Numpy
Arrays
Using reversed()
import numpy
def arrays(arr):
return numpy.array(list(reversed(arr)), float)
arr = input().strip().split(' ')
result = arrays(arr)
print(result)Using numpy.flipud()
import numpy
def arrays(arr):
return numpy.flipud(numpy.array(arr, float))
arr = input().strip().split(' ')
result = arrays(arr)
print(result)Shape and Reshape
Shape
The shape tool gives a tuple of array dimensions and can be used to change the dimensions of an array.
(a). Using shape to get array dimensions
import numpy
my__1D_array = numpy.array([1, 2, 3, 4, 5])
print my_1D_array.shape #(5,) -> 1 row and 5 columns
my__2D_array = numpy.array([[1, 2],[3, 4],[6,5]])
print my_2D_array.shape #(3, 2) -> 3 rows and 2 columns (b). Using shape to change array dimensions
import numpy
change_array = numpy.array([1,2,3,4,5,6])
change_array.shape = (3, 2)
print change_array
#Output
[[1 2]
[3 4]
[5 6]]Reshape
The reshape tool gives a new shape to an array without changing its data. It creates a new array and does not modify the original array itself.
import numpy
my_array = numpy.array([1,2,3,4,5,6])
print numpy.reshape(my_array,(3,2))
#Output
[[1 2]
[3 4]
[5 6]]Task
import numpy
print(numpy.reshape(numpy.array(list(map(int, input().split()))), (3, 3)))Transpose and Flatten
Transpose
We can generate the transposition of an array using the tool numpy.transpose.
It will not affect the original array, but it will create a new array.
import numpy
my_array = numpy.array([[1,2,3],
[4,5,6]])
print numpy.transpose(my_array)
#Output
[[1 4]
[2 5]
[3 6]]Flatten
The tool flatten creates a copy of the input array flattened to one dimension.
import numpy
my_array = numpy.array([[1,2,3],
[4,5,6]])
print my_array.flatten()
#Output
[1 2 3 4 5 6]Task
import numpy
n, m = map(int, input().split())
array = numpy.array([list(map(int, input().split())) for _ in range(n)])
print(numpy.transpose(array))
print(array.flatten())Concatenate
Two or more arrays can be concatenated together using the concatenate function with a tuple of the arrays to be joined:
import numpy
array_1 = numpy.array([1,2,3])
array_2 = numpy.array([4,5,6])
array_3 = numpy.array([7,8,9])
print numpy.concatenate((array_1, array_2, array_3))
#Output
[1 2 3 4 5 6 7 8 9]If an array has more than one dimension, it is possible to specify the axis along which multiple arrays are concatenated. By default, it is along the first dimension.
import numpy
array_1 = numpy.array([[1,2,3],[0,0,0]])
array_2 = numpy.array([[0,0,0],[7,8,9]])
print numpy.concatenate((array_1, array_2), axis = 1)
#Output
[[1 2 3 0 0 0]
[0 0 0 7 8 9]] Task
import numpy
n, m, p = map(int, input().split())
arr_n = numpy.array([list(map(int, input().split())) for _ in range(n)])
arr_m = numpy.array([list(map(int, input().split())) for _ in range(m)])
print(numpy.concatenate((arr_n, arr_m)))Zeroes and Ones
The zeros tool returns a new array with a given shape and type filled with 's.
import numpy
print numpy.zeros((1,2)) #Default type is float
#Output : [[ 0. 0.]]
print numpy.zeros((1,2), dtype = numpy.int) #Type changes to int
#Output : [[0 0]]The ones tool returns a new array with a given shape and type filled with 's.
import numpy
print numpy.ones((1,2)) #Default type is float
#Output : [[ 1. 1.]]
print numpy.ones((1,2), dtype = numpy.int) #Type changes to int
#Output : [[1 1]] Task
import numpy
inputs = tuple(map(int, input().split()))
print(numpy.zeros(inputs, int))
print(numpy.ones(inputs, int))Eye and Identity
The identity tool returns an identity array. An identity array is a square matrix with all the main diagonal elements as and the rest as . The default type of elements is float.
import numpy
print numpy.identity(3) #3 is for dimension 3 X 3
#Output
[[ 1. 0. 0.]
