The operation method of N-dimensional array object (hereinafter, ndarray) provided by Python's numerical calculation library "Numpy" is organized. Python is slow to calculate due to lack of data type support, and it is standard to use ndarray when calculating with a large amount of data.

Premise

import numpy as np

A. Array generation

Generate an ndarray.

【array(object, dtype=None, copy=True, order='K', subok=False, ndmin=0)】

Create an ndarray from the list.
object: The original list (or something that can be treated as such)
dtype: Data type of the element. If not specified, it is automatically selected based on the element. (Reference: NumPy data type dtype list and conversion by astype (cast) | note.nkmk.me)

y = np.array([1,2,3])
X = np.array([[1,2,3], [4,5,6]], dtype=np.int64)

【zeros(shape, dtype=float, order='C')】

Generate an ndarray with each element padded with 0s.
shape: Number of elements in each dimension (integer or tuple of integers)

y = np.zeros(3)
# array([0., 0., 0.])

X = np.zeros((2,3))
# array([[0., 0., 0.],
#       [0., 0., 0.]])

【ones(shape, dtype=None, order='C')】

Generate an ndarray in which each element is filled with 1.

y = np.ones(3)
# array([1., 1., 1.])

X = np.ones((2,3))
# array([[1., 1., 1.],
#       [1., 1., 1.]])

【empty(shape, dtype=None, order='C')】

Generate an ndarray in which each element is not initialized.

y = np.empty(3)
# array([0.39215686, 0.70980392, 0.80392157])

X = np.empty((2,3))
# array([[2.6885677e-316, 0.0000000e+000, 0.0000000e+000],
#       [0.0000000e+000, 0.0000000e+000, 0.0000000e+000]])

【identity(n, dtype=None)】

Generate an ndarray that is an identity matrix.

X = np.identity(3)
# array([[1., 0., 0.],
#       [0., 1., 0.],
#       [0., 0., 1.]])

【arange([start,] stop[, step,], dtype=None)】

Generate an ndarray that is an arithmetic progression.
start: Start value of arithmetic progression
stop: Reference value for the end of arithmetic progression (values greater than the specified value are not included in the sequence)
step: Difference

y = np.arange(5)
# array([0, 1, 2, 3, 4])

y = np.arange(2,5)
# array([2, 3, 4])

y = np.arange(5,2,-1)
# array([5, 4, 3])

【linspace(start, stop, num=50, endpoint=True, retstep=False, dtype=None)】

Generate an ndarray that is an arithmetic progression that divides the specified range.
start: Start value of arithmetic progression
stop: End value of arithmetic progression
step: Divided value (number of elements in the array)

y = np.linspace(2,10,3)
# array([ 2.,  6., 10.])

y = np.linspace(2,10,5)
# array([ 2.,  4.,  6.,  8., 10.])

【unique(ar, return_index=False, return_inverse=False, return_counts=False, axis=None)】

Generate an ndarray after sorting and removing duplicates.

y = np.unique(['C', 'E', 'C', 'A', 'B', 'E', 'D', 'C'])
# array(['A', 'B', 'C', 'D', 'E'], dtype='<U1')

B. Get array elements

The elements of ndarray can be obtained in the same way as Get list elements in Python. However, note that the specification method changes for multidimensional arrays.

X = [[1,2,3],[4,5,6]]
print(X[1][2])
# 6

X_numpy = np.array(X)
print(X_numpy[1,2])
# 6

In addition to the usual acquisition method, it can also be acquired by the following method.

1. Get an array of indexes.

X = np.array([[1,2,3],[4,5,6]])

print(X[[0,1,-1]])
# [[1 2 3],
#  [4 5 6],
#  [4 5 6]]

print(X[[0,1,-1], 0])
# [1, 4, 4]

print(X[[0,1,-1], ::-1])
# [[3 2 1],
#  [6 5 4],
#  [6 5 4]]

print(X[[0,1,-1],[1,0,-1]])
# [2, 4, 6]
"""
* This designation has the same result as the following.
np.array([X[0,1], X[1,0], X[-1,-1]])
"""

2. Get it with a conditional expression.

X = np.array([[1,2,3],[4,5,6]])

print(X > 4)
#  [[False, False, False],
#  [False,  True,  True]]

print(np.where(X > 4))
# (array([1, 1]), array([1, 2]))

print(X[X > 4])
# [5, 6]

print(X[np.where(X > 4)])
# [5, 6]

C. Acquisition of sequence information

Get ndarray information.

