{"id":88793,"date":"2023-12-04T18:00:28","date_gmt":"2023-12-04T12:30:28","guid":{"rendered":"https:\/\/techvidvan.com\/tutorials\/?p=88793"},"modified":"2023-12-04T18:00:28","modified_gmt":"2023-12-04T12:30:28","slug":"numpy-mathematical-functions","status":"publish","type":"post","link":"https:\/\/techvidvan.com\/tutorials\/numpy-mathematical-functions\/","title":{"rendered":"NumPy Mathematical Functions"},"content":{"rendered":"

In this tutorial, we will explore a variety of mathematical functions that Numpy offers, along with examples demonstrating their usage. Let’s dive in and see how these functions can enhance your data manipulation and analysis tasks.<\/p>\n

Trigonometric Functions<\/h2>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Function<\/span><\/td>\nDescription<\/span><\/td>\n<\/tr>\n
sin(x, \/[, out, where, casting, …])<\/span><\/td>\nCompute the sine of each element in the input array, element-wise.<\/span><\/td>\n<\/tr>\n
cos(x, \/[, out, where, casting, …])<\/span><\/td>\nCompute the cosine of each element in the input array, element-wise.<\/span><\/td>\n<\/tr>\n
tan(x, \/[, out, where, casting, …])<\/span><\/td>\nCompute the tangent of each element in the input array, element-wise.<\/span><\/td>\n<\/tr>\n
arcsin(x, \/[, out, where, casting, …])<\/span><\/td>\nCompute the inverse sine (arcsine) of each element in the input array, element-wise.<\/span><\/td>\n<\/tr>\n
arccos(x, \/[, out, where, casting, …])<\/span><\/td>\nCompute the inverse cosine (arccosine) of each element in the input array, element-wise.<\/span><\/td>\n<\/tr>\n
arctan(x, \/[, out, where, casting, …])<\/span><\/td>\nCompute the inverse tangent (arctangent) of each element in the input array, element-wise.<\/span><\/td>\n<\/tr>\n
hypot(x1, x2, \/[, out, where, casting, …])<\/span><\/td>\nCompute the hypotenuse of a right triangle given the “legs” x1 and x2.<\/span><\/td>\n<\/tr>\n
arctan2(x1, x2, \/[, out, where, casting, …])<\/span><\/td>\nCompute the arctangent of x1\/x2 with the correct quadrant, element-wise.<\/span><\/td>\n<\/tr>\n
degrees(x, \/[, out, where, casting, …])<\/span><\/td>\nConvert angles from radians to degrees, element-wise.<\/span><\/td>\n<\/tr>\n
radians(x, \/[, out, where, casting, …])<\/span><\/td>\nConvert angles from degrees to radians, element-wise.<\/span><\/td>\n<\/tr>\n
unwrap(p[, discont, axis, period])<\/span><\/td>\nUnwrap an array by complementing large deltas with respect to the specified period.<\/span><\/td>\n<\/tr>\n
deg2rad(x, \/[, out, where, casting, …])<\/span><\/td>\nConvert angles from degrees to radians, element-wise.<\/span><\/td>\n<\/tr>\n
rad2deg(x, \/[, out, where, casting, …])<\/span><\/td>\nConvert angles from radians to degrees, element-wise.<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Compute Tangent – numpy.tan()<\/h4>\n

The numpy.tan() function computes the tangent of each element in the input array.<\/p>\n

import numpy as np\n\n# Input array\narr = np.array([0, np.pi\/4, np.pi\/2])\n\n# Compute tangent\ntan_values = np.tan(arr)<\/pre>\n
Output<\/strong>
\ntan_values:<\/strong> [0.00000000e+00 1.00000000e+00 1.63312394e+16]<\/p>\n
Inverse Sine – numpy.arcsin()<\/h4>\n
The numpy.arcsin() function calculates the inverse sine (in radians) for each element in the input array.<\/p>\n
