def grade_Q9():
x = np.random.rand(100, 100)
y = prj01.Q9(8).compile(golden.Builder())(x=x)
x2 = prj01.Q3(x, x)
x4 = prj01.Q3(x2, x2)
x8 = prj01.Q3(x4, x4)
return np.allclose(y, x8)
def grade_Q3():
a = np.array([[i for i in range(10)]])
b = a.transpose()
c = prj01.Q3(a, b)
d = prj01.Q3(b, a)
if not hasattr(c, "shape") or not hasattr(d, "shape"):
return False
if c.shape != (1, 1) or d.shape != (10, 10):
return False
return c[0, 0] == 285 and all(
[d[i, j] == i * j for i in range(10) for j in range(10)])
def grade_Q8():
A = np.random.rand(100, 100)
x = np.random.rand(100, 1)
b = np.random.rand(100, 1)
y = prj01.Q8(A, b).compile(golden.Builder())(x=x)
return np.allclose(y, prj01.Q2(prj01.Q3(A, x), b))
def grade_Q7():
a = np.random.rand(100, 50)
b = np.random.rand(100, 10)
c = np.random.rand(10, 50)
d = prj01.Q7().compile(golden.Builder())(a=a, b=b, c=c)
return np.allclose(d, prj01.Q2(a, prj01.Q3(b, c)))
def grade_Q5():
A = -np.random.rand(100, 100) + np.diag([100] * 100)
b = np.random.rand(100, 1)
x = prj01.Q5(A, b)
Ax = prj01.Q3(A, x)
return np.allclose(Ax, b)
