def butter_filter(freq, fs=RATE, order=5): nyq = 0.5 * fs low = freq / nyq b, a = butter(order, low, 'lowpass') for i in streamData: i = np.asArray(i) i = lfilter(b, a, i) i = np.tolist(i)
def convert_NP_to_LIST(self, np) -> list:
"""
numpy의 array 형식의 데이터를 list로 변환
:return:
list 자료형의 값
"""
list = np.tolist()
return list
def concDisOxySaturated(pressure_mmHg, Temperature_degC):
# Calibration Table
# 160910
# http://www.vernier.com/files/manuals/odo-bta/odo-bta.pdf
# 100% SATURATED VALUES
x_pressmmHg = [770., 760., 750., 740.] # PRESSURE mmHg
x_pressmmHg = np.array(x_pressmmHg)
y_degC = [
0., 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 14., 16., 18.,
20., 22., 24., 26., 28., 30., 32., 34.
] # TEMPERATURE degC
y_degC = np.array(y_degC)
z_mgPerL = [ # 770 , 760 , 750 ,740
[14.76, 14.57, 14.38, 14.19], # 0 degC
[14.38, 14.19, 14, 13.82], # 1
[14.01, 13.82, 13.64, 13.46], # 2
[13.65, 13.47, 13.29, 13.12], # 3
[13.31, 13.13, 12.96, 12.79], # 4
[12.97, 12.81, 12.64, 12.47], # 5
[12.66, 12.49, 12.33, 12.16], # 6
[12.35, 12.19, 12.03, 11.87], # 7
[12.05, 11.90, 11.74, 11.58], # 8
[11.77, 11.62, 11.46, 11.31], #9
[11.50, 11.35, 11.20, 11.05], #10
[11.24, 11.09, 10.94, 10.80], #11
[10.98, 10.84, 10.70, 10.56], #12
[10.51, 10.37, 10.24, 10.10], #14
[10.07, 9.94, 9.81, 9.68], #16
[9.67, 9.54, 9.41, 9.29], #18
[9.29, 9.17, 9.05, 8.93], #20
[8.94, 8.83, 8.71, 8.59], #22
[8.62, 8.51, 8.40, 8.28], #24
[8.32, 8.21, 8.10, 7.99], #26
[8.04, 7.93, 7.83, 7.72], #28
[7.77, 7.67, 7.57, 7.47], #30
[7.51, 7.42, 7.32, 7.22], #32
[7.27, 7.17, 7.08, 6.98], #34
]
z_mgPerL = np.array(z_mgPerL)
# scipy.interpolate.interp2d
# http://docs.scipy.org/doc/scipy-0.13.0/reference/generated/scipy.interpolate.interp2d.html
#
# Define function to call
_concDisOxySaturated = interpolate.interp2d(x_pressmmHg,
y_degC,
z_mgPerL,
kind='linear')
x = _concDisOxySaturated(pressure_mmHg, Temperature_degC)
return np.tolist()
def convert_NP_to_LIST(self, np, dtype=None):
"""
numpy의 array 형식의 데이터를 list로 변환
:param np:
:param dtype:
:return:
list 자료형의 값
"""
list = np.tolist()
return list
def np_to_list(self, np, dtype=None):
list = np.tolist()
return list
#Support multidimensional arrays and matrices.
#It also support wide range of mathematical operations.
#Numpy
import numpy as np
ndarray - an N-dimensional array, which describes a collection of “items” of the same type
array(list) # constructor
asarray(a[, dtype, order]) # Convert the input to an array
Constants:
ndarray.shape #tuple of array dimensions
ndarray.size #number of elements in array
ndarray.itemsize #size of one element
ndarray.dtype #data type of elements
ndarray.flat #1D iterator over elements of array
Common Functions
np.tolist() #Return the array as a (possibly nested) list.
np.reshape(a, (3,2)) #Returns an array containing the same data with a new shape.
np.swapaxes(axis1, axis2) #Return a view of the array with axis1 and axis2 interchanged.
np.copy() #Return a copy of the array.
np.arange() #Return evenly spaced values within a given interval.
