How to solve a linear matrix system in scala breeze?

Question

How to solve a linear matrix system in scala breeze? those. has Ax = b, where A is a matrix (usually positive definite), and x and b are vectors.

I see that there is affordable choletic corruption, but I could not find a solver? (if it were matlab, I could do x = b \ A. If it was scipy, I could do x = A.solve (b))

Answer 1

Apparently, this is actually quite simple and is built into scala-breeze as an operator:

x = A \ b 

He does not use Cholesky, he uses LU decomposition, and I think about twice as fast, but they are both O (n ^ 3), so they are comparable.

Answer 2

Well, in the end I wrote my own solver. I'm not sure if this is the best way to do this, but it doesn't seem unreasonable?

 // Copyright Hugh Perkins 2012 // You can use this under the terms of the Apache Public License 2.0 // http://www.apache.org/licenses/LICENSE-2.0 package root import breeze.linalg._ object Solver { // solve Ax = b, for x, where A = choleskyMatrix * choleskyMatrix.t // choleskyMatrix should be lower triangular def solve( choleskyMatrix: DenseMatrix[Double], b: DenseVector[Double] ) : DenseVector[Double] = { val C = choleskyMatrix val size = C.rows if( C.rows != C.cols ) { // throw exception or something } if( b.length != size ) { // throw exception or something } // first we solve C * y = b // (then we will solve Ct * x = y) val y = DenseVector.zeros[Double](size) // now we just work our way down from the top of the lower triangular matrix for( i <- 0 until size ) { var sum = 0. for( j <- 0 until i ) { sum += C(i,j) * y(j) } y(i) = ( b(i) - sum ) / C(i,i) } // now calculate x val x = DenseVector.zeros[Double](size) val Ct = Ct // work up from bottom this time for( i <- size -1 to 0 by -1 ) { var sum = 0. for( j <- i + 1 until size ) { sum += Ct(i,j) * x(j) } x(i) = ( y(i) - sum ) / Ct(i,i) } x } }