【shape】

Get the number of elements in each dimension.

X = np.array([[1,2,3], [4,5,6]])
X.shape
# (2, 3)

【dtype】

Get the data type.

X = np.array([[1,2,3], [4,5,6]])
X.dtype
# dtype('int64')

【ndim】

Get the number of dimensions.

X = np.array([[1,2,3], [4,5,6]])
X.ndim
# 2

【size】

Get the number of elements.

X = np.array([[1,2,3], [4,5,6]])
X.size
# 6

D. Array manipulation

Manipulate the ndarray.

【<ndarray>.flatten(order='C')】

Make a one-dimensional array.

X = np.array([[1,2,3], [4,5,6]])
print(X.flatten())
# [1, 2, 3, 4, 5, 6]

【<ndarray>.reshape(shape, order='C')】

Change the shape of the array (number of dimensions and number of elements in each dimension).

X = np.array([1,2,3,4,5,6])
print(X.reshape((3,2)))
# [[1, 2],
#  [3, 4],
#  [5, 6]]

【sort(a, axis=-1, kind='quicksort', order=None)】

Rearranges. (Copy the target, sort and return the copy)
axis: Dimension to sort

X1 = np.array([[5,4,6], [3,1,2]])
X2 = np.sort(X1)
print(X1)
# [[5 4 6]
#  [3 1 2]]
print(X2)
# [[4 5 6]
#  [1 2 3]]

X3 = np.sort(X1, axis=0)
print(X3)
# [[3 1 2]
# [5 4 6]]

【<ndarray>.sort(axis=-1, kind='quicksort', order=None)】

Rearranges. (Sort the target)
axis: Dimension to sort

X = np.array([[5,4,6], [3,1,2]])

X.sort()
print(X)
# [4 5 6]
# [1 2 3]]

X.sort(axis=0)
print(X)
# [[3 1 2]
# [5 4 6]]

【<ndarray>.argsort(axis=-1, kind='quicksort', order=None)】

Get the index when sorted.

X = np.array([[5,4,6], [3,1,2]])

idxs = X.argsort()
print(idxs)
# [[1 0 2]
#  [1 2 0]]

idxs = X.argsort(axis=0)
print(idxs)
# [[1 1 1]
# [0 0 0]]

【<ndarray>.astype(dtype, order='K', casting='unsafe', subok=True, copy=True)】

Convert the data type of ndarray.

X = np.array([[1,2,3], [4,5,6]])
print(X.dtype)
# int64
print(X)
# [[1 2 3]
# [4 5 6]]

X2 = X.astype(np.float64)
print(X2.dtype)
# float64
print(X2)
# [[1. 2. 3.]
# [4. 5. 6.]]

E. Matrix manipulation

Perform matrix operations with ndarray.

【<ndarray>.T】

Transpose

X = np.array([[1,2,3], [4,5,6]])
print(X.T)
# [[1, 4],
#  [2, 5],
#  [3, 6]]

【numpy.dot】【<ndarray>.dot】

Inner product

X1 = np.array([[1, 2, 3], [4, 5, 6]])
X2 = np.array([[10, 20], [100, 200], [1000, 2000]])
print(np.dot(X1, X2))
# [[ 3210  6420]
#  [ 6540 13080]]

print(X1.dot(X2))
# [[ 3210  6420]
#  [ 6540 13080]]

【numpy.trace】【<ndarray>.trace】

Total of diagonal components

X = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
print(np.trace(X))
# 15

print(X.trace())
# 15

【numpy.linalg.det】

Determinant

X1 = np.array([[3., 2.], [5., 4.]])
print(np.linalg.det(X1))
# 2.0000000000000013

【numpy.linalg.eig】

Eigenvalue / eigenvector

X = np.array([[2, 0], [0, 0.25]])
print(np.linalg.eig(X))
# (array([2.  , 0.25]), array([[1., 0.], [0., 1.]]))

