def ac_analysis(circ, start, nsteps, stop, step_type, xop=None, mna=None,\
AC=None, Nac=None, J=None, data_filename="stdout", verbose=3):
"""Performs an AC analysis of the circuit (described by circ).
"""
if data_filename == 'stdout':
verbose = 0
#check step/start/stop parameters
if start == 0:
printing.print_general_error("AC analysis has start frequency = 0")
sys.exit(5)
if start > stop:
printing.print_general_error("AC analysis has start > stop")
sys.exit(1)
if nsteps < 1:
printing.print_general_error("AC analysis has number of steps <= 1")
sys.exit(1)
if step_type == options.ac_log_step:
omega_iter = utilities.log_axis_iterator(stop, start, nsteps)
elif step_type == options.ac_lin_step:
omega_iter = utilities.lin_axis_iterator(stop, start, nsteps)
else:
printing.print_general_error("Unknown sweep type.")
sys.exit(1)
tmpstr = "Vea =", options.vea, "Ver =", options.ver, "Iea =", options.iea, "Ier =", \
options.ier, "max_ac_nr_iter =", options.ac_max_nr_iter
printing.print_info_line((tmpstr, 5), verbose)
del tmpstr
printing.print_info_line(("Starting AC analysis: ", 1), verbose)
tmpstr = "w: start = %g Hz, stop = %g Hz, %d steps" % (start, stop, nsteps)
printing.print_info_line((tmpstr, 3), verbose)
del tmpstr
#It's a good idea to call AC with prebuilt MNA matrix if the circuit is big
if mna is None:
(mna, N) = dc_analysis.generate_mna_and_N(circ)
del N
mna = utilities.remove_row_and_col(mna)
if Nac is None:
Nac = generate_Nac(circ)
Nac = utilities.remove_row(Nac, rrow=0)
if AC is None:
AC = generate_AC(circ, [mna.shape[0], mna.shape[0]])
AC = utilities.remove_row_and_col(AC)
if circ.is_nonlinear():
if J is not None:
pass
# we used the supplied linearization matrix
else:
if xop is None:
printing.print_info_line(
("Starting OP analysis to get a linearization point...",
3),
verbose,
print_nl=False)
#silent OP
xop = dc_analysis.op_analysis(circ, verbose=0)
if xop is None: #still! Then op_analysis has failed!
printing.print_info_line(("failed.", 3), verbose)
printing.print_general_error(
"OP analysis failed, no linearization point available. Quitting."
)
sys.exit(3)
else:
printing.print_info_line(("done.", 3), verbose)
printing.print_info_line(("Linearization point (xop):", 5),
verbose)
if verbose > 4: xop.print_short()
printing.print_info_line(("Linearizing the circuit...", 5),
verbose,
print_nl=False)
J = generate_J(xop=xop.asmatrix(),
circ=circ,
mna=mna,
Nac=Nac,
data_filename=data_filename,
verbose=verbose)
printing.print_info_line((" done.", 5), verbose)
# we have J, continue
else: #not circ.is_nonlinear()
# no J matrix is required.
J = 0
printing.print_info_line(("MNA (reduced):", 5), verbose)
printing.print_info_line((str(mna), 5), verbose)
printing.print_info_line(("AC (reduced):", 5), verbose)
printing.print_info_line((str(AC), 5), verbose)
printing.print_info_line(("J (reduced):", 5), verbose)
printing.print_info_line((str(J), 5), verbose)
printing.print_info_line(("Nac (reduced):", 5), verbose)
printing.print_info_line((str(Nac), 5), verbose)
sol = results.ac_solution(circ,
ostart=start,
ostop=stop,
opoints=nsteps,
stype=step_type,
op=xop,
outfile=data_filename)
# setup the initial values to start the iteration:
nv = len(circ.nodes_dict)
j = numpy.complex('j')
Gmin_matrix = dc_analysis.build_gmin_matrix(circ, options.gmin,
mna.shape[0], verbose)
iter_n = 0 # contatore d'iterazione
#printing.print_results_header(circ, fdata, print_int_nodes=options.print_int_nodes, print_omega=True)
printing.print_info_line(("Solving... ", 3), verbose, print_nl=False)
tick = ticker.ticker(increments_for_step=1)
tick.display(verbose > 1)
x = xop
for omega in omega_iter:
(x, error, solved, n_iter) = dc_analysis.dc_solve(mna=(mna + numpy.multiply(j*omega, AC) + J), \
Ndc=Nac, Ntran=0, circ=circuit.circuit(title="Dummy circuit for AC", filename=None), Gmin=Gmin_matrix, x0=x, \
time=None, locked_nodes=None, MAXIT=options.ac_max_nr_iter, skip_Tt=True, verbose=0)
if solved:
tick.step(verbose > 1)
iter_n = iter_n + 1
# hooray!
sol.add_line(omega, x)
else:
break
tick.hide(verbose > 1)
if solved:
printing.print_info_line(("done.", 1), verbose)
ret_value = sol
else:
printing.print_info_line(("failed.", 1), verbose)
ret_value = None
return ret_value
def transient_analysis(circ, tstart, tstep, tstop, method=TRAP, x0=None, mna=None, N=None, \
D=None, data_filename="stdout", use_step_control=True, return_req_dict=None, verbose=3):
"""Performs a transient analysis of the circuit described by circ.
Important parameters:
- tstep is the maximum step to be allowed during simulation.
- print_step_and_lte is a boolean value. Is set to true, the step and the LTE of the first
element of x will be printed out to step_and_lte.graph in the current directory.
"""
if data_filename == "stdout":
verbose = 0
_debug = False
if _debug:
print_step_and_lte = True
else:
print_step_and_lte = False
HMAX = tstep
#check parameters
if tstart > tstop:
printing.print_general_error("tstart > tstop")
sys.exit(1)
if tstep < 0:
printing.print_general_error("tstep < 0")
sys.exit(1)
if verbose > 4:
tmpstr = "Vea = %g Ver = %g Iea = %g Ier = %g max_time_iter = %g HMIN = %g" % \
(options.vea, options.ver, options.iea, options.ier, options.transient_max_time_iter, options.hmin)
printing.print_info_line((tmpstr, 5), verbose)
locked_nodes = circ.get_locked_nodes()
if print_step_and_lte:
flte = open("step_and_lte.graph", "w")
flte.write("#T\tStep\tLTE\n")
printing.print_info_line(("Starting transient analysis: ", 3), verbose)
printing.print_info_line(("Selected method: %s" % (method,), 3), verbose)
#It's a good idea to call transient with prebuilt MNA and N matrix
#the analysis will be slightly faster (long netlists).
if mna is None or N is None:
(mna, N) = dc_analysis.generate_mna_and_N(circ)
mna = utilities.remove_row_and_col(mna)
N = utilities.remove_row(N, rrow=0)
elif not mna.shape[0] == N.shape[0]:
printing.print_general_error("mna matrix and N vector have different number of columns.")
sys.exit(0)
if D is None:
# if you do more than one tran analysis, output streams should be changed...
# this needs to be fixed
D = generate_D(circ, [mna.shape[0], mna.shape[0]])
D = utilities.remove_row_and_col(D)
# setup x0
if x0 is None:
printing.print_info_line(("Generating x(t=%g) = 0" % (tstart,), 5), verbose)
x0 = numpy.matrix(numpy.zeros((mna.shape[0], 1)))
opsol = results.op_solution(x=x0, error=x0, circ=circ, outfile=None)
else:
if isinstance(x0, results.op_solution):
opsol = x0
x0 = x0.asmatrix()
else:
opsol = results.op_solution(x=x0, error=numpy.matrix(numpy.zeros((mna.shape[0], 1))), circ=circ, outfile=None)
printing.print_info_line(("Using the supplied op as x(t=%g)." % (tstart,), 5), verbose)
if verbose > 4:
print "x0:"
opsol.print_short()
# setup the df method
printing.print_info_line(("Selecting the appropriate DF ("+method+")... ", 5), verbose, print_nl=False)
if method == IMPLICIT_EULER:
import implicit_euler as df
elif method == TRAP:
import trap as df
elif method == GEAR1:
import gear as df
df.order = 1
elif method == GEAR2:
import gear as df
df.order = 2
elif method == GEAR3:
import gear as df
df.order = 3
elif method == GEAR4:
import gear as df
df.order = 4
elif method == GEAR5:
import gear as df
df.order = 5
elif method == GEAR6:
import gear as df
df.order = 6
else:
df = import_custom_df_module(method, print_out=(data_filename != "stdout"))
# df is none if module is not found
if df is None:
sys.exit(23)
if not df.has_ff() and use_step_control:
printing.print_warning("The chosen DF does not support step control. Turning off the feature.")