import numpy as np\n\n# Input array\narr = np.array([0, 0.5, 1])\n\n# Compute inverse sine\narcsin_values = np.arcsin(arr)<\/pre>\n
Output<\/strong>
\narcsin_values:<\/strong> [0. 0.52359878 1.57079633]<\/p>\n
Trigonometric Inverse Cosine – numpy.arccos()<\/h4>\n
The numpy.arccos() function calculates the inverse cosine (in radians) for each element in the input array.<\/p>\n
import numpy as np\n\n# Input array\narr = np.array([1, 0.5, 0])\n\n# Compute inverse cosine\narccos_values = np.arccos(arr)<\/pre>\n
Output<\/strong>
\narccos_values:<\/strong> [0. 1.04719755 1.57079633]<\/p>\n
Trigonometric Inverse Tangent – numpy.arctan()<\/h4>\n
The numpy.arctan() function calculates the inverse tangent (in radians) for each element in the input array.<\/p>\n
import numpy as np\n\n# Input array\narr = np.array([0, 1, np.inf])\n\n# Compute inverse tangent\narctan_values = np.arctan(arr)<\/pre>\n
Output<\/strong>
\narctan_values:<\/strong> [0. 0.78539816 1.57079633]<\/p>\n
Element-wise Arc Tangent – numpy.arctan2()<\/h4>\n
The numpy.arctan2() function calculates the element-wise arc tangent of x1\/x2 while correctly choosing the quadrant.<\/p>\n
import numpy as np\n\n# Input arrays\nx1 = np.array([1, -1, 1])\nx2 = np.array([1, 1, -1])\n\n# Compute element-wise arc tangent\narctan2_values = np.arctan2(x1, x2)<\/pre>\n
Output<\/strong>
\narctan2_values:<\/strong> [ 0.78539816 -0.78539816 2.35619449]<\/p>\n
Convert Angles to Degrees – numpy.degrees()<\/h4>\n
The numpy.degrees() function converts angles from radians to degrees.<\/p>\n
import numpy as np\n\n# Input array in radians\narr_radians = np.array([0, np.pi\/2, np.pi])\n\n# Convert radians to degrees\narr_degrees = np.degrees(arr_radians)<\/pre>\n
Output<\/strong>
\narr_degrees:<\/strong> [ 0. 90. 180.]<\/p>\n
Convert Angles to Radians – numpy.radians()<\/h4>\n
The numpy.radians() function converts angles from degrees to radians.<\/p>\n
import numpy as np\n\n# Input array in degrees\narr_degrees = np.array([0, 90, 180])\n\n# Convert degrees to radians\narr_radians = np.radians(arr_degrees)<\/pre>\n
Output<\/strong>
\narr_radians:<\/strong> [0. 1.57079633 3.14159265]<\/p>\n
Hyperbolic Functions<\/h3>\n\n\n\n\n\n\n\n\n\n
Function<\/span><\/td>\nDescription<\/span><\/td>\n<\/tr>\n
sinh(x, \/[, out, where, casting, …])<\/span><\/td>\nCompute the hyperbolic sine (sinh) of each element in the input array, element-wise.<\/span><\/td>\n<\/tr>\n
cosh(x, \/[, out, where, casting, …])<\/span><\/td>\nCompute the hyperbolic cosine (cosh) of each element in the input array, element-wise.<\/span><\/td>\n<\/tr>\n
tanh(x, \/[, out, where, casting, …])<\/span><\/td>\nCompute the hyperbolic tangent (tanh) of each element in the input array, element-wise.<\/span><\/td>\n<\/tr>\n
arcsinh(x, \/[, out, where, casting, …])<\/span><\/td>\nCompute the inverse hyperbolic sine (arcsinh) of each element in the input array, element-wise.<\/span><\/td>\n<\/tr>\n
arccosh(x, \/[, out, where, casting, …])<\/span><\/td>\nCompute the inverse hyperbolic cosine (arccosh) of each element in the input array, element-wise.<\/span><\/td>\n<\/tr>\n
arctanh(x, \/[, out, where, casting, …])<\/span><\/td>\nCompute the inverse hyperbolic tangent (arctanh) of each element in the input array, element-wise.<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