Statistics Functions:
np.sum(a, axis) #Sum of array elements over a given axis.
np.prod #Return the product of array elements over a given axis.
np.min #Return the minimum along a given axis.
np.max #Return the maximum along a given axis.
np.mean #Compute the arithmetic mean along the specified axis.
np.std #Compute the standard deviation along the specified axis.
np.var #Compute the variance along the specified axis.
np.sort(axis) #Return a sorted copy of an array.
Other Functions:
String operations #A set of vectorized string operations for arrays.
def array2param(array,ptype):
if ptype == 'list':
return np.tolist(array)
if ptype == 'scalar':
return array[0]
def heat_eq_ui():
"""
Solve heat equation with arguments (all are optional) from the commands
line; Type of solver, constants, initial dist. from file, animation etc.
Run with "-h" for a complete description of available commands.
When using timeit via "-time RUNS ITER" animation and other output
are ignored. User settings i.e. f, m, t0 etc. are used if acceptable.
"""
parser = argparse.ArgumentParser()
parser.add_argument("-time", nargs=2, help="Turn on timeit-module. "+ \
"Run ARG1 tests with ARG2 iterations", type=int)
parser.add_argument("-n",
default=50,
help="The mesh points in X-direction",
type=int)
parser.add_argument("-m",
default=100,
help="The mesh points in Y-direction",
type=int)
parser.add_argument("-t0",
default=0,
help="The start time of computations [sec]",
type=int)
parser.add_argument("-t1",
default=1000,
help="The end time of computations [sec]",
type=int)
parser.add_argument("-dt",
default=0.1,
help="The time step (temporal resolution)",
type=float)
parser.add_argument("-nu",
default=1.0,
help="The thermal diffusivity",
type=float)
parser.add_argument("-f",
default=1.0,
help="The constant heat source term",
type=float)
parser.add_argument("-o",
"-output",
help="Filename (save to disk) of final solution u",
type=str)
parser.add_argument("-i",
"-input",
help="Filename (read from disk) of initial u",
type=str)
parser.add_argument("-s",
"-save",
help='Save plot of last solution: "last_u.png"',
action="store_true")
parser.add_argument("-v",
"-verbose",
help="Increase output verbosity",
action="store_true")
parser.add_argument("-a",
"-anim",
help="Animate solution while computation runs",
action="store_true")
group = parser.add_mutually_exclusive_group(
) # Pick only one solver-method
group.add_argument("-python",
help="Solve problem with pure python objects",
action="store_true")
group.add_argument("-numpy",
help="Solve problem with NumPy",
action="store_true")
group.add_argument("-weave",
help="Solve problem with Weave",
action="store_true")
# Store user options with readable names
args = parser.parse_args()
dt = args.dt
n = args.n
m = args.m
t0 = args.t0
t1 = args.t1
nu = args.nu
f_constant = args.f
verbose = args.v
save_last_fig = args.s
show_animation = args.a
# File handling switches
use_timeit = False if not args.time else True
output_last_u_to_file = False if not args.o else True
change_initial_u = False if not args.i else True
print_progress = True if verbose else False
if use_timeit:
timeit_repeats = args.time[0]
timeit_iter = args.time[1]
# Set method for solver
method = SolverPurePython if args.python else SolverNumpy if args.numpy else SolverWeave if args.weave else None
scheme_name = 'Python' if args.python else 'Numpy' if args.numpy else 'Weave' if args.weave else None
if not method:
if verbose:
print "\nNo method specified. Choosing 'weave' for speed!"
method = SolverWeave
scheme_name = 'Weave'
# Give the user options if dt is unstable/too large
# dt <= dx*dy / (4*nu) (and we have dx=dy=1 for any mesh size, see report)
max_stable_dt = 1.0 / (4 * nu)
if dt > max_stable_dt:
print "\nThe chosen dt (%.2e) is too large, solution might be unstable!" % dt
print "Choose what to do:"
print "- Press enter to use the max. stable dt (%.2e) and continue" % max_stable_dt
print "- Enter 'c' or 'cont' to continue anyway, or"
user_choice = raw_input(
"- Enter 'exit' (or anything else than the above options) to quit\n"
)
if not user_choice:
dt = max_stable_dt
elif user_choice in ['c', 'cont']:
pass
else:
sys.exit(1)
# Check that time parameters makes sense
if t0 >= t1 or t0 < 0:
print "\nStart time must be larger then end time. Also, start time can't be negative"
sys.exit(1)
# Load initial temp. dist. from file if specified.
# Using a human readable text format (little slower than np.save or pickle)
if change_initial_u:
if verbose:
print "\nReading initial temperature distribution u0 from file"
filename = args.i
try:
initial_u = np.loadtxt(filename)
except:
print "File does not exit or is not in txt-format. Exiting..."