[ 0. 1. 0.]
[ 0. 0. 1.]]The eye tool returns a 2-D array with 's as the diagonal and 's elsewhere. The diagonal can be main, upper or lower depending on the optional parameter . A positive is for the upper diagonal, a negative is for the lower, and a (default) is for the main diagonal.
import numpy
print numpy.eye(8, 7, k = 1) # 8 X 7 Dimensional array with first upper diagonal 1.
#Output
[[ 0. 1. 0. 0. 0. 0. 0.]
[ 0. 0. 1. 0. 0. 0. 0.]
[ 0. 0. 0. 1. 0. 0. 0.]
[ 0. 0. 0. 0. 1. 0. 0.]
[ 0. 0. 0. 0. 0. 1. 0.]
[ 0. 0. 0. 0. 0. 0. 1.]
[ 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0.]]
print numpy.eye(8, 7, k = -2) # 8 X 7 Dimensional array with second lower diagonal 1.Task
import numpy
numpy.set_printoptions(legacy='1.13')
n, m = map(int, input().split())
print(numpy.eye(n, m, k=0))Array Mathematics
Basic mathematical functions operate element-wise on arrays. They are available both as operator overloads and as functions in the NumPy module.
import numpy
a = numpy.array([1,2,3,4], float)
b = numpy.array([5,6,7,8], float)
print a + b #[ 6. 8. 10. 12.]
print numpy.add(a, b) #[ 6. 8. 10. 12.]
print a - b #[-4. -4. -4. -4.]
print numpy.subtract(a, b) #[-4. -4. -4. -4.]
print a * b #[ 5. 12. 21. 32.]
print numpy.multiply(a, b) #[ 5. 12. 21. 32.]
print a / b #[ 0.2 0.33333333 0.42857143 0.5 ]
print numpy.divide(a, b) #[ 0.2 0.33333333 0.42857143 0.5 ]
print a % b #[ 1. 2. 3. 4.]
print numpy.mod(a, b) #[ 1. 2. 3. 4.]
print a**b #[ 1.00000000e+00 6.40000000e+01 2.18700000e+03 6.55360000e+04]
print numpy.power(a, b) #[ 1.00000000e+00 6.40000000e+01 2.18700000e+03 6.55360000e+04]
import numpy
n, m = map(int, input().split())
A = numpy.array([list(map(int, input().split())) for _ in range(n)])
B = numpy.array([list(map(int, input().split())) for _ in range(n)])
print(numpy.add(A, B))
print(numpy.subtract(A, B))
print(numpy.multiply(A, B))
print(numpy.floor_divide(A, B))
print(numpy.mod(A, B))
print(numpy.power(A, B))Floor, Ceil and Rint
The tool floor returns the floor of the input element-wise. The floor of is the largest integer where .
import numpy
my_array = numpy.array([1.1, 2.2, 3.3, 4.4, 5.5, 6.6, 7.7, 8.8, 9.9])
print numpy.floor(my_array) #[ 1. 2. 3. 4. 5. 6. 7. 8. 9.]The tool ceil returns the ceiling of the input element-wise. The ceiling of is the smallest integer where .
import numpy
my_array = numpy.array([1.1, 2.2, 3.3, 4.4, 5.5, 6.6, 7.7, 8.8, 9.9])
print numpy.ceil(my_array) #[ 2. 3. 4. 5. 6. 7. 8. 9. 10.]The rint tool rounds to the nearest integer of input element-wise.
