# function without access to 'self' attributes
def function(x, *args):
print('0')
return 3.3 * np.array(np.sin(x[0]) + (x[1] - 1)**2)
# method with access to 'self' attributes
def method(self, x, *args):
print('1')
return 3.3 * np.array(np.sin(x[0]) + (x[1] - 1)**2)
if 1 or ALL:
s = 'Forward() with demo function build-in into Model'
print('-' * len(s) + '\n' + s + '\n' + '-' * len(s))
x, y = Forward(White(function))(x=grid(3, [0, 1], [0, 1]))
plotIsoMap(x[:, 0], x[:, 1], y[:, 0])
if 0 or ALL:
s = 'Forward() with demo function build-in into Model'
print('-' * len(s) + '\n' + s + '\n' + '-' * len(s))
x, y = Forward(White('demo'))(x=cross(5, [1, 2], [3, 4]))
plotIsoMap(x[:, 0], x[:, 1], y[:, 0], scatter=True)
if 0 or ALL:
s = "Forward, assign external function (without self-argument) to f"
print('-' * len(s) + '\n' + s + '\n' + '-' * len(s))
op = Forward(White(function))
_, y = op(x=rand(12, [2, 3], [3, 4]))
print('x:', op.model.x, '\ny1:', op.model.y)
def example4():
# 2D problem: three 1D user-defined functions f(x) are fitted,
# and a neural network
df = pd.DataFrame({'x': [13, 21, 32, 33, 43, 55, 59, 60, 62, 82],
'y': [.56, .65, .7, .7, 2.03, 1.97, 1.92, 1.81,
2.89, 7.83],
'u': [-0.313, -0.192, -0.145, -0.172, -0.563,
-0.443, -0.408, -0.391, -0.63, -1.701]})
def f1(x, c0=0, c1=0, c2=0, c3=0, c4=0, c5=0):
"""
Computes polynomium: u(x) = c0 + c1*x + ... + c5*x^5
"""
return c0+x*(c1+x*(c2+x*(c3+x*(c4+x*c5))))
def f2(x, c0=0, c1=0, c2=0, c3=0, c4=0, c5=0):
y = c0 / (x[0]*x[0]) + c1 / x[1] + c2 + c3*x[1] + c4 * x[0]*x[0]
return [y]
def f3(x, c0=0, c1=0, c2=0, c3=0, c4=0, c5=0):
return c0 * x*x + c1 / x + c2 + c3 * x
definitions = [f1, f2, f3,
[50, 10, 2],
f2]
# neural network options
opt = {'methods': 'bfgs rprop', 'neurons': []}
Y = np.array(df.loc[:, ['u']]) # extracts an 2D array
for f in definitions:
blk = Black()
if hasattr(f, '__call__'):
print(f.__name__)
print('f1==f', f1 == f, id(f) == id(f1))
print('f2==f', f2 == f, id(f) == id(f2))
print('f3==f', f3 == f, id(f) == id(f3))
if hasattr(f, '__call__') and f2 != f:
X = np.array(df.loc[:, ['x']])
else:
X = np.array(df.loc[:, ['x', 'y']])
blk.train(X, Y, **opt)
y = blk.predict(X)
dy = y - Y
# print(' shapes X:', X.shape, 'U:', U.shape, 'u:', u.shape,
# 'du:', du.shape)
# console output
print(' ' + 76 * '-')
su = '[j:0..' + str(Y.shape[1] - 1) + '] '
print(' i X[j:0..' + str(X.shape[1] - 1) + ']' +
'U' + su + 'u' + su + 'du' + su + 'rel' + su + '[%]:')
for i in range(X.shape[0]):
print('{:5d} '.format(i), end='')
for a in X[i]:
print('{:f} '.format(a), end='')
for a in Y[i]:
print('{:f} '.format(a), end='')
for a in y[i]:
print('{:f} '.format(a), end='')
for j in range(Y.shape[1]):
print('{:f} '.format(dy[i][j]), end='')
for j in range(Y.shape[1]):
print('{:f} '.format(dy[i][j] / Y[i][j] * 100), end='')
print()
print(' ' + 76 * '-')
# graphic presentation
if X.shape[1] == 1 and Y.shape[1] == 1:
plt.title('Approximation')
plt.xlabel('$x$')
plt.ylabel('$u$')
plt.scatter(X, Y, label='$u$', marker='x')
plt.scatter(X, Y, label=r'$\tilde u$', marker='o')
if y is not None:
plt.plot(X, y, label=r'$\tilde u$ (cont)')
plt.plot(X, dy, label=r'$\tilde u - u$')
plt.legend(bbox_to_anchor=(0, 0), loc='lower left')
