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Scientific Computing Articles
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Calculating the Minkowski distance using SciPy
The Minkowski distance, a generalized form of Euclidean and Manhattan distance, is the distance between two points. It is mostly used for distance similarity of vectors. Below is the generalized formula to calculate Minkowski distance in n-dimensional space −$$\mathrm{D= \big[\sum_{i=1}^{n}|r_i-s_i|^p\big]^{1/p}}$$Here, si and ri are data points.n denotes the n-space.p represents the order of the normSciPy provides us with a function named minkowski that returns the Minkowski Distance between two points. Let’s see how we can calculate the Minkowski distance between two points using SciPy library −Example# Importing the SciPy library from scipy.spatial import distance # Defining the points A = ...
Read MoreCalculating the Manhattan distance using SciPy
The Manhattan distance, also known as the City Block distance, is calculated as the sum of absolute differences between the two vectors. It is mostly used for the vectors that describe objects on a uniform grid such as a city block or chessboard. Below is the generalized formula to calculate Manhattan distance in n-dimensional space −$$\mathrm{D =\sum_{i=1}^{n}|r_i-s_i|}$$Here, si and ri are data points.n denotes the n-space.SciPy provides us with a function named cityblock that returns the Manhattan Distance between two points. Let’s see how we can calculate the Manhattan distance between two points using SciPy library−Example# Importing the SciPy library ...
Read MoreCalculating Euclidean distance using SciPy
Euclidean distance is the distance between two real-valued vectors. Mostly we use it to calculate the distance between two rows of data having numerical values (floating or integer values). Below is the formula to calculate Euclidean distance −$$\mathrm{d(r, s) =\sqrt{\sum_{i=1}^{n}(s_i-r_i)^2} }$$Here, r and s are the two points in Euclidean n-space.si and ri are Euclidean vectors.n denotes the n-space.Let’s see how we can calculate Euclidean distance between two points using SciPy library −Example# Importing the SciPy library from scipy.spatial import distance # Defining the points A = (1, 2, 3, 4, 5, 6) B = (7, 8, 9, 10, 11, ...
Read MoreImplementing K-means clustering of Diabetes dataset with SciPy library
The Pima Indian Diabetes dataset, which we will be using here, is originally from the National Institute of Diabetes and Digestive and Kidney Diseases. Based on the following diagnostic factors, this dataset can be used to place a patient in ether diabetic cluster or non-diabetic cluster −PregnanciesGlucoseBlood PressureSkin ThicknessInsulinBMIDiabetes Pedigree FunctionAgeYou can get this dataset in .CSV format from Kaggle website.ExampleThe example below will use SciPy library to create two clusters namely diabetic and non-diabetic from the Pima Indian diabetes dataset.#importing the required Python libraries: import matplotlib.pyplot as plt import numpy as np from scipy.cluster.vq import whiten, kmeans, vq ...
Read MoreImplementing K-means clustering with SciPy by splitting random data in 3 clusters?
Yes, we can also implement a K-means clustering algorithm by splitting the random data in 3 clusters. Let us understand with the example below −Example#importing the required Python libraries: import numpy as np from numpy import vstack, array from numpy.random import rand from scipy.cluster.vq import whiten, kmeans, vq from pylab import plot, show #Random data generation: data = vstack((rand(200, 2) + array([.5, .5]), rand(150, 2))) #Normalizing the data: data = whiten(data) # computing K-Means with K = 3 (3 clusters) centroids, mean_value = kmeans(data, 3) print("Code book :", centroids, "") print("Mean of Euclidean distances :", mean_value.round(4)) ...
Read MoreImplementing K-means clustering with SciPy by splitting random data in 2 clusters?
K-means clustering algorithm, also called flat clustering, is a method of computing the clusters and cluster centers (centroids) in a set of unlabeled data. It iterates until we find the optimal centroid. The clusters, we might think of a group of data points whose inter-point distances are small as compared to the distances to the point outside of that cluster. The number of clusters identified from unlabeled data is represented by ‘K’ in K-means algorithm.Given an initial set of K centers, the K-means clustering algorithm can be done using SciPy library by executing by the following steps −Step1− Data point ...
Read MoreWhat is scipy.cluster.hierarchy.fcluster()method?
scipy.cluster.hierarchy.fcluster(Z, t, criterion=’inconsistent’depth=2, R=None, monocrat=None)− The fcluster() method forms flat clusters from the hierarchical clustering. This hierarchical clustering is defined by the given linkage matrix, identifying a link between clustered classes.Below is given the detailed explanation of its parameters −ParametersZ− ndarrayIt represents the hierarchical clustering which is encoded with the linkage matrix.t− scalarThe value of t depends on the type of criteria. For ‘inconsistent’, ‘distance’, and ‘monocrit’ criteria, the value of t represents the threshold to apply when forming flat clusters. On the other hand, for ‘maxclust’, and ‘maxclust_monocrit’ criteria, the value of t represents the maximum number of clusters ...
Read MoreHow to solve triangular matrix equations using Python SciPy?
The linear function named scipy.linalg.solveh_triangular is used to solve the banded matrix equation. In the below given example we will be solving the triangular system ax = b where −$$\mathrm{a} = \begin{bmatrix} 3 & 0 & 0 & 0\ 2 & 1 & 0 & 0\ 1 &0 &1 &0 \ 1& 1& 1& 1 \end{bmatrix};\; \mathrm{b} =\begin{bmatrix} 1\ 2\ 1\ 2 \end{bmatrix}$$Examplefrom scipy.linalg import solve_triangular import numpy as np a = np.array([[3, 0, 0, 0], [2, 1, 0, 0], [1, 0, 1, 0], [1, 1, 1, 1]]) b = np.array([1, 2, 1, 2]) x = solve_triangular(a, b, lower=True) print (x)Outputarray([ 0.33333333, 1.33333333, 0.66666667, -0.33333333])
Read MoreWhich linear function of SciPy is used to solve triangular matrix equations?
The linear function named scipy.linalg.solve_triangular is used to solve the triangular matrix e8quation. The form of this function is as follows −scipy.linalg.solve_triangular(a, b, trans=0, lower=False, unit_diagonal=False, overwrite_b=False, debug=None, check_finite=True)This linear function will solve the equation ax = b for x where a is a triangular matrix.P ParametersBelow are given the parameters of the function scipy.linalg.solve_triangular() −a− (M, M) array_likeThis parameter represents the triangular matrix.b− (M, ) or (M, N)array_likeThis parameter represents the right-hand side matrix in the equation ax = b.lower− bool, optionalBy using this parameter, we will be able to use only the data that is contained in the ...
Read MoreComparing 'cubic' and 'linear' 1-D interpolation using SciPy library
Below python script will compare the ‘cubic’ and ‘linear’ interpolation on same data using SciPy library −ExampleFirst let’s generate some data to implement interpolation on that −import numpy as np from scipy.interpolate import interp1d import matplotlib.pyplot as plt A = np.linspace(0, 10, num=11, endpoint=True) B = np.cos(-A**2/9.0) print (A, B)OutputThe above script will generate the following points between 0 and 4 − [ 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.] [ 1. 0.99383351 0.90284967 0.54030231 -0.20550672 -0.93454613 -0.65364362 0.6683999 0.67640492 -0.91113026 0.11527995]Now, let’s plot these points as follows −plt.plot(A, B, '.') plt.show()Now, based on fixed data ...
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