From 8f6fb1c0fa4665ac137242e778b7fd636f921ec8 Mon Sep 17 00:00:00 2001
From: Kostas Vilkelis <kostasvilkelis@gmail.com>
Date: Wed, 12 Feb 2020 00:41:02 +0000
Subject: [PATCH] fixed plot in lecture 10
---
src/10_xray.md | 216 +++++++++++++++++++------------------------------
1 file changed, 81 insertions(+), 135 deletions(-)
diff --git a/src/10_xray.md b/src/10_xray.md
index 2493d7b3..9c85e63b 100644
--- a/src/10_xray.md
+++ b/src/10_xray.md
@@ -100,162 +100,108 @@ which is clearly 1.
### Example of a two-dimensional reciprocal lattice
```python
-# Define the lattice vectors
+# Define primitive lattice vectors
a1 = np.array([1,0])
a2 = np.array([0.5,sqrt(3)/2])
-a1_alt = -a1-a2
-a2_alt = a1_alt + a1
-a2_c = np.array([0,sqrt(3)])
+# Compute reciprocal lattice vectors
+b1,b2 = np.linalg.inv(np.array([a1,a2]).T) @ np.eye(2)*2*pi
-# Produces the lattice to be fed into plotly
-def lattice_generation(a1,a2,N=6):
+fig = make_subplots(rows=1, cols=2,shared_yaxes=True,subplot_titles=('Real Space', 'Reciprocal Space'))
+
+# Generates the lattice given the lattice vectors
+def lattice_generation(a1,a2,N):
grid = np.arange(-N//2,N//2,1)
xGrid, yGrid = np.meshgrid(grid,grid)
return np.reshape(np.kron(xGrid.flatten(),a1),(-1,2))+np.reshape(np.kron(yGrid.flatten(),a2),(-1,2))
-
-# Produces the dotted lines of the unit cell
-def dash_contour(a1,a2, vec_zero = np.array([0,0]), color='Red'):
- dotLine_a1 = np.transpose(np.array([a1,a1+a2])+vec_zero)
- dotLine_a2 = np.transpose(np.array([a2,a1+a2])+vec_zero)
+def subplot(a1,a2,col):
+ N = 6
+ lat_points = lattice_generation(a1,a2,N)
+ line_a1 = np.transpose([[0,0],a1])
+ line_a2 = np.transpose([[0,0],a2])
+ dotLine_a1 = np.transpose([a1,a1+a2])
+ dotLine_a2 = np.transpose([a2,a1+a2])
- def dash_trace(vec,color):
- trace = go.Scatter(
- x=vec[0],
- y=vec[1],
- mode = 'lines',
- line_width = 2,
- line_color = color,
- line_dash='dot',
- visible=False
- )
- return trace
- return dash_trace(dotLine_a1,color),dash_trace(dotLine_a2,color)
-
-# Makes the lattice vector arrow
-def make_arrow(vec,text,color = 'Red',vec_zero = [0,0],text_shift = [-0.2,-0.1]):
- annot = [dict(
- x=vec[0]+vec_zero[0],
- y=vec[1]+vec_zero[1],
- ax=vec_zero[0],
- ay=vec_zero[1],
- xref='x',
- yref='y',
- axref='x',
- ayref = 'y',
- showarrow=True,
- arrowhead=2,
- arrowsize=1,
- arrowwidth=3,
- arrowcolor = color
- ),
- dict(
- x=(vec[0]+vec_zero[0])/2+text_shift[0],
- y=(vec[1]+vec_zero[1])/2+text_shift[1],
- xref='x',
- ayref = 'y',
- text = text,
- font = dict(
- color = color,
- size = 20
- ),
- showarrow=False,
- )
- ]
- return annot
-
-# Create the pattern
-pattern_points = lattice_generation(a1,a2)
-pattern = go.Scatter(x=pattern_points.T[0],y=pattern_points.T[1],mode='markers',marker=dict(
- color='Black',
- size = 20,
- symbol = 'star-open-dot')
+ fig.add_trace(
+ go.Scatter(visible=False, x=line_a1[0],y=line_a1[1],mode='lines',line_color='red'
+ ), row = 1, col = col
)
-
-# Lattice Choice A
-latticeA = go.Scatter(visible = False,x=pattern_points.T[0],y=pattern_points.T[1],mode='markers',marker=dict(
- color='Red',
- size = 10,
- )
+ fig.add_trace(
+ go.Scatter(visible=False, x=line_a2[0],y=line_a2[1],mode='lines',line_color='red'
+ ), row = 1, col = col
)
-
-# Lattice Choice B
-latB_points = lattice_generation(a1,a2)
-latticeB = go.Scatter(visible = False, x=latB_points.T[0]+0.5,y=latB_points.T[1],mode='markers',marker=dict(
- color='Blue',
- size = 10,
- )
+ fig.add_trace(
+ go.Scatter(visible=False, x=dotLine_a1[0],y=dotLine_a1[1],mode='lines',line_color='red',line_dash='dot'
