Hi Zhiliang, For a system of equations AX = y, Linear Regression will give you a best-fit estimate for A (coefficient vector) for a matrix of feature variables X and corresponding target variable y for a subset of your data. OTOH, what you are looking for here is to solve for x a system of equations Ax = b, where A and b are known and you want the vector x.
This Math Stackexchange page [2] explains the math in more detail, but basically... A * x = b can be rewritten as x = A.I * b. You can get the pseudo-inverse of A using SVD (Spark MLLib supports SVD [1]). So the SVD decomposition would make A a product of three other matrices. A = U * S * V.T and the pseudo-inverse can be written as: A.I = V * S * U.T Then x can be found by multiplying A.I with b. -sujit [1] https://spark.apache.org/docs/1.2.0/mllib-dimensionality-reduction.html [2] http://math.stackexchange.com/questions/458404/how-can-we-compute-pseudoinverse-for-any-matrix On Fri, Oct 23, 2015 at 2:19 AM, Zhiliang Zhu <zchl.j...@yahoo.com> wrote: > Hi Sujit, and All, > > Currently I lost in large difficulty, I am eager to get some help from you. > > There is some big linear system of equations as: > Ax = b, A with N number of row and N number of column, N is very large, b > = [0, 0, ..., 0, 1]T > Then, I will sovle it to get x = [x1, x2, ..., xn]T. > > The simple solution would be to get inverse(A), and then x = (inverse(A)) > * b . > A would be some JavaRDD<Interable<double>> , however, for RDD/matrix there > is add/multply/transpose APIs, no inverse API for it! > > Then, how would it conveniently get inverse(A), or just solve the linear > system of equations by some other way... > In Spark MLlib, there was linear regression, the training process might be > to solve the coefficients to get some specific linear model, just is, > Ax = y, just train by (x, y) to get A , this might be used to solve the > linear system of equations. It is like that? I could not decide. > > I must show my deep appreciation torwards your all help. > > Thank you very much! > Zhiliang > > >