use_step_control = False
#use_aposteriori_step_control = False
printing.print_info_line(("done.", 5), verbose)
# setup the data buffer
# if you use the step control, the buffer has to be one point longer.
# That's because the excess point is used by a FF in the df module to predict the next value.
printing.print_info_line(("Setting up the buffer... ", 5), verbose, print_nl=False)
((max_x, max_dx), (pmax_x, pmax_dx)) = df.get_required_values()
if max_x is None and max_dx is None:
printing.print_general_error("df doesn't need any value?")
sys.exit(1)
if use_step_control:
thebuffer = dfbuffer(length=max(max_x, max_dx, pmax_x, pmax_dx) + 1, width=3)
else:
thebuffer = dfbuffer(length=max(max_x, max_dx) + 1, width=3)
thebuffer.add((tstart, x0, None)) #setup the first values
printing.print_info_line(("done.", 5), verbose) #FIXME
#setup the output buffer
if return_req_dict:
output_buffer = dfbuffer(length=return_req_dict["points"], width=1)
output_buffer.add((x0,))
else:
output_buffer = None
# import implicit_euler to be used in the first iterations
# this is because we don't have any dx when we start, nor any past point value
if (max_x is not None and max_x > 0) or max_dx is not None:
import implicit_euler
printing.print_info_line(("MNA (reduced):", 5), verbose)
printing.print_info_line((str(mna), 5), verbose)
printing.print_info_line(("D (reduced):", 5), verbose)
printing.print_info_line((str(D), 5), verbose)
# setup the initial values to start the iteration:
x = None
time = tstart
nv = len(circ.nodes_dict)
Gmin_matrix = dc_analysis.build_gmin_matrix(circ, options.gmin, mna.shape[0], verbose)
# lo step viene generato automaticamente, ma non superare mai quello fornito.
if use_step_control:
#tstep = min((tstop-tstart)/9999.0, HMAX, 100.0 * options.hmin)
tstep = min((tstop-tstart)/9999.0, HMAX)
printing.print_info_line(("Initial step: %g"% (tstep,), 5), verbose)
if max_dx is None:
max_dx_plus_1 = None
else:
max_dx_plus_1 = max_dx +1
if pmax_dx is None:
pmax_dx_plus_1 = None
else:
pmax_dx_plus_1 = pmax_dx +1
# setup error vectors
aerror = numpy.mat(numpy.zeros((x0.shape[0], 1)))
aerror[:nv-1, 0] = options.vea
aerror[nv-1:, 0] = options.vea
rerror = numpy.mat(numpy.zeros((x0.shape[0], 1)))
rerror[:nv-1, 0] = options.ver
rerror[nv-1:, 0] = options.ier
iter_n = 0 # contatore d'iterazione
lte = None
sol = results.tran_solution(circ, tstart, tstop, op=x0, method=method, outfile=data_filename)
printing.print_info_line(("Solving... ", 3), verbose, print_nl=False)
tick = ticker.ticker(increments_for_step=1)
tick.display(verbose > 1)
while time < tstop:
if iter_n < max(max_x, max_dx_plus_1):
x_coeff, const, x_lte_coeff, prediction, pred_lte_coeff = \
implicit_euler.get_df((thebuffer.get_df_vector()[0],), tstep, \
predict=(use_step_control and (iter_n >= max(pmax_x, pmax_dx_plus_1))))
else:
[x_coeff, const, x_lte_coeff, prediction, pred_lte_coeff] = \
df.get_df(thebuffer.get_df_vector(), tstep, predict=use_step_control)
if options.transient_prediction_as_x0 and use_step_control and prediction is not None:
x0 = prediction
elif x is not None:
x0 = x
(x1, error, solved, n_iter) = dc_analysis.dc_solve(mna=(mna + numpy.multiply(x_coeff, D)) , Ndc=N, Ntran=D*const, circ=circ, Gmin=Gmin_matrix, x0=x0, time=(time + tstep), locked_nodes=locked_nodes, MAXIT=options.transient_max_nr_iter, verbose=0)
if solved:
old_step = tstep #we will modify it, if we're using step control otherwise it's the same
# step control (yeah)
if use_step_control:
if x_lte_coeff is not None and pred_lte_coeff is not None and prediction is not None:
# this is the Local Truncation Error :)
lte = abs((x_lte_coeff / (pred_lte_coeff - x_lte_coeff)) * (prediction - x1))
# it should NEVER happen that new_step > 2*tstep, for stability
new_step_coeff = 2
for index in xrange(x.shape[0]):
if lte[index, 0] != 0:
new_value = ((aerror[index, 0] + rerror[index, 0]*abs(x[index, 0])) / lte[index, 0]) \
** (1.0 / (df.order+1))
if new_value < new_step_coeff:
new_step_coeff = new_value
#print new_value
new_step = tstep * new_step_coeff
if options.transient_use_aposteriori_step_control and new_step < options.transient_aposteriori_step_threshold * tstep:
#don't recalculate a x for a small change
tstep = check_step(new_step, time, tstop, HMAX)
#print "Apost. (reducing) step = "+str(tstep)
continue
tstep = check_step(new_step, time, tstop, HMAX) # used in the next iteration
#print "Apriori tstep = "+str(tstep)
else:
#print "LTE not calculated."
lte = None
if print_step_and_lte and lte is not None:
#if you wish to look at the step. We print just a lte
flte.write(str(time)+"\t"+str(old_step)+"\t"+str(lte.max())+"\n")
# if we get here, either aposteriori_step_control is
# disabled, or it's enabled and the error is small
# enough. Anyway, the result is GOOD, STORE IT.
time = time + old_step
x = x1
iter_n = iter_n + 1
sol.add_line(time, x)
dxdt = numpy.multiply(x_coeff, x) + const
thebuffer.add((time, x, dxdt))
if output_buffer is not None:
output_buffer.add((x, ))
tick.step(verbose > 1)
else:
# If we get here, Newton failed to converge. We need to reduce the step...
if use_step_control:
tstep = tstep/5.0
tstep = check_step(tstep, time, tstop, HMAX)
printing.print_info_line(("At %g s reducing step: %g s (convergence failed)" % (time, tstep), 5), verbose)
else: #we can't reduce the step
printing.print_general_error("Can't converge with step "+str(tstep)+".")
printing.print_general_error("Try setting --t-max-nr to a higher value or set step to a lower one.")
solved = False
break
if options.transient_max_time_iter and iter_n == options.transient_max_time_iter:
printing.print_general_error("MAX_TIME_ITER exceeded ("+str(options.transient_max_time_iter)+"), iteration halted.")
solved = False
break
if print_step_and_lte:
flte.close()
tick.hide(verbose > 1)
if solved:
printing.print_info_line(("done.", 3), verbose)
printing.print_info_line(("Average time step: %g" % ((tstop - tstart)/iter_n,), 3), verbose)
if output_buffer:
ret_value = output_buffer.get_as_matrix()
else:
ret_value = sol
else:
print "failed."
ret_value = None
return ret_value
def bfpss(circ, period, step=None, mna=None, Tf=None, D=None, points=None, autonomous=False, x0=None, data_filename='stdout', vector_norm=lambda v: max(abs(v)), verbose=3):
"""Performs a PSS analysis.
