection Section which to add the timing to. If None given, the default (first) section will be used """ self._get_section(section).add_timing(key, value)
[docs] def add_message(self, key, value, section=None, sep=";"): """ Add value to message. If key does not already exist in section then it is created with this value. If key already exists the value is added to the message The value will be converted to a string Parameters ---------- key : string key for the section.messages dictionary reusing a key will result in concatenation of value value : int Initial value of the message, or added to an existing message sep : string Message will be prefixed with this string when concatenating section: string or `class` : _StatsSection Section which to add the message to. If None given, the default (first) section will be used """ self._get_section(section).add_message(key, value, sep=sep)
[docs] def set_total_time(self, value, section=None): """ Sets the total time for the complete solve or for a specific section value is expected to be a float, and given in seconds Parameters ---------- value : float Time in seconds to complete the solver section section : string or `class` : _StatsSection Section which to set the total_time for If None given, the total_time for complete solve is set """ if not isinstance(value, float): try: value = float(value) except: raise TypeError("value is expected to be a float") if section is None: self.total_time = value else: sect = self._get_section(section) sect.total_time = value
[docs] def report(self, output=sys.stdout): """ Report the counts, timings and messages from the sections. Sections are reported in the order that the names were supplied in the constructor. The counts, timings and messages are reported in the order that they are added to the sections The output can be written to anything that supports a write method, e.g. a file or the console (default) The output is intended to in markdown format Parameters ---------- output : stream file or console stream - anything that support write - where the output will be written """ if not hasattr(output, 'write'): raise TypeError("output must have a write method") if self.header: output.write("{}\n{}\n".format(self.header, ("="*len(self.header)))) for name, sect in self.sections.items(): sect.report(output) if self.total_time is not None: output.write("\nSummary\n-------\n") output.write("{}\t solver total time\n".format( _format_time(self.total_time)))
[docs] def clear(self): """ Clear counts, timings and messages from all sections """ for sect in self.sections.values(): sect.clear() self.total_time = None
class _StatsSection(object): """ Not intended to be directly instantiated This is the type for the SolverStats.sections values The method parameter descriptions are the same as for those the parent with the same method name Parameters ---------- name : string key for the parent sections dictionary will also be used as the header parent : `class` : SolverStats The container for all the sections Attributes ---------- name : string key for the parent sections dictionary will also be used as the header parent : `class` : SolverStats The container for all the sections header : string Used as heading for section in report counts : OrderedDict The integer type statistics for the stats section timings : OrderedDict The timing type statistics for the stats section Expected to contain float values representing values in seconds messages : OrderedDict Text type output to be reported total_time : float Total time for processing in the section Can be None, meaning that section timing percentages will be reported """ def __init__(self, name, parent): self.parent = parent self.header = str(name) self.name = name self.counts = OrderedDict() self.timings = OrderedDict() self.messages = OrderedDict() self.total_time = None def add_count(self, key, value): """ Add value to count. If key does not already exist in section then it is created with this value. If key already exists it is increased by the given value value is expected to be an integer """ if not isinstance(value, int): try: value = int(value) except: raise TypeError("value is expected to be an integer") if key in self.counts: self.counts[key] += value else: self.counts[key] = value def add_timing(self, key, value): """ Add value to timing. If key does not already exist in section then it is created with this value. If key already exists it is increased by the give value value is expected to be a float, and given in seconds. """ if not isinstance(value, float): try: value = float(value) except: raise TypeError("value is expected to be a float") if key in self.timings: self.timings[key] += value else: self.timings[key] = value def