plt.show()
if 1:
plt.title('Absolute error')
plt.ylabel(r'$\tilde u - u$')
plt.plot(X, dy)
plt.show()
if 1:
plt.title('Relative error')
plt.ylabel('E [%]')
plt.plot(X, dy / Y * 100)
plt.show()
else:
if isinstance(f, str):
s = ' (' + f + ') '
elif not hasattr(f, '__call__'):
s = ' $(neural: ' + str(f) + ')$ '
else:
s = ''
try:
from plotArrays import plotIsoMap
except ImportError:
print("??? import of 'plotArrays' failed")
plotIsoMap(X[:, 0], X[:, 1], Y[:, 0],
labels=['$x$', '$y$', r'$u$' + s])
plotIsoMap(X[:, 0], X[:, 1], Y[:, 0],
labels=['$x$', '$y$', r'$\tilde u$' + s])
plotIsoMap(X[:, 0], X[:, 1], dy[:, 0],
labels=['$x$', '$y$', r'$\tilde u - u$' + s])
X[:, 1],
y[:, 0],
title='$y_{prd}$',
labels=['x', 'y', r'$Y_{trg}$'])
plotWireframe(X[:, 0],
X[:, 1],
Y[:, 0],
title='$Y_{trg}$',
labels=['x', 'y', r'$Y_{trg}$'])
plotWireframe(X[:, 0],
X[:, 1],
dy[:, 0],
title=r'$\Delta y$',
labels=['x', 'y', r'$\Delta y$'])
plotIsolines(X[:, 0], X[:, 1], y[:, 0], title='$y_{prd}$')
plotIsoMap(X[:, 0], X[:, 1], y[:, 0], title='$y_{prd}$')
plotIsoMap(X[:, 0], X[:, 1], Y[:, 0], title='$Y_{trg}$')
plotIsolines(X[:, 0], X[:, 1], Y[:, 0], title='$Y_{trg}$')
plotIsoMap(X[:, 0], X[:, 1], dy[:, 0], title=r'$\Delta y$')
plotSurface(X[:, 0], X[:, 1], dy[:, 0], title=r'$\Delta y$')
plotSurface(X[:, 0], X[:, 1], y[:, 0], title='$y_{prd}$')
if 0 or ALL:
s = 'Example 4: newff and train without class Neural'
print('-' * len(s) + '\n' + s + '\n' + '-' * len(s))
X = np.atleast_2d(np.linspace(-7, 7, 20)).T
Y = np.sin(X) * 10
norm_y = nl.tool.Norm(Y)
YY = norm_y(Y)
"""
nFit = 3
if x is None:
return nFit
c0, c1, c2 = args if len(args) > 0 else np.ones(nFit)
y0 = c2 * x[0]**2 + c1 * x[1] + c0
y1 = c2 * x[1]
return [y0, y1]
if 1 or ALL:
x = grid(100, [0.9, 1.1], [0.9, 1.1])
y_exa = White('demo')(x=x)
y = noise(y_exa, relative=20e-2)
plotIsoMap(x[:, 0], x[:, 1], y_exa[:, 0], title='$y_{exa,0}$')
plotSurface(x[:, 0], x[:, 1], y_exa[:, 0], title='$y_{exa,0}$')
plotIsolines(x[:, 0],
x[:, 1],
y_exa[:, 0],
title='$y_{exa,0}$',
levels=[0, 1e-4, 5e-4, .003, .005, .01, .02, .05, .1, .2])
plotIsoMap(x[:, 0], x[:, 1], y[:, 0], title='$y_0$')
plotIsoMap(x[:, 0],
x[:, 1], (y - y_exa)[:, 0],
title='$y_0-y_{exa,0}$')
if 0 or ALL:
x = grid(4, [0, 12], [0, 10])
y_exa = White(fUser)(x=x)
y = noise(y_exa, relative=20e-2)
s = 'Minimum, assigns random series of initial x'
print('-' * len(s) + '\n' + s + '\n' + '-' * len(s))
op = Minimum(White(f))
x, y = op(x=rand(10, [-5, 5], [-7, 7]), method='nelder-mead',
silent=True)
# op.plot()
print('x:', x, 'y:', y, '\nop.x:', op.x, 'op.y:', op.y)
if 0 or ALL:
s = 'Minimum, generates series of initial x on grid'
print('-' * len(s) + '\n' + s + '\n' + '-' * len(s))
x, y = Forward(White(f))(x=grid(3, [-2, 2], [-2, 2]))
plotSurface(x[:, 0], x[:, 1], y[:, 0])
plotIsoMap(x[:, 0], x[:, 1], y[:, 0])
op = Minimum(White(f))
x, y = op(x=rand(3, [-5, 5], [-7, 7]))
op.plot()
print('x:', x, 'y:', y)
if 1 or ALL:
s = 'Minimum, test all optimizers'
print('-' * len(s) + '\n' + s + '\n' + '-' * len(s))
if True:
op = Minimum(White('demo'))
methods = ['ga', 'BFGS']
y_exa[:, 0],
labels=(lx0, lx1, lYexa),
xrange=xRng,
yrange=yRng,
units=['m/s', 'mm$^2$/s', 'MPa'])
plotSurface(x[:, 1],