Time step is constant, IE will be used as DF
Parameters:
circ is the circuit description class
period is the period of the solution
mna, D, Tf are not compulsory they will be computed if they're set to None
step is the time step between consecutive points
points is the number of points to be used
step and points are mutually exclusive options:
- if step is specified, the number of points will be automatically determined
- if points is set, the step will be automatically determined
- if none of them is set, options.shooting_default_points will be used as points
autonomous has to be False, autonomous circuits are not supported
x0 is the initial guess to be used. Needs work.
data_filename is the output filename. Defaults to stdout.
verbose is set to zero (print errors only) if datafilename == 'stdout'.
Returns: nothing
"""
if data_filename == "stdout":
verbose = 0
printing.print_info_line(("Starting periodic steady state analysis:",3), verbose)
printing.print_info_line(("Method: brute-force",3), verbose)
if mna is None or Tf is None:
(mna, Tf) = dc_analysis.generate_mna_and_N(circ)
mna = utilities.remove_row_and_col(mna)
Tf = utilities.remove_row(Tf, rrow=0)
elif not mna.shape[0] == Tf.shape[0]:
printing.print_general_error("mna matrix and N vector have different number of rows.")
sys.exit(0)
if D is None:
D = transient.generate_D(circ, [mna.shape[0], mna.shape[0]])
D = utilities.remove_row_and_col(D)
elif not mna.shape == D.shape:
printing.print_general_error("mna matrix and D matrix have different sizes.")
sys.exit(0)
(points, step) = check_step_and_points(step, points, period)
n_of_var = mna.shape[0]
locked_nodes = circ.get_locked_nodes()
tick = ticker.ticker(increments_for_step=1)
CMAT = build_CMAT(mna, D, step, points, tick, n_of_var=n_of_var, \
verbose=verbose)
x = build_x(mna, step, points, tick, x0=x0, n_of_var=n_of_var, \
verbose=verbose)
Tf = build_Tf(Tf, points, tick, n_of_var=n_of_var, verbose=verbose)
# time variable component: Tt this is always the same in each iter. So we build it once for all
# this holds all time-dependent sources (both V/I).
Tt = build_Tt(circ, points, step, tick, n_of_var=n_of_var, verbose=verbose)
# Indices to differentiate between currents and voltages in the convergence check
nv_indices = []
ni_indices = []
nv_1 = len(circ.nodes_dict) - 1
ni = n_of_var - nv_1
for i in range(points):
nv_indices += (i*mna.shape[0]*numpy.ones(nv_1) + numpy.arange(nv_1)).tolist()
ni_indices += (i*mna.shape[0]*numpy.ones(ni) + numpy.arange(nv_1, n_of_var)).tolist()
converged = False
printing.print_info_line(("Solving... ",3), verbose, print_nl=False)
tick.reset()
tick.display(verbose > 2)
J = numpy.mat(numpy.zeros(CMAT.shape))
T = numpy.mat(numpy.zeros((CMAT.shape[0], 1)))
# td is a numpy matrix that will hold the damping factors
td = numpy.mat(numpy.zeros((points, 1)))
iteration = 0 # newton iteration counter
while True:
if iteration: # the first time are already all zeros
J[:, :] = 0
T[:, 0] = 0
td[:, 0] = 0
for index in xrange(1, points):
for elem in circ.elements:
# build all dT(xn)/dxn (stored in J) and T(x)
if elem.is_nonlinear:
oports = elem.get_output_ports()
for opindex in range(len(oports)):
dports = elem.get_drive_ports(opindex)
v_ports = []
for dpindex in range(len(dports)):
dn1, dn2 = dports[dpindex]
v = 0 # build v: remember we trashed the 0 row and 0 col of mna -> -1
if dn1:
v = v + x[index*n_of_var + dn1 - 1, 0]
if dn2:
v = v - x[index*n_of_var + dn2 - 1, 0]
v_ports.append(v)
# all drive ports are ready.
n1, n2 = oports[opindex][0], oports[opindex][1]
if n1:
T[index*n_of_var + n1 - 1, 0] = T[index*n_of_var + n1 - 1, 0] + elem.i(opindex, v_ports)
if n2:
T[index*n_of_var + n2 - 1, 0] = T[index*n_of_var + n2 - 1, 0] - elem.i(opindex, v_ports)
for dpindex in range(len(dports)):
dn1, dn2 = dports[dpindex]
if n1:
if dn1:
J[index*n_of_var + n1-1, index*n_of_var + dn1-1] = \
J[index*n_of_var + n1-1, index*n_of_var + dn1-1] + elem.g(opindex, v_ports, dpindex)
if dn2:
J[index*n_of_var + n1-1, index*n_of_var + dn2-1] =\
J[index*n_of_var + n1-1, index * n_of_var + dn2-1] - 1.0*elem.g(opindex, v_ports, dpindex)
if n2:
if dn1:
J[index*n_of_var + n2-1, index*n_of_var + dn1-1] = \
J[index*n_of_var + n2-1, index*n_of_var + dn1-1] - 1.0*elem.g(opindex, v_ports, dpindex)
if dn2:
J[index*n_of_var + n2-1, index*n_of_var + dn2-1] =\
J[index*n_of_var + n2-1, index*n_of_var + dn2-1] + elem.g(opindex, v_ports, dpindex)
J = J + CMAT
residuo = CMAT*x + T + Tf + Tt
dx = -1 * (numpy.linalg.inv(J) * residuo)
#td
for index in xrange(points):
td[index, 0] = dc_analysis.get_td(dx[index*n_of_var:(index+1)*n_of_var, 0], locked_nodes, n=-1)
x = x + min(abs(td))[0, 0] * dx
# convergence check
converged = convergence_check(dx, x, nv_indices, ni_indices, vector_norm)
if converged:
break
tick.step(verbose > 2)
if options.shooting_max_nr_iter and iteration == options.shooting_max_nr_iter:
printing.print_general_error("Hitted SHOOTING_MAX_NR_ITER (" + str(options.shooting_max_nr_iter) + "), iteration halted.")
converged = False
break
else:
iteration = iteration + 1
tick.hide(verbose > 2)
if converged:
printing.print_info_line(("done.", 3), verbose)
t = numpy.mat(numpy.arange(points)*step)
t = t.reshape((1, points))
x = x.reshape((points, n_of_var))
sol = results.pss_solution(circ=circ, method="brute-force", period=period, outfile=data_filename, t_array=t, x_array=x.T)
else:
print "failed."
sol = None
return sol
def ac_analysis(circ, start, points, stop, sweep_type, x0=None,
mna=None, AC=None, Nac=None, J=None,
outfile="stdout", verbose=3):
"""Performs an AC analysis of the circuit described by circ.
Parameters:
start (float): the start angular frequency for the AC analysis
stop (float): stop angular frequency
points (float): the number of points to be use the discretize the
[start, stop] interval.
sweep_type (string): Either 'LOG' or 'LINEAR', defaults to 'LOG'.
outfile (string): the filename of the output file where the results will be written.
'.ac' is automatically added at the end to prevent different
analyses from overwriting each-other's results.
If unset or set to None, defaults to stdout.
verbose (int): the verbosity level, from 0 (silent) to 6 (debug).
