Char Poly via Souriau method

[Jerry]

Hi,

I'm a newcomer to Breeze, attempting to use it to calculate the characteristic polynomial of a matrix via the Souriau/von_Faddejew/Leverrier method:

http://stackoverflow.com/questions/23937481/souriau-method-for-characteristic-polynomial

Below, is the code, which doesn't currently compile. There reported issues are:

1. For C + eyedash:

could not find implicit value for parameter op: breeze.linalg.operators.OpAdd.Impl2[breeze.linalg.Matrix[Double],breeze.linalg.DenseMatrix[Double],That]

I presume this is because breeze does not know that C is square? If so, how can I provide the required information?

2. For trace(C)

could not find implicit value for parameter impl: breeze.linalg.trace.Impl[breeze.linalg.Matrix[Double],VR

Is there something else I need to import?

/////////////////////////////////////////////////////////////////////////////////

import breeze.linalg._

import breeze.numerics._

import breeze.math._

// ...

  def charPoly(A: Matrix[Double]): DenseVector[Double] = { 

    require(A.rows == A.cols)

    var C = A.copy

    val n = A.rows

    val c = DenseVector.zeros[Double](n)

    val I = DenseMatrix.eye[Double](n)

    for( k <- 0 until n ) {

      if( k>0 ) {

        val eyedash = c(n-k) :* I

        val cplus = C + eyedash

        C = A * cplus

      }

      val x = -trace(C)/k 

      c(n−k) = x

    }

    c  

  }

Thanks,

Jerry.

[David Hall]

Hi Jerry,

Lots of stuff in Breeze still only works for DenseMatrix[Double] rather than Matrix[Double], I'm surprised about the OpAdd one, but that's what's going on. If you make A be a DenseMatrix, it should work fine.

-- David

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