matrix-inverse

I am trying to obtain the left inverse of a non-square matrix in python using either numpy or scipy. How can I translate the following Matlab code to Python? >> A = [0,1; 0,1; 1,0] A = 0 1 0 1 1 0 >> y = [2;2;1] y = 2 2 1 >> A\y ans = 1.0000 2.0000 Is there a numpy or scipy equivalent of the left inverse \ operator in Matlab? Use linalg.lstsq(A,y) since A is not square. See here for details. You can use linalg.solve(A,y) if A is square, but not in your case. Here is a method that will work with sparse matrices (which from your comments is what you want) which uses the leastsq function from the

I want to process Images with Inverse function and lot of functions. For code to run fastly can any one suggest fast method among the 3 inversion methods ? double cvInvert(const CvArr* src, CvArr* dst, int method=CV_LU) CV_LU Gaussian elimination with optimal pivot element chosen CV_SVD Singular value decomposition (SVD) method CV_SVD_SYM SVD method for a symmetric positively-defined matrix. In OpenCV2.x, there's a new interface called Mat::inv(int method) to compute the inverse of a matrix. See reference . C++: MatExpr Mat::inv(int method=DECOMP_LU) const Parameters: method – Matrix inversion

I have lots of large (around 5000 x 5000) matrices that I need to invert in Matlab. I actually need the inverse, so I can't use mldivide instead, which is a lot faster for solving Ax=b for just one b. My matrices are coming from a problem that means they have some nice properties. First off, their determinant is 1 so they're definitely invertible. They aren't diagonalizable, though, or I would try to diagonlize them, invert them, and then put them back. Their entries are all real numbers (actually rational). I'm using Matlab for getting these matrices and for this stuff I need to do with their

What is the fastest algorithm (a link to C or C++ example would be cool) to check if a small square matrix (<16*16 elements) is singular (non-invertible, det = 0) ? Best way is to compute the condition number via SVD and check if it is greater than 1 / epsilon, where epsilon is the machine precision. If you allow false negatives (ie. a matrix is defective, but your algorithm may not detect it), you can use the max(a_ii) / min(a_ii) formula from the Wikipedia article as a proxy for the condition number, but you have to compute the QR decomposition first (the formula applies to triangular

I have a badly conditioned matrix, whose rcond() is close to zero, and therefore, the inverse of that matrix does not come out to be correct. I have tried using pinv() but that does not solve the problem. This is how I am taking the inverse: X = (A)\(b); I looked up for a solution to this problem and found this link (last solution) for improving the matrix. The solution there suggests to use this: A_new = A_old + c*eye(size(A_old)); Where c > 0 . So far employing this technique works in making the matrix A better conditioned and the resultant solution looks better. However, I investigated

I would like to find the inverse of a matrix. I know this involves first LU factorisation then the inversion step but I cannot find the required function by searching apple's docs of 10.7! This seems like a useful post Symmetric Matrix Inversion in C using CBLAS/LAPACK , pointing out that the sgetrf_ and sgetri_ functions should be used. However searching these terms I find nothing in Xcode docs. Does anybody have boiler plate code for this matrix operation? Apple does not document the LAPACK code at all, I guess because they just implement the standard interface from netlib.org . It's a shame