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Update 'algorithm/optimization/gradient.py'

This commit is contained in:
TerenceLiu 2023-02-20 15:45:55 +08:00
parent 6a49d61a4d
commit 0a8eb87534
1 changed files with 16 additions and 8 deletions
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algorithm/optimization/gradient.py
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@ -150,7 +150,7 @@ class gd2d(object):
def initialization_default(self, environ): def initialization_default(self, environ):
pio.renderers.default = environ # 'notebook' or 'colab' or 'jupyterlab' pio.renderers.default = environ # 'notebook' or 'colab' or 'jupyterlab'
self.wg_expr = widgets.Dropdown(options=[("(1 - 8 * x1 + 7 * x1**2 - (7/3) * x1**3 + (1/4) * x1**4) * x2**2 * E**(-x2)", "(1 - 8 * x1 + 7 * x1**2 - (7/3) * x1**3 + (1/4) * x1**4) * x2**2 * E**(-x2)"), ("x1 - x2 + 2*x1*x2 + 2*x1**2 + x2**2", "x1 - x2 + 2*x1*x2 + 2*x1**2 + x2**2"), ("(4-x1)**2 + x2**2", "(4-x1)**2 + x2**2"), ("x1**2 + 10*x2**2", "x1**2 + 10*x2**2")], value="(1 - 8 * x1 + 7 * x1**2 - (7/3) * x1**3 + (1/4) * x1**4) * x2**2 * E**(-x2)", descrption="Expression") self.wg_expr = widgets.Dropdown(options=[("(1 - 8 * x1 + 7 * x1**2 - (7/3) * x1**3 + (1/4) * x1**4) * x2**2 * E**(-x2)", "(1 - 8 * x1 + 7 * x1**2 - (7/3) * x1**3 + (1/4) * x1**4) * x2**2 * E**(-x2)"), ("x1 - x2 + 2*x1*x2 + 2*x1**2 + x2**2", "x1 - x2 + 2*x1*x2 + 2*x1**2 + x2**2"), ("(4-x1)**2 + x2**2", "(4-x1)**2 + x2**2"), ("x1**2 + (10*x2)**2", "x1**2 + (10*x2)**2")], value="(1 - 8 * x1 + 7 * x1**2 - (7/3) * x1**3 + (1/4) * x1**4) * x2**2 * E**(-x2)", descrption="Expression")
self.wg_x0 = widgets.Text(value="0,2", description="Startpoint:") self.wg_x0 = widgets.Text(value="0,2", description="Startpoint:")
self.wg_lr = widgets.FloatText(value="1e-1", description="step size:") self.wg_lr = widgets.FloatText(value="1e-1", description="step size:")
self.wg_epsilon = widgets.FloatText(value="1e-5", description="criterion:") self.wg_epsilon = widgets.FloatText(value="1e-5", description="criterion:")
@ -214,8 +214,8 @@ class gd2d(object):
expression_list = ["(1 - 8 * x1 + 7 * x1**2 - (7/3) * x1**3 + (1/4) * x1**4) * x2**2 * E**(-x2)", "(1 - 8 * x1 + 7 * x1**2 - (7/3) * x1**3 + (1/4) * x1**4) * x2**2 * E**(-x2)"] expression_list = ["(1 - 8 * x1 + 7 * x1**2 - (7/3) * x1**3 + (1/4) * x1**4) * x2**2 * E**(-x2)", "(1 - 8 * x1 + 7 * x1**2 - (7/3) * x1**3 + (1/4) * x1**4) * x2**2 * E**(-x2)"]
if self.wg_expr.value in expression_list: if self.wg_expr.value in expression_list:
xx1, xx2 = np.arange(0, 5, 0.25), np.arange(0, 5, 0.25) xx1, xx2 = np.arange(0, 5, 0.25), np.arange(0, 5, 0.25)
else: elif self.wg_expr.value == "(4-x1)**2 + x2**2":
xx1, xx2 = np.arange(-5, 5, 0.25), np.arange(-5, 5, 0.25) xx1, xx2 = np.arange(-4, 12, 0.25), np.arange(-8, 8, 0.25)
xx1_tangent = np.arange(np.array(self.xn_list)[:, 0].min(), np.array(self.xn_list)[:, 0].max(), 0.1) xx1_tangent = np.arange(np.array(self.xn_list)[:, 0].min(), np.array(self.xn_list)[:, 0].max(), 0.1)
xx2_tangent = np.arange(np.array(self.xn_list)[:, 1].min(), np.array(self.xn_list)[:, 1].max(), 0.1) xx2_tangent = np.arange(np.array(self.xn_list)[:, 1].min(), np.array(self.xn_list)[:, 1].max(), 0.1)
xx1_o, xx2_o = xx1, xx2 xx1_o, xx2_o = xx1, xx2
@ -230,14 +230,22 @@ class gd2d(object):
partial_x2 = lambdify((x1, x2), diff(expr, x2), "numpy") partial_x2 = lambdify((x1, x2), diff(expr, x2), "numpy")
self.partial_x1, self.partial_x2 = partial_x1, partial_x2 self.partial_x1, self.partial_x2 = partial_x1, partial_x2