import numpy
my_array = numpy.array([1.1, 2.2, 3.3, 4.4, 5.5, 6.6, 7.7, 8.8, 9.9])
print numpy.rint(my_array) #[ 1. 2. 3. 4. 6. 7. 8. 9. 10.]Task
import numpy
numpy.set_printoptions(legacy='1.13')
A = numpy.array(list(map(float, input().split())))
print(numpy.floor(A))
print(numpy.ceil(A))
print(numpy.rint(A))Sum and Prod
The sum tool returns the sum of array elements over a given axis.
import numpy
my_array = numpy.array([ [1, 2], [3, 4] ])
print numpy.sum(my_array, axis = 0) #Output : [4 6]
print numpy.sum(my_array, axis = 1) #Output : [3 7]
print numpy.sum(my_array, axis = None) #Output : 10
print numpy.sum(my_array) #Output : 10By default, the axis value is None. Therefore, it performs a sum over all the dimensions of the input array.
The prod tool returns the product of array elements over a given axis.
import numpy
my_array = numpy.array([ [1, 2], [3, 4] ])
print numpy.prod(my_array, axis = 0) #Output : [3 8]
print numpy.prod(my_array, axis = 1) #Output : [ 2 12]
print numpy.prod(my_array, axis = None) #Output : 24
print numpy.prod(my_array) #Output : 24By default, the axis value is None. Therefore, it performs the product over all the dimensions of the input array.
Task
import numpy
n, m = map(int, input().split())
arr = numpy.array([list(map(int, input().split())) for _ in range(n)])
print(numpy.product(numpy.sum(arr, axis=0), axis=0))Min and Max
The tool min returns the minimum value along a given axis.
import numpy
my_array = numpy.array([[2, 5],
[3, 7],
[1, 3],
[4, 0]])
print numpy.min(my_array, axis = 0) #Output : [1 0]
print numpy.min(my_array, axis = 1) #Output : [2 3 1 0]
print numpy.min(my_array, axis = None) #Output : 0
print numpy.min(my_array) #Output : 0By default, the axis value is None. Therefore, it finds the minimum over all the dimensions of the input array.
The tool max returns the maximum value along a given axis.
import numpy
my_array = numpy.array([[2, 5],
[3, 7],
[1, 3],
[4, 0]])
print numpy.max(my_array, axis = 0) #Output : [4 7]
print numpy.max(my_array, axis = 1) #Output : [5 7 3 4]
print numpy.max(my_array, axis = None) #Output : 7
print numpy.max(my_array) #Output : 7By default, the axis value is None. Therefore, it finds the maximum over all the dimensions of the input array.
Task
import numpy
n, m = map(int, input().split())
arr = numpy.array([list(map(int, input().split())) for _ in range(n)])
print(numpy.max(numpy.min(arr, axis=1), axis=0))Mean, Var, and Std
The mean tool computes the arithmetic mean along the specified axis.
import numpy
my_array = numpy.array([ [1, 2], [3, 4] ])
print numpy.mean(my_array, axis = 0) #Output : [ 2. 3.]
print numpy.mean(my_array, axis = 1) #Output : [ 1.5 3.5]
print numpy.mean(my_array, axis = None) #Output : 2.5
print numpy.mean(my_array) #Output : 2.5By default, the axis is None. Therefore, it computes the mean of the flattened array.
The var tool computes the arithmetic variance along the specified axis.
import numpy
my_array = numpy.array([ [1, 2], [3, 4] ])
print numpy.var(my_array, axis = 0) #Output : [ 1. 1.]
print numpy.var(my_array, axis = 1) #Output : [ 0.25 0.25]
print numpy.var(my_array, axis = None) #Output : 1.25
print numpy.var(my_array) #Output : 1.25By default, the axis is None. Therefore, it computes the variance of the flattened array.
The std tool computes the arithmetic standard deviation along the specified axis.
import numpy
my_array = numpy.array([ [1, 2], [3, 4] ])
print numpy.std(my_array, axis = 0) #Output : [ 1. 1.]
print numpy.std(my_array, axis = 1) #Output : [ 0.5 0.5]
print numpy.std(my_array, axis = None) #Output : 1.11803398875
print numpy.std(my_array) #Output : 1.11803398875By default, the axis is None. Therefore, it computes the standard deviation of the flattened array.
