addes

ex_45.py

@@ -0,0 +1,28 @@
+import numpy as np
+from scipy import misc
+import matplotlib.pyplot as plt
+
+from util.io import readvalue
+def positive_int(s):
+	i = int(s)
+	if(i <= 0):
+		raise ValueError("{} is negative".format(i))
+	return i
+
+file_input_name = readvalue("Input file name > ", str)
+file_output_name = readvalue("Output file name > ", str)
+cutoff = readvalue("Frequencies to cut > ", positive_int)
+
+fin = misc.imread(file_input_name, flatten=True)
+
+
+transformed = np.fft.fft2(fin)
+
+
+new_transformed = np.zeros(transformed.shape, dtype=np.complex)
+new_transformed[cutoff:-cutoff, cutoff:-cutoff] = transformed[cutoff:-cutoff, cutoff:-cutoff]
+
+
+new = np.fft.ifft2(new_transformed).real
+
+misc.imsave(file_output_name, new)

ex_46.py

@@ -0,0 +1,58 @@
+
+def bisec(f, a, b, eps, nmax):
+	"""
+	Takes f:[a,b] -> |R and tries to compute the null point 
+	using bisection.
+	"""
+
+	if(f(a)*f(b) >= 0):
+		raise ValueError("f(a)*f(b) >= 0")
+	
+	x_minus = a
+	x_plus = b
+
+	if(a > b):
+		x_minus = b
+		x_plus = a
+
+	for i in range(nmax):
+		x_minus, x_plus, err = bisec_one(x_minus, x_plus, f, eps)
+		if(err < eps):
+			break
+	if(err < eps):
+		return x_minus, err
+	raise ValueError("bisection hit nmax")
+
+	
+def bisec_one(x_minus, x_plus, f, eps):
+	a = x_minus
+	b = x_plus
+
+	x_m = (b + a) / 2
+	y_m = f(x_m)
+
+	if(y_m < 0):
+		if(y_m > -1*eps):
+			return x_m, x_m, -y_m
+
+		if(f(x_m)*f(b) >= 0):
+			return a, x_m, -y_m
+		return x_m, b, -y_m
+	
+	if(y_m < eps):
+		return x_m, x_m, y_m
+	
+	if(f(a)*f(x_m) >= 0):
+		return x_m, b, y_m
+	return a, x_m, y_m
+
+
+if( __name__ == "__main__"):
+	f1 = lambda x: x
+	f2 = lambda x: x**3
+	f3 = lambda x: -x + 1
+	f4 = lambda x: -x**3 + 1
+
+	fs = [f1, f2, f3, f4]
+	for f in fs:
+		print(bisec(f, -12, 10, 0.001, 100))

ex_47.py

@@ -0,0 +1,9 @@
+import numpy as np
+from scipy.optimize import minimize
+
+f = lambda x: x*np.sin(7*x)*np.exp(-(x - 2)**2)
+
+x0 = f(np.arange(-20, 20, 0.1)).min()
+
+m = minimize(f, x0, method="CG")
+print(m)