【numpy.linalg.svd】

Singular value decomposition

X = np.array([[2, 0], [0, 0.25], [0, 1]])
print(np.linalg.svd(X))
# (array([[ 1.,  0.        ,  0.        ],
#         [ 0., -0.24253563, -0.9701425 ],
#         [ 0., -0.9701425 ,  0.24253563]]), 
#  array([2., 1.03077641]), 
#  array([[ 1.,  0.],
#         [-0., -1.]]))

【numpy.linalg.inv】

Inverse matrix

X = np.array([[1, 1], [1, -1]])
print(np.linalg.inv(X))
# [[ 0.5  0.5]
#  [ 0.5 -0.5]]

【numpy.linalg.pinv】

Moore Penrose's reciprocal

X = np.array([[1, 1], [1, -1], [1, 0]])
print(np.linalg.pinv(X))
# [[ 0.33333333  0.33333333  0.33333333]
#  [ 0.5        -0.5         0.        ]]

【numpy.linalg.qr】

QR decomposition

X = np.array([[1, 2], [3, 4], [5, 6]])
print(np.linalg.qr(X))
# (array([[-0.16903085,  0.89708523],
#         [-0.50709255,  0.27602622],
#         [-0.84515425, -0.34503278]]),
#  array([[-5.91607978, -7.43735744],
#         [ 0.        ,  0.82807867]]))

F. Arithmetic

Arithmetic operations are performed between two ndarrays.

【add】

Addition (addition)

a = np.array([[1, 2, 3], [4, 5, 6]])

print(np.add(a, 10))
# [[11 12 13]
#  [14 15 16]]
print(a + 10)
# [[11 12 13]
#  [14 15 16]]

print(np.add(a, [10, 20, 30]))
# [[11 22 33]
#  [14 25 36]]
print(a + [10, 20, 30])
# [[11 22 33]
#  [14 25 36]]

print(np.add(a, np.array([[10, 20, 30], [40, 50, 60]])))
# [[11 22 33]
#  [44 55 66]]
print(a + np.array([[10, 20, 30], [40, 50, 60]]))
# [[11 22 33]
#  [44 55 66]]

【subtract】

Subtraction

a = np.array([[11, 22, 33], [44, 55, 66]])

print(np.subtract(a, 10))
# [[ 1 12 23]
#  [34 45 56]]
print(a - 10)
# [[ 1 12 23]
#  [34 45 56]]

print(np.subtract(a, [10, 20, 30]))
# [[ 1  2  3]
#  [34 35 36]]
print(a - [10, 20, 30])
# [[ 1  2  3]
#  [34 35 36]]

print(np.subtract(a, np.array([[10, 20, 30], [40, 50, 60]])))
# [[1 2 3]
#  [4 5 6]] 
print(a - np.array([[10, 20, 30], [40, 50, 60]]))
# [[1 2 3]
#  [4 5 6]]

【multiply】

Multiplication

a = np.array([[1, 2, 3], [4, 5, 6]])

print(np.multiply(a, 10))
# [[10 20 30]
#  [40 50 60]]
print(a * 10)
# [[10 20 30]
#  [40 50 60]]

print(np.multiply(a, [10, 20, 30]))
# [[ 10  40  90]
#  [ 40 100 180]]
print(a * [10, 20, 30])
# [[ 10  40  90]
#  [ 40 100 180]]

print(np.multiply(a, np.array([[10, 20, 30], [40, 50, 60]])))
# [[ 10  40  90]
#  [160 250 360]]
print(a * np.array([[10, 20, 30], [40, 50, 60]]))
# [[ 10  40  90]
#  [160 250 360]]

【divide】

Division (division)

a = np.array([[10, 20, 30], [40, 50, 60]])

print(np.divide(a, 10))
# [[1. 2. 3.]
#  [4. 5. 6.]]
print(a / 10)
# [[1. 2. 3.]
#  [4. 5. 6.]]

print(np.divide(a, [10, 20, 30]))
# [[1.  1.  1. ]
#  [4.  2.5 2. ]]
print(a / [10, 20, 30])
# [[1.  1.  1. ]
#  [4.  2.5 2. ]]

print(np.divide(a, np.array([[10, 20, 30], [40, 50, 60]])))
# [[1. 1. 1.]
#  [1. 1. 1.]]
print(a / np.array([[10, 20, 30], [40, 50, 60]]))
# [[1. 1. 1.]
#  [1. 1. 1.]]