Compute Hyperbolic Tangent – numpy.tanh()<\/h4>\n
The numpy.tanh() function computes the hyperbolic tangent of each element in the input array.<\/p>\n
import numpy as np\n\n# Input array\narr = np.array([0, 0.5, 1])\n\n# Compute hyperbolic tangent\ntanh_values = np.tanh(arr)<\/pre>\n
Output<\/strong>
\ntanh_values:<\/strong> [0. 0.46211716 0.76159416]<\/p>\n
Inverse Hyperbolic Sine – numpy.arcsinh()<\/h4>\n
The numpy.arcsinh() function calculates the inverse hyperbolic sine for each element in the input array.<\/p>\n
import numpy as np\n\n# Input array\narr = np.array([0, 1, 2])\n\n# Compute inverse hyperbolic sine\narcsinh_values = np.arcsinh(arr)<\/pre>\n
Output<\/strong>
\narcsinh_values:<\/strong> [0. 0.88137359 1.44363548]<\/p>\n
Inverse Hyperbolic Cosine – numpy.arccosh()<\/h4>\n
The numpy.arccosh() function calculates the inverse hyperbolic cosine for each element in the input array.<\/p>\n
import numpy as np\n\n# Input array\narr = np.array([1, 2, 3])\n\n# Compute inverse hyperbolic cosine\narccosh_values = np.arccosh(arr)<\/pre>\n
Output<\/strong>
\narccosh_values:<\/strong> [0. 1.3169579 1.76274717]<\/p>\n
Inverse Hyperbolic Tangent – numpy.arctanh()<\/h4>\n
The numpy.arctanh() function calculates the inverse hyperbolic tangent for each element in the input array.<\/p>\n
import numpy as np\n\n# Input array\narr = np.array([0, 0.5, 0.9])\n\n# Compute inverse hyperbolic tangent\narctanh_values = np.arctanh(arr)<\/pre>\n
Output<\/strong>
\narctanh_values:<\/strong> [0. 0.54930614 1.47221949]<\/p>\n
Functions for Rounding<\/h3>\n\n\n\n\n\n\n\n\n\n\n
Function<\/span><\/td>\nDescription<\/span><\/td>\n<\/tr>\n
round(a[, decimals, out])<\/span><\/td>\nRound each element in the array ‘a’ to the given number of ‘decimals’ places.<\/span><\/td>\n<\/tr>\n
around(a[, decimals, out])<\/span><\/td>\nRound each element in the array ‘a’ to the given number of ‘decimals’ places, using “round half to even” rounding.<\/span><\/td>\n<\/tr>\n
rint(x, \/[, out, where, casting, order, …])<\/span><\/td>\nRound elements of the array ‘x’ to the nearest integer.<\/span><\/td>\n<\/tr>\n
fix(x[, out])<\/span><\/td>\nRound each element in the array ‘x’ to the nearest integer towards zero (truncate).<\/span><\/td>\n<\/tr>\n
floor(x, \/[, out, where, casting, order, …])<\/span><\/td>\nCompute the floor (round down) of each element in the array ‘x’.<\/span><\/td>\n<\/tr>\n
ceil(x, \/[, out, where, casting, order, …])<\/span><\/td>\nCompute the ceiling (round up) of each element in the array ‘x’.<\/span><\/td>\n<\/tr>\n
trunc(x, \/[, out, where, casting, order, …])<\/span><\/td>\nCompute the truncated value of each element in the array ‘x’, removing the decimal part.<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
Round to Nearest Integer Towards Zero – numpy.rint()<\/h4>\n
The numpy.rint() function rounds the elements of the input array to the nearest integer towards zero.<\/p>\n
import numpy as np\n\n# Input array\narr = np.array([1.1, 2.5, 3.9])\n\n# Round to nearest integer towards zero\nrint_values = np.rint(arr)<\/pre>\n
Output<\/strong>
\nrint_values:<\/strong> [1. 2. 3.]<\/p>\n
Round to Nearest Integer Towards Zero – numpy.fix()<\/h4>\n
