NumPy Lib

MOST IMPORTANT ATTRIBUTES ATTRIBUTES

Python
array.ndim     # number of axes (dimensions) of the array
array.shape  # dimensions of the array, tuple of integers
array.size  # total number of elements in the array
array.itemsize  # size in bytes of each element
array.data  # buffer containing the array elements

ARRAY CREATION

Unless explicitly specified np.array tries to infer a good data type for the array that it creates.
The data type is stored in a special dtype object.

Python
var = np.array(sequence)  # creates array
var = np.asarray(sequence)  # convert input to array
var = np.ndarray(*sequence)  # creates multidimensional array
var = np.asanyarray(*sequence)  # convert the input to an ndarray
# nested sequences will be converted to multidimensional array

var = np.zeros(ndarray.shape)  # array with all zeros
var = np.ones(ndarray.shape)  # array with all ones
var = np.empty(ndarray.shape)  # array with random values
var = np.identity(n)  # identity array (n x n)

var = np.arange(start, stop, step)  # creates an array with parameters specified
var = np.linspace(start, stop, num_of_elements)  # step of elements calculated based on parameters

DATA TYPES FOR NDARRAYS

Python
var = array.astype(np.dtype)  # copy of the array, cast to a specified type
# return TypeError if casting fails

The numerical dtypes are named the same way: a type name followed by a number indicating the number of bits per element.

TYPE	TYPE CODE	DESCRIPTION
int8, uint8	i1, u1	Signed and unsigned 8-bit (1 byte) integer types
int16, uint16	i2, u2	Signed and unsigned 16-bit integer types
int32, uint32	i4, u4	Signed and unsigned 32-bit integer types
int64, uint64	i8, u8	Signed and unsigned 32-bit integer types
float16	f2	Half-precision floating point
float32	f4 or f	Standard single-precision floating point. Compatible with C float
float64, float128	f8 or d	Standard double-precision floating point. Compatible with C double and Python float object
float128	f16 or g	Extended-precision floating point
complex64, complex128, complex256	c8, c16, c32	Complex numbers represented by two 32, 64, or 128 floats, respectively
bool	?	Boolean type storing True and False values
object	O	Python object type
string_	`S<num>`	Fixed-length string type (1 byte per character), `<num>` is string length
unicode_	`U<num>`	Fixed-length unicode type, `<num>` is length

OPERATIONS BETWEEN ARRAYS AND SCALARS

Any arithmetic operations between equal-size arrays applies the operation element-wise.

array + scalar → element-wise addition ([1, 2, 3] + 2 = [3, 4, 5]) array - scalar → element-wise subtraction ([1 , 2, 3] - 2 = [-2, 0, 1]) array * scalar → element-wise multiplication ([1, 2, 3] * 3 = [3, 6, 9]) array / scalar → element-wise division ([1, 2, 3] / 2 = [0.5 , 1 , 1.5])

array_1 + array_2 → element-wise addition ([1, 2, 3] + [1, 2, 3] = [2, 4, 6]) array_1 - array_2 → element-wise subtraction ([1, 2, 4] - [3 , 2, 1] = [-2, 0, 2]) array_1 * array_2 → element-wise multiplication ([1, 2, 3] * [3, 2, 1] = [3, 4, 3]) array_1 / array_2 → element-wise division ([1, 2, 3] / [3, 2, 1] = [0.33, 1, 3])

SHAPE MANIPULATION

Python
np.reshape(array, new_shape)  # changes the shape of the array
np.ravel(array)  #  returns the array flattened
array.resize(shape)  # modifies the array itself
array.T  # returns the array transposed
np.transpose(array)     # returns the array transposed
np.swapaxes(array, first_axis, second_axis)  # interchange two axes of an array
# if array is an ndarray, then a view of it is returned; otherwise a new array is created

JOINING ARRAYS

Python
np.vstack((array1, array2))   # takes tuple, vertical stack of arrays (column wise)
np.hstack((array1, array2))  # takes a tuple, horizontal stack of arrays (row wise)
np.dstack((array1, array2)) # takes a tuple, depth wise stack of arrays (3rd dimension)
np.stack(*arrays, axis)  # joins a sequence of arrays along a new axis (axis is an int)
np.concatenate((array1, array2, ...), axis) # joins a sequence of arrays along an existing axis (axis is an int)

SPLITTING ARRAYS

Python
np.split(array, indices)  # splits an array into equall7 long sub-arrays (indices is int), if not possible raises error
np.vsplit(array, indices)  # splits an array equally into sub-arrays vertically (row wise) if not possible raises error
np.hsplit(array, indices)  # splits an array equally into sub-arrays horizontally (column wise) if not possible raises error
np.dsplit(array, indices)  # splits an array into equally sub-arrays along the 3rd axis (depth) if not possible raises error
np.array_split(array, indices) # splits an array into sub-arrays, arrays can be of different lengths

VIEW()

Python
var = array.view()  # creates a new array that looks at the same data
# slicing returns a view
# view shapes are separated but assignment changes all arrays

COPY()