【floor_divide】

Division quotient

a = np.array([[22, 33, 44], [45, 67, 89]])

print(np.floor_divide(a, 2))
# [[11 16 22]
#  [22 33 44]]
print(a // 2)
# [[11 16 22]
#  [22 33 44]]

print(np.floor_divide(a, [2, 3, 4]))
# [[11 11 11]
#  [22 22 22]]
print(a // [2, 3, 4])
# [[11 11 11]
#  [22 22 22]]

print(np.floor_divide(a, np.array([[2, 3, 4], [4, 6, 8]])))
# [[11 11 11]
#  [11 11 11]]
print(a // np.array([[[2, 3, 4], [4, 6, 8]]]))
# [[11 11 11]
#  [11 11 11]]

【mod】

Remainder of division

a = np.array([[22, 33, 44], [45, 67, 89]])

print(np.mod(a, 2))
# [[0 1 0]
#  [1 1 1]]
print(a % 2)
# [[0 1 0]
#  [1 1 1]]

print(np.mod(a, [2, 3, 4]))
# [[0 0 0]
#  [1 1 1]]
print(a % [2, 3, 4])
# [[0 0 0]
#  [1 1 1]]

print(np.mod(a, np.array([[2, 3, 4], [4, 6, 8]])))
# [[0 0 0]
#  [1 1 1]]
print(a % np.array([[[2, 3, 4], [4, 6, 8]]]))
# [[0 0 0]
#  [1 1 1]]

【power】

Exponentiation

a = np.array([[1, 2, 3], [4, 5, 6]])

print(np.power(a, 2))
# [[ 1  4  9]
#  [16 25 36]]
print(a ** 2)
# [[ 1  4  9]
#  [16 25 36]]

print(np.power(a, [2, 3, 4]))
# [[   1    8   81]
#  [  16  125 1296]]
print(a ** [2, 3, 4])
# [[   1    8   81]
#  [  16  125 1296]]

print(np.power(a, np.array([[2, 3, 4], [1/2, 1/3, 1/4]])))
# [[ 1.          8.         81.        ]
#  [ 2.          1.70997595  1.56508458]]
print(a ** np.array([[2, 3, 4], [1/2, 1/3, 1/4]]))
# [[ 1.          8.         81.        ]
#  [ 2.          1.70997595  1.56508458]]

G. Comparison operation

Compare two ndarrays.

【greater】

Greater than

a1 = np.array([10, 10, 10, 10, 10])
a2 = np.array([9, 9.9, 10, 10.1, 11])

print(np.greater(a1, a2))
# [ True  True False False False]
print(a1 > a2)
# [ True  True False False False]

【greater_equal】

that's all

a1 = np.array([10, 10, 10, 10, 10])
a2 = np.array([9, 9.9, 10, 10.1, 11])

print(np.greater_equal(a1, a2))
# [ True  True True False False]
print(a1 >= a2)
# [ True  True True False False]

【less】

Less than

a1 = np.array([10, 10, 10, 10, 10])
a2 = np.array([9, 9.9, 10, 10.1, 11])

print(np.less(a1, a2))
# [False False False  True  True]
print(a1 < a2)
# [False False False  True  True]

【less_equal】

Less than

a1 = np.array([10, 10, 10, 10, 10])
a2 = np.array([9, 9.9, 10, 10.1, 11])

print(np.less_equal(a1, a2))
# [False False  True  True  True]
print(a1 <= a2)
# [False False  True  True  True]

【equal】

Equal

a1 = np.array([10, 10, 10, 10, 10])
a2 = np.array([9, 9.9, 10, 10.1, 11])

print(np.equal(a1, a2))
# [False False  True False False]
print(a1 == a2)
# [False False  True False False]

【not_equal】

Not equal

a1 = np.array([10, 10, 10, 10, 10])
a2 = np.array([9, 9.9, 10, 10.1, 11])

print(np.not_equal(a1, a2))
# [ True  True False  True  True]
print(a1 != a2)
# [ True  True False  True  True]

H. Logical operation

Logically operate two ndarrays.

