Mavzu: python tilida matematik hisoblashlarni realizatsiya qilish

Matematik funksiyalar. NumPy massiv elementlarida standart arifmetik amallarni amalga oshiradi.
3.3-jadval. Massivlar ustidagi arifmetik amallar

Funksiya	tavsifi
add(x, y)	elementlar bo'yicha qo'shish
subtract(x, y)	elementlar bo‘yicha ayirish
multiply(x, y)	elementlar bo'yicha ko'paytirish
divide(x, y)	elementlar bo'yicha bo'lish
power(x,y)	elementlar boʻyicha darajaga ko`tarish
negative(x)	massiv elementlarining ishorasini o'zgartiradi

Massivlarda elementar arifmetik amallardan foydalanishga misollar:

import numpy as np
a0 = np.linspace(1., 10., 10).reshape(2, 5)
print('a0:\n', a0)
a1 = np.ones(10).reshape(2, 5)
a1 = np.add(a1, 1.)
print('a1:\n', a1)
a2 = np.add(a0, a1)
print('a2:\n', a2)
a3 = np.multiply(a0, a1)
print('а3:\n', a3)
a4=np.power(a0, a1)
print('a4:\n',a4)
Natija:
a0:
[[ 1. 2. 3. 4. 5.]
[ 6. 7. 8. 9. 10.]]
a1:
[[2. 2. 2. 2. 2.]
[2. 2. 2. 2. 2.]]
a2:
[[ 3. 4. 5. 6. 7.]
[ 8. 9. 10. 11. 12.]]
a3:
[[ 2. 4. 6. 8. 10.]
[12. 14. 16. 18. 20.]]
a4:
[[ 1. 4. 9. 16. 25.]
[ 36. 49. 64. 81. 100.]]

Massivlarda element bo`yicha bajariladigan boshqa funksiyalar:

Trigonometrik: sin(x), cos(x), tan(x), arcsin(x), arccos(x), arctan(x), hypot(x, y), arctan2(x,y), degrees(x), radians(x);
Giperbolik: sinh(x), cosh(x), tanh(x), arcsinh(x), arccosh(x), arctanh(x);
Eksponensial va algoritmik: exp(x), expm1(x) (=exp(x)-1), log(x), logl0(x), log2(x), log1p(x)(=log(1+x)).
Boshqa funksiyalar Python standart kutubxonasining math modulidagi matematik funksiyalar yozuviga mos keladi (3.1-jadvalga qarang).
import numpy as np
a0 = np.linspace(0., np.pi, 9)
print('a0:\n', a0)
a1 = np.sin(a0)
print('a1:\n', a1)
a2 = np.cos(a0)
print('a2:\n', a2)
a3 = np.multiply(a1, a1) + np.multiply(a2, a2) - 1.
print('а3:\n', a3)
Natija:
a0:
[0. 0.39269908 0.78539816 1.17809725 1.57079633 1.96349541
2.35619449 2.74889357 3.14159265]
a1:
[0.00000000e+00 3.82683432e-01 7.07106781e-01 9.23879533e-01
1.00000000e+00 9.23879533e-01 7.07106781e-01 3.82683432e-01
1.22464680e-16]
a2:
[ 1.00000000e+00 9.23879533e-01 7.07106781e-01 3.82683432e-01
6.12323400e-17 -3.82683432e-01 -7.07106781e-01 -9.23879533e-01
-1.00000000e+00]
а3:
[0.00000000e+00 0.00000000e+00 2.22044605e-16 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00]

Elementlari kompleks sonlardan iborat bo`lgan massivlar bilan ishlash uchun quyidagi funksiyalar mavjud: angle(x) (phase(x) funksiyasiga oʻxshash), rcal(x), imag(x) va conj(.x), bu kompleks-bog`langan elementli massivni qaytaradi.

import numpy as np
a0 = np.linspace(1., 10., 10).reshape(2, 5)
print('а0:\n', a0)
a1 = np.add(a0, 1.j)
print('a1:\n', a1)
a2 = np.conj(a1)
print('a2:\n', a2)
a3 = np.real(a1)
print('а3:\n', a3)
a4 = np.imag(a1)
print('a4:\n', a4)
Natija:
а0:
[[ 1. 2. 3. 4. 5.]
[ 6. 7. 8. 9. 10.]]
a1:
[[ 1.+1.j 2.+1.j 3.+1.j 4.+1.j 5.+1.j]
[ 6.+1.j 7.+1.j 8.+1.j 9.+1.j 10.+1.j]]
a2:
[[ 1.-1.j 2.-1.j 3.-1.j 4.-1.j 5.-1.j]
[ 6.-1.j 7.-1.j 8.-1.j 9.-1.j 10.-1.j]]
а3:
[[ 1. 2. 3. 4. 5.]
[ 6. 7. 8. 9. 10.]]
a4:
[[1. 1. 1. 1. 1.]
[1. 1. 1. 1. 1.]]