x[:, 0],
y_exa[:, 0],
labels=(lx1, lx0, lYexa),
xrange=xRng,
yrange=yRng,
units=['m/s', 'mm$^2$/s', 'MPa'])
plotIsoMap(x[:, 0],
x[:, 1],
y_exa[:, 0],
labels=(lx0, lx1, lYexa),
figsize=figsize,
xrange=xRng,
yrange=yRng,
units=['m/s', 'mm$^2$/s', 'MPa'])
plotIsolines(x[:, 0],
x[:, 1],
y_exa[:, 0],
labels=(lx0, lx1, lYexa),
figsize=figsize,
xrange=xRng,
yrange=yRng,
units=['m/s', 'mm$^2$/s', 'MPa'])
plotIsoMap(X[:, 0],
X[:, 1],
Y[:, 0],
labels=(lx0, lx1, lY),
s = 'Error compensation (black box): Y(X) = A(mDot, p)'
print('-' * len(s) + '\n' + s + '\n' + '-' * len(s))
plotWireframes = False
plotIsoMaps = True
df = pd.read_csv(raw, sep=',', comment='#')
df.rename(columns=df.iloc[0])
df = df.apply(pd.to_numeric, errors='coerce')
X = np.asfarray(df.loc[:, ['mDot', 'p']])
Y = np.asfarray(df.loc[:, ['A']])
YDiff = round(Y[:, 0].max() - Y[:, 0].min(), 5)
plotIsoMap(X[:, 0],
X[:, 1],
Y[:, 0] * 1e3,
title=r'$A_{prc}\cdot 10^3' + r'\ \ (\Delta A$: ' +
str(YDiff * 1e3) + 'e-3)',
labels=[r'$\dot m$', '$p$'])
plotWireframe(X[:, 0],
X[:, 1],
Y[:, 0] * 1e3,
title=r'$A_{prc}\cdot 10^3$',
labels=[r'$\dot m$', '$p$'])
model = Black()
dyDiffAll = []
hidden = range(1, 20 + 1)
for hid in hidden:
print('+++ hidden:', hid, end='')
print(' ==> autodefinition') if hid == 0 else print()
if 0 or ALL:
s = 'Medium gray box model, measured Y(X) = E(mDot, p)'
print('-' * len(s) + '\n' + s + '\n' + '-' * len(s))
df = pd.read_csv(raw, sep=',', comment='#')
df.rename(columns=df.iloc[0])
df = df.apply(pd.to_numeric, errors='coerce')
X = np.asfarray(df.loc[:, ['mDot', 'p']])
Y = np.asfarray(df.loc[:, ['A']])
model = Black()
y = model(X=X, Y=Y, neurons=[], x=X)
print('*** x:', model.x, 'y:', model.y, y)
from plotArrays import plotIsoMap, plotWireframe
plotIsoMap(X.T[0], X.T[1], Y.T[0] * 1e3, title=r'$A_{prc}\cdot 10^3$')
plotIsoMap(X.T[0], X.T[1], y.T[0] * 1e3, title=r'$A_{blk}\cdot 10^3$')
plotIsoMap(X.T[0],
X.T[1], (Y.T[0] - y.T[0]) * 1e3,
title=r'$(A_{prc} - A_{blk})\cdot 10^3$')
plotWireframe(X.T[0],
X.T[1],
Y.T[0] * 1e3,
title=r'$A_{prc}\cdot 10^3$')
plotWireframe(X.T[0],
X.T[1],
y.T[0] * 1e3,
title=r'$A_{blk}\cdot 10^3$')
plotWireframe(X.T[0],
X.T[1], (Y.T[0] - y.T[0]) * 1e3,
title=r'$(A_{prc} - A_{blk})\cdot 10^3$')
0.003393, 0.260, NaN, -0.002922, 0.000471
0.003393, 0.500, NaN, -0.002774, 0.000619
0.003393, 0.770, NaN, -0.002710, 0.000682
0.003393, 1.000, NaN, -0.002770, 0.000623
0.003393, 1.000, NaN, -0.002688, 0.000705
0.003393, 1.000, NaN, -0.002686, 0.000707
""")
if 0 or ALL:
s = 'Dark gray box model 1'
print('-' * len(s) + '\n' + s + '\n' + '-' * len(s))
model = DarkGray('demo')
X, Y = model.frame2arrays(df, ['x0', 'x4'], ['y0'])
y = model(X=X, Y=Y, x=X, silent=True, neurons=[10])
plotIsoMap(X[:, 0], X[:, 1], Y[:, 0], title='Y(X)')
plotIsoMap(X[:, 0], X[:, 1], y[:, 0], title='y(X)')
plotIsoMap(X[:, 0], X[:, 1], (y - Y)[:, 0], title='y(X) -Y')
print('*** X:', X.shape, 'Y:', Y.shape, 'y:', y.shape)
if 0 or ALL:
s = 'Dark gray box model 2'
print('-' * len(s) + '\n' + s + '\n' + '-' * len(s))
df = pd.read_csv(raw, sep=',', comment='#')
df.rename(columns=df.iloc[0])
df = df.apply(pd.to_numeric, errors='coerce')
X = np.asfarray(df.loc[:, ['mDot', 'p']])
Y = np.asfarray(df.loc[:, ['A']])