【logical_and】

a1 = np.array([True, False, True, False])
a2 = np.array([True, False, False, True])

print(np.logical_and(a1, a2))
# [ True False False False]

【logical_or】

a1 = np.array([True, False, True, False])
a2 = np.array([True, False, False, True])

print(np.logical_or(a1, a2))
# [ True False  True  True]

【logical_xor】

a1 = np.array([True, False, True, False])
a2 = np.array([True, False, False, True])

print(np.logical_xor(a1, a2))
# [False False  True  True]

【logical_not】

a = np.array([True, False, True, False])

print(np.logical_not(a))
# [False  True False  True]

【<ndarray>.any()】

One of the elements is True

a1 = np.array([0, 1, 0, 0])
print(a1.any())
# True

a2 = np.array([1, 1, 1, 1])
print(a2.any())
# True

a3 = np.array([0, 0, 0, 0])
print(a3.any())
# False

【<ndarray>.all()】

All elements are True

a1 = np.array([0, 1, 0, 0])
print(a1.all())
# False

a2 = np.array([1, 1, 1, 1])
print(a2.all())
# True

a3 = np.array([0, 0, 0, 0])
print(a3.all())
# False

I. Set arithmetic

Perform a set operation with ndarray.

The set operation itself can also be performed with a Python set. Reference: Python set operation

【union1d(ar1, ar2)】

Union (OR)

X = np.unique([1,2,3,4,5,6])
Y = np.unique([4,5,6,7,8,9])

Z = np.union1d(X,Y)
print(Z)
# [1 2 3 4 5 6 7 8 9]

【intersect1d(ar1, ar2)】

Intersection (AND)

X = np.unique([1,2,3,4,5,6])
Y = np.unique([4,5,6,7,8,9])

Z = np.intersect1d(X,Y)
print(Z)
# [4 5 6]

【setxor1d(ar1, ar2)】

Symmetric difference (XOR)

X = np.unique([1,2,3,4,5,6])
Y = np.unique([4,5,6,7,8,9])

Z = np.setxor1d(X,Y)
print(Z)
# [1 2 3 7 8 9]

【setdiff1d(ar1, ar2)】

Difference set

X = np.unique([1,2,3,4,5,6])
Y = np.unique([4,5,6,7,8,9])

Z = np.setdiff1d(X,Y)
print(Z)
# [1 2 3]

【in1d(ar1, ar2)】

Determining whether each element of the former set is included in the latter

X = np.unique([1,2,3,4,5])
Y = np.unique([1,2,3])

Z = np.in1d(X,Y)
print(Z)
# [ True  True  True False False]

J. Maximum / minimum / code extraction

Extract the maximum / minimum / sign of ndarray.

【maximum】

Maximum value (compare two ndarrays and get the larger one)
If one element is NaN, get NaN.

a1 = np.array([4, 2, np.nan])
a2 = np.array([3, 6, 5])

print(np.maximum(a1, a2))
# [ 4.  6. nan]

【fmax】

Maximum value (compare two ndarrays and get the larger one)
If one element is NaN, get the other.

a1 = np.array([4, 2, np.nan])
a2 = np.array([3, 6, 5])

print(np.fmax(a1, a2))
# [4. 6. 5.]

【minimum】

Minimum value (compare two ndarrays and get the smaller one)
If one element is NaN, get NaN.

a1 = np.array([4, 2, np.nan])
a2 = np.array([3, 6, 5])

print(np.minimum(a1, a2))
# [ 3.  2. nan]

【fmin】

Minimum value (compare two ndarrays and get the smaller one)
If one element is NaN, get the other.

a1 = np.array([4, 2, np.nan])
a2 = np.array([3, 6, 5])

print(np.fmin(a1, a2))
# [3. 2. 5.]

【copysign】

Apply the sign of the corresponding element in the second ndarray to the first ndarray.

a1 = np.array([1, 2, 3, 4, 5])
a2 = np.array([0, -1, 1, 2, -2])

print(np.copysign(a1, a2))
# [ 1. -2.  3.  4. -5.]

