added option for normal space

app.py

@@ -10,13 +10,12 @@ ylim = (-10,10)
 
 st.title("Eigen Values and Eigen Vectors")
 st.write(
-    "This app shows the effect of linear transformation with respect to eigen values and eigen vectors"
-)
+    "This app shows the effect of linear transformation with respect to eigen values and eigen vectors")
 
 with st.sidebar:
     data = st.selectbox('Select type of dataset', ['Square', 'Circle'])
     st.write("---")
-    st.text("Enter transformation matrix elements")
+    st.text("Select elements of transformation\nmatrix (A)")
     minv = -5.0
     maxv = 5.0
     step = 0.1
@@ -24,7 +23,14 @@ with st.sidebar:
     a_01 = st.slider(label = '$A_{0,1}$', min_value = minv, max_value=maxv, value=0.0, step=step)
     a_10 = st.slider(label = '$A_{1,0}$', min_value = minv, max_value=maxv, value=0.0, step=step)
     a_11 = st.slider(label = '$A_{1,1}$', min_value = minv, max_value=maxv, value=1.0, step=step)
-    t = np.array([[a_00,a_01], [a_10, a_11]], dtype=np.float64)  
+    t = np.array([[a_00,a_01], [a_10, a_11]], dtype=np.float64)
+    st.write("---")
+    st.write("The transformation matrix A is:")
+    st.table(pd.DataFrame(t))
+    st.write("---")
+    showNormalSpace = st.checkbox(label= 'Show normal space (without transform)', value=False)
+
+    
 
 x = np.linspace(-1,1,1000)
 y = getSquareYVectorised(x) if data == 'Square' else getCircle(x)
@@ -33,18 +39,33 @@ x_dash_up, y_dash_up = transform(x,y,t)
 x_dash_down, y_dash_down = transform(x,-y,t)
 
 evl, evec = np.linalg.eig(t)
+det = np.linalg.det(t)
 fig, ax = plt.subplots()
+
+if showNormalSpace:
+    ax.plot(x, y, 'r', alpha=0.5)
+    ax.plot(x, -y, 'g', alpha=0.5)
+    if not np.iscomplex(evec).any():
+        ax.quiver(0,0,evec[0,0],evec[1,0],scale=1,scale_units ='xy',angles='xy', facecolor='black', alpha=0.5)
+        ax.quiver(0,0,evec[0,1],evec[1,1],scale=1,scale_units ='xy',angles='xy', facecolor='black', alpha=0.5)
+    plotGridLines(xlim,ylim,np.array([[1,0], [0,1]]),'#9D9D9D','Normal Space',0.4)
+
 ax.plot(x_dash_up,y_dash_up,'r')
 ax.plot(x_dash_down,y_dash_down, 'g')
 if not (np.iscomplex(evl).any() or np.iscomplex(evec).any()):
-    ax.quiver(0,0,evec[0,0]*evl[0],evec[1,0]*evl[0],scale=1,scale_units ='xy',angles='xy', facecolor='yellow', label='$eigen\ vector_{\lambda_0}$')
-    ax.quiver(0,0,evec[0,1]*evl[1],evec[1,1]*evl[1],scale=1,scale_units ='xy',angles='xy', facecolor='blue',label='$eigen\ vector_{\lambda_1}$')
+    ax.quiver(0,0,evec[0,0]*evl[0],evec[1,0]*evl[0],scale=1,scale_units ='xy',angles='xy', facecolor='cyan', label='$eigen\ vector_{\lambda_0}$')
+    ax.quiver(0,0,evec[0,1]*evl[1],evec[1,1]*evl[1],scale=1,scale_units ='xy',angles='xy', facecolor='blue', label='$eigen\ vector_{\lambda_1}$')
+plotGridLines(xlim,ylim,t,'#403B3B','Transformed space',0.6)
+ax.text(11,5,'|A|={}'.format(det))
 
-plotGridLines(xlim,ylim,t)
 ax.set_xlim(*xlim)
 ax.set_ylim(*ylim)
 ax.set_aspect('equal', adjustable='box')
-fig.legend()
+ax.xaxis.set_tick_params(labelbottom=False)
+ax.yaxis.set_tick_params(labelleft=False)
+ax.set_xticks([])
+ax.set_yticks([])
+fig.legend(bbox_to_anchor=(1.05, 0.86), loc=1, borderaxespad=0., fontsize=8)
 st.pyplot(fig)
 
 df = pd.DataFrame({'Eigen Values': evl, 'Eigen Vectors': [str(evec[:,0]), str(evec[:,1])],\

utils.py

@@ -17,15 +17,17 @@ def transform(x,y,t):
     result = t @ points
     return result[0,:], result[1,:]
 
-def plotGridLines(xlim,ylim,t):
+def plotGridLines(xlim,ylim,t,color,label,linewidth):
     for i in range(xlim[0]-20,xlim[1]+21):
         x = [i,i]
         y = [ylim[0]-20,ylim[1]+20]
         x,y = transform(x,y,t)
-        plt.plot(x,y, color='#DAD5D4',linestyle='dashed',linewidth=0.5)
+        if i == xlim[0]-20:
+            plt.plot(x,y, color=color,linestyle='dashed',linewidth=linewidth,label=label)
+        else:
+            plt.plot(x,y, color=color,linestyle='dashed',linewidth=linewidth)
     for i in range(ylim[0]-20,ylim[1]+21):
         y = [i,i]
         x = [xlim[0]-20,xlim[1]+20]
         x,y = transform(x,y,t)
-        plt.plot(x,y, color='#DAD5D4',linestyle='dashed',linewidth=0.5)
-
+        plt.plot(x,y, color=color,linestyle='dashed',linewidth=linewidth)