linear-algebra

问题 I'm trying to solve an equation system with a 3x3 matrix a and a right hand side b of arbitrary shape (3, ...) . If b has one or two dimensions, numpy.linalg.solve does the trick. It breaks down for more dimensions though: import numpy a = numpy.random.rand(3, 3) b = numpy.random.rand(3) numpy.linalg.solve(a, b) # okay b = numpy.random.rand(3, 4) numpy.linalg.solve(a, b) # okay b = numpy.random.rand(3, 4, 5) numpy.linalg.solve(a, b) # ERR ValueError: solve: Input operand 1 has a mismatch in

问题 This question already has answers here : Efficiently compute a 3D matrix of outer products - MATLAB (3 answers) Closed 4 months ago . I am trying to speed the process in evaluation the outer product matrix. I have a 4*n matrix named a . I want to evaluate the outer product matrix for every row of a , by the formula: K = a*a'; If I code this process using a for loop, it is as below: K=zeros(4,4,size(a,2)); for i=1:size(a,2) K(:,:,i) = a(:,i)*a(:,i)'; end I have found another method, using

问题 I want to do Cholesky decomposition of large sparse matrices in Java. Currently I'm using the Parallel Colt library class SparseDoubleCholeskyDecomposition but it's much slower than using my code I wrote in C for dense matrices which I use in java with JNI. For example for 5570x5570 matrices with a non-zero density of 0.25% with SparseDoubleCholeskyDecomposition takes 26.6 seconds to factor and my own code for the same matrix using dense storage only takes 1.12 seconds . However, if I set the

问题 I am trying to load a CPLEX LP file in to CPLEX using the "read" command. I believe that in this problem, I have a set of constraints that are quadratic. But, from what I understand CPLEX will still attempt to solve quadratic programming problems. However, when I try to read it in, I get this error: CPLEX Error 1437: Line 284: Illegal quadratic constraint sense. Is there something special I need to do to read in a quadratic programming problem? NOTE: I am able to load this LP file in to scip

问题 I'm not too familiar with MATLAB or computational mathematics so I was wondering how I might solve an equation involving the sum of squares, where each term involves two vectors- one known and one unknown. This formula is supposed to represent the error and I need to minimize the error. I think I'm supposed to use least squares but I don't know too much about it and I'm wondering what function is best for doing that and what arguments would represent my equation. My teacher also mentioned

问题 I have to solve a large amount of linear matrix equations of the type "Ax=B" for x where A is a sparse matrix with mainly the main diagonal populated and B is a vector. My first approach was to use dense numpy arrays for this purpose with numpy.linalg.solve, and it works fine with a (N,n,n)-dimensional array with N being the number of linear matrix equations and n the square matrix dimension. I first used it with a for loop iterating through all equations, which in fact is rather slow. But

问题 I have the following code: import numpy as np from numpy import array from scipy.optimize import nnls def by_nnls(A=None, B=None): """ Linear programming by NNLS """ #print "NOF row = ", A.shape[0] A = np.nan_to_num(A) B = np.nan_to_num(B) x, rnorm = nnls(A,B) x = x / x.sum() # print repr(x) return x def f(arrA, arrB): """ Check if two matrices overlap""" return not set(map(tuple, arrA)).isdisjoint(map(tuple, arrB)) Basically it runs Linear Programing by using NNLS. By taking matrix A and

问题 I have a A which is 640x1 cell. where the value of each cell A(i,1) varies from row to row, for example A(1,1) =[] , while A(2,1)=[1] and A(3,1)=[1,2,3] . There is another matrix B of size 480x640, where the row_index (i) of vector A corresponds to the col_index of matrix B . While the cell value of each row in vector A corresponds to the row_index in matrix B . For example, A(2,1)=[1] this means col_2 row_1 in matrix B , while A(3,1)=[1,2,3] means col_3 rows 1,2&3 in matrix B . What I'm

问题 In determine if line segment is inside polygon I noticed the accepted answer has an unusual 2d cross roduct definition of: (u1, u2) x (v1, v2) := (u1 - v2)*(u2 - v1) I have never encountered a definition of the 2d cross product such as this one. Can anyone enlighten me as to where such definition originates from? 回答1: I suggest you to take a look at Exterior Algebra. It generalizes the notion of cross product and determinant. The "Motivation examples" section describing areas in the plane

问题 I've a question regarding to the question mentioned above. I've a large data set. Each row corresponds to one day and the matrix is recorded in a vech form, i.e., by vectorizing the unique upper triangle of the matrix and transposing it into a row vector. I want to transform the whole data set back into the full matrices of each day (observation). A short reproducible example is below: structure(list(X01 = c(5.89378246085557, 5.75461814891448, 8.01511372310818 ), X02 = c(2.04749233527123, 1