Returns: an AC results object
"""
if outfile == 'stdout':
verbose = 0
# check step/start/stop parameters
nsteps = points - 1
if start == 0:
printing.print_general_error("AC analysis has start frequency = 0")
sys.exit(5)
if start > stop:
printing.print_general_error("AC analysis has start > stop")
sys.exit(1)
if nsteps < 1:
printing.print_general_error("AC analysis has number of steps <= 1")
sys.exit(1)
if sweep_type == options.ac_log_step:
omega_iter = utilities.log_axis_iterator(stop, start, nsteps)
elif sweep_type == options.ac_lin_step:
omega_iter = utilities.lin_axis_iterator(stop, start, nsteps)
else:
printing.print_general_error("Unknown sweep type.")
sys.exit(1)
tmpstr = "Vea =", options.vea, "Ver =", options.ver, "Iea =", options.iea, "Ier =", \
options.ier, "max_ac_nr_iter =", options.ac_max_nr_iter
printing.print_info_line((tmpstr, 5), verbose)
del tmpstr
printing.print_info_line(("Starting AC analysis: ", 1), verbose)
tmpstr = "w: start = %g Hz, stop = %g Hz, %d steps" % (start, stop, nsteps)
printing.print_info_line((tmpstr, 3), verbose)
del tmpstr
# It's a good idea to call AC with prebuilt MNA matrix if the circuit is
# big
if mna is None:
(mna, N) = dc_analysis.generate_mna_and_N(circ, verbose=verbose)
del N
mna = utilities.remove_row_and_col(mna)
if Nac is None:
Nac = generate_Nac(circ)
Nac = utilities.remove_row(Nac, rrow=0)
if AC is None:
AC = generate_AC(circ, [mna.shape[0], mna.shape[0]])
AC = utilities.remove_row_and_col(AC)
if circ.is_nonlinear():
if J is not None:
pass
# we used the supplied linearization matrix
else:
if x0 is None:
printing.print_info_line(
("Starting OP analysis to get a linearization point...", 3), verbose, print_nl=False)
# silent OP
x0 = dc_analysis.op_analysis(circ, verbose=0)
if x0 is None: # still! Then op_analysis has failed!
printing.print_info_line(("failed.", 3), verbose)
printing.print_general_error(
"OP analysis failed, no linearization point available. Quitting.")
sys.exit(3)
else:
printing.print_info_line(("done.", 3), verbose)
printing.print_info_line(
("Linearization point (xop):", 5), verbose)
if verbose > 4:
x0.print_short()
printing.print_info_line(
("Linearizing the circuit...", 5), verbose, print_nl=False)
J = generate_J(xop=x0.asmatrix(), circ=circ, mna=mna,
Nac=Nac, data_filename=outfile, verbose=verbose)
printing.print_info_line((" done.", 5), verbose)
# we have J, continue
else: # not circ.is_nonlinear()
# no J matrix is required.
J = 0
printing.print_info_line(("MNA (reduced):", 5), verbose)
printing.print_info_line((str(mna), 5), verbose)
printing.print_info_line(("AC (reduced):", 5), verbose)
printing.print_info_line((str(AC), 5), verbose)
printing.print_info_line(("J (reduced):", 5), verbose)
printing.print_info_line((str(J), 5), verbose)
printing.print_info_line(("Nac (reduced):", 5), verbose)
printing.print_info_line((str(Nac), 5), verbose)
sol = results.ac_solution(circ, ostart=start, ostop=stop,
opoints=nsteps, stype=sweep_type, op=x0, outfile=outfile)
# setup the initial values to start the iteration:
nv = len(circ.nodes_dict)
j = numpy.complex('j')
Gmin_matrix = dc_analysis.build_gmin_matrix(
circ, options.gmin, mna.shape[0], verbose)
iter_n = 0 # contatore d'iterazione
printing.print_info_line(("Solving... ", 3), verbose, print_nl=False)
tick = ticker.ticker(increments_for_step=1)
tick.display(verbose > 1)
x = x0
for omega in omega_iter:
(x, error, solved, n_iter) = dc_analysis.dc_solve(
mna=(mna + numpy.multiply(j * omega, AC) + J),
Ndc = Nac,
Ntran = 0,
circ = circuit.Circuit(
title="Dummy circuit for AC", filename=None),
Gmin = Gmin_matrix,
x0 = x,
time = None,
locked_nodes = None,
MAXIT = options.ac_max_nr_iter,
skip_Tt = True,
verbose = 0)
if solved:
tick.step(verbose > 1)
iter_n = iter_n + 1
# hooray!
sol.add_line(omega, x)
else:
break
tick.hide(verbose > 1)
if solved:
printing.print_info_line(("done.", 1), verbose)
ret_value = sol
else:
printing.print_info_line(("failed.", 1), verbose)
ret_value = None
return ret_value
def transient_analysis(circ, tstart, tstep, tstop, method=TRAP, x0=None, mna=None, N=None, \
D=None, data_filename="stdout", use_step_control=True, return_req_dict=None, verbose=3):
"""Performs a transient analysis of the circuit described by circ.
Important parameters:
- tstep is the maximum step to be allowed during simulation.
- print_step_and_lte is a boolean value. Is set to true, the step and the LTE of the first
element of x will be printed out to step_and_lte.graph in the current directory.
"""
if data_filename == "stdout":
verbose = 0
_debug = False
if _debug:
print_step_and_lte = True
else:
print_step_and_lte = False
HMAX = tstep
#check parameters
if tstart > tstop:
printing.print_general_error("tstart > tstop")
sys.exit(1)
if tstep < 0:
printing.print_general_error("tstep < 0")
sys.exit(1)
if verbose > 4:
tmpstr = "Vea = %g Ver = %g Iea = %g Ier = %g max_time_iter = %g HMIN = %g" % \
(options.vea, options.ver, options.iea, options.ier, options.transient_max_time_iter, options.hmin)
printing.print_info_line((tmpstr, 5), verbose)
locked_nodes = circ.get_locked_nodes()
if print_step_and_lte:
flte = open("step_and_lte.graph", "w")
flte.write("#T\tStep\tLTE\n")
printing.print_info_line(("Starting transient analysis: ", 3), verbose)
printing.print_info_line(("Selected method: %s" % (method, ), 3), verbose)
#It's a good idea to call transient with prebuilt MNA and N matrix
#the analysis will be slightly faster (long netlists).
if mna is None or N is None:
(mna, N) = dc_analysis.generate_mna_and_N(circ)
mna = utilities.remove_row_and_col(mna)
N = utilities.remove_row(N, rrow=0)
elif not mna.shape[0] == N.shape[0]:
printing.print_general_error(
"mna matrix and N vector have different number of columns.")
sys.exit(0)
if D is None:
# if you do more than one tran analysis, output streams should be changed...
# this needs to be fixed
D = generate_D(circ, [mna.shape[0], mna.shape[0]])
D = utilities.remove_row_and_col(D)
# setup x0
if x0 is None:
printing.print_info_line(("Generating x(t=%g) = 0" % (tstart, ), 5),
verbose)
x0 = numpy.matrix(numpy.zeros((mna.shape[0], 1)))
opsol = results.op_solution(x=x0, error=x0, circ=circ, outfile=None)
else:
if isinstance(x0, results.op_solution):
opsol = x0
x0 = x0.asmatrix()
else:
opsol = results.op_solution(x=x0,
error=numpy.matrix(
numpy.zeros((mna.shape[0], 1))),
circ=circ,
outfile=None)
printing.print_info_line(
("Using the supplied op as x(t=%g)." % (tstart, ), 5), verbose)
if verbose > 4:
print "x0:"
opsol.print_short()
# setup the df method
printing.print_info_line(
("Selecting the appropriate DF (" + method + ")... ", 5),
verbose,
print_nl=False)
if method == IMPLICIT_EULER:
import implicit_euler as df
elif method == TRAP:
import trap as df
elif method == GEAR1:
import gear as df
df.order = 1
elif method == GEAR2:
import gear as df
df.order = 2
elif method == GEAR3:
import gear as df
df.order = 3
elif method == GEAR4:
import gear as df
df.order = 4
elif method == GEAR5:
import gear as df
df.order = 5
elif method == GEAR6:
import gear as df
df.order = 6
else:
df = import_custom_df_module(method,
print_out=(data_filename != "stdout"))
# df is none if module is not found
if df is None:
sys.exit(23)
if not df.has_ff() and use_step_control:
printing.print_warning(
"The chosen DF does not support step control. Turning off the feature."
