from ipywidgets import StaticInteract, RangeWidget, RadioWidget

import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline

# here we define the function which depends on variables.
# one can define functions with as many variables as desired

def f(x,var):
    return np.sinc(x/var)**2

# this is the routine which calls the function f(x,var)
# and plots the variation with respect to var

def plot(var):
    fig, ax = plt.subplots(figsize=(4, 3),
                           subplot_kw={'axisbg':'#EEEEEE',
                                       'axisbelow':True})
    ax.grid(color='w', linewidth=2, linestyle='solid')
    x = np.linspace(-50, 50, 1001)
    ax.plot(x, f(x,var), lw=5, alpha=0.4, label=var)
    ax.set_xlim(-50, 50)
    ax.set_ylim(-0.1, 1.1)
    ax.legend(loc='upper right')
    return fig

# here we look at the function's dependence on the value of var.
# we can add any number of variables var1, var2 in the same way.
# the syntax in the RangeWidget is (start, end, increment)

StaticInteract(plot,var=RangeWidget(10, 100, 10))
the fraunhofer limit
x, y = np.linspace(-10,10,101), np.linspace(-10,10,101)
z1, z2, z3, z4 = np.zeros([101,101]), np.zeros([101,101]), np.zeros([101,101]), np.zeros([101,101])

a = 0
for i in x:
    b = 0
    for j in y:
        z1[a][b] = ((np.sinc(20*i/20))**2)*((np.sinc(10*j/20))**2)
        z2[a][b] = ((np.sinc(20*i/50))**2)*((np.sinc(10*j/50))**2)
        z3[a][b] = ((np.sinc(20*i/100))**2)*((np.sinc(10*j/100))**2)
        z4[a][b] = ((np.sinc(20*i/200))**2)*((np.sinc(10*j/200))**2)
        b += 1
    a += 1
a = 0

plt.subplot(221)
plt.imshow(z1)
plt.xticks([])
plt.title('z = 20')
plt.subplot(222)
plt.imshow(z2)
plt.title('z = 50')
plt.xticks([])
plt.subplot(223)
plt.imshow(z3)
plt.title('z = 100')
plt.subplot(224)
plt.imshow(z4)
plt.title('z = 200')

x, y = np.linspace(-10,10,101), np.linspace(-10,10,101)
z1, z2, z3, z4 = np.zeros([101,101]), np.zeros([101,101]), np.zeros([101,101]), np.zeros([101,101])

a = 0
for i in x:
    b = 0
    for j in y:
        z1[a][b] = ((np.sinc(10*i/20))**2)*((np.sinc(10*j/20))**2)
        z2[a][b] = ((np.sinc(10*i/50))**2)*((np.sinc(10*j/50))**2)
        z3[a][b] = ((np.sinc(10*i/100))**2)*((np.sinc(10*j/100))**2)
        z4[a][b] = ((np.sinc(10*i/200))**2)*((np.sinc(10*j/200))**2)
        b += 1
    a += 1
a = 0

plt.subplot(221)
plt.imshow(z1)
plt.xticks([])
plt.title('z = 20')
plt.subplot(222)
plt.imshow(z2)
plt.title('z = 50')
plt.xticks([])
plt.subplot(223)
plt.imshow(z3)
plt.title('z = 100')
plt.subplot(224)
plt.imshow(z4)
plt.title('z = 200')



from ipywidgets import StaticInteract, RangeWidget, RadioWidget

import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline

x = np.linspace(-100,100,201)
y = np.linspace(-100,100,201)
z = np.zeros([201,201])

xwin = 100
ywin = 100

#def f(xwin,ywin,var):
def f(var):
    a = 0
    for i in x:
        b = 0
        for j in y:
            z[a][b] = ((np.sinc(xwin*i/var))**2)*((np.sinc(ywin*j/var))**2)
            b += 1
        a += 1
    return z

#def plot(xwin,ywin,var):
def plot(var):
    fig, ax = plt.subplots(figsize=(4, 3),
                           subplot_kw={'axisbg':'#EEEEEE',
                                       'axisbelow':True})
    image = f(var)
    ax.imshow(image)
    return fig

#StaticInteract(plot, xwin = RangeWidget(100, 300, 100), ywin = RangeWidget(100, 300, 100),var=RangeWidget(2000, 10000, 1000))
StaticInteract(plot, var=RangeWidget(200, 2000, 100))





#temp = f(2000)
#var = 
def plot(var):
    fig, ax = plt.subplots(figsize=(4,3), subplot_kw = {'axisbg' : '#EEEEEE', 'axisbelow':True})
    image = f(var)
    ax.imshow(image)
    #return var
    return fig

#var = 200
#plt.imshow(plot)
StaticInteract(plot,var = RangeWidget(200,4200,2000))

plt.imshow(temp)

plt.subplot(221)
var = 1000
plt.imshow(f(var))
plt.xticks([])
#plt.title('z = 200')

plt.subplot(222)
plt.imshow(f(2000))
#plt.title('z = 500')
plt.xticks([])

plt.subplot(223)
plt.imshow(f(5000))
#plt.title('z = 1000')

plt.subplot(224)
plt.imshow(f(10000))
#plt.title('z = 2000')

plt.imshow(f(10000))

import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline

x, y = np.linspace(-100,100,201), np.linspace(-100,100,201)
z = np.zeros([201,201])

xwin = 20
ywin = 0.2
dist = 1000

a = 0
for i in x:
    b = 0
    for j in y:
        z[a][b] = ((np.sinc(xwin*i/dist))**2)*((np.sinc(ywin*j/dist))**2)
        b += 1
    a += 1    

plt.imshow(z)

vfrom ipywidgets import StaticInteract, RangeWidget

import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline

x, y = np.linspace(-100,100,201), np.linspace(-100,100,201)
z = np.zeros([201,201])

xwin = 20
ywin = 0.2
#var = 200

def plot(dist):
    fig, ax = plt.subplots(figsize=(4,3), subplot_kw = {'axisbg' : '#EEEEEE', 'axisbelow':True})
    a = 0
    for i in x:
        b = 0
        for j in y:
            z[a][b] = ((np.sinc(xwin*i/dist))**2)*((np.sinc(ywin*j/dist))**2)
            b += 1
        a += 1
    ax.imshow(z)
    return fig

StaticInteract(plot, dist = RangeWidget(200,4200,500))