model = Sequential()
dim = 28
nclasses = 10

model.add(Conv2D(filters=32, kernel_size=(5,5), padding='same', activation='relu', input_shape=(dim,dim,1)))
model.add(Conv2D(filters=32, kernel_size=(5,5), padding='same', activation='relu',))

model.add(MaxPool2D(pool_size=(2,2), strides=(2,2)))
model.add(Dropout(0.2))
model.add(Conv2D(filters=64, kernel_size=(5,5), padding='same', activation='relu'))

model.add(Conv2D(filters=64, kernel_size=(5,5), padding='same', activation='relu'))
model.add(MaxPool2D(pool_size=(2,2), strides=(2,2)))
model.add(Dropout(0.2))
model.add(Flatten())

model.add(Dense(120, activation='relu'))
model.add(Dense(84, activation='relu'))
model.add(Dense(nclasses, activation='softmax'))

opt = SGD(lr=0.001)
reduce_lr = ReduceLROnPlateau(monitor='val_acc', factor=0.9, patience=25, min_lr=0.000001, verbose=1)
model.compile(optimizer=opt, loss="categorical_crossentropy", metrics=["accuracy"])
history = model.fit(x=x_train,
                    y=y_train,
                    batch_size=10,
                    epochs=1,
                    verbose=1,
                    callbacks=[reduce_lr],
                    validation_data=(x_val,y_val),
                    shuffle=True)

plt.plot(history.history['val_acc'])
plt.plot(history.history['lr'])
plt.title('Plot of overall accuracy to larning rate for SGD optimizer')
plt.ylabel('accuracy')
plt.xlabel('learning rate')
plt.legend(['x_train', 'x_test'], loc='upper right')
plt.show()