plane = partial_x1(np.array(self.xn_list)[:, 0], np.array(self.xn_list)[:, 1]) * (x1 - np.array(self.xn_list)[:, 0]) + partial_x2(np.array(self.xn_list)[:, 0], np.array(self.xn_list)[:, 1]) * (x2 - np.array(self.xn_list)[:, 1]) + f_xn plane = partial_x1(np.array(self.xn_list)[:, 0], np.array(self.xn_list)[:, 1]) * (x1 - np.array(self.xn_list)[:, 0]) + partial_x2(np.array(self.xn_list)[:, 0], np.array(self.xn_list)[:, 1]) * (x2 - np.array(self.xn_list)[:, 1]) + f_xn
self.plane = plane
z = [lambdify((x1, x2), plane[i], "numpy")(xx1_tangent, xx2_tangent) for i in range(0, len(plane))] z = [lambdify((x1, x2), plane[i], "numpy")(xx1_tangent, xx2_tangent) for i in range(0, len(plane))]
self.z = z try:
if z[-1] == 0:
z[-1] = np.zeros(z[0].shape)
except:
pass
## projection ## projection
z_offset = (np.min(fx)) * np.ones(fx.shape) z_offset = (np.min(fx)) * np.ones(fx.shape)
proj_z = lambda x, y, z: z proj_z = lambda x, y, z: z
colorsurfz = proj_z(xx1, xx2, fx) colorsurfz = proj_z(xx1, xx2, fx)
self.z = z
self.xx1_tangent, self.xx2_tangent = xx1_tangent, xx2_tangent
self.f_xn = f_xn
fig = make_subplots(rows=1, cols=2, specs=[[{'type': 'surface'}, {'type': 'surface'}]]) fig = make_subplots(rows=1, cols=2, specs=[[{'type': 'surface'}, {'type': 'surface'}]])
fig.add_trace(go.Surface(contours = {"x": {"show": True}, "y":{"show": True}, "z":{"show": True}}, x=xx1, y=xx2, z=fx), row=1, col=1) fig.add_trace(go.Surface(contours = {"x": {"show": True}, "y":{"show": True}, "z":{"show": True}}, x=xx1, y=xx2, z=fx), row=1, col=1)
fig.add_trace(go.Scatter3d(x=None, y=None, z=None, marker=dict(size=5)), row=1, col=1) fig.add_trace(go.Scatter3d(x=None, y=None, z=None, marker=dict(size=5)), row=1, col=1)
@ -246,11 +254,11 @@ class gd2d(object):
fig.add_trace(go.Scatter3d(x=None, y=None, z=None, marker=dict(size=5)), row=1, col=2) fig.add_trace(go.Scatter3d(x=None, y=None, z=None, marker=dict(size=5)), row=1, col=2)
fig.add_trace(go.Scatter3d(x=None, y=None, z=None, marker=dict(size=5)), row=1, col=2) fig.add_trace(go.Scatter3d(x=None, y=None, z=None, marker=dict(size=5)), row=1, col=2)
frames = [go.Frame(data=[go.Surface(visible=True, showscale=False, opacity=0.8), frames = [go.Frame(data=[go.Surface(visible=True, showscale=False, opacity=0.8),
go.Scatter3d(x=np.array(self.xn_list)[:k,0], y=np.array(self.xn_list)[:k,1], z=f_xn, marker=dict(size=5), line={"color":"blue", "width":3, 'dash': 'dash'}), go.Scatter3d(x=np.array(self.xn_list)[:k+1,0], y=np.array(self.xn_list)[:k+1,1], z=f_xn, marker=dict(size=5), line={"color":"red", "width":3, 'dash': 'dash'}),
go.Surface(visible=False, x=xx1_tangent, y=xx2_tangent, z=z[k]), go.Surface(visible=False, x=xx1_tangent, y=xx2_tangent, z=z[k]),
go.Surface(visible=True, showscale=False, opacity=0.8), go.Surface(visible=True, showscale=False, opacity=0.8),
go.Scatter3d(x=np.array(self.xn_list)[:k, 0], y=np.array(self.xn_list)[:k, 1], z=f_xn, line={"color":"blue", "width":3, 'dash': 'dash'}), go.Scatter3d(x=np.array(self.xn_list)[:k+1, 0], y=np.array(self.xn_list)[:k+1, 1], z=f_xn, line={"color":"red", "width":3, 'dash': 'dash'}),
go.Scatter3d(x=np.array(self.xn_list)[:k, 0].flatten(), y=np.array(self.xn_list)[:k, 1].flatten(), z=z_offset.flatten(), marker=dict(size=5), line={"color":"green", "width":3, 'dash': 'dash'})], go.Scatter3d(x=np.array(self.xn_list)[:k+1, 0].flatten(), y=np.array(self.xn_list)[:k, 1].flatten(), z=z_offset.flatten(), marker=dict(size=5), line={"color":"green", "width":3, 'dash': 'dash'})],
traces=[0, 1, 2, 3, 4, 5]) for k in range(len(f_xn))] traces=[0, 1, 2, 3, 4, 5]) for k in range(len(f_xn))]
fig.frames = frames fig.frames = frames
self.fig_frames = frames self.fig_frames = frames