_check_coefficients is slow in Network and _BasePipe

[MassimoCimmino]

The methods Network._check_coefficents, _BasePipe._check_coefficents, and _BasePipe._check_model_variables are slowed down by the use of numpy.allclose.

Some timing comparisons:

>>> import numpy as np
>>> a = np.random.rand(5); b = np.random.rand(5)
>>> %timeit np.allclose(a, b, rtol=1e-6)
25.8 µs ± 257 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)
>>> %timeit np.all(np.abs(a - b) / (np.abs(b) + 1e-10) < 1e-6)
6.4 µs ± 21.8 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)

Other options may be available for these checks.

[MassimoCimmino]

Timings for PR #122

After initializing a network:

import matplotlib.pyplot as plt
import numpy as np
from scipy.constants import pi

import pygfunction as gt

# Borehole dimensions
D = 4.0             # Borehole buried depth (m)
H = 150.0           # Borehole length (m)
r_b = 0.075         # Borehole radius (m)

# Bore field geometry (rectangular array)
N_1 = 10            # Number of boreholes in the x-direction (columns)
N_2 = 10            # Number of boreholes in the y-direction (rows)
B = 7.5             # Borehole spacing, in both directions (m)

# The field is a retangular array
boreField = gt.boreholes.rectangle_field(N_1, N_2, B, B, H, D, r_b)

# Pipe dimensions
rp_out = 0.0211     # Pipe outer radius (m)
rp_in = 0.0147      # Pipe inner radius (m)
D_s = 0.052         # Shank spacing (m)
epsilon = 1.0e-6    # Pipe roughness (m)

# Pipe positions
# Single U-tube [(x_in1, y_in1), (x_out1, y_out1)]
pos = [(-D_s, 0.), (0., D_s)]

# Ground properties
k_s = 2.0           # Ground thermal conductivity (W/m.K)
T_g = 10.0          # Undisturbed ground temperature (degC)

# Grout properties
k_g = 1.0           # Grout thermal conductivity (W/m.K)

# Pipe properties
k_p = 0.4           # Pipe thermal conductivity (W/m.K)

# Fluid properties
m_flow_borehole = 0.25      # Total fluid mass flow rate per borehole (kg/s)
m_flow = m_flow_borehole*N_1*N_2    # Total fluid mass flow rate (kg/s)
# The fluid is propylene-glycol (20 %) at 20 degC
fluid = gt.media.Fluid('MPG', 20.)
cp_f = fluid.cp     # Fluid specific isobaric heat capacity (J/kg.K)
den_f = fluid.rho   # Fluid density (kg/m3)
visc_f = fluid.mu   # Fluid dynamic viscosity (kg/m.s)
k_f = fluid.k       # Fluid thermal conductivity (W/m.K)

# Single U-tube, same for all boreholes in the bore field
UTubes = []
for borehole in boreField:
	UTube = gt.pipes.SingleUTube(
		pos, rp_in, rp_out, borehole, k_s, k_g, 1e-6)
	UTubes.append(UTube)
# Build a network object from the list of UTubes
network = gt.networks.Network(boreField, UTubes, m_flow=m_flow, cp=cp_f)

Timing after changes:

>>> np.random.seed(seed=123456)
>>> m_flow_random = (np.random.rand(100) + 1.) * m_flow
>>> %timeit for m_flow_i in m_flow_random: network.get_network_inlet_temperature(1., 1., m_flow_i, cp_f, nSegments=1)
5.07 s ± 13 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
>>> %timeit for m_flow_i in m_flow_random: network._check_coefficients(m_flow_i, cp_f, 1, 1)
803 µs ± 1.35 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

Timing before changes:

>>> np.random.seed(seed=123456)
>>> m_flow_random = (np.random.rand(100) + 1.) * m_flow
>>> %timeit for m_flow_i in m_flow_random: network.get_network_inlet_temperature(1., 1., m_flow_i, cp_f, nSegments=1)
6.72 s ± 10.3 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
>>> %timeit for m_flow_i in m_flow_random: network._check_coefficients(m_flow_i, cp_f, 1, 1)
6.38 ms ± 21.5 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)