Step by Step solution about How to resolve the algorithm Multiple regression step by step in the Haskell programming language

The provided Haskell code is using the Numeric.LinearAlgebra and Numeric.LinearAlgebra.LAPACK libraries to solve a linear system and compute the inverse of a matrix.

Here's a step-by-step explanation of the code:

1. Import the necessary libraries:

   • import Numeric.LinearAlgebra imports the Linear Algebra library for working with matrices and vectors.
   • import Numeric.LinearAlgebra.LAPACK imports the LAPACK library for solving linear systems and computing matrix inverses.

2. Define the matrix m:

   • m :: Matrix Double declares m as a matrix of type Double.
   • The matrix is defined using the (3><3) constructor, which creates a 3x3 matrix.
   • The values in the matrix are provided as a list of lists.

3. Define the vector v:

   • v :: Matrix Double declares v as a matrix of type Double.
   • The vector is defined using the (3><1) constructor, which creates a 3x1 vector.
   • The values in the vector are provided as a list.

4. Compute the solution to the linear system Ax = b using the linearSolveLSR function:

   • linearSolveLSR m v computes the least squares solution to the linear system m * x = v.
   • The result is a 3x1 vector representing the solution x.

5. Compute the inverse of the matrix m using the inv function and multiply it by the vector v:

   • inv m computes the inverse of the matrix m.
   • inv m multiply v multiplies the inverse of m by the vector v.
   • The result is a 3x1 vector representing the product of the inverse of m and v.

The output shows that the solutions computed using the linearSolveLSR function and the inverse multiplication method are approximately the same. This demonstrates that the solution to the linear system is correct.

Overall, this code demonstrates how to use the linearSolveLSR function for solving linear systems and how to compute the inverse of a matrix using the inv function in Haskell.

import Numeric.LinearAlgebra
import Numeric.LinearAlgebra.LAPACK

m :: Matrix Double
m = (3><3) 
  [7.589183,1.703609,-4.477162,
    -4.597851,9.434889,-6.543450,
    0.4588202,-6.115153,1.331191]

v :: Matrix Double
v = (3><1)
  [1.745005,-4.448092,-4.160842]


*Main> linearSolveLSR m v
(3><1)
 [ 0.9335611922087276
 ,  1.101323491272865
 ,    1.6117769115824 ]


*Main> inv m `multiply`  v
(3><1)
 [ 0.9335611922087278
 ,  1.101323491272865
 , 1.6117769115824006 ]