The numpy.fix() function rounds the elements of the input array to the nearest integer towards zero.<\/p>\n
import numpy as np\n\n# Input array\narr = np.array([1.1, 2.5, 3.9])\n\n# Round to nearest integer towards zero\nfix_values = np.fix(arr)<\/pre>\n
Output<\/strong>
\nfix_values:<\/strong> [1. 2. 3.]<\/p>\n
Return the Floor of the Input – numpy.floor()<\/h4>\n
The numpy.floor() function returns the largest integer not greater than the input array element-wise.<\/p>\n
import numpy as np\n\n# Input array\narr = np.array([1.1, 2.5, 3.9])\n\n# Return floor of input\nfloor_values = np.floor(arr)<\/pre>\n
Output<\/strong>
\nfloor_values:<\/strong> [1. 2. 3.]<\/p>\n
Return the Ceiling of the Input – numpy.ceil()<\/h4>\n
The numpy.ceil() function returns the smallest integer not less than the input array element-wise.<\/p>\n
  \nimport numpy as np\n\n# Input array\narr = np.array([1.1, 2.5, 3.9])\n\n# Return ceiling of input\nceil_values = np.ceil(arr)<\/pre>\n
Output<\/strong>
\nceil_values:<\/strong> [2. 3. 4.]<\/p>\n
Return the Truncated Value – numpy.trunc()<\/h4>\n
The numpy.trunc() function returns the truncated value of the input array element-wise.<\/p>\n
import numpy as np\n\n# Input array\narr = np.array([1.1, 2.5, 3.9])\n\n# Return truncated values\ntrunc_values = np.trunc(arr)<\/pre>\n
Output<\/strong>
\ntrunc_values:<\/strong> [1. 2. 3.]<\/p>\n
Exponents and Logarithms Functions<\/h3>\n\n\n\n\n\n\n\n\n\n\n\n\n
Function<\/span><\/td>\nDescription<\/span><\/td>\n<\/tr>\n
exp(x, \/[, out, where, casting, …])<\/span><\/td>\nCompute the exponential (e^x) of each element in the input array.<\/span><\/td>\n<\/tr>\n
expm1(x, \/[, out, where, casting, …])<\/span><\/td>\nCompute e^x – 1 for each element in the input array.<\/span><\/td>\n<\/tr>\n
exp2(x, \/[, out, where, casting, …])<\/span><\/td>\nCompute 2^p for each p in the input array.<\/span><\/td>\n<\/tr>\n
log(x, \/[, out, where, casting, …])<\/span><\/td>\nCompute the natural logarithm (base e) of each element in the input array.<\/span><\/td>\n<\/tr>\n
log10(x, \/[, out, where, casting, …])<\/span><\/td>\nCompute the base 10 logarithm of each element in the input array.<\/span><\/td>\n<\/tr>\n
log2(x, \/[, out, where, casting, …])<\/span><\/td>\nCompute the base 2 logarithm of each element in the input array.<\/span><\/td>\n<\/tr>\n
log1p(x, \/[, out, where, casting, …])<\/span><\/td>\nCompute the natural logarithm of (1 + x) for each element in the input array.<\/span><\/td>\n<\/tr>\n
logaddexp(x1, x2, \/[, out, where, casting, …])<\/span><\/td>\nCompute the logarithm of the sum of exponentials of ‘x1’ and ‘x2’.<\/span><\/td>\n<\/tr>\n
logaddexp2(x1, x2, \/[, out, where, casting, …])<\/span><\/td>\nCompute the logarithm of the sum of exponentials in base-2 of ‘x1’ and ‘x2’.<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
Calculate exp(x) – 1 – numpy.expm1()<\/h4>\n
The numpy.expm1() function calculates exp(x) – 1 for each element in the input array.<\/p>\n
import numpy as np\n\n# Input array\narr = np.array([0, 0.5, 1])\n\n# Calculate exp(x) - 1\nexpm1_values = np.expm1(arr)<\/pre>\n
Output<\/strong>
\nexpm1_values:<\/strong> [0. 0.64872127 1.71828183]<\/p>\n
Calculate 2**p – numpy.exp2()<\/h4>\n
The numpy.exp2() function calculates 2**p for each element in the input array.<\/p>\n