Python
var = array.copy()  # creates a deep copy of the array

INDEXING, SLICING, ITERATING

1-dimensional → sliced, iterated and indexed as standard n-dimensional → one index per axis, index given in tuple separated by commas [i, j] (i, j) dots (...) represent as many colons as needed to produce complete indexing tuple

x[1, 2, ...] == [1, 2, :, :, :]
x[..., 3] == [:, :, :, :, 3]
x[4, ..., 5, :] == [4, :, :, 5, :] iteration on first index, use .flat() to iterate over each element
x[*bool] returns row with corresponding True index
x[condition] return only elements that satisfy condition
x[[*index]] return rows ordered by indexes
x[[*i], [*j]] return elements selected by tuple (i, j)
x[ np.ix_( [*i], [*j] ) ] return rectangular region

UNIVERSAL FUNCTIONS (ufunc)

Functions that performs element-wise operations (vectorization).

Python
np.abs(array)  # vectorized abs(), return element absolute value
np.fabs(array)  # faster abs() for non-complex values
np.sqrt(array)  # vectorized square root (x^0.5)
np.square(array) # vectorized square (x^2)
np.exp(array)  # vectorized natural exponentiation (e^x)
np.log(array)  # vectorized natural log(x)
np.log10(array)  # vectorized log10(x)
np.log2(array)  # vectorized log2(x)
np.log1p(array)  # vectorized log(1 + x)
np.sign(array)  # vectorized sign (1, 0, -1)
np.ceil(array)  # vectorized ceil()
np.floor(array)  # vectorized floor()
np.rint(array)     # vectorized round() to nearest int
np.modf(array)  #  vectorized divmod(), returns the fractional and integral parts of element
np.isnan(array)   # vectorized x == NaN, return boolean array
np.isinf(array)  # vectorized test for positive or negative infinity, return boolean array
np.isfineite(array)  # vectorized test fo finiteness, returns boolean array
np.cos(array)  # vectorized cos(x)
np.sin(array)  # vectorized sin(x)
np.tan(array)  # vectorized tan(x)
np.cosh(array)  # vectorized cosh(x)
np.sinh(array)   # vector sinh(x)
np.tanh(array)  # vectorized tanh(x)
np.arccos(array)  # vectorized arccos(x)
np.arcsinh(array)  # vectorized arcsinh(x)
np.arctan(array)  # vectorized arctan(x)
np.arccosh(array)  # vectorized arccosh(x)
np.arcsinh(array)  # vectorized arcsin(x)
np.arctanh(array)  # vectorized arctanh(x)
np.logical_not(array)  # vectorized not(x), equivalent to -array

np.add(x_array, y_array)  # vectorized addition
np.subtract(x_array, y_array)  # vectorized subtraction
np.multiply(x_array, y_array)  # vectorized multiplication
np.divide(x_array, y_array)  # vectorized division
np.floor_divide(x_array, y_array)  # vectorized floor division
np.power(x_array, y_array)  # vectorized power
np.maximum(x_array, y_array)  # vectorized maximum
np.minimum(x_array, y_array)  # vectorized minimum
np.fmax(x_array, y_array)  # vectorized maximum, ignores NaN
np.fmin(x_array, y_array)  # vectorized minimum, ignores NaN
np.mod(x_array, y_array)  # vectorized modulus
np.copysign(x_array, y_array)  #  vectorized copy sign from y_array to x_array
np.greater(x_array, y_array)  # vectorized x > y
np.less(x_array, y_array)  # vectorized x < y
np.greter_equal(x_array, y_array)  # vectorized x >= y
np.less_equal(x_array, y_array)  # vectorized x <= y
np.equal(x_array, y_array)  # vectorized x == y
np.not_equal(x_array, y_array)  # vectorized x != y
np.logical_and(x_array, y_array)  # vectorized x & y
np.logical_or(x_array, y_array)  # vectorized x | y
np.logical_xor(x_array, y_array)  # vectorized x ^ y

CONDITIONAL LOGIC AS ARRAY OPERATIONS

Python
np.where(condition, x, y)  # return x if condition == True, y otherwise

MATHEMATICAL AND STATISTICAL METHODS

np.method(array, args) or array.method(args).
Boolean values are coerced to 1 (True) and 0 (False).

Python
np.sum(array, axis=None)  # sum of array elements over a given axis
np.median(array, axis=None)  # median along the specified axis
np.mean(array, axis=None)  # arithmetic mean along the specified axis
np.average(array, axis=None)  #  weighted average along the specified axis
np.std(array, axis=None)  # standard deviation along the specified axis
np.var(array, axis=None)  # variance along the specified axis

np.min(array, axis=None)  # minimum value along the specified axis
np.max(array, axis=None)  # maximum value along the specified axis
np.argmin(array, axis=None)  # indices of the minimum values along an axis
np.argmax(array, axis=None)  # indices of the maximum values
np.cumsum(array, axis=None)  # cumulative sum of the elements along a given axis
np.cumprod(array, axis=None)  # cumulative sum of the elements along a given axis

