# import library, standard convention
import numpy as np

# To see what's in a package, type the name, a period, then hit tab
#np?
#np.
np.pi?

# Some examples of numpy functions and "things":
print(np.sqrt(4))
print(np.pi)  # Not a function, just a variable
print(np.sin(np.pi)) # A function on a variable :) 

arr1 = np.array([1, 2.3, 4])   
print(type(arr1))
print(arr1.dtype)

strarr = np.array([x for x in 'hello'])
strarr.dtype

[x for x in 'hello']

strarr

arr2 = np.array([1, 2.56, 4], dtype=int)   
print(type(arr2))
print(arr2.dtype)
print arr2

arr3 = np.ndarray((2, 3, 4), dtype=complex)  # Notice : `ndarray`, not `array`!
print(type(arr3))


## what are the values in arr3??

arr3

print(arr3.shape)

arr4 = np.arange(2, 5)
print(arr4)
arr5 = np.arange(1, 5, 2)
print(arr5)
arr6 = np.arange(2, 10, 2)
print arr6

np.arange(10)
np.arange?

np.arange(0, 10.5, .5)



A = np.arange(5)
B = np.arange(5, 10)

print 'A is ', A
print 'B is ', B
print (A+B)

print(B-A)

print(A*B)

A_10 = np.ones(10)
B_5 = np.zeros(5)
print A_10, B_5
A_10 + B_5

A = np.arange(5)
A+10
2*A
A**2

A, B
print A.dot(B)
print np.dot(A, B)
A.shape

big_a = np.ones((2,5))
print big_a.shape
big_a

a = np.array([1,2])
b = np.array([4,5])


def angle_between_vectors(a,b):
    """
    find the angle between two vectors
    """
    norm_a = np.sqrt(a.dot(a))
    norm_b = np.sqrt(b.dot(b))
    ab_dot = a.dot(b)
    theta = np.arccos(ab_dot / (norm_a * norm_b))
    return theta

theta = angle_between_vectors(a,b)
print theta


## create rotation matrix
def rotation_matrix(theta):
    """ create a rotation matrix given theta"""
    rot = np.array([
                    [np.cos(theta), -np.sin(theta)],
                    [np.sin(theta), np.cos(theta)],
                    ])
    return rot

ab_rot =  rotation_matrix(theta)
print ab_rot
    

## we know the angle between a and b
## find a vector rotated by the same amount relative to c = [7,8,9], 
c = np.array([7,8])
new = c.dot(ab_rot)
print angle_between_vectors(c,new)

arr1 = np.array([1, 2, 3, 4, 5])
arr2 = np.array([1, 1, 3, 3, 5])
print(arr1 == arr2)
c = (arr1 == arr2)
print c.dtype
print c.sum()

arr1[c]

for mybool, item in zip(c, arr1):
    if mybool:
        print item **2

arr2[c]**2

print(np.all(c))
print(c.all())
print(c.any())

a = np.array([1,2,3])
print a[0:2]

a[1:2]

c = np.random.rand(3,3)
print(c)
#print(c[1:,0:2])
#print a
c[0,:] = a
print


c[0,:] = 42
print(c)

myvals = np.ones(100) * 13 + np.random.random(100)
print myvals

# create A and slice to get upper corner


# create code that generates a square array, and outputs upper 4th quarter




A = np.arange(5, 10)
print(A)
print(A[[0, 2, 3]])
A[[0, 2, 3]] = 0
print(A)


random = np.random
A = np.array([random.randint(0, 10) for i in range(10)]) # Check out the list comprehension!
print 'A', (A)
A[A>5] = 5
print(A)

stuff_lessthan5 = A[A<5]
print  stuff_lessthan5

b = np.array([4,5,6])
print (a)
print (b)
print (a > 2)
print (a[a > 2])
print (b[a > 2])
b[a == 3] = 77
print(b)

# There are handy ways to make arrays full of ones and zeros
print(np.zeros(5))
print np.ones(5)
print np.identity(5), '\n'

A = np.arange(5)*2
print(A) 
B = range(5)*2
print(B)

A = np.arange(5) + np.arange(5)
print(A)
B =range(5) + range(5)
print(B)

A = np.arange(5)
B = A[0:1]
B[0] = 42
print(A)
"""
A = range(5)
B = A[0:1]
B[0] = 42
print(A)
"""
    
    

B = A[:2].copy()
print B

B[0] = 0
print A

## create an array of 10 random numbers
## np.random.random?


# create a view and change the first element in the view
## what is the value in the original


## now create a copy

A = np.arange(16).reshape(4, 4)
print(A)
print(A.T) # transpose
print(A.trace())

la = np.linalg
A = np.matrix([[3, 2, -1], [2, -2, 4], [-1, .5, -1]])
B = np.array([1, -2, 0])
print(la.solve(A, B))

A = np.arange(1,10)
print(np.log10(A))

# create list, and array
## calculate log on all elements in list (list comprehension)
## calculate log on all elements in array
## use timeit to compare processing time