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doc/specs/stdlib_linalg_iterative_solvers.md

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#### Description
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Implements the Preconditionned Conjugate Gradient (PCG) method for solving the linear system \( Ax = b \), where \( A \) is a symmetric positive-definite linear operator defined via the `linop` type. This is the core implementation, allowing flexibility for custom matrix types or parallel environments.
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Implements the Preconditioned Conjugate Gradient (PCG) method for solving the linear system \( Ax = b \), where \( A \) is a symmetric positive-definite linear operator defined via the `linop` type. This is the core implementation, allowing flexibility for custom matrix types or parallel environments.
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#### Syntax
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`A`: `class(linop_<kind>_type)` defining the linear operator. This argument is `intent(in)`.
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`M`: `class(linop_<kind>_type)` defining the preconditionner linear operator. This argument is `intent(in)`.
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`M`: `class(linop_<kind>_type)` defining the preconditioner linear operator. This argument is `intent(in)`.
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`b`: 1-D array of `real(<kind>)` defining the loading conditions of the linear system. This argument is `intent(in)`.
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`maxiter` (optional): scalar of type `integer` defining the maximum allowed number of iterations. If no value is given, a default of `N` is set, where `N = size(b)`. This argument is `intent(in)`.
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`precond` (optional): scalar of type `integer` enabling to switch among the default preconditionners available. If no value is given, no preconditionning will be applied. This argument is `intent(in)`.
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`precond` (optional): scalar of type `integer` enabling to switch among the default preconditioners available. If no value is given, no preconditionning will be applied. This argument is `intent(in)`.
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`M` (optional): `class(linop_<kind>_type)` defining a custom preconditionner linear operator. If given, `precond` will have no effect, a pointer is set to this custom preconditionner.
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`M` (optional): `class(linop_<kind>_type)` defining a custom preconditioner linear operator. If given, `precond` will have no effect, a pointer is set to this custom preconditioner.
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`workspace` (optional): `type(solver_workspace_<kind>_type)` holding the work temporal array for the solver. If the user passes its own `workspace`, then internally a pointer is set to it, otherwise, memory will be internally allocated and deallocated before exiting the procedure. This argument is `intent(inout)`.
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example/linalg/example_solve_custom.f90

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@@ -36,7 +36,7 @@ subroutine solve_pcg_custom(A,b,x,di,tol,maxiter,restart,workspace)
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! internal memory setup
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op%apply => my_apply
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op%inner_product => my_dot
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M%apply => my_jacobi_preconditionner
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M%apply => my_jacobi_preconditioner
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if(present(di))then
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di_ => di
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else
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if(.not.allocated(workspace_%tmp)) allocate( workspace_%tmp(n,size_wksp_pcg) , source = 0.d0 )
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workspace_%callback => my_logger
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!-------------------------
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! Jacobi preconditionner factorization
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! Jacobi preconditioner factorization
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call diag(A,diagonal)
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where(abs(diagonal)>epsilon(0.d0)) diagonal = 1._dp/diagonal
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!-------------------------
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call spmv( A , x, y , alpha, beta )
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y = merge( 0._dp, y, di_ )
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end subroutine
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subroutine my_jacobi_preconditionner(x,y,alpha,beta)
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subroutine my_jacobi_preconditioner(x,y,alpha,beta)
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real(dp), intent(in) :: x(:)
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real(dp), intent(inout) :: y(:)
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real(dp), intent(in) :: alpha

src/CMakeLists.txt

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stdlib_linalg_blas.fypp
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stdlib_linalg_lapack.fypp
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stdlib_linalg_iterative_aux.fypp
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stdlib_linalg_iterative_solvers.fypp
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stdlib_linalg_iterative_solvers_cg.fypp
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stdlib_linalg_iterative_solvers_pcg.fypp

src/stdlib_linalg_iterative_aux.fypp

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