add_message(self, key, value, sep=";"): """ Add value to message. If key does not already exist in section then it is created with this value. If key already exists the value is added to the message The value will be converted to a string """ value = str(value) if key in self.messages: if sep is not None: try: value = sep + value except: TypeError("It is not possible to concatenate the value " "with the given seperator") self.messages[key] += value else: self.messages[key] = value def report(self, output=sys.stdout): """ Report the counts, timings and messages for this section. Note the percentage of the section and solver total times will be given if the parent and or section total_time is set """ if self.header: output.write("\n{}\n{}\n".format(self.header, ("-"*len(self.header)))) # TODO: Make the timings and counts ouput in a table format # Generally make more pretty # Report timings try: ttt = self.parent.total_time except: ttt = None tt = self.total_time output.write("### Timings:\n") for key, value in self.timings.items(): l = " - {}\t{}\n".format(_format_time(value, tt, ttt), key) output.write(l) if tt is not None: output.write(" - {}\t{} total time\n".format(_format_time(tt), self.name)) # Report counts output.write("### Counts:\n") for key, value in self.counts.items(): l = " - {}\t{}\n".format(value, key) output.write(l) # Report messages output.write("### Messages:\n") for key, value in self.messages.items(): l = " - {}:\t{}\n".format(key, value) output.write(l) def clear(self): """ Clear counts, timings and messages from this section """ self.counts.clear() self.timings.clear() self.messages.clear() self.total_time = None def _solver_safety_check(H, state=None, c_ops=[], e_ops=[], args={}): # Input is std Qobj (Hamiltonian or Liouvillian) if isinstance(H, Qobj): Hdims = H.dims Htype = H.type _structure_check(Hdims, Htype, state) # Input H is function elif isinstance(H, (FunctionType, BuiltinFunctionType)): Hdims = H(0,args).dims Htype = H(0,args).type _structure_check(Hdims, Htype, state) # Input is td-list elif isinstance(H, list): if isinstance(H[0], Qobj): Hdims = H[0].dims Htype = H[0].type elif isinstance(H[0], list): Hdims = H[0][0].dims Htype = H[0][0].type elif isinstance(H[0], (FunctionType, BuiltinFunctionType)): Hdims = H[0](0,args).dims Htype = H[0](0,args).type else: raise Exception('Invalid td-list element.') # Check all operators in list for ii in range(len(H)): if isinstance(H[ii], Qobj): _temp_dims = H[ii].dims _temp_type = H[ii].type elif isinstance(H[ii], list): _temp_dims = H[ii][0].dims _temp_type = H[ii][0].type elif isinstance(H[ii], (FunctionType, BuiltinFunctionType)): _temp_dims = H[ii](0,args).dims _temp_type = H[ii](0,args).type else: raise Exception('Invalid td-list element.') _structure_check(_temp_dims,_temp_type,state) else: raise Exception('Invalid time-dependent format.') for ii in range(len(c_ops)): do_tests = True if isinstance(c_ops[ii], Qobj): _temp_state = c_ops[ii] elif isinstance(c_ops[ii], list): if isinstance(c_ops[ii][0], Qobj): _temp_state = c_ops[ii][0] elif isinstance(c_ops[ii][0], tuple): do_tests = False for kk in range(len(c_ops[ii][0])): _temp_state = c_ops[ii][0][kk] _structure_check(Hdims, Htype, _temp_state) else: raise Exception('Invalid td-list element.') if do_tests: _structure_check(Hdims, Htype, _temp_state) if isinstance(e_ops, list): for ii in range(len(e_ops)): if isinstance(e_ops[ii], Qobj): _temp_state = e_ops[ii] elif isinstance(e_ops[ii], list): _temp_state = e_ops[ii][0] else: raise Exception('Invalid td-list element.') _structure_check(Hdims,Htype,_temp_state) elif isinstance(e_ops, FunctionType): pass else: raise Exception('Invalid e_ops specification.') def _structure_check(Hdims, Htype, state): if state is not None: # Input state is a ket vector if state.type == 'ket': # Input is Hamiltonian if Htype == 'oper': if Hdims[1] != state.dims[0]: raise Exception('Input operator and ket do not ' 'share same structure.') # Input is super and state is ket elif Htype == 'super': if Hdims[1][1] != state.dims[0]: raise Exception('Input operator and ket do not ' 'share same structure.') else: raise Exception('Invalid input operator.') # Input state is a density matrix elif state.type == 'oper': # Input is Hamiltonian and state is density matrix if Htype == 'oper': if Hdims[1] != state.dims[0]: raise Exception('Input operators do not ' 'share same structure.') # Input is super op. and state is density matrix elif Htype == 'super': if Hdims[1] != state.dims: raise Exception('Input operators do not ' 'share same structure.') # # create a global instance of the SolverConfiguration class # config = SolverConfiguration() # for backwards compatibility Odeoptions = Options Odedata = Result