K. Rounding up / rounding down / rounding

Each value of ndarray processes the value after the decimal point.

【ceil(ndarray)】

Round up

y = np.array([-5.6, -5.5, -5.4, 0, 5.4, 5.5, 5.6])

z = np.ceil(y)
print(z)
# [-5. -5. -5.  0.  6.  6.  6.]

【floor(ndarray)】

Truncate

y = np.array([-5.6, -5.5, -5.4, 0, 5.4, 5.5, 5.6])

z = np.floor(y)
print(z)
# [-6. -6. -6.  0.  5.  5.  5.]

【rint(ndarray)】

Rounding

y = np.array([-5.6, -5.5, -5.4, 0, 5.4, 5.5, 5.6])

z = np.rint(y)
print(z)
# [-6. -6. -5.  0.  5.  6.  6.]

【modf(ndarray)】

Splitting integer and decimal parts

y = np.array([-3.6, -2.5, -1.4, 0, 1.4, 2.5, 3.6])

z = np.modf(y)
print(z)
# (array([-0.6, -0.5, -0.4,  0. ,  0.4,  0.5,  0.6]), array([-3., -2., -1.,  0.,  1.,  2.,  3.]))

L. Square root, square root, absolute value

Calculate the square root, square root, and absolute value for each value of ndarray.

【square(ndarray)】

Square

y = np.arange(1,6)

z = np.square(y)
print(z)
# [ 1  4  9 16 25]

z = y ** 2
print(z)
# [ 1  4  9 16 25]

【sqrt(ndarray)】

Square root

y = np.array([1,4,9,16,25])

z = np.sqrt(y)
print(z)
# [1. 2. 3. 4. 5.]

z = y ** 0.5
print(z)
# [1. 2. 3. 4. 5.]

【abs(ndarray)】

Absolute value

y = np.array([-1,-2,3,4,5j])

z = np.abs(y)
print(z)
# [1, 2, 3, 4, 5]

【fabs(ndarray)】

Absolute value (Imaginary / complex numbers are not possible, but faster than abs)

y = np.array([-1,-2,3,4,-5])

z = np.fabs(y)
print(z)
# [1, 2, 3, 4, 5]

M. Exponential / logarithmic function

Calculate the exponent and logarithm for each value of ndarray.

【exp(ndarray)】

Index

y = np.arange(1,6)

z = np.exp(y)
print(z)
# [  2.71828183   7.3890561   20.08553692  54.59815003 148.4131591 ]

print(np.e)
# 2.718281828459045

【log(ndarray)】

Natural logarithm

y = np.e ** np.array([1, 2, 3, 4, 5])

z = np.log(y)
print(z)
# [1. 2. 3. 4. 5.]

【log10(ndarray)】

Common logarithm

y = 10 ** np.array([1, 2, 3, 4, 5])

z = np.log10(y)
print(z)
# [1. 2. 3. 4. 5.]

【log2(ndarray)】

Binary logarithm

y = 2 ** np.array([1, 2, 3, 4, 5])

z = np.log2(y)
print(z)
# [1. 2. 3. 4. 5.]

N. Trigonometric function

Apply trigonometric functions to each value of ndarray.

【sin(ndarray)】

Sine

y = np.linspace(-1, 1, 5)  * np.pi

print(np.sin(y))
# [-1.2246468e-16 -1.0000000e+00  0.0000000e+00  1.0000000e+00 1.2246468e-16]

【cos(ndarray)】

Cosine

y = np.linspace(-1, 1, 5)  * np.pi

print(np.cos(y))
# [-1.000000e+00  6.123234e-17  1.000000e+00  6.123234e-17 -1.000000e+00]

【tan(ndarray)】

Tantangent

y = np.linspace(-1, 1, 5)  * np.pi

print(np.tan(y))
# [ 1.22464680e-16 -1.63312394e+16  0.00000000e+00  1.63312394e+16 -1.22464680e-16]

O. Hyperbolic function

Apply the hyperbolic function to each value of ndarray.

