Many resources are needed to download a project. Please understand that we have to compensate our server costs. Thank you in advance. Project price only 1 $
You can buy this project and download/modify it how often you want.
package breeze.linalg
import breeze.generic.UFunc
import breeze.linalg.svd.SVD
import com.github.fommil.netlib.LAPACK.{getInstance=>lapack}
import breeze.linalg.support.CanTraverseValues
import breeze.linalg.support.CanTraverseValues.ValuesVisitor
/**
* Computes the rank of a matrix.
*
* The rank of the matrix is computed using the SVD method. The singular values of the SVD
* which are greater than a specified tolerance are counted.
*
* @param m matrix for which to compute the rank
* @param tol optional tolerance for singular values. If not supplied, the default
* tolerance is: max(m.cols, m.rows) * eps * sigma_max, where
* eps is the machine epsilon and sigma_max is the largest singular value of m.
* @return the rank of the matrix (number of singular values)
*/
object rank extends UFunc {
implicit def implRankFromSVD[M, S](implicit canSVD: svd.Impl[M, SVD[_, S]],
maxS: max.Impl[S, Double],
travS: CanTraverseValues[S, Double]):Impl[M, Int] = {
new Impl[M, Int] {
def apply(m: M): Int = {
val SVD(u, s, vt) = svd(m)
// we called LAPACK for the SVD method, so this is the LAPACK definition of eps.
val eps: Double = 2.0 * lapack.dlamch("e")
val tol = eps * max(s)
var n = 0
travS.traverse(s, new ValuesVisitor[Double] {
def visit(a: Double): Unit = if(a > tol) n += 1
def zeros(numZero: Int, zeroValue: Double): Unit = ()
})
n
}
}
}
implicit def implRankTol[M, S](implicit canSVD: svd.Impl[M, (_, S, _)],
maxS: max.Impl[S, Double],
travS: CanTraverseValues[S, Double]):Impl2[M, Double, Int] = {
new Impl2[M, Double, Int] {
def apply(m: M, tol: Double): Int = {
val (u, s, vt) = svd(m)
// we called LAPACK for the SVD method, so this is the LAPACK definition of eps.
var n = 0
travS.traverse(s, new ValuesVisitor[Double] {
def visit(a: Double): Unit = if(a > tol) n += 1
def zeros(numZero: Int, zeroValue: Double): Unit = ()
})
n
}
}
}
}