sys.exit(1)
if method == SolverPurePython: # Must convert to nested list
initial_u = np.tolist(initial_u)
n_i = initial_u.shape[0]
m_i = initial_u.shape[1]
if n != n_i or m != m_i:
print "\nMesh dimensions of initial u from file (%d,%d) does NOT match" % (
n_i, m_i)
print "user (or default) specified values: (%d,%d)\nExiting..." % (
n, m)
sys.exit(1)
else:
initial_u = None
# If timeit is used and method = PurePython, give the user a warning
if method == SolverPurePython and use_timeit:
timeit_total_iter = timeit_repeats * timeit_iter # Total number of iterations (i.e. runs of solver)
if timeit_total_iter >= 2 and t1 - t0 >= 200:
estimate_time_used = int((t1 - t0) / 1000. * 55)
print "\nWarning: Testing the pure python implementation is really slow. "
if verbose:
print "Rough time estimate per iteration (and total time): %d, (%d) seconds" \
%(estimate_time_used, timeit_total_iter*estimate_time_used)
raw_input('Press enter to continue..')
# Fill the source term f (as a list or array)
if method == SolverPurePython:
f = SourceTermF_LIST(n, m, f_constant)
else: # All other methods use arrays
f = SourceTermF_ARRAY(n, m, f_constant)
# One call to rule them all
if use_timeit:
if verbose:
print "\nWhen running timeit, some user specified settings might"
print "be ignored for consistency and reproducability"
if method == SolverPurePython: # Sorry for long lines of code, but I get indent error otherwise...
setup_timeit = "from heat_equation import SolverPurePython, SourceTermF_LIST; method = SolverPurePython; f = SourceTermF_LIST(%d,%d,%f)" % (
n, m, f_constant)
elif method == SolverNumpy:
setup_timeit = "from heat_equation_numpy import SolverNumpy, SourceTermF_ARRAY; method = SolverNumpy; f = SourceTermF_ARRAY(%d,%d,%f)" % (
n, m, f_constant)
else:
setup_timeit = "from heat_equation_weave import SolverWeave, SourceTermF_ARRAY; method = SolverWeave; f = SourceTermF_ARRAY(%d,%d,%f)" % (
n, m, f_constant)
solver_call = "u = method(f,%f,%f,%d,%d,%d,%d,None,False,False)" % (
nu, dt, n, m, t0, t1)
timeit_results = timeit.Timer(solver_call, setup=setup_timeit).repeat(
timeit_repeats, timeit_iter)
best_time = min(timeit_results) / float(
timeit_iter
) # All noise in data is "positive", so minimum time is most accurate
if verbose:
print "\nTest repeats: %d, each with %d iterations" % (
timeit_repeats, timeit_iter)
print "Settings: f=1,nu=%.1f,dt=%.1f,n=%d,m=%d,t0=%d,t1=%d" % (
nu, dt, n, m, t0, t1)
print "Minimum CPU-time of scheme '%s': %f seconds" % (scheme_name,
best_time)
else:
print "Min. CPU-time: %f sec. (%s)" % (best_time, scheme_name)
else:
u = method(f,nu,dt,n,m,t0,t1,initial_u, \
show_animation=show_animation,print_progress=verbose)
if verbose: # Need to add some spacing for aesthetical purposes
print ""
print u.max()
# Save last u
if output_last_u_to_file:
if verbose:
print "\nSaving final temperature distribution u to file"
filename = args.o
np.savetxt(filename, u) # Works with both nested list and array
if save_last_fig:
if verbose:
print "\nSaving the final temperature plot of u to 'last_u.png'"
plt.ion()
im = plt.imshow(zip(*u),
cmap='gray') # Initiate plotting / animation
plt.title('u(x,y,t=%d)' % (t1)) # Update title time
plt.xlabel('X')
plt.ylabel('Y')
if not show_animation: # Do not add a second colorbar if already added!
plt.colorbar(im)
plt.savefig('last_u.png')
def heat_eq_ui():
"""
Solve heat equation with arguments (all are optional) from the commands
line; Type of solver, constants, initial dist. from file, animation etc.