)
use_step_control = False
#use_aposteriori_step_control = False
printing.print_info_line(("done.", 5), verbose)
# setup the data buffer
# if you use the step control, the buffer has to be one point longer.
# That's because the excess point is used by a FF in the df module to predict the next value.
printing.print_info_line(("Setting up the buffer... ", 5),
verbose,
print_nl=False)
((max_x, max_dx), (pmax_x, pmax_dx)) = df.get_required_values()
if max_x is None and max_dx is None:
printing.print_general_error("df doesn't need any value?")
sys.exit(1)
if use_step_control:
thebuffer = dfbuffer(length=max(max_x, max_dx, pmax_x, pmax_dx) + 1,
width=3)
else:
thebuffer = dfbuffer(length=max(max_x, max_dx) + 1, width=3)
thebuffer.add((tstart, x0, None)) #setup the first values
printing.print_info_line(("done.", 5), verbose) #FIXME
#setup the output buffer
if return_req_dict:
output_buffer = dfbuffer(length=return_req_dict["points"], width=1)
output_buffer.add((x0, ))
else:
output_buffer = None
# import implicit_euler to be used in the first iterations
# this is because we don't have any dx when we start, nor any past point value
if (max_x is not None and max_x > 0) or max_dx is not None:
import implicit_euler
printing.print_info_line(("MNA (reduced):", 5), verbose)
printing.print_info_line((str(mna), 5), verbose)
printing.print_info_line(("D (reduced):", 5), verbose)
printing.print_info_line((str(D), 5), verbose)
# setup the initial values to start the iteration:
x = None
time = tstart
nv = len(circ.nodes_dict)
Gmin_matrix = dc_analysis.build_gmin_matrix(circ, options.gmin,
mna.shape[0], verbose)
# lo step viene generato automaticamente, ma non superare mai quello fornito.
if use_step_control:
#tstep = min((tstop-tstart)/9999.0, HMAX, 100.0 * options.hmin)
tstep = min((tstop - tstart) / 9999.0, HMAX)
printing.print_info_line(("Initial step: %g" % (tstep, ), 5), verbose)
if max_dx is None:
max_dx_plus_1 = None
else:
max_dx_plus_1 = max_dx + 1
if pmax_dx is None:
pmax_dx_plus_1 = None
else:
pmax_dx_plus_1 = pmax_dx + 1
# setup error vectors
aerror = numpy.mat(numpy.zeros((x0.shape[0], 1)))
aerror[:nv - 1, 0] = options.vea
aerror[nv - 1:, 0] = options.vea
rerror = numpy.mat(numpy.zeros((x0.shape[0], 1)))
rerror[:nv - 1, 0] = options.ver
rerror[nv - 1:, 0] = options.ier
iter_n = 0 # contatore d'iterazione
lte = None
sol = results.tran_solution(circ,
tstart,
tstop,
op=x0,
method=method,
outfile=data_filename)
printing.print_info_line(("Solving... ", 3), verbose, print_nl=False)
tick = ticker.ticker(increments_for_step=1)
tick.display(verbose > 1)
while time < tstop:
if iter_n < max(max_x, max_dx_plus_1):
x_coeff, const, x_lte_coeff, prediction, pred_lte_coeff = \
implicit_euler.get_df((thebuffer.get_df_vector()[0],), tstep, \
predict=(use_step_control and (iter_n >= max(pmax_x, pmax_dx_plus_1))))
else:
[x_coeff, const, x_lte_coeff, prediction, pred_lte_coeff] = \
df.get_df(thebuffer.get_df_vector(), tstep, predict=use_step_control)
if options.transient_prediction_as_x0 and use_step_control and prediction is not None:
x0 = prediction
elif x is not None:
x0 = x
(x1, error, solved,
n_iter) = dc_analysis.dc_solve(mna=(mna + numpy.multiply(x_coeff, D)),
Ndc=N,
Ntran=D * const,
circ=circ,
Gmin=Gmin_matrix,
x0=x0,
time=(time + tstep),
locked_nodes=locked_nodes,
MAXIT=options.transient_max_nr_iter,
verbose=0)
if solved:
old_step = tstep #we will modify it, if we're using step control otherwise it's the same
# step control (yeah)
if use_step_control:
if x_lte_coeff is not None and pred_lte_coeff is not None and prediction is not None:
# this is the Local Truncation Error :)
lte = abs((x_lte_coeff / (pred_lte_coeff - x_lte_coeff)) *
(prediction - x1))
# it should NEVER happen that new_step > 2*tstep, for stability
new_step_coeff = 2
for index in xrange(x.shape[0]):
if lte[index, 0] != 0:
new_value = ((aerror[index, 0] + rerror[index, 0]*abs(x[index, 0])) / lte[index, 0]) \
** (1.0 / (df.order+1))
if new_value < new_step_coeff:
new_step_coeff = new_value
#print new_value
new_step = tstep * new_step_coeff
if options.transient_use_aposteriori_step_control and new_step < options.transient_aposteriori_step_threshold * tstep:
#don't recalculate a x for a small change
tstep = check_step(new_step, time, tstop, HMAX)
#print "Apost. (reducing) step = "+str(tstep)
continue
tstep = check_step(new_step, time, tstop,
HMAX) # used in the next iteration
#print "Apriori tstep = "+str(tstep)
else:
#print "LTE not calculated."
lte = None
if print_step_and_lte and lte is not None:
#if you wish to look at the step. We print just a lte
flte.write(
str(time) + "\t" + str(old_step) + "\t" + str(lte.max()) +
"\n")
# if we get here, either aposteriori_step_control is
# disabled, or it's enabled and the error is small
# enough. Anyway, the result is GOOD, STORE IT.
time = time + old_step
x = x1
iter_n = iter_n + 1
sol.add_line(time, x)
dxdt = numpy.multiply(x_coeff, x) + const
thebuffer.add((time, x, dxdt))
if output_buffer is not None:
output_buffer.add((x, ))
tick.step(verbose > 1)
else:
# If we get here, Newton failed to converge. We need to reduce the step...
if use_step_control:
tstep = tstep / 5.0
tstep = check_step(tstep, time, tstop, HMAX)
printing.print_info_line(
("At %g s reducing step: %g s (convergence failed)" %
(time, tstep), 5), verbose)
else: #we can't reduce the step
printing.print_general_error("Can't converge with step " +
str(tstep) + ".")
printing.print_general_error(
"Try setting --t-max-nr to a higher value or set step to a lower one."
)
solved = False
break
if options.transient_max_time_iter and iter_n == options.transient_max_time_iter:
printing.print_general_error("MAX_TIME_ITER exceeded (" +
str(options.transient_max_time_iter) +
"), iteration halted.")
solved = False
break
if print_step_and_lte:
flte.close()
tick.hide(verbose > 1)
if solved:
printing.print_info_line(("done.", 3), verbose)
printing.print_info_line(
("Average time step: %g" % ((tstop - tstart) / iter_n, ), 3),
verbose)
if output_buffer:
ret_value = output_buffer.get_as_matrix()
else:
ret_value = sol
else:
print "failed."
ret_value = None
return ret_value
def shooting(circ, period, step=None, x0=None, points=None, autonomous=False,
mna=None, Tf=None, D=None, outfile='stdout', vector_norm=lambda v: max(abs(v)), verbose=3):
"""Performs a periodic steady state analysis based on the algorithm described in
Brambilla, A.; D'Amore, D., "Method for steady-state simulation of
strongly nonlinear circuits in the time domain," Circuits and
Systems I: Fundamental Theory and Applications, IEEE Transactions on,
vol.48, no.7, pp.885-889, Jul 2001
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=933329&isnumber=20194
The results have been computed again by me, the formulas are not exactly the
same, but the idea behind the shooting algorithm is.
This method allows us to have a period with many points without having to
invert a huge matrix (and being limited to the maximum matrix size).
A tran is performed to initialize the solver.
We compute the change in the last point, calculating several matrices in
the process.
From that, with the same matrices we calculate the changes in all points,
starting from 0 (which is the same as the last one), then 1, ...
Key points:
- Only not autonomous circuits are supported.
