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feat: [linalg] add iterative solvers (CG and PCCG) #994
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This daft PR introduces the base for iterative solvers.
Two methods are proposed:
Each method is made public with two public interface flavors:
solve_<method>_kernel
: All arguments are mandatory (no optionals/no internal allocations), it contains the methods steps. The linear system (and preconditioner) is defined through a public DTlinop
which enables to extend two key procedures:apply
equivalent to a matrix-vector product andinner
equivalent to the dot_product. This is the interface recommended to extend the method when dealing with a matrix type not available instdlib
or when working in distributed-memory frameworks for which the matvec, dot_product and factorization steps need to be adapted to account for parallel synchronization.solve_<method>
: API with optional arguments, the linear system can be defined with dense orCSR_<>_type
matrices. For the PCCG, the following preconditioners are available:none
(identity),jacobi
(1/diagonal),SSOR
,LDLt
. It internally usessolve_<method>_kernel
.