a = np.arange(6).reshape(2,3)
b = np.arange(6).reshape(3,2)*2
print(a)
print(b)
print(np.dot(a,b))
print(np.einsum("ij,ji->i",a,b)) # sum(aij*bji)
print(np.einsum("ij,ji->j",a,b)) # sum(bij*aji)
print("====")
a = np.array([1,2,3,4]).reshape(2,2)
b = np.array([1,2,3,4]).reshape(2,2)*2
print(a)
print(b)
print(np.einsum("ii",a))
print(np.einsum("aa",a))
print(np.einsum("ij",a))
print(np.einsum("ii->i",a))
# print(np.einsum("ii->ii",a)) # invalid
print("====")
print(np.einsum("ab->a",a))
print(np.einsum("cd->dc",a))
print(np.einsum("ij,ji->i",a,b))
print(np.einsum("ij,ji->j",a,b))
# print(np.einsum("ij,ji->x",a,b)) # invalid
print("====i,j,k====")
print(np.einsum("ij,jk->k",a,b))
print(np.einsum("ij,jk->ik",a,b)) # ab
print("====")
# print(np.einsum("ii,ii",a,b)) # invalid
# print(np,einsum("ii,jj",a,b)) # invalid
print(np.einsum("ii,ii->i",a,b)) # (a11b11, a22b22): multiply diagonal components
print(np.einsum("ii,jj->j",a,b)) # (a11(b12+b21), a22(b12+b21)): multiply multiply a's diagonal matrix and b's anti-diagonal matrix
n = 2
A = np.random.uniform(0,1,(n,n))
B = np.random.uniform(0,1,(n,n))
print("====sum====")
s = time.time()
x = A * B.T
print(x)
print(np.sum(x, axis=1))
print("time:"+str(time.time()-s))
print("====einsum====")
s = time.time()
print(np.einsum("ij,ji->i", A, B))
print("time:"+str(time.time()-s))