Run with "-h" for a complete description of available commands.
When using timeit via "-time RUNS ITER" animation and other output
are ignored. User settings i.e. f, m, t0 etc. are used if acceptable.
"""
parser = argparse.ArgumentParser()
parser.add_argument("-time", nargs=2, help="Turn on timeit-module. "+ \
"Run ARG1 tests with ARG2 iterations", type=int)
parser.add_argument("-n", default=50, help="The mesh points in X-direction", type=int)
parser.add_argument("-m", default=100, help="The mesh points in Y-direction", type=int)
parser.add_argument("-t0", default=0, help="The start time of computations [sec]", type=int)
parser.add_argument("-t1", default=1000, help="The end time of computations [sec]", type=int)
parser.add_argument("-dt", default=0.1, help="The time step (temporal resolution)", type=float)
parser.add_argument("-nu", default=1.0, help="The thermal diffusivity", type=float)
parser.add_argument("-f", default=1.0, help="The constant heat source term", type=float)
parser.add_argument("-o", "-output", help="Filename (save to disk) of final solution u", type=str)
parser.add_argument("-i", "-input", help="Filename (read from disk) of initial u" , type=str)
parser.add_argument("-s", "-save", help='Save plot of last solution: "last_u.png"', action="store_true")
parser.add_argument("-v", "-verbose", help="Increase output verbosity", action="store_true")
parser.add_argument("-a", "-anim", help="Animate solution while computation runs", action="store_true")
group = parser.add_mutually_exclusive_group() # Pick only one solver-method
group.add_argument("-python", help="Solve problem with pure python objects", action="store_true")
group.add_argument("-numpy", help="Solve problem with NumPy", action="store_true")
group.add_argument("-weave", help="Solve problem with Weave", action="store_true")
# Store user options with readable names
args = parser.parse_args()
dt = args.dt
n = args.n; m = args.m
t0 = args.t0; t1 = args.t1
nu = args.nu
f_constant = args.f
verbose = args.v
save_last_fig = args.s
show_animation = args.a
# File handling switches
use_timeit = False if not args.time else True
output_last_u_to_file = False if not args.o else True
change_initial_u = False if not args.i else True
print_progress = True if verbose else False
if use_timeit:
timeit_repeats = args.time[0]
timeit_iter = args.time[1]
# Set method for solver
method = SolverPurePython if args.python else SolverNumpy if args.numpy else SolverWeave if args.weave else None
scheme_name = 'Python' if args.python else 'Numpy' if args.numpy else 'Weave' if args.weave else None
if not method:
if verbose:
print "\nNo method specified. Choosing 'weave' for speed!"
method = SolverWeave
scheme_name = 'Weave'
# Give the user options if dt is unstable/too large
# dt <= dx*dy / (4*nu) (and we have dx=dy=1 for any mesh size, see report)
max_stable_dt = 1.0/(4*nu)
if dt > max_stable_dt:
print "\nThe chosen dt (%.2e) is too large, solution might be unstable!" %dt
print "Choose what to do:"
print "- Press enter to use the max. stable dt (%.2e) and continue" %max_stable_dt
print "- Enter 'c' or 'cont' to continue anyway, or"
user_choice = raw_input("- Enter 'exit' (or anything else than the above options) to quit\n")
if not user_choice:
dt = max_stable_dt
elif user_choice in ['c','cont']:
pass
else:
sys.exit(1)
# Check that time parameters makes sense
if t0 >= t1 or t0 < 0:
print "\nStart time must be larger then end time. Also, start time can't be negative"
sys.exit(1)
