How to setting for solving A x = b with A in R^{2 \times 3}, x in R^{3} and b in R^{2}?

[Aijunly]

It looks like you're asking for help with setting up a linear equation system in the form ( Ax = b ) using Julia, where ( A ) is a ( 2 \times 3 ) matrix, ( x ) is a ( 3 )-dimensional vector, and ( b ) is a ( 2 )-dimensional vector. Your code snippet is almost correct, but there are a couple of minor adjustments needed for clarity and correctness.

Here's a corrected version of your code:

## Packages
using Pardiso
using SparseArrays
gpmt = MKLPardisoSolver() # or gpmt = PardisoSolver()

## Data
A = [1 1 1; 2 4 2.0]  # Define the matrix A
Acsr = sparse(A)
b = [35; 94.0]        # Define the vector b

## Solving...
set_msglvl!(gpmt, 1) 
xsol = solve(gpmt, Acsr , b)

The above gives me that

=== PARDISO is running in In-Core mode, because iparam(60)=0 ===
...
2-element Vector{Float64}:
 23.0
 12.0

But the result has only 2 elements. And i want 3 elements. If i write the code of

## Solving...
xs = zeros(3,1); 
solve!(gpmt, xs, Acsr , b)

It gives me errors of

ERROR: DimensionMismatch: solution has (3, 1), RHS has size as (2,).

Although, i know reason from the dims of A{2,3} * x{3,1} = b{2,1}. And I should write code of

## Packages
using Pardiso
using SparseArrays
gpmt = MKLPardisoSolver() # or gpmt = PardisoSolver()

## Data
A = [1 1 1; 2 4 2.0]  # Define the matrix A
Acsr = sparse(A'*A)
b = [35; 94.0]        # Define the vector b
brhs = reshape(A'*b,3,1)

## Solving...
set_msglvl!(gpmt, 1) 
xs = zeros(3,1); 
solve!(gpmt, xs, Acsr , brhs)

So that, i want ask a question of Ax = b with A in ( R^{m \times n } ), x in R^{n} and b in R^{m} satisfying m < n. Hence, how to setting for solving this type of A x = b? And i translate Ax = b into A'*A x = A'*b, then solving it by Pardiso?

Sincerely,
Aijunly, Jun Wang.

[mipals]

Pardiso only works for square systems. In your case what is happening is that it is actually solving the square system containing only first m columns.

Maybe we should update this so that it returns an error when trying to solve a non-square system.