METHODS FOR BOOLEAN ARRAYS

Python
np.all(array, axis=None)  # test whether all array elements along a given axis evaluate to True
np.any(array, axis=None)  # test whether any array element along a given axis evaluates to True

SORTING

Python
array.sort(axis=-1)  # sort an array in-place (axis = None applies on flattened array)
np.sort(array, axis=-1)  # return a sorted copy of an array (axis = None applies on flattened array)

SET LOGIC

Python
np.unique(array)  # sorted unique elements of an array
np.intersect1d(x, y)  # sorted common elements in x and y
np.union1d(x, y)  # sorte union of elements
np.in1d(x, y)  #  boolean array indicating whether each element of x is contained in y
np.setdiff1d(x, y)  # Set difference, elements in x that are not in y
np.setxor1d()  # Set symmetric differences; elements that are in either of the arrays, but not both

FILE I/O WITH ARRAYS

Python
np.save(file, array)  # save array to binary file in .npy format
np.savez(file, *array) # save several arrays into a single file in uncompressed .npz format
np.savez_compressed(file, *args, *kwargs)  # save several arrays into a single file in compressed .npz format
# *ARGS: arrays to save to the file. arrays will be saved with names "arr_0", "arr_1", and so on
# **KWARGS: arrays to save to the file. arrays will be saved in the file with the keyword names

np.savetxt(file, X, fmt="%.18e", delimiter=" ")   # save array to text file
# X: 1D or 2D
# FMT: Python Format Specification Mini-Language
# DELIMITER: {str} -- string used to separate values

np.load(file, allow_pickle=False)  # load arrays or pickled objects from .npy, .npz or pickled files
np.loadtxt(file, dtype=float, comments="#", delimiter=None)
# DTYPE: {data type} -- data-type of the resulting array
# COMMENTS: {str} -- characters used to indicate the start of a comment. None implies no comments
# DELIMITER: {str} -- string used to separate values

LINEAR ALGEBRA

Python
np.diag(array, k=0)  # extract a diagonal or construct a diagonal array
# K: {int} -- k>0 diagonals above main diagonal, k<0 diagonals below main diagonal (main diagonal k = 0)

np.dot(x ,y)  # matrix dot product
np.trace(array, offset=0, dtype=None, out=None)  # return the sum along diagonals of the array
# OFFSET: {int} -- offset of the diagonal from the main diagonal
# dtype: {dtype} -- determines the data-type of the returned array
# OUT: {ndarray} -- array into which the output is placed

np.linalg.det(A)  # compute the determinant of an array
np.linalg.eig(A)  # compute the eigenvalues and right eigenvectors of a square array
np.linalg.inv(A)  # compute the (multiplicative) inverse of a matrix
# A_inv satisfies dot(A, A_inv) = dor(A_inv, A) = eye(A.shape[0])

np.linalg.pinv(A)  # compute the (Moore-Penrose) pseudo-inverse of a matrix
np.linalg.qr()  # factor the matrix a as qr, where q is orthonormal and r is upper-triangular
np.linalg.svd(A)  # Singular Value Decomposition
np.linalg.solve(A, B)  # solve a linear matrix equation, or system of linear scalar equations AX = B
np.linalg.lstsq(A, B)  # return the least-squares solution to a linear matrix equation AX = B

RANDOM NUMBER GENERATION

Python
np.random.seed()
np.random.rand()
np.random.randn()
np.random.randint()
np.random.Generator.permutation(x)  # randomly permute a sequence, or return a permuted range
np.random.Generator.shuffle(x)  # Modify a sequence in-place by shuffling its contents

np.random.Generator.beta(a, b, size=None)  # draw samples from a Beta distribution
# A: {float, array floats} -- Alpha, > 0
# B: {int, tuple ints} -- Beta, > 0

np.random.Generator.binomial(n, p, size=None)  # draw samples from a binomial distribution
# N: {int, array ints} -- parameter of the distribution, >= 0
# P: {float, arrey floats} -- Parameter of the distribution, >= 0 and <= 1

np.random.Generator.chisquare(df, size=None)
# DF: {float, array floats} -- degrees of freedom, > 0

np.random.Generator.gamma(shape, scale=1.0, size=None)  # draw samples from a Gamma distribution
# SHAPE: {float, array floats} -- shape of the gamma distribution, != 0

np.random.Generator.normal(loc=0.0, scale=1.0, Size=None)  # draw random samples from a normal (Gaussian) distribution
# LOC: {float, all floats} -- mean ("centre") of distribution
# SCALE: {float, all floats} -- standard deviation of distribution, != 0

np.random.Generator.poisson(lam=1.0, size=None)  # draw samples from a Poisson distribution
# LAM: {float, all floats} -- expectation of interval, >= 0

np.random.Generator.uniform(low=0.0,high=1.0, size=None)  # draw samples from a uniform distribution
# LOW: {float, all floats} -- lower boundary of the output interval
# HIGH: {float, all floats} -- upper boundary of the output interval

np.random.Generator.zipf(a, size=None)  # draw samples from a Zipf distribution
# A: {float, all floats} -- distribution parameter, > 1