- The time step is constant
- Implicit euler is used as DF
Parameters:
circ is the circuit description class
period is the period of the solution
mna, D, Tf are not compulsory they will be computed if they're set to None
step is the time step between consecutive points
points is the number of points to be used
step and points are mutually exclusive options:
- if step is specified, the number of points will be automatically determined
- if points is set, the step will be automatically determined
- if none of them is set, options.shooting_default_points will be used as points
autonomous has to be False, autonomous circuits are not supported
outfile is the output filename. Defaults to stdout.
verbose is set to zero (print errors only) if datafilename == 'stdout'.
Returns: nothing
"""
if outfile == "stdout":
verbose = 0
printing.print_info_line(
("Starting periodic steady state analysis:", 3), verbose)
printing.print_info_line(("Method: shooting", 3), verbose)
if isinstance(x0, results.op_solution):
x0 = x0.asmatrix()
if mna is None or Tf is None:
(mna, Tf) = dc_analysis.generate_mna_and_N(circ, verbose=verbose)
mna = utilities.remove_row_and_col(mna)
Tf = utilities.remove_row(Tf, rrow=0)
elif not mna.shape[0] == Tf.shape[0]:
printing.print_general_error(
"mna matrix and N vector have different number of rows.")
sys.exit(0)
if D is None:
D = transient.generate_D(circ, [mna.shape[0], mna.shape[0]])
D = utilities.remove_row_and_col(D)
elif not mna.shape == D.shape:
printing.print_general_error(
"mna matrix and D matrix have different sizes.")
sys.exit(0)
(points, step) = check_step_and_points(step, points, period)
print "points", points
print "step", step
n_of_var = mna.shape[0]
locked_nodes = circ.get_locked_nodes()
printing.print_info_line(
("Starting transient analysis for algorithm init: tstop=%g, tstep=%g... " % (10 * points * step, step), 3), verbose, print_nl=False)
xtran = transient.transient_analysis(
circ=circ, tstart=0, tstep=step, tstop=10 * points * step, method="TRAP", x0=None, mna=mna, N=Tf,
D=D, use_step_control=False, outfile=outfile + ".tran", return_req_dict={"points": points}, verbose=0)
if xtran is None:
print "failed."
return None
printing.print_info_line(("done.", 3), verbose)
x = []
for index in range(points):
x.append(xtran[index * n_of_var:(index + 1) * n_of_var, 0])
tick = ticker.ticker(increments_for_step=1)
MAass_static, MBass = build_static_MAass_and_MBass(mna, D, step)
# This contains
# the time invariant part, Tf
# time variable component: Tt this is always the same, since the time interval is the same
# this holds all time-dependent sources (both V/I).
Tass_static_vector = build_Tass_static_vector(
circ, Tf, points, step, tick, n_of_var, verbose)
converged = False
printing.print_info_line(("Solving... ", 3), verbose, print_nl=False)
tick.reset()
tick.display(verbose > 2)
iteration = 0 # newton iteration counter
conv_counter = 0
while True:
dx = []
Tass_variable_vector = []
MAass_variable_vector = []
for index in range(points):
if index == 0:
xn_minus_1 = x[points - 1]
else:
xn_minus_1 = x[index - 1]
MAass_variable, Tass_variable = get_variable_MAass_and_Tass(
circ, x[index], xn_minus_1, mna, D, step, n_of_var)
MAass_variable_vector.append(MAass_variable + MAass_static)
Tass_variable_vector.append(
Tass_variable + Tass_static_vector[index])
dxN = compute_dxN(circ, MAass_variable_vector, MBass,
Tass_variable_vector, n_of_var, points, verbose=verbose)
td = dc_analysis.get_td(dxN, locked_nodes, n=-1)
x[points - 1] = td * dxN + x[points - 1]
for index in range(points - 1):
if index == 0:
dxi_minus_1 = dxN
else:
dxi_minus_1 = dx[index - 1]
dx.append(
compute_dx(MAass_variable_vector[index], MBass, Tass_variable_vector[index], dxi_minus_1))
td = dc_analysis.get_td(dx[index], locked_nodes, n=-1)
x[index] = td * dx[index] + x[index]
dx.append(dxN)
if (vector_norm_wrapper(dx, vector_norm) < min(options.ver, options.ier) * vector_norm_wrapper(x, vector_norm) + min(options.vea, options.iea)): # \
# and (dc_analysis.vector_norm(residuo) <
# options.er*dc_analysis.vector_norm(x) + options.ea):
if conv_counter == 3:
converged = True
break
else:
conv_counter = conv_counter + 1
elif vector_norm(dx[points - 1]) is numpy.nan: # needs work fixme
raise OverflowError
# break
else:
conv_counter = 0
tick.step(verbose > 2)
if options.shooting_max_nr_iter and iteration == options.shooting_max_nr_iter:
printing.print_general_error(
"Hitted SHOOTING_MAX_NR_ITER (" + str(options.shooting_max_nr_iter) + "), iteration halted.")
converged = False
break
else:
iteration = iteration + 1
tick.hide(verbose > 2)
if converged:
printing.print_info_line(("done.", 3), verbose)
t = numpy.mat(numpy.arange(points) * step)
t = t.reshape((1, points))
xmat = x[0]
for index in xrange(1, points):
xmat = numpy.concatenate((xmat, x[index]), axis=1)
sol = results.pss_solution(
circ=circ, method="shooting", period=period, outfile=outfile, t_array=t, x_array=xmat)
# print_results(circ, x, fdata, points, step)
else:
print "failed."
sol = None
return sol
def ac_analysis(circ, start, nsteps, stop, step_type, xop=None, mna=None,\
AC=None, Nac=None, J=None, data_filename="stdout", verbose=3):
"""Performs an AC analysis of the circuit (described by circ).
"""
if data_filename == 'stdout':
verbose = 0
#check step/start/stop parameters
if start == 0:
printing.print_general_error("AC analysis has start frequency = 0")
sys.exit(5)
if start > stop:
printing.print_general_error("AC analysis has start > stop")
sys.exit(1)
if nsteps < 1:
printing.print_general_error("AC analysis has number of steps <= 1")
sys.exit(1)
if step_type == options.ac_log_step:
omega_iter = utilities.log_axis_iterator(stop, start, nsteps)
elif step_type == options.ac_lin_step:
omega_iter = utilities.lin_axis_iterator(stop, start, nsteps)
else:
printing.print_general_error("Unknown sweep type.")
sys.exit(1)
tmpstr = "Vea =", options.vea, "Ver =", options.ver, "Iea =", options.iea, "Ier =", \
options.ier, "max_ac_nr_iter =", options.ac_max_nr_iter
printing.print_info_line((tmpstr, 5), verbose)
del tmpstr
printing.print_info_line(("Starting AC analysis: ", 1), verbose)
tmpstr = "w: start = %g Hz, stop = %g Hz, %d steps" % (start, stop, nsteps)
printing.print_info_line((tmpstr, 3), verbose)
del tmpstr
#It's a good idea to call AC with prebuilt MNA matrix if the circuit is big
if mna is None:
(mna, N) = dc_analysis.generate_mna_and_N(circ)
del N
mna = utilities.remove_row_and_col(mna)
if Nac is None:
Nac = generate_Nac(circ)
Nac = utilities.remove_row(Nac, rrow=0)
if AC is None:
AC = generate_AC(circ, [mna.shape[0], mna.shape[0]])
AC = utilities.remove_row_and_col(AC)
if circ.is_nonlinear():
if J is not None:
pass
# we used the supplied linearization matrix
else:
if xop is None:
printing.print_info_line(("Starting OP analysis to get a linearization point...", 3), verbose, print_nl=False)
#silent OP
xop = dc_analysis.op_analysis(circ, verbose=0)
if xop is None: #still! Then op_analysis has failed!
printing.print_info_line(("failed.", 3), verbose)
printing.print_general_error("OP analysis failed, no linearization point available. Quitting.")
