eigenvalue

问题 I am writing R code which uses compiled C code. From "Writing R Extensions" document, I learned there are many R executable/DLL that can be called from C code. The header file ‘Rmath.h’ lists many functions that are available and its source codes are listed on the this website: http://svn.r-project.org/R/trunk/src/nmath/ I need to calculate singular value decomposition of many matrices, however I do not find subroutines which does this on the above website. (So I am assuming that Rmath.h does

问题 This question already has answers here : Sign difference in eigenvectors taken form Matlab and Python (1 answer) Conflicting eigen vector outputs between Matlab and Numpy (1 answer) Matlab VS Python - eig(A,B) VS sc.linalg.eig(A,B) (1 answer) eigenvalue and eigenvectors in python vs matlab (1 answer) Closed 2 years ago . I have stiffness matrix and mass matrix. I want to calculate my structure vibration shapes and period (eigenvalue/vector) so I am using NumPy for this. Eigenvalues are the

问题 In Matlab, I have to study the eventual existence of common eigenvectors basis between 2 Fisher matrices FISH_sp and FISH_xc of size 7x7 and diagonalisable. I get from my computation the following result: >> x=null(FISH_sp*FISH_xc-FISH_xc*FISH_sp) x = -0.0085 -0.0048 -0.2098 0.9776 -0.0089 -0.0026 0.0109 In this result, It appears that condition to get a common eigenvectors basis on commutator is true. But I need to further examine the mathematics. If one gets a single column vector, then

问题 In Matlab, I have to study the eventual existence of common eigenvectors basis between 2 Fisher matrices FISH_sp and FISH_xc of size 7x7 and diagonalisable. I get from my computation the following result: >> x=null(FISH_sp*FISH_xc-FISH_xc*FISH_sp) x = -0.0085 -0.0048 -0.2098 0.9776 -0.0089 -0.0026 0.0109 In this result, It appears that condition to get a common eigenvectors basis on commutator is true. But I need to further examine the mathematics. If one gets a single column vector, then

问题 According to https://docs.scipy.org/doc/numpy-1.15.0/user/numpy-for-matlab-users.html, the equivalent numpy expression for the MATLAB [V,D]=eig(a,b) is V,D = np.linalg.eig(a,b) . But when I try this I get the error: TypeError: eig() takes 1 positional argument but 2 were given I'm confused, the documentation says np.linalg.eig can take two arguments? Curiously, when I look at the linalg documentation at https://docs.scipy.org/doc/numpy-1.15.1/reference/routines.linalg.html, under the heading

问题 According to https://docs.scipy.org/doc/numpy-1.15.0/user/numpy-for-matlab-users.html, the equivalent numpy expression for the MATLAB [V,D]=eig(a,b) is V,D = np.linalg.eig(a,b) . But when I try this I get the error: TypeError: eig() takes 1 positional argument but 2 were given I'm confused, the documentation says np.linalg.eig can take two arguments? Curiously, when I look at the linalg documentation at https://docs.scipy.org/doc/numpy-1.15.1/reference/routines.linalg.html, under the heading

问题 I am trying to find the stationary distribution of a Markov chain. I have a transition probability matrix (TPM). Here is the code: [V, D] = eigs(double(TPM'),1); Py = abs(V)/sum(V); My problem is that sum(V) < 0 so it gives me some negative values in the vector Py . I've tested the code using another probability matrix and it gives sum(V) > 0 . I don't know what is the problem, is it the TPM or the code I am using? EDIT: Here is a more "elaborated" version of the code (including the answer of

问题 I have a 3D image and I want to calculate the Hessian of Gaussian eigenvalues for this image. I would like to have the three eigenvalues of the Hessian approximation for each voxel. This feature seems to be something very common in image processing. Is there an existing implementation of this feature (like scipy.ndimage.laplace for laplacian calculation)? And is there one that parallels calculations? I tried to do it manually, through numpy operations but its not optimal because: I have to

问题 I test the theorem that A = Q * Lambda * Q_inverse where Q the Matrix with the Eigenvectors and Lambda the Diagonal matrix having the Eigenvalues in the Diagonal. My code is the following: import numpy as np from numpy import linalg as lg Eigenvalues, Eigenvectors = lg.eigh(np.array([ [1, 3], [2, 5] ])) Lambda = np.diag(Eigenvalues) Eigenvectors @ Lambda @ lg.inv(Eigenvectors) Which returns : array([[ 1., 2.], [ 2., 5.]]) Shouldn't the returned Matrix be the same as the Original one that was

问题 I test the theorem that A = Q * Lambda * Q_inverse where Q the Matrix with the Eigenvectors and Lambda the Diagonal matrix having the Eigenvalues in the Diagonal. My code is the following: import numpy as np from numpy import linalg as lg Eigenvalues, Eigenvectors = lg.eigh(np.array([ [1, 3], [2, 5] ])) Lambda = np.diag(Eigenvalues) Eigenvectors @ Lambda @ lg.inv(Eigenvectors) Which returns : array([[ 1., 2.], [ 2., 5.]]) Shouldn't the returned Matrix be the same as the Original one that was