Task
import numpy
n, m = map(int, input().split())
arr = numpy.array([list(map(int, input().split())) for _ in range(n)])
print(numpy.mean(arr, axis=1))
print(numpy.var(arr, axis=0))
print(round(numpy.std(arr), 11))Dot and Cross
The dot tool returns the dot product of two arrays.
import numpy
A = numpy.array([ 1, 2 ])
B = numpy.array([ 3, 4 ])
print numpy.dot(A, B) #Output : 11The cross tool returns the cross product of two arrays.
import numpy
A = numpy.array([ 1, 2 ])
B = numpy.array([ 3, 4 ])
print numpy.cross(A, B) #Output : -2Task
import numpy
n = int(input())
A = numpy.array([list(map(int, input().split())) for _ in range(n)])
B = numpy.array([list(map(int, input().split())) for _ in range(n)])
print(numpy.dot(A, B))Inner and Outer
The inner tool returns the inner product of two arrays.
import numpy
A = numpy.array([0, 1])
B = numpy.array([3, 4])
print numpy.inner(A, B) #Output : 4The outer tool returns the outer product of two arrays.
import numpy
A = numpy.array([0, 1])
B = numpy.array([3, 4])
print numpy.outer(A, B) #Output : [[0 0]
# [3 4]]Task
import numpy
A = numpy.array(list(map(int, input().split())))
B = numpy.array(list(map(int, input().split())))
print(numpy.inner(A, B))
print(numpy.outer(A, B))Polynomials
The poly tool returns the coefficients of a polynomial with the given sequence of roots.
print numpy.poly([-1, 1, 1, 10]) #Output : [ 1 -11 9 11 -10]The roots tool returns the roots of a polynomial with the given coefficients.
print numpy.roots([1, 0, -1]) #Output : [-1. 1.]The polyint tool returns an antiderivative (indefinite integral) of a polynomial.
print numpy.polyint([1, 1, 1]) #Output : [ 0.33333333 0.5 1. 0. ]The polyder tool returns the derivative of the specified order of a polynomial.
print numpy.polyder([1, 1, 1, 1]) #Output : [3 2 1]The polyval tool evaluates the polynomial at specific value.
print numpy.polyval([1, -2, 0, 2], 4) #Output : 34The polyfit tool fits a polynomial of a specified order to a set of data using a least-squares approach.
print numpy.polyfit([0,1,-1, 2, -2], [0,1,1, 4, 4], 2)
#Output : [ 1.00000000e+00 0.00000000e+00 -3.97205465e-16]The functions polyadd, polysub, polymul, and polydiv also handle proper addition, subtraction, multiplication, and division of polynomial coefficients, respectively.
Task
import numpy
p = list(map(float, input().split()))
x = int(input())
print(numpy.polyval(p, x))Linear Algebra
The NumPy module also comes with a number of built-in routines for linear algebra calculations. These can be found in the sub-module linalg.
The linalg.det tool computes the determinant of an array.
print numpy.linalg.det([[1 , 2], [2, 1]]) #Output : -3.0The linalg.eig computes the eigenvalues and right eigenvectors of a square array.
vals, vecs = numpy.linalg.eig([[1 , 2], [2, 1]])
print vals #Output : [ 3. -1.]
print vecs #Output : [[ 0.70710678 -0.70710678]
# [ 0.70710678 0.70710678]]The linalg.inv tool computes the (multiplicative) inverse of a matrix.
print numpy.linalg.inv([[1 , 2], [2, 1]]) #Output : [[-0.33333333 0.66666667]
# [ 0.66666667 -0.33333333]]Other routines can be found here
Task
import numpy
n = int(input())
arr = numpy.array([list(map(float, input().split())) for _ in range(n)])
print(round(numpy.linalg.det(arr), 2))Last updated
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