sys.exit(3)
else:
printing.print_info_line(("done.", 3), verbose)
printing.print_info_line(("Linearization point (xop):", 5), verbose)
if verbose > 4: xop.print_short()
printing.print_info_line(("Linearizing the circuit...", 5), verbose, print_nl=False)
J = generate_J(xop=xop.asmatrix(), circ=circ, mna=mna, Nac=Nac, data_filename=data_filename, verbose=verbose)
printing.print_info_line((" done.", 5), verbose)
# we have J, continue
else: #not circ.is_nonlinear()
# no J matrix is required.
J = 0
printing.print_info_line(("MNA (reduced):", 5), verbose)
printing.print_info_line((str(mna), 5), verbose)
printing.print_info_line(("AC (reduced):", 5), verbose)
printing.print_info_line((str(AC), 5), verbose)
printing.print_info_line(("J (reduced):", 5), verbose)
printing.print_info_line((str(J), 5), verbose)
printing.print_info_line(("Nac (reduced):", 5), verbose)
printing.print_info_line((str(Nac), 5), verbose)
sol = results.ac_solution(circ, ostart=start, ostop=stop, opoints=nsteps, stype=step_type, op=xop, outfile=data_filename)
# setup the initial values to start the iteration:
nv = len(circ.nodes_dict)
j = numpy.complex('j')
Gmin_matrix = dc_analysis.build_gmin_matrix(circ, options.gmin, mna.shape[0], verbose)
iter_n = 0 # contatore d'iterazione
#printing.print_results_header(circ, fdata, print_int_nodes=options.print_int_nodes, print_omega=True)
printing.print_info_line(("Solving... ", 3), verbose, print_nl=False)
tick = ticker.ticker(increments_for_step=1)
tick.display(verbose > 1)
x = xop
for omega in omega_iter:
(x, error, solved, n_iter) = dc_analysis.dc_solve(mna=(mna + numpy.multiply(j*omega, AC) + J), \
Ndc=Nac, Ntran=0, circ=circuit.circuit(title="Dummy circuit for AC", filename=None), Gmin=Gmin_matrix, x0=x, \
time=None, locked_nodes=None, MAXIT=options.ac_max_nr_iter, skip_Tt=True, verbose=0)
if solved:
tick.step(verbose > 1)
iter_n = iter_n + 1
# hooray!
sol.add_line(omega, x)
else:
break
tick.hide(verbose > 1)
if solved:
printing.print_info_line(("done.", 1), verbose)
ret_value = sol
else:
printing.print_info_line(("failed.", 1), verbose)
ret_value = None
return ret_value
def shooting(circ,
period,
step=None,
mna=None,
Tf=None,
D=None,
points=None,
autonomous=False,
data_filename='stdout',
vector_norm=lambda v: max(abs(v)),
verbose=3):
"""Performs a periodic steady state analysis based on the algorithm described in
Brambilla, A.; D'Amore, D., "Method for steady-state simulation of
strongly nonlinear circuits in the time domain," Circuits and
Systems I: Fundamental Theory and Applications, IEEE Transactions on,
vol.48, no.7, pp.885-889, Jul 2001
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=933329&isnumber=20194
The results have been computed again by me, the formulas are not exactly the
same, but the idea behind the shooting algorithm is.
This method allows us to have a period with many points without having to
invert a huge matrix (and being limited to the maximum matrix size).
A tran is performed to initialize the solver.
We compute the change in the last point, calculating several matrices in
the process.
From that, with the same matrices we calculate the changes in all points,
starting from 0 (which is the same as the last one), then 1, ...
Key points:
- Only not autonomous circuits are supported.
- The time step is constant
- Implicit euler is used as DF
Parameters:
circ is the circuit description class
period is the period of the solution
mna, D, Tf are not compulsory they will be computed if they're set to None
step is the time step between consecutive points
points is the number of points to be used
step and points are mutually exclusive options:
- if step is specified, the number of points will be automatically determined
- if points is set, the step will be automatically determined
- if none of them is set, options.shooting_default_points will be used as points
autonomous has to be False, autonomous circuits are not supported
data_filename is the output filename. Defaults to stdout.
verbose is set to zero (print errors only) if datafilename == 'stdout'.
Returns: nothing
"""
if data_filename == "stdout":
verbose = 0
printing.print_info_line(("Starting periodic steady state analysis:", 3),
verbose)
printing.print_info_line(("Method: shooting", 3), verbose)
if mna is None or Tf is None:
(mna, Tf) = dc_analysis.generate_mna_and_N(circ)
mna = utilities.remove_row_and_col(mna)
Tf = utilities.remove_row(Tf, rrow=0)
elif not mna.shape[0] == Tf.shape[0]:
printing.print_general_error(
"mna matrix and N vector have different number of rows.")
sys.exit(0)
if D is None:
D = transient.generate_D(circ, [mna.shape[0], mna.shape[0]])
D = utilities.remove_row_and_col(D)
elif not mna.shape == D.shape:
printing.print_general_error(
"mna matrix and D matrix have different sizes.")
sys.exit(0)
(points, step) = check_step_and_points(step, points, period)
print "points", points
print "step", step
n_of_var = mna.shape[0]
locked_nodes = circ.get_locked_nodes()
printing.print_info_line((
"Starting transient analysis for algorithm init: tstop=%g, tstep=%g... "
% (10 * points * step, step), 3),
verbose,
print_nl=False)
xtran = transient.transient_analysis(circ=circ, tstart=0, tstep=step, tstop=10*points*step, method="TRAP", x0=None, mna=mna, N=Tf, \
D=D, use_step_control=False, data_filename=data_filename+".tran", return_req_dict={"points":points}, verbose=0)
if xtran is None:
print "failed."
return None
printing.print_info_line(("done.", 3), verbose)
x = []
for index in range(points):
x.append(xtran[index * n_of_var:(index + 1) * n_of_var, 0])
tick = ticker.ticker(increments_for_step=1)
MAass_static, MBass = build_static_MAass_and_MBass(mna, D, step)
# This contains
# the time invariant part, Tf
# time variable component: Tt this is always the same, since the time interval is the same
# this holds all time-dependent sources (both V/I).
Tass_static_vector = build_Tass_static_vector(circ, Tf, points, step, tick,
n_of_var, verbose)
converged = False
printing.print_info_line(("Solving... ", 3), verbose, print_nl=False)
tick.reset()
tick.display(verbose > 2)
iteration = 0 # newton iteration counter
conv_counter = 0
while True:
dx = []
Tass_variable_vector = []
MAass_variable_vector = []
for index in range(points):
if index == 0:
xn_minus_1 = x[points - 1]
else:
xn_minus_1 = x[index - 1]
MAass_variable, Tass_variable = get_variable_MAass_and_Tass(
circ, x[index], xn_minus_1, mna, D, step, n_of_var)
MAass_variable_vector.append(MAass_variable + MAass_static)
Tass_variable_vector.append(Tass_variable +
Tass_static_vector[index])
dxN = compute_dxN(circ,
MAass_variable_vector,
MBass,
Tass_variable_vector,
n_of_var,
points,
verbose=verbose)
td = dc_analysis.get_td(dxN, locked_nodes, n=-1)
x[points - 1] = td * dxN + x[points - 1]
for index in range(points - 1):
if index == 0:
dxi_minus_1 = dxN
else:
dxi_minus_1 = dx[index - 1]
dx.append(
compute_dx(MAass_variable_vector[index], MBass,
Tass_variable_vector[index], dxi_minus_1))
td = dc_analysis.get_td(dx[index], locked_nodes, n=-1)
x[index] = td * dx[index] + x[index]
dx.append(dxN)
if (vector_norm_wrapper(dx, vector_norm) <
min(options.ver, options.ier) * vector_norm_wrapper(
x, vector_norm) + min(options.vea, options.iea)): #\
#and (dc_analysis.vector_norm(residuo) < options.er*dc_analysis.vector_norm(x) + options.ea):
if conv_counter == 3:
converged = True
break
else:
conv_counter = conv_counter + 1
elif vector_norm(dx[points - 1]) is numpy.nan: #needs work fixme
raise OverflowError
#break
else:
conv_counter = 0
tick.step(verbose > 2)
if options.shooting_max_nr_iter and iteration == options.shooting_max_nr_iter:
printing.print_general_error("Hitted SHOOTING_MAX_NR_ITER (" +
str(options.shooting_max_nr_iter) +
"), iteration halted.")
