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package com.nsrddyn.fpu
import scala.math._
import scala.collection.immutable.ListSet
import scala.collection.mutable.ArrayBuffer
class CholeskyDecomposition {
/*
* Floating point operation to stress the cpu
* Calculate the number of KFLOPS / FLOPS
* implementation of the Cholesky decomposition
* More information on the Cholesky decomposition at:
* https://en.wikipedia.org/wiki/Cholesky_decomposition
*
* Linpack uses the cholesky decomposition
* https://www.netlib.org/linpack/
*
* https://www.geeksforgeeks.org/dsa/cholesky-decomposition-matrix-decomposition/
*
* The Cholesky decomposition maps matrix A into the product of A = L · LH where L is the lower triangular matrix and LH is the transposed,
* complex conjugate or Hermitian, and therefore of upper triangular form (Fig. 13.6).
* This is true because of the special case of A being a square, conjugate symmetric matrix.
*/
def run(matrix: Vector[Vector[Int]]): Unit = {
val size: Int = matrix.size
val lower: ArrayBuffer[ArrayBuffer[Int]] = ArrayBuffer[ArrayBuffer[Int]]()
for
i <- 0 to size
j <- 0 until i
do
if i == j then lower(i)(j) = getSquaredSummation(lower, i, j, matrix) else lower(j)(j) = getReversedSummation(lower, i, j, matrix)
}
private def getReversedSummation(lower: ArrayBuffer[ArrayBuffer[Int]], i: Int, j: Int, matrix: Vector[Vector[Int]]) = {
math.sqrt(matrix(j)(j) - (0 until j).map { k => lower(i)(k) * lower(j)(k) }.sum).toInt
}
private def getSquaredSummation(lower: ArrayBuffer[ArrayBuffer[Int]], i: Int, j: Int, matrix: Vector[Vector[Int]]) = {
((matrix(i)(j) - (0 until j).map { k => math.pow(lower(j)(k), 2)}.sum) / lower(j)(j)).toInt
}
}
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