NumPy–Functions

NumPy–Functions

Numpy is a python package used for scientific computing. So certainly, it supports a vast variety of functions used for computation. The various functions supported by numpy are mathematical, financial, universal, windows, and logical functions. Universal functions are used for array broadcasting, typecasting, and several other standard features. While windows functions are used in signal processing. We will be learning mathematical functions in detail in this article.

Mathematical Functions in NumPy

Numpy is written purely in C language. Hence, its mathematical functions are closely associated with functions present is math.h library in C.

1. Arithmetic Functions

   Function	Description
   add(arr1, arr2,..)	Add arrays element wise
   reciprocal(arr)	Returns reciprocal of elements of the argument array
   negative(arr)	Returns numerical negative of elements of an array
   multiply(arr1,arr2,…)	Multiply arrays element wise
   divide(arr1,arr2)	Divide arrays element wise
   power(arr1,arr2)	Return the first array with its each of its elements raised to the power of elements in the second array (element wise)
   subtract(arr1,arr2,…)	Subtract arrays element wise
   true_divide(arr1,arr2)	Returns true_divide of an array element wise
   floor_divide(arr1,arr2)	Returns floor after dividing an array element wise
   float_power(arr1,arr2)	Return the first array with its each of its elements raised to the power of elements in the second array (elementwise)
   fmod(arr1,arr2)	Returns floor of the remainder after division elementwise
   mod(arr1,arr2)	Returns remainder after division elementwise
   remainder(arr1,arr2)	Returns remainder after division elementwise
   divmod(arr1,arr2)	Returns remainder and quotient after division elementwise

   The above-mentioned operations can be performed in the following ways :

   In the given code snippet, we try to do some basic operations on the arguments, array a and array b.

   Code:

   import numpy as np
   a = np.array([10,20,30])
   b= np.array([1,2,3])
   print("addition of a and b :",np.add(a,b))
   print("multiplication of a and b :",np.multiply(a,b))
   print("subtraction of a and b :",np.subtract(a,b))
   print("a raised to b is:",np.power(a,b))
   

   Output:

   

   In this code snippet, we try to perform division and related operations on the arguments, array a and array b. We can notice the difference between mod, remainder, divmod and simple division.

   Code:

   import numpy as np
   a = np.array([10,20,30])
   b= np.array([2,3,4])
   print("division of a and b :",np.divide(a,b))
   print("true division of a  :",np.true_divide(a,b))
   print("floor_division of a and b :",np.floor_divide(a,b))
   print("float_power of a raised to b :",np.float_power(a,b))
   print("fmod of a and b :",np.fmod(a,b))
   print("mod of a and b :",np.mod(a,b))
   print("quotient and remainder of a and b :",np.divmod(a,b))
   print("remainders when a/b :",np.remainder(a,b))
   

   Output:

   

2. Trigonometric Functions

   Function	Description
   sin(arr)	Returns trigonometric sine element wise
   cos(arr)	Returns trigonometric cos element wise
   tan(arr)	Returns trigonometric tan element wise
   arcsin(arr)	Returns trigonometric inverse sine element wise
   arccos(arr)	Returns trigonometric inverse cosine element wise
   arctan(arr)	Returns trigonometric inverse tan element wise
   hypot(a,b)	Returns hypotenuse of a right triangle with perpendicular and base as arguments
   degrees(arr) rad2deg(arr)	Covert input angles from radians to degrees
   radians(arr) deg2rad(arr)	Covert input angles from degrees to radians

   Here is an example of how to use trigonometric functions.

   Code:

   import numpy as np
   angles = np.array([0,np.pi/2, np.pi])     -----> input array angles
   sin_angles = np.sin(angles)
   cosine_angles = np.cos(angles)
   tan_angles = np.tan(angles)
   rad2degree = np.degrees(angles)
   print("sin of angles:",sin_angles)
   print("cosine of angles:",cosine_angles)
   print("tan of angles:",tan_angles)
   print("angles in radians",rad2degree)
   

   Output:

   

3. Logarithmic and Exponential Functions

   Function	Description
   exp(arr)	Returns exponential of an input array element wise
   expm1(arr)	Returns exponential exp(x)-1 of an input array element wise
   exp2(arr)	Returns exponential 2**x of all elements in an array
   log(arr)	Returns natural log of an input array element wise
   log10(arr)	Returns log base 10 of an input array element wise
   log2(arr)	Returns log base 2 of an input array element wise
   logaddexp(arr)	Returns logarithm of the sum of exponentiations of all inputs
   logaddexp2(arr)	Returns logarithm of the sum of exponentiations of the inputs in base 2

   Here is an example of using logarithmic functions:

   Code:

   import numpy as np
   a = np.array([1,2,3,4,5])
   a_log = np.log(a)
   a_exp = np.exp(a)
   print("log of input array a is:",a_log)
   print("exponent of input array a is:",a_exp)
   

   Output:

   

4. Rounding Functions

   Function	Description
   around(arr,decimal)	Rounds the elements of an input array upto given decimal places
   round_(arr,decimal)	Rounds the elements of an input array upto given decimal places
   rint(arr)	Round the elements of an input array to the nearest integer towards zero
   fix(arr)	Round the elements of an input array to the nearest integer towards zero
   floor(arr)	Returns floor of input array element wise
   ceil(arr)	Returns ceiling of input array element wise
   trunc(arr)	Return the truncated value of an input array element wise

   Example of using rounding functions with numpy arrays:

   Code:

   importnumpy as np
   a = np.array([1.23,4.165,3.8245])
   rounded_a = np.round_(a,2)
   print(rounded_a)
   

   Output:

   

   Code:

   floor_a = np.floor(a)
   print(floor_a)
   

   Output:

   

5. Miscellaneous Functions

   Function	Description
   sqrt(arr)	Returns the square root of an input array element wise
   cbrt(arr)	Returns cube root of an input array element wise
   absolute(arr)	Returns absolute value each element in an input array
   maximum(arr1,arr2,…)	Returns element wise maximum of the input arrays
   minimum(arr1,arr2,…)	Returns element wise minimum of the input arrays
   interp(arr, xp, fp)	Calculates one-dimensional linear interpolation
   convolve(arr, v)	Returns linear convolution of two one-dimensional sequences
   clip(arr, arr_min, arr_max)	Limits the values in an input array

   Some examples using the above functions.

   Finding the Maxima:

   Code:

   import numpy as np
   a = [1,2,3] b = [3,1,2] maximum_elementwise = np.maximum(a,b)
   print("maxima are:",maximum_elementwise)
   

   Output:

   

   Clipping an array between max_limit and min_limit:

   Code:

   import numpy as np
   a = [1,2,3] b = [3,1,2] limiting_a = np.clip(a,0,2)
   print("limiting a between 0 and 2:",limiting_a)
   

   Output:

   

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