converged = False
break
else:
iteration = iteration + 1
tick.hide(verbose > 2)
if converged:
printing.print_info_line(("done.", 3), verbose)
t = numpy.mat(numpy.arange(points) * step)
t = t.reshape((1, points))
xmat = x[0]
for index in xrange(1, points):
xmat = numpy.concatenate((xmat, x[index]), axis=1)
sol = results.pss_solution(circ=circ,
method="shooting",
period=period,
outfile=data_filename,
t_array=t,
x_array=xmat)
#print_results(circ, x, fdata, points, step)
else:
print "failed."
sol = None
return sol
def bfpss(circ,
period,
step=None,
points=None,
autonomous=False,
x0=None,
mna=None,
Tf=None,
D=None,
outfile='stdout',
vector_norm=lambda v: max(abs(v)),
verbose=3):
"""Performs a PSS analysis.
Time step is constant, IE will be used as DF
Parameters:
circ is the circuit description class
period is the period of the solution
mna, D, Tf are not compulsory they will be computed if they're set to None
step is the time step between consecutive points
points is the number of points to be used
step and points are mutually exclusive options:
- if step is specified, the number of points will be automatically determined
- if points is set, the step will be automatically determined
- if none of them is set, options.shooting_default_points will be used as points
autonomous has to be False, autonomous circuits are not supported
x0 is the initial guess to be used. Needs work.
outfile is the output filename. Defaults to stdout.
verbose is set to zero (print errors only) if datafilename == 'stdout'.
Returns: nothing
"""
if outfile == "stdout":
verbose = 0
printing.print_info_line(("Starting periodic steady state analysis:", 3),
verbose)
printing.print_info_line(("Method: brute-force", 3), verbose)
if mna is None or Tf is None:
(mna, Tf) = dc_analysis.generate_mna_and_N(circ, verbose=verbose)
mna = utilities.remove_row_and_col(mna)
Tf = utilities.remove_row(Tf, rrow=0)
elif not mna.shape[0] == Tf.shape[0]:
printing.print_general_error(
"mna matrix and N vector have different number of rows.")
sys.exit(0)
if D is None:
D = transient.generate_D(circ, [mna.shape[0], mna.shape[0]])
D = utilities.remove_row_and_col(D)
elif not mna.shape == D.shape:
printing.print_general_error(
"mna matrix and D matrix have different sizes.")
sys.exit(0)
(points, step) = check_step_and_points(step, points, period)
n_of_var = mna.shape[0]
locked_nodes = circ.get_locked_nodes()
tick = ticker.ticker(increments_for_step=1)
CMAT = build_CMAT(mna,
D,
step,
points,
tick,
n_of_var=n_of_var,
verbose=verbose)
x = build_x(mna,
step,
points,
tick,
x0=x0,
n_of_var=n_of_var,
verbose=verbose)
Tf = build_Tf(Tf, points, tick, n_of_var=n_of_var, verbose=verbose)
# time variable component: Tt this is always the same in each iter. So we build it once for all
# this holds all time-dependent sources (both V/I).
Tt = build_Tt(circ, points, step, tick, n_of_var=n_of_var, verbose=verbose)
# Indices to differentiate between currents and voltages in the
# convergence check
nv_indices = []
ni_indices = []
nv_1 = len(circ.nodes_dict) - 1
ni = n_of_var - nv_1
for i in range(points):
nv_indices += (i * mna.shape[0] * numpy.ones(nv_1) + \
numpy.arange(nv_1)).tolist()
ni_indices += (i * mna.shape[0] * numpy.ones(ni) + \
numpy.arange(nv_1, n_of_var)).tolist()
converged = False
printing.print_info_line(("Solving... ", 3), verbose, print_nl=False)
tick.reset()
tick.display(verbose > 2)
J = numpy.mat(numpy.zeros(CMAT.shape))
T = numpy.mat(numpy.zeros((CMAT.shape[0], 1)))
# td is a numpy matrix that will hold the damping factors
td = numpy.mat(numpy.zeros((points, 1)))
iteration = 0 # newton iteration counter
while True:
if iteration: # the first time are already all zeros
J[:, :] = 0
T[:, 0] = 0
td[:, 0] = 0
for index in xrange(1, points):
for elem in circ:
# build all dT(xn)/dxn (stored in J) and T(x)
if elem.is_nonlinear:
oports = elem.get_output_ports()
for opindex in range(len(oports)):
dports = elem.get_drive_ports(opindex)
v_ports = []
for dpindex in range(len(dports)):
dn1, dn2 = dports[dpindex]
v = 0 # build v: remember we trashed the 0 row and 0 col of mna -> -1
if dn1:
v = v + x[index * n_of_var + dn1 - 1, 0]
if dn2:
v = v - x[index * n_of_var + dn2 - 1, 0]
v_ports.append(v)
# all drive ports are ready.
n1, n2 = oports[opindex][0], oports[opindex][1]
if n1:
T[index * n_of_var + n1 - 1, 0] = T[index * n_of_var + n1 - 1, 0] + \
elem.i(opindex, v_ports)
if n2:
T[index * n_of_var + n2 - 1, 0] = T[index * n_of_var + n2 - 1, 0] - \
elem.i(opindex, v_ports)
for dpindex in range(len(dports)):
dn1, dn2 = dports[dpindex]
if n1:
if dn1:
J[index * n_of_var + n1 - 1, index * n_of_var + dn1 - 1] = \
J[index * n_of_var + n1 - 1, index * n_of_var + dn1 - 1] + \
elem.g(opindex, v_ports, dpindex)
if dn2:
J[index * n_of_var + n1 - 1, index * n_of_var + dn2 - 1] =\
J[index * n_of_var + n1 - 1, index * n_of_var + dn2 - 1] - 1.0 * \
elem.g(opindex, v_ports, dpindex)
if n2:
if dn1:
J[index * n_of_var + n2 - 1, index * n_of_var + dn1 - 1] = \
J[index * n_of_var + n2 - 1, index * n_of_var + dn1 - 1] - 1.0 * \
elem.g(opindex, v_ports, dpindex)
if dn2:
J[index * n_of_var + n2 - 1, index * n_of_var + dn2 - 1] =\
J[index * n_of_var + n2 - 1, index * n_of_var + dn2 - 1] + \
elem.g(opindex, v_ports, dpindex)
J = J + CMAT
residuo = CMAT * x + T + Tf + Tt
dx = -1 * (numpy.linalg.inv(J) * residuo)
# td
for index in xrange(points):
td[index, 0] = dc_analysis.get_td(dx[index * n_of_var:(index + 1) *
n_of_var, 0],
locked_nodes,
n=-1)
x = x + min(abs(td))[0, 0] * dx
# convergence check
converged = convergence_check(dx, x, nv_indices, ni_indices,
vector_norm)
if converged:
break
tick.step(verbose > 2)
if options.shooting_max_nr_iter and iteration == options.shooting_max_nr_iter:
printing.print_general_error("Hitted SHOOTING_MAX_NR_ITER (" +
str(options.shooting_max_nr_iter) +
"), iteration halted.")
converged = False
break
else:
iteration = iteration + 1
tick.hide(verbose > 2)
if converged:
printing.print_info_line(("done.", 3), verbose)
t = numpy.mat(numpy.arange(points) * step)
t = t.reshape((1, points))
x = x.reshape((points, n_of_var))
sol = results.pss_solution(circ=circ,
method="brute-force",
period=period,
outfile=outfile,
t_array=t,
x_array=x.T)
else:
print "failed."
sol = None
return sol
