bem_regularized_qr Module

Reusable column-scaled QR factorization for ridge-regularized least squares.


Uses

  • module~~bem_regularized_qr~~UsesGraph module~bem_regularized_qr bem_regularized_qr module~bem_kinds bem_kinds module~bem_regularized_qr->module~bem_kinds iso_fortran_env iso_fortran_env module~bem_kinds->iso_fortran_env

Used by

  • module~~bem_regularized_qr~~UsedByGraph module~bem_regularized_qr bem_regularized_qr module~bem_coulomb_fmm_periodic_root_ops bem_coulomb_fmm_periodic_root_ops module~bem_coulomb_fmm_periodic_root_ops->module~bem_regularized_qr module~bem_coulomb_fmm_plan_ops bem_coulomb_fmm_plan_ops module~bem_coulomb_fmm_plan_ops->module~bem_coulomb_fmm_periodic_root_ops module~bem_coulomb_fmm_core_build bem_coulomb_fmm_core_build module~bem_coulomb_fmm_core_build->module~bem_coulomb_fmm_plan_ops

Derived Types

type, public ::  regularized_qr_type

Components

Type Visibility Attributes Name Initial
real(kind=dp), public, allocatable :: q(:,:)
real(kind=dp), public, allocatable :: r(:,:)
real(kind=dp), public, allocatable :: col_scale(:)
integer(kind=i32), public :: mrow = 0_i32
integer(kind=i32), public :: ncol = 0_i32
integer(kind=i32), public :: preparation_count = 0_i32

Subroutines

public subroutine prepare_regularized_qr(factorization, matrix, ridge, qr_tolerance)

Arguments

Type IntentOptional Attributes Name
type(regularized_qr_type), intent(inout) :: factorization
real(kind=dp), intent(in) :: matrix(:,:)
real(kind=dp), intent(in) :: ridge
real(kind=dp), intent(in) :: qr_tolerance

public subroutine solve_regularized_qr(factorization, rhs, solution)

Arguments

Type IntentOptional Attributes Name
type(regularized_qr_type), intent(in) :: factorization
real(kind=dp), intent(in) :: rhs(:)
real(kind=dp), intent(out) :: solution(:)

public subroutine factor_tall_matrix_qr(matrix, q, r, qr_tolerance)

Re-orthogonalised (two-pass modified Gram-Schmidt) QR of a tall matrix. A column whose residual norm falls below qr_tolerance times its norm (at least 1) gets that floor as its pivot and a zero q column.

Arguments

Type IntentOptional Attributes Name
real(kind=dp), intent(in) :: matrix(:,:)
real(kind=dp), intent(out) :: q(:,:)
real(kind=dp), intent(out) :: r(:,:)
real(kind=dp), intent(in) :: qr_tolerance