# Load initial temp. dist. from file if specified.
# Using a human readable text format (little slower than np.save or pickle)
if change_initial_u:
if verbose:
print "\nReading initial temperature distribution u0 from file"
filename = args.i
try:
initial_u = np.loadtxt(filename)
except:
print "File does not exit or is not in txt-format. Exiting..."; sys.exit(1)
if method == SolverPurePython: # Must convert to nested list
initial_u = np.tolist(initial_u)
n_i = initial_u.shape[0]
m_i = initial_u.shape[1]
if n != n_i or m != m_i:
print "\nMesh dimensions of initial u from file (%d,%d) does NOT match" %(n_i,m_i)
print "user (or default) specified values: (%d,%d)\nExiting..." %(n,m)
sys.exit(1)
else:
initial_u = None
# If timeit is used and method = PurePython, give the user a warning
if method == SolverPurePython and use_timeit:
timeit_total_iter = timeit_repeats*timeit_iter # Total number of iterations (i.e. runs of solver)
if timeit_total_iter >= 2 and t1-t0 >= 200:
estimate_time_used = int((t1-t0)/1000. * 55)
print "\nWarning: Testing the pure python implementation is really slow. "
if verbose:
print "Rough time estimate per iteration (and total time): %d, (%d) seconds" \
%(estimate_time_used, timeit_total_iter*estimate_time_used)
raw_input('Press enter to continue..')
# Fill the source term f (as a list or array)
if method == SolverPurePython:
f = SourceTermF_LIST(n,m,f_constant)
else: # All other methods use arrays
f = SourceTermF_ARRAY(n,m,f_constant)
# One call to rule them all
if use_timeit:
if verbose:
print "\nWhen running timeit, some user specified settings might"
print "be ignored for consistency and reproducability"
if method == SolverPurePython: # Sorry for long lines of code, but I get indent error otherwise...
setup_timeit = "from heat_equation import SolverPurePython, SourceTermF_LIST; method = SolverPurePython; f = SourceTermF_LIST(%d,%d,%f)" %(n,m,f_constant)
elif method == SolverNumpy:
setup_timeit = "from heat_equation_numpy import SolverNumpy, SourceTermF_ARRAY; method = SolverNumpy; f = SourceTermF_ARRAY(%d,%d,%f)" %(n,m,f_constant)
else:
setup_timeit = "from heat_equation_weave import SolverWeave, SourceTermF_ARRAY; method = SolverWeave; f = SourceTermF_ARRAY(%d,%d,%f)" %(n,m,f_constant)
solver_call = "u = method(f,%f,%f,%d,%d,%d,%d,None,False,False)" %(nu,dt,n,m,t0,t1)
timeit_results = timeit.Timer(solver_call, setup=setup_timeit).repeat(timeit_repeats, timeit_iter)
best_time = min(timeit_results)/float(timeit_iter) # All noise in data is "positive", so minimum time is most accurate
if verbose:
print "\nTest repeats: %d, each with %d iterations" %(timeit_repeats, timeit_iter)
print "Settings: f=1,nu=%.1f,dt=%.1f,n=%d,m=%d,t0=%d,t1=%d" %(nu,dt,n,m,t0,t1)
print "Minimum CPU-time of scheme '%s': %f seconds" %(scheme_name, best_time)
else:
print "Min. CPU-time: %f sec. (%s)" %(best_time, scheme_name)
else:
u = method(f,nu,dt,n,m,t0,t1,initial_u, \
show_animation=show_animation,print_progress=verbose)
if verbose: # Need to add some spacing for aesthetical purposes
print ""
print u.max()
# Save last u
if output_last_u_to_file:
if verbose:
print "\nSaving final temperature distribution u to file"
filename = args.o
np.savetxt(filename, u) # Works with both nested list and array
if save_last_fig:
if verbose:
print "\nSaving the final temperature plot of u to 'last_u.png'"
plt.ion()
im = plt.imshow(zip(*u), cmap='gray') # Initiate plotting / animation
plt.title('u(x,y,t=%d)' %(t1)) # Update title time
plt.xlabel('X'); plt.ylabel('Y')
if not show_animation: # Do not add a second colorbar if already added!
plt.colorbar(im)
plt.savefig('last_u.png')
def np_to_vec(np): np=np.tolist() if np[3]: return vec3d(np[0], np[1], np[2], np[3]) return vec3d(np[0], np[1], np[2])
