Does it help to know that the matrix A has rank 2 instead of 3? > chol(a) > Error in chol.default(a) : > the leading minor of order 3 is not positive definite > > qr.R(qr(a)) > [,1] [,2] [,3] > [1,] -35.66511 -51.8153470 -6.796559e+01 > [2,] 0.00000 -0.4120817 -8.241634e-01 > [3,] 0.00000 0.0000000 4.218847e-15 > > svd(a)$d > [1] 9.261128e+01 3.887216e-01 5.102882e-15
I don't remember if I implemented a pivoting Cholesky or not. On Mon, Jul 15, 2013 at 5:03 PM, Dmitriy Lyubimov <[email protected]> wrote: > should read > > val axmb = (a %*% x) - b > > of course but it doesn't make difference, the Cholesky output doesn't make > sense to me even before that > > > On Mon, Jul 15, 2013 at 5:00 PM, Dmitriy Lyubimov <[email protected]> > wrote: > > > Hi Ted, > > > > I am getting Cholesky test failures when trying to solve of Ax=B > > > > The L matrix and solveLeft() output do not make much sense to me. For > > once, L doesn't even have the expected L-shape: > > > > Do you have an idea where i go wrong? (the test is wrapped into scala DSL > > but it is Mahout's cholesky underwraps) . > > > > test code: > > > > test("chol") { > > > > // try to solve Ax=b with cholesky: > > // this requires > > // (LL')x = B > > // L'x= (L^-1)B > > // x=(L'^-1)(L^-1)B > > > > val a = dense((1, 2, 3), (2, 3, 4), (3, 4, 5)) > > > > // make sure it is symmetric for a valid solution > > a := a.t %*% a > > > > printf("A= \n%s\n", a) > > > > val b = dense((9, 8, 7)).t > > > > printf ("b = \n%s\n", b) > > > > val ch = chol(a) > > > > printf ("L = \n%s\n", ch.getL) > > > > printf ( "(L^-1)b =\n%s\n", ch.solveLeft(b)) > > > > val x = ch.solveRight(diag(1,3)) %*% ch.solveLeft(b) > > > > printf("x = \n%s\n", x.toString) > > > > val axmb = (a %*% b) - b > > > > printf("AX - B = \n%s\n", axmb.toString) > > > > assert(axmb.norm < 1e-10) > > > > } > > > > > > > > Output: > > > > A= > > { > > 0 => {0:14.0,1:20.0,2:26.0} > > 1 => {0:20.0,1:29.0,2:38.0} > > 2 => {0:26.0,1:38.0,2:50.0} > > } > > b = > > { > > 0 => {0:9.0} > > 1 => {0:8.0} > > 2 => {0:7.0} > > } > > > > L = > > { > > 0 => {0:0.6928203230275511,2:3.676955262170047} > > 1 => {0:0.3464101615137781,2:5.374011537017761} > > 2 => {2:7.0710678118654755} > > } > > (L^-1)b = > > { > > 0 => {0:1.2727922061357855} > > 1 => {0:11.547005383792511} > > 2 => {} > > } > > X = > > { > > 0 => {0:0.18} > > 1 => {0:5.119661282874144} > > 2 => {} > > } > > AX - B = > > { > > 0 => {0:459.0} > > 1 => {0:670.0} > > 2 => {0:881.0} > > } > > > > org.scalatest.exceptions.TestFailedException was thrown. > > > > >