【sinh(ndarray)】

Hyperbolic sine

y = np.array([-np.inf, -2, -1, 0, 1, 2, np.inf])

print(np.sinh(y))
# [-inf -3.62686041 -1.17520119  0. 1.17520119  3.62686041 inf]

【cosh(ndarray)】

Hyperbolic cosine

y = np.array([-np.inf, -2, -1, 0, 1, 2, np.inf])

print(np.cosh(y))
# [inf 3.76219569 1.54308063 1. 1.54308063 3.76219569 inf]

【tanh(ndarray)】

Hyperbolic tangent

y = np.array([-np.inf, -2, -1, 0, 1, 2, np.inf])

print(np.tanh(y))
# [-1. -0.96402758 -0.76159416  0. 0.76159416  0.96402758 1.]

P. Inverse trigonometric function

Apply the inverse trigonometric function to each value of ndarray.

【arcsin(ndarray)】

Inverse sine

y = np.linspace(-1, 1, 5)

print(np.arcsin(y))
# [-1.57079633 -0.52359878  0. 0.52359878  1.57079633]

【arccos(ndarray)】

Reverse cosine

y = np.linspace(-1, 1, 5)

print(np.arccos(y))
# [3.14159265 2.0943951  1.57079633 1.04719755 0.]

【arctan(ndarray)】

Reverse tangent

y = np.linspace(-1, 1, 5)

print(np.arctan(y))
# [-0.78539816 -0.46364761  0. 0.46364761  0.78539816]

Q. Inverse hyperbolic function

Apply the inverse hyperbolic function to each value of ndarray.

【arcsinh(ndarray)】

Inverse hyperbolic sine

y = np.array([-np.inf, -3.62686041, -1.17520119,  0., 1.17520119,  3.62686041, np.inf])

print(np.arcsinh(y))
# [-inf  -2.  -1.   0.   1.   2.  inf]

【arccosh(ndarray)】

Inverse hyperbolic cosine

y = np.array([1., 1.54308063, 3.76219569, np.inf])

print(np.arccosh(y))
# [ 0.  1.  2. inf]

【arctanh(ndarray)】

Inverse hyperbolic tangent

y = np.array([-1., -0.96402758, -0.76159416,  0., 0.76159416,  0.96402758, 1.])

print(np.arctanh(y))
# [-inf -2. -1.00000001 0. 1.00000001 2. inf]

R. Random number generation

Generate random numbers with Numpy.

【numpy.random.rand(d0, d1, ..., dn)】

Uniform distribution
Generates a random number array with the specified number of elements / dimensions. (Random number range: 0 or more and less than 1)

print(np.random.rand())
# 0.5504876218756463

print(np.random.rand(2))
# [0.70029403 0.48969378]

print(np.random.rand(2, 2))
# [[0.98181874 0.47001957]
#  [0.79277853 0.12536121]]

【numpy.random.randint(low, high=None, size=None, dtype='l')】

Uniform distribution
Generate a random number with a specified range of integers.
low: Minimum value (or more. Included in the range of random numbers)
high: Maximum value (less than. Not included in the random number range)
size: number of elements / number of dimensions
dtype: Data type

print(np.random.randint(1,4))
# 2

print(np.random.randint(1,4, 2))
# [2 2]

print(np.random.randint(1,4, (2, 2)))
# [[3 2]
#  [3 1]]

【numpy.random.uniform(low=0.0, high=1.0, size=None)】

Uniform distribution
Generate a specified range of random numbers.
low: Minimum value (or more. Included in the range of random numbers)
high: Maximum value (less than. Not included in the random number range)
size: number of elements / number of dimensions

print(np.random.uniform(1,4))
# 3.5515484791542056

print(np.random.uniform(1,4, 2))
# [1.51270014 3.02435494]

print(np.random.uniform(1,4, (2, 2)))
# [[3.47188029 1.17177563]
#  [3.87198389 3.91458379]]

【numpy.random.randn(d0, d1, ..., dn)】

normal distribution
Generates a random number array with the specified number of elements / dimensions. (Average: 0, standard deviation: 1)

print(np.random.randn())
# -0.5775065521096695

print(np.random.randn(2))
# [-1.50501689  1.46743032]

print(np.random.randn(2, 2))
# [[ 1.16357112 -0.24601519]
#  [ 2.07269576 -0.39272309]]