+ ), row = 1, col = col
)
-
-# Annotate the lattice vectors
-# Button 2
-bt2_annot = make_arrow(a1,'$a_1$') + make_arrow(a2,'$a_2$') + make_arrow(a1_alt,'$a`_1$',color='Black',text_shift=[-0.55,-0.1]) + make_arrow(a2_alt,'$a`_2$',color='Black')
-#Button 3
-bt3_annot = make_arrow(a1,'$a_1$', vec_zero = [-0.5,0], color = 'Blue') + make_arrow(a2,'$a_2$',vec_zero = [-0.5,0], color = 'Blue')
-#Button 4
-bt4_annot = make_arrow(a2_c,'$a_2$') + make_arrow(a1,'$a_1$')
-
-# (0) Button 1, (0, 1-5) Button 2, (0, 6-8) Button 3, (0,1,9,10)
-data = [pattern,latticeA,*dash_contour(a1,a2),*dash_contour(a1_alt,a2_alt,color='Black'),
- latticeB, *dash_contour(a1,a2,vec_zero=[-0.5,0],color='Blue'),
- *dash_contour(a1, a2_c)]
-
-
-updatemenus=list([
- dict(
- type="buttons",
- direction="down",
- active=0,
- buttons=list([
- dict(label="Pattern",
- method="update",
- args=[{"visible": [True, False, False, False, False, False, False, False, False, False, False]},
- {"title": "Pattern",
- "annotations": []}]),
- dict(label="Lattice A",
- method="update",
- args=[{"visible": [True, True, True, True, True, True, False, False, False, False, False]},
- {"title": "Lattice A with a Primitive Unit Cell",
- "annotations": bt2_annot}]),
- dict(label="Lattice B",
- method="update",
- args=[{"visible": [True, False, False, False, False, False, True, True, True, False, False]},
- {"title": "Lattice B with a Primitive Unit Cell",
- "annotations": bt3_annot}]),
- dict(label="C.U.Cell",
- method="update",
- args=[{"visible": [True, True, False, False, False, False, False, False, False, True, True]},
- {"title": "Conventional Unit Cell",
- "annotations": bt4_annot}])
- ]),
+ fig.add_trace(
+ go.Scatter(visible=False, x=dotLine_a2[0],y=dotLine_a2[1],mode='lines',line_color='red',line_dash='dot'
+ ), row = 1, col = col
)
-]
-)
+ fig.add_trace(
+ go.Scatter(visible=False, x=lat_points.T[0],y=lat_points.T[1],mode='markers',marker=dict(
+ color='Black',
+ size = 20
+ )
+ ), row = 1, col = col
+ )
-plot_range = 2
-axis = dict(
+# Generate subplots to be used by the slider
+N_values = 10
+for i in np.linspace(2.5,3.5,N_values):
+ subplot(a1*i,a2*i,1)
+ subplot(b1/i,b2/i,2)
+
+# Define the default subplot
+active = 4
+for i in range(10):
+ fig.data[active*10+i].visible = True
+
+steps = []
+for i in range(N_values):
+ step = dict(
+ label = 'Lattice Constant',
+ method="restyle",
+ args=["visible", [False] * len(fig.data)],
+ )
+ for j in range(10):
+ step["args"][1][i*10+j] = True # Toggle i'th trace to "visible"
+ steps.append(step)
+
+sliders = [dict(
+ tickcolor = 'White',
+ font_color = 'White',
+ currentvalue_font_color = 'Black',
+ active = active,
+ name = 'Lattice Constant',
+ steps = steps
+)]
+
+plot_range = 5
+fig.update_layout(
+ sliders=sliders,
+ showlegend = False,
+ plot_bgcolor = 'rgb(254, 254, 254)',
+ width = 1000,
+ height = 500,
+ xaxis = dict(
range=[-plot_range,plot_range],
visible = False,
showgrid = False,
fixedrange = True
+ ),
+ yaxis = dict(
+ range = [-plot_range,plot_range],
+ visible = False,
+ showgrid = False,
+ fixedrange = True
)
-
-layout = dict(
- showlegend = False,
- updatemenus=updatemenus,
- plot_bgcolor = 'rgb(254, 254, 254)',
- width = 600,
- height = 600,
- xaxis = axis,
- yaxis = axis
)
-
-
-
-fig=dict(data=data, layout=layout)
-py.iplot(fig, filename='lattice_basics')
+fig.update_yaxes(range=[-plot_range, plot_range], row=1, col=2)
+fig.update_xaxes(range=[-plot_range, plot_range], row=1, col=2,visible=False)
+fig.show()
```
--
GitLab