import numpy as np\n\n# Input array\narr = np.array([0, 1, 2])\n\n# Calculate 2**p\nexp2_values = np.exp2(arr)<\/pre>\n
Output<\/strong>
\nexp2_values:<\/strong> [1. 2. 4.]<\/p>\n
Return the Base 10 Logarithm – numpy.log10()<\/h4>\n
The numpy.log10() function returns the base 10 logarithm of the input array element-wise.<\/p>\n
import numpy as np\n\n# Input array\narr = np.array([1, 10, 100])\n\n# Return base 10 logarithm\nlog10_values = np.log10(arr)<\/pre>\n
Output<\/strong>
\nlog10_values:<\/strong> [0. 1. 2.]<\/p>\n
Return the Base-2 Logarithm – numpy.log2()<\/h4>\n
The numpy.log2() function returns the base-2 logarithm of the input array element-wise.<\/p>\n
import numpy as np\n\n# Input array\narr = np.array([1, 2, 4])\n\n# Return base-2 logarithm\nlog2_values = np.log2(arr)<\/pre>\n
Output<\/strong>
\nlog2_values:<\/strong> [0. 1. 2.]<\/p>\n
Returns the Natural Logarithm of One Plus the Input given – numpy.log1p()<\/h4>\n
The numpy.log1p() function returns the natural logarithm of 1 + x for each element in the input array.<\/p>\n
import numpy as np\n\n# Input array\narr = np.array([0, 0.5, 1])\n\n# Return natural logarithm of 1 + x\nlog1p_values = np.log1p(arr)<\/pre>\n
Output<\/strong>
\nlog1p_values:<\/strong> [0. 0.40546511 0.69314718]<\/p>\n
Logarithm of the Sum of Exponentiations – numpy.logaddexp()<\/h4>\n
The numpy.logaddexp() function calculates the logarithm of the sum of exponentiations of the inputs.<\/p>\n
import numpy as np\n\n# Inputs\nx = np.array([1, 2, 3])\ny = np.array([0.5, 1, 1.5])\n\n# Logarithm of the sum of exponentiations\nlogaddexp_values = np.logaddexp(x, y)<\/pre>\n
Output<\/strong><\/p>\n
logaddexp_values:<\/strong> [1.31326169 2.12692801 3.20951501]<\/span><\/p>\n
The logarithm of the Sum of Exponentiations in Base-2 – numpy.logaddexp2()<\/h4>\n
The numpy.logaddexp2() function calculates the logarithm of the sum of exponentiations in base-2.<\/p>\n
  \nimport numpy as np\n\n# Inputs\nx = np.array([1, 2, 3])\ny = np.array([0.5, 1, 1.5])\n\n# Logarithm of the sum of exponentiations in base-2\nlogaddexp2_values = np.logaddexp2(x, y)<\/pre>\n
Output<\/strong>
\nlogaddexp2_values:<\/strong> [1.5849625 2.32192809 3.169925 ]<\/p>\n
Whether you’re a data scientist exploring trends in a massive dataset, an engineer simulating physical systems, or a researcher solving mathematical problems, NumPy’s functions have your back.<\/p>\n
Conclusion<\/h3>\n
In this blog, we’ve only scratched the surface of the myriad mathematical functions NumPy has to offer. To fully harness their power, one must continue exploring, experimenting, and applying them to real-world challenges.<\/p>\n
As you continue your journey in the world of Python programming and data analysis, remember that NumPy’s mathematical functions are your trusty companions, ready to assist you in unravelling the mysteries of the mathematical universe and turning data into knowledge.<\/p>\n
Remember to visit TechVidvan for more insightful tutorials and resources on data manipulation, analysis, and more. Happy coding with Numpy!<\/p>\n","protected":false},"excerpt":{"rendered":"
In this tutorial, we will explore a variety of mathematical functions that Numpy offers, along with examples demonstrating their usage. 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