【numpy.random.normal(loc=0.0, scale=1.0, size=None)】

normal distribution
Generate a random number with the specified mean and standard deviation.
loc: average
scale: standard deviation
size: number of elements / number of dimensions

print(np.random.normal(50, 10))
# 63.47995333571061

print(np.random.normal(50, 10, (2, 2)))
# [[56.02364177 55.25423891]
#  [45.44840171 29.8303964 ]]

print(np.random.normal((50, 0), (10, 1), (5, 2)))
# [[45.48754234 -0.74792452]
#  [60.84696747  1.01209036]
#  [42.38844146 -0.10453915]
#  [39.77544056  1.22264549]
#  [41.60250782  1.64150462]]

【numpy.random.binomial(n, p, size=None)】

Binomial distribution
Generate a random number with the specified number of trials and probability.
n: Number of trials
p: Probability
size: number of elements / number of dimensions

print(np.random.binomial(100, 0.5))
# 53

print(np.random.binomial(100, 0.5, (2, 2)))
# [[53 53]
#  [48 50]]

print(np.random.binomial((100, 1000), (0.3, 0.7), (5, 2)))
# [[ 33 699]
#  [ 30 660]
#  [ 34 698]
#  [ 26 688]
#  [ 25 683]]

【numpy.random.beta(a, b, size=None)】

Beta distribution

print(np.random.beta(3, 5))
# 0.09838262724430759
 
print(np.random.beta(8, 2, (2, 2)))
# [[0.92800788 0.86391443]
#  [0.67249524 0.97299346]]
 
print(np.random.beta((3, 8), (5, 2), (5, 2)))
# [[0.11825463 0.74320634]
#  [0.24992266 0.79029969]
#  [0.13345269 0.57807883]
#  [0.32374525 0.92666103]
#  [0.64669681 0.84867388]]

【numpy.random.chisquare(df, size=None)

Chi-square distribution

print(np.random.chisquare(1))
# 0.05074259859574817
 
print(np.random.chisquare(5, (2, 2)))
# [[ 6.15617206  5.54859677]
#  [ 2.60704305 10.35079434]]
 
print(np.random.chisquare((1, 5), (5, 2)))
# [[2.3942405  6.43803251]
#  [1.97544231 2.73456762]
#  [0.63389405 7.81526263]
#  [0.05035459 7.8224598 ]
#  [1.01597309 1.46098368]]

【numpy.random.gamma(shape, scale=1.0, size=None)】

Gamma distribution
shape: shape parameter k
scale: Scale parameter θ

print(np.random.gamma(1, 2))
# 0.48471788864900295
 
print(np.random.gamma(9, 1, (2, 2)))
# [[10.71101589 16.68686166]
#  [ 5.22150652  5.87160223]]
 
print(np.random.gamma((1, 9), (2, 1), (5, 2)))
# [[ 3.4102224   6.31938602]
#  [ 0.03882968  7.71108072]
#  [ 2.62781738 10.70853193]
#  [ 5.07929584  5.83489052]
#  [ 1.50577929 11.21572879]]

S. Basic statistics

Calculate the basic statistic from the value of ndarray.

【max】

Maximum value

a = np.array([10, 20, 30, 40, 50])
print(np.max(a))
# 50

【argmax】

Maximum index

a = np.array([10, 20, 30, 40, 50])
print(np.argmax(a))
# 4

【min】

minimum value

a = np.array([10, 20, 30, 40, 50])
print(np.min(a))
# 10

【argmin】

Minimum index

a = np.array([10, 20, 30, 40, 50])
print(np.argmin(a))
# 0

【sum】

total

a = np.array([10, 20, 30, 40, 50])
print(np.sum(a))
# 150

【mean】

Average value

a = np.array([10, 20, 30, 40, 50])
print(np.mean(a))
# 30.0

【var】

Distributed

a = np.array([10, 20, 30, 40, 50])
print(np.var(a))
# 200.0

【std】

standard deviation

a = np.array([10, 20, 30, 40, 50])
print(np.std(a))
# 14.142135623730951

【cumsum】

Cumulative sum

a = np.array([10, 20, 30, 40, 50])
print(np.cumsum(a))
# [ 10  30  60 100 150]